Tracking Knee Joint Functional Axes through Tikhonov Filtering and Plűcker Coordinates

Abstract

Researchers have reported several compensation methods to estimate bone and joint position from a cluster of skin-mounted markers as influenced by Soft Tissue Artifacts (STA). Tikhonov Regularization Filtering (TRF) as a means to estimate Instantaneous Screw Axes (ISA) was introduced here as a means to reduce the displacement of a rigid body to its simplest geometric form. Recent studies have suggested that the ISA of the knee, i.e., Knee Functional Axes (KFA), might be closely connected to the estimation of constraint forces such as those due to medial and lateral connective tissues. The estimations of ISAs were known to be highly sensitive to noisy data, which may be mathematically ill-posed, requiring smoothing such as that conducted by regularization. The main contribution in this work was to establish the reciprocal connection between the KFA and Ground Reaction Forces (GRF) as a means to estimate joint constraint forces. Presented results compare the computational performance with published kinetic and kinematic joint data generated from an instrumented total knee replacement. Implications of these preliminary findings with respect to dynamic alignment as a functional anatomic metric are discussed.

Novel computational approaches characterizing knee physiotherapy

“…The blue arrow indicates the gait pathway. (Adapted from the original figure published in Kim et al [14]. )…”

“…We now need to prove if a knee has a freedom of the first order, then there is always one (and only one) screw φ for the GRF that determines the DOF of the knee. Thus a kinetic impulsive wrench on the knee will create a given screw α as the instantaneous screw axis (ISA) within the IAK [14].…”

“…In this review, we propose an information based control theory whereby human locomotion is neither triggered nor commanded, but controlled [27,49]. The basis for this control is the information derived from perceiving oneself in the world [13][14][15][16]. Central to this information-based approach will be the observed experimental sensory data [17].…”

The Knee Proprioception as Patient-Dependent Outcome Measures within Surgical and Non-Surgical Interventions

“…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)).…”

Tibial Femoral Tunnel for Isokinetic Graft Placement Based on a Tensegrity Model of a Knee

“…Knee functional axis information is referred to the knee instantaneous axis (KIA) Figure 1. The tensegrity structure of surrounding forces applied to the knee joint: a native system of the knee where six constraints $΄ are collectively reciprocal to the KIA $ indicated by ⊗ that the virtual coefficient should vanish is necessary, and sufficient conditions [9,10] [12][13][14]. In that case, the intersegmental force such as ligaments and contact forces are in pure tension/compression and are surrounding the KIA in such a way that those forces result in no (virtual) works [9,10].…”