**Table**

*timescales;*

ϕ*—probability;*

*ρ*group*—group*

*synchronisation.*

 y *—*i

 τ*—*

> *Summary of the non-linear variables and respective equation, thresholds, advantages, disadvantages and practical application.*

*Methodological Procedures for Non-Linear Analyses of Physiological and Behavioural Data… DOI: http://dx.doi.org/10.5772/intechopen.102577*

lack of standardisation on non-linear measures, measurement and thresholds [20, 76]. It is even more evident in the physiological measures, therefore, the results obtained in studies that integrate positional and physiological datasets should be interpreted with caution [120]. The application of integrative approaches should also consider the boundaries between different key performance indicators such as the psychophysiological [45, 121–123], technical [44, 67, 93] and contextual factors [83, 84]. Also, acceleration outputs, metabolic power and body impacts have been poorly integrated with positional data. Behavioural data should still be better contextualised and the related-bias for physiological thresholds must be considered upon the time-dependent and transient reduction [84]. An integration approach to physiology and behavioural data must overcome some challenges on data visualisation, data processing (inherent to big data) and real-time tracking [13]. Moreover, futures researches should focus their analysis on women and sub-elite performers [20, 61].

#### **5. Conclusion**

Physiological assessment to monitoring training and match load has been carried out mainly under a linear perspective. Positional data to assess tactical behaviour considers fundamentally the theory of the complex systems and non-linear dynamics. Thus, an integrative approach allows a more holistic and extensive evaluation of the performance as a multifactorial phenomenon. This chapter summarises the theoretical concepts, mathematical models and methodological procedures to be applied by researchers and practitioners in training and match settings in football. The non-linear techniques reported more often in the literature were entropy, relative phase, complex indexes, correlation matrixes, clustering methods, frequency-based measures, fractals and multifractals. Correlation matrixes, clustering methods and fractality have not yet been applied in an integrative perspective in football. Finally, using non-linear approaches to integrate physiological and behavioural data remains a research-practice gap to be explored in the next years.

#### **Acknowledgements**

This research was supported by Portuguese Foundation for Science and Technology, I.P. (project UIDB04045/2021).

#### **Conflict of interest**

The authors declare no conflict of interest.

*Exercise Physiology*

#### **Author details**

José E. Teixeira1,2,3\*, Pedro Forte1,3,4, Ricardo Ferraz1,5, Luís Branquinho1,4,5, António J. Silva1,2, Tiago M. Barbosa1,3 and António M. Monteiro1,3

1 Research Centre in Sports, Health and Human Development, Covilhã, Portugal

2 Department of Sports, Exercise and Health Sciences, University of Trás-os-Montes e Alto Douro, Vila Real, Portugal

3 Department of Sport Science, Instituto Politécnico de Bragança, Bragança, Portugal

4 Department of Sports, Higher Institute of Educational Sciences of the Douro, Penafiel, Portugal

5 Department of Sports Sciences, University of Beira Interior, Covilhã, Portugal

\*Address all correspondence to: jose.eduardo@ipb.pt

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Methodological Procedures for Non-Linear Analyses of Physiological and Behavioural Data… DOI: http://dx.doi.org/10.5772/intechopen.102577*

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#### **Chapter 7**

## Justification of some Aspects of the Choice of Training Means Selection in Track-and-Field Jumps

*Mikhail Shestakov and Anna Zubkova*

#### **Abstract**

The chapter deals with the aspects of a take-off in track-and-field jumps with regard to biomechanics and physiological processes. In this chapter, we describe biomechanical and physiological processes underlying the main biomechanisms (BM), which are involved in track-and-field jumps. Our investigation aims at confirmation of the hypothesis that the concept of BM forms the basis of the approach to selecting technique development means in track-and-field. The aim of the first part of the research was to compare the contribution of different BMs. We have analyzed biomechanical parameters of the take-off in a group of elite jumpers (n = 50) during official competitions. Computer simulation modeling was used to detect how an increase in the run-up speed changed the contribution of different BMs. The aim of the second part of the research was to examine the peculiarities of a take-off in special exercises. Findings of the research demonstrated that the take-off in training exercises was performed using relatively independent BMs, similar to those used in competitive jumps. Being dependent on the motor task, key biomechanisms appear to be interdependent on the dynamic level. The role and contribution of the BMs depend on the type of exercise or conditions of its execution, initial conditions, and a motor task set to an athlete.

**Keywords:** track-and-field jumps, muscle-tendon unit, biomechanism, special exercises

#### **1. Introduction**

At present, having taken a systemic-structural approach, general biomechanics studies feature of the locomotor system of a man, biomechanical characteristics of movements, composition, and structure of motions in sports exercises and movements.

This approach suggests to single out spatial and temporal elements in a system of movements [1]. Just here, we see a contradiction, as a material system cannot be subdivided into spatial and temporal elements. From the point of view of contemporary philosophy of scientific cognition, it is incorrect to think of processes, properties, or relations as being systems. They all are no more than manifestations of various properties of a material object, while a system is a model of an original material object, the latter also consisting of material elements.

An approach used by J.G. Hay [2] is the most recognized in sport biomechanics now. Its essence (illustrated by a vertical standing jump) consists in subdivision of the trajectory of the body center of gravity (COG) into a few segments. The following identification of biomechanical characteristics responsible for the COG displacement and velocity of displacement is based on common sense. For example, arm lift-up shifts the COG upwards; legs extension produces the same effect; legs length ensures a certain position of the body COG at the end of take-off. On the ground of common sense, important parameters are selected and subjected to correlation analysis in order to find their relationship and to obtain multiple regression equations. The logic of this approach is similar to that of an empirical research aimed at formulation of an empirical law, which does not reveal the essence of a phenomenon, although enables to make some suggestions.

In biomechanics, we may be unfamiliar with brain organization and the central nervous system (CNS) can be considered as a "black box." Here lies the boundary between physiology and biomechanics. A biomechanist must be proficient in programming deliberate motor actions aimed at reaching a preset goal, i.e. motor programs. Physiological concepts of movement control do not substantiate the laws of mastering motor actions. However, to achieve success, a coach needs knowledge both in biomechanics and physiology in order to create training programs aimed at the development of motor programs of a competitive movement in an athlete. Thus, to work out a plan of technique development of a track-and-field athlete, it appears necessary to model a competitive movement, as well as training means to be used besides the principle movement.

To model the locomotor system of a man, we must use ideal models from theoretical mechanics [3]. Theoretical mechanics use models including the following elements: two- or three-dimensional space, time, point mass, perfectly rigid body (a rod), hinge, kinematic chain, ideal liquid or gas, etc. [4]. All these models are used in biomechanics, although to create an adequate model of a locomotor system, a model of muscle is needed. Hence, the subject of biomechanics matches that of theoretical mechanics only partially.

At every single instant, human existence can be considered as a combination of biomechanisms. In general, the concept of biomechanism includes biochemical objects (mitochondria, myofibrils, etc.), physiological systems (cardiovascular, endocrine, immune, central nervous, and other systems), and, the locomotor system.

In biomechanics, this concept should be referred to mechanics, in particular, to the theory of machines and mechanisms. Let us define a biomechanism (BM) as an aggregate of certain body parts movements, independent of other parts movements, transforming one type of energy into another that leads to changes in the position and speed of the athlete's body COG while accomplishing a certain movement task in certain external conditions [5–7].

To control a multilink system, the CNS combines separate links into subsystems (key kinematic mechanisms), which can act independently, although in doing so to pursue a common goal. A biomechanism as an integral system consists of a set of components, each possessing its own properties, which can manifest themselves in human movements in different ways.

The following components are singled out in a biomechanism:

#### 1.Muscle as:


*Justification of some Aspects of the Choice of Training Means Selection in Track-and-Field Jumps DOI: http://dx.doi.org/10.5772/intechopen.104839*

	- a lever for force and power transfer;
	- a pendulum for energy conversion;
	- a rod for support and reaction against external loads.

#### 3.Joint as:


Besides that, we should take into account controlling units containing control programs (motor programs that are formed, stored, and functioning in the athlete's CNS) [8, 9].

It is noteworthy that a CNS model must meet strict requirements. The model must reflect the process of controlling the object (in our case, the locomotor system) as well as model environment conditions and their relationship. Important is for both processes to be modeled as parallel [10]. The ability to perform deliberate movements means that a person can control target-oriented movements of the body or its parts more or less precisely. As the purpose of a movement is supposed to be solved by a certain BM and perceived by consciousness, it can be controlled and changed deliberately. The problem of movement spatial & temporal parameters differentiation, i.e. a method of performing a motor action, or, in other words, technique of a movement is, probably, solved by means of conscious control of certain BMs [6]. Hypothesis. Our investigation aims at confirmation of the hypothesis that the concept of bimechanism (BM) forms the basis of the approach to selecting technique development means in track-and-field. We examined one of the most important components of track-and-field jumps, i.e. a take-off.

The following BMs can be identified in the take-off in track-and-field jumps:


In the publication [11] the authors underscore three factors that play a key role in the biomechanism of the support leg and body extension. They are:


Swinging motions contribution. This mechanism increases the vertical component of the COG velocity after take-off [12]. It ensures:


The essence of the "overturned pendulum" biomechanism consists in the ability to increase the COG vertical velocity due to the athlete's body pivoting over the point of bearing [15, 16].

Relatively independent kinematic mechanisms are interdependent at dynamic level, i.e. realization of any of them affects the efficiency of the others. The role and contribution of the key kinematic mechanisms to the result demonstrated by an athlete depend on the type of a jump, initial conditions, and the task set. There exist different ways of realization of any BM as well as different interaction between BMs within the same jumping event.

Physiological basis of biomechanisms (BMs).

To study a concept of "biomechanism" (BM) in voluntary movements, we should understand physiological processes which take place in muscles directly involved in the biomechanisms.

An efficient take-off in jumps depends on well-coordinated simultaneous activation of three biomechanisms:


The BM of the "support leg and body extension" involves more muscle activity than the other two BMs ("overturned pendulum" and "swinging motion of the arms and swinging leg"), which play complementary roles by increasing the impact of the first one on the muscles.

In track-and-field jumps, athletes try to develop the maximal power of movement. Greater power of muscle contraction can result from an increase in either its strength, or its velocity, or both components. As a rule, the most significant gain in power is due to the increase of muscular strength.

Multiple studies demonstrate that manifestation of greater power in jumps may be related to physiological peculiarities of muscle-tendon unit (MTU) activity [17]. Elastic energy of tendons is used for solving various motor tasks, notably for increasing output power of the muscle-tendon unit (MTU) [7].

There are two ways to increase the efficiency of power development in the BM of the "support leg and body extension": pre-stretch of skeletal muscles and mechanical energy transfer via biarticular muscles.

As regards the first way of increasing power of a take-off (pre-stretch of skeletal muscles), it is known that pre-stretch of muscle-tendon unit (MTU) enhances strength of its subsequent contraction [18]. This mechanism can only be involved if

#### *Justification of some Aspects of the Choice of Training Means Selection in Track-and-Field Jumps DOI: http://dx.doi.org/10.5772/intechopen.104839*

extension starts from the most powerful hip joint due to m.gluteus maximus (GM) contraction. The energy is transferred from the hip joint to the shin via m. rectus femoris (RF) m. gastrocnemius (GA) is not involved into work immediately after the extension of the knee joint; it requires some time for GA to start contraсtion. Elastic energy is stored in the tendons of ankle extensors and then released quickly. As a result, the ankle joint being controlled by the weakest muscles can develop greater power due to the energy transferred from the proximal joint [19]. Thus, the maximal power of muscle contraction is achieved due to conjoint activity of muscles and tendons involved in the mechanism of energy transfer based on the pre-stretch effect.

The second way of increasing power of a take-off (energy transfer via biarticular muscles) was described in a few works including those related to jumps [17, 19]. It also involves processes which take place in the MTU. This mechanism is based on the fact that powerful monoarticular gluteus muscles, in particular GM contribute most to hip extension, thus increasing the angle in the hip joint. The energy is transferred from GM to the knee joint via the biarticular RF, and the knee joint is extended by RF and a group of monoarticular m. vastus (VA). Energy transfer via a biarticular muscle takes place when the muscle contracts, although it develops the greatest power when working in almost isometric regimen, i.e. contracting very slowly [20]. At the same time, knee extension causes plantar flexion in the ankle joint due to energy transfer via m. gastrocnemius (GA) that reinforces contraction of the triceps muscle of the calf [21].

The description of two ways to enhance power of a take-off shows that the MTU pre-stretch requires less time than energy transfer via biarticular muscles. In some works, the first way of power enhancement is called a "catapult" [22, 23]. This time difference is very important with regard to interaction of the BM of "support leg and body extension" with the other two BMs. In the first case (MTU pre-stretch) greater contribution of the "overturned pendulum" will decrease the effectiveness of the mechanism, whereas greater contribution of the "swing" will have positive effect on the result. Greater velocity of the swing owing to active contraction of the working muscles will lead to greater storage of elastic energy, greater stiffness of the support leg, and consequently greater power of the movement. Meanwhile shorter time of the movement will decrease the effect of MTU pre-stretch. In the second case (energy transfer via biarticular muscles) extra loading of the support leg due to greater contribution of the "overturned pendulum" will have positive effect. Greater contribution of the "overturned pendulum" is reached by increasing the step length and thereby lowering the COG trajectory that increases time of the take-off.

As a practical matter, this knowledge is important for correct planning and training. Training exercises should be performed by athletes taking into account their individual peculiarities based on different ratios of BMs contribution in the take-off power.

#### **2. Objective and methods**

We have analyzed biomechanical parameters of the take-off in a group of elite Russian male jumpers (n = 50) in competitive conditions (during official contests). The aim of this part of the research was to compare the contribution of different BMs involved into take-off in track-and-field jumps. Video recording was made by a digital camera JVC-9800 with the speed of 50 frames per second. Having been captured by standard computer programs, the image of the jumper's body was modeled by virtue of an anthropomorphic 12-segment [5]. The computer complex consisted of a few modules: calculation of mass-inertial parameters of an athlete;

calculation of kinematical and energy characteristics of movements of separate body links and the whole body based on videotape processing (it allowed to determine linear and angular indices of the body links kinematics as well as potential, kinetic and full energy of each link). The unique feature of this module is the capability to determine changes in length and contraction speed of 9 major muscles of the lower extremities. It permits to determine key peculiarities of the athlete's technique and to simulate conditions, under which top results could be achieved. Mathematical processing was done in the Scientific Research Institute of the Russian State University of Physical Education, Sport, and Tourism. The accuracy of measurements was determined in a metrological study and accounted for 0.01 m (linear parameters) and 0.02 mps (velocity parameters).

#### **3. Results of the first part of the research**

Having analyzed the results, we determined the contribution of BMs into takeoff in jumps regarding changes in the full energy of separate segments and links of the athlete's body. Simulation modeling enabled us to make conclusions concerning not only the ratio of BMs contribution into take-off in every jump event and a comparison of different jumps (horizontal and vertical) but to monitor the change of BMs contribution into take-off in case of 5% increase of the athlete's COG velocity at the last step of the approach run in each type of jumps and its effect on the result.

Results demonstrated by the athletes in the course of the experiment attained the level of master of sport, international class (**Table 1**). The simulation modeling showed that the growth of the approach speed would provide real chances of getting into the World championship finals.

**Table 2** displays proportion (in %) of the BMs contribution into take-off based on changes in the full energy of the athlete's body links measured in the experiment.

The greatest contribution of the BM of swinging links into the take-off is at once apparent. The contribution of the BM of the take-off leg extension is more pronounced in pole vault and less pronounced in high jump, whereas the contribution of the BM of "overturned pendulum" is greater in high and long jumps.

High and long jumps are the most similar in what concerns the structure of BMs operation at take-off, although the execution of the jumps is quite different (horizontal and vertical directions).


#### **Table 1.**

*Jumping results: Real and obtained by simulation modeling.*


#### **Table 2.**

*Contribution of different BMs into take-off in track-and-field jumps (%).*

#### *Justification of some Aspects of the Choice of Training Means Selection in Track-and-Field Jumps DOI: http://dx.doi.org/10.5772/intechopen.104839*

We decided to find out what would happen if the athlete's speed at the last step of the approach run (just prior to take-off) increased by 5%. We took the value 5% because the examination of strength-velocity qualities of top-class athletes permitted to suppose such an increase of speed to be attainable by advanced jumpers, who seem to be capable of bearing higher strength loads.

An increase in speed will naturally lead to an increase in the body links energy. The question arises if the energy growth will be proportional to the speed of the COG in every BM.

Important changes were observed in the BM of swinging links (**Figure 1**). In high and long jumps the contribution of this BM not only increased, but started earlier. As for triple jump, both temporal and amplitude parameters of the BM of swinging links grew. In pole vault, the increase was proportional to the increase of the COG velocity. The structure of the BM of the take-off leg extension for all the jumps under study remained the same. Considerable changes took place in the BM of "overturned pendulum" in high and long jumps. Its contribution became more important in triple jump but nearly did not change in pole vault.

Changes in the ratio (in %) of BMs contribution into take-off are shown in **Table 3**.

