**4. The affordance-based design applied to reconstructed knee joint function**

A joint 'gear' cannot perceive itself or its joint gear since gears are inanimate. Gears simply conjugate uniform motion transmission by virtue of their tensegrity structure, manifesting that structure influences behavior [31]. However, the knee is an active set of bone structures that come to equilibrium via a joint function. The function of a joint is not only to permit mobility of the articulated bones but also to maintain a stable bone position and movement. Knee structures include muscles/ tendons, anterior cruciate ligaments (ACL), posterior cruciate ligament (PCL), medial collateral ligament (MCL), lateral collateral ligament (LCL), and articular cartilage contact in the medial (P1) and lateral (P2) compartments (**Figure 2(b)**). From a biomechanical point of view, several studies have shown that these intraarticular knee structures work in synergy with the ACL [32–34]. The knee synergy engages afferent/efferent motor control loops that establish functional equilibrium gait patterns [35].

Neurophysiologist Nikolai Bernstein defined coordination as mastering the many degrees of freedom (DOF) of a particular movement by reducing the number of variables to be controlled [36]. Recently, a contemporary perspective on Bernstein's concept of synergies has been proposed [37]. The muscle synergy is equivalent to the complexity of lines, a manifold approximated by individual fibers (**Figure 3(a)**). Muscles are not functional units, even though this is a common misconception. Instead, most muscular movements are generated by many individual motor units distributed over some portions of one muscle, plus portions of other muscles. The tensional forces of these motor units are then transmitted to a complex network of fascia sheets, bags, and strings, which convert them into the final joint/ body movement [38].

Line manifold contraction is a linear line complex [39] defined by screws ( *IS*( ) **p** ) (**Figure 3(b)**). Bodies twist around a screw, called Instantaneous Screw [40]. In any screw motion along a line axis forming a linear complex, the lines remain within the complex. Additional cognitive processes or internal representations are not needed to explain these phenomena, as perception and action are coupled. Perceptual systems are active sets of organs designed to reach equilibrium through synergies [41]. A body

#### **Figure 3.**

*(a) Fiber tractography image of a portion of the lateral gastrocnemius muscle as demonstrated in an exemplar healthy subject. The overlying images were generated at one region of interest, corresponding to the muscle boundaries where the anatomical cross-section area was maximal (whole-body MRI scanner, Signa HDxT 1.5 T, GE Healthcare, USA). The patients were placed in the supine position, feet first, and the position of each participant was considered in relation to the long axis of the leg, which was placed in parallel to the magnetic field. (b) a manifold of muscle fibers in tension forms to the linear complex identified as an instantaneous screw IS*( ) **p** *and its perpendicular pole (***q***) within the synergy of gait.*

**57**

**Figure 4.**

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

cannot remain in equilibrium if the fiber forces that act upon the body have a nonbalance resultant force. The velocity vector of every point in the fiber segment is tangential to the helix passing through it. The pattern of this velocity vector is a helicoidal velocity field. Each point that does not coincide with the screw's twist *IS*( ) **p** is referred to as a pole (**q**). Associated with each pole is its corresponding polar plane. A polar plane and its corresponding pole, as defined by the instantaneous

In our previous research [42, 43], we introduced the concept of measurable invariant of the knee perceptual organ. In such invariant, six constraints (\$) are collectively reciprocal to the instantaneous knee screw (IKS or \$) indicated by ⊗ (**Figure 2(b)**). These metrics predicted the knee synergy model based on synergies [44]. Moreover, this perspective defines torque-free pure forces based on the tensegrity structure [45–48]. It is important to note that this configuration is a tensegrity configuration, as the system is pre-stressable in the absence of external forces, such as ground reaction forces during actual locomotion [49]. It was shown the knee tensegrity structure (KTS) has six constraints, and that it can balance the forces between tension and compression in the joint such that no work results

*(a) An exemplar Ball-Disteli diagram [52] with two generally disposed screws (T and S or* **p1** *and* **p2** *), conveniently placed on the z-axis along their common perpendicular (with b). The origin of coordinate* O *is* 

*(S, T). An instantaneous knee screw (IKS) after normalization is linearly dependent on the screws during any point of knee movement. The Ball-Disteli diagram aligns itself using the principle of three axes. (b) Representation of the IKS (green line); see Online Supplementary Video 1 (video is available via the following link: https://drive. google.com/file/d/18\_YtszzT3\_IvNIken5uxObj4jmSd0Zs\_/view?usp=sharing). The lines of action of the ligaments (blue lines) and cartilage contact (red areas and red lines) for wrenches identified every 30° within the range of knee motion for a given patient. The white or colored dots represent the closest point to the IKS for each wrench. The colors range from white (di > 5 mm) to the color of the corresponding intersecting line (di = 0 mm). Cartilage contact colors on the tibia are proportional to the tibial-femoral relative separation (red: Distance* ≤*0 mm; blue: Distance >7 mm). The original anatomic schematics and lines of action were published previously [51] and are* 

σ

 *between the two screws* 

*halfway between the screws, and the x-axis is inclined by half the included angle* 

*used by permission of professor Michele Conconi.*

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

screw, have been illustrated here (**Figure 3(b)**).

