Table 4.
Pre-determined parameters in the mathematical model
| Symbol | Biological meaning | Value | Units | Ref |
|---|---|---|---|---|
| dMΦ | Macrophage removal rate**(eqn 1) | 0.6 | day-1 | [29] |
| ρMΦ | maximal macrophage density (eqn 2) | 2500 | cells/mm3 | [28] |
| ρF | maximal fibroblast density(eqn 2) | 1250 | cells/mm3 | [28] |
| ρC | maximal collagen density (eqn 2) | 3300 | μg/mm3 | [28] |
| kF | Fibroblast growth rate* (eqn 3) | 0.924 | day-1 | [62] |
| dF | Fibroblast apoptosis rate (eqn 3) | 0.12 | day-1 | [33] |
| kMΦT | Macrophage TGF-β production rate (eqn 4) | 0.07 | pg/cell/day | [34] |
| kFT | Fibroblast TGF-β production rate (eqn 4) | 0.004 | pg/cell/day | [35] |
| dTβ | TGF-β degradation rate¥(eqn 4) | 15 | day-1 | [36] |
| KMφM9 | Macrophage secretion MMP9 rate (eqn 5) | 3 | pg/cell/day | estimated |
| dM9 | MMP-9 degradation rate(eqn 5) | 0.875 | day-1 | [63-65] |
| kon | Kinetic reaction speed (eqn 5) | 3 × 10-4 | 1/(μg/mm3)s-1 | [42,66,67] |
| koff | Kinetic reaction speed (eqn 5) | 4 × 10-4 | s-1 | [42,66,67] |
| konc | Kinetic reaction speed (eqn 6) | 0.004 | s-1 | [42,66,67] |
| kFC | Fibroblast collagen production rate (eqn 6) | 20 | μg/cell/day | [41] |
*The growth rate of cells was determined by the population doubling time (T2) via equation k = ln 2/T2 [68].
** Since macrophages emigrate from the scar tissue to lymph node system instead of dying locally in the scar tissue, the removal rate of macrophage, dMA, was used in our model.
¥ The decaying rate of chemical factors was calculated from their half-life (T1/2) via the equation d = ln 2/T1/2 [68].