We should also note an increase in the total energy of the BMs, the greatest being observed in high and triple jumps.

On present evidence, it may be suggested that high and long jumps are the most similar in the structure of take-off, lesser similarity being found with triple jump and pole vault. Therefore, horizontal and vertical jumps reveal a certain resemblance in the structure of take-off (**Table 4**).

The greatest increase in the body COG speed can be reached by intensifying movements of swinging links (as in amplitude, as in temporal parameters). At the same time, training means and methods aimed at the development of the BM of the take-off leg and body extension should not be excluded from training programs, because the links of this BM would have to bear the increased loads resulting from

**Figure 1.** *Change of BMs contribution to take-off.*

#### *Exercise Physiology*


**Table 3.**

*Changes in BMs contribution into take-off obtained by modeling a 5% increase in velocity at the last step of the approach.*


#### **Table 4.**

*Changes of the total energy in every BM (in %) obtained by modeling a 5% increase of speed at the last step of the approach.*

more intensive work of the swinging links. This will provide efficient work of the BM of "overturned pendulum".

Data obtained in this part of the research permit to conclude that the structure of take-off in track-and-field jumps is formed according to a certain motor objective that depends on the character of the jump.

The speed of the athlete's body COG at take-off in all jumping events is controlled to a great extent by swinging movements of the body links, in other words, it depends on amplitude and temporal parameters of the swing.

#### **3.1 Pedagogical requirements to training means selection**

In running jumps, the efficiency of key kinematic mechanisms and, consequently, the efficiency of the athlete's interaction with the support depends on movements pattern executed by an athlete and aimed at realization of the following pedagogical requirements:

For all jumps:


For taking off in long and high jumps:


The degree of realization of some of the requirements differently affects the realization of the others. For example, the COG lowering at the last approach strides in high and long jumps (contrary to triple jump and pole vault) creates favorable conditions for correct placement of the take-off foot and less angle of the body lean with the support, in spite of setting higher requirements for strength-velocity qualities of the take-off leg muscles. This should increase the contribution of the

#### *Justification of some Aspects of the Choice of Training Means Selection in Track-and-Field Jumps DOI: http://dx.doi.org/10.5772/intechopen.104839*

"overturned pendulum" and swinging links BMs in the phase of the body and takeoff leg pivoting upon the point of support so that the trunk becomes positioned vertically above it. The subsequent forward-downward rotation of the take-off leg causes lowering of the knee and coxofemoral joints that is compensated by the mechanism of the take-off leg and body extension. When the take-off leg is planted "under" the trunk at take-off (a popular method of learning technique in long jumps), the take-off leg is lowered (forward-downward rotation), that can be considered as a technique fault, because in this case the efficiency of the BM of the take-off leg and body extension and the contribution of the "overturned pendulum" decrease.

The realization of some of the requirements mentioned above does not always favor the realization of the others. For instance, a too fast approach increases high-impact and inertia loads on the take-off leg, in particular, when it is placed at narrow angle with the support.

Taking into account the take-off structure in a given type of jumps and the pedagogical requirements listed above, any training program in track-and-field should include special means, each affecting technical skills depending on the core and form of a certain movement.

The revealed phenomena allowed to set objectives for the second part of the research aimed at biomechanical investigation of training means most frequently used for technique development in track-and-field jumping events.

To examine biomechanical features of take-off in special exercises primarily used in technique development sessions by track-and-field jumpers (in different jumping events), we have carried out a laboratory experiment on a special complex "Qualisys" (Sweden) using high-speed recording camera (240 frames per second). 5 elite male track-and-field jumpers, regularly performing in international competitions took part in the experiments (2 long jumpers, 2 high jumpers, 1 pole-vaulter). The age of the subjects was 22 ± 1.4 yrs., duration of practicing track-and-field jumps 7 ± 2.3 yrs., height 1.84 ± 0.04 m, weight 74 ± 3.1 kg. Exercises performed in the experiment included: long jump, long jump over a hurdle (0.96 m) placed in 1 m distance from the take-off spot, long jump taking off a raised or lowered board (0.05 m), jump up with touching an object suspended at 2.5 m height and in 1 m distance from the take-off spot, a pattern of 3 hops after an approach run. All exercises were performed after 6 running strides at the maximal approach speed.

#### **4. Results of the second part of the research and their discussion**

#### **4.1 Biomechanism of the take-off leg and body extension**

In jumps, the greatest mechanical impact directed at stretching biarticular muscles of the lower extremities, in particular, rectus femoris, is achieved at take-off due to simultaneous forced bending of the take-off leg in the knee joint (at shock absorption) and its active straightening in the coxofemoral joint. In this case, the tractive force produced by this muscle is aimed at the knee joint extension. This element of the BM of the take-off leg and body extension at the phase of interaction with the support outwardly looks as the leg flexion with the simultaneous driving of the pelvis and knees forward while leaning backward.

Biceps femoris has two functions in running jumps. According to our data and that reported in other studies, the take-off leg hits the take-off board at the angle of 59–74° with the horizontal, the angles in the coxofemoral and knee joints varying within the range of 165–170° and 160–175° correspondingly, depending on a jump event (**Table 5**). The trunk having "run against" the support leg planted on a


#### **Table 5.**

*Kinematic characteristics of take-off in exercises under study (°).*

take-off board, starts pivoting forward. Less angles of the support leg touch-down and body lean (measured clockwise with respect to the horizontal) were observed in the following exercises: jump up with touching a suspended object by hand, long jump from a raised platform (0.05 m).

The analysis of the dynamics of αCFJ/αKJ (**Figure 2**) and values of angles in the involved joints in different types of jumps showed that the speed of contraction in biarticular muscles is lower than in those being monarticular, and consequently, the tractive force produced by biarticular muscles is greater.

It led us to suggest that biarticular muscles play more significant role in providing efficient interaction with the support in jumps. In this context, training means and exercises should be selected so that they could develop strength-velocity qualities of those muscles in plyometric regimen of contraction, primarily with oppositely directed change in angles (as in the pairs CFJ-KJ and KJ-AJ).

Maximal results in jumps are reached when the angle of the knee joint flexion at shock absorption is optimal. These optimal values are different for different jump events. Similar in all the jumps is that the amplitude of the forced leg bending varies within the range of 25–35° and is independent of the type of a jump.

The examination of the three key features of the BM of legs and body extension demonstrated that at dynamic level the structure of the locomotor system determined the specificity of interaction with support in jumping exercises. Under otherwise equal conditions, the following factors are thought to be the most important:

#### **Figure 2.**

*Changes in angles in the coxofemoral and knee joints (αCFJ/αKJ) of the take-off leg at take-off. 1- long jump, 2 - long jump over a hurdle; 3- long jump from a raised take-off platform (0.05 m), 4 - long jump from a lowered take-off platform (0.05 m), 5 -jump up with touching an object by hand °.*

*Justification of some Aspects of the Choice of Training Means Selection in Track-and-Field Jumps DOI: http://dx.doi.org/10.5772/intechopen.104839*

1) maximal values and ratio of force momentums in the joints being involved, and 2) plyometric regimen of contraction of monarticular and, in particular, biarticular muscles.

#### **4.2 Swinging links motion**

Additional stretching of the lower extremities muscles at the end of shock absorption is provided by external mechanical load originating from the vertical component of inertia forces (Fin) applied to the centers of mass of swinging links and transferred to the centrifugal force (Fcf), directed along the kinematic chain. The value of Fin depends as on the swinging movement of swinging links, as on the accelerated lift of the linkage points of those links: for arms – the shoulder girdle lift and trunk straightening; for the swinging leg – lift of the pelvis (due to the take-off leg straightening and/ or trunk pivoting over the point of bearing in accordance with the BM of the "overturned pendulum"). Contribution of the accelerated lift of the linkage points of the swinging links can be estimated from the difference between the values of Fin and Fcf.

The links are accelerated by:


Deceleration of the swinging links goes on in the reverse order – the radius of inertia grows and the sign of the force momentum changes from positive to negative one due to the action of antagonist muscles. This enables an abrupt reduction of Fin in the centers of mass of the swinging links up to zero that, consequently, reduces the load on the lower extremities muscles at the end of the transfer from the plyometric regimen of their contraction to the myometric one. It is the effect of a sudden release of a stretched active muscle [24] Therefore, at that instant the swinging links should have gained the maximal momentum in the direction of the take-off, and the lower extremities should work on the acceleration of the trunk solely.

Results displayed in **Table 6** show that inertia forces in swinging motions caused significant changes in the COG vertical velocity at take-off, which were due to:

creation of additional load on muscles-extensors of the lower extremities at the end of shock absorption phase (inertia forces being transferred to the support by kinematic chains);


**Table 6.**

*Maximal vertical component of inertia forces of the swinging links centers of mass at take-off (N).*


**Table 7.**

*Shift of the marker placed at the CFJ axis of rotation of the take-off leg at shock absorption.*

growth of the swinging links velocity until the start of the knee joint extension; swinging links position at the end of take-off.

#### **4.3 Biomechanism of the "overturned pendulum"**

According to our data, the highest (0.06 m) lift of the pelvis (or the marker attached at the point of the CFJ axis of rotation of the take-off leg) at shock absorption takes place in long running jumps with the take-off from a raised platform, despite the knee joint flexion.

It was found out that in a hop performed after an approach run the center of mass of the take-off leg thigh was raised by 0.03 m, while the motion of the swinging links was directed forward-downwards. As consequence of these compensatory movements in long jumps the body COG moves in parallel to the support, and in triple jump (step and jump phases) the body COG is lowered toward the support (**Table 7**).

The evidence concerning the BM of the "overturned pendulum" proved that its efficiency depends to a certain extent on the position of the athlete's body at touch-down. The less is the touch-down leg angle and the more is the body backward lean, the longer will the distance used for accelerating the pelvis, trunk, and the whole body be.

#### **5. Practical recommendations**

Findings of the second part of the research demonstrate that there exist specific biomechanical characteristics of training means used by track-and-field jumpers.

We have found out that in training exercises the take-off is performed using relatively independent BMs, similar to those recorded in competitive jumps. Being dependent of the motor task (conditions of performing the exercise), key biomechanisms appear to be interdependent on the dynamic level, i.e. the contribution of one of them affects that of the others. The role and contribution of the BMs depend on the type of an exercise or conditions of its execution, initial conditions, and a motor task set to an athlete. There exist different ways of realization of any BM as well as different interaction between BMs within the same jumping event.

Specific features of take-off in the examined exercises permitted to classify all the training means into four groups (**Table 8**):


*Justification of some Aspects of the Choice of Training Means Selection in Track-and-Field Jumps DOI: http://dx.doi.org/10.5772/intechopen.104839*


#### **Table 8.**

*Contribution of different BMs in track-and-field technique development exercises (%).*


Thus, different special exercises are intended to exert specific effects on the structure of take-off, those effects being dependent on the specifics of the content and form of an exercise.

This comparison of technical drills differs from the conventional one, in which every kinematic or dynamic parameter of an exercise is compared with the similar parameter of an actual competitive jump.

Several specific exercises that are currently used in training athletes in different jumping events are listed below as examples (**Table 9**). All the exercises are classified into groups I – IV and may be recommended for practical use by athletes of a corresponding specialization. The list of exercises is not full because of the scope limitations for materials to be presented, but it provides general notion about aspects of training means selection for solving concrete training tasks taking into account jumpers' specialization.



#### **Table 9.**

*Specific exercises that are currently used in training athletes in different jumping events.*

#### **Abbreviations**



*Justification of some Aspects of the Choice of Training Means Selection in Track-and-Field Jumps DOI: http://dx.doi.org/10.5772/intechopen.104839*


#### **Author details**

Mikhail Shestakov\* and Anna Zubkova Federal Science Center of Physical Culture and Sport (VNIIFK), Moscow, Russia

\*Address all correspondence to: mshtv@mail.ru

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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*Justification of some Aspects of the Choice of Training Means Selection in Track-and-Field Jumps DOI: http://dx.doi.org/10.5772/intechopen.104839*

[19] Umberger BR. CSCS mechanics of the vertical jump and two-joint muscles. Strength and Conditioning. 1998;**20**(5):70-74

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#### **Chapter 8**

## From Exercise Physiology to Network Physiology of Exercise

*Natàlia Balagué, Sergi Garcia-Retortillo, Robert Hristovski and Plamen Ch. Ivanov*

#### **Abstract**

Exercise physiology (EP) and its main research directions, strongly influenced by reductionism from its origins, have progressively evolved toward Biochemistry, Molecular Biology, Genetics, and OMICS technologies. Although these technologies may be based on dynamic approaches, the dominant research methodology in EP, and recent specialties such as Molecular Exercise Physiology and Integrative Exercise Physiology, keep focused on non-dynamical bottom-up statistical inference techniques. Inspired by the new field of Network Physiology and Complex Systems Science, Network Physiology of Exercise emerges to transform the theoretical assumptions, the research program, and the practical applications of EP, with relevant consequences on health status, exercise, and sport performance. Through an interdisciplinary work with diverse disciplines such as bioinformatics, data science, applied mathematics, statistical physics, complex systems science, and nonlinear dynamics, Network Physiology of Exercise focuses the research efforts on improving the understanding of different exercise-related phenomena studying the nested dynamics of the vertical and horizontal physiological network interactions. After reviewing the EP evolution during the last decades and discussing their main theoretical and methodological limitations from the lens of Complex Networks Science, we explain the potential impact of the emerging field of Network Physiology of Exercise and the most relevant data analysis techniques and evaluation tools used until now.

**Keywords:** complex systems, circular causality, nonlinear dynamics, timescales, self-organization

#### **1. Introduction**

Exercise physiology (EP), the study of how the body adapts physiologically to the acute and chronic stress of exercise or physical activity, has evolved extensively since the beginning of the early twentieth century. Due to an increased interest in exercise and health, initially motivated by the poor physical capacity of soldiers, is today a scientifically founded branch that provides the basis of physical fitness, exercise performance, training, testing, and rehabilitation programs addressed to all types of population, including elite athletes and clinical patients. Its potential to enrich Basic Physiology and diverse fields such as Sports Medicine, Sports Rehabilitation, Sport Science, or Training Science is still undervalued and has to be rediscovered under the framework of Complex Systems and Network Science approaches [1].

#### *Exercise Physiology*

In this chapter, the present and future of EP will be overseen from a historical and scientific perspective. The main limitations of the EP available evidence-based research, strongly influenced by excessively simplified theoretical and methodological assumptions, will be discussed using the example of the exercise-induced fatigue. Finally, the research approach of the new emerging field of Network Physiology of Exercise, focused on the coordination and integration among physiological systems across spatiotemporal scales (from the subcellular level to the entire organism), will be presented.

#### **2. Evolution of Exercise Physiology**

It is essential to understand the EP history when approaching the future [2]. As any scientific branch, the EP evolution has been constrained by multiple and multilevel factors acting at different timescales such as financial possibilities, organizational and ideological positions. Although historical data pertaining to EP spans more than 2000 years, first research contributions correspond to the early twentieth century, which was characterized by an increasing specialization and sub-specialization in many scientific fields. This state of affairs brought about a flood of fragmentation in science that promoted the naissance and development of the main EP research labs in the world.

First works, initiated by Scandinavian scientists, were related to metabolism and heat production during exercise and recovery. Maximal oxygen uptake was described as the upper limit of performance [3], and lactate production (from glucose metabolism) was related to fatigue [4]. Research was focused later on circulation, muscle physiology, or environmental physiology and provided the basis of exercise as medicine. While the major concern of research after the World War II was the health and fitness of soldiers, the most recent concern is the obesity epidemic and other diseases related to the food abundance and lack of physical activity.

With the development of labs and the creation of world organizations such as the American College of Sports Medicine (ACSM), and the European College of Sport Sciences (ECSS), the field of EP has become enormously specialized in the last years, and EP researchers usually work in one area (e.g., cardiovascular, muscular, etc.). This has produced a loss of the original essence of Physiology, the unique branch of Biology specifically dealing with synthesis and integration. Although technological advances have led to create more sophisticated and better equipped labs, the type of inquiry and research focus of EP has been kept in general quite immutable, and clinical exercise physiologists keep mainly directed to testing energy production (e.g., aerobic power, anaerobic thresholds, etc.) [5].

Influenced by reductionism, Biology has traditionally emphasized: the decomposition of systems responsible for a given phenomenon into component parts and processes. Identifying such components and describing their mechanisms apart during exercise have been one of the main EP endeavors. Using a range of experimental models from cells to animals and humans, main approaches have laid the description of the biological mechanisms of temporary and persistent functional changes in response to acute and repeated exercise [5, 6]. It is worth noticing that despite the evolution of biology and the technological advances of the last years, the initial theoretical assumptions of EP have kept almost intact.

Even if "why" questions, related to teleological explanations, have been traditionally avoided because the final purpose of physiological systems is assumed to be unknown or nonexistent, research questions often reflect the excessively simplistic assumptions that have characterized EP from the very beginning (see Section 3 for further detailed explanation). The linear and reductionist approach of the scientific production is reflected in the redundant expression "Effects of," highlighted in the content analysis done on over 22.000 ECSS abstracts submitted during almost two decades [7].

