Veritas is the daughter of Chronos.

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.

Sunday, October 31, 2010

-dp/dt max is equivalent to Tau

Recently, an editorial (1) from Circulation Heart Failure claimed “Tau derived from the monoexponential model is less dependent on loading conditions than peak -dp/dt and has been used as a reliable index for LV relaxation in many clinical and experimental studies.”

I think –dp/dt max and Tau are the SAME in terms of clinical significance.

This is the proof:
Weiss’ formula:
                   P = e(exp)(t /T+B) +C
The derivative of both sides:
                  dp = e(exp)(t /T+B) (1/T )dt    or:
              dp/dt = e(exp)(t /T+B) (1/T )
Since t starts from peak -dp/dt,  when t=0, we have:
      dp/dt max = e(exp)B (1/T ) = e(exp)B /Tau

Because e(exp)B is a constant, it means -dp/dt max and Tau share a relationship of one to one correspondence. We can draw the conclusion that -dp/dt max and Tau are equivalent indices in clinical significance.


(1)   Kazuhiro Yamamoto. The Time Constant of Left Ventricular Relaxation: Extrication from Load Dependence and overestimation of Functional Abnormality. Circ Heart Fail. 2010;3:178-180.

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