Agent-based model illustrates the role of the microenvironment in regeneration in healthy and mdx skeletal muscle

Abstract

Duchenne muscular dystrophy (DMD) is a progressive muscle-wasting disease with no effective treatment. Multiple mechanisms are thought to contribute to muscle wasting, including increased susceptibility to contraction-induced damage, chronic inflammation, fibrosis, altered satellite stem cell (SSC) dynamics, and impaired regenerative capacity. The goals of this project were to 1) develop an agent-based model of skeletal muscle that predicts the dynamic regenerative response of muscle cells, fibroblasts, SSCs, and inflammatory cells as a result of contraction-induced injury, 2) calibrate and validate the model parameters based on comparisons with published experimental measurements, and 3) use the model to investigate how changing isolated and combined factors known to be associated with DMD (e.g., altered fibroblast or SSC behaviors) influence muscle regeneration. Our predictions revealed that the percent of injured muscle that recovered 28 days after injury was dependent on the peak SSC counts following injury. In simulations with near-full cross-sectional area recovery (healthy, 4-wk mdx, 3-mo mdx), the SSC counts correlated with the extent of initial injury; however, in simulations with impaired regeneration (9-mo mdx), the peak SSC counts were suppressed relative to initial injury. The differences in SSC counts between these groups were emergent predictions dependent on altered microenvironment factors known to be associated with DMD. Multiple cell types influenced the peak number of SSCs, but no individual parameter predicted the differences in SSC counts. This finding suggests that interventions to target the microenvironment rather than SSCs directly could be an effective method for improving regeneration in impaired muscle.

NEW & NOTEWORTHY A computational model predicted that satellite stem cell (SSC) counts are correlated with muscle cross-sectional area (CSA) recovery following injury. In simulations with impaired CSA recovery, SSC counts are suppressed relative to healthy muscle. The suppressed SSC counts were an emergent model prediction, because all simulations had equal initial SSC counts. Fibroblast and anti-inflammatory macrophage counts influenced SSC counts, but no single factor was able to predict the pathological differences in SSC counts that lead to impaired regeneration.

INTRODUCTION

Duchenne muscular dystrophy (DMD) is an X-linked recessive disorder caused by a mutation in the dystrophin gene, resulting in incomplete translation of the transmembrane protein dystrophin (31, 36, 37). The lack of dystrophin makes the muscle more susceptible to contraction-induced damage and alters cell signaling processes, leading to a state of chronic inflammation (66, 80, 89). As the disease progresses, chronic damage and impaired regenerative capacity lead to muscle wasting as the contractile muscle tissue is replaced by fibrotic tissue and fatty infiltrate (35). Recent experiments have also shown that without dystrophin, satellite stem cells (SSCs) undergo impaired asymmetric division resulting in either senescent cells or decreased differentiated myocytes (19). Despite extensive experimental research, there remains no cure for this disease. One of the reasons DMD is so challenging to treat is that all these mechanisms are hypothesized to contribute to the pathophysiology of the disease. Therefore, it is difficult to discern which cells and mechanisms would be the best targets for therapies.

Because impaired muscle regeneration is thought to drive disease progression in DMD, preclinical testing of potential treatments often utilizes a skeletal muscle injury and regeneration assay. Muscle regeneration, even in healthy muscle, is a complex, dynamic process involving numerous cell types, including SSCs, fibroblasts, and inflammatory cells. The inflammatory cell behaviors following injury have been well defined in the literature and serve to breakdown debris and release growth factors that promote the downstream repair process (3, 12, 70, 87). A less well defined but critical aspect of regeneration is the codependent interaction of SSCs and fibroblasts. Work by Murphy et al. (55) has shown that both SSCs and fibroblasts are necessary for complete muscle regeneration. Fibroblasts and SSC counts peak approximately 3 to 7 days after injury (33, 55). The SSCs divide to maintain the stem cell pool and differentiate into myocytes to repair the injured muscle (20, 39, 102).

Translating successful preclinical therapies in animal models, such as the mdx mouse, to humans is a critical barrier in developing effective therapies for DMD (28, 98). One challenge is the less severe phenotype in the mdx mouse compared with humans (54, 60). Furthermore, the temporal variations in disease phenotype as the mdx mouse ages, coupled with the multifaceted nature of DMD, make the results of experimental studies challenging to interpret. Therefore, we believe this is an opportunity to use computational models to aid experimental design and interpretation. We aim to develop a computational model to examine the interactions between these complex mechanisms of disease in a way that would be prohibitively difficult using experimental tools alone.

The extensive literature on muscle disease and regeneration provides a data-rich field to develop and test these computational models (5, 16, 57, 58, 60, 66, 88, 89, 97). A few recent computational models have made use of this wealth of information to examine specific aspects of disease in dystrophic muscle (15, 32, 90). We previously created micromechanical finite element models that examined the importance of the mechanical properties of the extracellular matrix (ECM) in determining the damage susceptibility of the muscle (90). Other studies used mathematical models to explore the extent to which the immune response in the mdx mouse contributes to the muscle degeneration and regeneration (15, 32). However, these previously published models were not developed to simulate the interactions between multiple mechanisms of disease in DMD. Therefore, we developed a new computational model to study the cellular pathophysiology contributing to muscle damage and regeneration in mdx mice. The specific goals of this work were to 1) develop a computational model to predict mouse muscle regeneration following injury that focuses on the dynamics of SSCs and fibroblasts, 2) tune the model such that it replicates key cell population dynamics from experimental studies in the literature, and 3) use this model to analyze how known changes in the microenvironment contribute to impaired muscle regeneration in computational models of healthy and mdx mice.

METHODS

Overview of approach to developing the agent-based model.

There are extensive experimental studies that investigate the roles of individual factors, such as signaling molecules and cell types, on muscle regeneration following injury. The challenge of developing this model was to synthesize all these skeletal muscle regeneration studies to predict how muscle regeneration emerges from the behaviors and interactions of the various cell types in the muscle. To simulate these behaviors we utilized an agent-based model (ABM). ABMs simulate the actions of autonomous agents to analyze their effects on the system as a whole, providing an ideal platform for studying complex cellular dynamics (8, 26, 48, 68, 82, 84).

To develop our model of regeneration following contraction-induced injury, we used over 100 published experimental studies to define over 40 rules (outlined in Agent action overview) that govern the behaviors of muscle, SSC, fibroblast, and inflammatory cell agents. We determined that there were 13 model parameters that could not be determined from experimental data in the literature (unknown parameters will be addressed in Baseline model parameterization). To determine these parameters, we ran simulations and varied the unknown parameters within a physiologic range. The parameter values were determined based on the predictions that best replicated 1) cell counts and muscle fiber cross-sectional area (CSA) for healthy muscle and 2) the results of healthy muscle perturbation studies published in the literature. This process revealed that only a very specific combination of parameter values could provide predictions that met both criteria.

