**5. The affordance-based design applied to graft placements during reconstruction**

It has been hypothesized that a tensegrity system serves the medium of haptic perception, from the individual cells to the whole body, maintaining continuous tension and discontinuous compression [53], which clearly exhibit the determinate character of the entire body system perception [38, 40]. In this study, we present the positive affordance-based design on graft placement while in continuous tension, rather than designing against the negative affordance by preventing impingement. As described, we use the invariant structure of the KTS [54] as an appropriate ecological frame of reference to locate the tibial tunnel placement. For the ACL-patient to engage the IKS directly, clinicians have to measure the tunnel placement relative to the posture and behavior of the person being considered, making continuous graft tension possible. First, an invariant should not be applied to the patient directly, for it is not a stimulus. Second, invariants can be considered qualitative rather than quantitative so that other clinical assessments can make it available to their surgeons/observers in an exact mathematical description [14].

The IKS is defined in terms of the second-order invariant by a linear combination of the two screws of the first-order invariant, *S* and *T*, instantaneous screw axes of the shank and thigh (**Figure 4(a)**) [55]. Then the IKS must be a screw that has been picked up from the many candidate screws on the cylindroids [40], which is reciprocal to KTS (via Eq. 1). Hence, the ratio of the amplitudes about *S* and *T*

**59**

*The Knee Proprioception as Patient-Dependent Outcome Measures within Surgical…*

may be determined (**Figure 4(a)**), which manifests the fact that the sensitivity of the knee joint to its disposition is of crucial importance in picking up information. Two lines were projected respectively to the sagittal plane so that the path of the graft could be aligned to any transversal axis intersecting the IKS (\$), the central line of KTS that is the second-order invariant line, also called the IKS (**Figure 1(a)**). The lines were generated at full knee joint extension. Notice that if the graft line is not precisely aligned with the member line within the KTS, due to position errors, for example, the velocity difference on the graft line would not be zero, but would still be small. If the path of an ACL graft is so selected that it cuts the IKS of the KTS, then the line becomes a member of the KTS, which ensures the isokinetic graft placement related to trans-tibial-femoral tunneling. Consider now the necessary kinematic relations in that contact point *c* as the common point belonging to both

The velocity of the point *c* residing on the femoral tunnel (*VF* ) can be resolved into two components: one component is perpendicular to the graft line and the other element parallel to it. Similarly, the velocity of the point on the tibial tunnel coincident with point *c* (*VT* ) can also be resolved into two components. For the two bony bodies (femur and tibia) to remain through one continuous body, the parallel component of the graft line for velocity must be equal, by projecting *VF* and *VT* onto the graft line (**Figure 1(a)**). The graft without that qualification would experience impingements. The difference in the perpendicular component represents the relative transverse velocities between the articulating tunnels and is closely related to an essential factor in choosing the proper tunnel width. Widening of the tunnel diameter might be performed, allowing more tolerance for this transverse velocity relationship, taking into account the width of the graft and the

As described, we identified the measurable second-order invariant of knee synergy and proposed it as a new view of the basis of tunnel placement by using Eq. (1). The knee synergy approach identifies the information as a means to perceive the affordance of uniform motion transmission. To apply the described approach and identify the invariant, we characterized the shank to the thigh (the tibia to the femur) relative motion, i.e., the second-order invariance of the knee synergy. These results were then compared with experimental data for validation as provided by the "Grand Challenge Competition to Predict *In Vivo* Knee Loads" as part of the

Contrasting the established idea of senses, Gibson considered separate anatomical units as perceptual systems [29]. In the present case, a joint yields spatial information, skin-nerve conveys contact information, and in certain dynamic combinations, joint and skin-nerve yield synchronization, or entrainment specify-

Behavioral dynamics in a consistent approach has proposed to account for the dynamics of perception and action [57]. This approach followed Gibson's idea that rather than being localized in an internal (or external) structure, control is distributed over the agent-environment system, in the present case, the user-artifactsurface system. Therefore, Warren's behavioral dynamics argues for a one-to-one correspondence between the internal structure IKS, constituted by the internal forces formed by the distal end of the femur and the proximal end of the tibia, and the external structure, represented by the ground reaction forces (GRFs) on foot [58].

ing information about the layout of external surfaces during locomotion.

