A Coupled Mechanobiological Model of Muscle Regeneration In Cerebral Palsy

Abstract

Cerebral palsy is a neuromusculoskeletal disorder associated with muscle weakness, altered muscle architecture, and progressive musculoskeletal symptoms that worsen with age. Pathological changes at the level of the whole muscle have been shown; however, it is unclear why this progression of muscle impairment occurs at the cellular level. The process of muscle regeneration is complex, and the interactions between cells in the muscle milieu should be considered in the context of cerebral palsy. In this work, we built a coupled mechanobiological model of muscle damage and regeneration to explore the process of muscle regeneration in typical and cerebral palsy conditions, and whether a reduced number of satellite cells in the cerebral palsy muscle environment could cause the muscle regeneration cycle to lead to progressive degeneration of muscle. The coupled model consisted of a finite element model of a muscle fiber bundle undergoing eccentric contraction, and an agent-based model of muscle regeneration incorporating satellite cells, inflammatory cells, muscle fibers, extracellular matrix, fibroblasts, and secreted cytokines. Our coupled model simulated damage from eccentric contraction followed by 28 days of regeneration within the muscle. We simulated cyclic damage and regeneration for both cerebral palsy and typically developing muscle milieus. Here we show the nonlinear effects of altered satellite cell numbers on muscle regeneration, where muscle repair is relatively insensitive to satellite cell concentration above a threshold, but relatively sensitive below that threshold. With the coupled model, we show that the fiber bundle geometry undergoes atrophy and fibrosis with too few satellite cells and excess extracellular matrix, representative of the progression of cerebral palsy in muscle. This work uses in silico modeling to demonstrate how muscle degeneration in cerebral palsy may arise from the process of cellular regeneration and a reduced number of satellite cells.

Keywords: FEM; agent-based modeling; finite element modeling; mechanobiology; satellite cell; skeletal muscle.

FIGURE 1

Geometry for both the agent-based models and FE models were generated from a single histological section. The coordinates for each pixel were extracted in MATLAB and used to recreate (A) pixels on ABM grid, and (B) to extrude muscle fibers for the FE models.

FIGURE 2

Overview of agent-based model steps. FE model resultant strains are mapped from each element center coordinate to the corresponding pixel coordinates of fibrils in the agent-based model. Fibers, SCs, neutrophils, macrophages, fibroblasts and ECM components work to regenerate damaged tissue.

FIGURE 3

Mapping FE element centers into ABM coordinate space. (A) FE element centers were calculated based on nodal points. (B) ABM pixels were imported with associated X, Y coordinates. (C) Element center coordinates and associated strain per element were then registered to ABM coordinates.

FIGURE 4

ABM and FE modeling coupling workflow. The initial pixel values and coordinates were used to build both starting ABM and FE modeling geometry. (A) FE simulations were run to model active eccentric contraction of a fiber bundle. (B) FE strain values were recorded with associated coordinate points. (C) Points of high strain were imported into the agent-based models as local damage. The agent-based models were run, and mean endpoint geometry (D) was used to generate a new FE geometry.

FIGURE 5

ABM simulation of muscle regeneration over time. At the first time point, regions of the muscle fiber bundle show damage. This damage signals for the mobilization of macrophages, neutrophils, satellite cells and fibroblasts, which interact in the muscle regeneration process. Note that the dominant change from t = 216 to t = 672 is ECM remodeling.

FIGURE 6

Fibril recovery post injury at varied damage levels of 0% fibrils to 20% with 5% steps. (A) Fibril recovery at 5 and 10% showed average end fibril count increase. At 15% clearance of damaged cells was effective and repair was close to recovery, however, at 20% damage, the clearance of damaged fibrils did not reach 20% (arrow) and therefore (B) inflammatory cells and damaged fibrils remain within the fibers.

FIGURE 7

ABM simulated cell counts over time. (A) SC simulation results (mean ± SD) compared to Snijders et al. (Snijders et al., 2015) (B) Simulated inflammatory cell counts of neutrophil and macrophage (mean ± SD) over time (solid line) compared to the generalized time course of when neutrophil, M1 macrophage and M2 macrophage cell counts are above 20% from baseline (dashed line), adapted from (Wosczyna and Rando, 2018).

FIGURE 8

ABM cell counts over time (mean ± SD) seeded with CP (SC = 4) or TD (SC = 10) initial conditions. (A) Iteration one cell counts over the first 672 h, based on initial geometry. TD fibril count exceeded initial count whereas CP fibril recovery was impaired. (B) ABM cell counts (mean ± SD) using TD and CP iteration two geometry and strain values seeded with CP (SC = 4) or TD (SC = 10) conditions. TD fibril recovery continued to exceed initial counts and CP fibril recovery was further impaired. (C) Iteration three of the ABM cell counts. TD fibril count peaked above the original value during repair however stabilised to just below initial values by the end of the simulation. CP fibril recovery decreased to 8,763 ± 315 (mean ± SD).

FIGURE 9

In the coupled ABM-FE modeling mechanobiological simulations, the initial geometry leads to two unique endpoint geometries, according to whether the agent-based models had a cellular milieu based on CP or TD muscle. Each of those endpoint geometries then leads to a new FE model geometry and simulation, where high strains differ based on the geometry from the previous step. Ultimately, divergent geometries emerge, reflecting the different CP vs TD muscle outcomes, where TD muscle regenerates fully each cycle and CP muscle fibers cyclically degenerate.

FIGURE 10

Sensitivity analysis for SC count and the effect on fibril count (mean ± SD) over simulation time course. SC count was set to 4 (CP), 5, 7, 10 (TD), and 13. Mean fibril count increased with increase in seeded SC count.

FIGURE 11

(A) ECM recovery over the third month 28 days post injury simulation. CP muscle environment (SC = 4) had higher end point ECM count of 2,240 ± 176 and the TD environment had a lower endpoint count of 1932 ± 139. (B) Tissue composition changed from initial simulations to the end of the third month. ECM percentage increased by 4.6% in the CP scenario and marginally increased by 0.3% in the TD scenario.