A theoretical derivation of the nomograms for permanent prostate brachytherapy

This study calculates the required minimum radioactivity to deliver a presc ribed dose of radiation to a target using radioisotopes in permanent prosta te brachytherapy. Assuming the radioactivity to be in a continuous form, an integral equation - Fredholm equation of the first kind, can be formulated with the radioactivity density used as the variable. The density distribut ion to produce a uniform volume dose rate is determined using a quadrature method and the radial profile behaves smoothly from the zero radius, and pe aks sharply approaching the volume boundary. The density for Pd-103 is abou t 1.5 times that of I-125 due to its higher spatial attenuation. A nomogram is the relationship between the total activity per unit dose (A) and the d imension of the volume (d). Expressing the nomogram as A=cXd(n) U/Gy, then (c,n) = [(0.0098, 2.09) I-125] and [(0.031, 2.25) Pd-103]. Compared with th e Memorial nomogram, (c,n)=[(0.011,2.2) I-125] and [(0.036,2.56) Pd-103], o r that quoted by AAPM TG64, (c,n)=[(0.014,2.05) I-125] and [(0.056,2.22) Pd -103], our calculation determined an average 33% and 35% decrease for I-125 , and 89% and 77% decrease for Pd-103, respectively. Two reasons for the ex tra total activity found in the Memorial and AAPM nomograms are: (a) An imp erfect clinical situation limited by the restraints of implant techniques ( e.g., use of templates) associated with the presence of adjacent normal org ans, and (b) source discretization into seeds. When radioactivity is clumpe d as discrete seeds, higher activity is needed because of ''wastage" in two aspects: (a) Dose cold-spots at intersource spaces, (b) hot-spots around t he sources. Thus in theory, use of lower activity seeds will require less t otal activity to deliver a prescribed dose. Based on our study, Pd-103 deli vers a higher therapeutic ratio and a lower integral dose to the patient co mpared to 1-125. (C) 2001 American Association of Physicists in Medicine.