This expression reflects a very specific mode of inquiry, and its consequential data acquisition tools, analysis techniques, and inductive methods, commonly and uncontroversially used in EP research.

A century of reductionist research has produced a lot of information and descriptive knowledge, some obtained through very well-designed experiments, but has provided only a partial understanding of exercise-related phenomena, and led to several controversial findings. In fact, some of the main questions still remain without clear responses. For instance, which are the limits of performance, what limits VO2max, what causes fatigue, why are there responders and non-responders to exercise, etc. The extant controversies seem strongly affected by the excessively simplified theoretical and methodological assumptions that characterize the field.

#### **2.1 Molecular Exercise Physiology. Are explanations only in the cell?**

Due to the lack of clear responses to the main topics obtained investigating at system and organ levels (e.g., cardiovascular system, muscle), the reductionist rationale led EP investigation, and medical investigation in general, in which disease is increasingly understood in molecular terms, toward microscopic levels (Molecular Biology, Genetics, and OMICS technologies). The acknowledgment of the role of exercise on health status and the pathway toward personalized medicine has also reinforced the micro-level research focus of EP [8–11].

While the 1970s were the decade of Biochemistry, the 1980s represented the Molecular Biology era. Technological advances played a fundamental role in this evolution. The introduction of DNA microarrays, a fast technology to study thousands of DNA and protein molecules simultaneously, supposed a revolution in biological research. Coupled with computational methods, pushed the development of Systems Biology (e.g., [12]), a branch that focuses on complex interactions within biological systems, and enabled to investigate the behavior of the genes of an organism under different conditions [13]. The identification of new biomarkers, the improved sensitivity and specificity of the existing ones, and new insights into the personalized therapeutic strategies to improve athletic performance and human health through precision exercise medicine is the main aim [14].

Research in Molecular Exercise Physiology and "sportomics" [15–17] is mostly focused on omics data collection and analysis efforts to catalog exercise-regulated pathways. Although Molecular Biology dwells on dynamic principles, the dominant research methodology in Molecular Exercise Physiology, and Integrative Physiology [10, 18] keep focused on non-dynamic bottom-up group-pooled statistical inference modes of inquiry. Main properties of CAS as synergies, established not only horizontally (e.g., among molecules) but vertically (among molecular, cellular, tissular, organ, and system levels), are neglected. The embeddedness of lower levels in upper levels, the circular causality (bottom-up, top-down) relationship among the levels, the different timescales of activity, the nonlinear dynamic processes that suffer qualitative changes through self-organization are also some of the main neglected properties.

Many component processes can lose or gain on significance during exercise; for instance, as fatigue develops (see Section 2.2). Physiological and psychobiological synergies compensate critical quantitative values registered at micro-level keeping stable behavioral variables registered at action level. In biological systems, the same effect at microscopic level can be produced by many different macroscopic phenomena. In addition, genes are dominantly pleiotropic, that is, the same gene can be involved in different physiological effects and states. Hence, the informativeness of the microscopic (Molecular Biology levels) may be at best an initial point in a much more elaborate study of the organism-environment interaction to conclude on the real macroscopic phenomenon that is involved in a health or performance problem.

Personal health and performance cannot be reduced to molecular and genetic levels as medicine cannot be geneticized. In addition, the network relations do not operate only bottom-up, but also top-down, that is, from the entire person to the genes level following the circular causality property of complex systems [19].

The view that everything can be explained at microscopic (molecular) level directly implies that health can be intervened and repaired only at this level, that is, through pharmacological substances. However, a person-environment approach [19] implies that health and performance are products of the interaction of many different levels, and health can be also improved intervening at environment or psychological level. In fact, interventions at macroscopic (social, psychological) level have been proven as crucial in changing the processes at subcellular level [20, 21]. Results seems to show that in a sick society, where more often than not, the competition for socially imposed success becomes a goal for itself, there is an increased likelihood of cell aging and poor personal health [22]. In multilevel complex networks, the macroscopic ambience strongly constrains its embedded components [23, 24]. While the use of pharmacological substances may be promoted somewhat by the big financial benefits that lie behind, mental interventions, usually cheaper and requiring only the development of self-knowledge and self-discipline [20], receive in general less scientific attention. In particular, exercise is a privileged type of intervention because it may affect all personal levels in a correlated cascade way [7, 25].

Systems Biology and Integrative Physiology strive for the same goal: to understand Biology whole-istically [18]. Systems Biology is focused on systems operating at a cellular level and has evolved over the past decade (called the "omics era") as a direct result of advances in high-throughput molecular biology platforms and associated bioinformatics. In fact, Systems Biology has been described as: "the study of an organism, viewed as an integrated and interacting network of genes, proteins and biochemical reactions which give rise to life." Instead of analyzing individual components or aspects of the organism, such as sugar metabolism or a cell nucleus, systems biologists focus on all the components and the interactions among them, all as part of one system. These interactions are ultimately responsible for an organism's form and function [26].

Physical exercise dictates the magnitude and pattern of how networks of genes, proteins, and biochemical reactions will integrate and interact. This is an important point, because to the exercise physiologist most, if not all, cellular-network-based change will be secondary to the physiological stimulus causing that change, e.g., muscle contraction, rather than originating at the level of the network per se. This in essence is one important difference between the molecular biology focus at the core of Systems Biology and functional feedback approach of Integrative Physiology, a difference eloquently described by Noble [27]. In conclusion, although there is a tremendous potential for omics approaches to fill critical gaps in our understanding of the integrative networks underlying the health benefits of exercise [28] and allow going beyond the one-size-fits-all model of prescription [29], the complexity and interconnectedness of exercise biological networks cannot be unraveled and understood by studying single tissues or molecular targets alone. They require dynamic, multilevel, and global approaches. For instance, whether molecular processes can inform about the level of stress, the macroscopic phenomenon of stress cannot be explained only at microscopic level.

#### **2.2 From microscopic to systemic hypotheses in Exercise Physiology. Example of exercise-induced fatigue research**

The research performed to respond to the question about the causes of exerciseinduced fatigue and spontaneous task failure is a good example of the current tendencies in EP research.

Over the last century, physiologists have tried to find the etiology and underlying mechanisms of exercise-induced fatigue [30]. Despite a wealth of knowledge about individual components intervening in the fatigue process and their adaptation to different types of exercise, they have failed to detect a single component or process responsible of the phenomenon and the limits of exercise tolerance in general [31]. The questions of "what causes exercise-induced fatigue" or "are limiting mechanisms central or peripheral, are there in the brain or in the muscle [32, 33]?" are clear examples of the type of inquiry searching for cause-effect relationships and the fragmentation tendencies derived from the reductionist models applied to the EP research.

The research investigating central and peripheral mechanisms of exerciseinduced fatigue has not provided either a clear response to the question [34–37]. The impaired action potential propagation, the inhibition of reflex mechanisms, the stimulation of chemical and nociceptive afferent signals, the corticospinal stimulation changes, the increase in extracellular serotonin, the cytokines liberation, the muscle acidosis, the accumulation of NH4, H+, Mg2+, Pi, the hyperthermia, the inhibition of Ca2+ liberation, the glycogen reduction, the increase of K+ and free radicals are all associated processes to the fatigue development but cannot explain it.

In a similar way, assumed cause-effect or dose–response relationships among biochemical and performance variables have been proven to be often wrong. For instance, lactic acid, initially thought to be the consequence of oxygen lack in contracting skeletal muscle and related to the limits of high-intensity short-duration exercise, now it is recognized as being formed under fully aerobic conditions and associated to ergogenic and antifatigue properties [38, 39].

Fatigue is a macroscopic phenomenon and reflects itself in macroscopic behavior of performers [40]. Microscopic processes associated to it are not linearly independent (as it is usually tacitly assumed), and their total effects cannot be treated as a sum of individual effects. In particular, when knowing that there is a circular causality spread over the levels in all complex systems. Instead of focusing on isolated central and peripheral processes, the exercise-induced fatigue and task failure can be studied at behavioral coordination level, which integrates all network levels [41]. Using a macroscopic kinematic variable extracted at action level, the authors studied the time-variability properties of the elbow angle, considered as order parameter, during an effort performed until exhaustion. Critical behavior such as critical slowing down, enhancement of fluctuations, and correlation enhancement in interlimb coordination was reproducibly observed [42]. In this way, fatigue was understood as a process that leads to a *system-level* phase transition (spontaneous task disengagement), due to the circular causality mechanism that spreads over the levels in CAS.

In this way, it was hypothesized that the spontaneous task failure consists of a percolation process, produced by the impaired ability of the psychobiological network system to make the necessary short-term adjustments for negotiating the imposed external workload. In this scenario, the spontaneous task failure/disengagement, represent a giant (at systemic level), protective inhibitory fluctuation that causes a temporary abrupt switch to a lower energy expenditure level, a critical phenomenon prominent in complex systems, such as human psychobiological networks. This means that the loss of stability at systemic level is the cause of the task disengagement and not a singular process at singular level that can be pinpointed.

#### **3. Limitations of Exercise Physiology. Contrasting approaches from complex network science**

In contrast to decomposition, EP has paid much less attention to re-composition of physiological mechanisms [43]. The greatest challenge today, not just in Biology

but in all of science, is then to reassemble such decomposed mechanisms capturing the key properties of the entire ensembles [44]. If composing and closing the sequence of the Krebs cycle and/or describing the sequence of reactions of the glycolysis was years ago a key innovation, the challenge today is defining the nonlinear dynamics of embedded network processes under constraints.

New technologies and interdisciplinary work have promoted the introduction of complex systems thinking on EP, but there is still a long way to go. The sophistication and capacity of modern technology, able to shift the landscape of basic life sciences research from that of traditional biological reductionism to a much more integrative, holistic systems approach [45], are not enough. In fact, a change from a reductionist to holistic paradigm cannot be achieved only via the technical world. Together with new techniques and technologies, the development of new theoretical assumptions, conceptual frameworks, and analysis tools is necessary. New ways of doing and understanding based on complex systems, proven as successful in other disciplines, should be also implemented in EP [46]. As pointed by Greenhaff and Hargreaves [26], "perhaps the tools of Systems Biology should be viewed increasingly as a valuable addition to the arsenal that exercise scientists can use to interrogate physiological function and adaptation" (**Table 1**).

#### a.Theoretical assumptions

Instead of fragmenting and studying separately the functions of different physiological components and processes, the focus of Networks Science is put on the interaction dynamics among such components and processes. Classical cybernetics, inspiring the basic biological control system model of EP, is replaced by Dynamical Systems Theory (DST), which provides concepts and tools to describe


#### **Table 1.**

*Contrast of some limiting theoretical and methodological assumptions of EP research with assumptions based on Networks Science.*

and study the coordinative changes occurring in the physiological network over time.

According to classical cybernetics, different components and processes operate through feedback loops to maintain physical or chemical physiological parameters constant (homeostasis). The predictions of this "engineering" approach are linear, i.e., proportional between inputs and outputs and are displayed through descriptive block diagrams, commonly used in EP to represent how organic structures and processes interact. The basic assumption of these diagrams is that of time-invariant encapsulated modules, processes, and regulation profiles. While the concept of feedback works fine in simple systems that have only two parts to be joined, each of which affects the other, when a few more parts are interlaced together, the system very quickly becomes impossible to treat in terms of explicit feedback circuits.

In complex systems, there is no reference state with which feedback can be compared and no place where comparison operations are performed. Nonequilibrium steady states emerge from the nonlinear interactions among the system's components, but there are no feedback-regulated set points or reference values as in a thermostat. For instance, it is not possible to explain through feedback loops phenomena such as the fatigue-induced task disengagement [47], the overtraining syndrome [47, 48], or the macroscopic emergence of noncontact injuries [49].

Feedback homeostatic mechanisms are replaced from a Networks Science point of view by the concept of homeodynamics or dynamic stability, i.e., a constantly changing interrelatedness of body components and processes while an overall equilibrium is maintained [50].

It is common among exercise physiologists to propose conceptual models where the main regulator or programmer is the Central Nervous System (CNS) (see, e.g., [45, 51]). Integrative Physiology also neglects that CAS does not need any internal or external programmer to regulate their functions [52]. Properties of such functions (i.e., stability, instability, switches among states, etc.) are parametrically regulated, and the CNS is also a regulated subsystem. This means that physiological states emerge from the interaction among multilevel system components (the CNS being another component) through a self-organized process. The search for the ultimate high-level regulator would end in infinite regress (who regulates the regulator that regulates…?) and represents a loan on understanding exercise-related physiological phenomena.

#### b.Methodological traits

Instead of isolated variables, the use of macroscopic collective variables is proposed because they behave as order parameters integrating all network levels and capturing the system organization. The dynamics of such variables, reflected in their time variability properties, may inform about the interactions among system components and may help detecting different states and anticipate qualitative changes.

Instead of using only molecular data to establish bottom-up statistical timeless inferences from micro to macroscopic phenomena, the study of the time-variability properties of behavioral macroscopic variables, extracted at action level (e.g., the elbow angle in Section 2.2) during exercise, may inform about the vicinity of qualitative changes. This approach helps to detect dynamic features such as stable and unstable states, critical behavior (phase transitions, bifurcations, critical slowing down, enhancement of fluctuations). It is worth to remark that such behavior can be produced at different quantitative values of physiological parameters or set points [41].

Specific proposals of Network Physiology are developed in sections 4 and 5.

Most of the available research on EP, based on inductive analytical research, infers intra-individual phenomena from the analysis of inter-individual variations obtained through group data means and comparison designs. This approach has some basic debatable methodological issues that should be discussed.

The main aim of physiological (systemic, biochemical, genetic, epigenetic) research is to find the mechanisms of regulation and causal changes that occur at intra-individual (i.e., organism) level as an effect of various internal and external factors. In other words, the intra-organismic processes and not the population are the explanatory target. It is important to note here that intra-individual variability and co-variability unfold in time and hence, need to be measured through time series analytical tools. While the problem of sample to population generalization has been much discussed, investigated, and used, in inferential statistics, much less attention has been focused on the question of sample or population to individual generalization. A tacit assumption has been that the results obtained at sample and generalized to population level are representative of the changes of a "typical" (i.e., average) individual [53–55]. In other words, the group-pooled data merely would enhance the typical phenomenon that already exists in every and each individual. However, in order for this assumption to be correct, there are some strict conditions to be fulfilled. These conditions are the non-violation of ergodicity1 assumption. On the other hand, pooling over group subjects is the predominant research practice in exercise and health-related research. Even the state-of-the-art analytical software packages for time series analysis [56] are based on pooling-over-subjects approaches.

The correctness of the tacit assumption of ergodicity conditions, to our knowledge, has never been explicitly tested EP. Hence, the generalization of results from population to individual (or between clusters of individuals) may be typically not valid for developmental biological systems. This means that the structure of causal changes may drastically vary from individual to individual, and these differences are not detectable at the group-pooled level. Some approaches to overcome these serious problems have been proposed [57–60].

Using molecular data, Integrative Exercise Physiology and OMICS techniques are focused on establishing non-dynamical bottom-up statistical inferences between micro- and macro-level states, ignoring one of the main properties of CAS: the tendency to form multilevel synergies. Synergies acting at different levels (e.g., molecular, cellular, tissue, organ, etc.) allow reciprocal compensations among physiological components and processes to satisfy a task goal during exercise. Such synergies are flexible assembled patterns of coordination, which form emergent structures and functions responding to the exercise requisites. Without them, life would not, and could not, exist. Through circular causality relations, components form new synergies, which govern, in turn, the components' behavior [61, 62]. While computer scientists build programs that tell circuits what to do, nature builds synergies [63, 64].

Synergetic is also manifested through the CAS property of degeneracy: different components produce the same function, and different synergies may be activated to attain the same task goal [65, 66]. For instance, different motor units cooperate and reciprocally compensate their activation over several timescales to perform an effective or functional motor action over time during a running competition. The self-assembled, adaptive interactions of CAS underpin also another robustness enabling property: pleiotropy or multifunctionality, that is, the same components

<sup>1</sup> Ergodicity: The system's stochastic evolution in time is stationary (stationarity assumption) and the structure of the intraindividual multivariable dynamics is the same in all individuals (the homogeneity assumption). Typically, jointly these conditions are not fulfilled in biological systems.

may be assembled to produce multiple functions. For instance, the skeletal muscle, with genuine/primordial contractile functions, may exert as well immunological and endocrine functions [67, 68]. Such properties enable CAS to switch between diverse coordinative states and maintain a metastable dynamic [69].

### **4. Network physiology of exercise: A paradigm shift**

Dynamic models, initially rejected by biologists, initiated some 40 years ago a paradigm shift in general biology [70, 71], molecular and cell biology [72], genomics [73], and all the "omic"-based approaches [74], which are now at the forefront of science. Such interaction-based approaches have started to spread in EP and relevant fields of medical research such as cancer [75]. However, Physiology, and in particular EP, should do a substantial effort for reassembling biological processes and focusing not only on horizontal interactions at molecular level and establishing non-dynamical statistical inferences to the entire person (e.g., performance or health status, see **Figure 1**, left), but integrate all vertical network levels (e.g., molecular, cellular, tissue, organ, systems, see **Figure 1**, right). That is, avoiding the gap between micro and macro structures and functions and considering the multiple vertical synergies that may act among them.

