The anterior cruciate ligament (ACL) is a critical knee joint, bone-to-bone connected, stability ligament attached from an anterior location of the proximal tibia to a posterior site of the distal femur. The ACL is highly susceptible to failure during athletic activities and slip-fall events [1]. ACL reconstruction surgery aims to rebuild the ligament attachments as closely as possible to the native anatomy to restore pre-injury knee function and normal proprioception in the affected knee [2]. Personalized medicine in surgery allows the customization of insertion sites, graft size, tunnel placement, and graft tension for each individual patient [3]. A critical pre-operative decision concerns the placement of a tibial-femoral tunnel mimicking the native orientation of the ACL attachment [3]. Therefore, surgeons need to consider particular aspects of the local anatomy and, by extension, the biomechanical artifacts introduced during surgery for better outcomes [4]. Considering the importance of the sensory function of the joint structure, it would seem sensible to minimize the sensory damage of the joint whenever operative treatment is necessary [5]. This is because the joints are exploratory sense organs, but they are also performative motor organs; that is to say, the equipment for feeling is anatomically the same as the equipment for doing [6]. Here, we report an alternative approach based on the understanding of knee affordances to guide surgeons in the design/assessment of knee reconstruction strategies.

This is the first study to use psychological theory to address this surgical assessment concept [7]. Traditional rating systems to assess clinical outcomes after joint arthroplasty are often based on the surgeon's objective ratings, such as range of motion and strength, or clinical ratings of function and pain [8]. However, the patient's perceptions after arthroplasty may differ significantly from those of their clinician. Moreover, surgeons often underappreciate the needs and views of their patients [9]. There is, therefore, increasing awareness of the need to include patient-reported outcome (PRO) instruments in evaluating surgical procedures. Indeed, these patient-centered assessments of treatment outcomes are becoming today's standard [10]. Patient-reported outcome metrics (PROMs) can be simply described as a patient's health status self-report. A 'forgotten joint score,' corresponding to when a patient forgets an artifact in their everyday life, was introduced in PROM as the ultimate goal in joint reconstruction [11]. 'Forgotten joint scores' are often observed in patients after surgery [12]. Nevertheless, these ratings do not replace the need to understand the general role of artifacts and affordances in reconstruction surgery. Therefore, this study aims to identify measurable invariants using a (positive) affordance-based assessment strategy for the structural function of the joint during ACL reconstruction. The term `affordance' is conventionally traced to James J. Gibson and his programmatic approach to perception and action, Ecological Psychology [13]. The notion appears simple at its core, and yet upon closer examination, it has the potential to reveal a radically altered view of the relation between an organism and its environment [14].

The fundamental hypothesis of the ecological approach and this work is that active organisms of the knee that can obtain and utilize information about persisting properties of their tissue environments in which the grafts are to be located will have a definite advantage over organisms that cannot do this. Gibson demonstrated how animal perception and action are continuous, interacting with inanimate objects or surfaces [13]. The affordances of a product are what it provides, offers, or furnishes to a user. Gibson's 'system theory' of perception corresponds to an open system, somewhat different from the view of isolated artifacts [6]. The resources encountered by an animal or thinking humans are the affordances of the environment. Affordances are opportunities for action, not causes or stimuli [15]. The impetus for any knee surgery project can be understood in terms of creating and changing affordances. The design process is the construction of an artifact that offers specific affordances but not particular undesired affordances. An artifact with more positive affordances is considered better, while an artifact with more negative affordances is considered worse.

For example, the general kinematic possibility of a knee motion is a twist about the instantaneous knee screw (IKS). Therefore, the possibility of knee motion requires the sum of all moments about the direction of the given axis to vanish for equilibrium [16], that is, the affordances of the knee. We have adopted the screw theory to relate the general kinematic possibilities of a bone to the concept of affordance. “Theory of Scew” is not a general dynamical calculus. It is the discussion of a particular class of dynamical problems-for example, its use in biomechanics to help understand the motion of joints-which does not admit any other enunciation except that which the screw theory provides. The bones in the human joints are kinematically constrained in translation. So it must twist at some screw-all points in the same body twisting at the same rate. The knee perceptual system perceives that the given ground reaction forces (GRFs) may always be borne by the skeletal system, which itself is reciprocal to the degree of freedom of the knee (Figure 2(b)) [17]. Active touch and movement refer to what is ordinarily called touching-variations in skin stimulation caused by surfaces are altered together by motor activity variations. This fact is worth noting because it is often neglected that locomotion and its surfaces form an inseparable pair [18]. Contrasting the established idea of senses, Gibson considered separate anatomical units as perceptual systems [6]. In the present case, a joint yields spatial information, a 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 have been proposed to account for the dynamics of perception and action [19]. 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-artifact-surface system. Therefore, Warren's behavioral dynamics argues for a one-to-one correspondence between the internal structure IKS [17], 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 [20]. To test such an ecological approach to perception and action during the stance phase, we compared previously published experimental data sets [21] with our predicted datasets [22] in terms of medial and lateral contact forces. Available data included limb motion capture, fluoroscopy images, GRFs, electro myographical 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).

