Modeling the dynamics of HIV-1 and CD4 and CD8 lymphocytes

Switching control strategy for the HIV dynamic system with some unknown parameters

In human immunodeficiency virus (HIV) infection, many factors may influence the counts of healthy cells, immune cells and viruses. Drug treatment design for the HIV dynamic system is a valuable subject to be studied. This study considers an HIV dynamic system model with some unknown parameters and unmeasurable CD8 + T cell count and proposes a switching control strategy to force all states of the system to achieve a healthy status. It is a switching form with two different drug therapies and is designed based on the Lyapunov function theory such that the states of the HIV system approach the health equilibrium asymptotically without the influence of unknown parameters and unmeasurable cell counts. The values of all states and drug concentrations are assured to be positive in the control process so that the control strategy can satisfy the actual treatment requirements. Finally, a numerical example is illustrated to show the effectiveness of the proposed control strategy.

Comparison of particle swarm and bacterial foraging optimization algorithms for therapy planning in HIV/AIDS patients

In HIV/AIDS patients, antiretroviral therapy (ART) is used for reducing the viral load and helps in increasing the life span of the individual. However, severe side effects are associated with the use of antiretroviral drugs. Hence, a treatment schedule, using minimal amount of drugs, is required for maintaining a low viral load and a healthy immune system. The objective of this work is to compute the optimal dosage of antiretroviral drugs for therapy planning in HIV/AIDS patients, using intelligent optimization techniques. In this work, two computational swarm intelligence techniques known as the particle swarm optimization (PSO) and bacterial foraging optimization (BFO) in conjunction with the three-dimensional mathematical model of HIV/AIDS have been used for estimating the optimal drug dosage for administering therapy by minimization of viral load as well as the total drug concentration. Results demonstrate that, using the proposed method, it is possible to achieve minimal viral load and an improved immune system, with the estimated drug dosage. Further, it was observed that the efficiency of BFO (CD4 cells [Formula: see text][Formula: see text]cells/mm3 at seventh year of infection) for estimation of optimal drug dosage is higher than the PSO method (CD4 cells [Formula: see text][Formula: see text]cells/mm3 at seventh year of infection). This work seems to be of high clinical relevance since, at present, ART is the widely used procedure for treatment of HIV infected patients.

Microfluidic CD4+ and CD8+ T lymphocyte counters for point-of-care HIV diagnostics using whole blood

Roughly 33 million people worldwide are infected with HIV; disease burden is highest in resource-limited settings. One important diagnostic in HIV disease management is the absolute count of lymphocytes expressing the CD4(+) and CD8(+) receptors. The current diagnostic instruments and procedures require expensive equipment and trained technicians. In response, we have developed microfluidic biochips that count CD4(+) and CD8(+) lymphocytes in whole blood samples, without the need for off-chip sample preparation. The device is based on differential electrical counting and relies on five on-chip modules that, in sequence, chemically lyses erythrocytes, quenches lysis to preserve leukocytes, enumerates cells electrically, depletes the target cells (CD4 or CD8) with antibodies, and enumerates the remaining cells electrically. We demonstrate application of this chip using blood from healthy and HIV-infected subjects. Erythrocyte lysis and quenching durations were optimized to create pure leukocyte populations in less than 1 min. Target cell depletion was accomplished through shear stress-based immunocapture, using antibody-coated microposts to increase the contact surface area and enhance depletion efficiency. With the differential electrical counting method, device-based CD4(+) and CD8(+) T cell counts closely matched control counts obtained from flow cytometry, over a dynamic range of 40 to 1000 cells/μl. By providing accurate cell counts in less than 20 min, from samples obtained from one drop of whole blood, this approach has the potential to be realized as a handheld, battery-powered instrument that would deliver simple HIV diagnostics to patients anywhere in the world, regardless of geography or socioeconomic status.