ABM design.

The ABM spatially represented a cross-section of a mouse lower limb muscle consisting of ~50 muscle fibers (Fig. 1). We chose to model mouse muscle so that we could leverage the literature describing experimental studies performed in healthy and mdx mice. Our ABM simulated the cellular behaviors governing muscle regeneration following an acute injury, as this is a common assay used to study regeneration experimentally. We defined an acute muscle injury as an injury induced by a single intervention (e.g., eccentric-contraction, freeze injury, cardiotoxin) that results in significant loss of strength that can recover within a time period of 4–6 wk. We built the ABM in Repast, a java-based modeling platform (Argonne National Laboratory, Lemont, IL). The spatial agents in the model included muscle fibers, ECM, necrotic muscle tissue, fibroblasts, myofibroblasts, quiescent and activated SSCs, myoblasts, myocytes, and fused myotubes. The nonspatial agents included the following inflammatory cells: resident macrophages, neutrophils, three phenotypes of proinflammatory (M1) macrophages, and anti-inflammatory (M2) macrophages.

Fig. 1.

ABM simulates contraction-induced muscle damage and regeneration over 28 days. Histological images were imported into the ABM to define the spatial geometry. A contraction-induced muscle injury was simulated by replacing fiber elements with necrotic elements, and regeneration was tracked over time by measuring cell counts and fiber CSA. ABM, agent-based model; CSA, cross-sectional area.

The model represented 170,000 square microns with a 20-micron thickness cross-section of muscle using 13,000 grid elements. The muscle cross-section was generated by importing muscle histology, masking the image in MATLAB (Mathworks, Natick, MA) to differentiate the fibers and ECM and mapping the masked image onto the ABM grid. Initial injury was simulated by stochastically replacing a percentage of the fiber elements with necrotic elements, according to the initial damage input parameter. For our healthy muscle simulations we varied the level of initial damage to determine its effect on muscle regeneration. In our mdx models we utilized data from the literature to define the extent of initial injury (explained in detail in Analysis of mdx mouse models). Although this approach simplified the mechanics of contraction-induced damage, it allowed us to focus on the cellular behaviors that lead to regeneration following the initial damage. Simulations were run with a 1-h time step for a simulated 28 days following injury. All simulations were repeated 10 times to sample the stochastic nature of the model. The key model outputs included the CSA of the muscle fibers and the time-varying counts for each cell type in the model. Muscle fiber CSA was determined by summing all of the healthy muscle fiber elements in the simulation. CSA recovery was defined as the current fiber CSA normalized to the original fiber CSA (preinjury).

At each time step, literature-derived rules governed the behavior of the agents in the model (https://simtk.org/projects/abm-dmd). At model initialization, the ABM spatial representation and baseline cell (agents) numbers were defined. At subsequent time steps, each agent individually followed a probability-based decision tree to determine its action (Fig. 2). For instance, based on the magnitude of the differentiation signal, SSC agents may differentiate into myoblasts or remain SSC agents. The collective actions of all of the autonomous agents (cells) lead to emergent, system-level behaviors (CSA changes, cell population dynamics) that were analyzed in the simulations.

Fig. 2.

Flowchart of ABM rules. First the model is initialized, during each subsequent time step the inflammatory cells and growth factors are calculated. Then the spatial agents, fibroblasts, SSCs, fibers, and ECM follow a probability-based decision tree to guide their actions. In the flow chart, boxes represent a final action for the agent for the current time step. ABM, agent-based model; ECM, extracellular matrix; ODE, ordinary differential equation; SSC, satellite stem cell.

Agent action overview.

The simulated behaviors of the fibroblast and SSC agents included secretion of growth factors, migration, quiescence, activation, recruitment, division, differentiation, and apoptosis. The 31 growth factors in the model represented the change in growth factors from homeostatic conditions (before injury) to levels following an eccentric contraction injury. At each time step, growth factors were added based on the defined secretions for each cell type. To migrate, the agents moved to a neighboring element within the model. Quiescent agents did not migrate or secrete growth factors until they were activated. If an agent was recruited, then a new agent was added to the simulation. An active agent could migrate, secrete growth factors, divide, differentiate, and apoptose. Agent division was represented by adding an additional agent to the simulation, and agent differentiation was represented by changing the agent type to the differentiated state. If an agent apoptosed, it was removed from the simulation.

SSC agents.

At model initialization, the SSC agents were spatially located at the fiber edge in a quiescent state (64), with ~1 SSC agent per 4 fibers, for a 20-micron thickness cross-section. Following injury, SSC agents became activated by damage and the presence of hepatocyte growth factor (2, 53, 83). Additionally, SSC agents were recruited to injured fibers based on a recruitment signal of growth factors (13, 25, 34, 76). SSC agents divided, both symmetrically (into two SSC agents) and asymmetrically (into one SSC agent, one committed myogenic progenitor agent), based on the microenvironmental cues and growth factors (outlined in Table 1). The probability that an SSC divided asymmetrically varied in the literature from 0.3 to 0.6, with the remaining divisions being symmetric (19, 40, 101). Although the asymmetric cell division parameter is important to replicate experimental observations in the model, variation within the range (0.3–0.6) did not greatly influence our model predictions. Therefore, we selected a probability of 0.5 for both asymmetric and symmetric divisions. The SSC agents terminally differentiated (based on a differentiation signal) and fused with the injured fiber agents to repair the muscle (1, 3, 4). To simulate regeneration of the fiber, fused myocytes added muscle fiber elements to the periphery of the fiber. Approximately 10% of the SSC agents did not terminally differentiate and helped to restore the SSC agent pool until returning to quiescence (24, 40).

Table 1.

