Annals of Biomedical Engineering

, Volume 38, Issue 7, pp 2314–2330 | Cite as

Incorporating Autoregulatory Mechanisms of the Cardiovascular System in Three-Dimensional Finite Element Models of Arterial Blood Flow

  • H. J. Kim
  • K. E. Jansen
  • C. A. TaylorEmail author


The cardiovascular system is a closed-loop system in which billions of vessels interact with each other, and it enables the control of the systemic arterial pressure and varying organ flow through autoregulatory mechanisms. In this study, we describe the development of mathematical models of autoregulatory mechanisms for systemic arterial pressure and coronary flow and discuss the connection of these models to a hybrid numerical/analytic closed-loop model of the cardiovascular system. The closed-loop model consists of two lumped parameter heart models representing the left and right sides of the heart, a three-dimensional finite element model of the aorta with coronary arteries, three-element Windkessel models and lumped parameter coronary vascular models that represent the systemic circulation, and a three-element Windkessel model to approximate the pulmonary circulation. Using the connection between the systemic arterial pressure and coronary flow regulation systems, and the hybrid closed-loop model, we studied how the heart, coronary vascular beds, and arterial system respond to physiologic changes during light exercise and showed that these models can realistically simulate temporal behaviors of the heart, coronary vascular beds, and arterial system during exercise of healthy subjects. These models can be used to study temporal changes occurring in the heart, coronary vascular beds, and arterial system during cardiovascular intervention or changes in physiological states.


Blood flow Autoregulation Coronary Aorta Exercise Finite elements 



Hyun Jin Kim was supported by a Stanford Graduate Fellowship. The authors gratefully acknowledge the assistance of Jessica Shih for the construction of the thoracic aorta model with coronary arteries, Dr. C. Alberto Figueroa for providing with a computer tomography image, and Dr. Nathan Wilson for assistance with software development. We also wish to thank Dr. Farzin Shakib for the use of his linear algebra package AcuSolve™ ( and the support of Simmetrix, Inc. for the use of the MeshSim™ ( mesh generator.


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Copyright information

© Biomedical Engineering Society 2010

Authors and Affiliations

  1. 1.Department of Aerospace Engineering SciencesUniversity of Colorado at BoulderBoulderUSA
  2. 2.Department of BioengineeringStanford UniversityStanfordUSA
  3. 3.Department of SurgeryStanford UniversityStanfordUSA
  4. 4.StanfordUSA

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