Application of a comprehensive, user-friendly, digital computer circulatory model to estimate hemodynamic and ventricular variables.
Methods
The closed-loop lumped parameter circulatory model represents the circulation at the level of large vessels. A variable elastance model reproduces ventricular ejection. The circulatory model has been modified embedding an algorithm able to adjust the model parameters reproducing specific circulatory conditions. The algorithm reads input variables: heart rate, aortic pressure, cardiac output, and left atrial pressure. After a preliminary estimate of circulatory parameters and ventricular elastance, it adjusts the amount of circulating blood, the value of the systemic peripheral resistance, left ventricular elastance, and ventricular rest volume. Input variables and the corresponding calculated variables are recursively compared: the procedure is stopped if the difference between input and calculated variables is within the set tolerance. At the procedure end, the model produces an estimate of ventricular volumes and Emaxl along with systemic and pulmonary pressures (output variables). The procedure has been tested using 4 sets of experimental data including left ventricular assist device assistance.
Results
The algorithm allows the reproduction of the circulatory conditions defined by all input variable sets, giving as well an estimate of output variables.
Conclusions
The algorithm permits application of the model in environments where the simplicity of use and velocity of execution are of primary importance. Due to its modular structure, the model can be modified adding new circulatory districts or changing the existing ones. The model could also be applied in educational applications.
DaganJ.. Pulsatile mechanical and mathematical model of the cardiovascular system.Med Biol Eng Comput1982; 20: 601–7.
2.
ZhouJ., ArmstrongG.P., MedvedevA.L., SmithW.A., GoldingL.A., ThomasJ.D.. Numeric modeling of the cardiovascular system with a left ventricular assist device.ASAIO J1999; 45: 83–9.
3.
PantalosG.M., SharpM.K., WoodruffS.J.. Influence of gravity on cardiac performance.Ann Biomed Eng1998; 26: 931–43.
4.
GeertsemaA.A., RakhorstG., MihaylovD., BlanksmaP.K., VerkerkeG.J.. Development of a numerical simulation model of the cardiovascular system.Artif Organs1997; 21: 1297–301.
5.
KhirA.W., SwalenM.J., SegersP., VerdonckP., PepperJ.R.. Hemodynamics of a pulsatile left ventricular assist device driven by a counterpulsation pump in a mock circulation.Artif Organs2006; 30: 308–12.
6.
PontrelliG.. A multiscale approach for modelling wave propagation in an arterial segment.Comput Methods Biomech Biomed Engin2004; 7: 79–89.
7.
ShiY., KorakianitisT., BowlesC.. Numerical simulation of cardiovascular dynamics with different types of VAD assistance.J Biomech2007; 40: 2919–33.
8.
FerrariG., De LazzariC., de KroonT.L., ElstrodtJ.M., RakhorstG., GuY.J.. Numerical simulation of hemodynamic changes during beating heart surgery: analysis of the effects of cardiac position alteration in an animal model.Artif Organs2007; 31: 73–9.
9.
SagawaK., MaughanL., SugaH., SunagawaK.. Cardiac contraction and the pressure-volume relationship.New York: Oxford University Press, 1988.
10.
FerrariG., GórczyńskaK., De LazzariC.. In vitro testing of a left ventricular assist device: study of the effect of its control strategy on energetic relationships inside the left ventricle.Technol Health Care1996; 3: 231–39.
11.
FerrariG., GórczyńskaK., MimmoR.. Mono and biventricular assistance: their effect on ventricular energetics.Int J Artif Organs2001; 24: 380–91.
12.
FerrariG., GórczyńskaK., MimmoR.. IABP assistance: a test bench for the analysis of its effects on ventricular energetics and hemodynamics.Int J Artif Organs2001; 24: 274–80.
13.
ColombetI., DartT., LeneveutL., ZuninoS., MénardJ., ChatellierG.. A computer decision aid for medical prevention: a pilot qualitative study of the Personalized Estimate of Risks (EsPeR) system.BMC Med Inform Decis Mak2003; 3: 13. Published online 2003 November 27. doi: 10.1186/1472–6947–3–13.
14.
MontgomeryA.A., FaheyT., PetersT.J., MacIntoshC., SharpD.J.. Evaluation of computer based clinical decision support system and risk chart for management of hypertension in primary care: randomised controlled trial.BMJ2000; 11: 320: 686–90.
15.
SmithB.W., ChaseJ.G., ShawG.M., NokesR.I.. Experimentally verified minimal cardiovascular system model for rapid diagnostic assistance.Control Engineering Practice2005; 13: 1183–93.
16.
HeldtT., ShimE.B., KammR.D., MarkR.G.. Computational modeling of cardiovascular response to orthostatic stress.J Appl Physiol2002; 92: 1239–54.
