/*
 * Computational modeling of cardiovascular response to orthostatic
 * stress
 * 
 * Model Status
 * 
 * This CellML model runs in both COR and PCEnv to reproduce the
 * published results. The units have been checked and they balance.
 * This is a lumped parameter model for cardiac activation based
 * on the work of Heldt et al. 2002. This CellMl model represents
 * the left ventricle but it can be easily modified to represent
 * left and right atria and both ventricles.
 * 
 * Model Structure
 * 
 * ABSTRACT: The objective of this study is to develop a model
 * of the cardiovascular system capable of simulating the short-term
 * (less than or equal to 5 min) transient and steady-state hemodynamic
 * responses to head-up tilt and lower body negative pressure.
 * The model consists of a closed-loop lumped-parameter representation
 * of the circulation connected to set-point models of the arterial
 * and cardiopulmonary baroreflexes. Model parameters are largely
 * based on literature values. Model verification was performed
 * by comparing the simulation output under baseline conditions
 * and at different levels of orthostatic stress to sets of population-averaged
 * hemodynamic data reported in the literature. On the basis of
 * experimental evidence, we adjusted some model parameters to
 * simulate experimental data. Orthostatic stress simulations are
 * not statistically different from experimental data (two-sided
 * test of significance with Bonferroni adjustment for multiple
 * comparisons). Transient response characteristics of heart rate
 * to tilt also compare well with reported data. A case study is
 * presented on how the model is intended to be used in the future
 * to investigate the effects of post-spaceflight orthostatic intolerance.
 * 
 * model diagram
 * 
 * [[Image file: heldt_2002a.png]]
 * 
 * Schematic diagram of the Heldt et al. 2002 heart model.
 * 
 * The original paper reference is cited below:
 * 
 * Computational modeling of cardiovascular response to orthostatic
 * stress, T. Heldt, E.B. Shim, R.D. Kamm, and R.G. Mark, 2002,
 * Journal of Applied Physiology, 92, 1239-1254. PubMed ID: 11842064
 */

import nsrunit;
// Warning: unit conversion turned off due to unit errors in 1 equation(s)
unit conversion off;
unit elastance=1.33322E8 kilogram^1*meter^(-4)*second^(-2);
unit s=1 second^1;
unit Hz=1 second^(-1);
unit ratepm=60 second^(-1);
unit Hz2rpm=60  dimensionless;
unit per_s=1 second^(-1);

math main {
	realDomain realtime s;
	realtime.min=0;
	extern realtime.max;
	extern realtime.delta;
	real HR ratepm;
	HR=70;
	real hrf Hz;
	real PRint s;
	PRint=0.00012;
	real beattime(realtime) s;
	real Esys elastance;
	Esys=5.6;
	real Edia elastance;
	Edia=0.19;
	real TsK s;
	TsK=0.35;
	real Ts s;
	real E_LV(realtime) elastance;
	real dummy(realtime) dimensionless;
	when(realtime=realtime.min) dummy=10;

	// <component name="Environment">
	hrf=(HR/(60 Hz2rpm));

	// <component name="LVTiming">
	beattime=(realtime-floor(realtime/hrf)*hrf-PRint);

	// <component name="LVElastanceFunction">
	Ts=(TsK*sqrt((1 s)*hrf));
	E_LV=(if ((beattime>=(0 s)) and (beattime<=Ts)) Edia+(Esys-Edia)*(1-cos(3.141592653589793*beattime/Ts))/2 else if ((beattime<(1.5*Ts)) and (beattime>=Ts)) Edia+(Esys-Edia)*(1+cos(2*3.141592653589793*(beattime-Ts)/Ts))/2 else Edia);

	// <component name="dummy">
	dummy:realtime=(dummy*((-1)*(3 per_s)));
}