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Effects of muscle mass on muscle force predictions in human movement

Chen Ing-Jeng, Ameur LatrecheiD, Stephanie A. RossiD, Javier A. AlmonacidiD, Taylor J. M. DickiD, Evie VereeckeiD, James M. WakelingiD

Abstract

Muscle mass significantly influences skeletal muscle behaviour, potentially explaining why traditional massless Hill-type models struggle to predict the forces generated by larger muscles during dynamic, submaximal contractions. However, the applicability of mass-enhanced Hill-type models in human locomotion remains unexplored. Here, we compared the predicted force from a 1D mass-enhanced Hill-type muscle model with a traditional 1D massless Hill-type muscle model across a range of experimentally measured human movements. Kinematic and electromyographic data were collected from twenty participants performing locomotor tasks and supplemented with existing cycling data. Muscle size was geometrically scaled by factors from 0.1 to 10, which causes lengths to be scaled proportionally, cross-sectional area and peak isometric force F0 with the square, and mass with the cube of the factor. Muscle tissue mass (inertia) and cadence increased the differences between mass-enhanced and massless predictions of force and power. At high cadence and the largest scale, the normalized root mean square difference between force traces reached 7% of F0, (averaged across muscles). However, differences between models were minimal (<1%) at human-sized scale 1. Real muscle additionally deforms in 3D, we still do not know the extent to which this extra dimensionality affects muscle forces for these human movements.

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Claude Opus 5.5 · xhigh effort · 8 Nov 2026 · from the full text of version 2 (2 May 2026) · CC BY 4.0

Adding distributed muscle mass to 1D Hill-type models alters predicted human leg-muscle forces by under 1% at natural size; differences grow with scale and cadence.

Standard 1D Hill-type models used in musculoskeletal simulation ignore tissue mass, even though inertia scales with volume while force capacity scales with cross-sectional area, and earlier mass-enhanced models were never applied to human-sized muscles in everyday tasks. This work measures how much omitting mass biases force, power and work predictions across real human movements and across geometrically scaled muscle sizes.

Key results

  1. ShownIn these 1D simulations, adding tissue mass barely changed the predicted forces of human-sized muscles. Mass-enhanced and massless force traces nearly coincided at natural and reduced scale, especially in slow daily activities.

    Massless predictions did not vary beyond numerical error at scales 0.1, 1 and 10. Mass-enhanced traces overlapped them at scales 0.1 and 1. Between-model normalized force RMSD was <1% at human scale 1. · Abstract; Results; Discussion

  2. ShownThe gap between the models grew steadily with geometric muscle scale. This fits inertia (mass ∝ s^3) outpacing force capacity (∝ s^2), and the gap became notable only well above human size.

    In 140 rpm cycling, log RMSD rose monotonically with log scale factor for all tested muscles. At the largest scale and high cadence, RMSD reached 7% of F0 averaged across muscles. The peak was 7.23% (r^2 0.68) for vastus lateralis running at scale 10. Derived RMSD scaling ranged from scale^1.9 to scale^2. · Abstract; Results; Discussion; Relative effect of activation, mass and…

  3. ShownMovement cadence (muscle acceleration), not load, drove the divergence between models. Faster tasks and higher pedalling cadence increased RMSD, while raising crank torque, which mainly changes activation, did not.

    VL RMSD averaged across scales was 1.60±0.11, 2.47±0.20 and 3.33±0.21 % at 80, 100 and 140 rpm (13-14 Nm; P<0.05). Load from 14-44 Nm at 80 rpm had no significant effect. At scale 1, running, hopping and cycling exceeded walking and sit-to-stand (P<0.05). Errors exceeded 5 % at 140 rpm for 6^3-fold mass. · Results; Discussion; Figure legends

  4. SuggestedAs muscle mass increased, the mass-enhanced model predicted less volume-specific net work per cycling cycle, because positive work fell and negative work grew. The losses were steeper with higher cadence than with lower crank load.

