Analysis of Hepatitis C Virus Decline during Treatment with the Protease Inhibitor Danoprevir Using a Multiscale Model

Abstract

The current paradigm for studying hepatitis C virus (HCV) dynamics in patients utilizes a standard viral dynamic model that keeps track of uninfected (target) cells, infected cells, and virus. The model does not account for the dynamics of intracellular viral replication, which is the major target of direct-acting antiviral agents (DAAs). Here we describe and study a recently developed multiscale age-structured model that explicitly considers the potential effects of DAAs on intracellular viral RNA production, degradation, and secretion as virus into the circulation. We show that when therapy significantly blocks both intracellular viral RNA production and virus secretion, the serum viral load decline has three phases, with slopes reflecting the rate of serum viral clearance, the rate of loss of intracellular viral RNA, and the rate of loss of intracellular replication templates and infected cells, respectively. We also derive analytical approximations of the multiscale model and use one of them to analyze data from patients treated for 14 days with the HCV protease inhibitor danoprevir. Analysis suggests that danoprevir significantly blocks intracellular viral production (with mean effectiveness 99.2%), enhances intracellular viral RNA degradation about 5-fold, and moderately inhibits viral secretion (with mean effectiveness 56%). The multiscale model can be used to study viral dynamics in patients treated with other DAAs and explore their mechanisms of action in treatment of hepatitis C.

Hepatitis C virus cures after direct acting antiviral-related drug-induced liver injury: Case report

“…The fact that the patient achieved SVR despite a very short course of therapy (24 d) was striking since her viral load level 10 d before DAA therapy stopped (3/15/15) was 97 IU/mL, which is several log IU/mL higher than the cure boundary. To estimate, retrospectively, when the patient reached cure we used the standard biphasic HCV treatment model [11,12] and the multiscale HCV treatment model [13,14] . Both these models predicted that cure occurred 3 to 6 wk after therapy was stopped (not shown).…”

A Robust and Efficient Numerical Method for RNA-Mediated Viral Dynamics

“…In the short-term approximation, it was assumed that after therapy is initiated the infected cells maintain their steady-state levels of HCV, whereas in the long-term approximation all new infections after the onset of therapy are neglected. While the short-term approximation has been shown to be precise only in the first half-day of treatment, the long-term approximation is in agreement after several days post-treatment initiation with a simple numerical solution that utilized a canned solver (an ODE solver used in higher level languages such as Matlab and Mathematica, or Python) [41].…”

“…In the age of DAAs, new models are being developed to meet the challenge associated with these new agents [37][38][39]. Notably, the first age-based multiscale mathematical model for HCV kinetics has been developed [25,40,41] providing a more comprehensive understanding of viral treatment response kinetics observed in patients treated with IFN, HCV protease inhibitors (telaprevir and danoprevir), or the HCV NS5A inhibitor daclatasvir as well as modes of action of these drugs.…”

“…As such, it is considerably more difficult to solve compared to the standard biphasic model. Previously short-term and long-term analytical approximations were derived [25,41,43]. In the short-term approximation, it was assumed that after therapy is initiated the infected cells maintain their steady-state levels of HCV, whereas in the long-term approximation all new infections after the onset of therapy are neglected.…”

“…The goal is to considerably improve the numerical solution presented in Rong et al [41] that used a canned solver (an ODE solver used in higher level languages such as Matlab and Mathematica, or Python), making the numerical solution a flexible and robust entity alongside the analytical approximations. As it turns out, because of the properties of this multiscale model and the fact that the differential equations are stiff, some advanced numerical methods that involve adaptive stepsize are needed.…”