Pharmacodynamics of PEG-IFN alpha differentiate HIV/HCV coinfected sustained virological responders from nonresponders

Mechanistic Modeling of SARS-CoV-2 and Other Infectious Diseases and the Effects of Therapeutics

Modern viral kinetic modeling and its application to therapeutics is a field that attracted the attention of the medical, pharmaceutical, and modeling communities during the early days of the AIDS epidemic. Its successes led to applications of modeling methods not only to HIV but a plethora of other viruses, such as hepatitis C virus (HCV), hepatitis B virus and cytomegalovirus, which along with HIV cause chronic diseases, and viruses such as influenza, respiratory syncytial virus, West Nile virus, Zika virus, and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which generally cause acute infections. Here we first review the historical development of mathematical models to understand HIV and HCV infections and the effects of treatment by fitting the models to clinical data. We then focus on recent efforts and contributions of applying these models towards understanding SARS-CoV-2 infection and highlight outstanding questions where modeling can provide crucial insights and help to optimize nonpharmaceutical and pharmaceutical interventions of the coronavirus disease 2019 (COVID-19) pandemic. The review is written from our personal perspective emphasizing the power of simple target cell limited models that provided important insights and then their evolution into more complex models that captured more of the virology and immunology. To quote Albert Einstein, "Everything should be made as simple as possible, but not simpler," and this idea underlies the modeling we describe below.

Intrahepatic Viral Kinetics During Direct-Acting Antivirals for Hepatitis C in Human Immunodeficiency Virus Coinfection: The AIDS Clinical Trials Group A5335S Substudy

BACKGROUND

Direct-acting antivirals (DAAs) targeting hepatitis C virus (HCV) have revolutionized outcomes in human immunodeficiency virus (HIV) coinfection.

METHODS

We examined early events in liver and plasma through A5335S, a substudy of trial A5329 (paritaprevir/ritonavir, ombitasvir, dasabuvir, with ribavirin) that enrolled chronic genotype 1a HCV-infected persons coinfected with suppressed HIV: 5 of 6 treatment-naive enrollees completed A5335S.

RESULTS

Mean baseline plasma HCV ribonucleic acid (RNA) = 6.7 log10 IU/mL and changed by -4.1 log10 IU/mL by Day 7. In liver, laser capture microdissection was used to quantify HCV. At liver biopsy 1, mean %HCV-infected cells = 25.2% (95% confidence interval [CI], 7.4%-42.9%), correlating with plasma HCV RNA (Spearman rank correlation r = 0.9); at biopsy 2 (Day 7 in 4 of 5 participants), mean %HCV-infected cells = 1.0% (95% CI, 0.2%-1.7%) (P < .05 for change), and DAAs were detectable in liver. Plasma C-X-C motif chemokine 10 (CXCL10) concentrations changed by mean = -160 pg/mL per day at 24 hours, but no further after Day 4.

CONCLUSIONS

We conclude that HCV infection is rapidly cleared from liver with DAA leaving <2% HCV-infected hepatocytes at Day 7. We extrapolate that HCV eradication could occur in these participants by 63 days, although immune activation might persist. Single-cell longitudinal estimates of HCV clearance from liver have never been reported previously and could be applied to estimating the minimum treatment duration required for HCV infection.

Pharmacokinetics/Pharmacodynamics of Antiviral Agents Used to Treat SARS-CoV-2 and Their Potential Interaction with Drugs and Other Supportive Measures: A Comprehensive Review by the PK/PD of Anti-Infectives Study Group of the European Society of Antimicrobial Agents

There is an urgent need to identify optimal antiviral therapies for COVID-19 caused by SARS-CoV-2. We have conducted a rapid and comprehensive review of relevant pharmacological evidence, focusing on (1) the pharmacokinetics (PK) of potential antiviral therapies; (2) coronavirus-specific pharmacodynamics (PD); (3) PK and PD interactions between proposed combination therapies; (4) pharmacology of major supportive therapies; and (5) anticipated drug-drug interactions (DDIs). We found promising in vitro evidence for remdesivir, (hydroxy)chloroquine and favipiravir against SARS-CoV-2; potential clinical benefit in SARS-CoV-2 with remdesivir, the combination of lopinavir/ritonavir (LPV/r) plus ribavirin; and strong evidence for LPV/r plus ribavirin against Middle East Respiratory Syndrome (MERS) for post-exposure prophylaxis in healthcare workers. Despite these emerging data, robust controlled clinical trials assessing patient-centred outcomes remain imperative and clinical data have already reduced expectations with regard to some drugs. Any therapy should be used with caution in the light of potential drug interactions and the uncertainty of optimal doses for treating mild versus serious infections.

A pharmacokinetic/viral kinetic model to evaluate treatment of chronic HCV infection with a non-nucleoside polymerase inhibitor

BACKGROUND

Viral kinetic models have proven useful in characterizing treatment effectiveness during HCV therapy with interferon (IFN) as well as with direct-acting antivirals (DAAs).

METHODS

Here we use a pharmacokinetic/viral kinetic (PK/VK) model to describe HCV RNA kinetics during treatment with setrobuvir, a non-nucleosidic inhibitor of the HCV NS5B polymerase enzyme. Using PK data from three studies in healthy volunteers and PK and VK data from a Phase I study, where setrobuvir was administered for 3 days, we fitted a two-compartment PK model with first-order absorption and lag-time, an Emax pharmacodynamics model and a standard biphasic VK model.

RESULTS

Setrobuvir's EC₅₀ and Hill coefficient and the viral clearance rate were significantly different (P=0.014, P<0.001 and P=0.004, respectively) between patients infected with HCV subtypes 1b and 1a, leading to an increased viral load decline in patients infected with genotype 1b virus.

CONCLUSIONS

Understanding the combined effects of PK/VK on the performance of a non-nucleoside polymerase inhibitor such as setrobuvir could provide valuable insights into their use in combination with other DAAs as well as to optimize future therapy. Further, our work suggests that patients infected with subtype 1a would need higher doses than those infected with subtype 1b to achieve the same effectiveness. Whether this is true for other non-nucleoside polymerase inhibitors needs to be examined.

Hepatotoxicity and nephrotoxicity in rats induced by carbon tetrachloride and the protective effects of Teucrium polium and vitamin C

This work investigated the protective effects of Teucrium polium (T. polium) and vitamin C (Vit C) against carbon tetrachloride (CCl₄) induced hepatotoxicity and nephrotoxicity in rats. T. polium reduced the Fer reduced antioxidant power (FRAP) (IC₅₀ = 0.89 mg/ml) and 2, 2-diphenyl-1-picrylhydrazyl (DPPH) (IC₅₀ = 0.049 µg/ml) than Vit C, FRAP (IC₅₀ = 0.71 mg/ml) and DPPH (IC₅₀ = 0.029 µg/ml). Male albino Wistar rats were divided into six groups: Group I was used as controls, Group II received CCl₄ in olive oil (0.5 ml/kg) by gavage, Group III received CCl₄ in olive oil (0.5 ml/kg) by gavage after 3 d of receiving T. polium (5 g/l), orally, Group IV received T. polium (5 g/l) alone, by gavage, for 7 d, Group V received CCl₄ in olive oil (0.5 ml/kg) by gavage after 3 d of receiving Vit C (250 mg/kg) by gavage and Group VI received Vit C (250 mg/kg) alone by gavage. CCl₄ showed an increase of serum hepatic and renal markers aspartate aminotransferase (AST), alanine aminotransferase (ALT), urea, and creatinine. Moreover, we noted an increase of lipid peroxidations and a decrease in antioxidants enzymes: superoxide dismutase (SOD), catalase (CAT), glutathione peroxidase (GPx) of CCl₄ rats compared to controls. The pretreatment with (200 mg/kg) of T. polium and with Vit C (250 mg/kg) by gavage, for 7 d, displayed their ability to protect against oxidative damage and biochemical changes induced by CCl₄. Our results were in accordance with histopathological observations.

