Algorithm 1.

Algorithm for simulating activation scenarios

1:  initialize relative diameters α(0) = 1

2:  deactivate secondary constraints ϵ = 0

3:  ν ← 0

4:  while simulation is running do

5:       BLOOD FLOW WITH RBC DYNAMICS

6:       for each time step $t=1\dots N_{\Delta t}^{(\nu )}$ do

7:           compute q[t] and p[t] based on the current RBC distribution (Equations 1–6)

8:           move RBCs for a time step Δt

9:       compute averages 〈q〉(ν) and 〈p〉(ν) (Equation 8)

10:      compute ρ(ν) (Equation 28)

11:      update cost function J(ν) (Equation 27)

12:      if J(ν) > tol then

13:           UPDATE RELATIVE DIAMETERS

14:           compute ${\tilde{T}}^n$, ${\tilde{\mu }}_{rel}^{(\nu )}$ and $\frac{\partial {\tilde{T}}^{(\nu )}}{\partial {\alpha }^{(\nu )}}$ (Equations 9,25,26)

15:           compute $\frac{\partial {\tilde{g}}^{(\nu )}}{\partial {\alpha }^{(\nu )}}$ and $\frac{\partial {\tilde{g}}^{(\nu )}}{\partial {\langle p\rangle }^{(\nu )}}$ (Equations 22,23),

16:           compute $\frac{\partial J^{(\nu )}}{\partial {\alpha }^{(\nu )}}$ (Equation 29) and $\frac{\partial J^{(\nu )}}{\partial {\langle p\rangle }^{(\nu )}}$ (Equation 30)

17:           compute sensitivity $\frac{d{J}^{(\nu )}}{d{\alpha }^{(\nu )}}$ (Equations 13 and 14)

18:           update parameters α(ν+1) (Equation 12)

19:      else

20:           UPDATE SECONDARY CONSTRAINTS

21:           if ϵ = 0 then

22:               activate secondary constraints, e.g., ϵ = 1

23:           set new ${\rho }_{min}<{\rho }^{(\nu )}$

24:      ν ← ν + 1

25:  return final parameters α(ν)