Symbiosis project funded by the National Institutes of Health [56].

*DOI: http://dx.doi.org/10.5772/intechopen.94887*

the tibial and femoral tunnels (**Figure 1(a)**).

existing diameter of the notch.

**6. Entrainment of touch and posture**

#### *The Knee Proprioception as Patient-Dependent Outcome Measures within Surgical… DOI: http://dx.doi.org/10.5772/intechopen.94887*

may be determined (**Figure 4(a)**), which manifests the fact that the sensitivity of the knee joint to its disposition is of crucial importance in picking up information.

Two lines were projected respectively to the sagittal plane so that the path of the graft could be aligned to any transversal axis intersecting the IKS (\$), the central line of KTS that is the second-order invariant line, also called the IKS (**Figure 1(a)**). The lines were generated at full knee joint extension. Notice that if the graft line is not precisely aligned with the member line within the KTS, due to position errors, for example, the velocity difference on the graft line would not be zero, but would still be small. If the path of an ACL graft is so selected that it cuts the IKS of the KTS, then the line becomes a member of the KTS, which ensures the isokinetic graft placement related to trans-tibial-femoral tunneling. Consider now the necessary kinematic relations in that contact point *c* as the common point belonging to both the tibial and femoral tunnels (**Figure 1(a)**).

The velocity of the point *c* residing on the femoral tunnel (*VF* ) can be resolved into two components: one component is perpendicular to the graft line and the other element parallel to it. Similarly, the velocity of the point on the tibial tunnel coincident with point *c* (*VT* ) can also be resolved into two components. For the two bony bodies (femur and tibia) to remain through one continuous body, the parallel component of the graft line for velocity must be equal, by projecting *VF* and *VT* onto the graft line (**Figure 1(a)**). The graft without that qualification would experience impingements. The difference in the perpendicular component represents the relative transverse velocities between the articulating tunnels and is closely related to an essential factor in choosing the proper tunnel width. Widening of the tunnel diameter might be performed, allowing more tolerance for this transverse velocity relationship, taking into account the width of the graft and the existing diameter of the notch.

As described, we identified the measurable second-order invariant of knee synergy and proposed it as a new view of the basis of tunnel placement by using Eq. (1). The knee synergy approach identifies the information as a means to perceive the affordance of uniform motion transmission. To apply the described approach and identify the invariant, we characterized the shank to the thigh (the tibia to the femur) relative motion, i.e., the second-order invariance of the knee synergy. These results were then compared with experimental data for validation as provided by the "Grand Challenge Competition to Predict *In Vivo* Knee Loads" as part of the Symbiosis project funded by the National Institutes of Health [56].

### **6. Entrainment of touch and posture**

Contrasting the established idea of senses, Gibson considered separate anatomical units as perceptual systems [29]. In the present case, a joint yields spatial information, skin-nerve conveys contact information, and in certain dynamic combinations, joint and skin-nerve yield synchronization, or entrainment specifying information about the layout of external surfaces during locomotion.

Behavioral dynamics in a consistent approach has proposed to account for the dynamics of perception and action [57]. This approach followed Gibson's idea that rather than being localized in an internal (or external) structure, control is distributed over the agent-environment system, in the present case, the user-artifactsurface system. Therefore, Warren's behavioral dynamics argues for a one-to-one correspondence between the internal structure IKS, constituted by the internal forces formed by the distal end of the femur and the proximal end of the tibia, and the external structure, represented by the ground reaction forces (GRFs) on foot [58].

*Proprioception*

behave in a particular way [37].

the following relationship [40],

as distinguished from the environment.

**reconstruction**

[50]. The KTS can be pre-stressed to obtain the same configuration as if external loads were applied. The selected pre-stress may yield the same configuration in the swing phase (external forces are absent) as in the stance phase (external forces are present) [49]. Notably, preparedness is not only a reactive aspect of the movement apparatus, but it also relates to anticipatory adjustments that predispose a system to

If a knee joint is only free to twist about a screw IKS while in equilibrium, despite being acted upon by the fiber reaction, the mechanical work during a small displacement against the reaction forces \$′ in the KTS must be zero, according to

Uniform motion transmission between two axes (defining the thigh and shank,

The knee synergy approach proposed herein was recently validated experimentally [51]. The authors calculated if all the lines of action intersect at the IKS (\$) following natural knee motion to describe the knee surgery invariant. The results show the mean distances between each constraint line of action, and the IKS stayed below 3.4 mm and 4.5 mm for *ex vivo* and *in vivo* assessments, respectively (**Figure 4(b)**).

