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Kinetic Modeling of 3'-Deoxy-3'-Fluorothymidine in Somatic Tumors: Mathematical Studies

Department of Radiology, University of Washington, Seattle, Washington

We present a method to measure the regional rate of cellular proliferation using a positron-emitting analog of thymidine (TdR) for human imaging studies. The method is based on the use of 3'-deoxy-3'-¹⁸F-fluorothymidine (FLT) to estimate the flux of TdR through the exogenous pathway. The model reflects the retention of FLT-monophosphate (FLTMP), which is generated by the phosphorylation of FLT by thymidine kinase 1 (TK1), the initial step in the exogenous pathway. Methods: A model of FLT kinetics has been designed based on the assumptions of a steady-state synthesis and incorporation of nucleotides into DNA, an equilibration of the free nucleoside in tissue with the plasma level, and the relative rates of FLT and TdR phosphorylation from prior data using direct analysis with in vitro assays. A 2-compartment model with 4 rate constants adequately describes the kinetics of FLT uptake and retention over 120 min and leads to an estimation of the rate of cellular proliferation using the measured FLT blood clearance and the dynamic FLT uptake curve. Results: Noise characteristics of kinetic parameter estimates for 3 tissues were assessed under a range of conditions representative of human cancer patient imaging. The FLT flux in these tissues can be measured with a SE of <5%, and FLT transport can be estimated with a SE of <15%. Abbreviating the data collection to 60 min or neglecting k₄, giving a 3-parameter model, results in an unsatisfactory loss of accuracy in the flux constant in tumor simulations. Conclusion: These analyses depict model behavior and provide expected values for the accuracy of parameter estimates from FLT imaging in human patients. Our companion paper describes the performance of the model for human data in patients with lung cancer. Further studies are necessary to determine the fidelity of K_FLT (FLT flux) as a proxy for K_TDR (thymidine flux), the gold standard for imaging cellular proliferation.

Key Words: 3'-deoxy-3'-fluorothymidine • thymidine kinase 1 • compartmental modeling • kinetic analysis

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