Network Physiology of Exercise (NPE) emerged inspired by the field of Network Physiology [76–84] and Networks Science [1]. Network Physiology addresses the fundamental question of how physiological systems and subsystems coordinate, synchronize, and integrate their dynamics to optimize functions at the organism level and to maintain health. It aims at uncovering the biological dynamic mechanisms [85–88] since it satisfies both the mechanistic requirement of structure and localization (e.g., nodes and edges/links in dynamic networks may represent localized integrated organ systems, subsystems, localized components or processes, and interactions among them across various levels in the human organism) and the requirement of dynamical invariance and generality that is enabled by dynamical systems approach [89].

In the context of exercise, NPE aims to transform the theoretical assumptions, the research program, and the current practical issues of current EP. It focuses the research efforts on improving the knowledge of the nested dynamics of the vertical (among levels) and horizontal (among organs and components) network

#### **Figure 1.**

*Contrast between Molecular Exercise Physiology (left), focused on non-dynamical bottom-up statistical inference techniques, and Network Physiology of Exercise (right), focused on the nested dynamics of the vertical and horizontal physiological network interactions.*

interactions to understand how physiological states and functions emerge under different constraints and contexts.

Studying the organism as a dynamical system means studying a set of variables that interact over time, that is, their time series, that may exhibit various patterns. DST comprises a highly general set of mathematical concepts and techniques for modeling, analyzing, and interpreting these patterns in time series data. Therefore, DST is not applied exclusively to the area of biomedical sciences, it can also be used to describe social and psychological phenomena, among others [90–92].

Many physiological mechanisms exhibit oscillations or more complex dynamical behavior, which is crucial for orchestrating operations within the mechanism. Such complex behavior is non-sequential, because some of the interactions in the mechanism are nonlinear, and the system is open to energy. Initial positive adaptations of physiological functions are followed by stagnation or decrease of such functions when workload increases further (e.g. overtraining syndrome, see [47, 48, 93]).

Interactions, generate novel information that determines the future of elements, and thus of the system itself [94]. The interaction-dominant dynamics of humans, in contrast with the typical component-dominant dynamics of machines [95], has been emphasized in the EP literature [41, 96, 97]. This means that the behavior of CAS cannot be simply explained through linearly independent variability sources, processes, or local mechanisms. For instance, exercise physiologists cannot rely on critical quantitative endpoints in cardiovascular, respiratory, metabolic, or neuromuscular systems to explain the limits of performance [31, 98, 99] and should reformulate their research hypothesis on the basis of CAS properties.

#### **4.1 Network Physiology of Exercise. Data analysis techniques**

Novel data analysis techniques have been successfully applied in the context of Network Physiology to explore how physiological systems dynamically integrate as a network to produce distinct physiologic functions [80, 85, 86, 100]. The goal of such tools is to develop a general theoretical framework and a computational instrumentarium tailored to infer and quantify interactions among diverse dynamical systems—specifically, (i) systems of oscillatory, stochastic, or mixed type; (ii) systems with noisy, nonstationary, and nonlinear output signals; (iii) systems acting on widely different timescales from milliseconds to hours; (iv) systems coupled through multiple coexisting forms of interaction. Some of the most relevant data analysis techniques to infer couplings among several physiological systems, with potential to be utilized under exercise settings, are the following:

#### *4.1.1 Time delay stability (TDS) method*

Integrated physiologic systems are coupled by feedback and/or feed-forward loops with a broad range of time delays. To probe the network of physiologic coupling, a novel concept has been introduced, time delay stability, and a new TDS method has been developed to study the time delay with which modulations/bursts in the output dynamics of a given system are consistently followed by corresponding modulations in the signal output of other systems. Periods with constant time delay indicate stable interactions, and stronger coupling between systems results in longer periods of TDS (**Figure 2**) [80, 101]. Thus, the strength of the links in the physiologic network is determined by the percentage of time when TDS is observed: higher percentage of TDS corresponds to stronger links. To identify physiologically relevant interactions, represented as links in the physiologic network, we determine a significance threshold level for the TDS based on comparison with surrogate data:

*From Exercise Physiology to Network Physiology of Exercise DOI: http://dx.doi.org/10.5772/intechopen.102756*

#### **Figure 2.**

*Schematic presentation of the TDS method: Segments of (a) heart rate (HR) and (b) respiratory rate (Resp) in 60 sec time windows (I), (II), (III) and (IV). Synchronous bursts in HR and Resp lead to pronounced cross-correlation (c) within each time window in (a) and (b), and to a stable time delay characterized by segments of constant* τ*0 as shown in (d)— four red dots high- lighted by a blue box in panel (d) represent the time delay for the 4 time windows. Note the transition from strongly fluctuating behavior in* τ*0 to a stable time delay regime at the transition from deep sleep to light sleep at* ∼*9400 sec and inversely from light sleep back to deep sleep at* ∼*10,100 sec (shaded areas) in panel (d). The TDS analysis is performed on overlapping moving windows with a step of 30 sec. Long periods of constant* τ*0 indicate strong TDS coupling.*

only interactions characterized by TDS values above the significance threshold are considered. The TDS method is robust and can track in fine temporal detail how the network of connections between organ systems changes in time. The method is general and can be applied to diverse systems.

#### *4.1.2 Phase synchrogram algorithm (PSA)*

Nonlinear oscillatory systems are characterized by nonidentical eigenfrequencies and highly irregular signal output can synchronize even when their coupling is weak—i.e., their respective frequencies and phases "lock" at a particular ratio. Despite the significant difference in the periodicity of the cardiac and respiratory rhythms represented by the heartbeat and respiratory intervals, and despite the complex noisy variability in the cardiac and respiratory signals, previous work found that episodes of heartbeat-respiration phase synchronization emerge. Previous authors developed a synchrogram algorithm able to identify segments of cardiorespiratory phase synchronization and to track how the degree of this nonlinear form of coupling changes in time and across physiologic states ([85]; **Figure 3**). The PSA synchrogram algorithm is robust and can identify interrelations between output signals of nonlinear coupled systems even when these signals are not cross-correlated [86]. Thus, the PSA can quantify the degree of coupling between nonlinear systems when other conventional methods (such as cross-correlation or cross-coherence analysis) cannot.

#### *4.1.3 Cross-correlation of instantaneous phases (CCIP) method*

Due to the nonstationary trends embedded in physiologic signals, traditional cross-correlation and cross-coherence analyses fail to accurately quantify the interrelation between physiological systems. This approach based on the cross-correlation between the instantaneous phase increments of the output signals of nonlinear

#### **Figure 3.**

*Schematic presentation of the PSA method: (A) three consecutive breathing cycles and (B) a simultaneously recorded ECG signal. (C) Demonstration of phase synchronization between the heartbeats and respiratory cycles shown in (A) and (B). For each breathing cycle, all first heartbeats occur at the same respiratory phase* φ*1r(t), and all second and third heartbeats within each breathing cycle occur at* φ*2r (t) and* φ*3r (t), respectively (symbols collapse), indicating robust phase synchronization. (D) each heartbeat in the ECG signal (B) is shown with its phase* φ*r (t) relative to the beginning of the breathing cycle in which it occurs. Different symbols represent heartbeats in different breathing cycles as in (A) and (C), and vertical dashed lines show the beginning of each breathing cycle. Three horizontal lines formed respectively by the first, second, and third heartbeats in the three breathing cycles indicate robust 3:1 phase synchronization despite noisy heart rate and respiratory variability.*

coupled systems is not affected by the nonstationarity of the signals. Chen et al. [86] successfully applied this new approach to study cerebral autoregulation in healthy subjects and in stroke patients. The approach is sensitive to uncover previously unknown differences in the coupling between cerebral blood flow velocity and peripheral blood pressure in the limbs for healthy and post-stroke subjects (**Figure 4**). In contrast, linear cross-correlations and other traditional methods cannot identify changes in cerebral autoregulation after stroke.

#### *4.1.4 Principal components analysis (PCA)*

PCA has been recently conducted on the time series of several cardiorespiratory parameters during maximal exercise (**Figure 5**). The PCA pinpoints and quantifies whether the increment and decrement of time patterns from different physiological processes are statistically correlated. In this way, the magnitude to which time patterns of physiological responses covary in time is reflected. The covariation of several (two or more) cardiorespiratory parameters shows the mutual information that they share. This common variance, in turn, enables time patterns of single cardiorespiratory outcomes to be represented through fewer principal components (PCs). The PCs are obtained in decreasing order of importance and reflect the highest possible fraction of the variability from the original dataset. Thus, the total number of PCs indicates the level of coordination among the initial cardiovascular and respiratory parameters. More concretely, a dimensionality reduction is indicative of the creation of new

*From Exercise Physiology to Network Physiology of Exercise DOI: http://dx.doi.org/10.5772/intechopen.102756*

#### **Figure 4.**

*The CCIP approach: Identifies breakdown of coupling mechanisms of cerebral autoregulation after stroke. Signals of peripheral blood pressure (BP) in the limbs and blood flow velocity (BFV) in the brain for (a) healthy and (b) post-stroke subject during a quasi-steady supine state without external perturbations. (c-d) Traditional cross-correlation function C(*τ*) for the BP and BFV signals for the same subjects shown in (a) and (b) does not identify differences in the BP-BFV coupling between healthy and post-stroke subjects. (e-f) In contrast, cross-synchronization function S(*τ*) obtained from the phase increments of BP and BFV signals using our CCIP method shows a significant difference in the BP-BFV coupling between healthy and post-stroke subjects, even though patterns in the pairs of BP-BFV signals are visually similar (a, b) for both healthy and stoke subjects.*

#### **Figure 5.**

*Typical example of the reduction of cardiorespiratory variables to time series of cardiorespiratory coordination variables (PCs) in two consecutive maximal cardiorespiratory tests interspersed by 10-min resting: Test 1 and test 2. Top graphs: Original time series of the six selected cardiorespiratory variables in test 1 and test 2. Bottom graphs: Time series of PC scores (standardized z-values in the space spanned by PCs) in both tests. The six time series are collapsed to one time series (test 1) or two time series (test 2) as a consequence of the PC dimension reduction. The black and the red lines show the average trend of both processes as calculated by weighted least squares method. Data points of the x-axis of both graphs refer to the number of measurements recorded along the cardiorespiratory test.*

coordinative patterns [102]; therefore, the reduction in the quantity of PCs suggests an enhancement in the efficiency of cardiorespiratory system [103].

#### **4.2 Evaluation tools based on Network Physiology: Network-based biomarkers**

The common testing variables used in Exercise Physiology (e.g., VO2max, ventilatory thresholds, etc.) do not provide sufficient information about the dynamic interactions among physiological systems and their common role in an integrated network. In this line, previously published works have shown a lower sensitivity of gold standards such as VO2max compared with other coordinative variables able to determine dynamic interactions among physiological systems [104–107]. The different data analysis techniques described in the previous section have the potential to be used as novel evaluation tools to investigate interactions among physiological systems under exercise settings. More specifically, these techniques can lead to the development of new network-based biomarkers able to quantify how different key organ systems (e.g., brain, heart, skeletal muscles) coordinate and synchronize as a network during exercise and track how these network interactions change in response to fatigue and training. The use of new network-based biomarkers will break new ground in the study of multilevel inter-organ interactions and will provide new understanding of Basic Physiology and diverse exercise-related phenomena such as sports performance, fatigue, overtraining, or muscle-skeletal injuries.

#### *4.2.1 Inter-muscular interactions*

Inter-muscular coordination is defined as a distribution of muscle activation or force among individual muscles to produce a given combination of joint moments [108]. Therefore, neuromuscular control during exercise or activities of daily living is not limited to switching muscles on or off but includes fine-tuned control to select the appropriate muscle fiber types with precise timing and activation [109–111]. Techniques based on the frequency domain of the surface EMG [112, 113] are the most suitable to infer information on motor unit recruitment and muscle fiber since (i) the average conduction velocity of the active motor unit is related to fiber-type proportions, and (ii) the changes in the spectral properties are linked to the changes in the average conduction velocity. Inter-muscular coherence (IMC) is one of the most utilized methods to investigate inter-muscular interactions in the frequency domain—it estimates the amount of common neural input between two muscles during voluntary motor tasks [114]. Despite its clinical relevance to evaluate inter-muscular coordination, IMC has been recently questioned for its lack of potential to identify nonlinear dynamic coupling across frequencies [115] and, thus, ignore the interactions between distinct types of muscle fibers across muscles. Therefore, new data analysis approaches are needed to investigate the physiological mechanisms underlying cross-frequency network communication among distinct muscle fiber types across muscles during exercise.

#### *4.2.2 Cortico-muscular interactions*

Skeletal muscle activity is continuously modulated across physiologic states to provide coordination, flexibility, and responsiveness to body tasks and external inputs. Despite the central role the muscular system plays in facilitating vital body functions, the network of brain-muscle interactions required to control hundreds of muscles and synchronize their activation in relation to distinct physiologic states has not been sufficiently investigated. In this line, to identify and quantify the cortico-muscular interaction network and uncover basic features of

#### *From Exercise Physiology to Network Physiology of Exercise DOI: http://dx.doi.org/10.5772/intechopen.102756*

neuro-autonomic control of muscle function, a recently published work [116] has investigated the coupling between synchronous bursts in cortical rhythms and peripheral muscle activation during sleep and wake. The findings demonstrate previously unrecognized basic principles of brain-muscle network communication and control and provide new perspectives on the regulatory mechanisms of brain dynamics and locomotor activation, with potential clinical implications for neurodegenerative, movement, and sleep disorders and for developing efficient treatment strategies. Further research is warranted to investigate cortico-muscular interactions during exercise and their changes in response to fatigue and different training methodologies.

#### *4.2.3 Cardiorespiratory interactions*

Previous research has demonstrated that the cardiac and respiratory systems exhibit three distinct forms of coupling: respiratory sinus arrhythmia (RSA), cardiorespiratory phase synchronization (CRPS), and time-delay stability (TDS) [76, 85, 101]. While RSA is a measure of amplitude modulation of the heart rate during the breathing cycle, CRPS and TDS characterize the temporal coordination between the cardiac and respiratory systems. Specifically, the CRPS reflects the degree of clustering of heartbeats at specific relative phases within each breathing cycle (despite continuous fluctuations in heart rate and in breathing intervals), and the TDS quantifies the stability of the time delay with which bursts in the activity in one system are consistently followed by corresponding bursts in the other system. The findings indicate that these three distinct and independent forms of cardiorespiratory coupling are of transient nature, with nonlinear temporal organization of intermittent "on" and "off " periods, even during the same episode of any given physiologic state (sleep stage), and that these coupling forms can simultaneously coexist.

In the context of exercise, cardiorespiratory coordination has been investigated through a Principal Components Analysis (PCA) performed on time series of cardiovascular and respiratory variables registered during cardiorespiratory exercise testing (expired fraction of O2, expired fraction of CO2, ventilation, systolic blood pressure, diastolic blood pressure, and heart rate). Cardiorespiratory coordination has been utilized to assess changes produced by different training programs [103, 105], testing manipulations [104, 106, 117, 118], nutritional interventions [107], and pathological conditions [119]. The main findings of this set of studies point toward a higher sensitivity and responsiveness of cardiorespiratory coordination to exercise effects compared with isolated cardiorespiratory parameters, such as VO2max and other gold standard markers of aerobic fitness.

It should be noted that the aforementioned network-based biomarkers (intermuscular interactions, cortico-muscular interactions and cardiorespiratory interactions) can provide relevant information about how different key organ systems coordinate and synchronize as a network during exercise and track how these network interactions reorganize with accumulation of fatigue and in response to different training programs. However, these network-based biomarkers can only provide information at the organic (macroscopic) level by using equipment capable of recording continuous high-frequency physiological signals (time series of EEG, ECG, EMG). Therefore, the development of adequate technology able to register continuous and synchronous data extracted from different levels is needed to investigate the dynamics of physiological network interactions (i) not only at a macroscopic level, but also at lower levels of integration (i.e., cellular and subcellular); and (ii) among multilevel systems components—that is, capturing the synergies, embeddednes, and circular causality (bottom-up, top-down) between lower and upper levels.

#### **5. Conclusions**

Despite the fundamental discoveries, vast progress and achievements in the field of EP for over a century, the reductionist framework that has traditionally dominated research in the field has imposed limitations to the exploration and understanding of the regulatory mechanisms underlying complex exercise-related phenomena.

EP research, characterized by an inductive analytic mode of inquiry, has progressively evolved toward Biochemistry, Molecular Biology, Genetics, and OMICS technologies. Although such biology branches can be subjected to dynamical approaches, Molecular Exercise Physiology and Integrative Physiology keep focused on qüestionable non-dynamic bottom-up group-pooled statistical inferences.

