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

Department of Radiology, University of Washington, Seattle, Washington

View larger version (12K): [in a new window]   FIGURE 1. Biochemical fate of FLT is similar to native thymidine but with 2 important distinctions for modeling flux through the DNA salvage pathway: (a) FLTTP is not incorporated into DNA and (b) FLT does not generate significant metabolites during the imaging procedure as does native thymidine. TMP, TDP, and TTP represent mono-, di-, and triphosphates of thymidine. Enzymes identified in pathways are TK1 = thymidine kinase 1; dNT = 5'(3')-deoxyribonucleotidase; TP = thymidine phosphorylase.

View larger version (12K): [in a new window]   FIGURE 2. Kinetic model of FLT metabolism is comprised of an exchangeable tissue compartment (Qe) and a compartment of trapped FLT phosphorylated nucleotides (Qm). Four rate constants describe kinetic transfer rates between the 2 compartments and blood. FLT-gluc = FLT-glucuronide; CpFLT = concentration of FLT in arterial plasma; Cmet = concentration of metabolites in arterial plasma.

View larger version (10K): [in a new window]   FIGURE 3. Blood clearance curve (input function) for FLT (solid line) is determined by combining total blood activity (dotted line) over time and fraction of activity associated with FLT. FLT input function applied to model presented in this report is derived from 9 patients with arterial sampling and using an independent assay to determine proportion of activity associated with FLT.

View larger version (18K): [in a new window]   FIGURE 4. (A) Representative simulated tissue curves for marrow (dotted line), tumor (solid line), and muscle (dashed line) were based on estimated parameter values from lung cancer patients in a companion report (10). The SD at each point is based on errors observed in patient studies. (B) Expansion of curves in A, revealing the simulated error range during first 20 min.

View larger version (25K): [in a new window]   FIGURE 5. Sensitivity function represents time-dependent percentage change in model solution Ct resulting from ±1% change in parameter value. Sensitivity curves for FLT representative of 3 tissue types (marrow = dotted line, tumor = solid line, muscle = dashed line) are plotted with respect to floating model parameters K1 (A), Vd (B), k3 (C), and k4 (D). A 1% change in Ct would indicate a sensitivity function of 1 as defined in Equation 6.

View larger version (28K): [in a new window]   FIGURE 6. Comparisons of estimated vs. "true" parameters K1 (A), Vd (B), k3 (C), k4 (D), and KFLT (E) are plotted for simulated data. The 200 simulated curves represented in plots were generated by randomly varying parameters over a clinically expected range and then adding Poisson noise to each curve based on noise profiles typical in patient studies. Curves were fit by the model optimization process, and the true parameter was compared with the estimated parameter. Estimated value is plotted vs. true value. True value is parameter value used to generate simulated curves.