Supplementary code: Mechanochemical modeling of exercise-induced skeletal muscle hypertrophy

Supplementary code: Mechanochemical modeling of exercise-induced skeletal muscle hypertrophy#

This repository contains the implementation of the coupled signaling-mechanics model of exercise-induced skeletal muscle growth described in the paper

Devold, I. S., Rognes, M. E. & Rangamani, P. Mechanochemical modeling of exercise-induced skeletal muscle hypertrophy. bioRxiv (2025) DOI: 10.64898/2025.12.17.694686.

The framework couples a tissue-level transversely isotropic hyperelastic model with a system of ODEs representing the IGF1-AKT-mTOR-FOXO signaling pathway. This multiscale approach links exercise-driven cellular signaling events to macroscopic volumetric growth.

Key Features

ODE signaling model: Simulates protein synthesis/degradation via IGF1, AKT, mTOR, and FOXO dynamics
Finite element mechanical model: Hyperelasticity with volumetric growth kinematics
Bidirectional coupling: Signaling drives growth tensor; muscle cross-sectional area modulates protein synthesis rate
Geometries: Supports both idealized and anatomically realistic meshes (from the Visible Human Dataset)

Installation and Dependencies#

The project is based on FEniCSx v0.10.0. The workflow management system Snakemake is used to run scripts and reproduce the paper results.

FEM & numerics: fenics-dolfinx, openmpi, scipy, numpy
Mesh & I/O: gmsh, meshio, adios2, adios4dolfinx
Plotting: matplotlib, seaborn, scienceplots, pyvista
Utilities: pyyaml, typer, imageio, imageio-ffmpeg
Sensitivity analysis: SALib, tqdm
Workflow: Snakemake

These dependencies are listed in environment.yml, and additionally in environment_pinned.yml with versions pinned.

Conda#

Set up the main Conda environment musclex with all required dependencies, including the musclex package from this repository with:

conda env create -f environment.yml

This should take around 1 minute.

Additionally, for workflow management, we set up a separate environment for Snakemake (and its cluster plugin if running on HPC systems like eX3):

conda create --name snakemake_env -c conda-forge -c bioconda snakemake snakemake-executor-plugin-cluster-generic

Docker#

Alternatively, the latest Docker image containing musclex and its dependencies can be pulled as:

docker pull ghcr.io/ingvilddevold/muscle-growth:main

Usage#

Reproducing Paper Results#

The workflow is organized into four distinct Snakefiles in scripts/, each corresponding to a Results section and figure from the paper.

Before running, activate the snakemake_env:

conda activate snakemake_env

Run the specific Snakefile for the desired figure. Snakemake will automatically activate the musclex environment for computational rules.

Snakefile	Description	Figure
`Snakefile_signaling.smk`	Signaling Dynamics (ODE only) Simulates the time evolution of IGF1, AKT, FOXO, and mTOR under three exercise protocols (MWF, Weekly, Every-3-days).	Fig. 3
`Snakefile_idealized.smk`	Muscle Growth in Idealized Geometry Runs the full coupled model on an idealized fusiform geometry. Outputs include time-courses for Cross-Sectional Area (CSA), Volume, and the feedback-regulated protein synthesis rate \(k_M\), as well as the full 3D displacement data.	Fig. 4
`Snakefile_realistic.smk`	Realistic Geometries Simulates growth across 12 anatomically realistic meshes derived from the Visible Human Dataset (Biceps Femoris Long Head, Semitendinosus, Tibialis Anterior).	Fig. 6
`Snakefile_heterogeneity.smk`	Signaling Heterogeneity Runs an ensemble simulation with spatially perturbed signaling parameters (IGF1, AKT, FOXO, mTOR) to assess the impact of local biological variability on macroscopic tissue deformation. Uses the female left BFLH geometry and the MWF protocol.	Fig. 7

Running the Snakefiles#

To run on a cluster with Slurm, use the provided profile (or a similar profile adapted to your system):

snakemake -s scripts/Snakefile_XYZ.smk --profile scripts/ex3

To run locally, use Conda and specify the number of cores:

snakemake -s scripts/Snakefile_XYZ.smk --use-conda --cores 4

Note: Snakefile_realistic.smk and Snakefile_heterogeneity.smk are intended for HPC (eX3) due to long run times. For local runs, especially for plotting, you may need to remove xvfb-run commands.

Demo Scripts#

The following standalone demo scripts are available in demos/ and illustrate how to interact with the framework.

Script	Description	Expected run time
`demo_signaling_model.py`	Signaling model simulation for an example exercise protocol.	< 10 sec
`demo_muscle_contraction.py`	Muscle contraction in an idealized fusiform geometry.	~ 1.5 min
`demo_coupled_model.py`	Coupled signaling-mechanics model in an idealized fusiform geometry.	~ 5 min

These can be run on a standard laptop as

conda activate musclex
python demo_XYZ.py

and are also available as tutorials in the docs, illustrating the expected outputs.

The demo scripts can be readily adapted, for example by changing the geometry in use or adjusting the driving exercise protocol.

Realistic Muscle Geometries#

The realistic muscle geometries used in this study were derived from the Visible Human Dataset as processed by Andreassen et al. (2023). A copy of the original surface geometries is included under data/VHF_surfaces (female) and data/VHM_surfaces (male), while the processed meshes and fiber fields required to run Snakefile_realistic.smk are available in the meshes/ directory. These processed geometries include the Biceps Femoris Long Head, Semitendinosus, and Tibialis Anterior muscles, with four instances of each (male and female, left and right).

Data License & Attribution#

The geometry data included in data/ are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). Accordingly, please attribute the original datasets to the following works:

Andreassen, T. E., et al. (2023). Three Dimensional Lower Extremity Musculoskeletal Geometry of the Visible Human Female and Male. Scientific Data, 10. DOI: 10.1038/s41597-022-01905-2

Andreassen, T. E., et al. (2024). “Automated 2D and 3D finite element overclosure adjustment and mesh morphing using generalized regression neural networks.” Medical Engineering & Physics, 126. DOI: 10.1016/j.medengphy.2024.104136

Note: The software code in this repository remains licensed under the MIT License.