# Pareto-Based Diagnostics and Selection for Mechanics–Synergy Trade-Offs in Unmeasured Muscle Activation Reconstruction

## TL;DR

This paper introduces a method to reconstruct unmeasured muscle activations by balancing mechanical accuracy and synergy patterns, improving diagnostics in sparse measurement scenarios.

## Contribution

A synergy-informed, physics-constrained framework with Pareto-based diagnostics for muscle activation reconstruction under sparse measurements.

## Key findings

- Using J1-dominant selections from the Pareto set reduces joint-moment error from 0.154 to ≈0.138 in synthetic Arm26 cases.
- Pareto diagnostics reveal identifiability and selection sensitivity in scenarios with sparse measurements and no ground truth.

## Abstract

Background: Reconstructing full muscle activation trajectories from sparse measurements is underdetermined: many activation patterns can explain similar joint moments, and purely mechanical inverse formulations can yield non-physiological solutions. Methods: We propose a synergy-informed, physics-constrained framework to reconstruct unmeasured muscle activations when only a subset of muscles is observed. A synergy reconstruction prior (SynRc) is obtained by identifying a synergy basis from proxy activations via non-negative matrix factorization (NMF) and estimating time-varying synergy excitations from measured channels. Unmeasured activations are then solved via bound-constrained multi-objective optimization that jointly minimizes (i) normalized joint-moment error between OpenSim forward-computed moments and inverse-dynamics moments and (ii) deviation from the SynRc prior, with an optional smoothness refinement stage. Results: Verification on synthetic OpenSim Arm26 (2-DOF) cases with known ground truth shows that J1-dominant selections from the stage-I Pareto set reduce normalized joint-moment error from 0.154 (SynRc-only) to ≈0.138, at the cost of larger deviation from the synergy prior. These Pareto diagnostics expose identifiability and selection sensitivity under sparse measurements when ground truth is unavailable. Conclusions: The proposed framework makes mechanics–synergy trade-offs explicit and provides structured diagnostics and selection guidance for sparse-measurement scenarios.