Diplomski rad - Matematičko modeliranje ateroskleroze

Implementacija u Fenicsu 1D modela

$$\begin{array}{rl}{\displaystyle \frac{\partial M}{\partial t}}& =d_1{\displaystyle \frac{{\partial }^{2}M}{\partial x^2}}+f_1(A)-{\lambda }_{1}M,\\ {\displaystyle \frac{\partial A}{\partial t}}& =d_2{\displaystyle \frac{{\partial }^{2}A}{\partial x^2}}+f_2(A)M-{\lambda }_{2}A,\end{array}$$

i 2D modela

$$\begin{array}{rl}{\displaystyle \frac{\partial M}{\partial t}}& =d_1\mathrm{\Delta }M-{\lambda }_{1}M,\\ {\displaystyle \frac{\partial A}{\partial t}}& =d_2\mathrm{\Delta }A+f_2(A)M-{\lambda }_{2}A,\end{array}$$

Gdje su

$$\begin{array}{rl}{f}_1(A)& =\frac{{\alpha }_1+{\beta }_{1}A}{1+A/{\tau }_1},\\ f_2(A)& =\frac{{\alpha }_{2}A}{1+A/{\tau }_2}\end{array}$$