Abstract

In human physiological and pathological flow systems, it is not possible to rule out diffusion in all advective processes because perfusion goes hand in hand with diffusion processes. It is the perfusion throughout the capillary bed and then the diffusion of fluids throughout the tissue that is the subject of most magnetic resonance functional imaging procedures. It is observed from literature that basic theory of perfusion is mostly based on experimental observation which makes it entirely computational with quite a lot of data fitting. Therefore, it is quite rigorous and has many phenomena that seem not to have a common background. It is very important to attempt developing a theory that would take most issues (if not all) into consideration under a common phenomenon. In this study, based on the Bloch NMR flow equations along with the Boubaker polynomials expansion scheme (BPES), we describe analytically the dynamics of perfusion processes by an equation which combines both diffusive and advective properties.  

Key words: Bloch NMR flow equations, diffusion-advection equation, blood vessels, BPES scheme.