Variation in tau, the time constant for isovolumic relaxation, along the left ventricular base-to-apex axis

Tau (tau), the time constant for isovolumic relaxation, is often used as a measure of cardiac diastolic function. However, several methods of calculating tau have been published which may produce different results and, thereby, different conclusions. The purpose of this study was to determine if the method of tau calculation effects the results when left ventricular pressure (LVP) is measured at different positions along the base-to-apex axis. In 16 dogs, we measured LVP at 6 positions along the base-to-apex axis. We calculated tau using three different methods: 1) a monoexponential model (P(t) = [P0-Pasym]eAt + Pasym, where t = time, P0 = LVP at t = 0, Pasym is asymptotic pressure as t-->infinity, A is -1/tau) with a zero asymptote 2) a monoexponential model with a variable asymptote in which the monoexponential decay equation is differentiated with respect to time and substituted into the original equation so that dP/dt vs. LVP is A (-1/tau), and 3) a monoexponential decay model with variable asymptote in which Pasym and A are varied until the best fit line is reached by minimizing the residual sum of squares. When tau is calculated using method 1, tau measured at the LV base is 98.01% +/- 8.85% of tau at the apex. If calculated using method 2, tau measured at the LV base was 75.46 +/- 39.4% of tau measured at the apex. When method 3 is used for tau calculations, base tau increases to 117.76 +/- 4.91% of the apical tau. We conclude: 1) the method used to calculate tau will effect the results and, thus, conclusions drawn from tau data. 2) When using Method 3, which appears to be the best method for tau calculation, tau increases at the LV base compared to the apex.