Annals of Biomedical Engineering

, Volume 35, Issue 1, pp 1–18 | Cite as

Coupling of a 3D Finite Element Model of Cardiac Ventricular Mechanics to Lumped Systems Models of the Systemic and Pulmonic Circulation

  • Roy C. P. Kerckhoffs
  • Maxwell L. Neal
  • Quan Gu
  • James B. Bassingthwaighte
  • Jeff H. Omens
  • Andrew D. McCulloch


In this study we present a novel, robust method to couple finite element (FE) models of cardiac mechanics to systems models of the circulation (CIRC), independent of cardiac phase. For each time step through a cardiac cycle, left and right ventricular pressures were calculated using ventricular compliances from the FE and CIRC models. These pressures served as boundary conditions in the FE and CIRC models. In succeeding steps, pressures were updated to minimize cavity volume error (FE minus CIRC volume) using Newton iterations. Coupling was achieved when a predefined criterion for the volume error was satisfied. Initial conditions for the multi-scale model were obtained by replacing the FE model with a varying elastance model, which takes into account direct ventricular interactions. Applying the coupling, a novel multi-scale model of the canine cardiovascular system was developed. Global hemodynamics and regional mechanics were calculated for multiple beats in two separate simulations with a left ventricular ischemic region and pulmonary artery constriction, respectively. After the interventions, global hemodynamics changed due to direct and indirect ventricular interactions, in agreement with previously published experimental results. The coupling method allows for simulations of multiple cardiac cycles for normal and pathophysiology, encompassing levels from cell to system.


Multi-scale model Ventricular interactions Cardiovascular Ventricular–vascular coupling Pulmonary artery constriction Ischemia 



This work was supported by the National Biomedical Computation Resource (NIH Grant P41 RR08605) (to A.D.M), National Science Foundation Grants BES-0096492 and BES-0506252 (to A.D.M) and BES-0506477 (to M.L.N.), NIH Grant HL32583 (to J.H.O.), and NIH Grant EB001973 (to J.B.B.). This investigation was conducted in a facility constructed with support from Research Facilities Improvement Program Grant Number C06 RR-017588-01 from the National Center for Research Resources, National Institutes of Health. A.D.M. and J.H.O. are co-founders of Insilicomed Inc., a licensee of UCSD-owned software used in this research. Furthermore, we are grateful to our programmers Sherief Abdel-Rahman, Ryan Brown, and Fred Lionetti for their excellent work on improving and extending Continuity.


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Copyright information

© Biomedical Engineering Society 2006

Authors and Affiliations

  • Roy C. P. Kerckhoffs
    • 1
  • Maxwell L. Neal
    • 2
  • Quan Gu
    • 3
  • James B. Bassingthwaighte
    • 4
  • Jeff H. Omens
    • 1
    • 5
  • Andrew D. McCulloch
    • 1
  1. 1.Department of Bioengineering, The Whitaker Institute for Biomedical EngineeringUniversity of California, San DiegoLa JollaUSA
  2. 2.Department of Medical Education and Biomedical InformaticsUniversity of WashingtonSeattleUSA
  3. 3.Department of Structural EngineeringUniversity of California, San DiegoLa JollaUSA
  4. 4.Department of BioengineeringUniversity of WashingtonSeattleUSA
  5. 5.Department of MedicineUniversity of California, San DiegoLa JollaUSA

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