Abstract
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Objectives: For some malignancies, more than one radiopharmaceutical is available as a treatment agent. In the case where these radiopharmaceuticals are associated with different critical organs, it may be possible to increase tumor dose without exceeding critical organ dose limits by administering both agents in combination. In this investigation we develop a mathematical model that predicts the conditions where combined agent therapy is advantageous and calculates the optimal activity of each agent to achieve the maximum tumor dose within the constraints imposed by the dose to the critical organs.
Methods: It is assumed that values of the tumor dose/MBq (T1 and T2) and the values of the critical organ dose/MBq (Ca1, Ca2, Cb1 and Cb2) have been determined. Ca denotes the critical organ associated with the first agent and Cb denotes the critical organ associated with the second agent. Dose equations are developed in terms of A1 and A2, which are the maximum activities that can be administered of each agent given individually. The combined agent tumor dose (CTD) is expressed as αA1T1 + βA2T2, where T1 and T2 are the tumor dose/MBq for the respective agents and α and β are fractions between 0 and 1. The optimum values of α and β are calculated from the simultaneous equations that determine the total dose to the respective critical organs. The fraction increase in dose (FID) resulting from the combined agent approach is expressed as (CTD – AnTn)/ AnTn, where n = 1 or 2 depending on which agent yields the highest tumor dose when administered alone. Simple algebraic manipulations allowed the expression of FID as a function of T2/T1.
Results: The optimized fractions, αopt and βopt are uniquely determined solely from the critical organ dosimetric parameters. The model predicts that combined agent therapy is effective (i.e., FID > 0) in the range where T2/T1 is greater than Ca2/Ca1 but less than Cb2/Cb1, where Ca1 and Ca2 are the dose/MBq for the two agents of critical organ Ca and Cb1 and Cb2 are the dose/MBq for the two agents of critical organ Cb. Below the lower limit, agent 1 is superior to the agents used in combination and above the upper limit, agent 2 is superior. The model also predicts that the FID is a maximum when T2/T1 = A1/A2 and that the magnitude of the maximum dose increase is given by αopt + βopt – 1.
Conclusions: The model calculates the optimal activities that should be administered in combined agent therapy and makes quantitative predictions about the conditions where it will be beneficial. Under favorable conditions, the combined agent approach can increase the tumor dose substantially more than 50% without exceeding critical organ limits.
- Society of Nuclear Medicine, Inc.