SSC agent behaviors are defined based on literature-derived rules

SSC Agent Behavior	Sources
SSC activation
Activation signal: fiber damage; HGF	(2, 53, 83)
Recruitment signal: HGF + IGF + FGF + MMP − TGF-β	1, 13, 34, 76, 93)
Migrate if MMPs break down dense ECM	(13, 93)
Migrate along fiber edge to damaged site	(25, 76)
SSC Division
Enter cell cycle/divide: 3 × IGF + 3 × FGF + TNF-α + IFN + IL6 + VEGF + PDGF + GCSF − IL10 −TGF-β	(1, 3, 4, 22, 52, 70, 72, 79, 100);
50% cell divisions are symmetric, 50% asymmetric	(19, 40, 101)
10% of cells never express Myf5 and will not differentiate into myocytes	(24, 40)
Chance of division decreases with each cell division; 1st division 85%; 2nd 65%; 3rd 20%	(77)
After symmetric cell division, sister cells remain in contact for 3 h	(76, 77)
After asymmetric cell division, sister cells remain in contact for 8 h	(76, 77)
Time to initial division: 18–24 h	(40, 65, 77)
Time to divide: 10 h	(65, 77)
Decreased fibronectin = decreased chance of symmetric division	(7)
SSC Differentiation
Exit cell cycle/terminally differentiate: 4 × IL10 + IL4 − 2 × FGF − 2 × IGF – 2 × HGF − IFN − TNF-α	(1, 3, 4, 53)
Activated SSCs differentiate into myoblasts; myoblasts differentiate into myocytes	(83a, 94)
Differentiated myocytes fuse at damaged fiber edge	(83a, 94, 102)
SSC Behaviors
Initial count: 1 quiescent SSC per 4 fibers (assumes 20-micron-thick slice)	(64)
Secretions: fibronectin; MMPs; IL1; VEGF; CCL22	(7, 12, 43)
Inflammation dependent secretions: TNF-α; IL6; IL8; MCP	(12, 67)
Differentiated myoblasts fuse and repair muscle fiber	(44, 92)
If M1 macrophage count > SSC count, SSCs are protected from apoptosis	(12)

CCL, chemokine (C-C motif) ligand; ECM, extracellular matrix; GCSF, granulocyte colony-stimulating factor; HGF, hepatocyte growth factor; IFN, interferon; M1, proinflammatory macrophage; MCP, monocyte chemoattractant protein; MMP, matrix metalloproteinase; SSC, satellite stem cell; TNF, tumor necrosis factor.

Fibroblast agents.

At initialization, the fibroblast agents were distributed throughout the ECM (55). Following injury, additional fibroblast agents were recruited at a rate that was proportional to the amount of IL-4 secreted by eosinophil agents (30). Recent experiments have revealed that connective tissue fibroblasts in the muscle proliferate in the presence of SSCs; therefore, we incorporated a rule that caused fibroblast agents to proliferate in the presence of activated SSC agents (55). The likelihood of fibroblast agent apoptosis was elevated by the presence of TNF-α, whereas active transforming growth factor (TGF)-β blocked the apoptosis (41). We modeled both inactive and active TGF-β as growth factors and included a period of activation for TGF-β based on experimental data showing a 3–4-day delay between inactive TGF-β and active TGF-β peaks (41). However, myofibroblast agents were able to release activated TGF-β immediately (17, 99). Fibroblast agents had an increasing likelihood of differentiating into myofibroblast agents when TGF-β was elevated for an extended period of time. We tuned the length of time at which high TGF-β exposure caused myofibroblast agent differentiation so that myofibroblast agent differentiation did not occur in the healthy muscle, consistent with published observations (14, 41). The fibroblast and myofibroblast agents (Table 2) secreted growth factors and collagen following injury (33, 48, 59, 61, 67, 78, 99, 103).

Table 2.

Fibroblast agent behaviors are defined based on literature-derived rules

Fibroblast Agent Behavior	Sources
Initial count: 1 per every 2 fibers (assumes 20-micron-thick section)	(55)
Recruitment signal: eosinophil secreted IL-4	(30)
Proliferation signal: SSC proliferation	(41)
Extended TGF-β saturation causes fibroblast differentiation into myofibroblasts	(17, 99)
Secretions: TGF-β; IGF1; PDGF; MMPs; IL6; FGF; fibronectin	(33, 48, 59, 61, 78, 103)
Inflammation dependent secretions: IL1; IL8; MCP	(67)
Secrete collagen to rebuild ECM following injury	(71, 104)
Migrate toward damage/low collagen at 5–20 microns/hour	(18, 56)
Myofibroblast secretions: 2× collagen; active TGF-β	(61, 99, 103)
Apoptosis signal: TNF-α	(41)
TGF-β blocks TNF-α-induced apoptosis	(41)

ECM, extracellular matrix; MCP, monocyte chemoattractant protein; MMP, matrix metalloproteinase; SSC, satellite stem cell; TNF, tumor necrosis factor.

ECM and muscle fiber agents.

The muscle fiber and ECM agents were comprised of multiple elements in the model. An average of 180 elements (2,400 square microns) represented the area of a single muscle fiber. The ECM elements were prescribed a collagen density parameter based on literature measurements (60). To simulate injury, the initial damage parameter (input to the simulation) defined the percent of the healthy muscle fiber elements that were replaced by necrosis elements. The rate of necrosis element removal was dependent on the number of M1 macrophage agents. Elements corresponding to cleared necrosis converted to a low-density collagen element. Fibroblast agents secreted collagen in these locations to restore the stiffness of the damaged tissue (71, 104). Additionally, if areas of very low collagen remained, then two neighboring ECM elements with low collagen were merged into a single element (with the sum of both collagen density factors). This simulated behavior reduced the overall size of the muscle (muscle fibers and ECM), which is seen during muscle recovery (55). When myocyte agents fused to the fiber edge, muscle fiber elements were added at the periphery of the fiber, increasing the muscle fiber size (83a, 94, 102).

Inflammatory cell ordinary differential equation.

The inflammatory cell dynamics were defined based on previous work by Martin et al. (49, 50). Our goal was to reduce the computational cost of the ABM but still retain the dynamic behaviors of the inflammatory cells that were previously established. Therefore, we converted the rules for each of the inflammatory cells in the ABM described by Martin et al. (49, 50) into a system of seven coupled ordinary differential equations (ODEs). The seven ODEs represented the seven inflammatory cell phenotypes in Martin’s model (49, 50), including resident macrophages (RM), neutrophils (N), apoptotic neutrophils (N_a), M1s, apoptotic neutrophil phagocytosing M1 macrophages (M1_ae), debris phagocytosing M1s (M1_de), and M2s (Eqs. 1–7). To test if our ODE was equivalent to the ABM by Martin et al., we ran simulations of the inflammatory cell dynamics following injury with both models and confirmed that the results of our ODE fell within the 95% confidence interval of the predictions from the Martin ABM.