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

cannot remain in equilibrium if the fiber forces that act upon the body have a nonbalance resultant force. The velocity vector of every point in the fiber segment is tangential to the helix passing through it. The pattern of this velocity vector is a helicoidal velocity field. Each point that does not coincide with the screw's twist *IS*( ) **p** is referred to as a pole (**q**). Associated with each pole is its corresponding polar plane. A polar plane and its corresponding pole, as defined by the instantaneous screw, have been illustrated here (**Figure 3(b)**).

In our previous research [42, 43], we introduced the concept of measurable invariant of the knee perceptual organ. In such invariant, six constraints (\$) are collectively reciprocal to the instantaneous knee screw (IKS or \$) indicated by ⊗ (**Figure 2(b)**). These metrics predicted the knee synergy model based on synergies [44]. Moreover, this perspective defines torque-free pure forces based on the tensegrity structure [45–48]. It is important to note that this configuration is a tensegrity configuration, as the system is pre-stressable in the absence of external forces, such as ground reaction forces during actual locomotion [49]. It was shown the knee tensegrity structure (KTS) has six constraints, and that it can balance the forces between tension and compression in the joint such that no work results

#### **Figure 4.**

*Proprioception*

gait patterns [35].

body movement [38].

structure, manifesting that structure influences behavior [31]. However, the knee is an active set of bone structures that come to equilibrium via a joint function. The function of a joint is not only to permit mobility of the articulated bones but also to maintain a stable bone position and movement. Knee structures include muscles/ tendons, anterior cruciate ligaments (ACL), posterior cruciate ligament (PCL), medial collateral ligament (MCL), lateral collateral ligament (LCL), and articular cartilage contact in the medial (P1) and lateral (P2) compartments (**Figure 2(b)**). From a biomechanical point of view, several studies have shown that these intraarticular knee structures work in synergy with the ACL [32–34]. The knee synergy engages afferent/efferent motor control loops that establish functional equilibrium

Neurophysiologist Nikolai Bernstein defined coordination as mastering the many degrees of freedom (DOF) of a particular movement by reducing the number of variables to be controlled [36]. Recently, a contemporary perspective on Bernstein's concept of synergies has been proposed [37]. The muscle synergy is equivalent to the complexity of lines, a manifold approximated by individual fibers (**Figure 3(a)**). Muscles are not functional units, even though this is a common misconception. Instead, most muscular movements are generated by many individual motor units distributed over some portions of one muscle, plus portions of other muscles. The tensional forces of these motor units are then transmitted to a complex network of fascia sheets, bags, and strings, which convert them into the final joint/

Line manifold contraction is a linear line complex [39] defined by screws ( *IS*( ) **p** ) (**Figure 3(b)**). Bodies twist around a screw, called Instantaneous Screw [40]. In any screw motion along a line axis forming a linear complex, the lines remain within the complex. Additional cognitive processes or internal representations are not needed to explain these phenomena, as perception and action are coupled. Perceptual systems are active sets of organs designed to reach equilibrium through synergies [41]. A body

*(a) Fiber tractography image of a portion of the lateral gastrocnemius muscle as demonstrated in an exemplar healthy subject. The overlying images were generated at one region of interest, corresponding to the muscle boundaries where the anatomical cross-section area was maximal (whole-body MRI scanner, Signa HDxT 1.5 T, GE Healthcare, USA). The patients were placed in the supine position, feet first, and the position of each participant was considered in relation to the long axis of the leg, which was placed in parallel to the magnetic field. (b) a manifold of muscle fibers in tension forms to the linear complex identified as an instantaneous* 

*screw IS*( ) **p** *and its perpendicular pole (***q***) within the synergy of gait.*

**56**

**Figure 3.**

*(a) An exemplar Ball-Disteli diagram [52] with two generally disposed screws (T and S or* **p1** *and* **p2** *), conveniently placed on the z-axis along their common perpendicular (with b). The origin of coordinate* O *is halfway between the screws, and the x-axis is inclined by half the included angle* σ *between the two screws (S, T). An instantaneous knee screw (IKS) after normalization is linearly dependent on the screws during any point of knee movement. The Ball-Disteli diagram aligns itself using the principle of three axes. (b) Representation of the IKS (green line); see Online Supplementary Video 1 (video is available via the following link: https://drive. google.com/file/d/18\_YtszzT3\_IvNIken5uxObj4jmSd0Zs\_/view?usp=sharing). The lines of action of the ligaments (blue lines) and cartilage contact (red areas and red lines) for wrenches identified every 30° within the range of knee motion for a given patient. The white or colored dots represent the closest point to the IKS for each wrench. The colors range from white (di > 5 mm) to the color of the corresponding intersecting line (di = 0 mm). Cartilage contact colors on the tibia are proportional to the tibial-femoral relative separation (red: Distance* ≤*0 mm; blue: Distance >7 mm). The original anatomic schematics and lines of action were published previously [51] and are used by permission of professor Michele Conconi.*

[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 behave in a particular way [37].

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 the following relationship [40],

$$\boldsymbol{\mathfrak{s}}^T \cdot \boldsymbol{K} \boldsymbol{T} \mathbf{S} = \mathbf{0} \tag{1}$$

Uniform motion transmission between two axes (defining the thigh and shank, 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) as distinguished from the environment.

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)**).
