Modeling the short-, middle- and long-term viral load responses for comparing estimated dynamic parameters

A virologic marker, the number of HIV RNA copies or viral load, is currently used to evaluate antiviral therapies in AIDS clinical trials. This marker can be used to assess the antiviral potency of therapies, but is easily affected by drug exposures, drug resistance and other factors during the long-term treatment evaluation process. The study of HIV dynamics is one of the most important development in recent AIDS research for understanding the pathogenesis of HIV-1 infection and antiviral treatment strategies. Although many HIV dynamic models have been proposed by AIDS researchers in the last decade, they have only been used to quantify short-term viral dynamics and do not correctly describe long-term virologic responses to antiretroviral treatment. In other words, these simple viral dynamic models can only be used to fit short-term viral load data for estimating dynamic parameters. In this paper, a mechanism-based differential equation models is introduced for characterizing the long-term viral dynamics with antiretroviral therapy. We applied this model to fit different segments of the viral load trajectory data from a simulation experiment and an AIDS clinical trial study, and found that the estimates of dynamic parameters from our modeling approach are very consistent. We may conclude that our model can not only characterize long-term viral dynamics, but can also quantify short- and middle-term viral dynamics. It suggests that if there are enough data in the early stage of the treatment, the results from our modeling based on short-term information can be used to capture the performance of long-term care with HIV-1 infected patients.     

Predicting differential responses to structured treatment interruptions during HAART

Highly active antiretroviral therapy (HAART) has been used clinically in various administration schemes for several years. However, due to the development of drug resistance, evolution of viral strains, serious side effects, and poor patient compliance, the combination of drugs used in HAART fails to effectively contain virus long term in a high proportion of patients. Our group and others have suggested a change to the usual regimen of continuous HAART through structured treatment interruptions (STIs). STIs may provide similar clinical benefits as continuous treatment such as reduced viral loads and reestablishment of CD4⁺ T cells while allowing patients drug holidays. We explore the use of STIs using a previously published model that accurately represents CD4⁺ T-cell counts and viral loads during both untreated HIV-1 infection and HAART therapy. We simulate the effects of different STI regimens including weekly and monthly interruptions together with variations in treatment initiation time. We predict that differential responses to STIs as observed in conflicting clinical trial data are impacted by the duration of the interruption, stage of infection at initiation of treatment, strength of the immune system in suppressing virus, or pre-therapy CD4⁺ T-cell count or virus load. Our results indicate that dynamics occurring below the limit of detection (LOD) are influenced by these factors, and contribute to reemergence or suppression of virus during interruptions. Simulations predict that short-term viral suppression with varying interruptions strategies does not guarantee long-term clinical benefit.     

Immunologic pressure within class I-restricted cognate human immunodeficiency virus epitopes during highly active antiretroviral therapy

Cytotoxic T lymphocytes (CTL) and highly active antiretroviral therapy (HAART) are known to exert strong evolutionary pressures on the virus population during human immunodeficiency virus (HIV) infection. However, it is not known whether CTL responses continue to substantially affect viral evolution during treatment. To study the effect of immunologic pressure on viral sequences during HAART, we identified 10 targeted HIV-specific CD8+-T-cell epitopes in five treatment-naive patients, sequenced each epitope in plasma-derived viruses, and then identified evidence of immunologic pressure at these epitopes by comparing the frequency of viral variants in plasma to the frequency of the CD8+-T-cell response for each variant identified. For one of the five patients, evidence of viral evolution was found during therapy. The sequence of the CTL-targeted epitope changed from an apparent escape variant prior to the initiation of therapy, to the sequence that is best recognized by the CTL response after the initiation of therapy, and then finally to a new escape variant during continued therapy. These data show that CTL-mediated pressure can continue to affect viral evolution after the initiation of HAART, even when treatment drives the viral load below detectable levels, and suggest that antiretroviral therapy may preferentially inhibit those virus variants that escape the CTL response.     

