TY - JOUR
T1 - A PDE multiscale model of hepatitis C virus infection can be transformed to a system of ODEs
AU - Kitagawa, Kosaku
AU - Nakaoka, Shinji
AU - Asai, Yusuke
AU - Watashi, Koichi
AU - Iwami, Shingo
N1 - Funding Information:
This work was supported in part by the JST PRESTO and CREST program (to S.I.), the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Numbers 16H04845 , 16K13777 , 15KT0107 and 26287025 (to S.I.), a Grant-in-Aid for Scientific Research on Innovative Areas from the Ministry of Education, Culture, Science, Sports, and Technology (MEXT) of Japan 16H06429 , 16K21723 , and 17H05819 (to S.I.), J-PRIDE 17fm0208006h0001, 17fm0208019h0101, 17fm0208014h0001 (to K.W. and S.I.) and 17fm0208019j0001 (to K.W.), the Program on the Innovative Development and the Application of New Drugs for Hepatitis B 17fk0310114h0101 (to K.W.) and 17fk0310114j0001, AMED (to K.W.), the Mitsui Life Social Welfare Foundation (to S.I.), the Shin-Nihon of Advanced Medical Research (to S.I.), a GSK Japan Research Grant 2016 (to S.I.), the Mochida Memorial Foundation for Medical and Pharmaceutical Research (to S.I.), the Suzuken Memorial Foundation (to S.I.), the SEI Group CSR Foundation (to S.I.), the Life Science Foundation of Japan (to S.I.), the SECOM Science and Technology Foundation (to S.I.), and the Center for Clinical and Translational Research of Kyushu University Hospital (to S.I.). We also thank Leonie Pipe, PhD, from Edanz Group ( www.edanzediting.com/ac ) for editing a draft of this manuscript.
Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2018/7/7
Y1 - 2018/7/7
N2 - Direct-acting antivirals (DAAs) treat hepatitis C virus (HCV) by targeting its intracellular viral replication. DAAs are effective and deliver high clinical performance against HCV infection, but optimization of the DAA treatment regimen is ongoing. Different classes of DAAs are currently under development, and HCV treatments that combine two or three DAAs with different action mechanisms are being improved. To accurately quantify the antiviral effect of these DAA treatments and optimize multi-drug combinations, we must describe the intracellular viral replication processes corresponding to the action mechanisms by multiscale mathematical models. Previous multiscale models of HCV treatment have been formulated by partial differential equations (PDEs). However, estimating the parameters from clinical datasets requires comprehensive numerical PDE computations that are time consuming and often converge poorly. Here, we propose a user-friendly approach that transforms a standard PDE multiscale model of HCV infection (Guedj J et al., Proc. Natl. Acad. Sci. USA 2013; 110(10):3991–6) to mathematically identical ordinary differential equations (ODEs) without any assumptions. We also confirm consistency between the numerical solutions of our transformed ODE model and the original PDE model. This relationship between a detailed structured model and a simple model is called “model aggregation problem” and a fundamental important in theoretical biology. In particular, as the parameters of ODEs can be estimated by already established methods, our transformed ODE model and its modified version avoid the time-consuming computations and are broadly available for further data analysis.
AB - Direct-acting antivirals (DAAs) treat hepatitis C virus (HCV) by targeting its intracellular viral replication. DAAs are effective and deliver high clinical performance against HCV infection, but optimization of the DAA treatment regimen is ongoing. Different classes of DAAs are currently under development, and HCV treatments that combine two or three DAAs with different action mechanisms are being improved. To accurately quantify the antiviral effect of these DAA treatments and optimize multi-drug combinations, we must describe the intracellular viral replication processes corresponding to the action mechanisms by multiscale mathematical models. Previous multiscale models of HCV treatment have been formulated by partial differential equations (PDEs). However, estimating the parameters from clinical datasets requires comprehensive numerical PDE computations that are time consuming and often converge poorly. Here, we propose a user-friendly approach that transforms a standard PDE multiscale model of HCV infection (Guedj J et al., Proc. Natl. Acad. Sci. USA 2013; 110(10):3991–6) to mathematically identical ordinary differential equations (ODEs) without any assumptions. We also confirm consistency between the numerical solutions of our transformed ODE model and the original PDE model. This relationship between a detailed structured model and a simple model is called “model aggregation problem” and a fundamental important in theoretical biology. In particular, as the parameters of ODEs can be estimated by already established methods, our transformed ODE model and its modified version avoid the time-consuming computations and are broadly available for further data analysis.
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U2 - 10.1016/j.jtbi.2018.04.006
DO - 10.1016/j.jtbi.2018.04.006
M3 - Article
C2 - 29634960
AN - SCOPUS:85045258263
VL - 448
SP - 80
EP - 85
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
SN - 0022-5193
ER -