Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 80-85 |
| Number of pages | 6 |
| Journal | Journal of Theoretical Biology |
| Volume | 448 |
| DOIs | |
| Publication status | Published - Jul 7 2018 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Modelling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics
Cite this
A PDE multiscale model of hepatitis C virus infection can be transformed to a system of ODEs. / Kitagawa, Kosaku; Nakaoka, Shinji; Asai, Yusuke; Watashi, Koichi; Iwami, Shingo.
In: Journal of Theoretical Biology, Vol. 448, 07.07.2018, p. 80-85.Research output: Contribution to journal › Article
}
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
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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UR - http://www.scopus.com/inward/citedby.url?scp=85045258263&partnerID=8YFLogxK
U2 - 10.1016/j.jtbi.2018.04.006
DO - 10.1016/j.jtbi.2018.04.006
M3 - Article
AN - SCOPUS:85045258263
VL - 448
SP - 80
EP - 85
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
SN - 0022-5193
ER -