Inspired by the field of Network Physiology and Complex Systems Science, Network Physiology of Exercise emerges to transform the theoretical assumptions, the research program and the practical applications of EP. The cybernetic Control Theory is replaced by Dynamic Systems Theory (DST), the centralized control of the CNS by a multilevel self-organization of body functions, and the static regulatory mechanisms by dynamic mechanisms with synergetic properties. The inductive analytical research, generalizing from group inter-individual inferences to intra-individual phenomena, is replaced by an inductive/deductive research based on intra-individual time series analysis techniques. Furthermore, it fills the gap of current research in Molecular Exercise Physiology, which is almost exclusively based on establishing bottom-up static statistical inferences from molecular data to the physiology of the entire person.

Network Physiology of Exercise focuses the research efforts on investigating the nested dynamics of the vertical (among levels) and horizontal physiological network interactions. The embeddedness of lower network levels in upper levels, the circular causality (bottom-up, top-down) among levels acting at different timescales and the emergence of nonlinear network phenomena are some of its genuine expected contributions. Network Physiology provides a wide range of data analysis techniques that have the potential to be utilized as novel evaluation tools to investigate interactions among physiological systems under exercise settings. These techniques can lead to the development of new network-based biomarkers (e.g., cardiorespiratory interactions, inter-muscular interactions, and cortico-muscular interactions) able to identify how different key organ systems coordinate and synchronize as a network during exercise and track how these network interactions change in response to different physiological states and exercise interventions. The use of new network-based biomarkers will open new and exciting horizons on exercise testing, will enrich Basic Physiology and diverse fields such as Exercise Physiology, Sports Medicine, Sports Rehabilitation, Sport Science, or Training Science, and will improve the understanding of diverse exercise-related phenomena such as sports performance, fatigue, overtraining, or sport injuries.

#### **Acknowledgements**

It includes funding information.

*From Exercise Physiology to Network Physiology of Exercise DOI: http://dx.doi.org/10.5772/intechopen.102756*

### **Author details**

Natàlia Balagué1 \*, Sergi Garcia-Retortillo1,2,3, Robert Hristovski4 and Plamen Ch. Ivanov3,5,6

1 Complex Systems in Sport, INEFC Universitat de Barcelona (UB), Barcelona, Spain

2 University School of Health and Sport (EUSES), University of Girona, Girona, Spain

3 Keck Laboratory for Network Physiology, Department of Physics, Boston University, Boston, MA, United States

4 Faculty of Physical Education, Sport and Health, Ss. Cyril and Methodius University, Skopje, North Macedonia

5 Harvard Medical School and Division of Sleep Medicine, Brigham and Women's Hospital, Boston, MA, United States

6 Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria

\*Address all correspondence to: nataliabalague@gmail.com

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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*From Exercise Physiology to Network Physiology of Exercise DOI: http://dx.doi.org/10.5772/intechopen.102756*

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#### **Chapter 9**

## Energy Cost of Walking and Running

*Vaclav Bunc*

#### **Abstract**

Walking and running are the basic means of influencing an individual's condition, his or her health and fitness. Due to the fact that various forms of physical load are used in movement training, the cause must be described by a single number, which reflects the volume, intensity, and form of physical load. One of the possibilities is to determine the energy cost (EC) of the applied physical activities. Possibilities of evaluation of EC in laboratory and field conditions using the speed of movement allow to streamline movement training. To achieve the desired lasting effect, it is necessary that the total EC exceeds the so-called stimulus threshold, that is, the subject of physical training must reach a certain minimum level of total EC of applied physical training. The total energy content of exercise allows you to design individual exercise programs. In the paper, we present the relationships between energy and speed of movement for the most commonly used physical activities to increase fitness in people without regular physical training–walking and running in different age groups and for men and women and the principles of design of movement interventions using this parameter, as well as the implemented programs and their effect.

**Keywords:** walking, running, energy, intensity of exercise, energy cost of movement, movement economy

#### **1. Introduction**

Determining the energy intensity of physical activity is a basic problem in evaluating the impact of this activity on the human body, either in terms of certain civilization diseases prevention, or in terms of increasing the functional (physical) fitness of people, or to assess the body's response to a given type of load.

The goal of all non-pharmacological intervention programs – movement programs in primary and secondary prevention is to determine the minimum amount of exercise load that will cause the necessary persistent changes in the state of the organism [1–3].

In general, the amount of energy that an organism consumes in a given physical activity is directly proportional to the intensity of that activity [1, 4, 5]. Throughout the range of movement load intensities–movement speed v, the energy E required to provide locomotor activity is proportional to the power of the velocity of movement. This relationship is generally nonlinear over the entire range of load intensities v and can be described by the following Equation [2, 6, 7].

$$\mathbf{E} = \mathbf{c} \ast \mathbf{v}^{\mathrm{n}} \tag{1}$$

Where c is the energy cost of movement, n for human movement ranges from 1 to 3 and expresses the density of the environment in which the movement is realized. The higher the density of the environment, the higher the value of n. The coefficient c characterizes the economics of motion and it is true that the lower its value, the better the economics of movement and the better its technique [2, 8].

The energy demands for submaximal movement intensity (i.e. movement economy) can be quantified by calculating the steady-state V̇O2, expressed with respect to body mass and time, for a standardized, submaximal movement intensity [1, 9]. Because this variable represents an aerobic need for physical activity, ATP resynthesis from ADP must be paid exclusively from substrates stored in the body and oxygen obtained from pulmonary ventilation and not from substantial protein catabolism. In untrained individuals, research has shown that at low to moderate speeds, steady state oxygen consumption is reached in approximately 3 minutes. Trained individuals reach a steady state earlier than untrained individuals. Although the existence of steady state is limited by a number of methodological limitations, this steady state can also be demonstrated by a non-increasing accumulation of lactate in the blood and RER lower than 1.00. All this is significantly influenced by diet, where in the case of predominant protein intake, the RER is less than one [1].

With a constant speed or running, at submaximal exercise intensities, the relationship between E and speed of running v is linear Energy necessary to proceed at a given running speed can be regarded as the product of c coefficient times the speed itself

$$\mathbf{E} = \mathbf{c} \ast \mathbf{v} \tag{2}$$

Where c is in J.kg�<sup>1</sup> .m�<sup>1</sup> and running speed in m.s�<sup>1</sup> , thus yielding energy E in W.kg�<sup>1</sup> . the range of linearity depends not only on the actual training state, but also on the metabolic state, age, sex, and speed potential of the subjects studied [6, 10].

The linearity of this dependence depends on the subject's training state. For running, it is in the range of 20–80% of the maximum intensity of movement in the untrained, and in the range of 10–90% of the maximum intensity in the trained [10].

Direct measurement of energy during real physical activity is relatively complicated. For practical reasons, we have often expressed E as oxygen uptake for the activity. In these cases, it has been convenient to express c in J.kg�<sup>1</sup> .m�<sup>1</sup> and running speed in m.min�<sup>1</sup> , to obtain E in more customary units ml.kg�<sup>1</sup> .m�<sup>1</sup> . Thus the last equation may be rearranged as follows:

$$\mathbf{VO\_2 = c \ast v} \tag{3}$$

Under aerobic conditions, since the energy E can be identified with VO2max, and in the submaximal range of intensities v, the last equation becomes:

$$\mathbf{f} \ast \mathbf{V} \mathbf{O}\_{2\text{max}} = \mathbf{c} \ast \mathbf{v} \tag{4}$$

where f is the fraction of VO2max which may be utilized over a prolonged period of time [2, 11]. The duration of the competition and thus also the performance in training is obviously a decisive factor in determining the magnitude off. It is larger the longer the duration of the competitive performance [2, 6, 12].

The movement speed thus may be calculated as follows

$$\mathbf{v} = \mathbf{f} \* \mathbf{V} \mathbf{O}\_{2\text{max}} \* \mathbf{c}^{-1} \tag{5}$$

It follows from the above relationship that the better the economy of movement the lower c, the higher the speed the individual can move.

### **2. Energy cost of movement**

Coefficient of movement energy cost during running (expressed in J.kg�<sup>1</sup> .m�<sup>1</sup> ), and indicates how much energy is needed to transfer the body mass of 1 kg to the distance of 1 m. It holds that the better the economy of movement, the lower the values of c we find. In our older study, we found the following values of the coefficient c for different sports, gender, and age. The value of this coefficient ranges from 3.5 for highly trained runners on middle distances to values of about 4.2 for untrained people. For example for men and women respectively in adult middle distance runners C = 3.57 +/� 0.15 and 3.65 +/� 0.20, in adult long-distance runners C = 3.63 +/� 0.18 and 3.70 +/� 0.21, in adult canoeists C = 3.82 +/� 0.34 and 3.80 +/� 0.24, in young middle-distance runners C = 3.84 +/� 0.18 and 3.78 +/� 0.26 and in young long-distance runners C = 3.85 +/� 0.12 and 3.80 +/� 0.24 [2]. This similarity may be explained by the similar training states of both sexes, resulting from the intense training which did not differ in its relative intensity and frequency between the groups of men and women. Bunc and Heller [2] found a negative relationship was found between the energy cost of running and maximal oxygen uptake (VO2max) expressed relative to body mass (for men r = �0.471, p < 0.001; for women r = �0.589, p < 0.001). Thus, the better the adaptation to a given movement load, the higher the values of the maximum consumption an individual can achieve and the lower the density of the coefficient c, and the better the technique of movement.

The energy demands of higher stride frequency at a given speed are frequently cited as the most plausible explanation for the higher energy cost of movement, for the higher coefficient c. This concept is based on the assumption that the energy required to move body mass should directly reflect the muscle tension created by each stride [13].

If we assume that differences in stored energy are not significant between different subjects [1, 2] then we may conclude that in the non-trained subjects with increasing body fat percentage, and generally with increasing body mass, the coefficient of the energy cost of movement increases, and the energy cost of movement decreases when training state decreases. The prerequisites for using stored chemical energy for moving are reduced and thus the moving capacity and movement economy decline. For improving of predispositions for moving (transfer of body mass), it is necessary to reduce body mass to the subject's "optimal" body mass [4].

#### **3. Energy cost of running**

Movement economy c, which has traditionally been measured as the oxygen cost of running at a given velocity, has been accepted as the physiological criterion for 'efficient' performance and has been identified as a critical element of overall distance running performance [4, 6, 7, 11, 14]. It follows from the above that there is a relationship between the mechanics of running and its energy intensity, but previous research does not allow to determine a clear biomechanical profile of a runner with a high economy of movement - the high technique of movement. Through movement training, individuals seem to be able to adapt to achieve

movement as economically as possible and minimize energy degradation [15]. Information in the literature suggests that biomechanical factors are likely to contribute to a better economy in any runners [16].

Atropometric parameters can significantly affect the biomechanics of movement, movement technique, and its energy intensity. These include height, ponderal index, and ectomorphic or ectomesomorphic figure; body fat percentage; foot morphology, pelvic size, foot size, and shape [13].

The economy of running can be influenced by movement patterns of running, their kinematics. These factors include the length of the step, which is freely chosen depending on the current fatigue; vertical oscillation of the center of gravity of the body; knee angle during the swing; range of motion, angular velocity of plantar flexion during toe-off; arm movement with smaller amplitude; peak ground reaction forces; rotation of the arms in the transverse plane; angular deflection of the hips and shoulders about the polar axis in the transverse plane; and efficient use of stored elastic energy [7, 17, 18]. Other factors that can significantly affect the running economy are: the shoes mainly their weight and the elasticity of the sole; higher share of higher and high training intensities of training history; and medium flexibility base. This information can be crucial in identifying talents for medium and long-distance running. At higher levels of training, it is likely that "natural selection" tends to eliminate athletes who have either failed to inherit or develop traits that support the economy of movement [19, 20].

It turns out that intra-individual variations in running economics range between 2% and 11% for a particular speed. Most of these variations are probably due to biological measurement error [21]. While the sources do not support gender differences in movement economics, data from some studies suggest that men may have better movement economics than women due to more muscle mass and less body fat. The economics of running change depending on age, depending on the amount of physical training completed. Pre-adolescent children have a worse economy than older children and adults, while older adults show the same trend compared to younger counterparts [9]. Air resistance at higher speeds fundamentally affects the economy of movement. Running on a treadmill at speeds higher than 13 km.h�<sup>1</sup> due to air resistance significantly underestimates the cost of energy intensity compared to running speeds at the same speed in the field [9]. Oxygen consumption increases as a result of the "Q 10 effect" [22, 23]. There is also no consensus on the impact of different types and intensities of training on running economics, and significant differences in economics between long-distance runners who undergo the same load (eg track) suggest that non-training factors may also affect the running economy, such as the amount and type of muscle fibers [13, 20, 24].

From a study by Black et al. [19] show that anthropometric parameters and body composition are important predictors of running economics. Relative slenderness indices, especially segment perimeters, have been commonly associated with running economy, suggesting that a slimmer individual can be expected to expend less energy and thus be more economical at any given speed [25]. It should be noted that the amount of energy available for physical activity stored in the body per kg of free fat mass is practically the same for virtually all persons of the same sex. The importance of running economics in medium and long-distance running, we recommend to trainers, applied practitioners, and athletes to evaluate anthropometric parameters and body composition as part of the evaluation of training. This is especially important in identifying talented athletes and preparing top athletes to achieve maximum individual performance [26].

Studies comparing different groups of runners with different training and focus have shown that the maximum differences in energy intensity between runners are

#### *Energy Cost of Walking and Running DOI: http://dx.doi.org/10.5772/intechopen.102773*

around 20%. Factors influencing the value of coefficient c include body dimensions: body height and weight, the architecture of the lower calves, mostly the length of the calcaneal tuberosity, which are responsible for 60–80% variability of this coefficient. Children have higher c values than adults. This can be explained by their higher resting metabolism, lower running technique, and lower leg/leg ratio [9, 27]. The storage of elastic energy and its reuse also contributes to the variability of c. The coefficient c increases with the increasing speed of movement due to the increase in mechanical work is blunted to speed of 6–7 m.s�<sup>1</sup> by increasing the vertical stiffness and shortening the contact time with the ground. Fatigue caused by prolonged or intense running is associated with up to a 10% increase in c; the influence of metabolic and biomechanical factors on the energy intensity of running remains unclear. Women show c similar to men of similar body weight, despite differences in running technique. The higher performance of black African endurance athletes is probably related to their leg architecture and better elastic storage and reuse of elastic energy [20].

Speed and movement techniques are considered to be the main sources of changes in the energy intensity of running in individuals with different body masses. The linear dependence of energy on running speed is approximately up to a speed of 3.6 m.s�<sup>1</sup> . In the case of higher speeds, this dependence is nonlinear. At6speeds higher than 3.6 m.s�<sup>1</sup> , runners are less likely to achieve aerobic performance - steady state oxygen consumption [28].

Walking and running are the basic means of influencing an individual's condition, his health and fitness. Possibilities of evaluation of energy intensity in laboratory and field conditions using the speed of movement, allows to streamline movement training. Energy intensity allows you to design individual exercise programs, for example, for the needs of primary and secondary prevention of obesity, cardiovascular disease, reducing the impact of current lifestyles, etc. [3, 4, 29].

Human locomotion is characterized by two principal gaits, walking and running. This makes it possible to move either at a slow speed for long periods of time or at over 10 m.s�<sup>1</sup> during a sprint [30]. The basic features of both locomotion modes are the same: each step represents one posture phase and one swing phase, but then they differ because the foot controls have two separate operating modes for walking and running. The timing of each phase of the movement is different. The frequency of steps is usually lower when walking than when running, so the contact time with the surface of each foot is longer when walking and shorter when running, while the swing shows the opposite trend. When walking, there is always at least one foot on the ground, while running there is a flight phase where both feet are above the ground and the amplitudes of the contractions of the flexor and extensor muscles during the two phases of the step are different [31, 32].

Studies examining the interaction between stride length, energy absorption, and impact attenuation have only been performed on level ground. Stepped running places unique demands on the musculoskeletal system compared to running on a plane, resulting in differences in physiological requirements and the kinematics and kinetics of the run [5]. Downhill running is associated with greater impact magnitudes and increased energy absorption when compared to level running [5]. The increased eccentric muscular work required to absorb more energy during downhill running may also be associated with muscle damage and delayed onset muscle soreness (DOMS), which negatively affects running performance. In contrast, uphill running is more energetically costly than level or downhill running [32] but is associated with lower impact magnitudes and reduced lower extremity energy absorption, especially when compared to downhill running [32]. Step length and frequency are also known to change during graded running [5], and step length manipulation may aid in understanding the injury and performance implications of these natural changes to preferred step length [18].

The evaluation of the energy intensity of running is a suitable criterion for examining the efficiency of mechanical work, evaluation of movement technique, and analysis of endurance performance during endurance running [24, 33].

Once energy cost values (V̇O2 and caloric expenditure) are standardized using bodyweight, the primary determinant of energy cost was the speed of movement [1, 33]. The derived generalized models make it possible to determine both V̇O2 (ml.kg�<sup>1</sup> .min�<sup>1</sup> ) and the energy intensity (kcal.kg�<sup>1</sup> .min�<sup>1</sup> ) of walking and running. The relationship between walking speed or number of steps and the energy intensity of walking is parabolic, while the relationship between running speed and energy intensity of running is in the range of about 20–80% for untrained and 20–90% for trained line runners is linear [34]. Neither age nor body height significantly improved the prediction of the energy cost of movement from its speed.

