Is Tau dispensable?

Left ventricular diastolic time constant, Tau is the most established index to describe diastolic function. A Harvard method of Tau was invented by Dr JD Thomas has been dominant non-invasive Tau measurement for more than two decades. Now, Tau is dead clinically. Only when the logically flawed celebrity method is objectively reassessed and discarded, can Tau be given a chance. A new method is dawning and promising…

A Brief History of Tau with Links You Might Need!

A Brief History of Tau

1976, Tau was born in John Hopkins.
1992, the first non-invasive try, Harvard.
1992, the first formula, with four assumptions, Harvard.
1993, another non-invasive try with decent data, Mayo Clinic.
1995, a similar strategy applied to AI patients, Japan.
1995, I published a MR based formula with one assumption.
1997, the Harvard formula was validated in Cleveland.
2005, Langer presented a non-zero asymptote model.
2008, I improved my MR based formulas, without assumption.
2008, I did a similar deduction for AI based Tau.
2008, Chen developed program for my formulas, free download.
2008, my poster in ASE 19th Annual Scientific Sessions.
2009, my poster in CSE forum.
2009, DF guideline (ASE) recommended Harvard formula.
2009, I gave my opinion about the guideline recommendation.
2009, "Response to Bai" from guideline writing group. It motivated me to create this Blog.
2010, Dr Wang and me presented general Tau.
2011-11-29, I gave a talk in National Capital Echo Round (Ottawa)
2016-03-29, I gave a talk at the Heart Institute, the North Hospital (Shenyang, China)
2016-04-01, I gave a talk at the Cardiac Function Dept., the 1st Clinical College, Chinese University of Medicine. (Shenyang, China)
2016, Symmetry inspired by the approach of Tau.
2017, Calculation of LAP (based on my formulas) got a Chinese Natural Science Founding.

Saturday, March 13, 2021

Doppler spectrum precision measurement will reveal more secrets of hemodynamics


For many years, the Doppler spectrum was measured manually in most of times. Their shortcomings include time-consuming, less accuracy and unacceptable variation between operators. A promising automatic measurement is dawning thanks to the Doppler spectrum enveloping widely used in vascular ultrasound, yet the technology needs dramatically improved. In the point of view of engineering, a more accurate measurement is doable with the neck breaking developing computer technology. This issue is overlooked mainly for sake of barely no clinical demand. And now, it is brought in front of us due to measurement of Tau. Tau, left ventricular diastolic time constant is an established best index to describe diastolic function. The non-invasive measurement of tau theory is perfect, [1,5] the practice lags behind because the Doppler measurement accuracy is not satisfactory. From other point of view, less accurate measurement can lead to weird conclusions, even for some celebrities. [6,7]


The Doppler spectrum envelop is simply a curve outlining the spectrum. To get a precision measurement, we need a curve similar to the spectrum envelop, but our curve is totally different due to the way how it will be generated.  Every point of the curve represents the velocity we need at certain time of the spectrum. The velocity is the peak velocity of the most rapid moving red blood cells. In another word, the peak velocity is best correspondence to the pressure gradient at the certain time point. It is unique. Many unique points located by mathematical method create our new curve, thus the Doppler spectrum precision measurement issue will be addressed. 


1.     Measurement of Tau will be more pragmatic. Similarly, LAP measurement is also readily available.

2.     Dp/dt will benefit from it too. dp/dt is an index to describe how powerful the cardiac muscle is during systole, no alternatives. Thought dp/dt measurement has been widely integrated into Echo machines, the application is scarce. Again, a precision measurement is not available, clinicians reluctant to proceed. A precision measurement will revive dp/dt in daily clinic. 

3.     The precision measurement will make all the Doppler spectrum measurement more accurate, convenient, objective. Literally, there is not measurement variation among operations. 

4.     Basically, our curve is an ideal velocity-time curve. On top of it, the first order derivative will give us an accelerated curve, which will be very helpful to better appreciate the hemodynamics at certain time.  We have good faith that extensive applications are on the way. 

5.     Precision measurement will effectively help to get rid of harmful explanations of Doppler spectrum due to ill measurement. 



1.      Bai X. 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.

2.      Wen C, Sun J, Fan C, Dou J. Calculation of Left Ventricular Diastolic Time Constant (TAU) in Dogs with Mitral Regurgitation Using Continuous-Wave Doppler. Ultrasound Med Biol. 2018 Aug;44(8):1778-1785.

3.      Bai X. Calculation of left ventricular relaxation time constant-Tau in patients with aortic regurgitation by continuous-wave Doppler. Open Cardiovasc Med J, 2008, 2:28-30.

4.      Wen C, Calculation of Left Ventricular Diastolic Time Constant (Tau) in Dogs with Mitral Regurgitation Using Continuous-Wave Doppler Spectra. J Geriatr Cardiol. 2021 (accepted)

5.      Bai X, Wang Q. Time constants of cardiac function and their calculations. Open Cardiovasc Med J, 2010,4:168-172.

6.      Bai X. Are we on the right way to calculate tau? J Am Soc Echocardiogr, 2009,22(7):859;author reply 860.

7.      Horning A, Bai X. The Harvard Method Tau Calculation is Incorrect. J Geriatr Cardiol. 2019 May; 16(5): 429–430.

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