Viral Dynamics during Structured Treatment Interruptions of Chronic Human Immunodeficiency Virus Type 1 Infection

Although antiviral agents which block human immunodeficiency virus (HIV) replication can result in long-term suppression of viral loads to undetectable levels in plasma, long-term therapy fails to eradicate virus, which generally rebounds after a single treatment interruption. Multiple structured treatment interruptions (STIs) have been suggested as a possible strategy that may boost HIV-specific immune responses and control viral replication. We analyze viral dynamics during four consecutive STI cycles in 12 chronically infected patients with a history (>2 years) of viral suppression under highly active antiretroviral therapy. We fitted a simple model of viral rebound to the viral load data from each patient by using a novel statistical approach that allows us to overcome problems of estimating viral dynamics parameters when there are many viral load measurements below the limit of detection. There is an approximate halving of the average viral growth rate between the first and fourth STI cycles, yet the average time between treatment interruption and detection of viral loads in the plasma is approximately the same in the first and fourth interruptions. We hypothesize that reseeding of viral reservoirs during treatment interruptions can account for this discrepancy, although factors such as stochastic effects and the strength of HIV-specific immune responses may also affect the time to viral rebound. We also demonstrate spontaneous drops in viral load in later STIs, which reflect fluctuations in the rates of viral production and/or clearance that may be caused by a complex interaction between virus and target cells and/or immune responses.     

Complex patterns of viral load decay under antiretroviral therapy: influence of pharmacokinetics and intracellular delay

We present a model of HIV dynamics under antiretroviral therapy that combines drug pharmacokinetics and intracellular delay. A two compartment pharmacokinetic model is employed to determine the time evolution of the intracellular concentrations of the active forms of drugs, and thereby drug efficacy. The viral replication period is divided into pre- and post-drug action parts, allowing for the introduction of an intracellular delay in drug action. The standard model of viral dynamics is modified to account for the drug dependence of intracellular delay and continuously varying drug efficacy. Model calculations reveal that viral load decay in HIV infected patients under monotherapy can exhibit remarkably complex patterns depending on the relative magnitudes of the pharmacokinetic, intracellular, and intrinsic viral dynamic time-scales. The commonly assumed exponential decay is only a special case. However, uncertainties in measurement and the low sampling frequencies employed in present clinical studies preclude the identification of these patterns from existing clinical viral load data.     

Computational methods for the design of effective therapies against drug resistant HIV strains

The development of drug resistance is a major obstacle to successful treatment of HIV infection. The extraordinary replication dynamics of HIV facilitates its escape from selective pressure exerted by the human immune system and by combination drug therapy. We have developed several computational methods whose combined use can support the design of optimal antiretroviral therapies based on viral genomic data.     

Joint Modeling of the Clinical Progression and of the Biomarkers' Dynamics Using a Mechanistic Model

Summary Joint models are used to rigorously explore the relationship between the dynamics of biomarkers and clinical events. In the context of HIV infection, where the multivariate dynamics of HIV‐RNA and CD4 are complex, a mechanistic approach based on a system of nonlinear differential equations naturally takes into account the correlation between the biomarkers. Using data from a randomized clinical trial comparing dual antiretroviral therapy to a single drug regimen, a full maximum likelihood approach is proposed to explore the relationship between the evolution of the biomarkers and the time to a clinical event. The role of each marker as an independent predictor of disease progression is assessed. We show that the joint dynamics of HIV‐RNA and CD4 captures the effect of antiretroviral treatment; the CD4 dynamics alone is found to capture most but not all of the treatment effect.     

Impact of Different Oseltamivir Regimens on Treating Influenza A Virus Infection and Resistance Emergence: Insights from a Modelling Study

