The plan for this week are to find equations for the flow and the pressure of blood in the arterial tree and to transfer the equations into MATLAB language.
Well I researched and I found an article called "A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree" for "Yunlong Huo and Ghassan S. Kassab" this article is simple and I the blood pressure and flow equation for 1D simulation and I took it as refrence
Quotation from article:
"
The details of the mathematical derivations are outlined in APPENDIX A. Briefly, the governing equations for flow and pressure may be expressed through conservation of mass and momentum as
(1)
(2)where A is cross-sectional area (CSA) of the vessel, q is volumetric flow rate, ρ is density, Estat is static Young's modulus, h is wall thickness, R0, h0, and A0 are original radius of the vessel, original wall thickness, and original CSA, respectively, and ν is kinematic viscosity.
(1)(2)where A is cross-sectional area (CSA) of the vessel, q is volumetric flow rate, ρ is density, Estat is static Young's modulus, h is wall thickness, R0, h0, and A0 are original radius of the vessel, original wall thickness, and original CSA, respectively, and ν is kinematic viscosity.
"
Article http is:
http://ajpheart.physiology.org/content/292/6/H2623.full
Now I have to translate these two equations to MATLAB language.
After I organized the equation I wrote the equation at MATLAB as apeared below
MATLAB APPENDIX for EQUATION 2:
A = ?;
q = ?;
p = ?;
v = ?;
h0 =?;
R0 = ?;
A0 = ?;
Estat = ?;
E = ((-4/3)*(q/A^2)+((A/p)*((Estat*h0)/(R0*A0)));
F = (8/3)*(q/A);
G = v;
K =(dt/dx);
E =(dt^2)/(dx^2));