In this study, the IKS was introduced as the intermediate screw by a linear combination of two separate instantaneous screw axes of the shank (S) and thigh (T), denoted by (S, T) (Figure 1(a)). Let the general kinematic possibilities of (S, T) refer to the relative instantaneous screw between their respective screw, the instantaneous shank screw (ISS) and the instantaneous thigh screw (ITS), respectively (Figure 1(a)). Since S and T are appropriated to two different elements of the mass-chain, no kinematical significance can be attached to the composition of the two twists on S and T. If, however, the two twists on S and T having the proper ratio of amplitudes, had been applied to a single body, the displacement produced is one which could have been effected by a single twist about a single screw on the (S, T). This is because the concept of a single rigid body can transfer its weights as directly as possible to the base. If this intermediate screw is given, the ratio of the amplitudes of the twists on the screw, S, and T, is determined. Then IKS must be that screw on the (S, T), which is equilibrium, though acted upon by GRF. The criterion for the equilibrium of an arbitrary system of forces at the given knee is that the total virtual work of all forces vanishes [23]. This criterion involves virtual, not actual, displacements; at that instant, the actual motions of the T and S do not enter into account shown as the invariant ISS and ITS (Figure 1(a)). Nevertheless, since the virtual displacement, the variation of the IKS, involves a possible but purely mathematical experiment, it can be applied at a certain definite time (even if such a displacement would involve physiologically infinite velocities) (figure 2(a)). As an affordance of the knee for a patient, the IKS has to be measured relative to the patient. Therefore, they have unity relative to the posture and touch of the patient being considered [13]. We found that the rule is that the ground reaction force (GRF) vector line is very close to the instantaneous knee axis (IKA). Therefore, it aligns the knee joint with the GRF such that the reaction forces are torqueless. The reaction to the GRF will then be carried by the whole skeletal system instead. The fundamental hypothesis of this work is that affordances of the knee create selection pressure on the behavior of individual limbs, as perceived by its invariant, ISS, and ITS; hence is regulated with respect to the affordances of the environment for a given patient. One of the most profound is that a pair of invariants (ISS, ITS) can be so selected regarding the other couple of invariants belonging to the knee system (IKS, GRF) that the IKS nearly coincides with a reciprocal screw of the GRF, as indicated in a magnified inset image in Figure 1(b). As a result, the motion of one limb is no longer entirely independent of the phase and velocity of the other. The IKS is perceived as an affordance for the entrainment of the (S, T) movement.

A perceptual system can reach equilibrium since twists of amplitudes S and T neutralize. We thus see that the two kinds of action: actual motion at the knee joint (S, T), can be selected with reference to the virtual work function of (IKS, GRF) as also categorized as the performative and exploratory action during human walking [13]. Therefore, active organisms of the knee that can obtain and utilize information about persisting properties of their tissue environments in which the grafts are located will have a definite advantage over organisms that cannot do this. 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) (Figure 1(c)).

Figure 1(a) (b): An actual displacement by performative actions on the instantaneous screw axes (ISA) from the posteromedial side of the shank (a) and the thigh (b). The endpoints of axes are at the intersections with medial and lateral sagittal planes, which are located -60 mm to 60 mm off the origin of the global frame. The first axis, indicated by 1, represents the first step of IKS. The arrow indicates where the subsequent axes are migrated at every subsequent 0.05 sec time increment (units in mm).

Figure 1(c): A virtual displacement by exploratory actions of perception and action during the stance phase of gait entrain the knee joint rotation with the foot's touch pattern (GRF). The invariant knee-manifolds demonstrate that an affordance for postural stability is measured relative to the patient's posture, as represented by the entrainment of the GRF with the IKS at any point in the gait pathway.

