Flowchart of ABM rules. The model starts with initialization of the geometry and the prescribed injury. This is followed by recruitment of cells based on relative cytokine amounts within the microenvironment. The inflammatory cells, SSCs, and fibroblasts follow their literature defined rules and probability-based decision tree to govern their behaviors. The boxes represent the behavior that the agent completes during that timestep given the appropriate conditions and the circles represent the uptake that occurs as a result of the simulated binding with microenvironmental factors for certain cell behaviors. ABM, agent-based model; SSC, satellite stem cell; ECM, extracellular matrix; TGF-β, transforming growth factor β; HGF, hepatocyte growth factor; TNF-α, tumor necrosis factor α; VEGF-A, vascular endothelial growth factor A; MMP-9, matrix metalloproteinase-9; MCP-1, monocyte chemoattractant protein-1; IL-10; interleukin 10.

Overview of ABM simulation of muscle regeneration following an acute injury. A. Simulated cross-sections of a muscle fascicle that was initially defined by spatial geometry from a histology image. Muscle injury was simulated by replacing a section of the healthy fibers with necrotic elements. In response to the injury, a variety of factors are secreted in the microenvironment which impacts the behavior of the cells. The colors correspond with those typically seen in H&E staining. B. ABM screen captures show the spatial locations of the cells throughout the 28-day simulation. The agent colors were matched to those typically seen in IHC-stained muscle sections.

Neutrophil Agent Rules

Macrophage Agent Rules

SSC Agent Rules

Fibroblast Agent Rules

Fiber Agent Rules

Microvasculature Rules

Model parameters of spatial mechanisms

Model perturbation input conditions and corresponding published experimental results

Summary of cytokine sensitivity analysis. Significance was determined with α=0.05, and a Bonferroni correction for the number of tests. + and - represent statistically significant positive and negative correlations, respectively.

ABM calibration and validation. ABM parameters were calibrated so that model outputs for CSA recovery, SSC, and fibroblast counts were consistent with experimental data (A-C)77,102. Separate outputs from those used in calibration were compared to experimental data99,102,105,106 to validate the ABM (D-H). Error bars represent experimental standard deviation, and model 95% confidence interval is indicated by the shaded region. Cell count data were normalized by number of cells on the day of the experimental peak to allow for comparison between experiments and simulations.

ABM perturbation outputs are compared to various literature experimental results. Each perturbation model output is compared to the available corresponding published result. The top triangles indicate the literature findings and the bottom triangles indicate the model outputs. Red triangles represent a decrease, blue represents an increase, and gray represents no significant change. Time points of comparison were based on which time points were available from published experimental data.

Dose dependent response with VEGF-A injection compared to hindered angiogenesis. VEGF-A concentration response to varied levels of VEGF injection (A). Hindered angiogenesis resulted in slower and overall decreased CSA recovery (B). Capillary count was dependent on VEGF-A injection level (C). Total macrophage count was similar between control and VEGF-A injections perturbations but macrophage count was higher in later time points in the hindered angiogenesis simulation (D). SSC peak varied with VEGF-A injection level and counts were prolonged in the hindered angiogenesis simulations (E). The fibroblast peak was lower for the hindered angiogenesis perturbation and highest with the extra high VEGF-A injection. In contrast to the other simulations, the fibroblast count was trending upwards at later time points in the hindered angiogenesis perturbation (F). HGF levels were consistent between control and VEGF-A injection perturbations but was significantly elevated in the hindered angiogenesis perturbation (G). MCP-1, TGF-β, and IL-10 concentrations were elevated a later stages of regeneration with hindered angiogenesis (H, I, L). TNF-α was elevated with the extra high VEGF-A injection and lower with hindered angiogenesis (J). MMP-9 concentration was lower at the simulation midpoint but elevated at late regeneration stages (K).

