Cluster Gauss-Newton method and its potential application
to optimal experimental design in drug discovery
Yasunori Aoki 1

yasunori.aoki@farmbio.uu.se
12Peter Gennemark 2

peter.gennemark@astrazeneca.com

Andrew C. Hooker 1

andrew.hooker@farmbio.uu.se

Pharmacometrics Group, Uppsala University, P.O. Box 256 , Uppsala SE-751 05, Sweden
CVMD iMed, AstraZeneca R&D Mölndal, Pepparedsleden 1 Mölndal, SE -431 83, Sweden

Keywords: Optimal Design, Pharmacokinetics, Pharmacodynamics, Bootstrap me thod
Inspired by the Cluster Newton method for an underdetermined inverse problem [1], we haveconstructed a variant that can be used to conduct a bootstrap analysis on an over -determined
inverse problem [2]. The resulting method is more efficient compar ed to a conventional
approach. We then demonstrate how this quick bootstrap method can potentially be used for theoptimal experimental design workflow in preclinical drug discovery studies.
In such studies, in vivo experiments for a drug candidate are typically run in series, and we canrefine the subsequent experiments using the experimental data from the previous experiments. On
the other hand, the time we can spend to design an experiment is very limited and acomputationally efficient algorithm is therefore necessary. We propose an experimental design
workflow where we conduct bootstrap analysis using the data from previously ran experiments
using the Cluster Gauss-Newton method to obtain the parameter and its estimation uncertainty andthen use these information to compute a robust optimal design (ED optimal design) for thesubsequent experiments.
Finally, we demonstrate PopED lite which is an optimal design software for preclinical studies [3].
[1] Yasunori Aoki, Ken Hayami, Hans De Sterck, and Akihiko Konagaya: Cluster Newton Methodfor Sampling Multiple Solutions of Underdetermined Inverse Problems: Application to a
Parameter Identification Problem in Pharmacokinetics , SIAM Journal on Scientific Computing,
Volume 36, Issue 1, 2014, Pages B14-B44.
[2] Yasunori Aoki, Ben Holder, Hans De Sterck, and Ken Hayami: A practical algorithm forpractical parameter identifiability analysis, PAGE 21 (2012) Abstr 2333
[www.page-meeting.org/?abstract=2333][3] Yasunori Aoki, Peter Gennemark, and Andrew C. Hooker: PopED lite - A software package
for the computation of optimal Experimental Designs for preclinical studies .
https://itunes.apple.com/se/app/poped-lite/id836277613?l=en&mt=12, 2014.

Improvements to the Cluster Newton Method for
Underdetermined Inverse Problems
Philippe Gaudreau 1

Ken Hayami 2

pjgaudre@ualberta.ca

hayami@nii.ac.jp

Yasunori Aoki 3

Hassan Safouhi 4yasunori.aoki@farmbio.uu.se

hsafouhi@ualberta.ca

Akihiko Konagaya 5
kona@dis.titech.ac.jp
12345

University of Alberta, Canada
National Institute of Informatics, JapanUppsala University, Sweden
University of Alberta / Campus Saint -Jean, Canada
Tokyo Institute of Technology, Japan

Keywords: Cluster Newton method; Underdetermined inverse problem; Beta distribution;