In practice, results of spiroergometric surveys often need to be checked using the relationship between oxygen consumption and movement speed. The relationship between energy and speed of running may be used as a linear form as follows

$$\text{VO}\_2\text{.kg}^{-1}\left(\text{ml.}\text{kg}^{-1}.\text{min}^{-1}\right) = \mathbf{a} \ast \mathbf{v} \left(\text{km.}\text{h}^{-1}\right) + \mathbf{b} \tag{6}$$

Where a and b are constants that depend generally on the training status, sex, age and speed, and strength predisposition.

Many equations can be found in the literature for predicting energy expenditure during walking or running. Not only can the amount of energy that was "burned" during a training unit be determined, but often these relationships are implemented in miniaturized electronic devices that provide the user with relevant data on the energy intensity of the physical activity performed. At the same time, it should be noted that the energy estimation error from walking or running speed is around 10% and these relationships can be used for so-called biological testing of spiroergometric analyzers. We include in the text those prediction equations which are currently the most frequently used and which provide relevant information for a given population. We have chosen the following tables and equations because they have often been cited in the literature. The ACSM Equation [35] was used because most exercise physiologists know the ACSM guidelines. McArdle's [33] walking and running tables have been used because they are found in commonly used exercise physiology textbooks and are often used by researchers in the field to estimate energy expenditure. Other equations were chosen because they were cited in the literature and provided additional estimates of walking and running. The prediction formulas that were used are listed below:

**ACSM** [34]:

$$\begin{aligned} \text{Running.} \dot{\text{VO}}\_2 \left( \text{mL} \cdot \text{kg}^{-1} \cdot \text{min}^{-1} \right) &= \text{0.2} \left( \text{m} \cdot \text{s}^{-1} \right) \\ + \text{0.9} \left( \text{m} \cdot \text{s}^{-1} \right) &\left( \text{fractional grade} \right) + \text{3.5} \end{aligned} \tag{7}$$

$$\begin{aligned} \text{Walking.} \dot{\text{VO}}\_2 \left( \text{mL} \cdot \text{kg}^{-1} \cdot \text{min}^{-1} \right) &= \text{0.1} \left( \text{m} \cdot \text{s}^{-1} \right) \\ + \text{1.8 } \left( \text{m} \cdot \text{s}^{-1} \right) &\left( \text{fractional grade} \right) + \text{3.5} \end{aligned} \tag{8}$$

**Bunc & Heller** [14] *Running men*

$$\left(\text{VO}\_2\text{.kg}^{-1}\left(\text{mL}\cdot\text{kg}^{-1}\cdot\text{min}^{-1}\right) - 3.749 \ast\text{v}\left(\text{km.h}^{-1}\right) - 2.133\right) \tag{9}$$

*Energy Cost of Walking and Running DOI: http://dx.doi.org/10.5772/intechopen.102773*

**Bunc et al.** [12]

*Running women*

$$\text{VO}\_2\text{kg}^{-1} \left(\text{mL} \cdot \text{kg}^{-1} \cdot \text{min}^{-1}\right) = \text{3.54} \cdot \text{s} \cdot \left(\text{km} \cdot \text{h}^{-1}\right) + \text{3.008} \tag{10}$$

**Bunc & Dlouhá** [34] *Walkimg*

$$\left(\text{VO}\_2.\text{kg}^{-1}\left(\text{mL}\cdot\text{kg}^{-1}\cdot\text{min}^{-1}\right) - 3.207 \ast\text{v}\left(\text{km}.\text{h}^{-1}\right) - 1.777\right) \tag{11}$$

$$\begin{aligned} \text{VO}\_2\text{.kg}^{-1} \left( \text{mL} \cdot \text{kg}^{-1} \cdot \text{min}^{-1} \right) &= -0.108 \ast \text{v} \left( \text{km.h}^{-1} \right) \\ &+ 0.379 \ast \text{v}^2 \left( \text{km.h}^{-1} \right) + 4.503 \end{aligned} \tag{12}$$

**McArdle** [33]: McArdle's tables are available in the referenced text. **Van der Walt** and Wyndham [36]: *Walking*

$$\dot{\mathbf{V}} \mathbf{O}\_2 \left( \mathbf{L} \cdot \text{min}^{-1} \right) = \mathbf{0}.00599 \ast \mathbf{M} + \mathbf{0}.000366 \ast \mathbf{M} \ast \mathbf{V}^2 \tag{13}$$

*Running*.

$$\dot{\mathbf{V}} \mathbf{O}\_2 \left( \mathbb{I} \cdot \text{min}^{-1} \right) = -0.419 + 0.03257 \ast \mathbf{M} + 0.000117 \ast \mathbf{M} \ast \mathbf{V}^2 \tag{14}$$

**Pandolf, Givoni & Goldman** [37]:

$$\rm{W} \left(\rm{J}\cdot\rm{s}^{-1}\right) = \rm{1.5 M} + 2.0\*(\rm{M}+\rm{L})\*\left(\rm{L}/\rm{M}\right)^{2} + n\*(\rm{M}+\rm{L})\*\left[\rm{1.5\*}\rm{v}^{2}+0.35\*\rm{v}\*\rm{G}\right] \tag{15}$$

M = body mass (kg), L = load carried, v = velocity (m�s �1 ), G = grade, and n is the terrain factor. For unloaded, level walking on a track or treadmill, the following formula is used:

$$\mathbf{W} \left( \mathbf{1} \,\mathrm{J} \cdot \mathrm{s}^{-1} \right) = \mathbf{1}. \mathbf{5} \ast \mathbf{W} + \mathbf{1}. \mathbf{5} \ast \mathbf{v}^2 \ast \mathbf{W} \tag{16}$$

**Léger** & Mercier [38]:

$$\dot{\rm VO}\_2 \left( \text{ml.} \text{kg}^{-1}.\text{min}^{-1} \right) = 2.209 + 3.1633 \ast \text{v} \left( \text{km.h}^{-1} \right) \tag{17}$$

**Epstein,** Stroschein & Pandolf [39]:

$$\text{Mr.} = \text{Mw} - 0.5 \ast (\text{1-0.01 L}) \ast (\text{Mw} - \text{15 L} - 850) \tag{18}$$

Mr. = metabolic cost of running, Mw = metabolic cost of walking, L = clothing weight

With the maximal error of estimation in the range of running speeds 8–16 km.h.�<sup>1</sup> about 10%.

For walking in the range of intensities the oxygen consumption inaccuracy at the speeds from 4 to 10 km.h�<sup>1</sup> is around 12% [12, 34].

Running has a greater energy cost than walking on both the track and treadmill. For running, the Léger equation, ACSM [35], and Bunc [12] prediction model appear to be the most suitable for the prediction of running energy expenditure.

The ACSM [35], Pandolf, Givoni & Goldman [37], and Bunc [12] linear prediction equation also closely predict walking energy expenditure, whereas McArdle's [32] table or the equations by Epstein and van der Walt were not as strong predictors of energy expenditure.

For movement speeds lower than 7 km.h�<sup>1</sup> , the energy cost of running is higher than walking For movement speeds higher than 7 km.h�<sup>1</sup> , the energy cost of walking is higher and increases exponentially with increasing movement intensity [34] that ACSM [35], Bunc [12] and Léger [38] predictive energy performance models for running straight are more accurate in a young healthy population. For horizontal walking, the ACSM [34, 35], and Pandolfova [37] reduction models also appear to be more accurate than other prediction equations.

The energy intensity of both running and walking represents the total energy consumption using many different mechanisms in the body, including muscle dynamics, blood circulation, and aerobic processes of energy release. In both running and walking energy-intensive experiments in humans, this is usually determined from oxygen consumption and carbon dioxide production values minus the basal metabolic rate at rest to achieve net metabolic performance. The energy intensity of exercise is commonly expressed in two different ways: energy consumed per unit time (metabolic rate or power) or energy consumed per unit distance [40].

The negative relationship between maximal oxygen consumption expressed relative to body mass and coefficient energy cost of running c means that athletes with higher aerobic capacity, higher VO2max have lower values of c, i.e. better running economy [2, 41]. These findings may bet the results of the prolonged duration of the competitions and, thus, of the training performance of these athletes when they are forced to turn out a highly economical performance over a prolonged period of time, and it may also bet the result of a high degree of adaptation to running [25].

#### **4. Energy cost of walking**

An energetic economy has been shown to have a large influence on human walking behavior. For example, at a given speed, humans tend to walk with a preferred step length that coincides with minimum metabolic cost [40]. Despite the complexity of the relationship between walking biomechanics and its energy expenditure, relevant studies have shown significant contributors to overall walking energy intensity, such as step-by-step work to redirect the center of gravity and energy in generating muscle strength to support weight transfer and swing. Feet.

The biomechanics of complex movements, such as those that occur when walking and running, which involve a large number of cooperating body segments, can be better understood by considering the energy counterpart, ie the energy expended on muscle contraction, which must work continuously to drive the body forward. Running and especially walking are basic physical activities to which a person is maximally adapted. This adaptation has evolved over many generations in order to minimize the energy requirements of a given physical activity. Walking is an energetically beneficial physical activity, its energy intensity is only about 50% higher than the basal metabolic rate (at speed of 0.6 ms�<sup>1</sup> it is about 2.44 W.kg�<sup>1</sup> ) [16], and this has in the past allowed populations to expand their ecological niches. Conversely, running can be very challenging and can be continued without slowing down for untrained individuals for less than an hour and sprinting for a much

#### **Figure 1.**

*Dependence of energy cost coefficient on speed of movement in walking and running.*

shorter time; but while the energy intensity of walking varies with the speed of movement, when running the same distance, the energy expended, although higher overall, is independent of movement speed [32].

Our older study [34] tries to answer the question of the energy cost of walking (VO2) could be accurately predicted with the simple models which analyze the relationship oxygen uptake-speed of walking. Employing the new modification of this model from 1986 [42] to analyze VO2 - speed of walking relationship leads to the elaboration of a simple linear model, two-compartment linear model, a polynomial model of second-order and monoexponential model of the metabolic cost of treadmill walking. To verify and compare these models 87 males, age ranged from 19 to 62 years, were evaluated on a motor-driven treadmill. They walked at 0% slope on a treadmill at various velocities ranged from 3 to 12 km.h�<sup>1</sup> .

The linear model has in range of intensities 3–12 km.h�<sup>1</sup> a form of VO2.kg�<sup>1</sup> (ml.kg�<sup>1</sup> .min�<sup>1</sup> ) = 5.228\*v (km.h�<sup>1</sup> )-11.158, r = 0.812, SEE = 4.16 ml.kg�<sup>1</sup> .min�<sup>1</sup> . The two-compartment linear model has in range of intensities of 3–7 km.h�<sup>1</sup> a form of VO2.kg�<sup>1</sup> = 3.207\*v(km.h�<sup>1</sup> )-1.777, r = 0.932, and SEE = 1.5 ml.kg�<sup>1</sup> .min�<sup>1</sup> . In the range of 7.1–12 km. VO2.kg�<sup>1</sup> = 7.120\*v-29.168, r = 0.901, SEE = 3.78 ml.kg�<sup>1</sup> .min�<sup>1</sup> . In the range of intensities from 3 to 12 km.h�<sup>1</sup> a polynomial model was found in the form VO2.kg�<sup>1</sup> = 4.501–0.108\*v + 0.379\*v<sup>2</sup> , r = 0.891, SEE = 4.43 ml.kg�<sup>1</sup> .min�<sup>1</sup> , and the exponential model had a form VO2.kg�<sup>1</sup> = 4.360\*exp.(0.223\*v), r = 0.861, SEE = 6.84 ml.kg�<sup>1</sup> .min�<sup>1</sup> . All these correlation coefficients were highly significant (p < 0.001 in all cases) [34].

It was concluded that when applied to adult population, the models provide a reasonable estimate of the actual requirement for treadmill walking provided the subjects in an oxygen uptake steady-state [43]. From the above, an important conclusion for practice follows: with adequate accuracy of about 10%, a linear model of the dependence of oxygen consumption and walking speed can be used in the range of walking speeds of 4–12 km.h�<sup>1</sup> .

As with other researches for VO2.step�<sup>1</sup> or speed of movement, we have found U-shaped curves of the coefficient energy cost of walking (see **Figure 1**). The minimum was at a speed of about 4 km.h�<sup>1</sup> . This finding supports the speculation

that does exists the "optimal" speed of moving which reflects the minimal energy expenditure during walking [34].

The energy coefficient of walking varies depending on the increasing speed of walking. In contrast, the coefficient c for running is practically constant in the range of running speeds 6–15 km.h�<sup>1</sup> (see **Figure 1**) [7, 44].

In general, the dependence on walking speed or number of steps has a nonlinear parabolic course with a clearly defined minimum of around 4 km.h�<sup>1</sup> see Figure [34, 42, 45, 46] over the entire range of walking load intensity intensities. From a speed of about 4.5 km.h�<sup>1</sup> , the value of the coefficient c when walking increases exponentially. For practical use, on the basis of the above, a linear description of the dependence between the energy or oxygen consumption and the speed of movement can be used in practice to determine the energy intensity of the movement.

For movement speeds lower than approx. 7 km.h�<sup>1</sup> , the coefficient of energy intensity of walking is lower than for running [34]. For practice, this means that in the case of mainly patients, walking at speeds lower than 7 km.s�<sup>1</sup> is more energetically advantageous than running at the same speed.

During treadmill running most well-trained runners run at step frequencies that minimize their energy expenditure. However, outdoor running, with air resistance and wind, is different from treadmill running [23, 47].

#### **5. Air resistance by movement**

The resistance of the environment, in our case walking and running air, is characterized by forces that act against the movement of an object that moves in space. These resistive forces act in the opposite direction to the speed of the approaching flow, thus slowing down the object. Unlike other resistance forces, resistance depends directly on speed, because it is a component of the net aerodynamic force acting against the direction of movement, on the front profile of the moving individual, and on the air density. Therefore, world records on sprinters have often been broken at higher altitudes, where the air density is lower [48, 49].

Air resistance, or drag, can be put into one of three categories; lift induced, parasitic, and wave. Each of these types of air resistance affects an object's ability to stay up and the power it will need to keep it there [49].

Lift-induced air resistance happens as the result of the creation of lift on a threedimensional lifting body (wing or fuselage).

Parasitic drag happens when a solid object moves through a fluid. This type of air resistance is made up of lots of components like "form drag" and "skin friction drag".

Wave drag is made when an object moves at a high speed through a compressible fluid.

Air resistance is usually calculated using the "drag equation", which determines the force experienced by an object moving through a fluid or gas at a relatively large velocity. This can be expressed mathematically as [49, 50]:

$$\mathbf{F\_D = 0.5} \ast \rho \ast \mathbf{v^2} \ast \mathbf{C\_D} \ast \mathbf{A} \tag{19}$$

In this equation, FD represents the resistance force, ρ is the air density, v is the velocity of the object relative to the speed of sound, A is the cross-sectional area, and CD is the coefficient of resistance. The result is what is called "quadratic resistance." For movement in an air environment, these constants can be determined as follows.

<sup>A</sup> <sup>¼</sup> <sup>0</sup>*:*<sup>266</sup> <sup>∗</sup> <sup>0</sup>*:*<sup>2025</sup> <sup>∗</sup> height0*:*<sup>725</sup> <sup>∗</sup> body mass0*:*<sup>425</sup> ½ � <sup>21</sup> , CD <sup>¼</sup> <sup>0</sup>*:*9 51 ½ � (20)

The energy required to overcome air resistance was estimated at 2% for running outdoors at 5 m.s on a calm windless day [48]. Jones and Doust showed that HR was about 3–4 beats higher when running outdoors (quiet day) compared to running on a treadmill [52]. Pugh found an increase in VO2 of about 14% as the rate of the ventilator in the laboratory increased from 0 to 10 m.s�<sup>1</sup> for a subject running on a treadmill at 3.75 m.s�<sup>1</sup> [23]. This would correspond to the difference between a treadmill running at 3.5 m.s�<sup>1</sup> and running at the same speed at a headwind of 6.5 m. s-1. Based on our study of trained runners, there is a significant difference in running energy intensity and at running speeds higher than 13 km.h�<sup>1</sup> [10, 12]. In another study, 6 runners ran in the headwind at a speed of about 6.5 ms�<sup>1</sup> . The HR value was 4–8 bpm.min�<sup>1</sup> higher in the headwind compared to the windless, which illustrates the significant effects that wind can have on the energy intensity of the run [53].

The technique of movement changes depending on the increasing resistance of the air at higher speeds. Therefore, in order to maintain the correct movement technique even at speeds above 13 km.h�<sup>1</sup> running behind the car is often used in the training of runners, which reduces the direct impact of air resistance on the runners.