**5. The affordance-based design applied to graft placements during** 

It has been hypothesized that a tensegrity system serves the medium of haptic perception, from the individual cells to the whole body, maintaining continuous tension and discontinuous compression [53], which clearly exhibit the determinate character of the entire body system perception [38, 40]. In this study, we present the positive affordance-based design on graft placement while in continuous tension, rather than designing against the negative affordance by preventing impingement. As described, we use the invariant structure of the KTS [54] as an appropriate ecological frame of reference to locate the tibial tunnel placement. For the ACL-patient to engage the IKS directly, clinicians have to measure the tunnel placement relative to the posture and behavior of the person being considered, making continuous graft tension possible. First, an invariant should not be applied to the patient directly, for it is not a stimulus. Second, invariants can be considered qualitative rather than quantitative so that other clinical assessments can make it available to their surgeons/observers in an exact mathematical description [14]. The IKS is defined in terms of the second-order invariant by a linear combination of the two screws of the first-order invariant, *S* and *T*, instantaneous screw axes of the shank and thigh (**Figure 4(a)**) [55]. Then the IKS must be a screw that has been picked up from the many candidate screws on the cylindroids [40], which is reciprocal to KTS (via Eq. 1). Hence, the ratio of the amplitudes about *S* and *T*

respectively) is affordable only if their lines of action pass through the IKS, as expressed in the Eq. (1). Thus, the affordances of the knee synergy must be positive, and the joint ligaments should remain in an isometric/isokinetic condition or continuous length/tension. If not, the ligaments become slack or loose, resulting in roof impingement, post-reconstruction [5]. Moreover, Eq. (1) also implies that the moving self (\$) and the invariant structure of the KTS reaction are reciprocal aspects of the same perception. Gibson called this information gathering approach propriospecific, as opposed to exterospecific, to specify the observer (here the self)

\$ 0 *<sup>T</sup>* ⋅ = *KTS* (1)

**58**

Behavioral dynamics control laws indicate that the entrainment or coordination of shank and thigh (S, T) follows the same physical laws as the entrainment between the knee and ground (IKS, GRF). Therefore, the cross-ratio [59] of the ordered pair (IKS, GRF) with respect to the ordered pair (S, T) is

$$\left| \left( (I \text{KS}, \text{GRF}); (\text{S}, T) \right) \right| = -1. \tag{2}$$

For a given IKS (when an observer perceives the affordance of the surface) and the location of the center of pressure (COP) on the axis of the GRF is known, then the GRF vector is limited to a plane in the screw system of the first order [47, 48] (**Figure 5(a)**). The muscle synergy η and GRF φ are then compounded into an invariant, limited to the plane of the COP in reciprocity with the IKS. This theorem was originally proposed by Möbius, who showed that forces from six lines could be equilibrated, and also, if five of the lines are given along with a point on the sixth line, then the sixth line is limited to a polar plane [40].

To test such ecological approach to perception and action during the stance phase of a gait, we compared previously published experimental data sets [56] with our predicted datasets [47, 48] in terms of medial and lateral contact forces. Available data included limb motion capture, fluoroscopy images, GRFs, electromyographical readings determining muscle forces, as well as medial and lateral knee contact forces derived from GRFs. Data were collected from an adult male with a right knee reconstruction (65 kg mass and 1.7 m height). When the variations in the ground contact (magnitudes and direction) were shown along with the variations of knee movement in terms of IKS, an invariant was determined uniquely by the two corresponding pairs, see Eq. (2) (**Figure 5(b)**).