Pharmacokinetics
The Cluster Newton method (CN method) has proved to be very efficient at finding multiple
solutions to underdetermined inverse problems. In the case of pharmacokinetics, underdetermined
inverse problems are often given extra constraints to restrain the variety of solutions. In thispresentation, we introduce an algorithm based on the two parameters of the Beta distribu tion tofind families of solution near a solution of interest. This allows for a much greater control of thevariety of solutions that can be obtained with the CN method. In addition, this algorithm facilitates
the task of obtaining pharmacologically feasi ble parameters.
[1] Y.Aoki K. Hayami, H. De Sterck, and A. Konagaya, Cluster Newton Method for Sampling Multiple
Solutions of an Underdetermined Inverse Problem: Parameter Identification for Pharmacokinetics.
SIAM Journal on Scientific Computing, 36(1):B14-B44, 2014 .
[2] T. Arikuma, S. Yoshikawa, R. Azuma, K. Watanabe, K. Matsumura, and A. Konagaya, Druginteraction prediction using ontology-driven hypothetical assertion framework for pathway
generation followed by numerical simulation. BMC Bioinformatics, 9(Suppl 6):S11, 2008 .
[3] P. Deuflhard, Newton Methods for Nonlinear Problems -Affine Invariance and Adaptive
Algorithms-, Springer, 2004.
[4] A. Konagaya, Towards an In Silico Approach to Personalized Pharmacokinetics, MolecularInteractions, Prof. Aurelia Meghea (Ed.), ISBN: 978-953-51-0079-9, InTech, 2012 .
[5] K. Yoshida, K. Maeda, H. Kusuhara, and A. Konagaya, Estimation of feasible solution space using
Cluster Newton Method: application to pharmacokinetic analysis of irinotecan withphysiologically-based pharmacokinetic models, BMC Systems Biology Supplement, 7(Suppl3):S3,2013.

Application of Cluster Newton Method for thephysiologically-based pharmacokinetic analyses ofdrug-drug interactions
Kenta Yoshida 1,2,*

kenta.yoshida@fda.hhs.gov

123*

Kazuya Maeda 1

kmaeda@mol.f.u-tokyo.ac.jp

Yuichi Sugiyama 3

ychi.sugiyama@riken.jp

Hiroyuki Kusuhara 1

Akihiko Konagaya 2

kusuhara@mol.f.u-tokyo.ac.jp

kona@dis.titech.ac.jp

Graduate School of Pharmaceutical Sciences, The University of Tokyo, 7 -3-1 Hongo,
Bunkyo-ku, Tokyo 113-0033, Japan
Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology,
4256 Nagatsuta-cho, Midori-ku, Yokohama 226-8503, JapanRIKEN Research Cluster for Innovation, 1-6, Suehiro-cho, Tsurumi-ku, Yokohama 230-0045,
Japan(Current affiliation: Center for Drug Evaluation and Research, U.S. Food and Drug
Administration, 10903 New Hampshire Avenue, Silver Spring, MD 20993, USA )Keywords: drug–drug interactions, pharmacokinetics, PBPK model
Pharmacokinetic drug–drug interactions (DDIs) are one of the major causes of unexpected changeof pharmacological/toxicological effects of victim drugs . For the analyses and predictions of DDIs,
physiologically-based pharmacokinetic (PBPK) models are widely used in the process of drug
development. However, reliable estimations of parameters in PBPK models remain difficult, due tothe difficulties in rationally setting up model parameters only from in vitro experimental results or
estimating the values of large number of unknown parameters . To overcome these issues, we
introduced Cluster Newton Method (CNM) [1,2] in PBPK analyses of DDIs. We analyzed twotypes of DDIs that are difficult to analyze with conventional parameter optimization methods: (1) ahepatic transporter-mediated DDI between pitavastatin and cyclosporine A, and (2) DDIs involving
the inhibition of various cytochrome P450 (CYP) enzymes with pharmacokinetic alterations of themetabolites of victim drugs. As a result, we could successfully obtain multiple parameter sets
reproducing clinical observations. Inhibition constants (K i ), which are important in the predictionof new DDI cases, were estimated well, while most of the other parameters had certain deviations
in estimated values. Further application of the CNM may improve in vitro-in vivo extrapolations ofK i , which can lead to the accurate preclinical prediction of DDIs.
[1] Aoki, Y., et al., Cluster Newton Method for Sampling Multiple Solutions ofUnderdetermined Inverse Problems: Application to a Parameter Identificat ion Problem
in Pharmacokinetics , Siam J Sci Comput, 36(1): B14-B44, 2014.
[2] Yoshida, K., et al., Estimation of feasible solution space using Cluster Newton Method:
application to pharmacokinetic analysis of irinotecan with physiologically -based
pharmacokinetic models , BMC Systems Biology, 7(Suppl 2):S3, 2013.