The ODE was defined by 51 parameters that represented the recruiting and deterring interactions between the different cells types. The interactions were determined based on the growth factor secretions and the response to growth factors for each cell type. Within the ABM simulation framework, the inflammatory cell ODEs were solved nonspatially using Euler’s method with a 1-h time-step. To couple the inflammatory cell ODEs with the behaviors of the other spatial cell agents, we included the following rules for inflammatory cell agents, based on the cell counts at the beginning of each time step: 1) secretion of growth factors, 2) removal of necrosis elements, and 3) M1-dependent protection of SSC apoptosis. Additionally, the inflammatory cell ODEs are dependent on the spatial (fibroblast and SSC) agent counts at each time-step. Inflammatory cell ODEs include the following, where %_necrotic is the current ratio of the muscle that is necrotic, and RM₀ is the starting number of resident macrophages, Fb is the current number of fibroblast agents, and SSC is the current number of SSC agents:

$$\frac{dRM}{dt}=1.054R{M}_0-0.18RM$$ (1)

$$\frac{dN}{dt}=2.40RM*{\%}_{necrotic}+0.00033Fb+0.016N-0.024N_a-0.082M1-0.020M{1}_{ae}-0.0019M{1}_{de}-0.045M2+0.0023SSC-0.13N*{\%}_{necrotic}$$ (2)

$$\frac{d{N}_a}{dt}=0.13N*{\%}_{necrotic}-0.0058M1*N_a-0.0058N_a$$ (3)

$$\frac{dM1}{dt}=0.0046RM*{\%}_{necrotic}-0.0018Fb+0.033N-0.0018N_a+0.0058M1-0.0054M{1}_{ae}+0.0096M{1}_{de}-0.0092M2+0.0017SSC-0.0011M1*N_a-0.0046M1*{\%}_{necrotic}$$ (4)

$$\frac{dM{1}_{ae}}{dt}=0.003M1*N-0.018M{1}_{ae}$$ (5)

$$\frac{dM{1}_{de}}{dt}=0.012M1*{\%}_{necrotic}-0.012M{1}_{de}$$ (6)

$$\frac{dM2}{dt}=0.0054RM*{\%}_{necrotic}-0.0026Fb-0.019N-0.00079N_a+0.043M1+0.0053M{1}_{ae}+0.015M{1}_{de}-0.0096M2+0.0026SSC$$ (7)

Baseline model parameterization.

To parameterize the baseline model, we ran simulations and iteratively adjusted the unknown model parameters (Table 3), such that the model predictions (95% confidence intervals) were consistent with published experimental data. The published experimental data included 1) fibroblast and SSC counts (55), inflammatory cell counts (3), and CSA recovery measurements (62) for healthy muscle regeneration following injury, and 2) results from healthy muscle regeneration perturbation studies. The perturbation studies included 1) fibroblast depletion (55), 2) SSC depletion (55), 3) TNF-α blockade (41), and 4) increased TGF-β (41).

Table 3.

Unknown model parameters were tuned to recapitulate published literature

Parameter	Equation	Range Tested	Value
Normalization factor for fibroblast recruitment, x1	Fibroblast recruitment probability = 1/(x1−recruitment signal)	35–120	70
Maximum probability of fibroblast recruitment per hour, x2	If fibroblast recruitment probability > x2, recruitment probability = x2	1/50–1/5	1/15
Normalization factor for fibroblast expansion, x3	fibroblast expansion probability = 1/(x3−expansion signal)	50–140	90
Maximum probability of fibroblast expansion per hour, x4	If fibroblast expansion probability > x4, expansion probability = x4	1/100–1/10	1/35
Minimum required time (hours) in high TGF- β environment for fibroblasts to differentiate into myofibroblasts, x5	Minimum required time (hours) in high TGF-β environment for fibroblasts to differentiate into myofibroblasts = x5	0–4	12
Normalization factor for SSC division, x6	SSC division probability = 1/(x6−division signal)	150–300	220
Maximum probability of SSC division per hour, x7	If SSC division probability > x7, division probability = x7	1/100–1/10	1/60
Normalization factor for SSC differentiation, x8	SSC differentiation probability = 1/(x8−differentiation signal)	−30–40	0
Maximum probability of SSC differentiation per hour, x9	If SSC differentiation probability > x9, differentiation probability = x9	1/50–1/2	1/5
Normalization factor for SSC migration, x10	SSC migration probability = 1/(x10−migration signal)	100–180	150
Maximum probability of SSC migration per hour, x11	If SSC migration probability > x11, migration probability = x11	1/50–1/5	1/30
Probability of adding a fiber element, when SSC is fused with myofiber per hour, x12	Probability of adding a fiber element, when SSC is fused with myofiber per hour = x12	1/20–1	1/4
Maximum number of fiber elements added per SSC, x13	Maximum number of fiber elements added per SSC = x13	5–200	60

SSC, satellite stem cell.

When comparing the cell counts with published experiments, we focused on the critical window of 3–7 days postinjury, because this is when SSCs and fibroblasts peak in the literature. Cell counts were normalized such that the peak counts were similar for all the different cells in the model. The growth factor secretions from each cell were then scaled to be consistent with literature observations. To confirm the validity of this normalization scheme, we performed simulations with both normalized and unnormalized cell counts and found no differences in the simulations’ predictions. The literature consistently uses percent of peak isometric torque as the biomarker of active muscle tissue regeneration; therefore, we tuned our unknown model parameters such that the fiber CSA predictions encompassed the peak torque measurements from the literature. Once the model parameters were tuned, we ran simulations to verify the model predictions. To verify the model predictions, we replicated experimental perturbations in literature (Table 4) and compared our model predictions with the experimental results from the respective studies.

Table 4.

Input parameters for model verification simulations

Simulation	Revised Model Input	Source
Fibroblast depletion	Decreased baseline fibroblast counts by 60% and fibroblast recruitment by 60%	(55)
Macrophage decrease	Decreased macrophage levels by 80%	(81)
SSC depletion	Set SSC counts to 0	(55)
No asymmetric division	Set the chance of asymmetric division to 0	(38)
Block TNF-α	Set TNF-α parameter to 0	(41)
Add TGF-β	Increased TGF-β 1.5×	(41)
Fibronectin knockdown	Set fibronectin parameter to 0	(7)
Block eosinophil secreted IL4	Set eosinophil-secreted IL4 parameter to 0	(30)

SSC, satellite stem cell; TNF, tumor necrosis factor.

Analysis of individual mechanisms of disease.

After developing the model to replicate various experimental observations of healthy muscle regeneration, we modified individual cellular behaviors to examine how each mechanism can contribute to the disease phenotype. To do this, we independently varied the number of fibroblast, SSC, and inflammatory cell agents, the ability to asymmetrically divide, and the extent of initial damage in a range from healthy to values relevant to dystrophic muscle. We then simulated a muscle injury and tracked the CSA recovery over time (fiber CSA relative to original CSA). We examined the simulation predictions in two ways. First, we quantified the time-varying muscle fiber CSA (relative to original size) for 10 repeated simulations of variations in each input parameter. Second, we compared muscle fiber CSA (relative to original size) at specific time points for all simulations within a physiologic range of the input parameters.

