Volume 22, Issue 7 , Page 859, July 2009
Are We on the Right Way to Calculate Tau?
Article Outline
To the Editor:
The time constant of left ventricular (LV) relaxation, τ, is the most established index to describe diastolic function. However, almost nobody uses it in daily clinical practice.
The 2009 guideline document “Recommendations for the Evaluation of Left Ventricular Diastolic Function by Echocardiography”1 uses a method to calculate τ that was originally published in 19972: “It is possible to combine IVRT [isovolumic relaxation time] with noninvasive estimates of LV end-systolic pressure and LA [left atrial] pressure to derive τ (IVRT/[ln LV end-systolic pressure − ln LA pressure]). This approach has been validated…and can be used to provide a quantitative estimate of τ in place of a qualitative assessment of LV relaxation.”1
Although this method has been validated by simultaneous catheter-derived τ and has been in existence for 12 years, in my opinion, there are too many potentially harmful theoretical assumptions to maintain mathematical and practical integrity. I review those assumptions in the following.
First, the deduction of the formula τ = IVRT/(ln LV end-systolic pressure − ln LA pressure [LAP]) is based on a simplified zero-asymptote method instead of a non-zero-asymptote model.3 It is now widely accepted that a non-zero-asymptote model is better, while a zero-asymptote model is merely acceptable. This assumption is therefore acceptable, but note that several acceptable assumptions in row might be unacceptable.
Second, according to Weiss et al's4 original work, −dP/dtmax begins shortly after aortic valve closure. Thus, −dP/dtmax and aortic valve closure are two different points. However, Nagueh et al1 assumed that they are one point. This is, at the very least, a bold assumption.
Third, Nagueh et al1 similarly assumed that LAP is the same at aortic valve closure and at mitral valve opening. From Figure 1 in their guideline document,1 it is clear that LAP at aortic valve closure is almost at its peak, whereas LAP at mitral valve opening is very low.
Fourth, with LAP still elusive, Nagueh et al1 made another assumption: that LAP equals 10 mm Hg. It is now known that LAP is closely related to τ. If LAP increases from 10 to 30 mm Hg, τ is almost doubled.5
The authors' fifth and final dubious assumption concerns LV pressure at aortic valve closure. Clinically obtainable peak systolic blood pressure was initially tried as a substitute; however, the difference between these values is huge. In the guideline document,1 LV end-systolic pressure is suggested as a substitution. My understanding is that it is diastolic blood pressure. It is more reasonable but clinically difficult to get it accurately on some occasions. Theoretically, it is necessary to measure IVRT and diastolic blood pressure in the same heartbeat to minimize beat-by-beat variability, which may be partly why τ is rarely measured in daily clinical practice.
Consider the above formula in another way. Assuming that IVRT = 80 ms, τ = 80/[ln LV end-systolic pressure − ln 10]. It is then possible to compare different pressures and corresponding values of τ (Table 1).
Table 1. Comparison of different pressures and corresponding values of τ
| Pressure (mm Hg) | τ |
|---|---|
| 60 | 44.6 |
| 70 | 41.1 |
| 80 | 38.5 |
| 90 | 36.4 |
| 100 | 34.7 |
| 110 | 33.4 |
| 120 | 32.2 |
| 130 | 31.2 |
| 140 | 30.3 |
In terms of the substitution for LV pressure at aortic valve closure, peak systolic blood pressure (90-140 mm Hg) will give a “good” result but makes no sense, whereas diastolic blood pressure (60-90 mm Hg) seems more reasonable but produces τ values toward the high end of the scale. The reason for this dilemma is the aforementioned assumptions, especially several fatal ones in a row, leading to a mutation of Weiss et al's4 theory.
Weiss et al4 stated, “The length of this time constant is, by definition, independent of the initial value for pressure and thus does not depend upon aortic valve closure.…These results show that the T for isovolumic pressure fall after [maximum negative] dP/dt is independent of peak ventricular systolic pressure, end-systolic volume or fiber length, minimally dependent on heart rate, and principally a function of systolic fiber shortening.” Now τ must be calculated on the basis of LV end-systolic pressure.
So, are we on the right way to calculate τ? Can validation with catheterization answer all these questions?
Acknowledgment
I sincerely thank Andrew Horning for the preparation of this letter.
References
- Recommendations for the evaluation of left ventricular diastolic function by echocardiography. J Am Soc Echocardiogr. 2009;22:107–133
- . Noninvasive assessment of the ventricular relaxation time constant in humans by Doppler echocardiography. Circulation. 1997;95:151–155
- . Estimation of the left ventricular relaxation time constant tau requires consideration of the pressure asymptote. Physiol Res. 2005;54:601–610
- . Hemodynamic determinants of the time-course of fall in canine left ventricular pressure. J Clin Invest. 1976;58:751–760
- . Calculation of left ventricular relaxation time constant-tau in patients with mitral regurgitation by continuous-wave Doppler. Open Cardiovasc Med J. 2008;2:9–11
PII: S0894-7317(09)00488-X
doi:10.1016/j.echo.2009.05.011
© 2009 American Society of Echocardiography. Published by Elsevier Inc. All rights reserved.
Volume 22, Issue 7 , Page 859, July 2009
