Evaluation of the time constant as an index of isovolumic ventricular relaxation in the normal cat

Ventricular relaxation is of considerable importance to the overall performance of the heart. Because relaxation cannot be measured directly in the intact heart, clinicians and physiologists are dependent upon indirect indices of relaxation. The time constant of isovolumic pressure decline (T) is currently the most frequently used index of ventricular relaxation.

The time constant describes the rate of left ventricular pressure (LVP) decline, and has been calculated either by fitting the LVP data to one of two monoexponential models or determined directly from the left ventricular pressure recording. The time constant Texp is derived by fitting LVP to the function: P = Ae^bt + Pb, where Texp = -1/b and Pb is a variable pressure asymptote. The time constant Tln is calculated from a simplification of the above model. The asymptote Pb is assumed to be equal to zero, and the function is linearized using a logarithmic transformation so that: lnP = lnPo + bt, with Tln = -1/b. A third time constant T½ is determined directly from the pressure-time data as the time required for the pressure at the beginning of isovolumic relaxation to decline by one-half.

Although the time constant has been used frequently as an index of relaxation, the appropriateness of the methods used to estimate T is controversial. It is not clear whether the values of Tln, Texp, and T½ are affected by changes in other hemodynamic conditions, or whether the three estimates of T provide equivalent information regarding relaxation.

The present study was designed to define the limitations of the three estimates of T. The effects of independent increases in preload, afterload, contractility, and heart rate on the values of Tln, Texp, and T½ were evaluated using normal cats anesthetized with isoflurane. In addition, the appropriateness of the mathematical models used to calculate Tln and Texp were assessed by comparing how well each of the models predicted actual LVP decline.

The values of Tln, Texp, and T½ were unaffected by changes in heart rate, inotropic state, and afterload. The index Texp also proved to be independent of preload, but the values of Tln and T½ both increased as preload was increased. Whereas the values of Tln and T½ were consistently related across all hemodynamic conditions, Texp was not consistently related to either Tln or T½ due to variability in the values of Texp.

These results indicate that T½ and Tln provide similar information regarding relaxation, but both indices must be interpreted carefully in experiments in which preload is changed. Although the mathematical model used to calculate Texp is somewhat better statistically than the model used to calculate Tln, the complexity of the model used to calculate Texp introduces variability which may confound attempts to measure small changes in ventricular relaxation. On the basis of these results, it is recommended that T½ may be the most practical and reliable method of determining a time constant in experiments in which preload is constant.