A simulation to tissue homogeneity model for capillary of brain by statistical method

Analytical methods for solving adiabatic equations with non-uniform permeability and real arterial input function (AIF) are complicated. We consider crossing of contrast agent through the capillary and BBB as intrinsically statistical processes. Therefore, it is simulated by a stochastic method (Monte Carlo method). In our model, capillary is divided into multiple sections as in Patlak model and contrast agent moves from one section to other sections. For capillary input, AIF is made by Monte Carlo method from real data. Without solving an equation, we derive the concentration of contrast agent as a function of time and distance in the capillary for normal (not permeable due to BBB) and abnormal capillary with uniform and non-uniform permeability.