Ventricular ejection pressure and stroke-volume approximation (source code)

= Ventricular ejection pressure and stroke-volume approximation
{title2=$\widehat p_a=(C_ap_a^++V^+-V_0)/(C_a+C_s)$}

After a rapid switch to systolic compliance $C_s$, negligible valve resistance equalizes arterial and ventricular pressures. Neglecting runoff during this short stage conserves combined stored volume and gives the displayed <pressure>. Thereafter, with closed <mitral valve>, negligible venous <pressure> and constant $C_s$, the <pressure> decays as $\widehat p_a e^{-t/[R_c(C_a+C_s)]}$. At firing duration $\Delta t_F$, the <stroke volume> is $V^+-V_0-C_s\widehat p_a e^{-\Delta t_F/[R_c(C_a+C_s)]}$. Each approximation follows from an explicit valve or time-scale separation condition.