Several studies have proven oseltamivir to be efficient in reducing influenza viral titer and symptom intensity. However, the usefulness of oseltamivir can be compromised by the emergence and spread of drug-resistant virus. The selective pressure exerted by different oseltamivir therapy regimens have received little attention. Combining models of drug pharmacokinetics, pharmacodynamics, viral kinetics and symptom dynamics, we explored the efficacy of oseltamivir in reducing both symptoms (symptom efficacy) and viral load (virological efficacy). We simulated samples of 1000 subjects using previously estimated between-subject variability in viral and symptom dynamic parameters to describe the observed heterogeneity in a patient population. We simulated random mutations conferring resistance to oseltamivir. We explored the effect of therapy initiation time, dose, intake frequency and therapy duration on influenza infection, illness dynamics, and emergence of viral resistance. Symptom and virological efficacies were strongly associated with therapy initiation time. The proportion of subjects shedding resistant virus was 27-fold higher when prophylaxis was initiated during the incubation period compared with no treatment. It fell to below 1% when treatment was initiated after symptom onset for twice-a-day intakes. Lower doses and prophylaxis regimens led to lower efficacies and increased risk of resistance emergence. We conclude that prophylaxis initiated during the incubation period is the main factor leading to resistance emergence.     

Design of long-term HIV dynamic studies using semiparametric mixed-effects models

Studies of HIV dynamics in AIDS research are very important in understanding the pathogenesis of HIV-1 infection and also in assessing the effectiveness of antiviral therapies. There are many AIDS clinical trials on HIV dynamics currently in development worldwide, giving rise to many design issues yet to be addressed. For example, most studies are focused on short-term viral dynamics and the existing models may not be applicable to describe long-term virologic response. In this paper, we use a simulation-based approach to study the designs of long-term viral dynamics under semiparametric nonlinear mixed-effects models. These models not only can preserve the meaningful interpretation of the short-term HIV dynamics, but also characterize the long-term virologic responses to antiretroviral (ARV) treatment. We investigate a number of feasible clinical protocol designs similar to those currently used in AIDS clinical trials. In particular, we evaluate whether earlier samplings can result in more useful information about the viral response trajectory; we also evaluate the effectiveness of two strategies: more frequent samplings per subject with fewer subjects versus fewer samplings per subject with more subjects while keeping the total number of samplings constant. The results of our investigation provide quantitative guidance for designing and selecting ARV therapy.     

Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system

HIV dynamics studies have significantly contributed to the understanding of HIV infection and antiviral treatment strategies. But most studies are limited to short-term viral dynamics due to the difficulty of establishing a relationship of antiviral response with multiple treatment factors such as drug exposure and drug susceptibility during long-term treatment. In this article, a mechanism-based dynamic model is proposed for characterizing long-term viral dynamics with antiretroviral therapy, described by a set of nonlinear differential equations without closed-form solutions. In this model we directly incorporate drug concentration, adherence, and drug susceptibility into a function of treatment efficacy, defined as an inhibition rate of virus replication. We investigate a Bayesian approach under the framework of hierarchical Bayesian (mixed-effects) models for estimating unknown dynamic parameters. In particular, interest focuses on estimating individual dynamic parameters. The proposed methods not only help to alleviate the difficulty in parameter identifiability, but also flexibly deal with sparse and unbalanced longitudinal data from individual subjects. For illustration purposes, we present one simulation example to implement the proposed approach and apply the methodology to a data set from an AIDS clinical trial. The basic concept of the longitudinal HIV dynamic systems and the proposed methodologies are generally applicable to any other biomedical dynamic systems.     

Modeling the role of macrophages in HIV persistence during antiretroviral therapy

HIV preferentially infects activated CD4+ T cells. Current antiretroviral therapy cannot eradicate the virus. Viral infection of other cells such as macrophages may contribute to viral persistence during antiretroviral therapy. In addition to cell-free virus infection, macrophages can also get infected when engulfing infected CD4+ T cells as innate immune sentinels. How macrophages affect the dynamics of HIV infection remains unclear. In this paper, we develop an HIV model that includes the infection of CD4+ T cells and macrophages via cell-free virus infection and cell-to-cell viral transmission. We derive the basic reproduction number and obtain the local and global stability of the steady states. Sensitivity and viral dynamics simulations show that even when the infection of CD4+ T cells is completely blocked by therapy, virus can still persist and the steady-state viral load is not sensitive to the change of treatment efficacy. Analysis of the relative contributions to viral replication shows that cell-free virus infection leads to the majority of macrophage infection. Viral transmission from infected CD4+ T cells to macrophages during engulfment accounts for a small fraction of the macrophage infection and has a negligible effect on the total viral production. These results suggest that macrophage infection can be a source contributing to HIV persistence during suppressive therapy. Improving drug efficacies in heterogeneous target cells is crucial for achieving HIV eradication in infected individuals.

