Introduction

The generation of human arm movements requires the nervous system to determine a spatial path for the fingertip, a time-varying arm configuration, and a feasible muscle-tension distribution across redundant muscles. Previous computational models have mainly focused on the trajectory and posture components of this problem, including the minimum hand-jerk model (Flash and Hogan 1985), the minimum angular-jerk (AJ) model (Hogan 1984; Nakano et al. 1999; Wada et al. 2001), and the minimum torque-change (TC) model (Uno et al. 1989; Nakano et al. 1999). Although these models have contributed substantially to understanding movement selection, they do not specify how the required joint torques are implemented by individual muscles. To examine muscle recruitment, the optimization criterion must be formulated at the muscle level. Models such as the minimum muscle-tension-change (MTC) model (Dornay et al. 1996), the minimum motor-command-change model (Kawato 1996), and the minimum muscle-stress-change (MSC) model (Katayama 2025) provide such a framework because they compute muscle tensions while satisfying musculoskeletal constraints. Katayama (2025) showed that the MSC model could reproduce fingertip trajectories and arm postures in human three-joint reaching with accuracy comparable to, or better than, that of the AJ and TC models. Previous studies of these computational models have often used simplified arm models, such as a two-joint, six-muscle model (e.g., Katayama and Kawato 1993) or the three-joint, eight-muscle model used by Katayama (2025). These reduced models are useful for evaluating whether a computational model can reproduce arm movements at the level of fingertip trajectories and arm postures. However, because they include only a minimal set of agonist–antagonist muscle pairs, they are insufficient for examining how redundancy among many muscles is resolved or for predicting physiologically meaningful muscle recruitment. Thus, Katayama (2025) tested whether MSC-based optimization could reproduce arm movements using a three-joint, eight-muscle model with constant moment arms, but did not thoroughly investigate whether the model could generate anatomically interpretable recruitment patterns.

To predict muscle recruitment during arm movements, the arm model must include a number of muscles comparable to that in the human musculoskeletal system. High muscular redundancy is particularly important because many muscles act around the same joint and multiple muscles with similar functional roles coexist. However, increasing only the number of muscles is not sufficient. The model must also represent anatomical differences among muscles, especially differences in physiological cross-sectional area (PCSA) and moment arm. Accurate PCSA and moment-arm values are therefore essential for evaluating muscle recruitment predicted by the MSC framework. PCSA values determine how muscle stresses are computed, whereas moment arms determine how muscle tensions generate joint torques. Because moment arms change with joint angle during movement, joint-angle-dependent moment arms are required for realistic evaluation of muscle recruitment. A more detailed musculoskeletal arm model is consequently needed to evaluate whether a computational principle can select muscle recruitment patterns that reflect the balance among muscles with different PCSAs and angle-dependent moment arms.

Accordingly, the present study evaluates the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {MSC}_2$$\end{document}MSC2, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {MSC}_3$$\end{document}MSC3, MTC, combined \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {MTC}_s$$\end{document}MTCs, and minimum muscle-torque-change (MTRC) models using anatomically detailed three-joint arm models, with the AJ model used as a benchmark for evaluating the reproducibility of arm movements. Model performance was assessed at three levels: task space (fingertip trajectories), joint space (arm postures and the direction-dependent wrist-joint contribution, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_w$$\end{document}Cw), and the muscle level (muscle recruitment and sensitivity to PCSA and moment-arm values). The present study therefore extends the work of Katayama (2025) from movement-level reproduction with a three-joint, eight-muscle arm model to muscle-recruitment prediction with anatomically expanded arm models.