17.
FerrariG., De LazzariC., MimmoR., TostiG., AmbrosiD.. A modular numerical model of the cardiovascular system for studying and training in the field of cardiovascular physiopathology.J Biomed Eng1992; 14: 91–107.
18.
VandenbergheS., SegersP., SteendijkP.. Modeling ventricular function during cardiac assist: does time-varying elastance work?ASAIO J2006; 52: 4–8.
19.
ShroffS.G., JanickiJ.S., WeberK.T.. Evidence and quantitation of left ventricular systolic elastance.Am J Physiol1985; 249: H358–70.
20.
CampbellK.B., KirkpatrickR.D., KnowlenG.G., RingoJ.A.. Latesystolic pumping properties of the left ventricle: deviation from elastance-resistance behaviour.Circ Res1990; 66: 218–33.
21.
GilbertJ.C., GlantzS.A.. Determinants of left ventricular filling and of the diastolic pressure-volume relation.Circ Res1989; 64: 827–52.
22.
FerrariG., KozarskiM., De LazzariC.. A hybrid (numerical-physical) model of the left ventricle.Int J Artif Organs2001; 24: 456–62.
23.
KozarskiM., FerrariG., ClementeF.. A hybrid mock circulatory system: development and testing of an electro-hydraulic impedance simulator.Int J Artif Organs2003; 26: 53–63.
24.
FerrariG., KozarskiM., De LazzariC., GórczyńskaK., TostiG., DarowskiM.. Development of a hybrid (numerical-hydraulic) circulatory model: prototype testing and its response to IABP assistance.Int J Artif Organs2005; 28: 750–9.
25.
KozarskiM., FerrariG., ZielińskiK.. A new hybrid electro-numerical model of the left ventricle.Comput Biol Med2008; 38: 979–89.
26.
WesterhofN., ElzingaG., SipkemaP.. An artificial arterial system for pumping hearts.J Appl Physiol1971; 31: 776–81.
27.
BurkhoffD., AlexanderJ.Jr., SchipkeJ.. Assessment of Windkessel as a model of aortic input impedance.Am J Physiol1988; 255(4 Pt 2): H742–53.
28.
SegersP., BrimioulleS., StergiopulosN.. Pulmonary arterial compliance in dogs and pigs: the three-element Windkessel model revisited.Am J Physiol1999; 277(2 Pt 2): H725–31.
29.
StergiopulosN., MeisterJ.J., WesterhofN.. Evaluation of methods for estimation of total arterial compliance.Am J Physiol1995; 268(4 Pt 2): H1540–8.
30.
DowneyJ.M., KirkE.S.. Inhibition of coronary blood flow by a vascular waterfall mechanism.Circ Res1975; 36: 753–60.
31.
De LazzariC., DarowskiM., FerrariG., ClementeF., GuaragnoM.. Computer simulation of haemodynamic parameters changes with left ventricle assist device and mechanical ventilation.Comput Biol Med2000; 30: 55–69.
32.
GuytonA.C., JonesC.E., ColemanT.G.. Circulatory physiology: cardiac output and its regulation.Philadelphia, PA: WB Saunders, 1973.
33.
KomamuraK., ShannonR.P., PasipoularidesA.. Alterations in left ventricular diastolic function in conscious dogs with pacing-induced heart failure.J Clin Invest1992; 89: 1825–38.
34.
SenzakiH., ChenC.H., KassD.A.. Single-beat estimation of end-systolic pressure-volume relation in humans: a new method with the potential for noninvasive application.Circulation1996; 94: 2497–506.
35.
GrundemanP.F., BorstC., van HerwaardenJ.A., VerlaanC.W., JansenE.W.. Vertical displacement of the beating heart by the octopus tissue stabilizer: influence on coronary flow.Ann Thorac Surg1998; 65: 1348–52.
36.
FerrariG., MimmoR., MercoglianoD.. A method for Emax trend evaluation: in vitro and in vivo results.Int J Artif Organs1999; 22: 217–25.
37.
KassD.A., BeyarR., LankfordE., HeardM., MaughanW.L., SagawaK.. Influence of contractile state on curvilinearity of in situ end-systolic pressure-volume relations.Circulation1989; 79: 167–78.
38.
SadiqS.K., MazzeoM.D., ZasadaS.J.. Patient-specific simulation as a basis for clinical decision-making.Philos Transact A Math Phys Eng Sci2008; 366: 3199–219.
39.
GolczewskiT., DarowskiM.. Virtual respiratory system for education and research: simulation of expiratory flow limitation for spirometry.Int J Artif Organs2006; 29(10): 961–72.
