Doubling time

The doubling time (or TD) is the time necessary so that a characteristic of the phenomenon studied way its value to double. It is a concept which applies to several fields: the Demography, the Medicine…

It is used in Biologie (growth of the bacteria) and in Radiologie where anomalies are measured and followed. The doubling time is for example the duration necessary so that a lesion (like a Tumeur) double of volume.

The shorter the doubling time is, the more the tumor is aggressive (malignant), the more it is long, the more the tumor appears benign.

The calculation of the TD integrates the two simultaneous parameters which are the size of the lesion and the time of interval. It determines a speed of growth or of decrease Mr. has biomathematical approach to clinical tumor growth. Cancer 1961; 14: 1272-1294.

The equation of the TD requires the measurement of the initial diameter, the final diameter and the knowledge of time separating the two examinations.

The equation is: $TD = T_i \ cdot \ log ({2 \ over 3}) \ cdot \ log (\ frac {D_i} {D_t})$

With Ti = time interval between two measurements, Di = initial diameter and Dt = final diameter.

The formula of calculation volume of an Ellipsoidal (i.e., an ellipse 3D like any full nodule) given starting from measures to the three plans, is $V = \ frac {4 \ pi} {3} \ cdot \ frac {W} {2} \ cdot \ frac {T} {2} \ cdot \ frac {L} {2} \ approx 0,524 \ cdot W \ cdot T \ cdot L$ where L is the maximum length, W the maximum width and T the maximum thickness.

If the double diameter, volume is multiplied 3 times of continuation and grows roughly of $d \ cdot \ exp (\ frac {2} {3})$ If double volume, the increase in the diameter is of 26%.

See too

Internal bonds

Half-life, contrary concept

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