Heatmaps of changes in cytokine concentration at various timepoints throughout regeneration following individual cytokine knockout (KO) demonstrating cross-talk between cytokines. With MCP-1 KO there was an increase in all cytokines except VEGF-A at 12 hours post injury. Over the course of regeneration there was continued increasing elevation of HGF, increases in VEGF-A, and TGF-β decreased at day 7 followed by a strong increase by day 28 post injury (A). In the TNF-α KO simulations, there was an early decrease in TGF-β that shifts to strong increases by day 28. MMP-9 increased throughout the duration, HGF and IL-10 were decreased, VEGF-A lagged in the beginning but was increased during mid to late timepoints (B). Following IL-10 KO there were increases in TNF-α, decreases in HGF and TGF-β, and elevated MMP-9 at day 7 that decreased by day 28 (C).

Combined alterations of various cytokine dynamics enhance muscle regeneration outcomes. All tested alterations except higher MCP-1 decay resulted in higher CSA recovery compared to the control (A). M1 cell count was higher for all perturbations with the highest peaks with increased MCP-1 diffusion and the combined cytokine alteration perturbation (B). Higher MCP-1 decay resulted in the largest M2 peak and higher MCP-1 diffusion, higher TGF-β decay, and the combined cytokine alteration had a lower M2 peak than the control (C). Fibroblasts had the largest increase in cell count with the higher TGF-β decay and the cytokine combination perturbations (D). All perturbations resulted in an increased in SSC count with the largest increase resulting from the combined cytokine alteration (E). All perturbations except the combined and higher MMP-9 decay resulted in increased capillaries as a result of additional capillary sprouts (F).

Overview of Calibration Methods. Latin hypercube sampling is used to generate 600 unique parameter sets given starting bounds, each of which was run in triplicate. The simulations were filtered given specified criteria (i.e. fitting within experimental bounds for CSA recovery) and then alternative density subtraction (ADS) was used to narrow in the parameter bounds. Partial rank squared correlation coefficient (PRCC) was used to gain insight into model sensitivity and adjust the bounds in case initial parameter bounds were too wide or too narrow. This method also allowed for model rule execution refinement to correct cases that interfere with the dynamics of other cell types.

Unknown model parameters calibrated using LHS to recapitulate published literature

Criteria utilized for CaliPro model calibration

PRCC plots for various model outputs over time to illustrate how the significance of cytokine decay and diffusion parameters varies at different points throughout regeneration. Black dots indicate statistically significant (P < 0.05) correlation for that timepoint. (A) CSA recovery had correlations with HGF, TGF-β, and MMP-9 decay. (B) SSC count was correlated with HGF, TGF-β, MMP-9 decay and MCP-1 and TND diffusion. (C) Fibroblast count was correlated with HGF, TGF-β, MMP-9, and TNF-α decay. (D) HGF, TGF-β, MMP-9, VGEF decay and MCP-1 diffusion were correlated with the number of non-perfused capillaries. (E) Myoblast cell count was correlated with HGF, TGF-β, MMP-9, and IL-10 decay. (F) Myocyte cell count was correlated with HGF, TGF-β, and MMP-9 decay and TNF-α diffusion. (G) HGF and MCP-1 decay as well as MCP-1 diffusion were correlated with neutrophil count. (H) M1 macrophage cell count was correlated with TGF-β, VEGF-A, IL-10, and MCP-1 decay and MCP-1 diffusion. (I) M2 macrophage count was correlated with HGF, TGF-β, MMP-9, TNF-α, VEGF-A, MCP-1 decay and MCP-1 diffusion.

Cytokine concentrations are correlated with cell counts and recovery metrics at various stages of regeneration. There is an optimal MCP-1 concentration that tends to result in higher M1 counts 1 day post injury (A). IL-10 concentration is positively correlated with M2 count 3 days post injury (B). VEGF-A concentration is negatively correlated with the number of fragmented (non-perfused) capillaries 5 days post injury (C). Higher TGF-β concentrations tends to result in lower SSC cell count 7 days post injury (D). Fibroblasts cell count is highest at an optimal TNF-α concentration with higher or lower levels hindering cell count 14 days post injury (E). HGF concentration is positively correlated with CSA recovery at day 28 post injury but there appears to be a threshold where high HGF is no longer correlated with increased recovery (F).

Cytokine perturbations based on PRCC

Non-perfused capillaries for each cytokine perturbation. The combined cytokine perturbation had the lowest number of non-perfused capillaries and all other perturbations resulted in less non-perfused capillaries compared to the control.