A Mathematical Model of Skeletal Muscle Disease and Immune Response in the mdx Mouse

Table 1

The model parameters and their estimated numerical values (in 1 mm³ of muscle tissue). Here “c” is for cell and “w” is for week.

Parameter	Description	Value	Unit
𝑏𝐻	Turnover rate of CD4+ T cells	𝑑𝐻𝐻0	c w^−1
𝑘1	Damage-driven proliferation rate of CD4+ T cells	0.0324139	(cent)^−1 w^−1
𝑑𝐻	Death rate of CD4+ T cells	0.83355	w^−1
𝑏𝐶	Turnover rate of CD8+ T cells	𝑑𝐶𝐶0	c w^−1
𝑘2	Damage-driven proliferation rate of CD8+ T cells	0.115375	(cent)^−1 w^−1
𝑑𝐶	Death rate of CD8+ T cells	1.61511	w^−1
𝑏𝑀	Turnover rate of macrophages	𝑑𝑀𝑀0	c w^−1
𝑘3	Infiltration rate of macrophages	0.766576	(cent)^−1 w^−1
𝑑𝑀	Death rate of macrophages	0.781155	w^−1
𝑘4	Generation rate of healthy fibers	0.123848	w^−1
𝑘5	Cytotoxicity degradation rate	4.09948×10^−3	c^−1 w^−1
𝑘6	Cleaning rate by macrophages	3.23097×10^−4	c^−1 w^−1
𝑑𝐷	Physiological cleaning rate	1.34671	w^−1
𝜎	Standard deviation of the initial damage	2.92815
𝑚	The time of the peak of the initial damage	4.22686
ℎ	Proportional to the magnitude of the damage	0.511657
𝐻0	The initial number of CD4 T cells	0	c
𝐶0	The initial number of CD8 T cells	4	c
𝑀0	The initial number of macrophages	400	c