Mathematical modeling of within-host Zika virus dynamics

Recent Zika virus outbreaks have been associated with severe outcomes, especially during pregnancy. A great deal of effort has been put toward understanding this virus, particularly the immune mechanisms responsible for rapid viral control in the majority of infections. Identifying and understanding the key mechanisms of immune control will provide the foundation for the development of effective vaccines and antiviral therapy. Here, we outline a mathematical modeling approach for analyzing the within-host dynamics of Zika virus, and we describe how these models can be used to understand key aspects of the viral life cycle and to predict antiviral efficacy.

In-host modeling

Understanding the mechanisms governing host-pathogen kinetics is important and can guide human interventions. In-host mathematical models, together with biological data, have been used in this endeavor. In this review, we present basic models used to describe acute and chronic pathogenic infections. We highlight the power of model predictions, the role of drug therapy, and advantage of considering the dynamics of immune responses. We also present the limitations of these models due in part to the trade-off between the complexity of the model and their predictive power, and the challenges a modeler faces in determining the appropriate formulation for a given problem.

A Computational Model of Inhibition of HIV-1 by Interferon-Alpha

Type 1 interferons such as interferon-alpha (IFNα) inhibit replication of Human immunodeficiency virus (HIV-1) by upregulating the expression of genes that interfere with specific steps in the viral life cycle. This pathway thus represents a potential target for immune-based therapies that can alter the dynamics of host-virus interactions to benefit the host. To obtain a deeper mechanistic understanding of how IFNα impacts spreading HIV-1 infection, we modeled the interaction of HIV-1 with CD4 T cells and IFNα as a dynamical system. This model was then tested using experimental data from a cell culture model of spreading HIV-1 infection. We found that a model in which IFNα induces reversible cellular states that block both early and late stages of HIV-1 infection, combined with a saturating rate of conversion to these states, was able to successfully fit the experimental dataset. Sensitivity analysis showed that the potency of inhibition by IFNα was particularly dependent on specific network parameters and rate constants. This model will be useful for designing new therapies targeting the IFNα network in HIV-1-infected individuals, as well as potentially serving as a template for understanding the interaction of IFNα with other viruses.

A strategy for residual error modeling incorporating scedasticity of variance and distribution shape

Nonlinear mixed effects models parameters are commonly estimated using maximum likelihood. The properties of these estimators depend on the assumption that residual errors are independent and normally distributed with mean zero and correctly defined variance. Violations of this assumption can cause bias in parameter estimates, invalidate the likelihood ratio test and preclude simulation of real-life like data. The choice of error model is mostly done on a case-by-case basis from a limited set of commonly used models. In this work, two strategies are proposed to extend and unify residual error modeling: a dynamic transform-both-sides approach combined with a power error model (dTBS) capable of handling skewed and/or heteroscedastic residuals, and a t-distributed residual error model allowing for symmetric heavy tails. Ten published pharmacokinetic and pharmacodynamic models as well as stochastic simulation and estimation were used to evaluate the two approaches. dTBS always led to significant improvements in objective function value, with most examples displaying some degree of right-skewness and variances proportional to predictions raised to powers between 0 and 1. The t-distribution led to significant improvement for 5 out of 10 models with degrees of freedom between 3 and 9. Six models were most improved by the t-distribution while four models benefited more from dTBS. Changes in other model parameter estimates were observed. In conclusion, the use of dTBS and/or t-distribution models provides a flexible and easy-to-use framework capable of characterizing all commonly encountered residual error distributions.

Multi-scale model for hepatitis C viral load kinetics under treatment with direct acting antivirals

Hepatitis C virus (HCV) infections are a global health problem, and extensive research over the last decades has been targeted at understanding its molecular biology and developing effective antiviral treatments. Recently, a number of potent direct acting antiviral drugs have been developed targeting specific processes in the viral life cycle. Here, we developed a mathematical multi-scale model of the within-host dynamics of HCV infection by integrating a standard model for viral infection with a detailed model of the viral replication cycle inside infected cells. We use this model to study patient time courses of viral load under treatment with daclatasvir, an inhibitor of the viral non-structural protein NS5A. Model analysis predicts that treatment efficacy can be increased by combining daclatasvir with dedicated viral polymerase inhibitors, corresponding to promising current strategies in drug development. Hence, our model presents a predictive tool for in silico simulations, which can be used to study and optimize direct acting antiviral drug treatment.

PEGylation and its impact on the design of new protein-based medicines

PEGylation is the covalent conjugation of PEG to therapeutic molecules. Protein PEGylation is a clinically proven approach for extending the circulation half-life and reducing the immunogenicity of protein therapeutics. Most clinically used PEGylated proteins are heterogeneous mixtures of PEG positional isomers conjugated to different residues on the protein main chain. Current research is focused to reduce product heterogeneity and to preserve bioactivity. Recent advances and possible future directions in PEGylation are described in this review. So far protein PEGylation has yielded more than 10 marketed products and in view of the lack of equally successful alternatives to extend the circulation half-life of proteins, PEGylation will still play a major role in drug delivery for many years to come.

Modelling hepatitis C therapy--predicting effects of treatment

Mathematically modelling changes in HCV RNA levels measured in patients who receive antiviral therapy has yielded many insights into the pathogenesis and effects of treatment on the virus. By determining how rapidly HCV is cleared when viral replication is interrupted by a therapy, one can deduce how rapidly the virus is produced in patients before treatment. This knowledge, coupled with estimates of the HCV mutation rate, enables one to estimate the frequency with which drug resistant variants arise. Modelling HCV also permits the deduction of the effectiveness of an antiviral agent at blocking HCV replication from the magnitude of the initial viral decline. One can also estimate the lifespan of an HCV-infected cell from the slope of the subsequent viral decline and determine the duration of therapy needed to cure infection. The original understanding of HCV RNA decline under interferon-based therapies obtained by modelling needed to be revised in order to interpret the HCV RNA decline kinetics seen when using direct-acting antiviral agents (DAAs). There also exist unresolved issues involving understanding therapies with combinations of DAAs, such as the presence of detectable HCV RNA at the end of therapy in patients who nonetheless have a sustained virologic response.