     

A quantitative basis for antiretroviral therapy for HIV-1 infection

Highly active antiretroviral therapy (HAART) has dramatically decreased mortality from HIV-1 infection and is a major achievement of modern medicine. However, there is no fundamental theory of HAART. Elegant models describe the dynamics of viral replication, but a metric for the antiviral activity of drug combinations relative to a target value needed for control of replication is lacking. Treatment guidelines are based on empirical results of clinical trials in which other factors such as regimen tolerability also affect outcome. Why only certain drug combinations control viral replication remains unclear. Here we quantify the intrinsic antiviral activity of antiretroviral drug combinations. We show that most single antiretroviral drugs show previously unappreciated complex nonlinear pharmacodynamics that determine their inhibitory potential at clinical concentrations. We demonstrate that neither of the major theories for drug combinations accurately predicts the combined effects of multiple antiretrovirals. However, the combined effects can be understood with a new approach that considers the degree of independence of drug effects. This analysis allows a direct comparison of the inhibitory potential of different drug combinations under clinical concentrations, reconciles the results of clinical trials, defines a target level of inhibition associated with treatment success and provides a rational basis for treatment simplification and optimization.     

Computational Models of HIV-1 Resistance to Gene Therapy Elucidate Therapy Design Principles

Gene therapy is an emerging alternative to conventional anti-HIV-1 drugs, and can potentially control the virus while alleviating major limitations of current approaches. Yet, HIV-1''s ability to rapidly acquire mutations and escape therapy presents a critical challenge to any novel treatment paradigm. Viral escape is thus a key consideration in the design of any gene-based technique. We develop a computational model of HIV''s evolutionary dynamics in vivo in the presence of a genetic therapy to explore the impact of therapy parameters and strategies on the development of resistance. Our model is generic and captures the properties of a broad class of gene-based agents that inhibit early stages of the viral life cycle. We highlight the differences in viral resistance dynamics between gene and standard antiretroviral therapies, and identify key factors that impact long-term viral suppression. In particular, we underscore the importance of mutationally-induced viral fitness losses in cells that are not genetically modified, as these can severely constrain the replication of resistant virus. We also propose and investigate a novel treatment strategy that leverages upon gene therapy''s unique capacity to deliver different genes to distinct cell populations, and we find that such a strategy can dramatically improve efficacy when used judiciously within a certain parametric regime. Finally, we revisit a previously-suggested idea of improving clinical outcomes by boosting the proliferation of the genetically-modified cells, but we find that such an approach has mixed effects on resistance dynamics. Our results provide insights into the short- and long-term effects of gene therapy and the role of its key properties in the evolution of resistance, which can serve as guidelines for the choice and optimization of effective therapeutic agents.     

HIV-1 dynamics in vivo: implications for therapy

The advent of potent combination antiretroviral therapy has been an important breakthrough in the treatment of HIV-1 infection, resulting in marked reductions in HIV-1-related morbidity and mortality. Antiretroviral therapy has also provided researchers with a powerful tool to perturb the equilibrium of viral production and viral clearance, allowing them to dissect the underlying dynamics that control the pathogenesis of AIDS. Here, we review our current understanding of the sources of HIV-1 production, the estimates for the virion and the host-cell half-lives, and the pathways of virion trafficking and clearance. We also discuss the obstacles that result from the ability of HIV-1 to remain dormant for a prolonged period of time in a subset of long-lived cells, despite an apparently effective antiretroviral treatment.     

