Model number

The MultiCompartment Circulatory System is based on pages 450-452 from J. Keener and J. Sneyd, Mathematical Physiology, Vol. 8 in series Interdisciplinary Applied Mathematics, Springer-Verlag New York Inc.,


fig 1

This is an algebraic model for a Multicompartment Circulatory System based
on the reference, pages 450-452. The values for the various parameters and
the ratios of the compliances were chosen so that the compliances and initial
volumes would all be positive. The volumes were distributed so that the systemic
volume was eleven times greater than the pulmonary volume, and the venous volumes
were 60% of the total volume. The flow, pressures, beats per minute, volumes and ratio
of compliances were set, and the resistances, compliances, and initial volumes
were solved for.

The second model in this project, MultiCircSystem2, sets the compliances
and resistances, and solves for the pressures, volumes, and ratios of
the compliances. 

The subscript conventions are given as
	a	arterial
	v	venous
	s	systemic
	p	pulmonary
	r	right
	l	left
	d	diastolic
	s	systolic

	Csa	Compliance of the systemic arteries.
	Cld	Diastolic compliance of left heart.
	Ps1	Pressure at the ill-defined border
		between systemic arteries and systemic


Figure (above) is a diagram of the MultiCircSystem model and is derived from Figure 15.8 of reference.


The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

Download JSim model project file

Help running a JSim model.

J. Keener and J. Sneyd, Mathematical Physiology, Vol. 8 in series
Interdisciplinary Applied Mathematics, Springer-Verlag New York Inc., 1998.
Key terms
two chambers

Please cite in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.