Prediction of long-term treatment outcome in HCV following 24 day PEG-IFN alpha-2b therapy using population pharmacokinetic-pharmacodynamic mixture modeling and classification analysis

Mathematical models have been widely used for understanding the dynamics of the hepatitis C virus (HCV). We propose a method to predict final clinical outcome for 24 HIV-HCV - coinfected patients with the help of a mathematical model based on the first two weeks of PEG-IFN therapy. Applying a pharmacokinetic-pharmacodynamic (PKPD) approach, together with mixture models, to the adapted model of viral dynamics developed by Neumann et al., we have analyzed the influence of PEG-IFN on the kinetics and interaction of target cells, infected cells and virus mRNA. It was found that PEG-IFN pharmacokinetic parameters were similar in sustained virological responders and nonresponders, while the plasma PEG-IFN concentration that decreases HCV production by 50% (EC50) and the rate of infected cell death were different. The treatment outcome depended mainly on the initial viral mRNA concentration and the rate of infected cell death. The population PKPD approach with a mixture model enabled the determination of individual PKPD parameters and showed high sensitivity (93.5%) and specificity (97.4%) for the prediction of the treatment outcome.

Gene expression analysis in serial liver fine needle aspirates

No method with low morbidity presently exists for obtaining serial hepatic gene expression measurements in humans. While hepatic fine needle aspiration (FNA) has lower morbidity than core needle biopsy, applicability is limited due to blood contamination, which confounds quantification of gene expression changes. The aim of this study was to validate FNA for assessment of hepatic gene expression. Liver needle biopsies and FNA procedures were simultaneously performed on 17 patients with chronic hepatitis C virus infection with an additional FNA procedure 1 week later. Nine patients had mild/moderate fibrosis and eight advanced fibrosis. Gene expression profiling was performed using Affymetrix microarrays and TaqMan qPCR; pathway analysis was performed using Ingenuity. We developed a novel strategy that applies liver-enriched normalization genes to determine the percentage of liver in the FNA sample, which enables accurate gene expression measurements overcoming biases derived from blood contamination. We obtained almost identical gene expression results (ρ = 0.99, P < 0.0001) comparing needle biopsy and FNA samples for 21 preselected genes. Gene expression results were also validated in dogs. These data suggest that liver FNA is a reliable method for serial hepatic tissue sampling with potential utility for a variety of preclinical and clinical applications.

Understanding early serum hepatitis D virus and hepatitis B surface antigen kinetics during pegylated interferon-alpha therapy via mathematical modeling

There is little information on the early kinetics of hepatitis delta virus (HDV) and hepatitis B surface antigen (HBsAg) during interferon-α therapy. Here a mathematical model was developed and fitted to frequent HDV and HBsAg kinetic data from 10 patients during the first 28 weeks of pegylated-interferon-α2a (peg-IFN) therapy. Three patients achieved a complete virological response (CVR), defined as undetectable HDV 6 months after treatment stopped with loss of HBsAg and anti-HBsAg seroconversion. After initiation of therapy, a median delay of 9 days (interquartile range [IQR]: 5-15) was observed with no significant changes in HDV level. Thereafter, HDV declined in a biphasic manner, where a rapid first phase lasting for 25 days (IQR: 23-58) was followed by a slower or plateau second phase. The model predicts that the main effect of peg-IFN is to reduce HDV production/release with a median effectiveness of 96% (IQR: 93-99.8). Median serum HDV half-life (t1/2 ) was estimated as 2.9 days (IQR: 1.5-5.3) corresponding to a pretreatment production and clearance of about 10(10) (IQR: 10(9.7) -10(10.7) ) virions/day. None of the patients with flat second phase in HDV achieved CVR. HBsAg kinetics of decline paralleled the second phase of HDV decline consistent with HBsAg-productive-infected cells being the main source of production of HDV, with a median t1/2 of 135 days (IQR: 20-460). The interferon lambda-3 polymorphism (rs12979860) was not associated with kinetic parameters.

CONCLUSION

Modeling results provide insights into HDV-host dynamics, the relationship between serum HBsAg levels and HBsAg-infected cells, IFN's mode of action, and its effectiveness. The observation that a flat second phase in HDV and HBsAg kinetics was associated with failure to achieve CVR provides the basis to develop early stopping rules during peg-IFN treatment in HDV-infected patients.

Using pharmacokinetic and viral kinetic modeling to estimate the antiviral effectiveness of telaprevir, boceprevir, and pegylated interferon during triple therapy in treatment-experienced hepatitis C virus-infected cirrhotic patients

Triple therapy combining a protease inhibitor (PI) (telaprevir or boceprevir), pegylated interferon (PEG-IFN), and ribavirin (RBV) has dramatically increased the chance of eradicating hepatitis C virus (HCV). However, the efficacy of this treatment remains suboptimal in cirrhotic treatment-experienced patients. Here, we aimed to better understand the origin of this impaired response by estimating the antiviral effectiveness of each drug. Fifteen HCV genotype 1-infected patients with compensated cirrhosis, who were nonresponders to prior PEG-IFN/RBV therapy, were enrolled in a nonrandomized study. HCV RNA and concentrations of PIs, PEG-IFN, and RBV were frequently assessed in the first 12 weeks of treatment and were analyzed using a pharmacokinetic/viral kinetic model. The two PIs achieved similar levels of molar concentrations (P=0.5), but there was a significant difference in the 50% effective concentrations (EC50) (P=0.008), leading to greater effectiveness for telaprevir than for boceprevir in blocking viral production (99.8% versus 99.0%, respectively, P=0.002). In all patients, the antiviral effectiveness of PEG-IFN was modest (43.4%), and there was no significant contribution of RBV exposure to the total antiviral effectiveness. The second phase of viral decline, which is attributed to the loss rate of infected cells, was slow (0.19 day(-1)) and was higher in patients who subsequently eradicated HCV (P=0.03). The two PIs achieved high levels of antiviral effectiveness. However, the suboptimal antiviral effectiveness of PEG-IFN/RBV and the low loss of infected cells suggest that a longer treatment duration might be needed in cirrhotic treatment-experienced patients and that a future IFN-free regimen may be particularly beneficial in these patients.

A hepatitis C virus infection model with time-varying drug effectiveness: solution and analysis

Simple models of therapy for viral diseases such as hepatitis C virus (HCV) or human immunodeficiency virus assume that, once therapy is started, the drug has a constant effectiveness. More realistic models have assumed either that the drug effectiveness depends on the drug concentration or that the effectiveness varies over time. Here a previously introduced varying-effectiveness (VE) model is studied mathematically in the context of HCV infection. We show that while the model is linear, it has no closed-form solution due to the time-varying nature of the effectiveness. We then show that the model can be transformed into a Bessel equation and derive an analytic solution in terms of modified Bessel functions, which are defined as infinite series, with time-varying arguments. Fitting the solution to data from HCV infected patients under therapy has yielded values for the parameters in the model. We show that for biologically realistic parameters, the predicted viral decay on therapy is generally biphasic and resembles that predicted by constant-effectiveness (CE) models. We introduce a general method for determining the time at which the transition between decay phases occurs based on calculating the point of maximum curvature of the viral decay curve. For the parameter regimes of interest, we also find approximate solutions for the VE model and establish the asymptotic behavior of the system. We show that the rate of second phase decay is determined by the death rate of infected cells multiplied by the maximum effectiveness of therapy, whereas the rate of first phase decline depends on multiple parameters including the rate of increase of drug effectiveness with time.

