Model number


Cardiac output estimation in reference human. An open-loop cardiovascular model composed of a four-chamber varying-elastance heart, a systemic circulation, a pulmonary circulation, a coronary circulation, and baroreceptors.


 This is an open-loop cardiovascular and baroreceptor system used to estimate cardiac output 
 from arterial blood pressure and heart rate data. The model is composed of a four-chamber, 
 varying-elastance heart, a systemic circulation, a pulmonary circulation, a coronary circulation, 
 and baroreceptor control of arteriolar resistance, tone, and cardiac contractility.

 An arterial pressure curve sets the proximal aortic afterload at the downstream end of the 
 circulatory network and acts as input to the baroreceptor equations. At the upstream end a 
 non-pulsatile aortic flow input function automatically adjusts to match simulated mean arterial 
 pressure to the target (measured) mean arterial pressure. The smoothed flow across the pulmonary 
 valve is then taken as the estimated cardiac output. The model also simulates many other 
 physiological features such as total blood volume, end-diastolic left ventricular volume, and 
 coronary capillary flow. 

fig 1


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.

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Primary reference:

(primary) Neal ML, Bassingthwaighte JB. Subject-specific model estimation of cardiac output and blood 
 volume during hemorrhage. Cardiovascular Engineering. Volume 7, Number 3, September, 2007

Altman PL and Dittmer DS (Editors). Respiration and Circulation Bethesda, Maryland:
   Federation of American Societies for Experimental Biology, 1971, 930 pp.

Athanasiades A, Ghorbel F, Clark JW Jr, Niranjan SC, Olansen J, Zwischenberger JB,
   and Bidani A. Energy analysis of a nonlinear model of the normal human lung. J Biol
   Syst 8: 115-139, 2000.

Avolio AP. Multi-branched model of the human arterial system. Med & Biol Eng & Comput
   18: 709-718, 1980.

Bourgeois MJ, Gilbert BK, Von Bernuth G, and Wood EH. Continuous determination of beat 
   to beat stroke volume from aortic pressure pulses in the dog. Circ Res 39: 15-24,

(Primary) Dash RK and Bassingthwaighte JB. Erratum to: 
Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2, pH, 2,3-DPG and Temperature Levels. 
Ann Biomed Eng 38(4): 1683-1701, 2010.

Dash RK, Li Z, and Bassingthwaighte JB. Simultaneous blood-tissue exchange of oxygen,
   carbon dioxide, bicarbonate, and hydrogen ion. Ann Biomed Eng 34: 2006.

Feigl EO. Coronary circulation. Textbook of Physiology, edited by Patton HD, Fuchs AF,
   Hille B, Scher AM, and Steiner R. Philadelphia, PA: W. B. Saunders, 1989, 
   p. 933-951.

Goedje O, Hoeke K, Lichtwarck-Aschoff M, Faltchauser A, Lamm P, and Reichart B.
   Continuous cardiac output by femoral arterial thermodilution calibrated pulse
   contour analysis: comparison with pulmonary arterial thermodilution. Crit Care Med
   27: 2407-2412, 1999.

Guyton AC, Coleman TG, and Granger HJ. Circulation: overall regulation. Annu Rev 
   Physiol 34: 13-44, 1972.

Hamilton TT, Huber LM, and Jessen ME. PulseCO: A less-invasive method to monitor 
   cardiac output from arterial pressure after cardiac surgery. Ann Thorac Surg 74:
   S1408-S1412, 2002.

Heldt T, Shim EB, Kamm RD, and Mark RG. Computational modeling of cardiovascular 
   response to orthostatic stress. J Appl Physiol 92: 1239-1254, 2002.

International Commission on Radiological Protection. Basic Anatomical and
   Physiological Data for Use in Radiological Protection: Reference Values. New York:
   Elsevier Science, 2003, 320 pp.

Jansen JRC, Schreuder JJ, Mulier JP, Smith NT, Settels JJ, and Wesseling KH. A
   comparison of cardiac output derived from the arterial pressure wave against 
   thermodilution in cardiac surgery patients. Br J Anaesth 87: 212-222, 2001.

Kassab G, Lin DH, and Fung Y-CB. Morphometry of pig coronary venous system. Am J 
   Physiol 267 (Heart Circ. Physiol. 36): H2100-H2113, 1994.

Kassab GS, Rider CA, Tang NJ, and Fung Y-CB. Morphometry of pig coronary arterial 
   trees. Am J Physiol Heart Circ Physiol 265: H350-H365, 1993.

Klotz S, Hay I, Dickstein ML, Yi G-H, Wang J, Maurer M, Kass DA, and Burkhoff D.
   Single beat estimation of the end-diastolic pressure-volume relationship: a novel 
   method with the potential for noninvasive application. Am J Physiol Heart Circ 
   Physiol 10.1152/ajpheart.01240.2005: January 20, 2006.

Kouchoukos NT, Sheppard LC, and McDonald DA. Estimation of stroke volume in the dog 
   by a pulse contour method. Circ Res 26: 611-623, 1970.

Lakin WD, Stevens SA, Tranmer BI, and Penar PL. A whole-body mathematical model for 
   intracranial pressure dynamics. J Math Biol 46: 347-383, 2003.