    Massless model (44 Nm, 80 rpm), roughly constant across scales: VL net/positive/negative 5.49/10.50/−5.01 kJ m^−3 and SOL 2.37/6.47/−4.10 kJ m^−3. The mass-enhanced model matched these at scale factor 3 or less; beyond scale factor 4, positive work decreased and negative work magnitude increased. · Results; Figure legends

  5. ShownVariation between participants significantly affected model differences in self-paced daily activities but not in tightly constrained cycling. Participant sex had no detectable effect.

    ANOVA on log-transformed RMSD: the participant factor was significant for daily activities but not for cycling. There was no significant sex effect across scales (Fig. S1). Preferred walking and running speeds were 0.73±0.20 and 1.51±0.30 m s^−1. · Results; Discussion; Figure legends

Methods, data and reproducibility

OpenSim inverse kinematics on participant-scaled models gave muscle-tendon unit lengths, and EMG gave activations. Both drove a massless Hill-type model and a mass-enhanced variant (16 in-series segments with point masses). Muscles were geometrically scaled (length s, force s^2, mass s^3), and force RMSD was tested by ANOVA.

  • Motion capture, ground reaction forces and lower-limb surface EMG (MG, LG, SOL, RF, VM, VL) during treadmill walking, running, hopping and sit-to-stand · human · n = 20 participants; 100 cycles per gait/hop task, 20 sit-to-stand
  • Previously reported cycling kinematics and EMG across five pedalling conditions (14, 26, 44 Nm at 80 rpm; 100 and 140 rpm at 13 Nm) · human · n = 14 competitive cyclists; 210 cycles
  • Participant-scaled OpenSim 4.3 musculoskeletal model parameters (optimal fibre length, tendon slack length, pennation) used to derive optimal MTU lengths · human
Methods & tools
OpenSim 4.3 (model scaling, Inverse Kinematics tool), IBM SPSS Statistics Version 27 (general linear model ANOVA), Massless 1D Hill-type muscle model, Mass-enhanced 1D Hill-type muscle model (16 point masses; Ross et al., 2018a), Optotrak Certus optical motion capture (NDI), 100 Hz, Norotrode bipolar Ag/AgCl surface EMG electrodes (Myotronics), Biovision EMG amplification and band-pass filtering, 2000 Hz sampling, Bertec FP6012-15 instrumented treadmill force plates, 300 Hz, Wavelet-based EMG intensity analysis, Bézier-curve force-length, force-velocity and tendon force-strain relationships
Reagents & environment
OpenSim 4.3 (Inverse Kinematics tool); IBM SPSS Statistics Version 27
Reproducibility gaps
No code or data availability statement or repository links are provided; the cycling dataset is reused from a prior study described elsewhere.
Limitations (6)
  • The findings come solely from simulations. Neither muscle forces nor mechanical work were validated experimentally, so in vivo magnitudes remain unconfirmed. · stated by the authors
  • Driving the models with prescribed muscle-tendon unit lengths from inverse kinematics blocks feedback from muscle dynamics to joint motion. Predictive simulations with antagonist restoring forces could reveal larger mass effects. · stated by the authors
  • The models assume zero pennation, a uniform non-dimensional tendon stiffness, uniform geometric scaling and a simple series elastic element. They therefore ignore dynamic pennation, architectural gearing and nonuniform aponeurosis strain, which limits generalization. · stated by the authors
  • The 1D models let mass move only along the muscle axis, omitting bulging and transverse or shear tissue acceleration. The authors note that the net in vivo effect could be larger or smaller than these estimates. · stated by the authors
  • Scaled muscles (up to s = 10) reuse human-derived kinematics, activations and intrinsic contractile properties. The large-scale results are therefore a sensitivity analysis, not predictions for real large-bodied muscles. · noted in this summary
  • ANOVA outcomes are reported only as P<0.05 thresholds, without F statistics, exact p-values or effect sizes. This makes it hard to judge the practical relevance of significant differences at scale 1. · noted in this summary

Who should read:Read this if you build Hill-type musculoskeletal simulations and need evidence on whether modelling muscle tissue mass changes force or work predictions for human gait, hopping or cycling.

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