In this study, the IKS was determined by a linear combination of two instantaneous screw axes of the shank and thigh (**Figure 4(a)**). The IKS nearly coincides with a reciprocal screw of the GRF, as indicated in a magnified inset image in **Figure 5(b)**. A perceptual system of the knee can come to equilibrium since twists of amplitudes S and T neutralize. We thus see that the evanescence of one

#### **Figure 5.**

*(a) The framework for estimating responses to constraints on the knee joint (ligament forces and contact forces) is influenced by the inclusion of muscle synergy (*η*) and GRF (*φ*) relative to the center of pressure (COP). The judicious generation of the IKS for the one DOF in knee equilibrium simplifies the estimation. This figure was adapted from the original figure published previously [47, 48]. (b) Perception and action during the stance phase of gait entrain the knee joint rotation with the touch pattern (GRF) of the foot. The invariant knee-manifolds demonstrates that an affordance for postural stability is measured relative to the posture of the patient, as represented by the entrainment of the GRF with the IKS at any point in the gait pathway.*

**61**

*The Knee Proprioception as Patient-Dependent Outcome Measures within Surgical…*

panies exteroception; information is available to specify both poles [14].

function must afford all that is necessary for subordinate organs (S, T) belong to an IKS of the superordinate organ for information pickup over paths of locomotion. This reciprocity is captured by the concept of a mutual relationship between the constraints and the DOF [60, 61]. Information about the person accompanies information about the environment. Here it is shown that proprioception accom-

A lateral radiograph of the knee in extension was the traditional approach to diagnose any roof impingement, and a portion of the tibial tunnel was traditionally placed anterior to the intercondylar roof [5] (**Figure 1(b)**). However, the available information on the experimental images can not be applied to another patient because they do not provide environmental information. Thus, AUA has the potential to diagnose pathologies. The last decade has seen a paradigm shift in the measurement of clinical outcomes, with an increasing focus on the user's perspective, PROMs. Many clinicians, though, are less confident in self-reported PROMs, than in 'objective measurements' [11]. Recent studies identified several sensations, activities, and psychological factors such as feelings of instability and knee-related fears that make the patients aware of their artificial knee joint [62]. They concluded that joint awareness might work as an overarching parameter. This is aligned with Gibson's statement that an affordance cuts across the dichotomy of subjectiveobjective and helps us to understand its inadequacy [14]. Affordances have to be designed in relation to the uniqueness of each patient, and thus posture and movement need to be measured in terms of a specific patient-environment system, not in

This study presented an affordance based design supporting knee reconstruction surgery, with applications to the user/surgeon/therapist. It brings ecological theory to robustly explain knee biomechanics and clarifying the general role of physical artifacts and affordances in surgery. The mutuality of user and artifact that we defended here is not traditionally guiding individualized ACL reconstruction. Instead, the anatomic ACL reconstruction seems to lead to the idea that a deficient ACL is not understandable within knee joint biomechanics [32]. As we argued, the ACL is a highly organized synergy with intra- and extra-articular components [34] and yet still an identifiable system within the anatomic environment. The knee complexes in Eq. (2) reinforce how perception and action are coupled. A unique combination of invariants, a compound invariant, is just another invariant [14]. In particular, this study identified the knee complexes as the measurable invariable structures that

specify the persisting placement of the tunnel during ACL reconstruction.

Constraints That Makes Natural Motion Possible" available to us.

Author WK extends thanks to Ms. Flávia Yázigi for her hard work with the radiography and a long recruitment process. WK also thanks to his mother-in-law, Ms. Sun Lee, for her continuous encouragement for this research. The experimental data used for validation were provided by the "Grand Challenge Competition to Predict *In Vivo* Knee Loads" as part of the Symbiosis project funded by the US National Institutes of Health via the NIH Roadmap for Medical Research (Grant # U54 GM072970). WK also thanks Dr. Michele Conconi of University of Bologna, for making the videos "The Geometrical Arrangement of Knee

*DOI: http://dx.doi.org/10.5772/intechopen.94887*

patient-centered terms.

**Acknowledgements**

**7. Conclusion**

*The Knee Proprioception as Patient-Dependent Outcome Measures within Surgical… DOI: http://dx.doi.org/10.5772/intechopen.94887*

function must afford all that is necessary for subordinate organs (S, T) belong to an IKS of the superordinate organ for information pickup over paths of locomotion. This reciprocity is captured by the concept of a mutual relationship between the constraints and the DOF [60, 61]. Information about the person accompanies information about the environment. Here it is shown that proprioception accompanies exteroception; information is available to specify both poles [14].

