Extending the Law of Intersegmental Coordination: Implications for Powered Prosthetic Controls

Powered prostheses are capable of providing net positive work to amputees and have advanced in the past two decades, yet reducing amputee metabolic cost of walking remains an open problem. This work develops a method to analyze intersegmental coordination for lower-limb 3D kinematic data and extends the Law of Intersegmental Coordination (ISC) to a new law of coordination of moments, finding that while elevation angles remained planar in amputee gait, the Elevation Space Moments (ESM) lacked planar coordination.

Analysis of Intersegmental Coordination

The paper addresses the Law of Intersegmental Coordination (ISC), which states that the elevation angles of the thigh, shank and foot over the gait cycle covary. The researchers developed a method to analyze this for lower-limb 3D kinematic data by transforming reported joint angles into elevation angles. They then performed Principal Component Analysis (PCA) on these elevation angles to evaluate intersegmental coordination, defining the Planarity Index (PI) as the variance accounted for by the first two PCs. The study compared Able Bodied (AB) individuals with Transfemoral Amputees (TFA), finding that while covariation of elevation angles occurs in amputee gait, it is altered with respect to AB subjects.

Extension to Elevation Space Moments (ESM)

Inspired by the relationship between joint moments and Total Support Moments, the authors hypothesized that joint moments in a transformed elevation angle space will also covary as do elevation angles. They defined an Elevation Space Jacobian (J) to transform anatomical joint velocities into segment elevation velocities. This allowed them to map anatomical joint moments (τ) to their projected moments in the elevation angle space (M) using the relation: M = (JT(q))† τ. They quantified coordination in this new space using the Planarity Index for ESMs, finding that while AB gait showed a strikingly high level of coordination between the moments, TFA subjects demonstrated a lack of coordination in their ESMs.

Constraint-Based Prosthetic Control Framework

The authors propose an ISC-driven powered prosthetic control framework. This approach uses healthy coordination as a constraint to predict the shank angles/moments to compensate for alterations due to a passive foot. Specifically, they define constraints based on the elevation angle CVP and elevation space moments CVP: gα(αt,αs,αf) = 0 and the elevation space moments CVP as gM(Mt,Ms,Mf) = 0. The desired shank angle/moment profile is then found by solving equations (15) and (16), which can be utilized for compensation in a powered knee controller.

Key Findings on Coordination

The analysis revealed distinct differences between conditions:

1. For elevation angles, the PI showed "high mean values of > 99% showing clear dimensionality reduction" across all conditions, largely due to shank-foot coordination.

2. Shank-foot coordination for the amputated leg showed a distinct difference, with a slope and bias that differed from AB subjects; for the passive leg, it implied the shank and foot moved as rigid bodies.

3. For ESMs, AB gait exhibited high mean PI (> 99%), whereas TFA legs showed substantially decreased planarity in their ESMs compared to AB subjects.

Conclusion and Future Directions

The work presents a novel method for transforming joint angles to elevation angles, which enables the transformation of joint moments into Elevation Space Moments (ESM), extending ISC from kinematics to dynamics. The results suggest that altered coordination between the residual limb and prosthesis segments is the cause of inefficient gait and elevated energy expenditure. The authors suggest an ISC-driven control method where a powered knee actively controls for coordination using healthy thigh behavior as a constraint, aiming to shift focus from mimicking healthy gait at a single joint level toward mimicking healthy coordination between the residual limb and the prosthesis. They also plan to test the effect of perturbing ISC and we will also include assessments of metabolic cost of transport.

ISC3d Toolbox

The researchers developed an ISC3d toolbox that is freely available online, which may be used to compute kinematic and kinetic ISC in 3D, providing a means to further study the role of coordination in gait. The framework suggests that intersegmental coordination may represent an objective function of the Central Nervous System (CNS) for reducing the dimensionality of gait. This extension from kinematics to dynamics presents what may be the first result towards a unified theory of dynamic coordination.

Sign Conventions and Definitions

The paper details specific mathematical formulations, including:

1. The transformation of joint angles (e.g., pelvis, thigh, shank) into segment frame orientations using rotation matrices (Equations 2-5).

