Cluster Gauss-Newton method : An algorithm for finding multiple approximate minimisers of nonlinear least squares problems with applications to parameter estimation of pharmacokinetic models

Parameter estimation problems of mathematical models can often be formulated as nonlinear least squares problems. Typically these problems are solved numerically using iterative methods. The local minimiser obtained using these iterative methods usually depends on the choice of the initial iterate. Thus, the estimated parameter and subsequent analyses using it depend on the choice of the initial iterate. One way to reduce the analysis bias due to the choice of the initial iterate is to repeat the algorithm from multiple initial iterates (i.e. use a multi-start method). However, the procedure can be computationally intensive and is not always used in practice. To overcome this problem, we propose the Cluster Gauss-Newton (CGN) method, an efficient algorithm for finding multiple approximate minimisers of nonlinear-least squares problems. CGN simultaneously solves the nonlinear least squares problem from multiple initial iterates. Then, CGN iteratively improves the approximations from these initial iterates similarly to the Gauss-Newton method. However, it uses a global linear approximation instead of the Jacobian. The global linear approximations are computed collectively among all the iterates to minimise the computational cost associated with the evaluation of the mathematical model. We use physiologically based pharmacokinetic (PBPK) models used in pharmaceutical drug development to demonstrate its use and show that CGN is computationally more efficient and more robust against local minima compared to the standard Levenberg-Marquardt method, as well as state-of-the art multi-start and derivative-free methods

Revisiting Nonlinear Bosentan Pharmacokinetics by Physiologically Based Pharmacokinetic Modeling: Target Binding, Albeit Not a Major Contributor to Nonlinearity, Can Offer Prediction of Target Occupancy

Bosentan is a high-affinity antagonist of endothelin receptors and one of the earliest examples for target-mediated drug disposition [a type of nonlinear pharmacokinetics (PKs) caused by saturable target binding]. The previous physiologically based PK (PBPK) modeling indicated that the nonlinear PKs of bosentan was explainable by considering saturable hepatic uptake. However, it remained unexamined to what extent the saturable target binding contributes to the nonlinear PKs of bosentan. Here, we developed a PBPK model incorporating saturable target binding and hepatic uptake and analyzed the clinical bosentan PK data using the cluster Gauss-Newton method (CGNM). The PBPK model without target binding fell short in capturing the bosentan concentrations below 100 nM, based on the PK profiles and the goodness-of-fit plot. Both global and local identifiability analyses (using the CGNM and Fisher information matrix, respectively) informed that the target binding parameters were identifiable only if the observations from the lowest dose (10 mg) were included. By analyzing blood PK profiles alone, the PBPK model with target binding yielded practically identifiable target binding parameters and predicted the maximum target occupancies of 0.6-0.8 at clinical bosentan doses. Our results indicate that target binding, albeit not a major contributor to the nonlinear bosentan PKs, may offer a prediction of target occupancy from blood PK profiles alone and potential guidance on achieving optimal efficacy outcomes, under the condition when the high-affinity drug target is responsible for the efficacy of interest and when the dose ranges cover varying degrees of target binding. SIGNIFICANCE STATEMENT By incorporating saturable target binding, our physiologically based pharmacokinetic (PBPK) model predicted in vivo target occupancy of bosentan based only on the blood concentration-time profiles obtained from a wide range of doses. Our analysis highlights the potential utility of PBPK models that incorporate target binding in predicting target occupancy in vivo.N

A Simple Decision Tree Suited for Identification of Early Oral Drug Candidates With Likely Pharmacokinetic Nonlinearity by Intestinal CYP3A Saturation

To identify oral drugs that likely display nonlinear pharmacokinetics due to saturable metabolism by intestinal CYP3A, our previous report using CYP3A substrate drugs proposed an approach using thresholds for the linear index number (LIN3A = dose/K-m; K-m, Michaelis-Menten constant for CYP3A) and the intestinal availability (FaFg). Here, we aimed to extend the validity of the previous approach using both CYP3A substrate and non-substrate drugs and to devise a decision tree suited for early drug candidates using in vitro metabolic intrinsic clearance (C-Lint,C- vitro) instead of FaFg. Out of 152 oral drugs (including 136 drugs approved in Japan, US or both), type I nonlinearity (in which systemic drug exposure increases in a more than dose-proportional manner) was noted with 82 drugs (54%), among which 58 drugs were identified as CYP3A substrates based on public information. Based on practical feasibility, 41 drugs were selected from CYP3A substrates and subjected to in-house metabolic assessment. The results were used to determine the thresholds for C-Lint,C- vitro (0.45 mL/min/pmol CYP3A4) and LIN3A (1.0 L). For four drugs incorrectly predicted, potential mechanisms were looked up. Overall, our proposed decision tree may aid in the identification of early drug candidates with intestinal CYP3Aderived type I nonlinearity. (C) 2020 American Pharmacists Association (R). Published by Elsevier Inc. All rights reserved.N

