Fractal kinetic implementation in population modeling
Woojin Jung1, Yujoung Choi 1, Jung-woo Chae1,2*, Hwi-yeol Yun1,2*
1: College of Pharmacy, Chungnam National University, Daejeon, South Korea, 2: Bio-AI Convergence Research Center, Chungnam National University, South Korea, *: Those of authors contributed equally as correspondence.
Objectives: Compartment modeling is a widely accepted technique in the field of pharmacokinetic analysis. However, conventional compartment modeling is commonly performed under a homogeneity assumption that is not occurring condition in nature. Since the assumption lacks physiological considerations, the respective modeling approach has been questioned, as novel drugs are increasingly characterized by physiological or physical features, thus recent drug models prone to be made complicated and overparameterized to account for the mechanistic part of the model. Alternative approaches have focused on fractal kinetics, but evaluations of their applications are lacking. In this study, a simulation was performed to identify desirable fractal-kinetics applications in conventional modeling. Visible changes in the profiles were then investigated and common diagnostics for the model were compared.
Methods: As a fractal-like kinetic, Kopelman’s method was applied to the absorption part of the model. Five cases of finalized population models were collected for implementation. For model diagnosis, the objective function value (OFV), Akaike’s information criterion (AIC), and corrected Akaike’s information criterion (AICc) were used as performance metrics, and the goodness of fit (GOF), visual predictive check (VPC), and normalized prediction distribution error (NPDE) were used as visual diagnostics. NONMEM (version 7.5.0.) and PsN (Perl-speaks-NONMEM, version 5.2.6.) is chosen for estimation study. Depending on the model, different ADVAN routines were used for its integration methods to make the minimization success. The test was performed without modifying the model structure, except the rate parameter itself to the fractal-like form. Structure change was made only when the model’s improvement was not significant.
Results: : In most cases, model performance was enhanced by the fractal rate, as shown in a simulation study. The necessary parameters of the fractal rate in the model varied and were successfully estimated between 0 and 1. GOF, VPC, and NPDE diagnostics show that models with the fractal rate described the data well and were robust. In the simulation study, the fractal absorption process was, therefore, chosen for testing. In the estimation study, the rate application yielded improved performance and good prediction–observation agreement in early sampling points and did not cause a large shift in the original estimation results. Among the five cases, four cases were improved by simple introduction of heterogeneity exponent, the improvement was significant in performance metrics (-33.62, -385.10, -16.79, -8.34) without any change in given model structure. Structure change was made together with fractal-like kinetics of time-dependent rate coefficient and Weibull-absorption function, and the rest model was also shown to be improved.
Conclusions: The fractal rate yielded explainable parameters by setting only the heterogeneity exponent, which reflects true physiological behavior well. This approach can be expected to provide useful insights in pharmacological decision making.
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