Analysis of mdx mouse models.

We created variations of the ABM that represented mdx mice at three stages of disease (Table 5) by altering parameters consistent with observations of muscle pathophysiology at different ages of mdx mice. We selected three ages of mdx mice to differentiate between three phenotypes of the disease that occur at different ages. The 4-wk-old mdx mouse has a significant inflammatory response and exhibits increased markers of degeneration. The 3-mo-old mdx mouse represents a more stable phenotype, in which the inflammatory cells, SSCs, and fibroblast are more similar to a healthy mouse with increased damage susceptibility. The-9-mo-old mdx mouse represents a more profibrotic phenotype.

Table 5.

Model input parameters were altered to develop models of mdx mice at three disease stages

Parameter	Healthy (3-mo-old)	4-wk-old mdx	3-mo-old mdx	9-mo-old mdx
Fibrosis (%ECM above healthy) (14, 60)	0	0	+5	+10
Relative initial fibroblast count (14)	1	1	1.5	2
Initial damage (16, 57), %	10	35	26	29
Relative collagen density (29, 51, 60)	1	1	1.5	3
Relative initial SSC count (64, 73)	1	1	1	1
Relative telomere shortening (46, 69)	1	1	1	1
Probability symmetric division (19, 27, 40, 101)	0.5	0.5	0.5	0.5
Probability asymmetric division (19, 27, 40, 101)	0.5	0.1	0.1	0.1
Probability abnormal division (19, 27, 40, 101)	0.5	0.4	0.4	0.4
Relative resident macrophage count (87, 97)	1	2	1.3	1.8
Relative chance of secondary necrosis (87, 88)	1	2	1.5	1.5
Eosinophil scalar (11)	1	1.3	1	1
M1 macrophage scalar (87, 97)	1	1.25	1	1
M2 macrophage scalar (86, 87)	1	0.8	1.25	2.5
Relative initial active-TGF-B1 (4a, 60)	1	1	1	1.3

ECM, extracellular matrix; M1, proinflammatory macrophage; M2, anti-inflammatory macrophage; SSC, satellite stem cell.

The spatial representations were defined by importing histology from correspondingly aged mdx muscle. The histology defined the pathological variations in CSA, fibrosis, and collagen density (14, 60).

To capture both the increased damage susceptibility in mdx mice, and a significant force-loss from injury, we used work by Dellorusso et al. (16), which analyzed the injury from supraphysiologic strains in different ages of mdx mice. Our model representation of damage represents the factors that recover as a result of SSC behavior and thus does not include factors that can recover without SSCs (e.g., excitation-contraction uncoupling). Therefore, we aimed to exclude the contribution of excitation-contraction coupling in our initial damage input parameter by excluding the percent of force-loss that recovers 15 min postinjury, as this portion of the force deficit has been shown not to depend on SSC regeneration (16). We also reduced the level of initial damage, while maintaining the ratios of damage between the groups based on the assumption that 50% of the torque deficit can be recovered without SSCs (63). From these data, we calculated the ratio of damage between healthy, 3-mo mdx, and 9-mo mdx mice to be 10%:26%:29%. To predict the damage in the 4-wk mdx mouse, we used a previously published finite-element model to simulate the contraction. The model predicted that the lack of dystrophin proteins (9, 23) and low-density collagen (before fibrosis) resulted in 35% damage. In these simulations, we have assumed that the mechanism of injury (damage to contractile muscle tissue) is the same between healthy and mdx mice.

Baseline cell counts for fibroblasts were altered according to experimental data (14). Baseline SSC counts were kept the same between healthy and mdx models because many studies have shown that mdx mice do not show direct changes in SSC counts or regeneration (measured by telomere shortening) in the lower limb for the age groups modeled (69, 73). However, asymmetric division of SSC agents was modified according to experimental observations (19). The inflammatory cell behaviors were altered to represent the significantly elevated proinflammatory environment in the 4-wk mdx mouse model with increased cytotoxicity of macrophage agents (87, 88, 97). In the 3-mo-old mdx mouse model, the inflammatory response was elevated relative to the healthy values. In the 9-mo-old mdx mouse model, the inflammatory response was shifted to a highly anti-inflammatory phenotype (higher M2 agent counts relative to M1 agent counts) with a TGF-β-enriched environment (added TGF-β) (4a, 60, 87, 88).

RESULTS

ABM simulated healthy muscle regeneration dynamics.

While tuning the unknown model parameters (Table 3), the simulations revealed emergent muscle regeneration behaviors that were consistent with key experimental studies in the field. For example, the fibroblast agents peaked between days 3 and 7 following injury (Fig. 3A), with fibroblast agents remaining elevated throughout most of regeneration (6, 55). The SSC agents peaked between days 3 and 7, and the differentiating myocyte agents appeared in the simulated muscle by day 4, peaking in number by day 10 (6, 55). The inflammatory cell ODEs also recapitulated the timing of inflammatory cell peaks, including M1s at days 2–3 and M2s at days 4–5 (3, 12, 70, 87) (Fig. 3B). The simulated muscle fiber CSA returned to 100% of its original fiber size by 14 days postinjury (Fig. 3C) (62).

Fig. 3.

ABM of healthy muscle regeneration recapitulates peak cell populations and fiber CSA following injury. The model recapitulated experimental data for SSCs, fibroblasts, M1s, and M2s following injury, within the model’s predicted 95% confidence interval for cell counts (3, 55) (A and B). Regeneration in the ABM is measured as a percent of the current fiber CSA relative to the original fiber CSA (preinjury). The model recapitulated experimental regeneration data (peak isometric torque loss) for healthy muscle following injury (C). The day 0 time point has been excluded from this figure to reduce the contributions from neuromuscular failure (62). *Cell counts have been normalized for comparison to model results, as described in methods. ABM, agent-based model; CSA, cross-sectional area; M1, proinflammatory macrophage; M2, anti-inflammatory macrophage.

ABM simulations of initial damage perturbations.

We varied the amount of initial damage and tracked the CSA recovery (defined as the normalized CSA) over 28 days (Fig. 4A). The ABM predicted that the time to recovery (time for the fiber CSA to return to 100%) is not linearly dependent on the extent of initial damage (Fig. 4B). At early time points (day 7), the percent CSA recovery had a one-to-one relationship with the initial damage. However, at later time points (days 14 and 28), the CSA percent recovery was similar for the different damage levels. This implies that the magnitude of the regenerative response is positively correlated with the amount of muscle damage, and the timing of regeneration remains relatively constant across damage levels.

Fig. 4.

