Physical derivation of nomograms in permanent prostate brachytherapy

Abstract 

Purpose

To demonstrate the physical origin of nomograms in permanent prostate brachytherapy, by using the correlation between fractional integral target dose (FITD) and target volume.

Methods and Materials

The integral dose (ID) E delivered by unit activity is given by the integration of 4πr²D(r)/r²dr×1.44T_1/2 using the point source model from AAPM TG43. If A is the total activity implanted, then total ID will be A×E. Integral target dose are obtained by multiplying the prostate volume V with mean dose D_mean by definition, assuming prostate gland has a unity density. The FITD the target receives is defined as FITD=D_meanV/AE by energy conservation in the target volume. From this equation, the total activity needed to achieve given dose for a target of volume V is obtained. Results are compared with existing nomograms for ¹²⁵I and ¹⁰³Pd, and available clinical data for ¹³¹Cs.

Results

Agreement within 10.0% for ¹²⁵I and ¹⁰³Pd compared with existing nomograms for gland sizes from 18 to 80cc is observed. For ¹³¹Cs, the agreement is within 8.0% compared with available clinical data.

Conclusions

It is shown that the correlation between the FITD and target volume can be used to obtain the total activity needed to achieve prescribed dose. This correlation is inherent rather than empirical. It suggests that the correlation between fraction of energy deposition in target and target volume is the underlying physical origin for nomograms used in permanent prostate brachytherapy.

Keywords: Fractional integral target dose (FITD), Integral dose, Nomogram, Prostate permanent brachytherapy, Total activity