Problems in the Application of Cardiovascular Models

Our knowledge about the function of a system can be expressed by a model. In fact, knowledge about the function of a system is equivalent to a model. In practice a model can be used to predict certain phenomena and to validate the accuracy of our knowledge by comparison with the reality. Reasoning in terms of modeling of the peripheral circulation began in the 17th century. I mention here Borelli, a contemporary of Galilei, who was the first to describe the function of the arterial system in terms of the systolic storage of blood in the elastic tube of the aorta. Basically his description is equivalent to the windkessel model. Supposedly the analogy between arteries and a windkessel was first used by Steven Hales in the middle of the 18th century. The German word windkessel describes the air chamber which is used to smooth pressure oscillations in pumps and water pipes. The mathematical models developed in the 19th century e.g. by E. H. Weber and his brother, and particularly by Joseph v. Kries were surprisingly complete and were forerunners of modern computer models. It seems that the availability of fast data processing recently revived the application of models for diagnostic purposes which, was first started by O. Frank, Ph. Broemser, O.F. Ranke, and E. Wetterer in this century.