Mechanochemical modeling of exercise-induced skeletal muscle hypertrophy

Figures

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  Fig 1. Conceptual overview of exercise-induced muscle adaptation and the modeling framework. (A) Different exercise types are characterized by distinct patterns of muscle activation, leading to physiological adaptations and ultimately affecting muscle performance. Here, “progress” refers to improvements in physical performance (strength), which is driven initially by rapid neural adaptations and later by structural muscle growth. (B) In this work, we focus on the IGF1-AKT signaling pathway, which is a key regulator of muscle hypertrophy. Mechanical stimuli through exercise activate IGF1, which in turn activates AKT. AKT promotes protein synthesis via mTOR and inhibits protein degradation via FOXO. (C) Schematic of the proposed multiscale model, coupling a signaling model with tissue-level mechanics to predict exercise-induced muscle growth. Abbreviations: CSA: cross-sectional area; IGF1: insulin-like growth factor 1; AKT: protein kinase B; mTOR: mechanistic target of rapamycin; FOXO: forkhead box transcription factor. Figure partially created in BioRender. Rangamani, P. (2026) [https://BioRender.com/wfzzhb7].

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  Fig 2. Computational model components and workflow. (A) The passive and active fiber forces are dependent on stretch λ. (B) A muscle contraction, showing the inactive (α=0) and active (α>0) states. (C) Illustration of one week of the three exercise protocols used in growth simulations. (D) The coupling scheme between signaling and growth mechanics used in our computational framework. The exercise model determines an incremental growth tensor 𝐆k, which updates the mechanical model through the cumulative growth framework. The resulting cross-sectional area ACS feeds back to modulate the signaling model via the protein synthesis rate kM. (E) Schematic of the cumulative growth framework, based on the multiplicative decomposition of deformation, 𝐅=𝐀𝐆. Between growth steps, computational unloading (𝐀1−1, green pathway) is required to avoid applying new deformation to a residually stressed state ν2 (red arrow). (F) Example geometries showing the computational mesh, surfaces for boundary conditions (Γtop,Γbottom), and prescribed fiber architecture.

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  Fig 3. Dynamics of the IGF1-AKT signaling model in response to different exercise protocols. (A–E) Time courses of the normalized populations (A) IGF1, (B) AKT, (C) FOXO, (D) mTOR, and (E) myofibrils N for three different exercise protocols. Insets in (A) and (B) display a zoomed-in 24-hour time window to highlight the rapid transient spikes in IGF1 and AKT signaling. (F) Sobol sensitivity analysis quantifying the influence of each model parameter on the final myofibril number obtained using a standardized daily exercise protocol. The plot shows the mean Sobol index versus its standard deviation for each parameter. Marker colors identify the associated signaling molecule, with split colors indicating coupling parameters.

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  Fig 4. Coupled model simulation of exercise-induced hypertrophy in an idealized fusiform muscle. (A) Fiber orientation a0 computed from a spline expression. (B) Mechanical state variables (displacement, fiber stretch λ, and fiber stress) at zero and full activation (α=1). (C–E) Predicted time courses of cross-sectional area, muscle volume, and the protein synthesis rate kM in response to three distinct exercise protocols. (F) Final muscle configurations after the simulation period for each protocol, with the growth-induced displacement amplified 10x for visualization.

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  Fig 5. Realistic muscle geometries derived from the Visible Human dataset. (A) Anatomical placement of the semitendinosus (ST), biceps femoris long head (BFLH), and tibialis anterior (TA) muscles, visualized within the Visible Human Female. (B) Comparison of computed muscle volumes and cross-sectional areas for the twelve meshes derived from the bilateral ST, BFLH, and TA muscles of the Visible Human Female and Male. (C) Fiber arrangements generated using Stokes flow simulations within meshes derived from the surface geometries shown in (A). Labels indicate gender (F: Female, M: Male) and laterality (L: Left, R: Right).

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  Fig 6. Coupled model simulation of exercise-induced hypertrophy in realistic muscle geometries. (A) Final muscle configurations of the female left biceps femoris long head (BFLH) following the simulation period for each exercise protocol. Growth-induced displacements are amplified 10x for visualization. (B) Predicted temporal evolution of the protein synthesis rate (kM) in response to three distinct loading protocols (shown for the female left BFLH geometry). (C–D) Predicted final CSA and volume after three protocols in the BFLH, ST, and TA muscles. Error bars indicate standard error.

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  Fig 7. Impact of signaling parameter heterogeneity on local and global growth dynamics. (A) Predicted time courses of the local ODE states (IGF1, AKT, FOXO, mTOR, and myofibril population N). Heterogeneity was introduced by sampling rate parameters (ai, bi, cij) from uniform distributions within ±1% of their baseline values. Gray lines and shading indicate the mean ±1 standard deviation across five samples; the dashed blue line represents the baseline uniform case. (B) Predicted evolution of normalized cross-sectional area (CSA), normalized volume, and the protein synthesis rate kM under the MWF protocol (colors as in A). (C) Spatial maps of final myofibril density (N), local volume change (J), and growth-induced displacement magnitude (amplified 10x) for the uniform case versus a representative heterogeneous sample.