#### **6. Movement programs based on walking and/or running**

Walking and running are very often used in intervention programs for cultivating fitness or for body mass reduction [3, 29, 54, 55]. Exercise intervention with a mean weekly energy intensity of 20.40 � 4.51 kcal.kg�<sup>1</sup> .week�<sup>1</sup> or with a mean energy cost per day of 5.4 kcal.kg�<sup>1</sup> .day�<sup>1</sup> which are applied for at least 7 weeks, will cause significant changes in functional and morphological parameters. These changes are independent of age and gender. In the case of weight, the total energy intensity of physical activities increases with increasing body mass [3, 27].

Physical intervention based on walking or running with an intensity corresponding to 80–90% SFmax, at least 80% of the total load must consist of running or walking for at least 8 weeks will cause changes in aerobic capacity expressed by changes in VO2peak are on average around 16% of the initial value. We find the same relative change in the speed of movement at which the load on the treadmill is terminated due to subjective exhaustion. The weight reduction is around 14% of the initial weight and the average improvement of the kinetic load assumptions as measured by the ECM / BCM coefficient is around 15% [3, 54].

Recent cross-sectional studies have demonstrated the ability to economize movement, either alone or in combination with V02max, a crucial factor that may explain a substantial portion of performance variations between trained longdistance runners and untrained subjects of comparable levels of exercise and fitness. Limited data from short-term and long-term longitudinal research also suggest that the success of endurance running is related to training and improving the economics of movement leading to a reduction in the energy intensity of movement [53].

In practice, this leads to the clear conclusion that the first step in any endurance training is to improve the economics of running - running techniques leading to reduced energy consumption and delayed fatigue due to depletion of energy resources stored in the body.

#### **7. Discussion**

Walking and running are the basic locomotor activities of a person. They are not demanding on the environment and are implemented in practically any weather

and in almost all environments - on flat and changing surfaces, movement on the plane, and downhill or uphill. We adopt very well to these forms of physical activity, which results from their long-term use for livelihood and the implementation of work and leisure activities. The energy intensity coefficient of walking depends on the speed of movement and reaches a minimum at a speed of about 4 km.h-1 [34]. On the contrary, the coefficient of energy intensity of the run is practically independent of the running speed. The minimum dependence of the coefficient of walking energy intensity on its speed is probably due to the optimal use of the recovery of elastic forces at this speed of movement.

This minimum of energy intensity is often used in the rehabilitation of cardiac patients because the changes caused by the speed corresponding to this minimum are the smallest [56, 57].

Evaluation of the degree of adaptation to running, with the help of c coefficient as an additional characteristic during laboratory tests, enables us to ascertain, along with other parameters, not only the effectiveness of training procedures, but also helps in the evaluation of the technique of the movement performed. This is essential in sports events where training is started at an early age and enables us to determine the energy cost of the training stimulus used [1, 2, 24].

Movement economization in the case of long-term exercise loads is associated with the maximum use of automated movements, which are less energy-intensive than non-automated movements. In practice, this makes key recommendations. At the beginning of each movement intervention, it is always necessary to focus on economizing movement, improving technique \ movement, and only then concentrating on managing the required volume of exercise loads [41].

To master the necessary movement techniques in the case of deepening fatigue, ie in the case of deepening acidosis and reducing the amount of energy substrates is possible only as a result of long-term intensive training [4, 32]. Running economics - the energy intensity of running is primarily dependent on completed training, but the genetic disposition of the runner also plays a role here, i.e. its current level is given by the intersection of genetic preconditions and completed running training [58].

Based on the energy cost of walking or running for a particular individual, it is possible to design a movement intervention that allows you to optimize the effect of this intervention and mainly minimize the time required for this intervention [59].

Evidence suggests that several internal (sex, running biomechanics, anatomy) and external factors (experience, mileage, training routines) may contribute to the risk of injury in recreational runners [60]. Good exercise technique, its good economy, a good value of the energy intensity coefficient of running c, can significantly delay the onset of fatigue during long-term running training load and can act preventively against muscle injuries [61]. Therefore, special attention should be paid to cultivating running techniques in preparation for long-distance races, such as marathons and ultra-endurance races, in order to ensure the necessary condition without increasing the risk of injury from overload.

#### **8. Conclusions**

Evaluation of energy cost of majority of physical movement activities and subsequent cultivation, used to influence fitness or in primary and secondary prevention, allows to increase the effectiveness of the applied physical intervention. At the same time, it can delay the onset of fatigue and thus reduce the incidence of muscle injuries. Assessing the energy intensity of running or walking in laboratory or field functional tests can significantly expand the information content of these surveys

*Energy Cost of Walking and Running DOI: http://dx.doi.org/10.5772/intechopen.102773*

and should therefore be an integral part of these surveys. Models relating energy and intensity to exercise are useful for quantifying the training load of both recreational and trained runners and allow you to minimize the time devoted to endurance training.

### **Author details**

Vaclav Bunc Faculty of P.E. and Sports Charles University Prague, Czech Republic

\*Address all correspondence to: bunc@ftvs.cuni.cz

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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#### **Chapter 10**

## Mechanical Limits of Cardiac Output at Maximal Aerobic Exercise

*Sheldon Magder*

#### **Abstract**

This chapter uses an analytic approach to the factors limiting maximal aerobic exercise. A person's maximal aerobic work is determined by their maximal oxygen consumption (VO2max). Cardiac output is the dominant determinant of VO2 and thus the primary determinant of population differences in VO2max. Furthermore, cardiac output is the product of heart rate and stroke volume and maximum heart rate is determined solely by a person's age. Thus, maximum stroke volume is the major factor for physiological differences in aerobic performance. Stroke output must be matched by stroke volume return, which is determined by the mechanical properties of the systemic circulation. These are primarily the compliances of each vascular region and the resistances between them. I first discuss the physiological principles controlling cardiac output and venous return. Emphasis is placed on the importance of the distribution of blood flow between the parallel compliances of muscle and splanchnic beds as described by August Krogh in 1912. I then present observations from a computational modeling study on the mechanical factors that must change to reach known maximum cardiac outputs during aerobic exercise. A key element that comes out of the analysis is the role of the muscle pump in achieving high cardiac outputs.

**Keywords:** aerobic limit, oxygen consumption, stressed volume, venous return, cardiac output, stroke volume, heart rate, time constants

#### **1. Introduction**

Sustainable work at high levels of energy consumption requires oxygen (O2) based metabolism. Maximum O2 consumption (VO2) thus determines a person's maximal aerobic power [1]. A young active healthy male of standard size can increase VO2 from a resting value of around 0.25 L/min to between 3.00 and 3.5 L/ min, a 12–14 fold increase [1, 2]. In elite athletes, values greater than 6.0 L/min have been measured [3]. The physiological basis of these numbers can be understood by considering the Fick principle, which is essentially a statement of the conservation of mass [1, 4]. VO2 is the product of how much volume per minute/min (L/min) is delivered to tissues, in other words, cardiac output, and how much O2 is extracted from each volume unit of blood [1, 2].

$$\dot{V}O\_2 = Q\_\circ \propto \begin{bmatrix} Hb \end{bmatrix} \propto \mathbf{1.36} (\text{Sat}\_\circ O\_2 - \text{Sat}\_\circ O\_2) \tag{1}$$

Q is cardiac output (L/min), [Hb] is hemoglobin concentration (in g/L), 1.36 is the constant for the amount of O2 (ml) per g of Hb, SataO2 is the arterial O2 saturation (as a decimal) and SatvO2 is the venous O2 saturation (as a decimal). Thus, the limit of aerobic function is based on the maximum extraction of O2 from the blood and the maximum cardiac output.

The capacity of arterial blood to carry O2 is determined by the concentration of hemoglobin ([Hb]) and the amount of O2 that each gram of Hb can bind [5]. The constant for binding of O2 to Hb with no other substances present is 1.39 ml O2 per gram of Hb, but normally other molecules in blood, such as methemoglobin and carboxyhemoglobin, take up some of the binding sites. Thus, constants of 1.34–1.39 are used in the literature to account for these factors. The actual content of O2 in blood is dependent upon [Hb] and the saturation of Hb molecules with O2; the saturation is in-turn is dependent upon the partial pressure of O2 in blood (PO2 in mmHg). [Hb] concentration thus sets the upper limit of how much O2 is present to be extracted from the blood. As an example, with a [Hb] of 145 g/L, a saturation of 98%, and capacity of Hb to carry O2 of 1.36 ml O2/g Hb, the arterial O2 content would be 197.1 ml/L. The saturation of arterial blood usually is slightly less than 100% because of some shunting of blood across the lungs and venous blood returning to the left ventricle from the coronary circulation. [Hb] is similar in a standard male and endurance athlete (unless there has been some kind of unfair manipulation of [Hb]!) so that this factor does not play a large role in differences in maximum VO2. During exercise [Hb] increases slightly because of a loss of plasma and hemoconcentration [6].

The O2 content of blood returning to the right heart gives the overall extraction of O2 by all tissues. This is called mixed venous O2 content (MvO2). At rest, about 25% of the arterial blood O2 content is extracted, which gives a MvO2 of around 150 ml/L in both a standard male and elite athlete [6]. During peak aerobic exercise, the greatest proportion of the blood goes to the working muscle, which is capable of extracting almost all the delivered O2 it receives at peak performance. Under resting conditions about 60% of blood flow goes to the muscle vasculature and 40%, or about 2 L/min, goes to the non-muscle vasculature [7, 8]. At peak exercise, the amount going to non-working muscle remains largely unchanged, or decreases by a small amount, so that greater than 90% of blood flow goes to the working muscle [7], which at peak performance can extract almost all the O2 it receives. The percent of blood flow going to non-working tissues sets a lower limit of O2 extraction [9]. The maximal amount of O2 extracted is similar in standard young healthy males and endurance athletes, although extraction can be slightly greater in endurance athletes. This is likely because they have larger amount of muscle mass per total body mass, and thus a higher fraction of blood flow can go to the working muscle, which results in greater total extraction. A greater capacity to endure discomfort may also play a role. A typical MvO2 at peak performance is in the range of 22 ml/L in the standard male and 18 ml/L in elite endurance athletes, which is less than a 1% difference in the total amount extracted [10]. Thus, differences in O2 extraction between standard and elite athletes contribute little to differences in their maximum VO2 unless the arterial O2 carrying capacity is significantly increased, although this potentially could limit extraction by increasing blood viscosity and reducing blood flow to tissues.

Based on the Fick equation, the other determinant of maximum VO2 is cardiac output. In a typical young male, cardiac output can increase from a resting value of around 5 L/min to 20–25 L/min, a 4–5 fold increase [1, 2]. In elite athletes maximal cardiac output can be in the range of 30 L/min to even over 40 L/min in some high performing cyclist and cross-country skiers [11]. The athletes thus can have a 6–7 fold increase in cardiac output from resting levels and this increase in cardiac

*Mechanical Limits of Cardiac Output at Maximal Aerobic Exercise DOI: http://dx.doi.org/10.5772/intechopen.103908*

output is the major factor explaining their higher aerobic capacity [4]. If [Hb] is normal there is a tight linear relationship between cardiac output and VO2 that is independent of body size, fitness, or age [2, 4]. The slope of this relationship is the same in women and men but the relationship is shifted downward in women because of they generally have lower [Hb] [2].

Cardiac output is the product of beats per minute, that is, heart rate, and stroke volume. Maximum heart rate at peak aerobic performance is solely determined by age and not by differences in fitness, body size, heart size, or sex; the rise in heart rate is dependent upon the percent of the maximal capacity of the muscles being used [2]. This means that the primary difference in aerobic power of the standard male and elite aerobic athletes is the maximum possible stroke volume for that person [1, 3]. Furthermore, stroke volume is dependent upon heart size, which for healthy hearts is related to lean body size as determined by the person's genetic make-up [12]. There is little change in stroke volume capacity with training [10], although increases in maximum stroke volume often are observed in studies with training [10, 13]. These observed increases in stroke volume are likely related to reductions in submaximal heart rate, which occur due to alterations in neuro-humeral mechanisms with training [9]. A lower heart rate at a given VO2 requires that there be a larger stroke volume for the same venous return and cardiac output so that the relationship of cardiac output to VO2 is maintained, but this does not mean that there was an intrinsic change in heart structure.

#### **2. Basic principles of the determinants of blood flow in the circulation**

It often is thought that blood flow around the circuit is dependent on the arterial pressure regenerated by the heart [14]. This view is of presented as an electrical model with the arterial pressure being the equivalent of a fixed voltage from a source. In this construct, vascular volume, which the electrons in the circuit, is not a fixed value, but can increase or fall based on current for the fixed pressure drop. In contrast, Arthur Guyton [15], and for that matter, Ernest Starling [16], used a hydraulic approach in which the elastic energy, that is pressure, produced by a fixed volume in the circuit determines the return of blood to the heart. The action of the heart in this approach is to pump the returning blood back to the circuit [17]. In the Guyton approach, blood flow around the circuit is determined by two functions: cardiac function and a function that describes the return of blood to the heart from a large venous compliant region [15]. These are discussed next.

#### **2.1 Cardiac function**

The basis of cardiac function is the Frank-Starling law, which says that the greater the initial cardiac muscle length the greater the force produced by the heart up to a limit [16]. The determinants of cardiac output are heart rate and stroke volume, and stroke volume is determined by the preload, afterload and contractility. Cardiac function is plotted with right atrial pressure (Pra) at the end-of diastole. This determines right ventricular end-diastolic muscle length, and the preload, on the x-axis, and cardiac output on the y-axis (**Figure 1**) [18]. This relationship assumes a constant heart rate, afterload and contractility. An increase in cardiac function is produced by an increase in heart rate, increase in contractility, or a decrease in afterload and is indicated by upward shift of the curve (**Figure 1**). The opposites cause a decrease in cardiac function and a

#### **Figure 1.**

*Schematic plots of venous return and cardiac function curves at rest and maximal aerobic exercise. The resting state is shown with solid lines and exercise state with dashed lines. The change in cardiac output was from 5 to 25 L/min. The x-axis is right atrial pressure (Pra) in mmHg and the y-axis is blood flow in L/min. The curved red lines are cardiac function curves and the blue lines are venous return curves. The slope of the venous return curve is −1/resistance to venous return (Rv). During exercise there is a marked increase in the cardiac function curve due to primarily to the rise in heart rate and to a lesser extent, stroke volume. This is matched by a marked decrease in Rv and a small increase in MSFP due a decrease in vascular capacitance.*

downward shift of the curve. Importantly, the cardiac function curve has a sharp plateau [19], and when reached, further increases in preload, that is Pra, do not increase cardiac output.

#### **2.2 Venous return function**

The typical total blood volume of a 70 kg male is approximately 5.5 L. When there is no flow in the circulation the contained volume still stretches vascular walls and creates a pressure of 7–10 mmHg; this is called mean circulatory filling pressure (MCFP) [15, 20]. About 70% of vascular volume resides in small veins and venules. The compliance of the walls of these vessels, that is change in volume per change in pressure, is 30–40 times greater than that of arterial and capillary vessels and seven times the compliance of the pulmonary vessels [21]; because systemic veins dominate the volume of the circulation, they are the major determinant of MCFP [22]. Under flow conditions, volume redistributes throughout the vasculature so that there can be some change in volume and pressure in the veins and venules. Since the pressure in veins and venules is the upstream pressure determining blood return to the heart, it is given a separate name, mean systemic filling pressure (MSFP). When there is no flow, MSFP and MCFP are equal as is Pra.

Another important concept is vascular capacitance [23, 24]. Some of the total vascular volume just rounds out vessels, but this volume does not stretch vessel walls. This volume is thus "unstressed" in that it does not produce a pressure. Only the volume above unstressed volume stretches vessels walls and accordingly is called stressed volume. Under resting conditions about 70% of blood volume is unstressed and 30%, or about 1.3–1.4 L, is stressed [25]. Only this stressed volume produces

the elastic force that drives venous blood back to the heart. However, activation of sympathetic activity can result in constriction of veins and venules and thereby convert unstressed into stressed volume [24, 26–28]. By this means, unstressed volume acts as a vascular reserve, and stressed volume can be increased by 6–10 ml/ kg, and sometimes more. This is the equivalent to a vascular infusion of fluid and can greatly increase MSFP almost instantly.

Venous blood returns to the right heart through the resistance downstream from the venous compliant regions [15]. Although small, and only produces a pressure drop only of 4–8 mmHg, this resistance it is a major determinant of the return of blood to the heart because it controls the emptying of the large upstream venous reservoir.

The final determinant of venous return is Pra. This is the downstream pressure for venous drainage. In this context, it can be considered that the primary role of the heart in the control of cardiac output is to keep Pra low so as to allow venous return [18]. In this sense, the right ventricle has primarily a "permissive function" in that it "allows" venous blood to return. Importantly, the best that the heart can do is lower Pra to zero, that is, atmospheric pressure. Below this value the pressure inside the floppy great veins is less than the surrounding pressure and collapse, thereby creating flow limitation or what is called a vascular waterfall. When this happens, lowering Pra further does not increase venous return and accordingly, cardiac output [29].

