Validating activity prescription schemes in radionuclide therapy based on TCP and NTCP indexes calculation

Full text: In this work a formulation for evaluation and acceptance of activity prescription schemes (single or multiple administrations) in radionuclide therapy based on the calculation of Tumor Control Probability (TCP) and Normal Tissue Complication Probability (NTCP) is presented. The Poisson model was used for TCP calculation and NTCP by using the Lyman-Kutcher-Burman's (LKB) model. All calculations for biological evaluation of the activity prescription schemes are made from the absorbed dose in mGy/MBq of injected activity calculated from the gammagraphic images. The input data for calculations are activity (MBq) per administration, the number of administration proposed and time interval between administrations (equally spaced). The TCP (Poisson model) calculation was made by determination of Biological Equivalent Dose (BED) using a formulation of linear-quadratic (LQ) model in which cell repair and proliferation during the irradiation at low dose rate (LDR) were considered [2]. Similarly, NTCP (LKB's model) calculation was also done from BED determination, but those calculated for LDR were converted to 2Gy-equivalent dose at high dose rate in order to use the tolerance values tabulated [8] and because it is more understandable for physicians. Kidneys, bone marrow and whole body were considered as critical organs. Proliferation was considered only for bone marrow during the BED calculations. The BED model for LDR reported was extended for multi-exponential dose rate function with any number of terms. A formulation for multiple administrations, equally time-spaced where cumulative dose effects are included, is also tested. The dose distribution was considered homogeneous in tumor volume, keeping in mind that some dose distribution parameters, like equivalent uniform dose (EUD), could be used for description of irradiation effects for non-homogeneous dose distribution, as we could find in applications of radionuclide therapy in real clinical situation. Similarly dose distribution in normal tissue is considered as uniform. The tolerance values used where those for whole-volume irradiation of the organ. As acceptance criteria was considered NTCP<0.05; the treatment is not accepted if the critical value is overcame for any critical organs for the proposal. The evaluation/verification of prescription could be done by two ways: (a) direct evaluation in the expression obtained for TCP and NTCP or (b) determination of optimal activity value by iterative methods for given values of time inter-administration and number of administration. The results obtained for two examples (based on clinical data) are discussed where alternative treatment schemes should be evaluated because of toxicity in critical tissues. Nevertheless, the tolerance (maximum tolerable activity) in radionuclide therapy is established considering the absorbed dose in whole body (below 2Gy), other critical organs (kidneys, bone marrow or any other) should be carefully controlled. The whole body absorbed dose may be below the tolerance limit, but the critical limit in critical tissues may be exceeded if lesion uptake is reduced. Although the formulation presented here consider a uniform dose distribution in tumour and normal tissues, it could be easily used with dose distribution parameters that describes more realistically the effects of non-uniform dose distributions more realistically