Altering initial damage, fibroblast agent counts, and macrophage agent counts revealed complex, temporal dynamics. We analyzed the effects of modifying initial damage (A and B), fibroblast agent counts (C and D), and macrophage agent counts (E and F) in our healthy muscle ABM. Parameters were varied in a range from healthy to expected values in dystrophic muscle. Output includes muscle regeneration curves for 10 repeated simulations with a single input parameter (A, C, E) and muscle fiber CSA (relative to original size) at specific time points for all simulations within a range of input parameters (B, D, F). Altering the initial damage revealed relatively consistent timing of recovery (A). Low fibroblast counts resulted in initial increased fiber CSA but ultimate impairment (C). Both high and low levels of macrophages were predicted to impair regeneration (E). ABM, agent-based model; CSA, cross-sectional area.

ABM simulations of fibroblast perturbations.

We simulated the effects of varying the number of fibroblast agents in the model across a physiologic range (0- to 2.5-fold change in the number of fibroblast agents, relative to healthy controls) (Fig. 4D). With increased numbers of fibroblast agents in the muscle, we found no change in muscle regeneration (fiber CSA) compared with healthy muscle (Fig. 4D). Simulations with a 0–0.5-fold change in fibroblast agents (relative to healthy controls) resulted in an 11% decrease in fiber CSA at the end of the 28-day simulation (Fig. 4C).

ABM simulations of inflammation perturbations.

We varied the number of macrophages to investigate the effects of inflammation on muscle regeneration in our ABM (Fig. 4, E and F). Our model predicted that a 0–0.3-fold change in macrophage agents (relative to healthy controls) resulted in increased fiber CSA for the first 6 days following injury but ultimately resulted in a 13% decrease in fiber CSA at the end of the 28-day simulation. Additionally, we found that greatly increasing the number of macrophage agents (2.5–3-fold increase from healthy controls) resulted in a decreased fiber CSA at 2 time periods, days 0–5 and day 10–28, with a 7% decrease in fiber CSA at day 28.

ABM simulations of SSC perturbations.

The simulations predicted that varying SSC agent counts by 0–1.5-fold (relative to healthy controls) affected muscle regeneration significantly (Figs. 4B and 5A). Depletion of SSC agents (0 SSC agents) resulted in a 36% decrease (relative to healthy controls) in fiber CSA by day 28, whereas low SSC agent counts (0.1–0.4-fold change relative to healthy controls) resulted in a 22% decrease (relative to healthy controls) in fiber CSA by day 28. Increasing the SSC agent counts 1.5-fold only minimally enhanced the fiber CSA (3%) compared with the healthy controls. We simulated the effects of impaired SSC agent asymmetric division on the normalized fiber CSA. Allowing for 0% SSC agent asymmetric division (100% symmetric divisions) lead to impaired muscle regeneration at all time points after 7 days, with a 6% decrease in fiber CSA at day 28 (Fig. 5C). One hundred percent of SSC agent asymmetric division resulted in no difference in fiber CSA at all time points.

Fig. 5.

Altering SSC agent counts and impairing SSC agent asymmetric division revealed complex, temporal dynamics. We analyzed the effects of modifying SSC agent counts (A and B), and percent of SSC agent asymmetric divisions (C and D) in our healthy muscle ABM. Parameters were varied in a range from healthy to expected values in dystrophic muscle. Output includes muscle regeneration curves for 10 repeated simulations with a single input parameter (A and C) and muscle fiber CSA (relative to original size) at specific time points for all simulations within a range of input parameters (B and D). Depleted and low levels of SSC agents impaired regeneration, whereas high levels lead to a small but significant increase in fiber CSA (A). Zero SSC agent asymmetric divisions resulted in impaired regeneration for all time points (C). ABM, agent-based model; CSA, cross-sectional area; SSC, satellite stem cell.

Comparison of ABM perturbations with the published literature.

The results of fibroblast and inflammatory cell perturbation simulations were generally consistent with the available literature (Fig. 6). For example, decreasing the number of fibroblast agents by 60% predicted decreased regeneration, and published experiments have shown that depletion of 60% of Tcf4+ fibroblasts resulted in premature differentiation of SSCs and impaired regeneration (21, 55). The model predicted that decreasing the number of macrophage agents impaired muscle regeneration, increased fibroblast agent counts, and had no effect on SSC agent counts. Comparable experimental studies similarly showed that decreased macrophage counts resulted in decreased regeneration at days 9 and 21 (3, 75, 81). Additionally, in mice with decreased monocytes (C-C chemokine receptor type 2^−/− mouse strain), fibro/adipogenic progenitor cell [the main source of myofibroblasts in skeletal muscle (42, 85)] clearance is impaired, leading to increased fibro/adipogenic progentior cell counts (41). Experimentally, the effect of decreased macrophage counts on SSC counts is difficult to interpret in the literature, as some studies have shown no effect on SSCs (81, 96), whereas others have shown delayed proliferation and differentiation of SSCs (74).

Fig. 6.

ABM predictions are verified through comparison with experimental results from published literature. Top triangles represent a decrease (red), increase (blue), no change (gray), or inconclusive published data (checkered) for regeneration, SSC counts, or fibroblast counts. Lower triangles represent the model prediction. Inconclusive data are due to conflicting published data or our inability to identify published experimental studies that recapitulated our ABM perturbations. Regeneration increases and decreases represent an increase or decrease in fiber CSA at the end of the 28-day simulation, respectively. To verify model predictions we simulated experiments in the literature and compared our model predictions to the experimental results. Experimental sources from the literature used for comparison: 1 (21, 55); 2 (3, 41, 75, 81); 3 (55); 4 (38); 5 (41, 95); 6 (41, 60); 7 (7, 45); 8 (30). ABM, agent-based model; SSC, satellite stem cell; TNF, tumor necrosis factor.

The ABM predictions of in silico perturbations of SSC agents were also consistent with data in the literature. Our model predicted that decreasing the number of SSC agents resulted in decreased fibroblast agent counts and impaired regeneration. Similarly, experimental studies showed that depletion of Pax7+ SSCs resulted in decreased Tcf4+ fibroblast counts at days 5 and 28 (Tcf4+ cell density was increased following normalization to muscle area) and impaired regeneration (55). The model predicted impaired regeneration and decreased SSC agent counts following impaired SSC agent asymmetric division. A comparable experimental study similarly demonstrated that impaired SSC asymmetric division resulted in lower SSC counts and impaired regeneration (38).

