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Author Notes:

Ajit P. Yoganathan, Wallace H. Coulter School of Biomedical Engineering, Georgia Institute of Technology and Emory University, Room 2119, U. A. Whitaker Building, 313 Ferst Drive, Atlanta, GA 30332-0535, USA. Electronic ajit.yoganathan@bme.gatech.edu.


Research Funding:

The authors gratefully acknowledge the Bioengineering Research Partnership (BRP) grant from NIH (HL67622).


  • Science & Technology
  • Technology
  • Engineering, Biomedical
  • Engineering
  • Power
  • Energy
  • Dissipation
  • Dimensional analysis
  • Aortic stenosis
  • Circulation
  • Fontan
  • FLOW

Hemodynamic Energy Dissipation in the Cardiovascular System: Generalized Theoretical Analysis on Disease States


Journal Title:

Annals of Biomedical Engineering


Volume 37, Number 4


, Pages 661-673

Type of Work:

Article | Post-print: After Peer Review


Background: We present a fundamental theoretical framework for analysis of energy dissipation in any component of the circulatory system and formulate the full energy budget for both venous and arterial circulations. New indices allowing disease-specific subject-to-subject comparisons and disease-to-disease hemodynamic evaluation (quantifying the hemodynamic severity of one vascular disease type to the other) are presented based on this formalism. Methods and Results: Dimensional analysis of energy dissipation rate with respect to the human circulation shows that the rate of energy dissipation is inversely proportional to the square of the patient body surface area and directly proportional to the cube of cardiac output. This result verified the established formulae for energy loss in aortic stenosis that was solely derived through empirical clinical experience. Three new indices are introduced to evaluate more complex disease states: (1) circulation energy dissipation index (CEDI), (2) aortic valve energy dissipation index (AV-EDI), and (3) total cavopulmonary connection energy dissipation index (TCPC-EDI). CEDI is based on the full energy budget of the circulation and is the proper measure of the work performed by the ventricle relative to the net energy spent in overcoming frictional forces. It is shown to be 4.01 ± 0.16 for healthy individuals and above 7.0 for patients with severe aortic stenosis. Application of CEDI index on single-ventricle venous physiology reveals that the surgically created Fontan circulation, which is indeed palliative, progressively degrades in hemodynamic efficiency with growth (p < 0.001), with the net dissipation in a typical Fontan patient (Body surface area = 1.0 m2) being equivalent to that of an average case of severe aortic stenosis. AV-EDI is shown to be the proper index to gauge the hemodynamic severity of stenosed aortic valves as it accurately reflects energy loss. It is about 0.28 ± 0.12 for healthy human valves. Moderate aortic stenosis has an AV-EDI one order of magnitude higher while clinically severe aortic stenosis cases always had magnitudes above 3.0. TCPC-EDI represents the efficiency of the TCPC connection and is shown to be negatively correlated to the size of a typical "bottle-neck" region (pulmonary artery) in the surgical TCPC pathway (p < 0.05). Conclusions: Energy dissipation in the human circulation has been analyzed theoretically to derive the proper scaling (indexing) factor. CEDI, AV-EDI, and TCPC-EDI are proper measures of the dissipative characteristics of the circulatory system, aortic valve, and the Fontan connection, respectively.

Copyright information:

© 2009 Biomedical Engineering Society.

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