Antiretroviral therapy, interferon sensitivity, and virologic setpoint in human immunodeficiency virus/hepatitis C virus coinfected patients

Human immunodeficiency virus (HIV) and hepatitis C virus (HCV) cause substantial mortality, especially in persons chronically infected with both viruses. HIV infection raises plasma HCV RNA levels and diminishes the response to exogenous alpha interferon (IFN). The degree to which antiretroviral therapy (ART) control of infection overcomes these HIV effects is unknown. Participants with HIV-HCV coinfection were enrolled in a trial to measure HCV viral kinetics after IFN administration (ΔHCVIFN ) twice: initially before (pre-ART) and then after (post-ART) HIV RNA suppression. Liver tissue was obtained 2-4 hours before each IFN injection to measure interferon stimulated genes (ISGs). Following ART, the ΔHCVIFN at 72 hours (ΔHCVIFN,72 ) increased in 15/19 (78.9%) participants by a median (interquartile range [IQR]) of 0.11 log10 IU/mL (0.00-0.40; P < 0.05). Increases in ΔHCVIFN,72 post-ART were associated with decreased hepatic expression of several ISGs (r = -0.68; P = 0.001); a 2-fold reduction in a four-gene ISG signature predicted an increase in ΔHCVIFN,72 of 0.78 log10 IU/mL (95% confidence interval [CI] 0.36,1.20). Pre- and post-ART ΔHCVIFN,72 were closely associated (r = 0.87; P < 0.001). HCV virologic setpoint also changed after ART (ΔHCVART ): transient median increases of 0.28 log10 IU/mL were followed by eventual median decreases from baseline of 0.21 log10 IU/mL (P = 0.002). A bivariate model of HIV RNA control (P < 0.05) and increased expression of a nine-gene ISG signature (P < 0.001) predicted the eventual decreased ΔHCVART .

CONCLUSION

ART is associated with lower post-IFN HCV RNA levels and that change is linked to reduced hepatic ISG expression. These data support recommendations to provide ART prior to IFN-based treatment of HCV and may provide insights into the pathogenesis of HIV-HCV coinfection.

Viral kinetic modeling: state of the art

Viral kinetic (VK) modeling has led to increased understanding of the within host dynamics of viral infections and the effects of therapy. Here we review recent developments in the modeling of viral infection kinetics with emphasis on two infectious diseases: hepatitis C and influenza. We review how VK modeling has evolved from simple models of viral infections treated with a drug or drug cocktail with an assumed constant effectiveness to models that incorporate drug pharmacokinetics and pharmacodynamics, as well as phenomenological models that simply assume drugs have time varying-effectiveness. We also discuss multiscale models that include intracellular events in viral replication, models of drug-resistance, models that include innate and adaptive immune responses and models that incorporate cell-to-cell spread of infection. Overall, VK modeling has provided new insights into the understanding of the disease progression and the modes of action of several drugs. We expect that VK modeling will be increasingly used in the coming years to optimize drug regimens in order to improve therapeutic outcomes and treatment tolerability for infectious diseases.

Impact of the peginterferon-α 2a and ribavirin plasma levels on viral kinetics and sustained virological response in genotype 1 HCV/HIV-co-infected patients with the unfavourable non-CC IL28B genotypes

Studies on the association between the peginterferon-α and ribavirin levels and sustained virological response (SVR) have shown yielded conflicting results, but most of them were performed before the influence of IL28B polymorphisms was known. Our aim was to assess the effects of peginterferon-α 2a and ribavirin plasma levels on viral kinetics and SVR in hepatitis C virus genotype 1 HCV-1/HIV-co-infected patients according to IL28B genotype. This was a cohort study of HCV-1/HIV-co-infected patients who were HCV-treatment naïve and for whom the efficacy of peginterferon-α 2a plus ribavirin was evaluated by per-protocol analysis. The peginterferon-α 2a and ribavirin levels were measured by ELISA and HPLC-UV, respectively. The relationships among host and viral factors, the trough drugs levels and virological responses were analysed by multivariate regression analyses. A total of 131 Caucasian patients were included (cirrhosis:38.9%). Overall, SVR rate was 39.6%. In patients with CC IL28B genotype, SVR was related neither to peginterferon-α 2a nor to ribavirin plasma levels, while higher levels of both drugs were the only variables independently associated with SVR in individuals with CT/TT IL28B genotypes (OR, 5.02; CI95 , 1.45-17.1; P = 0.001 and 4.0; CI95 , 1.08-14.7; P = 0.038, respectively). Moreover, faster viral declines were observed in CT/TT patients when pegIFN-α 2a and ribavirin plasma levels were greater than 3400 pg/mL and 1.6 μg/mL, respectively. In contrast to the results for CC patients, the results in patients carrying the unfavourable CT/TT IL28B genotypes showed that plasma levels of both drugs have significant effects on viral kinetics and SVR.

Multi-agent model of hepatitis C virus infection

OBJECTIVES

The objective of this study is to design a method for modeling hepatitis C virus (HCV) infection using multi-agent simulation and to verify it in practice.

METHODS AND MATERIALS

In this paper, first, the modeling of HCV infection using a multi-agent system is compared with the most commonly used model type, which is based on differential equations. Then, the implementation and results of the model using a multi-agent simulation is presented. To find the values of the parameters used in the model, a method using inverted simulation flow and genetic algorithm is proposed. All of the data regarding HCV infection are taken from the paper describing the model based on the differential equation to which the proposed method is compared.

RESULTS

Important advantages of the proposed method are noted and demonstrated: these include flexibility, clarity, re-usability and the possibility to model more complex dependencies. Then, the simulation framework that uses the proposed approach is successfully implemented in C++ and is verified by comparing it to the approach based on differential equations. The verification proves that an objective function that performs the best is the function that minimizes the maximal differences in the data. Finally, an analysis of one of the already known models is performed, and it is proved that it incorrectly models a decay in the hepatocytes number by 40%.

CONCLUSIONS

The proposed method has many advantages in comparison to the currently used model types and can be used successfully for analyzing HCV infection. With almost no modifications, it can also be used for other types of viral infections.

Analysis of hepatitis C virus decline during treatment with the protease inhibitor danoprevir using a multiscale model

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.

Chronic infection with hepatitis C virus (HCV) remains an important health-care problem worldwide despite significant progress in the development of HCV therapy since the discovery of the virus in 1989. Current treatment options are focused on direct-acting antiviral agents (DAAs) that target specific steps of the HCV life cycle. Danoprevir, one of the DAAs that inhibit the HCV NS3-4A protease, has induced substantial viral load reductions in patients receiving therapy. We study the viral decline during therapy using a multiscale age-structured model that accounts for the dynamics of intracellular viral replication, and which includes the major steps in the HCV life cycle that are targeted by DAAs. We examine the biological parameters contributing to different phases of the viral decline after treatment initiation. We also explore the mechanisms of action of danoprevir and estimate its treatment effectiveness. The multiscale model provides a theoretical framework for studying virus dynamics in hepatitis C patients treated with other DAAs currently in clinical development, and may help one to optimally combine drugs with complementary modes of action to maximize the HCV cure rate.