Finally, we evaluated the effects of varying four individual parameters that have been shown in the literature to be critical regulators of muscle regeneration: levels of TNF-α, TGF-β, fibronectin, and eosinophil-secreted IL-4. The model predicted that blocking TNF-α resulted in increased fibroblast agent counts and impaired regeneration at day 14. Similarly, experimental studies showed that blocking TNF-α resulted in increased fibroblasts at day 7 (41) and impared regeneration at day 14 (95). Simulations with increased TGF- β expression predicted increased fibroblast agent counts and impaired regeneration. Comparable experimental studies showed increased fibroblasts at day 7 (41) and impaired regeneration, as measured by decreased force production 1 mo following injury (60). The simulation of fibronectin knockdown predicted decreased SSC agent counts, in agreement with experimental studies (7, 45). Finally, simulations that blocked eosinophil-secreted IL-4 resulted in decreased regeneration and fibroblast agent counts. Similarly, experimental studies have shown that that blocking the IL-4 receptor resulted in decreased fibro/adipogenic progenitor cell numbers and impaired regeneration (30).

Simulated mdx mice displayed altered cell dynamics at all ages and impaired regeneration in 9-mo-old mdx mice.

Models of the 4-wk-old and 3-mo-old mdx mouse muscle recovered to within 96% of original fiber CSA (Fig. 7A), whereas the model of the 9-mo-old mdx mouse recovered to 88% of its original size by day 28. Interestingly, although the predictions of fiber CSA regeneration appear similar for some of the mdx ages, the cellular dynamics driving the regeneration differ substantially for each mdx age. For example, following injury, the number of SSC agents was significantly increased (2.8× healthy controls) in the 4-wk-old mdx mice with a 2-day delay in initial SSC agent differentiation (Fig. 7, B and C), whereas the 9-mo-old mdx mice had the highest levels of peak fibroblast agent counts (1.6× healthy controls) (Fig. 7D). In the 4-wk-old mdx mice, the inflammatory response was dominated by M1 agents, and the activity of M2 agents was less substantial (Fig. 7, E and F). By contrast, both the young and 9-mo-old mdx mice were dominated by an anti-inflammatory phenotype with higher counts of M2 agents as compared with M1 agents. All the macrophage counts were elevated in the mdx mice relative to the healthy controls.

Fig. 7.

Three models of mdx mice simulate regeneration and cell counts following injury. Three models of mdx mice were developed for three stages of disease: 4-wk-old mdx, 3-mo-old mdx, and 9-mo-old mdx. Injury and regeneration were simulated and CSA and cell counts were tracked over time. The 4-wk-old and 3-mo-old mdx mice recovered to 96% of the original fiber CSA 28 days after injury, whereas 9-mo-old mdx mice recovered to 88% of their original size (A). SSC agents were significantly increased in 4-wk-old mdx mice with delayed SSC agent differentiation (B and C). Nine-month-old mdx mice had high levels of fibroblast agents and low levels of SSC agents and differentiated SSC agents (B–D). The 4-wk-old mdx mouse was dominated by inflammatory (M1) macrophage agents, whereas the young and 9-mo-old mdx mice were dominated by anti-inflammatory (M2) macrophage agents. CSA, cross-sectional area; SSC, satellite stem cell.

We analyzed the relationship between the model cell counts and muscle CSA recovery in the healthy and mdx simulations. Peak SSC agent counts, normalized by the area of injury (μm²), correlated with the percent of the injured muscle that recovered 28 days after injury (Fig. 8A). Because the initial SSC count parameter was not different in any of the mdx simulations, the predicted differences in peak SSC agent counts between the healthy and mdx mouse simulations were emergent model predictions that resulted from changes in the microenvironment. Therefore, we analyzed the relationship between SSC agent counts and other model predictions, to investigate how changes in individual factors associated with disease influence SSCs. Peak fibroblast agent and M2 agent counts, normalized by the area of injury, influenced the peak SSC agent counts, but no single model parameter was able to predict the differences in SSC counts (Fig. 8, B–D).

Fig. 8.

Peak SSC agent counts correlate with percent of injured muscle area recovered by day 28. Peak SSC agent counts from the healthy and mdx simulations, normalized by area of injury, correlate with the percent of injured muscle area recovered 28 days after injury (A). Percent of injured muscle area recovered is calculated as the (final fiber CSA−fiber CSA following injury)/area of the injury. Data points represent model results from individual simulations with n = 10 simulations per group (healthy, 4-wk-old mdx, 3-mo-old mdx, 9-mo-old mdx). Peak SSC agent counts are poorly correlated with fibroblast, M1, and M2 agent counts (B–D). CSA, cross-sectional area; M1, proinflammatory macrophage; M2, anti-inflammatory macrophage; SSC, satellite stem cell.

DISCUSSION

The goal of this study was to synthesize the available literature to develop a computational model that predicts muscle regeneration following injury based on the autonomous behaviors of skeletal muscle cells, fibroblasts, SSCs, and inflammatory cells. By incorporating literature-derived rules from over 100 sources, we were able to capture behaviors from a wide breadth of experimental studies. We created a model that is sensitive to a broad range of parameters, yet able to simulate regeneration dynamics that are not explicitly defined in the model. We then used the model to probe disease mechanisms in insolation and within our models of the mdx mouse. The simulation results provided insight into the drivers of impaired regeneration in mdx muscle.

The simulations of healthy and mdx mice revealed that the percent of injured muscle recovered by day 28 is dependent on the peak number of SSC agents following injury (Fig. 8A). In our healthy and mdx models with near-full CSA recovery 28 days after injury, (healthy, 4-wk mdx, and 3-mo mdx), the peak number of SSC agents was directly correlated with the extent of initial damage, where higher levels of initial damage led to higher numbers of SSC agents (Fig. 7B). Comparatively, in the 9-mo mdx mouse with impaired regeneration, the peak SSC agent counts were suppressed relative to the initial damage. Because in our model SSCs are the primary cells responsible for repair and maintenance of skeletal muscle, it is not surprising that regeneration would correlate with SSC counts. However, it is important to note that we did not explicitly alter the SSC agent counts in our different models of mdx mice. Rather, the pathological differences in SSC agent counts during regeneration were an emergent model prediction driven by other microenvironmental factors. Our model analyses predicted that fibroblast and M2 agents influenced peak SSC counts, but no single model parameter was able to predict the differences in SSC populations that ultimately led to impaired regeneration. Because SSC counts have been implicated in DMD and used as therapeutic targets (69), our model suggests that it may be beneficial to target an upstream microenvironmental factor driving pathological differences in SSCs.

The model simulations also revealed that the cellular dynamics driving regeneration are time dependent and that perturbing disease mechanisms often leads to temporally conflicting regeneration results. For example, reducing the number of macrophage or fibroblast agents initially increased fiber CSA but ultimately lead to impaired regeneration at the end of the 28-day simulation. Because these time-dependent cell types are often therapeutic targets, it is critical to understand the temporal variations that may occur following experimental perturbations. Current experimental techniques make continuous monitoring of the cellular and regenerative environment very difficult; therefore, computational modeling should be used to understand the temporal complexities and adequately define experimental time points to capture those dynamics.

