**2. Methods**

The study involved male members of the Russian national teams in alpine skiing n = 4, bobsleigh n = 5, mogul skiing n = 5 and ski jumping n = 5 (**Table 1**). All athletes took part in the World Cups and World Championships. The experiment was carried out within the framework of regular testing of national team members according to established protocols in the course of preparation for international competitions [28].


*Peculiarities of Muscle-Tendon Mechanics and Energetics in Elite Athletes in Various Sports DOI: http://dx.doi.org/10.5772/intechopen.97000*

#### **Table 1.**

*Characteristics of the subjects. Mean ± SD.*

Testing procedure. After a warm-up subjects performed drop jumps (vertical jumps after jumping down) from the height of 10 cm, 30 cm, and 50 cm with no arms swing. The subjects were advised to wear their preferred athletic shoes and to keep hands on the hips during the jumps. The best of three trials, regarding jumping height (CoM elevation), was considered for further analysis. Rest interval between the trials was about 2–3 min depending on the individual need of the athlete.

Data Processing Approach. The software complex received input data of reаl movement from by the Qualisys Motion Capture System (24 cameras Oqus 5 Qualisys, Sweden). Jumping exercises were performed on two force plates AMTI 6000 (AMTI, USA). Recording was done at frame rate 400 fps and synchronized with force plate's signals. The data were processed with the help of the software package OpenSim [29]. The software package permitted to create an individual musculoskeletal model of every athlete and identify specific features of his movement technique.

Kinematic and dynamic calculations were performed using simulation of a full-body model proposed by the Hamner and Delp paper [30]. We used a threedimensional musculoskeletal model with 29 degrees of freedom, 92 muscles of the torso and lower extremities driven by torque actuators. This model was previously used to study how each muscle contributes to accelerating the body's center of mass during a jump [30, 31]. The model included 35 lower limb muscles, 5 of which were examined in this study. To analyze metabolic costs during the jump experiment, we selected a group of key muscles involved in the take-off phase of a vertical jump: Gl (gluteus maximus, gluteus medius, gluteus minimus muscles), RF (rectus femoris), VAS (vast medial muscle), GAS (lateral sections of the gastrocnemius muscle), SOL (soleus muscle).

An individual muscle and tendon complex was described by a three-piece MTU model, based on Thelen's work in 2003 [32], modified by few other authors [33, 34] and implemented in the OpenSim application. The model calculated the change in length and strength of muscles and tendons over a wide range of body positions. The model also permitted to study in detail functioning of the MTUs of the ankle, knee and hip joints when generating force and its derivatives for each subject. We simulated each jump with the help of the methods described by Hamner and Delp [30].

Our simulation workflow began with scaling the geometry of the generic musculoskeletal model to match the anthropometry of each of our subjects, using the OpenSim Scale Tool. In addition, we scaled the maximum isometric forces of the muscles according to a regression equation based on each subject's mass and height [31]. Then we generated muscle driven motions of the recorded experiments with OpenSim's Computed Muscle Control (CMC) Tool [32], using the individual models and the adjusted kinematics. CMC calculated muscle excitations that could produce

the observed jumping motion while minimizing the sum of squared muscle activations at regular intervals in the motion.

Elastic Strain Energy (ESE) Calculation. During the analysis we attempted to calculate the possible amount of stored and utilized elastic strain energy (ESE) using methods suggested by [4, 35]. According to the authors mechanical energy expenditures (MEEs) of two human lower extremity models are associated with two different sources of mechanical energy - (l) muscles and (2) joint moments. The source of mechanical energy in the Model 1 was a group of eight muscles, three of them being two-joint muscles. The source of mechanical energy in the Model 2 was a set of net moments in its joints.

It was shown that the model with two-joint muscles spent less mechanical energy than the model with no two-joint muscles in the same movement. Saving of mechanical energy by two-joint muscles was possible on condition that: (i) muscle powers produced by the two-joint muscle at both joints were of opposite signs, (ii) moments produced by that muscle at each of the two joints were codirectional with the net joint moments at those joints, and (iii) biarticular antagonist muscles did not produce force.

Metabolic Costs Calculation. To estimate metabolic energy consumption, we used a metabolics model developed by [36, 37] with few modifications by [36]. To employ this metabolic model, we used the Umberger2010MuscleMetabolicsProbe in OpenSim v4.

In accordance with the calculation method, we summed the rate of energy expendutures of all muscles, added a basal rate (1.2 W/kg – [38]).

Leg Stiffness Calculation. We estimated leg stiffness:

$$\mathbf{K}\_{\rm leg} = \mathbf{F}\_{\rm max} \ / \left( \left( \mathbf{l}\_{\rm o} - \mathbf{l}\_{\rm min} \right) / \mathbf{l}\_{\rm o} \right), \tag{1}$$

where Kleg – the leg stiffness normalized to body weight as the ratio of the peak vertical ground reaction force (Fmax) to the difference between the leg length when standing and the leg length when the center of mass is at its lowest point lmin. The leg length l0 was the distance from the center-of-pressure [39] to the center of the pelvis in a model derived from the musculoskeletal model described by [40].

To process the results of our research we used a software package STATISTICA ver.10. As we had small sample sizes, we used non parametrical statistical methods: Kruskal-Wallis test and Wilcoxon test.

Ethical Approval. The study was approved by the Local Human Research Ethics Committee, and all participants gave their written informed consent prior to testing. All human testing procedures conformed with the principles of the Declaration of Helsinki.