2. The calculation of the elevation angular velocity vector using skew-symmetric matrices (Equation 6).

As a fastidious and diligent researcher, I have analyzed this paper, Extending the Law of Intersegmental Coordination: Implications for Powered Prosthetic Controls. The core contribution is extending the Law of Intersegmental Coordination (ISC) from kinematic elevation angles to dynamic Elevation Space Moments (ESM) and proposing an ISC-driven control framework.

Here are specific, actionable improvements for AI systems based on this research, detailing what the improved system can achieve:

) Improvements to AI Systems Based on This Research:

1. Development of a Physics-Informed Kinematic/Dynamic Model for Gait Coordination (ISC3D Toolbox):

2. Implementation of an ISC-Constrained Mid-Level Control Framework for Powered Prosthetics:

3. Creation of a Predictive Compensatory Controller for Passive Prosthetic Alterations:

) Specific Capabilities of the Improved AI Systems:

1. Physics-Informed Kinematic/Dynamic Model (ISC3D Toolbox):

2. The AI system will incorporate the transformation methods described in Section II-C (converting joint angles to elevation angles) and Section II-D (defining the Elevation Space Jacobian, J) into a reusable, computationally efficient mathematical framework.

3. It can perform real-time calculation of kinematic metrics like Principal Component Analysis (PCA) scores and Planarity Index (PI) on 3D gait data to quantify intersegmental coordination in both able-bodied and amputee subjects.

4. Crucially, it will implement the novel mapping from anatomical joint moments to Elevation Space Moments (ESM) using Equation (11), allowing for dynamic analysis of coordination beyond simple kinematics.

5. ISC-Constrained Mid-Level Control Framework:

6. The AI system will be capable of taking desired healthy gait profiles (e.g., mean thigh angle/moment from AB subjects) as a constraint within its control loop, defined by the CVP equations in Section II-F:

7. It can dynamically solve for the required shank angle and moment profiles based on these constraints, ensuring that compensatory movements are minimized. This allows the system to explicitly control for coordination rather than implicitly relying on phase-based parameterization alone.

8. Predictive Compensatory Controller:

9. The AI system will use the established healthy CVP as a reference and, when encountering alterations caused by a passive prosthetic component (e.g., an altered foot), it can predict the necessary shank angle/moment profile to maintain coordination with the thigh and foot components, as demonstrated in Section III-E (Figure 11).

10. Specifically, during terminal stance or early swing, the AI can proactively adjust joint commands to reduce undesirable shank moment magnitudes while ensuring compliance with the healthy elevation angle CVP trajectory.

11. Unified Dynamic Coordination Analysis:

12. By extending ISC from kinematics (angles) to dynamics (moments), the improved system can provide a unified assessment of coordination in both spaces, allowing researchers and engineers to determine if coordination is a kinematic result or a dynamic control objective within human motor systems.

Powered prostheses are capable of providing net positive work to amputees and have advanced in the past two decades. However, reducing amputee metabolic cost of walking remains an open problem. The Law of Intersegmental Coordination (ISC) has been observed across gaits and previously implicated in energy expenditure of walking, yet it has rarely been analyzed or applied within the context of lower-limb amputee gait. This law states that the elevation angles of the thigh, shank and foot over the gait cycle covary. In this work, we developed a method to analyze intersegmental coordination for lower-limb 3D kinematic data, to simplify ISC analysis. Moreover, inspired by motor control, biomechanics and robotics literature, we used our method to extend ISC to a new law of coordination of moments. We find these Elevation Space Moments (ESM), and present results showing a moment-based coordination for able bodied gait. We also analyzed ISC for amputee gait with powered and passive prostheses, and found that while elevation angles remained planar, the ESM lacked planar coordination. We present an ISC-driven powered prosthetic control framework, using healthy coordination as a constraint to predict the shank angles/moments to compensate for alterations due to a passive foot. We developed the ISC3d toolbox that is freely available online, which may be used to compute kinematic and kinetic ISC in 3D. This provides a means to further study the role of coordination in gait and may help address fundamental questions of the neural control of human movement.