Assumptions and boundary conditions

In order to identify all the coefficients needed to connect the model to the experimental readouts, we estimated boundary conditions for the variables at specific time points (S4 Table) on the basis of biological considerations and the conservation law.

Based on the equations presented in the table, we see the linear dependence between the BV_i(t_A) and EDSS(t_A) for the time points outside of the relapses, such as

where

And

Taking into account that

for each individual patient or group of patients having both BV and EDSS measurements, the constants and coefficients necessary for the model predictions could be defined from the estimation of C_i and B_i as follows:

And, for each individual:

And,

Where C_i and B_i are patient-specific linear coefficients, identified based on the dependence between EDSS and BV measurements. EDSS_s(t) and V_s(t) are normalized simulated values, and A_mi(0) is 1 for young people under 20 or dependent on the age as 1-(age of onset-20)*0.01, bearing in mind that the decline in the volume of myelinated fibers is about 1% per year [39, 40].