Original Paper

Cardiovascular Engineering

, Volume 6, Issue 2, pp 51-70

First online:

The Donders Model of the Circulation in Normo- and Pathophysiology

  • Gerrit J. NoordergraafAffiliated withDepartment of Anesthesia and Resuscitation, St Elisabeth Hospital Email author 
  • , Johnny T. OttesenAffiliated withDepartment of Mathematics and Physics, University of Roskilde
  • , Wil J.P.M. KortsmitAffiliated withDepartment of Mathematics and Informatics, Technical University
  • , Wil H.A. SchildersAffiliated withDepartment of Mathematics and Informatics, Technical University
  • , Gert J. SchefferAffiliated withDepartment of Anesthesiology, University Medical Center Nijmegen
  • , A. NoordergraafAffiliated withCardiovascular Studies Unit, University of Pennsylvania

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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 modeling Equations Impedance-defined flow Physiology Cardiopulmonary resuscitation (CPR) Circulation