Modeling the circulation with three-terminal electrical networks containing special nonlinear capacitors

Joshua E. Tsitlik, Henry R. Halperin, Aleksander S. Popel, Artin A. Shoukas, Frank C.P. Yin, Nicolaas Westerhof

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


Development, first of analog and later of digital computers, as well as algorithms for analysis of electrical circuits, stimulated the use of electrical circuits for modeling the circulation. The networks used as building blocks for electrical models can provide accurate representation of the hydrodynamic equations relating the inflow and outflow of individual segments of the circulation. These networks, however, can contain connections in which voltages and currents have no analogues in the circulation. Problems arise because (a) electrical current must flow in closed loops, whereas no such constraints exist for hydraulic models; and (b) electrical capacitors have a number of characteristics that are not analogous to those of hydraulic compliant chambers. Disregarding these differences can lead to erroneous results and misinterpretation of phenomena. To ensure against these errors, we introduce an imaginary electrical element, the nonlinear residual-charge capacitor (NRCC), with characteristics equivalent to those of a compliant chamber. If one uses appropriate circuit connections and incorporates the residual-charge capacitor, then all voltages and currents in the model are proper analogues of pressures and flows in the circulation. It is shown that the capacitive current represents the rate of change of volume of blood inside the vessel, as well as the rate of the corresponding displacement of volume of the surrounding tissue.

Original languageEnglish (US)
Pages (from-to)595-616
Number of pages22
JournalAnnals of biomedical engineering
Issue number6
StatePublished - Nov 1992


  • Circulation
  • Electrical model
  • Hydraulic model
  • Mathematical model
  • Modeling of circulation
  • Modeling of physiological systems

ASJC Scopus subject areas

  • Biomedical Engineering


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