Rapid human immunodeficiency virus decay in highly active antiretroviral therapy (HAART)-experienced children after starting mega-HAART

Increasing numbers of patients are treated with mega-highly active antiretroviral therapy (HAART), or multiple-combination antiretroviral therapy, in an attempt to overcome the viral resistance that has contributed to treatment failure. Studies of human immunodeficiency virus (HIV) viral dynamics are used to quantify the potency of a given regimen. While mega-HAART is expected to provide potent therapy, its potency among heavily experienced HIV-infected children who have failed previous treatment is untested. HIV dynamics studies performed in children have provided minimal information on viral dynamics during mega-HAART. The present study estimates first- and second-phase viral dynamics in six children on mega-HAART, following failure of combination therapy. The first phase of viral decay was rapid, relative to rates reported in previous pediatric studies (median delta = 0.778d(-1), range = 0.583 to 1.088, half-life 1 [t1(1/2)] = 0.894d), while the second phase revealed results similar to those of previous studies (median mu = 0.026d(-1), range = -0.005 to 0.206, t2(1/2) = 9.316d). This indicates that mega-HAART can provide potent therapy among heavily experienced pediatric patients.     

Mathematical analysis of multiscale models for hepatitis C virus dynamics under therapy with direct-acting antiviral agents

Chronic hepatitis C virus (HCV) infection remains a world-wide public health problem. Therapy with interferon and ribavirin leads to viral elimination in less than 50% of treated patients. New treatment options aiming at a higher cure rate are focused on direct-acting antiviral agents (DAAs), which directly interfere with different steps in the HCV life cycle. In this paper, we describe and analyze a recently developed multiscale model that predicts HCV dynamics under therapy with DAAs. The model includes both intracellular viral RNA replication and extracellular viral infection. We calculate the steady states of the model and perform a detailed stability analysis. With certain assumptions we obtain analytical approximations of the viral load decline after treatment initiation. One approximation agrees well with the prediction of the model, and can conveniently be used to fit patient data and estimate parameter values. We also discuss other possible ways to incorporate intracellular viral dynamics into the multiscale model.     

Non-linear dynamics models characterizing long-term virological data from AIDS clinical trials

Human immunodeficiency virus (HIV) dynamics represent a complicated variant of the text-book case of non-linear dynamics: predator-prey interaction. The interaction can be described as naturally reproducing T-cells (prey) hunted and killed by virus (predator). Virus reproduce and increase in number as a consequence of successful predation; this is countered by the production of T-cells and the reaction of the immune system. Multi-drug anti-HIV therapy attempts to alter the natural dynamics of the predator-prey interaction by decreasing the reproductive capability of the virus and hence predation. These dynamics are further complicated by varying compliance to treatment and insurgence of resistance to treatment. When following the temporal progression of viral load in plasma during therapy one observes a short-term (1-12 weeks) decrease in viral load. In the long-term (more than 12 weeks from the beginning of therapy) the reduction in viral load is either sustained, or it is followed by a rebound, oscillations and a new (generally lower than at the beginning of therapy) viral load level. Biomathematicians have investigated these dynamics by means of simulations. However the estimation of the parameters associated with the dynamics from real data has been mostly limited to the case of simplified, in particular linearized, models. Linearized model can only describe the short-term changes of viral load during therapy and can only predict (apparent) suppression. In this paper we put forward relatively simple models to characterize long-term virus dynamics which can incorporate different factors associated with resurgence: (Fl) the intrinsic non-linear HIV-1 dynamics, (F2) drug exposure and in particular compliance to treatment, and (F3) insurgence of resistant HIV-1 strains. The main goal is to obtain models which are mathematically identifiable given only measurements of viral load, while retaining the most crucial features of HIV dynamics. For the purpose of illustration we demonstrate an application of the models using real AIDS clinical trial data involving patients treated with a combination of anti-retroviral agents using a model which incorporates compliance data.     

Joint Inference on HIV Viral Dynamics and Immune Suppression in Presence of Measurement Errors

Summary : In an attempt to provide a tool to assess antiretroviral therapy and to monitor disease progression, this article studies association of human immunodeficiency virus (HIV) viral suppression and immune restoration. The data from a recent acquired immune deficiency syndrome (AIDS) study are used for illustration. We jointly model HIV viral dynamics and time to decrease in CD4/CD8 ratio in the presence of CD4 process with measurement errors, and estimate the model parameters simultaneously via a method based on a Laplace approximation and the commonly used Monte Carlo EM algorithm. The approaches and many of the points presented apply generally.