Hepatitis C viral kinetics: the past, present, and future

Mathematical modeling of hepatitis C viral kinetics has been an important tool in understanding hepatitis C virus (HCV) infection dynamics and in estimating crucial in vivo parameters characterizing the effectiveness of HCV therapy. Because of the introduction of direct-acting antiviral agents, there is a need to extend previous models so as to understand, characterize, and compare various new HCV treatment regimens. Here we review recent modeling efforts in this direction.

Mathematical modelling of HCV infection: what can it teach us in the era of direct-acting antiviral agents?

HCV infection is a major cause of chronic liver disease and affects nearly 170 million people worldwide. Whereas the previous standard of care with pegylated interferon and ribavirin had a modest effectiveness, the recent approval of two highly potent protease inhibitors and the ongoing development of dozens of direct-acting antiviral agents (DAAs) constitute a major milestone for HCV therapy. Mathematical modelling of viral kinetics under treatment has played an instrumental role in improving our understanding of virus pathogenesis and in guiding drug development. Here, we review the current state of HCV kinetic modelling, and challenges to the standard biphasic viral decline model that arise when fitting viral kinetic models to data obtained with DAAs.

Understanding silibinin's modes of action against HCV using viral kinetic modeling

BACKGROUND & AIMS

Legalon® SIL (SIL) is a chemically hydrophilized version of silibinin that has exhibited high antiviral effectiveness against hepatitis C virus (HCV). Its main mode of action (MOA) remains unclear, with contradicting in vitro studies supporting either suppression of entry and cell-to-cell spread or suppression of viral RNA synthesis as the main MOA. We sought to provide new insights into SIL's MOA in HCV genotype-1/4 patients receiving intravenous SIL monotherapy for 7 days via mathematical modeling.

METHODS

Changes in HCV RNA in 25 patients receiving 10, 15, or 20mg/kg/day of SIL were analyzed and modeled using viral kinetic methods.

RESULTS

In 15 patients, the virus declined in a biphasic manner, in which a sharp drop between days 0 and 2 was followed by a slower second phase of decline. In 10 patients, the initial decline was weaker and the virus declined in a single phase over the 7-day period. The blocking production effectiveness, ε, was dose-dependent with mean ε=0.49 and 0.89 in the 10 or 15 and 20mg/kg/day dosing groups, respectively (p=0.02). The effectiveness of blocking viral infection, η, was estimated as 0.60 with no significant differences across dosing groups. For all patients, the mean rate of viral load decline measured between days 2 and 7 was high (0.3 log(10)IU/ml/day), i.e., 4-fold higher than typically observed during the 2nd phase of (pegylated)-interferon-α±ribavirin treatment.

CONCLUSIONS

Modeling HCV kinetics in vivo suggests that SIL may block both viral infection and viral production/release with its main dose-dependent effect being blocking viral production/release.

Hepatitis C virus viral kinetics during α-2a or α-2b pegylated interferon plus ribavirin therapy in liver transplant recipients with different immunosuppression regimes

BACKGROUND

Predictors of sustained virological response (SVR) to antiviral therapy post-liver transplantation (LT) for chronic hepatitis C are needed. In non-transplanted patients, viral kinetics can predict SVR.

OBJECTIVES

To determine the early viral kinetics in LT recipients with different immunosuppression (tacrolimus - Tac- vs. cyclosporine - CsA-) during treatment with peg-IFN+RBV.

STUDY DESIGN

Prospective pilot study in HCV-1b infected patients: (LT CsA n=8; Tac n=8; non-LT n=4), treated with IFN α-2a vs. α-2b (180 μg or 1.5 μg/kg, respectively) once weekly plus weight-based RBV. Median CsA or Tac baseline trough levels were 141 and 7.70 ng/mL, respectively. HCV-RNA was quantified before treatment and after 3, 6, 12h; days 1-6; and weeks 4, 12, 24, 48 and 78 (follow-up).

RESULTS

Different kinetics were observed: early viral load declines with shoulder phase (n=12), delayed monophasic without first phase (n=5, all CsA), and biphasic (n=1) or flat (n=1), without influence of IL28B rs12979860 donor/recipient alleles. In LT, median declines (log(10)UI/mL) at week 4 were -3.62 and -1.49 for Tac vs. CsA; and -2.10 vs.-1.50 for IFN α-2a vs. α-2b (NS), with a trend for faster declines in Tac patients. Generalized additive models suggested a cut-off for predicting response in LT patients of 30 days for Tac, but beyond day 40 for CsA.

CONCLUSION

In LT, the viral kinetics during peg-IFN+RBV treatment is delayed. HCV-RNA at 48 h. may not be predictive of response, and CsA-immunosupressed patients with delayed monophasic declines may potentially achieve ETVR and SVR despite unfavourable or absent early viral load declines.

Influence of HCV genotype 1 subtypes on the virus response to PEG interferon alpha-2a plus ribavirin therapy

New factors that influence the viral response in HCV non-genotype 2/3 patients must be identified in order to optimize anti-HCV treatment. This multicenter prospective study evaluates the influence of HCV variability and pharmacological parameters on the virological response of these patients to pegylated interferon α2a (peg-IFN-α2a: 180 µg/week) and ribavirin (RBV; 800-1,200 mg/day) for 48 weeks. HCV subtypes were identified by sequencing the NS5B region. Serum RBV and peg-IFN-α2a concentrations were measured at weeks 4 and 12. The 115 patients (67 men; median age = 49, range 31-76) included 64 who had never been treated and 27 co-infected with HIV. The mean baseline HCV RNA was 6.30 ± 0.06 log IU/ml and the HCV genotypes were: G1 (n = 93) with 1a (n = 37) and 1b (n = 50), G4 (n = 20) and G5 (n = 2). Most patients (79/108; 73%) had an early virological response. Independent predictors of an early virological response were interferon naive patients (OR=  2.98, 95% CI: 1.15-7.72) and RBV of >2,200 ng/ml at week 12 (OR = 3.41, 95% CI: 1.31-8.90). Forty of 104 patients (38%) had a sustained virological response. The only independent predictors of a sustained virological response were subtype 1b (OR = 6.82, 95% CI: 1.7-26.8), and HCV RNA <15 IU/ml at week 12 (OR = 25, 95% CI: 6.4-97.6). Thus a serum RBV concentration of >2,200 ng/ml was associated with an early virological response and patients infected with HCV subtype 1b had a better chance of a sustained virological response than did those infected with subtype 1a.

OPTIMALLY CONTROLLED TREATMENT STRATEGY USING INTERFERON AND RIBAVIRIN FOR HEPATITIS C

The main goal of this paper is to determine an optimal treatment strategy using interferon and ribavirin, through mathematical modeling. We formulate a mathematical model using a system of ordinary differential equations, which describes the interaction of target cells (hepatocytes), infected cells, infectious virions, non-infectious virions and the two drugs, namely, interferon and ribavirin. We solve an optimal control problem with an objective functional that minimizes the viral load as well as the side effects of treatment. Finally we derive optimal treatment strategy and then solve it numerically.

