A computational model of fibroblast and macrophage spatial/temporal dynamics in foreign body reactions

Abstract

The implantation of medical devices often triggers several immune responses, one kind of which is categorized as foreign body reactions. It is well established that macrophages and many other cells participate in the complex processes of foreign body reactions, and cause severe inflammations and fibrotic capsule formation in surrounding tissues. However, the detailed mechanisms of macrophage responses, recruitment and activation, in foreign body reactions are not totally understood. In the meantime, mathematical models have been proposed to systematically decipher the behavior of this complex system of multiple cells, proteins and biochemical processes in wound healing responses. Based on these early works, this study introduces a mathematical model in two spatial dimensions to investigate the transient behavior of macrophages, fibroblasts and their interactions during the formation of fibrotic tissue. We find that the simulation results are consistent with the experimental observations. These findings support that the model can reveal quantitative insights for studying foreign body reaction processes.

Keywords: Computational model; Fibroblast; Foreign body reactions; Macrophage; Medical implant; Spatial and time dynamics.

Fig. 1

Boundary conditions: At the outer edge 1, 2, 5, and 8, F = F₀, M = M₀e^–γ₂t, E = E₀, and $\frac{\partial r}{\partial c}=0$, where γ₂ is the decay coefficient at the boundary for macrophages; at the inner edge 3, 4, 7, and 6, d = d₀. The axes present dimensionless values.

Fig. 2

The sketch graph for the experiment design and data collection.

Fig. 3

The experimental slices with fluorescent dye. For each image, left side is adjacent to the implant. (a) Left column shows that slices obtained from 5 rats have been implanted disks for 7 days. (b) Right column shows that slices obtained from 5 rats have been implanted disks for 28 days.

Fig. 4

Statistical results of simulated data of macrophages as compared with experimental results on day 7. (A) 7th day experimental data (all five rats) plotted together with the average curve; and (B) average experimental data versus the simulated result on day 7.

Fig. 5

Statistical results of simulated data of macrophages as compared with experimental results on day 28. (A) 28th day experimental data (all five rats) plotted together with the average curve; and (B) average experimental data versus the simulated result on day 28.

Fig. 6

Statistical results of simulated data of fibroblast cells as compared with experimental results on day 7. (A) 7th day experimental data (all five rats) plotted together with the average curve; and (B) average experimental data versus the simulated result on day 7.

Fig. 7

Statistical results of simulated data of fibroblast cells as compared with experimental results on day 28. (A) 28th day experimental data (all five rats) plotted together with the average curve; and (B) average experimental data versus the simulated result on day 28.

Fig. 8

Computational results for foreign body reaction processes at different compositions of macrophage phenotypes. λ₁, λ₂, and λ₃ are the proportions of macrophages for M₁ — classical macrophages, M₂ — regulatory macrophages, and M₃ — inflammatory macrophages, respectively. The variables are (A) debris, (B) chemoattractant, (C) fibroblast, (D) macrophage, and (E) ECM. Red is at (λ₁,λ₂,λ₃) = (0.6,0.2,0.2), blue represents the ratio at (0.2,0.6,0.2), and magenta is at the ratio (0.2,0.2,0.6).

Fig. 9

Computational results for foreign body reaction processes at different compositions of macrophage phenotypes. λ₁, λ₂, and λ₃ are the proportions of macrophages for M₁ — classical macrophages, M₂ — regulatory macrophages, and M₃ — inflammatory macrophages, respectively. The variables are (A) debris, (B) chemoattractant, (C) fibroblast, (D) macrophage, and (E) ECM. Red is at (λ₁,λ₂,λ₃) = (0.6,0.2,0.2), blue represents the ratio at (0.2, 0.6, 0.2), and magenta is at the ratio (0.2, 0.2, 0.6).