Non-invasive measurement of pulmonary arterial pressure: I. A haemodynamic modelling approach

In order to monitor pulmonary arterial pressure (P) by any non-invasive imaging technique, a haemodynamic model of blood flow kinetics and wall mechanics has been developed. It is a one-dimensional model of pulsatile flow in an elastic pulmonary arterial trunk, assuming that blood is an incompressible fluid and viscous effects are negligible. The equations are P(t)-Pd = rho c2lnS(t)/Sd-1/2pw-2(t) Pd = (Sd/Ss)1/2Pp where, at any time of the ejection phase of systole, P(t), S(t) and w(t) are the pulmonary arterial pressure, cross-sectional area of the pulmonary artery and blood velocity averaged on the cross section S, respectively, PP is the pulse pressure, the difference between the peak systolic pressure and the diastolic pressure Pd; rho is blood density, c pulse wave velocity, and Ss and Sd are maximum (systolic) and minimum (diastolic) values of the cross-sectional area S. Using these equations, P(t) can be calculated if the three parameters, i.e. c, S(t) and w(t) are measured. So far, it has been impossible to measure the pulse wave velocity c non-invasively. We have investigated the calculation of c from S(t) and w(t) using the equation of continuity in the absence and presence of reflected pressure waves. The hypotheses of the haemodynamic model are discussed.