Linton NWF and Linton RAF. Estimation of changes in cardiac output from the arterial 
   blood pressure waveform in the upper limb. Br J Anaesth 86: 486-496, 2001.

Lu K, Clark JW Jr, Ghorbel FH, Ware DL, Zwischenberger JB, and Bidani A. Whole-body 
   gas exchange in human predicted by a cardiopulmonary model. Cardiovasc Eng 3: 1-19,

Lu K, Clark JW Jr, Ghorbel FH, Ware DL, and Bidani A. A human cardiopulmonary system 
   model applied to the analysis of the Valsalva maneuver. Am J Physiol Heart Circ 
   Physiol 281: H2661-H2679, 2001.

Marino PL. The ICU Book Baltimore: Williams & Wilkins, 1998, 928 pp.

McCombie DB, Reisner AT, and Asada HH. Laguerre-model blind system identification: 
   cardiovascular dynamics estimated from multiple peripheral circulatory signals.
   IEEE Trans Biomed Eng 52: 1889-1901, 2005.

Milnor WR. Hemodynamics Baltimore: Williams and Wilkins, 1982, 390 pp.

Mohrman DE and Heller LJ. Cardiovascular Physiology, Fifth Edition New York:
   McGraw-Hill, 2003, 257 pp.

Nelder JA and Mead R. A simplex method for function minimization. Comput J 7: 308-313,

Olansen JB, Clark JW, Khoury D, Ghorbel F, and Bidani A. A closed-loop model of the 
   canine cardiovascular system that includes ventricular interaction. Comp Biomed 
   Res 33: 260-295, 2000.

Redling JD and Akay M. Noninvasive cardiac output estimation: a preliminary study. 
   Biol Cybern 77: 111-122, 1997.

Rideout VC. Mathematical computer modeling of physiological systems Englewood Cliffs,
   NJ: Prentice Hall, 1991, 261 pp.

Rodig G, Prasser C, Keyl C, Liebold A, and Hobbhahn J. Continuous cardiac output 
   measurement: pulse contour analysis vs thermodilution technique in cardiac surgical 
   patients. Brit J Anaesth 82: 525-530, 1999.

Romano SM and Pistolesi M. Assessment of cardiac output from systemic arterial pressure 
   in humans. Crit Care Med 30: 1834-1841, 2002.

Rosse C and Gaddum-Rosse P. Hollinshead's Textbook of Anatomy, 5th Edition. 
   Philadelphia: Lippincott-Raven, 1997, 902 pp.

Saeed M and Mark RG. Multiparameter Trend Monitoring and Intelligent Displays Using 
   Wavelet Analysis. Comp in Cardiol 27: 797-800, 2000.

Sagawa K, Lie RK, and Schaefer J. Translation of Otto Frank's Paper "Die Grundform des 
   Arteriellen Pulses" Zeitschrift fur Biologie 37: 438-526 (1899). J Mol Cell Cardiol 
   22: 253-277, 1990.

Scher AM. Events of the cardiac cycle: measurements of pressure, flow and volume. 
   Textbook of Physiology, Volume 2., edited by Patton HD, Fuchs AF, Hille B, Scher AM,
   and Steiner R. Philadelphia: W. B. Saunders, 1989, p. 834-847.

Scoletta S, Romano SM, Biagioli B, Capannini G, and Giomarelli P. Pressure recording 
   analytical method (PRAM) for measurement of cardiac output during various 
   haemodynamic states. Br J Anaeth 95: 159-165, 2005.

Spickler JW, Kezdi P, and Geller E. Transfer characteristics of the carotid sinus 
   pressure control system. Baroreceptors and Hypertension, edited by Kezdi P. Dayton:
   Pergamon, 1967, p. 31-40.

Sun Y, Beshara M, Lucariello RJ, and Chiaramida SA. A comprehensive model for 
   right-left heart interaction under the influence of pericardium and baroreflex.
   Am J Physiol Heart Circ Physiol 272: H1499-H1515, 1997.

Toyota E, Fujimoto K, Ogasawara Y, Kajita T, Shigeto F, Matsumoto T, Goto M, and 
   Kajiya F. Dynamic changes in three-dimensional architecture and vascular volume 
   of transmural coronary microvasculature between diastolic- and systolic-arrested 
   rat hearts. Circulation 105: 621-626, 2002.

Warner HR, Swan HJC, Connolly DC, Tompkins RG, and Wood EH. Quantitation of 
   beat-to-beat changes in stroke volume from the aortic pulse contour in man. J 
   Appl Physiol 5: 495-507, 1953.

Wesseling KH, Jansen JRC, Settels JJ, and Schreuder JJ. Computation of aortic flow 
   from pressure in humans using a nonlinear, three-element model. J Appl Physiol 74: 
   2566-2573, 1993.

Wesseling KH and Settels JJ. Circulatory model of baro- and cardio-pulmonary reflexes.
   Blood Pressure and Heart Rate Variability, edited by Di Rienzo M. IOS Press, 1992,
   p. 56-67.

Zinemanas D, Beyar R, and Sideman S. Relating mechanics, blood flow and mass transport 
   in the cardiac muscle. Int J Heat Mass Trans 37 Suppl. 1: 191-205, 1994.

Key terms
cardiac output estimation
cardiovascular system
systemic circulation
pulmonary circulation
coronary circulation
clinical application
automated parameterization
Integrative Physiology

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.