Microdosimetry and radiocurability: Modelling targeted therapy with beta-emitters

Tumour control probability (TCP) is a more relevant quantity than the dose distribution in the target volume for estimating the likely efficacy of any type of radiation therapy, be it external beam or targeted using radionuclides. This paper concentrates on a TCP modelling study, for tumour spheres of different radii assuming a uniform uptake of six different beta emitters (ranging from Cu-67 to Y-90 or 0.58 to 2.3 MeV in endpoint energy). The dose at varying radii, expressed as a fraction of the equilibrium dose, D-beta(R)/D-eq, was computed by numerical integration of the point-dose kernel over the sphere volume, and shows clearly the effect of electron disequilibrium for small radii and also at the edges of the spheres. These D-beta(R)/D-eq were converted into volume-dose distributions V(D) and thence into clonogenic cell numbers, n(D), from which the TCPs for spheres of different radii were computed, for different cumulated activities per unit mass, in megabecquerel hours per gram assuming a clonogenic cell density of 10(8) cm(-3) and a tumour-cell radiosensitivity alpha of 1.0 Gy(-1). Using V(D) rather than simply the mean dose decreases the TCP at both large and small tumour radii for a given number of megabecquerel hour per gram. Curves of iso-TCP go through a shallow minimum in megabecquerel hour per gram at a tumour radius approximately equal to the maximum beta-particle range. The fall in dose at small radii outweighs the reduction in cell number, making it improbable that micrometastases can be eliminated solely by beta-emitters targeted to the tumour cells. An explicit comparison with external-beam therapy for a fixed number of tumour cells divided into different numbers of spheres further emphasizes the difficulties caused by small rumours in beta-particle targeted therapy. Alternative strategies to overcome these limitations are briefly discussed.