Cardiovascular Engineering

, Volume 6, Issue 2, pp 51–70

The Donders Model of the Circulation in Normo- and Pathophysiology


    • Department of Anesthesia and ResuscitationSt Elisabeth Hospital
  • Johnny T. Ottesen
    • Department of Mathematics and PhysicsUniversity of Roskilde
  • Wil J.P.M. Kortsmit
    • Department of Mathematics and InformaticsTechnical University
  • Wil H.A. Schilders
    • Department of Mathematics and InformaticsTechnical University
  • Gert J. Scheffer
    • Department of AnesthesiologyUniversity Medical Center Nijmegen
  • A. Noordergraaf
    • Cardiovascular Studies UnitUniversity of Pennsylvania
Original Paper

DOI: 10.1007/s10558-006-9004-6

Cite this article as:
Noordergraaf, G., Ottesen, J., Kortsmit, W. et al. Cardiovasc Eng (2006) 6: 51. doi:10.1007/s10558-006-9004-6


The solution of some recent as well as of long standing problems, unanswerable due to experimental inaccessibility or moral objections are addressed. In this report, a model of the closed human cardiovascular loop is developed. This model, using one set of 88 equations, allows variations from normal resting conditions to exercise, as well as to the ultimate condition of a circulation following cardiac arrest. The principal purpose of the model is to evaluate the continuum of physiological conditions to cardiopulmonary resuscitation (CPR) effects within the circulation.

Within the model, Harvey’s view of the circulation has been broadened to include impedance-defined flow as a unifying concept, and as a mechanism in CPR. The model shows that depth of respiration, sympathetic stimulation of cardiac contractile properties and baroreceptor activity can exert powerful influences on the increase in cardiac output, while heart and respiratory rate increases tend to exert an inhibiting influence, with the pressure and flow curves compatible with accepted references. Impedance-defined flow encompasses both positive and negative effects.

The model also demonstrates the limitations to cardiopulmonary resuscitation caused by external force applied to intrathoracic structures, with effective cardiac output being limited by collapse and sloshing. Stroke volumes from 6 to 51 ml are demonstrated. It shows that the clinical inclination to apply high pressures to intrathoracic structures may not be rewarded with improved net flow.


Cardiovascular system modelingEquationsImpedance-defined flowPhysiologyCardiopulmonary resuscitation (CPR)Circulation

Copyright information

© Springer Science+Business Media, Inc. 2006