Tikhonov adaptively regularized gamma variate fitting to assess plasma clearance of inert renal markers

Abstract

The Tk-GV model fits Gamma Variates (GV) to data by Tikhonov regularization (Tk) with shrinkage constant, λ, chosen to minimize the relative error in plasma clearance, CL (ml/min). Using (169)Yb-DTPA and (99m)Tc-DTPA (n = 46, 8-9 samples, 5-240 min) bolus-dilution curves, results were obtained for fit methods: (1) Ordinary Least Squares (OLS) one and two exponential term (E₁ and E₂), (2) OLS-GV and (3) Tk-GV. Four tests examined the fit results for: (1) physicality of ranges of model parameters, (2) effects on parameter values when different data subsets are fit, (3) characterization of residuals, and (4) extrapolative error and agreement with published correction factors. Test 1 showed physical Tk-GV results, where OLS-GV fits sometimes-produced nonphysical CL. Test 2 showed the Tk-GV model produced good results with 4 or more samples drawn between 10 and 240 min. Test 3 showed that E₁ and E₂ failed goodness-of-fit testing whereas GV fits for t > 20 min were acceptably good. Test 4 showed CL(Tk-GV) clearance values agreed with published CL corrections with the general result that CL(E1) > CL(E2) > CL(Tk-GV) and finally that CL(Tk-GV) were considerably more robust, precise and accurate than CL(E2), and should replace the use of CL(E2) for these renal markers.