Estimation of time constant of left ventricular relaxation

Abstract

When the fall in left ventricular pressure during isovolumic relaxation is treated as a monoexponential the rate of relaxation can be measured by a time constant. Though an empirical measurement, the time constant has been used extensively to study relaxation. It can be accepted, however, as a valid measurement only if isovolumic pressure fall approximates very closely to a monoexponential in a wide range of circumstances. We analysed 60 beats recorded at different heart rates in 20 patients with a variety of left ventricular disease. In the first part of the study a powerful non-linear regression program was used off-line to test three exponential models: (1) a monoexponential, the asymptote of which is zero, (2) a monoexponential with a variable asymptote, and (3) a biexponential. The pressures predicted by models 2 and 3 were in very close agreement with measured pressure, whereas the predictions of model 1 were consistently less accurate. Model 3 had no advantage over model 2. Thus, in all the beats tested isovolumic pressure fall approximated very closely to a monoexponential of which both the time constant and asymptote are variable. A second exponential term does not increase precision, and is an unnecessary complication. In the second part of the study the same 60 beats were analysed by a small program on the catheter laboratory computer. The time constant was estimated by two methods, corresponding to models 1 and 2 described above: (1) from the slope of 1n (pressure) against time, and (2) by a method of exponential analysis. The first method underestimated the time constant of model 1, particularly in beats where pressure fell to low levels. The second method accurately estimated the time constant of model 2. It is concluded that isovolumic pressure fall approximates closely to a monoexponential in a wide variety of circumstances, and it is legitimate, therefore, to describe the rate of relaxation by a time constant. But the time constant must be estimated by a method based upon an exponential model of which both the time constant and asymptote are variable. We have shown that such a time constant can be estimated reliably by a small program suitable for use on-line. The usual method of estimating the time constant, from the slope of 1n (pressure) against time, provides an unreliable estimate of the time constant of an unsatisfactory model.