Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
Review
. 2018 Mar;68(2):103-111.
doi: 10.1007/s12576-017-0585-1. Epub 2017 Dec 21.

Lumped parameter model for hemodynamic simulation of congenital heart diseases

Shuji Shimizu  1 , Dai Une  2 , Toru Kawada  2 , Yohsuke Hayama  2 , Atsunori Kamiya  2 , Toshiaki Shishido  3 , Masaru Sugimachi  2
Affiliations
Review

Lumped parameter model for hemodynamic simulation of congenital heart diseases

Shuji Shimizu et al. J Physiol Sci. 2018 Mar.

Abstract

The recent development of computer technology has made it possible to simulate the hemodynamics of congenital heart diseases on a desktop computer. However, multi-scale modeling of the cardiovascular system based on computed tomographic and magnetic resonance images still requires long simulation times. The lumped parameter model is potentially beneficial for real-time bedside simulation of congenital heart diseases. In this review, we introduce the basics of the lumped parameter model (time-varying elastance chamber model combined with modified Windkessel vasculature model) and illustrate its usage in hemodynamic simulation of congenital heart diseases using examples such as hypoplastic left heart syndrome and Fontan circulation. We also discuss the advantages of the lumped parameter model and the problems for clinical use.

Keywords: Congenital heart diseases; Hemodynamic simulation; Lumped parameter model; Time-varying elastance; Windkessel model.

PubMed Disclaimer

Conflict of interest statement

The authors declare that they have no conflicts of interest.

Figures

Fig. 1
Fig. 1
Simulated normalized elastance curves (T es = 175 ms). a A sine curve. b A sine curve combined with exponential curve. Time constant of relaxation (τ) is 25 ms for the solid line and 100 ms for the dotted line. An increase in τ prolongs the tail
Fig. 2
Fig. 2
Windkessel vasculature models. a Two-element model; b Three-element model; c Four-element model. R resistance, C capacitance, R c characteristic impedance, L inductance
Fig. 3
Fig. 3
Electrical analogs of cardiovascular systems of a normal heart, b Fontan circulation, c patient with atrial septal defect (ASD), and d patient with ventricular septal defect (VSD). LA left atrium, LV left ventricle, RA right atrium, RV right ventricle, SA single atrium, SV single ventricle, MV mitral valve, TV tricuspid valve, AV aortic valve, PV pulmonary valve, AVV atrioventricular valve. R CS, R AS, and R VS denote systemic characteristic impedance, arterial resistance, and venous resistance, respectively. R CP, R AP, and R VP denote pulmonary characteristic impedance, arterial resistance, and venous resistance, respectively. C AS and C VS denote pulmonary arterial and venous capacitances, respectively. C AP and C VP denote pulmonary arterial and venous capacitances, respectively. R ASD and R VSD denote the resistances across ASD and VSD, respectively
Fig. 4
Fig. 4
a The electrical analog of the modified Norwood procedure with right ventricle (RV) to pulmonary artery (PA) shunt (Sano modification). The pressure gradient across the RV–PA shunt is described as a non-linear function. b Simulated aortic (black solid line), right ventricular (gray solid line) and pulmonary artery pressures (gray dashed line) of the Sano modification. AP aortic pressure, RVP right ventricular pressure, PAP pulmonary artery pressure
See this image and copyright information in PMC

References

    1. Baker CE, Corsini C, Cosentino D, Dubini G, Pennati G, Migliavacca F, Hsia TY, Modeling of Congenital Hearts Alliance (MOCHA) Investigators Effects of pulmonary artery banding and retrograde aortic arch obstruction on the hybrid palliation of hypoplastic left heart syndrome. J Thorac Cardiovasc Surg. 2013;146:1341–1348. doi: 10.1016/j.jtcvs.2013.01.038. - DOI - PubMed
    1. Riesenkampff E, Rietdorf U, Wolf I, Schnackenburg B, Ewert P, Huebler M, Alexi-Meskishvili V, Anderson RH, Engel N, Meinzer HP, Hetzer R, Berger F, Kuehne T. The practical clinical value of three-dimensional models of complex congenitally malformed hearts. J Thorac Cardiovasc Surg. 2009;138:571–580. doi: 10.1016/j.jtcvs.2009.03.011. - DOI - PubMed
    1. Corsini C, Baker C, Kung E, Schievano S, Arbia G, Baretta A, Biglino G, Migliavacca F, Dubini G, Pennati G, Marsden A, Vignon-Clementel I, Taylor A, Hsia TY, Dorfman A, Modeling of Congenital Hearts Alliance (MOCHA) Investigators An integrated approach to patient-specific predictive modeling for single ventricle heart palliation. Comput Methods Biomech Biomed Engin. 2014;17:1572–1589. doi: 10.1080/10255842.2012.758254. - DOI - PMC - PubMed
    1. Qian Y, Liu JL, Itatani K, Miyaji K, Umezu M. Computational hemodynamic analysis in congenital heart disease: simulation of the Norwood procedure. Ann Biomed Eng. 2010;38:2302–2313. doi: 10.1007/s10439-010-9978-5. - DOI - PubMed
    1. Jalali A, Jones GF, Licht DJ, Nataraj C. Application of mathematical modeling for simulation and analysis of hypoplastic left heart syndrome (HLHS) in pre- and postsurgery conditions. Biomed Res Int. 2015;2015:987293. doi: 10.1155/2015/987293. - DOI - PMC - PubMed