A lateral radiograph of the knee in extension was the traditional approach to diagnose any roof impingement, and a portion of the tibial tunnel was traditionally placed anterior to the intercondylar roof [5] (**Figure 1(b)**). However, the available information on the experimental images can not be applied to another patient because they do not provide environmental information. Thus, AUA has the potential to diagnose pathologies. The last decade has seen a paradigm shift in the measurement of clinical outcomes, with an increasing focus on the user's perspective, PROMs. Many clinicians, though, are less confident in self-reported PROMs, than in 'objective measurements' [11]. Recent studies identified several sensations, activities, and psychological factors such as feelings of instability and knee-related fears that make the patients aware of their artificial knee joint [62]. They concluded that joint awareness might work as an overarching parameter. This is aligned with Gibson's statement that an affordance cuts across the dichotomy of subjectiveobjective and helps us to understand its inadequacy [14]. Affordances have to be designed in relation to the uniqueness of each patient, and thus posture and movement need to be measured in terms of a specific patient-environment system, not in patient-centered terms.

## **7. Conclusion**

*Proprioception*

Behavioral dynamics control laws indicate that the entrainment or coordination of shank and thigh (S, T) follows the same physical laws as the entrainment between the knee and ground (IKS, GRF). Therefore, the cross-ratio [59] of the ordered pair

For a given IKS (when an observer perceives the affordance of the surface) and the location of the center of pressure (COP) on the axis of the GRF is known, then the GRF vector is limited to a plane in the screw system of the first order [47, 48] (**Figure 5(a)**). The muscle synergy η and GRF φ are then compounded into an invariant, limited to the plane of the COP in reciprocity with the IKS. This theorem was originally proposed by Möbius, who showed that forces from six lines could be equilibrated, and also, if five of the lines are given along with a point on the sixth

To test such ecological approach to perception and action during the stance phase of a gait, we compared previously published experimental data sets [56] with our predicted datasets [47, 48] in terms of medial and lateral contact forces. Available data included limb motion capture, fluoroscopy images, GRFs, electromyographical readings determining muscle forces, as well as medial and lateral knee contact forces derived from GRFs. Data were collected from an adult male with a right knee reconstruction (65 kg mass and 1.7 m height). When the variations in the ground contact (magnitudes and direction) were shown along with the variations of knee movement in terms of IKS, an invariant was determined uniquely by

In this study, the IKS was determined by a linear combination of two instantaneous screw axes of the shank and thigh (**Figure 4(a)**). The IKS nearly coincides with a reciprocal screw of the GRF, as indicated in a magnified inset image in **Figure 5(b)**. A perceptual system of the knee can come to equilibrium since twists of amplitudes S and T neutralize. We thus see that the evanescence of one

*(a) The framework for estimating responses to constraints on the knee joint (ligament forces and contact forces) is influenced by the inclusion of muscle synergy (*η*) and GRF (*φ*) relative to the center of pressure (COP). The judicious generation of the IKS for the one DOF in knee equilibrium simplifies the estimation. This figure was adapted from the original figure published previously [47, 48]. (b) Perception and action during the stance phase of gait entrain the knee joint rotation with the touch pattern (GRF) of the foot. The invariant knee-manifolds demonstrates that an affordance for postural stability is measured relative to the posture of the patient, as represented by the entrainment of the GRF with the IKS at any point in the gait pathway.*

{( )( ) *IKS GRF S T* , ; , 1. } = − (2)

(IKS, GRF) with respect to the ordered pair (S, T) is

line, then the sixth line is limited to a polar plane [40].

the two corresponding pairs, see Eq. (2) (**Figure 5(b)**).

**60**

**Figure 5.**

This study presented an affordance based design supporting knee reconstruction surgery, with applications to the user/surgeon/therapist. It brings ecological theory to robustly explain knee biomechanics and clarifying the general role of physical artifacts and affordances in surgery. The mutuality of user and artifact that we defended here is not traditionally guiding individualized ACL reconstruction. Instead, the anatomic ACL reconstruction seems to lead to the idea that a deficient ACL is not understandable within knee joint biomechanics [32]. As we argued, the ACL is a highly organized synergy with intra- and extra-articular components [34] and yet still an identifiable system within the anatomic environment. The knee complexes in Eq. (2) reinforce how perception and action are coupled. A unique combination of invariants, a compound invariant, is just another invariant [14]. In particular, this study identified the knee complexes as the measurable invariable structures that specify the persisting placement of the tunnel during ACL reconstruction.
