(Pressure-Volume Relationship, and Time-Varying Elastance): A powerful tool for studying cardiac mechanics and the interactions between ventricle and circulatory system is the pressure-volume (PV) relationship. Cardiac contractions can be viewed “through the window of the pressure-volume diagram”. Thus, it is possible to link the instantaneous pressure Plv(t) and the instantaneous blood volume Vlv(t) inside the ventricle by means of the following pressure-volume relationship: where P0 is the external pressure, V0 is the ventricular volume at zero transmural pressure [P(t)-P0], and E(t) is the time-varying ventricular elastance. By neglecting the term P0, the ratio: states that in one cardiac cycle the relationship between the instantaneous pressure Plv(t) and the instantaneous volume Vlv(t) inside the ventricle is a time-dependent parameter, which is the time-varying elastance E(t). By connecting isochronous sets of instantaneous pressure-volume data points, a family of curves whose slope rise and fall can be plotted. This results in an increase and decrease of the elastance. All the elastance curves E(t), if normalized with respect to the peak value Emax and the time to peak Tmax would reduce a single curve which has unique shape for any heart, loading conditions, contractile state, or heart rate. As a consequence, Emax and Tmax can serve as a reliable index of ventricular contractility and are independent of preload (end diastolic ventricular volume/atrial pressure) and afterload (aortic pressure/arterial impedance). A more accurate formulation of the pressure-volume relationship is the non-linear time-varying elastance model, where a non-linear time varying function is used instead of the linear one, E(t). Nevertheless, the classical linear formulation of the elastance is still meaningful and much easier to use in most of the cases.
Published in Chapter:
Hybrid Mock Circulatory System to Test Cardiovascular Prostheses on the Grid
Francesco Maria Colacino (University Magna Graecia of Catanzaro and University of Calabria, Italy), Maurizio Arabia (University of Calabria, Italy), and Gionata Fragomeni (University Magna Graecia of Catanzaro, Italy)
Copyright: © 2009
|Pages: 15
DOI: 10.4018/978-1-60566-374-6.ch021
Abstract
In the last decades cardiovascular diseases greatly increased worldwide, and bioengineering provided new technologies and cardiovascular prostheses to medical doctors and surgeons. The design of active and passive devices aroused notable interests becoming more and more challenging as well as crucial. In this framework, it is important to faithfully reproduce the interaction between the prostheses and the cardiovascular system when in-vitro experiments are performed. For this reason, a new and improved kind of test benches becomes necessary. Purely hydraulic mock circulatory systems showed low flexibility to allow tests of different cardiovascular devices and low precision when a reference mathematical model must be reproduced. In this chapter a new bench is described. It combines the computer model of the cardiovascular system and its real-time interaction with the device to be tested. The solution adopted can be exploited in a Grid environment to allow remote experimentation.