Physiologically‐Based Pharmacokinetic Modeling Analysis for Quantitative Prediction of Renal Transporter–Mediated Interactions Between Metformin and Cimetidine

Metformin is an important antidiabetic drug and often used as a probe for drug-drug interactions (DDIs) mediated by renal transporters. Despite evidence supporting the inhibition of multidrug and toxin extrusion proteins as the likely DDI mechanism, the previously reported physiologically-based pharmacokinetic (PBPK) model required the substantial lowering of the inhibition constant values of cimetidine for multidrug and toxin extrusion proteins from those obtained in vitro to capture the clinical DDI data between metformin and cimetidine.(1) We constructed new PBPK models in which the transporter-mediated uptake of metformin is driven by a constant membrane potential. Our models successfully captured the clinical DDI data using in vitro inhibition constant values and supported the inhibition of multidrug and toxin extrusion proteins by cimetidine as the DDI mechanism upon sensitivity analysis and data fitting. Our refined PBPK models may facilitate prediction approaches for DDI involving metformin using in vitro inhibition constant values.Y

Application of PBPK Modeling and Virtual Clinical Study Approaches to Predict the Outcomes of CYP2D6 Genotype‐Guided Dosing of Tamoxifen

The Tamoxifen Response by CYP2D6 Genotype‐based Treatment‐1 (TARGET‐1) study (n = 180) was conducted from 2012–2017 in Japan to determine the efficacy of tamoxifen dosing guided by cytochrome P450 2D6 (CYP2D6) genotypes. To predict its outcomes prior to completion, we constructed the comprehensive physiologically based pharmacokinetic (PBPK) models of tamoxifen and its metabolites and performed virtual TARGET‐1 studies. Our analyses indicated that the expected probability to achieve the end point (demonstrating the superior efficacy of the escalated tamoxifen dose over the standard dose in patients carrying CYP2D6 variants) was 0.469 on average. As the population size of this virtual clinical study (VCS) increased, the expected probability was substantially increased (0.674 for n = 260). Our analyses also informed that the probability to achieve the end point in the TARGET‐1 study was negatively impacted by a large variability in endoxifen levels. Our current efforts demonstrate the promising utility of the PBPK modeling and VCS approaches in prospectively designing effective clinical trials

Improved Prediction of the Drug-Drug Interactions of Pemafibrate Caused by Cyclosporine A and Rifampicin via PBPK Modeling: Consideration of the Albumin-Mediated Hepatic Uptake of Pemafibrate and Inhibition Constants With Preincubation Against OATP1B

Pemafibrate (PMF) is highly albumin-bound (>99.8%) and a substrate for hepatic uptake transporters (OATP1B) and CYP enzymes. Here, we developed a PBPK model of PMF to capture drug-drug interactions (DDI) incurred by cyclosporine (CsA) and rifampicin (RIF), the two OATP1B inhibitors. Initial PBPK modeling of PMF utilized in vitro hepatic uptake clearance (PSinf) obtained in the absence of albumin, but failed in capturing the blood PMF pharmacokinetic (PK) profiles. Based on the results that in vitro PSinf of unbound PMF was enhanced in the presence of albumin, we applied the albumin-facilitated dissociation model and the resulting PSinf parameters improved the prediction of the blood PMF PK profiles. In refining our PBPK model toward improved prediction of the observed DDI data (PMF co-administered with single dosing of CsA or RIF; PMF following multiple RIF dosing), we adjusted the previously obtained in vivo OATP1B inhibition constants (K-i,K-OATP1B) of CsA or RIF for pitavastatin by correcting for substrate-dependency. We also incorporated the induction of OATP1B and CYP enzymes after multiple RIF dosing. Sensitivity analysis informed that the higher gastrointestinal absorption rate constant could further improve capturing the observed DDI data, suggesting the possible inhibition of intestinal ABC transporter(s) by CsA or RIF. (C) 2020 American Pharmacists Association (R). Published by Elsevier Inc. All rights reserved.N