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 169Yb-DTPA and 99mTc-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 CLTk-GV clearance values agreed with published CL corrections with the general result that CLE1 > CLE2 > CLTk-GV and finally that CLTk-GV were considerably more robust, precise and accurate than CLE2, and should replace the use of CLE2 for these renal markers.

A gamma-distribution convolution model of 99mTc-MIBI thyroid time-activity curves

“…For example, the GDC residuals were homoscedastic over the entire sampling space, which is never the case for washout-only models as washout models are at a maximum value initially, when actual concentration is zero. It has been shown in other systems that washout models, even with a 10 min start time, statistically significantly mismatched early data and agreed better with late data [12]. …”

“…However, washout models do not form accurate models of early time TACs—see Fig. 1d—and [45], and that is a good motive for creating more complete models, i.e., that better fit the data, with the alternatives being (1) to ignore the early data, extend the data collection for hours, and to use models whose misregistration magnifies substantially outside of fit range—see [12, 45], or (2) include the early data and suffer significant, large misregistration within the fit range—see [12]. Despite the pleomorphic shapes of an assumed fast function, and the noise problem, the resulting GDC functions’ misregistration of the TACs counts was only 0.80% with a total fit error of 1.44% (see Misregistration in the Appendix section).…”

“…One of these latter, Tk-GV; the Tikhonov regularized gamma variate herein adaptively minimizes the relative error of β or alternatively the minimum relative error of plasma clearance [12, 13, 32]. Briefly, Tk-GV is an approximate inverse solution to Eq.…”

“…Exponential distributions are not the preferred shapes to explain organ bolus input function shapes, for which GDs or other functions are more useful [27–29]. To model the prolonged washout kinetics, which models are only fit following peak organ activity, GDs, one of several possible generalizations of EDs, have better fidelity than mono- and bi-exponential models [12, 13, 30–33]. One reason for this is that GD washout models imply zero initial drug volume with no initial mixing [33].…”

“…Thus, at the earliest times following a bolus, there is a severe mismatch between a washout model and the signal it models. Consequently, most of the routinely used pharmacokinetic models, e.g., classic compartmental washout models, do a poor job of fitting early-time organ activity [12, 13]. Thus, washout functions do not fit concentration or time-activity curves well enough to serve as accurate simulation study models.…”