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 In (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 In (pressure) against time, provides an unreliable estimate of the time constant of an unsatisfactory model.During isovolumic relaxation the fall in left ventricu-must decay exponentially during relaxation. Its use lar pressure from the point of its maximum rate of can be justified only if isovolumic pressure fall change until it reaches the level of end-diastolic pres-approximates closely to a monoexponential in a wide sure of the preceding beat approximates to a monoex-range of circumstances. In addition, the estimate of ponential and can be characterised by a time con-the time constant is highly dependent upon its stant. 14 Though it has been used widely to study method of calculation.89 The purpose of this study relaxation of the intact ventricle' -7 the time constant was ...

SUMMARY When a decrease in left ventricular isovolumic pressure is considered as an exponential, the rate of relaxation can be defined by a time constant (T). Previously, T has been calculated from the slope of In (pressure) against time, but this method is valid only when the asymptote of the exponential is zero. In this study two estimates of T were made: Tin from the slope of In (pressure) against time, and TEXP by a method of exponential analysis that also estimated the asymptote. These techniques were applied to measurements of left ventricular pressure made at increasing pacing rates in three groups of patients catheterized for chest pain: group 1 (n = 9) normal coronary arteriograms; group 2 (n = 9) -coronary artery disease (CAD) but no angina or lactate production during pacing; and group 3 (n = 9) CAD and angina during pacing. Tjn was always shorter than TEXP, and in groups 1 and 2 TEXP was dependent on heart rate, whereas Tin was not. The asymptote was negative, and increased toward zero during pacing in groups 1 and 2. The difference between TEXP and Tin could be related to the value of the asymptote. In 18 of 20 beats tested, pressures calculated from TEXP and the asymptote were in closer agreement with measured pressures than were the pressures predicted by T1n. Despite their different values, TEXP and Tin each distinguished between the three groups. Although the choice of an exponential model is arbitrary, isovolumic pressure decrease approximates to a single expontial; but this study suggests that both T and the asymptote are variable.THE STUDY of the decrease in left ventricular pressure during isovolumic relaxation is hindered by the lack of a method of quantifying pressure decrease that can be used to compare individual subjects. The maximal rate of pressure decrease (dP/dt min) can decrease during ischemia,l but dependence on endsystolic pressure and fiber length limits its value.2' More recently, a pressure decrease from the point of dP/dt min has been treated as a single exponential, which allows derivation of a time constant that describes relaxation.4 6 The time constant is calculated as the negative reciprocal of the slope of ln (pressure) against time, and the correlation coefficient is used to test the validity of the monoexponential model.4-6 The time constant so derived is relatively insensitive to heart rate, ventricular volume and the level from which pressure decreases,4 7 8 but is prolonged during ischemia.6' This semilogarithmic method of estimating the time constant of an exponential is valid only when the asymptote of the exponential is zero. The zero reference for pressure measurement is an external point; one cannot assume that it corresponds to the asymptote of ventricular pressure decrease or that the asymptote remains constant under different conditions. In this study, we estimated the time constant of isovolumic pressure decrease both from the plot of In (pressure) against time and by a method of exponential analysis that also estimates the asymptote. We used these techn...

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SUMMARY High fidelity measurements of left ventricular pressure were made at increasing pacing rates in 21 patients with hypertrophic cardiomyopathy and a control group of 11 patients investigated for chest pain who proved to have normal hearts. In both groups the fall in pressure during isovolumic relaxation from the point of min dp/dt approximated closely to a monoexponential, and could be described by a time constant and asymptote.The time constant shortened and the asymptote increased as heart rate rose in both groups. The time constant was longer and mi dp/dt less in the cardiomyopathy group than controls at all heart rates. In the cardiomyopathy patients min dp/dt, but not the time constant, was related to systolic pressure. During pacing, eight cardiomyopathy patients developed metabolic evidence of myocardial ischaemia, but indices of relaxation did not differ between these eight and the other 13 either at basal heart rate or the highest pacing rate.In 10 cardiomyopathy patients measurements were repeated at comparable pacing rates after propranolol (0.2 mg/kg). Left ventricular end-diastolic pressure and indices of contractility decreased after the drug, but the time constant did not change. Eight patients received verapamil (20 mg) after which there were substantial reductions in systolic pressure and contractility. Min dp/dt decreased in proportion to systolic pressure, but the time constant was unchanged. At the highest pacing rate before drug administration three patients had abnormal lactate extraction which was corrected by either propranolol (one patient) or verapamil (two patients). Despite abolition of metabolic evidence of ischaemia, relaxation did not improve.It is concluded that abnormal isovolumic relaxation is common in patients with hypertrophic cardiomyopathy, but its severity correlates poorly with other features of the disease. Abnormal relaxation is not the result of ischaemia, and pressure derived indices of relaxation do not improve after the administration of propranolol or verapamil.Impairment of left ventricular relaxation and diastolic function is common in patients with hypertrophic cardiomyopathyl-5 and may reflect the severity and distribution of inappropriate hypertrophy3 4 or be the result of myocardial ischaemia. I 5 Relaxation and diastolic function can improve after the administration of beta blocking drugsl 6 or verapamil.5 It is uncertain whether these drugs act directly upon the diseased myocardiums or by relieving ischaemia.IThe physiology of ventricular relaxation is poorly understood7 and its study is limited by the lack of Accepted for publication 2 August 1982 methods of quantifying isovolumic pressure fall. Min dp/dt is measured easily, but describes only one point during relaxation, and because it depends upon systolic pressure8 is of little use in comparing patients or investigating drugs that change arterial pressure. The fall in left ventricular pressure from the point of min dp/dt until mitral valve opening approximates to a monoexponential so that the rate...

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