2013 - Glasgow - Scotland

PAGE 2013: Methodology - New Modelling Approaches
Wojciech Krzyzanski

Physiologically Structured Population Model of Intracellular Hepatitis C Virus Dynamics

Wojciech Krzyzanski (1), Xavier Woot de Trixhe (2), Filip De Ridder (2), An Vermeulen (2)

(1) University at Buffalo, NY, USA; (2) Janssen Research & Development, a division of Janssen Pharmaceutica NV, Beerse, Belgium

Objectives: To develop a physiologically structured population model capable of describing intracellular dynamics of viral RNA and its integration with observable circulating HCV RNA levels.

Methods: The standard model of viral dynamics [1] consists of target cells (T), infected cells (I), and viral load (V). The circulating virus levels are determined by the production (pI) and elimination rate (cV). The drug inhibits the viral production rate. To explain the discrepancy in the estimates of the half-life of the circulating HCV RNA, the standard cellular infection (CI) model was expanded by including the drug effects on intracellular processes of viral RNA production and virion assembly [2]. The central part of this model is the intracellular level of HCV RNA (R). The link between the intracellular and cellular infection (ICCI) model and CI model has been achieved by replacing the constant p with a time dependent p(t) = rR(t). To account for the time scale of intracellular processes, the time from infection a was introduced [3].  a was interpreted as an individual cell characteristic (structure) and an a-structured population model was applied.We propose a new physiologically structured population (PSP) model where R rather than a is the individual cell structure. The production rate for circulating HCV RNA is expressed as rRtot(t), where the total intracellular viral RNA is a new link between ICCI and CI models. The drug effect is dose dependent [4].The p-state equations of the PSP model were integrated resulting in a CI model augmented by a new variable Rtot(t). The model parameters were obtained from [3]. Simulations were performed to compare the time courses of V(t) with the results presented in [3]. Additional simulations were done to study the impact of dose on V(t). All simulations were performed using MATLAB R2012b.

Results: The circulating levels of HCV RNA predicted by the R-structured population model overlap with that for the a-structured model. The dose effect on V(t) exhibits a critical dose Dosecrit. For Dose > Dosecrit, V(t) vanish for larger times implicating virus eradication. For Dose < Dosecrit, those variables approach new steady-states that are dose dependent.

Conclusion: The R-structured population model describes the drug effect on the intracellular processes and allows integration with the cell infection model. The viral load time courses predicted by the PSP model are similar to the time courses generated by the standard CI model.

[1] Neumann AU, Lam NP, Dahari H, Greatch DR, Wiley TE, Mika B, Perelson AS, Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy. Science (1998) 282:103-107.
[2] Guedj J, Neumann AU, Understanding hepatitis C viral dynamics with direct-acting antiviral agents due to the interplay between intracellular replication and cellular infection dynamics. J. Theor. Biol. (2010) 267:330-340.
[3] Guedj J, Dahari H, Rong L, Sansone ND, Nettles RE, Cotler SJ, Layden TJ, Uprichard SL, Perelson AS, Modeling shows that the NS5A inhibitor daclatasvir has two modes of action and yields a shorter estimate of the hepatitis C virus half-life. PNAS (2013) 110: 3991-6.
[4] Snoeck E, Chanu P, Lavielle M, Jacqmin P, Jonsson EN, Jorga K, Goggin T, Grippo J, Jumbe NL, Frey N, A comprehensive hepatitis C viral kinetic model explaining cure. Clin. Pharmacol. Ther. (2010) 87:706-713.

Reference: PAGE 22 (2013) Abstr 2819 [www.page-meeting.org/?abstract=2819]
Oral: Methodology - New Modelling Approaches
Click to open PDF poster/presentation (click to open)