Also, in figure 2(a) is drawn the general trajectory of the path at a position and time to illustrate the virtual displacement. It is performed at a fixed time and therefore has nothing to do with the knee system's actual, infinitesimal motion (d-process) during the time change dt (i.e., the real displacement). Loosely speaking, one may visualize the mechanical knee system as a half-timbered building that must fit in between the adjacent bones on a given surface (these are the constraints), which should be stable. In order to test its ability, one shakes the knee system a little without violating the constraints.

Figure 2(a): For the path trajectory and its virtual trajectory at a position  and time . The virtual displacement is . The starting and ending positions for both courses are at and respectively. Lagrange's ingenious idea was to introduce a special symbol for the process of variations to emphasize its virtual character. This symbol is [23]. The analogy to  recalls that both symbols refer to infinitesimal changes. However,  refers to an actual change and  to a virtual change. Since both types of change need to be considered simultaneously in problems involving the variation of definite paths, the distinction is vital.

Figure 2(b): After arthroplasty, a new motor skill emerges from the multiple body segments within a given tissue environment as presented by the lines of action of the ligaments and cartilage contacts transmitting forces across the bones. The organic unit at the knee joint and its reciprocal connection with mechanical freedom is represented by six constraints ( ), which are not only collectively reciprocal to the instantaneous knee screw ($) as indicated by their intersections (at the ' s), but severally would be unable to stir the knee only to twist about $. A balance of forces happens when the virtual work vanishes for knee equilibrium. The original anatomic schematics and lines of action were published previously [29,32,34} and are used with the permission of Professor Michele Conconi

A given system of impressed forces containing muscular actions and GRF during the stance phase will generally not be in equilibrium. This requires the agency of the proprioceptive system to fulfill special conditions. As a result, the total virtual work of the impressed forces at the IKS will usually differ from zero. In this case, the knee motion makes up for the deficiency. Through the proprioceptive mechanism, the knee moves so that the additional inertia forces produced by the knee motion bring the balance up to zero. Therefore, GRFs should be borne not through muscular actions but by the skeletons themselves. Bones are the wight-bearers. The role of proprioception in daily activities, exercise, and sports has been extensively investigated using different techniques. Yet, the proprioceptive mechanisms underlying nonsurgical treatment for patients with knee osteoarthritis control are still unclear. The first peak of the external knee abduction moment (KAM) is often used as a surrogate measure of the medial compartment loading. It has been correlated with pain and progression of knee osteoarthritis (O.A.) [24,25].

However, the recent study [16] puts an alternative measure on how O.A. patients are likely to develop overloaded medial compartments during walking with their inappropriate reflexes due to slight projection of the external load onto the constraints at the knee. High loads incur from the impaired condition of this knee proprioceptive system. For example, suppose Vasti and Soleus muscles are called upon to lift and hold reaction forces unnecessarily instead of moving bones in a balanced relationship. In that case, such action violates their relationship with the nervous system, as the reflex circle that arises is not designed to induce the appropriate reflexes, which controls the timing of the alternate contraction and relaxation of muscles to facilitate the action of inertia forces-holding parts in fixed and strained relations impede nervous system's circular action of the nervous system. The resultant congestion of one part and defrauding another can work havoc throughout the system, operating overloaded in the medial compartment. Thus, measuring the affordance of the knee 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. However, many clinicians are less confident in self-reported PROMs than in 'objective measurements' [12]. 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 [26]. They concluded that joint awareness might work as an overarching parameter. In other words, the neural input with the covariation of cutaneous and articular motion is projected into the somatosensory area of the cortex to the same area as a particular invariant unit [27-30].

This aligns with Gibson's statement that an affordance cuts across the subjective-objective dichotomy and helps us understand its inadequacy [13,31-37]. Affordances have to be designed in relation to the uniqueness of each patient. Thus posture and movement need to be measured in terms of a specific patient-environment system, not in patient-centered terms.

This research was funded by PROCIENCIA under contract N° PE501080681-2022-PROCIENCIA Proyectos Especiales: Proyectos de Investigadores Visitan. The author WK extends thanks to Michele Conconi from the University of Bologna for the available video. In addition, the authors acknowledge the support from The MIT-Peru UTEC Seed Fund, awarding the project titled "Development of Proper Tunnel Syndrome Placement Device to Avoid Impingement" and the UTEC Fondo Semilla 2022-2, awarding "Aprendizaje Perceptivo de los Movimientos de las Piernas y Pateo de Infantes con Espina Bífida utilizando un Sistema de Entrenamiento de Realidad Virtual." In addition, 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 U.S. National Institutes of Health via the NIH Roadmap for Medical Research (Grant # U54 GM072970).

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