Calibrations and validations of biological models with an application on the renal fibrosis

Georgios Karagiannis; Wenrui Hao; Guang Lin

doi:10.1002/cnm.3329

Calibrations and validations of biological models with an application on the renal fibrosis

Int J Numer Method Biomed Eng. 2020 May;36(5):e3329. doi: 10.1002/cnm.3329. Epub 2020 Mar 17.

Authors

Georgios Karagiannis¹, Wenrui Hao², Guang Lin^{3

4}

Affiliations

¹ Department of Mathematical Sciences, University of Durham, Durham, UK.
² Department of Mathematics, Penn State University, University Park, Pennsylvania, USA.
³ Department of Mathematics, School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, USA.
⁴ Department of Statistics (by Courtesy), Purdue University, West Lafayette, Indiana, USA.

PMID: 32101373
DOI: 10.1002/cnm.3329

Abstract

We calibrate a mathematical model of renal tubulointerstitial fibrosis by Hao et al which is used to explore potential drugs for Lupus Nephritis, against a real data set of 84 patients. For this purpose, we present a general calibration procedure which can be used for the calibration analysis of other biological systems as well. Central to the procedure is the idea of designing a Bayesian Gaussian process (GP) emulator that can be used as a surrogate of the fibrosis mathematical model which is computationally expensive to run massively at every input value. The procedure relies on detecting influential model parameters by a GP-based sensitivity analysis, and calibrating them by specifying a maximum likelihood criterion, tailored to the application, which is optimized via Bayesian global optimization.

Keywords: Gaussian process emulation; calibration; renal tubulointerstitial fibrosis; surrogate model.

Publication types

Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

Bayes Theorem
Calibration
Fibrosis*
Kidney Diseases*
Likelihood Functions
Models, Theoretical
Normal Distribution