Reference attached

1. The diagram below defines a model for a centrifugal LVAD connected from left ventricle to aorta. Derive the two differential equations based on E(t) the left ventricular elastance and C the arterial compliance. A) Using the initial conditions as shown, plot Pa from time 0 to 10 seconds using the time varying elastance model as listed in the reader and class slides. B) Set Fva =0 and plot Pa for 0 to 10 seconds to compare responses without the LVAD. Submit your Matlab code and report in a Word document C) The flow through the aortic valve will vary as a function of the zero flow pressure (130 mm Hg). Determine the critical zero flow pressure where aortic valve flow is zero for the entire cardiac cycle. Pv=15 mm Hg Fva^2 RV=.0275 mm Hg/(ml/sec) Pva Rc=.51 Mitral Valve Ry Pven Rc Pa Rp=1.05 C=1.6 ml/mm Hg Pv E(D) C Rp VIv(0)=185 mL Fva=sqrt(130+Plv-Pa)*16.7 mL/sec VPa(0)=131 ml Emax=2.3*.25 Fva=centrifugal LVAD flow Emin=.06 T=1 sec