Drug effectiveness explained: the mathematics of antiviral agents for HIV

Antiretroviral therapy has improved the quality and length of life of millions of individuals affected by human immunodeficiency virus type 1 (HIV-1). The capacity of these drugs to indefinitely suppress HIV-which has a well-known capacity for escaping antiviral pressures-is surprising. In this issue of Science Translational Medicine, Shen et al. use a combination of mathematical modeling and experiment to examine the potency of anti-HIV drugs. They show that non-nucleoside reverse transcriptase inhibitors and protease inhibitors exhibit cooperative dose-response curves-a finding that has implications for the treatment of HIV as well as other viral infections, such as hepatitis C.

Hepatitis C Viral Kinetics in the Era of Direct Acting Antiviral Agents and IL28B

In the last decade hepatitis C virus (HCV) kinetics has become an important clinical tool for the optimization of therapy with (pegylated)-interferon-α (IFN) and ribavirin (RBV). Mathematical models have generated important insights into HCV pathogenesis, HCV- host dynamics, and IFN and RBV's modes of action. Clinical trials with direct acting agents (DAAs) against various steps of the HCV life cycle have revealed new viral kinetic patterns that have not been observed with IFN±RBV. Very recently, studies have showed that single nucleotide polymorphisms (SNPs) in the IL28B gene region were associated with race/ethnicity and with response to IFN±RBV. Here we review our current knowledge of HCV kinetics and related mathematical models during IFN±RBV and/or DAA based therapies, HCV pathogenesis, and the role of IL28B polymorphism on early HCV kinetics. Better understanding of the mode of actions of drug(s) and viral kinetics may help to develop, in the near future, new individualized therapeutic regimens that include DAAs in combination with IFN+RBV.

Twice-weekly pegylated interferon-α-2a and ribavirin results in superior viral kinetics in HIV/hepatitis C virus co-infected patients compared to standard therapy

BACKGROUND

Hepatitis C virus (HCV)/HIV co-infected patients have more rapid progression of liver fibrosis and only modest cure rates (sustained virologic responses, SVRs) when compared to HCV monoinfected patients.

METHOD

We compared the virologic responses of either twice-weekly peginterferon-α-2a 180 μg/week (for 4 weeks, followed by weekly dosing) or weekly peginterferon-α-2a 180 μg/week, and weight-based ribavirin (1-1.2 g/day), among HIV/HCV co-infected genotype-1 individuals.

RESULTS

Patients receiving the investigational dosing had lower levels of HCV RNA at all time points after initiation of therapy. More patients on this arm achieved clinically relevant early virological responses at weeks 1, 2, 4, 12, and 24. The enhanced early virologic response observed with the investigational arm was associated with a higher induction of interferon-stimulated genes. This early double dose regimen also resulted in a rapid normalization of liver enzymes. Twice-weekly peginterferon-α-2a was associated with more frequent early virological responses with similar safety profiles when compared with standard therapy.

CONCLUSION

Our results, when confirmed in larger randomized clinical trials, may provide a novel therapeutic approach to improve SVR among HIV/HCV co-infected patients, especially African-American patients.

Very early prediction of response to HCV treatment with PEG-IFN-alfa-2a and ribavirin in HIV/HCV-coinfected patients

The objective of this study was to find very early viral kinetic markers to predict nonresponse to hepatitis C virus (HCV) therapy in a group of human immunodeficiency virus (HIV)/HCV-coinfected patients. Twenty-six patients (15 HCV genotype-1 and 11 genotype-3) were treated with a 48-week regimen of peginterferon-alfa-2a (PEG-IFN) (180 μg/week) and weight-based ribavirin (11 mg/kg/day). Samples were collected at baseline; 4, 8, 12, 18, 24, 30, 36 and 42 h; days 2, 3, 4, 7, 8, 15, 22, 29, 43 and 57 then weekly and monthly. Five patients discontinued treatment. Seven patients (27%) achieved a sustained virological response (SVR). Nadir HCV RNA levels were observed 1.6 ± 0.3 days after initiation of therapy, followed by a 0.3- to 12.9-fold viral rebound until the administration of the second dose of PEG-IFN, which were not associated with SVR or HCV genotype. A viral decline <1.19 log for genotype-1 and <0.97 log for genotype-3, 2 days after starting therapy, had a negative predictive value (NPV) of 100% for SVR. The day 2 virological response had a similar positive predictive value for SVR as a rapid virological response at week 4. In addition, a second-phase viral decline slope (i.e., measured from day 2 to 29) <0.3 log/week had a NPV = 100% for SVR. We conclude that first-phase viral decline at day 2 and second-phase viral decline slope (<0.3 log/week) are excellent predictors of nonresponse. Further studies are needed to validate these viral kinetic parameters as early on-treatment prognosticators of nonresponse in patients with HCV and HIV.

Design evaluation and optimization for models of hepatitis C viral dynamics

Mathematical modeling of hepatitis C viral (HCV) kinetics is widely used for understanding viral pathogenesis and predicting treatment outcome. The standard model is based on a system of five non-linear ordinary differential equations (ODE) that describe both viral kinetics and changes in drug concentration after treatment initiation. In such complex models parameter estimation is challenging and requires frequent sampling measurements on each individual. By borrowing information between study subjects, non-linear mixed effect models can deal with sparser sampling from each individual. However, the search for optimal designs in this context has been limited by the numerical difficulty of evaluating the Fisher information matrix (FIM). Using the software PFIM, we show that a linearization of the statistical model avoids most of the computational burden, while providing a good approximation to the FIM. We then compare the precision of the parameters that can be expected using five study designs from the literature. We illustrate the usefulness of rationalizing data sampling by showing that, for a given level of precision, optimal design could reduce the total number of measurements by up 50 per cent. Our approach can be used by a statistician or a clinician aiming at designing an HCV viral kinetics study.

A perspective on modelling hepatitis C virus infection

By mathematically describing early hepatitis C virus (HCV) RNA decay after initiation of interferon (IFN)-based antiviral therapy, crucial parameters of the in vivo viral kinetics have been estimated, such as the rate of production and clearance of free virus, and the rate of loss of infected cells. Furthermore, by suggesting mechanisms of action for IFN and ribavirin mathematical modelling has provided a means for evaluating and optimizing treatment strategies. Here, we review recent modelling developments for understanding complex viral kinetics patterns, such as triphasic HCV RNA declines and viral rebounds observed in patients treated with pegylated interferon and ribavirin. Moreover, we discuss new modelling approaches developed to interpret the viral kinetics observed in clinical trials with direct-acting antiviral agents, which induce a rapid decline of wild-type virus but also engender a higher risk for emergence of drug-resistant variants. Lastly, as in vitro systems have allowed a better characterization of the virus lifecycle, we discuss new modelling approaches that combine the intracellular and the extracellular viral dynamics.

Pharmacodynamics of PEG-IFN-alpha-2a in HIV/HCV co-infected patients: implications for treatment outcomes

BACKGROUND & AIMS

The pharmacokinetics and pharmacodynamics of pegylated-interferon-alpha-2a (PEG-IFN) have not been described in HCV/HIV co-infected patients. We sought to estimate the pharmacokinetics and pharmacodynamics of PEG-IFN and determine whether these parameters predict treatment outcome.