The mdx simulation results compared favorably with the available published literature. Both our 3-mo-old mdx mouse simulation (Fig. 7A) and comparable literature showed near-full CSA recovery by day 21 (62). The 4-wk-old mdx mouse simulation had 2.7- (Fig. 7B) and 2.4- (Fig. 7C) fold increases in SSC and differentiated SSC agents. Comparatively, a published experiment for the mdx diaphragm, a skeletal muscle that represents a more severe phenotype than the lower limb muscle in the model, showed similar increases in SSCs (58). The 4-wk-old mdx mouse simulation predicted a 4.8-fold increase in total macrophage agents, relative to healthy controls (Fig. 7, E and F), whereas an experimental study similarly showed a 4.5-fold increase in total macrophages between these groups (87). Additionally, the predictions from our healthy muscle model perturbations were similar to experimental results in the literature (Fig. 6). However, it is important to note that, although we aimed to include the most representative studies available in the literature, the perturbation analysis does not include the results of all studies.

It is important to consider the limitations of our model. In developing the healthy model, we focused on the complex dynamics of a subset of cells (particularly the SSCs and fibroblasts), rather than aiming to recapitulate all aspects of regeneration. As a result, some aspects of regeneration, such as additional cell types, excitation-contraction uncoupling, neuromuscular junction changes, cytoskeletal disruption, myonuclei, and microvascular network, were not included. Therefore, we can only draw conclusions from perturbations of our modeled cell types. Furthermore, we recapitulated the impaired regeneration in mdx mice by altering specific parameters in our healthy model. We modified parameters to represent the key differences between healthy and mdx cell behaviors, such as the increased cytotoxity of macrophages or increased fibroblast numbers. For the unaltered parameters, we assumed that the cell behaviors (Table 1 and 2) and the tuned model parameters (Table 3) remained constant. There were sufficient data to prescribe the altered input conditions; however, there was limited time course data available to verify many of our mdx simulation predictions. This highlights the paucity of time course regeneration data in mdx mice, and future experiments could be used to verify the assumptions in our mdx model.

We originally tuned our models to Tcf4+ fibroblast and Pax7+ SSC counts. However, many rules were defined based on studies using different markers, potentially representing different cell phenotypes, such as fibro-adipogenic cells (33, 41). To address this, the agents in our model do not represent a marker for a specific cell type, such as Tcf4+ fibroblasts or Pax7+ SSCs. Rather, the agents represent a spectrum of phenotypes for the primary cell types. Based on agent parameters (e.g., cell cycle state, activation, or myogenic commitment), we can determine which population of agents in the model would be identified by experimental markers. We then use these agent populations to compare our model predictions to the respective published literature.

It is important to address the differences between muscle repair and regeneration, as well as the role of different injury mechanisms. We used published measurements of eccentric contractions to define our mdx model initial damage parameters to incorporate differences in damage susceptibility between mdx and healthy mice. However, experiments have shown that a significant portion of the force loss following eccentric contraction injuries can recover without SSCs (63) (e.g., contributions from excitation-contraction uncoupling), and these contributions may be different between healthy and mdx mice. Our model does not include contributions from these factors, so we addressed this challenge into two ways. First, we used supraphysiologic strains from the literature to ensure there was sufficient damage to the contractile muscle tissue that required SSC regeneration. Lower strains would alter the injury mechanism to include a greater contribution from the factors that we have not included in our model. Second, we decreased the input damage parameter while maintaining the ratio of damage between groups, because it has been shown that 50% of the force-deficit can be attributed to factors that do not require SSCs for regeneration (63). To address the uncertainty in this damage parameter we ran simulations at varying levels of initial damage (Fig. 4, A and B), and the model predicted that the magnitude of the regenerative response scaled with the input damage level. For instance, the peak SSCs counts increased with increasing levels of initial damage, but the time to recovery (in healthy muscle) was relatively conserved. This result supports our assumption that the most important aspect of the input damage parameter in our model was the ratio of damage between groups. Furthermore, in our mdx simulation analyses we excluded the contribution of the initial damage parameter by normalizing the results (Fig. 8) by the area of damage. From these results we drew our conclusions about the role of the SSCs.

Finally, to track recovery in our model, we used measurements of fiber CSA. However, experiments have shown that CSA does not perfectly predict muscle function, particularly between mdx and healthy mice where pseudohypertrophy contributes to increased muscle CSA, without subsequent increases in contractile fiber tissue (73). To address these factors, we measured CSA by summing the fiber elements and did not include ECM elements to reduce the contribution of pseudohypertrophic increases in CSA in the mdx models. Additionally, we excluded factors that contribute to force-deficits but do not require regeneration of muscle tissue to recover the force (e.g., excitation-contraction uncoupling and protein repair mechanisms as explained above). Therefore, the force deficits from eccentric contractions shown in the literature are greater than the fiber CSA deficit that we have modeled, particularly in the first 24 h following injury (e.g., Fig. 3) (62). Despite the fact that CSA does not perfectly predict muscle function, we believe our model is useful for comparing the effect of disease mechanisms on muscle regeneration between our simulation groups.

Future work aims to extend the model to represent more severe animal models and patients with DMD, as well as incorporating chronic, long-term damage to the muscle. These models will be used for in silico testing to probe the effects of a wide range of potential therapies, such as therapies targeting upstream microenvironmental factors to alter SSC counts. The simulations will then be used to design insightful experiments to test those predictions. Ultimately, this new ABM recapitulated muscle regeneration following injury and suggested new hypotheses regarding the influence of the microenvironment on SSC behaviors and regeneration. The simulations revealed that regeneration is dependent on SSC counts and that pathological differences in SSC counts may be driven by microenvironment factors. Broadly, this study also demonstrated the utility of computational models for providing insight into therapy development and experimental design for complex, multifaceted disease.

GRANTS

The work was funded by the National Science Foundation Grant No. 1235224 and the National Institutes of Health Grant No. U01-AR-06393.

DICLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

K.M.V., K.S.M., S.M.P., and S.S.B. conceived and designed research; K.M.V. performed experiments; K.M.V. analyzed data; K.M.V., K.S.M., S.M.P., and S.S.B. interpreted results of experiments; K.M.V. prepared figures; K.M.V., K.S.M., S.M.P., and S.S.B. drafted manuscript; K.M.V., K.S.M., S.M.P., and S.S.B. edited and revised manuscript; K.M.V., K.S.M., S.M.P., and S.S.B. approved final version of manuscript.