Cluster Newton Method


Prof. Ken Hayami (National Institute of Informatics)

Dr. Yasunori Aoki (Uppsala University)


Cluster Newton Method Source Code:

Copyright Notice

COPYRIGHT © 2014-2022 Yasunori Aoki, Ken Hayami and Akihiko Konagaya

Released under the MIT license:

Release Note:

Here is the procedure to make the MATLAB code work with version R2015b.

To make the MATLAB code work for version R2015b, please change the
following lines:

In main.m, change line 3 from
  matlabpool open
  poolobj = parpool;
and remove line 17
  matlabpool close

In PBPK_model.m, change line 46 from
  function [ans]=RHS(t,u)
  function [answer]=RHS(t,u)
and change line 49 from

Then running main.m should perform as usual.

Please provide feedback if you have any questions or suggestions.

info-elsi [at] 

The following MATLAB codes of Aoki’s original Cluster Newton Method[1] and  Arikuma Irinotecan PBPK model[2]  are released under the MIT license:

In zipfile: inverse_prob_PBPK_model_start_here

PBPK_model.m *

[1]Yasunori Aoki, Ken Hayami, Hans De Sterck, Akihiko Konagaya: Cluster Newton Method for Sampling Multiple Solutions of Underdetermined Inverse Problems:Application to a Parameter Identification Problem in Pharmacokinetics, SIAM J. Scientific Computing, 36 (1), B14-B44 (2014); available at 10.1137/120885462  and  NII-2011-002E

[2] Arikuma T, Yoshikawa S, Azuma R, Watanabe K, Muramatsu K, Konagaya A.: Drug interaction prediction using ontology-driven hypothetical assertion framework for pathway generation followed by numerical simulation, BMC Bioinformatics, vol. 9 (Suppl 6), S11 (2008); available at doi:10.1186/1471-2105-9-S6-S11

* Arikuma irinotecan PBPK model was originally written by Takeshi Arikuma in GNU Octave in 2008, and then rewritten and improved by Yasunori Aoki in Matlab in 2011.

The following MATLAB codes of Yoshida’s Cluster Newton Method[3], Gaudreau’s Cluster Newton Method[4] are published as some derivatives of the original cluster newton method under the Academic Free License, version 3.0 specified below. The following references should be cited when publishing related topics with these codes, respectively.

[3]Yoshida K, Maeda K, Kusuhara H, Konagaya A: Estimation of feasible solution space using Cluster Newton Method: application to pharmacokinetic analysis of irinotecan with physiologically-based pharmacokinetic models, BMC Systems Biology 2013, 7 (Suppl 3): S3 (2013); available at doi:10.1186/1752-0509-7-S3-S3

[4]Philippe Gaudreau, Ken Hayami, Y. Aoki, Hassan Safouhi, Akihiko Konagaya:
Improvements to the cluster Newton method for underdetermined inverse problems.J. Computational Applied Mathematics283:122-141(2015); available at doi:10.1016/  and  NII-2013-002E

In zipfile: invprob_140127