METHODS

Twenty-six HCV/human immunodeficiency virus (HIV)-co-infected patients were treated with a 48-week regimen of PEG-IFN (180 microg/week) plus ribavirin (11 mg/kg/day). HCV RNA and PEG-IFN concentrations were obtained from samples collected until week 12. A modeling framework that includes pharmacokinetic and pharmacodynamic parameters was developed.

RESULTS

Five patients discontinued treatment. Seven patients achieved a sustained virological response (SVR). PEG-IFN concentrations at day 8 were similar to steady-state levels (p=0.15) and overall pharmacokinetic parameters were similar in SVRs and non-SVRs. The maximum PEG-IFN effectiveness during the first PEG-IFN dose and the HCV-infected cell loss rate (delta), were significantly higher in SVRs compared to non-SVRs (median 95% vs. 86% [p=0.013], 0.27 vs. 0.11 day(-1) [p=0.006], respectively). Patients infected with HCV genotype 1 had a significantly lower average first-week PEG-IFN effectiveness (median 70% vs. 88% [p=0.043]), however, 4- to 12-week PEG-IFN effectiveness was not significantly different compared to those with genotype 3 (p=0.114). Genotype 1 had a significantly lower delta compared to genotype 3 (median 0.14 vs. 0.23 day(-1) [p=0.021]). The PEG-IFN concentration that decreased HCV production by 50% (EC(50)) was lower in genotype 3 compared to genotype 1 (median 1.3 vs. 3.4 [p=0.034]).

CONCLUSIONS

Both the HCV-infected cell loss rate (delta) and the maximum effectiveness of the first dose of PEG-IFN-alpha-2a characterised HIV co-infected patients and were highly predictive of SVR. Further studies are needed to validate these viral kinetic parameters as early on-treatment prognosticators of response in patients with HCV and HIV.

Hepatitis C viral kinetics during treatment with peg IFN-alpha-2b in HIV/HCV coinfected patients as a function of baseline CD4+ T-cell counts

BACKGROUND

HIV/hepatitis C virus (HCV) coinfected patients are known to have lower sustained viral response (SVR) rates than HCV monoinfected patients. However, the role of CD4+ T-cell counts on viral kinetics and outcome is not fully understood.

METHODS

HCV RNA kinetics (bDNA v3, lower limit of detection [LD] = 615 IU/mL) was analyzed in 32 HIV/HCV coinfected persons treated with Pegylated-interferon-alpha2b (1.5 microg/kg weekly) and ribavirin (1-1.2 g daily) for 48 weeks and compared with results obtained from 12 HCV monoinfected patients treated with the same regimen.

RESULTS

Baseline CD4+ T-cell counts > or =450 cells/mm3 were significantly (P < 0.002) associated with SVR in coinfected genotype 1 patients. First phase decline was significantly lower among patients with low as compared with high CD4 counts (P < 0.03) and among coinfected compared with monoinfected patients (P < 0.002). Second phase decline slope showed a similar trend for coinfected patients.

CONCLUSIONS

Low baseline CD4+ T-cell count is associated with slower HCV viral kinetics and worse response to treatment among HIV coinfected patients, suggesting HCV treatment response depends on immune status. HCV genotype 1 coinfected patients have slower first phase viral kinetics than HCV monoinfected patients. First phase viral decline (>1.0 log) and second phase viral decline slope (>0.3 log/wk) are excellent predictors of SVR for coinfected patients.

Therapeutic response to peg-IFN-alpha-2b and ribavirin in HIV/HCV co-infected African-American and Caucasian patients as a function of HCV viral kinetics and interferon pharmacodynamics

METHOD

In this study we sought to characterize the relationship between several pharmacokinetic and pharmacodynamic parameters and virologic responses among HIV/hepatitis C virus genotype-1 co-infected patients receiving pegylated interferon-alpha-2b (peg-IFN2b) and ribavirin. We also tried to establish the underlying mechanisms that lead to poor sustained virologic responder rates observed with African-Americans against Caucasians and compared their results with those observed in a cohort of hepatitis C virus mono-infected patients.

RESULTS

Among our studied population, a viral decline of more than 1.0 log at day 3 combined with viral load of less than 5.0 log IU/ml at day 28 predicted sustained virologic responders with negative predictive value 100% and positive predictive value 100%. African-Americans had significantly (P < 0.01) slower hepatitis C virus viral kinetics as compared to Caucasians. However, peg-IFN2b concentrations and pharmacokinetic parameters, peg-IFN2b(max) and peg-IFN2b half-life, were similar in both groups and did not predict sustained virologic responders. Nevertheless, the pharmacodynamic parameter EC(50), estimated from nonlinear fitting of the viral kinetics together with peg-IFN2b concentration data, showed that HIV/ hepatitis C virus co-infected African-Americans have lower sensitivity to interferon-alpha thus giving rise to slower viral decline. The combined pharmacokinetic/pharmacodynamic parameter IFN(max)/EC(90) was an excellent predictor of sustained virologic responders, thus showing the importance of maintaining peg-IFN2b levels above EC(90) to achieve successful treatment.

CONCLUSION

Further studies are needed to evaluate whether these pharmacodynamic predictions are a result of differential host response to peg-IFN2b or other viral factors conferring relative resistance to peg-IFN2b.

Pegylated interferon and ribavirin promote early evolution of nonstructural 5A protein in individuals with hepatitis C who demonstrate a response to treatment

BACKGROUND

Hepatitis C virus (HCV) quasispecies diversity is more likely to affect early viral decline during treatment of hepatitis C than is having human immunodeficiency virus (HIV) infection. We evaluated the influence of HCV therapy on changes in the nonstructural 5A (NS5A) protein.

METHODS

Fifteen patients with HCV genotype 1 infection with or without HIV infection were recruited for the present study, and the decrease in the HCV RNA level was measured at early time points. The evolution of HCV NS5A quasispecies within the first week was analyzed by comparing the clones observed at later times in the study with the baseline consensus sequence of individual patients. The response to therapy was defined as an early response (ER; ie, an HCV RNA level <615 IU/mL at week 4) or a slow response (SR; ie, a detectable HCV RNA level at week 4).

RESULTS

HIV infection did not affect early viral kinetics. At baseline, lower diversity was seen in NS5A and in the amino and carboxyl termini of patients with an ER, compared with those with an SR. Rapid evolution of the NS5A genetic region occurred in patients with an ER (P = .01) but not in those with an SR (P = .73). The evolution was the result of an increase in the number of amino acid substitutions in the carboxyl region (P = .02) in patients with an ER.

CONCLUSIONS

Selective pressure appears to result in more-marked changes in individuals with an ER than in those with an SR. The carboxyl terminus was subject to the most change and may be an important determinant of phenotypic resistance to interferon-based therapy.