Venous return was plotted by Arthur Guyton with flow on the y-axis and Pra on the x-axis (**Figure 1**) [15]. The x-intercept is MSFP and the slope of the line is the negative inverse of the resistance to venous return (−1/Rv). The venous return curve has the same axes as the cardiac function curve. Thus cardiac function and return function can be plotted on the same graph and this plot can be used to mathematically solve the interaction of these two functions [15].

#### **2.3 Interaction of the return function and cardiac function**

Actual cardiac output is determined by the intersection of the cardiac function and return function (**Figure 1**) [15]. An isolated increase in cardiac function produces an increase in cardiac output and a decrease in Pra. An isolated increase in the return function produces an increase in cardiac output with a rise in Pra [18]. A study in normal young males showed that at the onset of pedaling on an upright stationary cycle, Pra immediately increased from –2 to ~4 mmHg [30] and then changed little all the way to maximum effort [31]. This indicates that after an initial moderate increase in preload because of volume being squeezed out the working muscle, increases in cardiac and return functions are perfectly matched. Interestingly, in a group of patients with denervated transplanted hearts, although it took a longer time for equilibration to occur, as exercise continued they too had little change in Pra with increasing cardiac outputs. The slope of the rise in their cardiac output with the rise in VO2 also was the same range as normal subjects [31–33].

#### **2.4 Two compartment model**

So far in this discussion, I have applied the Guyton model of the circulation which considers that there is only one large venous compliant region [20]. In 1912 August Krogh [34] observed that if a closed circuit has two regions with different compliances in parallel, changes in the fractional distribution of flow between the two regions produced by changes in their inflow resistances, alters the rate of flow around the system (**Figure 2**). This is because when more volume goes to the less compliant region, the pressure rises in this region, which then increases the rate of

#### **Figure 2.**

*The two compartment model of the circulation—Krogh model. In this model there are two parallel venous compartments. One, the equivalent of the splanchnic bed (s) has a large compliance (i.e., large volume for given height) and the other, the equivalent of the peripheral-muscle bed (p), a low compliance (smaller volume for a given height). Flow into each compartment is determined by their arterial resistances (Ra) which act like taps controlling the flows. Drainage occurs through their venous resistances (Rv) which also can be regulated. The top shows the cardiac function-venous return plot as in Figure 1. a is the system at rest and b shows what could happen with exercise. Increasing flow to the muscle bed by lowering its inflow reisistance (Ra-p), raises the pressure in this region and increases the outflow. This is seen on the cardiac function-venous return plot as a steeper slope to the venous return curve. This allows an increase in cardiac function to produce a higher cardiac output.*

outflow from that region. This concept was subsequently further developed for the cardiovascular system by Permutt and co-workers [35, 36]. The venous compartment of the splanchnic circulation is much more compliant than that of the muscle vasculature [37, 38]. This makes sense from an evolutionary point of view because there is a lot more space in the abdominal region to take up volume reserves than in the actively contracting and thinner limbs. A shift of blood flow to muscle beds because of metabolic dilation with exercise thus increases net venous return. This appears on the cardiac-venous return plot as a steepening of the slope of the venous return function, which has resistance units. However, the x-intercept, which is MSFP, does not change because when flow is zero the pressures is the same everywhere in the vasculature (**Figure 2**).

Permutt and coworkers further explored the mathematical basis for this. The product of a resistance and compliance draining a vascular bed gives its time constant of drainage (τ) [35, 36]. The τ is the time it takes to get to ~63% of a new steady state pressure and volume when there is a step change in flow into a region. Based on animal studies, estimates of the τ draining the splanchnic bed are in the 20–24 second range, and those of the muscle compartment 4–6 second.

#### **2.5 Importance of τ in the circulation**

The τ for filling and draining regions in the vasculature are of great importance because pressure and flow in the system are pulsatile. This creates a periodicity that fixes times for flow into and out of vascular regions. As the frequency of cardiac pulsations increase, the τ of a region can limit flow. As a reminder, τ is the product of the compliance and resistance of a system. Since the left ventricle develops a very high elastance during ejection [39], and thus a low compliance, and it pumps into

#### *Mechanical Limits of Cardiac Output at Maximal Aerobic Exercise DOI: http://dx.doi.org/10.5772/intechopen.103908*

large conductance vessels with low a low input resistance, the τ of emptying of the left ventricle is much shorter than the τ of emptying of systemic veins returning blood to the heart. However, even then, the ventricle does not eject all its volume during systole. Similarly, right ventricular filling does not normally reach the limit of filling during diastole because there is not enough time to do so. There is thus room in the system to respond to faster inflow to the right ventricle, and for the left ventricle to handle the increased volume per minute. However, as heart rate increases, diastole and systole shorten and there is less time for ejection and filling. Ejection is aided by the marked decrease in arterial resistance with exercise which shortens the τ of ejection. On the diastolic side, there needs to be a shortening of diastolic relaxation and a shortening of the period of ejection to allow more time for flow to come back. The increase in the rate of venous return is aided by the decrease in venous resistance through a number of mechanism. These include a decrease in the venous resistance of muscle because of passive dilation from higher flow as well as possible flow-mediated active dilatation and decreased resistance to the venous drainage of the splanchnic bed which is driven by beta-adrenergic activity [28, 40]. As discussed above, another factor is the distribution of blood flow between the splanchnic and muscle beds which is discussed next.

#### **3. Two compartment computational model of the circulation and determination of maximal cardiac output**

Based on the rational above, we adapted a computational model of the circulation so that it had two parallel venous compartments [41]. One compartment represented the splanchnic bed and had a τ at rest of 22 sec and the other represented the muscle compartment with a resting τ of 4 sec. Resting parameters used in the model were based on animal and human data and adjusted to give known resting hemodynamic values in humans [2, 6, 42]. These included a resting heart rate of 65 b/min, cardiac output of 5 l/min, and a mean blood pressure of 93 mmHg. Adjustments were then made in circuit parameters as needed to aim for a peak cardiac output in the range of 20–25 L/min and a mean blood pressure of 115 mmHg. Values for resistances and compliances in the model, and their changes with sympathetic activation, were based on animal studies [26–28, 36, 38, 40]. Modeling cardiac parameters turned out to be very challenging. Two critical assumptions were the limit of diastolic filling of the right heart because it sets the maximum stroke volume and second, the constants that determine the shape of the diastolic passive filling curve of the right and left ventricles because these affect diastolic filling pressure and thus the gradient for venous return. Based on values in the literature, we set the limit of a normal right ventricular diastolic volume to 140 ml. With a heart rate of 180 b/min, this gave an upper limit to the maximum possible cardiac output of 25 L/min.

To simulate the maximal exercise condition we first increased the heart rate to 180 b/min. Without any adjustments in the mechanics of the circulation this actually lowered cardiac output. Even when we shortened the systolic ejection time and the τ for diastolic relaxation of the ventricles, in the absence of adjustment other circuit factors, there still was little change in resting cardiac output. This is because blood needed to come back faster. When we increased the distribution of blood flow going to the muscle bed from 60 to 90% as expected during exercise, t cardiac output increased only moderately and arterial pressure fell markedly, which contributed to lower than expected muscle blood flow. Based on a previous study of baroreceptor regulation of the systemic circulation [28], we reduced the resistance draining the splanchnic bed as well as the capacitance of that bed to produce an increase in stressed volume of 6 ml/kg. From studies on the τ of isolated contracting skeletal muscle [43, 44] we lowered the venous resistance of the muscle bed during the simulated exercise condition from 4 to 2 sec. Each of these individually only produced small changes in cardiac output. However, when they were all put together, and arterial resistances were adjusted to obtain the expected arterial pressure, cardiac output was still only around 17 L/min, and much less than what we were aiming for, which was 20–25 L/min. Another consequence was that the venous pressures markedly increased in the veins of muscles, which means that capillary pressures would have been markedly elevated and there would be major capillary leak.

The two compartment model and the τ draining the regions can be used to give a mathematical formulations of the maximum cardiac output:

$$Q = \frac{\gamma - \left(C\_T \propto Pra\right)}{F\_S \tau\_S + F\_M \tau\_M} \tag{2}$$

Q = cardiac output (L/min), γ = stressed vascular volume (L), CT = total vascular compliance (ml/mmHg, and is the sum of splanchnic and muscle compliances), F = fractional of total cardiac output to the region, τ = time constant (sec) and subscripts S and M = splanchnic and muscle vasculatures, respectively. This simplification omits the small variation that would occur if volume accumulates or is lost in the pulmonary circuit.

#### **3.1 Muscle pump**

The solution for reaching known high values of cardiac output at peak exercise was to add the equivalent of a muscle pump by having active compressions on the muscle venous compartment. This increased cardiac output to the 22–23 L/min range we were aiming for. The muscle pump acted through a number of mechanisms. The marked decrease in arterial resistance that is required to increase blood flow to the working muscle results in capillary and venous pressures that approach arterial pressure. The high venous pressure then stretches the compliant venous walls and a large amount of volume would accumulate in the muscle vasculature. This effectively creates a loss of a large proportion of stressed volume from the circuit. By forcefully squeezing veins during contraction, muscle contractions transiently empty the venous volume to almost zero. This appears as a large venous pulse of flow from the veins of contracting muscles [30, 44, 45]. Transiently lowering local venous volume also ensures that the capillary pressures do not remain persistently high when exercising and thereby reduces capillary leak. Another effect of the muscle pump is that it "speeds" up the movement of blood from the muscle veins to the heart, effectively decreasing the time constant of venous drainage [43]. The importance of this will be discussed below under factors affecting RV filling.

Muscle contractions do not send blood in the retrograde direction because of the presence of a Starling resistor-like mechanism at the arteriolar level [46]. Because of this mechanism, the muscle also does not "suck" blood from the arteries and does not act as an auxiliary pump; rather, it facilitates flow by preventing volume accumulation in the muscle vasculature. When strong enough, muscle contractions likely even pump blood through the tricuspid and pulmonary valves during systole and diastole, and thereby increase the time and the cycles for flow to go through the right heart.

A number of factors determine the effectiveness of the muscle pump. The most obvious is that the force generated must be adequate to compress the venous compartment. In the modeling study, the effect was evident with a force of 0.25 mmHg/ml. The larger the muscle groups, the larger the affect because there is more volume to empty.

#### **4. Implications for peak performance of the observations from the modeling study**

Since stroke volume is a key determinant of the maximum cardiac output, a person's innate heart size as determined by their genetic make-up is a key variable. This does not change much with training. Rather, training changes the characteristic of the kinetics of the return. This is largely related to the amount of muscle. Basic muscle mass generally evolves in proportion to heart size and these are genetically linked. Muscle mass, though, can be increased by training and this likely is what accounts for the expected potential 20% increase in aerobic power with training in someone who has not been previously active [10, 13, 47]. More muscle means that more blood can come back to the heart. If someone has already been active aerobically there likely is little more to gain in VO2-max with training. This does not mean, though, that they cannot do more with what they have by an increase in their anaerobic threshold [48].

The importance of the amount of muscle as a determinant of cardiac output becomes an issue when trying to restore lost muscle. A question that needs to be answered for rehabilitation of lost muscle is what level of aerobic activity is needed to be to promote return of the original muscle mass? If the person's capacity starts very low, it then may not be possible to do a high enough level activity to generate the increase in blood flow in working muscle to generate an increase in aerobic activity. Age likely plays a role, too, in the capacity of muscle to recover. There are many examples of athletes with high aerobic power who have had significant injuries but still are able to return to performing at high aerobic levels. With aging though, return of full mass might be less effective despite high levels of training. There is evidence of this in recovering critically ill patients beyond age 50 [49].

Since maximum stroke volume is largely determined at birth, and does not increase to any significant degree after full growth, the fall in heart rate that occurs with aging directly impacts maximum cardiac output with aging. There can be some compensation by an increase in stroke volume because there usually are some stroke volume reserves but these are limited. In the modeling study, decreasing maximum heart rate to 160 b/min only lowered cardiac output by 2%, but lowering it to 140 b/ min decreased maximum cardiac output by 16% with little further change until it was lowered to below 120 b/min.

Regulation of blood pressure during exercise turned out to be very complicated. A key variable for the increase in cardiac output was the increase in fractional flow to the muscle bed. This could occur by just decreasing the arterial resistance going to the muscle vasculature, by increasing the resistance to the non-muscle splanchnic vasculature, or by some combination of both. If the fractional flow to the muscle only was produced by decreasing the arterial resistance in that region, and without muscle contractions, arterial pressure markedly fell in the model because of the increased trapped blood in muscle veins. When muscle contractions were added, the normal volume distribution was restored and blood pressure markedly increased above expected levels. It was then necessary to decrease splanchnic resistance in the model to obtain the expected arterial pressure. Higher arterial pressures also increase the fractional flow to the muscle compartment because the time constant of inflow is much faster to muscle because of its lower arterial resistance. It is the ratio of the arterial resistances between the two compartments that ultimately counts for the slope of venous return, so we found that we had to adjust the two arterial resistances to obtain known values. Failure of compensation of the arterial resistances to the splanchnic and muscle compartments could lead to clinically significant exercise induced hypertension or even hypotension in some cases.

**Additional factors**: There were no atria in the modeling study. In unpublished studies we have added atrium. Under resting conditions, atrial contractions had little effect on cardiac output but with all the processes in place at peak performance, atrial contractions added as much as a 10–20% further increase in cardiac output.

Besides the muscle pump, there are two other pumping mechanisms that can increase venous return and cardiac output during exercise. The descent of the diaphragm during the vigorous respiratory efforts at peak performance can transiently raise abdominal pressure [50, 51] which will compress the splanchnic venous compartment and increase the rate of venous return from this region. In the thorax, the inspiratory fall in pleural pressure can increase venous return although this effect only can work by lowering venous pressure to atmospheric pressure. Below that the Starling resistor mechanism limits any further increase in the rate of return. Active expiration can increase intrathoracic pressure, which could aid left ventricular ejection, but this benefit is more likely offset by the positive pleural pressure decreasing venous return. The final effect would depend upon the balance of potential recruitment of volume from the splanchnic compartment versus the inhibition to flow in the thorax.

#### **5. Conclusion**

Maximum cardiac output is a key determinant of maximum aerobic performance [4]. A fundamental principle in the circular circulatory system is that what goes out per time must come back at the same rate. Thus, the maximum ejected stroke volume per beat must be matched by an equal stroke return. The determinants of stroke return often are under-appreciated in discussions of the limits of aerobic performance. I have reviewed these factors in detail based on an analysis obtained from a computational model of the mechanics of the circulation at maximal exercise [41]. The role of the muscle pump was very evident in the analysis. Besides the obvious importance of muscles for performing work, muscle contractions play an essential role in increasing cardiac output by decompressing the volume that otherwise would accumulate in the muscle venous compartment, and by speeding

#### **Figure 3.**

*Effect of muscle contractions on blood flow in isolated gastrocnemius. The gastrocnemius muscle of a dog was isolated, maximally dilated and perfused with a constant flow pump. The top line is arterial pressure (Part, mmHg), the second is inflow (Qin, ml/min measured with an electromagnetic flow probe), the third is outflow (Qout, ml/min) and the fourth the generated longitudinal muscle tension (T, gm). Muscle contractions raised arterial pressure. There was a small transient fall in Qin because the contractions obstruct flow. There are large increases in Qout with the contraction, which make it look like more total flow went out but Qin is constant so the flow is unchanged. This tracing is the same as that of Folkow et al. [52] who based on the venous pulsations concluded that muscle contractions increase muscle blood flow but they did not measure Qin which indicates that mean flow does not change. Reproduced with permission from Naamani et al. Eur J Appl Physiol 1995 [44].*

#### *Mechanical Limits of Cardiac Output at Maximal Aerobic Exercise DOI: http://dx.doi.org/10.5772/intechopen.103908*

up the return of blood to heart. These roles of contracting muscle in determining cardiac output and decompressing the muscle vascular beds could be a fruitful area for further investigations with implications for maximizing athletic performance, as well rehabilitating persons with reduced muscle capacity. Issues that should be important are ideal rates of contraction and force of contraction needed to have training effect. In our modeling study, increasing contraction rates from 50 to 150 contractions/minute or force of contraction of greater than 0.25 mm Hg/ml did not change cardiac output, presumably because the veins were maximally compressed, but this was an idealized assessment and treated all muscles as one. The rate and force factors could be a much more important factor in arm versus leg exercise, and in debilitated and elderly patients with limited capacity for production of muscle force.

With normal cardiac function, the heart can handle what comes back as evident by maintenance of a low Pra. However, the heart does not have volume reserves that it can use to increase rate of return to the heart by increasing MSFP. Increased cardiac output thus is very dependent upon the increased of the return function and the effect of muscle contractions. On the other side, muscle performance is very dependent upon the delivered blood flow so that flow from the muscle and into it are intricately connected for optimal performance (**Figure 3**).

### **Author details**

#### Sheldon Magder1,2

1 Department of Critical Care, McGill University, Montreal, Quebec, Canada

2 Department of Physiology, McGill University, Montreal, Quebec, Canada

\*Address all correspondence to: sheldon.magder@mcgill.ca

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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