Mathematical modeling of HCV infection and treatment

In the last decade, viral kinetic modeling has played an important role in the analysis of HCV RNA decay after the initiation of antiviral therapy. Models have provided a means of evaluating the antiviral effectiveness of therapy and of estimating parameters, such as the rate of virion clearance and the rate of loss of HCV-infected cells, and they have suggested mechanisms of action for both interferon-alpha and ribavirin. The inclusion of homeostatic proliferation of infected and uninfected hepatocytes in existing viral kinetic models has allowed prediction of most observed HCV RNA profiles under treatment, for example, biphasic and triphasic viral decay and viral rebound to baseline values after the cessation of therapy. In addition, new kinetic models have taken into consideration the different pharmacokinetics of standard and pegylated forms of interferon and have incorporated alanine aminotransferase kinetics and aspects of immune responses to provide a more comprehensive picture of the biology underlying changes in HCV RNA during therapy. Here, we describe our current understanding of the kinetics of HCV infection and treatment.

Autoimmune hepatitis in the HIV-infected patient: a therapeutic dilemma

Autoimmune hepatitis (AIH) is a progressive, chronic hepatitis that has rarely been reported in HIV-infected individuals. Among patients who are candidates for hepatitis C virus (HCV) treatment, screening for AIH should be considered, because interferon has the potential to cause fulminant hepatic failure in the setting of immune-mediated injury. During a 4-year period, we identified four HIV-infected patients who were referred for evaluation of persistently elevated aminotransferases, two of whom were also infected with HCV. Serologic testing and the hepatic histologic appearance were consistent with AIH. Although each patient initiated treatment with corticosteroids and immunosuppressive agents, all four eventually developed life-threatening infectious or adverse metabolic effects that resulted in treatment discontinuation. Of note, one HIV/HCV co-infected patient was able to initiate HCV treatment with interferon after AIH remission was documented. While these cases illustrate that AIH can produce hepatic injury in virally infected individuals, we recommend that treatment for AIH in HIV-infected patients should be individualized after careful consideration of the potential risks and likely benefits.

Modeling HCV kinetics under therapy using PK and PD information

BACKGROUND

Mathematical models have proven helpful in analyzing the virological response to antiviral therapy in hepatitis C virus (HCV) infected subjects.

OBJECTIVE

To summarize the uses and limitations of different models for analyzing HCV kinetic data under pegylated IFN therapy.

METHODS

We formulate mathematical models and fit them by nonlinear least square regression to patient data to estimate model parameters. We compare the goodness of fit and parameter values estimated by different models statistically.

RESULTS/CONCLUSION

The best model for parameter estimation depends on the availability and the quality of data as well as the therapy used. We also discuss the mathematical models that will be needed to analyze HCV kinetic data from clinical trials with new antiviral drugs.

Modelling Hepatitis C virus Kinetics: The Relationship between the Infected Cell Loss rate and the Final Slope of Viral Decay

Background

Patients infected with hepatitis C virus (HCV) who respond to treatment with interferon-α plus ribavirin exhibit biphasic or triphasic viral load decreases. While the rapid first phase is indicative of the effectiveness of therapy in blocking viral production (e), the slope of the final phase ( X), that is, the second phase in biphasic decreases and the third phase in triphasic decreases, depends on the infected cell loss rate (δ). In standard models, X is approximately εδ when the viral clearance rate c>>δ, as has been previously estimated.

Methods

The relationship among e, S, X and the baseline fraction of HCV-infected hepatocytes (π) was investigated in a model that included proliferation of hepatocytes.

Results

We found that X was not proportional to e, but rather obeyed a complex relationship that could lead to dramatic increases in estimates of 8 as e increased. In particular, when ε<99%, X moderately underestimated 8 in patients with a small π, whereas δ might be up to 10-fold larger than λ in patients with a large π. Interestingly, when ε>99%, δ∼λ regardless of π.

Conclusions

Our results indicated that in patients undergoing therapy who achieved a 2 log10 reduction in viral load (ε<99%), previously estimated δ values might represent only a minimal estimate of the infected cell loss rate. Moreover, combining interferon-α with new antiviral agents to achieve ε>99% should allow for a more accurate estimate of 8 in HCV RNA kinetic studies. This might be important when using viral kinetics to estimate the effect of the immune response on viral elimination and the attainment of sustained virological response.

Viral dynamics of hepatitis B virus DNA in human immunodeficiency virus-1-hepatitis B virus coinfected individuals: similar effectiveness of lamivudine, tenofovir, or combination therapy

Following treatment of hepatitis B virus (HBV) infection with nucleos(t)ide reverse transcriptase inhibitors (NRTIs), there is a biphasic clearance of HBV, similar to that seen following treatment of human immunodeficiency virus-1 (HIV-1) and hepatitis C virus. Little is known about the impact of combination NRTIs and HIV-1 coinfection on HBV viral kinetic parameters following the initiation of HBV-active highly active antiretroviral therapy (HAART). HIV-1-HBV coinfected patients (n = 21) were enrolled in a viral kinetics substudy of the Tenofovir in HIV-1-HBV Coinfection study (TICO). TICO was a randomized (1:1:1) trial of tenofovir disoproxil fumarate (TDF, 300 mg) versus lamivudine (LMV, 300 mg) versus TDF/LMV within an efavirenz based HAART regimen initiated in HIV-1-HBV coinfected antiretroviral naïve individuals in Thailand. HBV DNA was measured frequently over the first 56 days. To fit the viral load data, we used a model of HBV kinetics that allows the estimation of treatment effectiveness, viral clearance and infected cell loss. We observed a biphasic decline in HBV DNA in almost all patients. We did not observe any significant differences in HBV viral dynamic parameters between the three treatments groups. Overall, median (interquartile range) HBV treatment effectiveness was 98% (95%-99%), median HBV virion half-life was 1.2 days (0.5-1.4 days), and median infected cell half-life was 7.9 days (6.3-11.0 days). When we compared hepatitis B e antigen (HBeAg)-positive and HBeAg-negative individuals, we found a significantly longer infected cell half-life in HBeAg-positive individuals (6.2 versus 9.0 days, P = 0.02).

CONCLUSION

HBV viral dynamic parameters are similar following anti-HBV NRTI monotherapy and dual combination therapy in the setting of HIV-1-HBV coinfection. HIV-1 coinfection has minimal effect on HBV viral dynamics, even in the setting of advanced HIV-1-related immunosuppression.

Modelling of viral dynamics in hepatitis B and hepatitis C clinical trials

In the recent years, studies of hepatitis B (HBV) and hepatitis C virus (HCV) dynamics have drawn great attention as they provide insight into the process of virus elimination/production and of infected cells decay during antiviral treatment. Estimates of viral dynamic parameters may be used to determine the lifetime of HCV/HBV virions and of infected cells, to estimate how long patients need to be treated and to evaluate antiviral therapies. The implementation of viral dynamics studies is difficult because they involve an intensive blood-sampling schedule and subsequent viral load quantification. In the majority of these studies, a model proposed by Neumann et al. (Science 1998; 282:103-107) is used under various assumptions, such as ignoring the delay in initial viral load decay, assuming time-constant treatment efficacy in reducing virion production and/or complete blocking of new infections, etc. However, only recently the effect of some of these assumptions on the estimated parameters has been evaluated. In this paper we provide a detailed review of the model, its underlying assumptions as well as the assumptions usually made by researchers during the design and analysis of viral dynamics studies. Then, we investigate the effect of these assumptions on the estimated parameters using simulations and draw useful conclusions concerning the analysis of these studies. Real data examples from a clinical trial on hepatitis B are provided as illustrations.