Modeling the three stages in HIV infection

A typical HIV infection response consists of three stages: an initial acute infection, a long asymptomatic period and a final increase in viral load with simultaneous collapse in healthy CD4+T cell counts. The majority of existing mathematical models give a good representation of either the first two stages or the last stage of the infection. Using macrophages as a long-term active reservoir, a deterministic model is proposed to explain the three stages of the infection including the progression to AIDS. Simulation results illustrate how chronic infected macrophages can explain the progression to AIDS provoking viral explosion. Further simulation studies suggest that the proposed model retains its key properties even under moderately large parameter variations. This model provides important insights on how macrophages might play a crucial role in the long term behavior of HIV infection.

Optimal control of HIV-virus dynamics

In this paper we consider a mathematical model of HIV-virus dynamics and propose an efficient control strategy to keep the number of HIV virons under a pre-specified level and to reduce the total amount of medications that patients receive. The model considered is a nonlinear third-order model. The third-order model describes dynamics of three most dominant variables: number of healthy white blood cells (T-cells), number of infected T-cells, and number of virus particles. There are two control variables in this model corresponding to two categories of antiviral drugs: reverse transcriptase inhibitors (RTI) and protease inhibitors (PI). The proposed strategy is based on linearization of the nonlinear model at the equilibrium point (steady state). The corresponding controller has two components: the first one that keeps the system state variables at the desired equilibrium (set-point controller) and the second-one that reduces in an optimal way deviations of the system state variables from their desired equilibrium values. The second controller is based on minimization of the square of the error between the actual and desired (equilibrium) values for the linearized system (linear-quadratic optimal controller). The obtained control strategy recommends to HIV researchers and experimentalists that the constant dosages of drugs have to be administrated at all times (set point controller, open-loop controller) and that the variable dosages of drugs have to be administrated on a daily basis (closed-loop controller, feedback controller).

A model predictive control based scheduling method for HIV therapy

Recently developed models of the interaction of the human immune system and the human immunodeficiency virus (HIV) suggest the possibility of using interruptions of highly active anti-retroviral therapy (HAART) to simulate a therapeutic vaccine and induce cytotoxic lymphocyte (CTL) mediated control of HIV infection. We have developed a model predictive control (MPC) based method for determining optimal treatment interruption schedules for this purpose. This method provides a clinically implementable framework for calculating interruption schedules that are robust to errors due to measurement and patient variations. In this paper, we discuss the medical motivation for this work, introduce the MPC-based method, show simulation results, and discuss future work necessary to implement the method.

Nonlinear control of a dynamic model of HIV-1

Highly active antiretroviral therapy (HAART) reduces the viral burden in human immunodeficiency virus type 1 (HIV-1) infected patients. The paper addresses the problem of controlling the predator-prey like model of the interaction among CD4+ T-cell, CD8+ T-cell, and HIV-1 by an external drug agency. By exploring the dynamic properties of the system, the original system is first regrouped into two subsystems, then a nonlinear global controller is presented by designing two controllers over two complementary zones: a local controller on a finite region and a global controller over its complement. The local controller is designed to guarantee nonnegativty, and avoids the problem of control singularity within the neighborhood of the origin omega. The complementary controller is designed via backstepping for both subsystems over the complementary region. The closed-loop system is globally stable at nominal values through the introduction of a novel bridging virtual control, and the resulting controller is singularity free and guarantees nonnegativity. In this paper, simulations are conducted in discrete-time with sampling time Ts to show the effectiveness of the proposed method.

Computer simulations of slow progression of human immunodeficiency virus infection and relapse during anti-HIV treatment with reverse transcriptase inhibitors and protease inhibitors

Human immunodeficiency virus (HIV) infection and acquired immunodeficiency syndrome (AIDS) have been very serious problems since the 1980s. The progression of HIV infection into AIDS can be suppressed to some extent with reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs); however, there are some serious problems with treatments using the anti-HIV drugs (e.g. very high expense, complicated administration, and drug resistance). Hence, more studies on HIV and the development of more effective anti-HIV treatments are required. We consider it important to understand the complex dynamics involved in HIV infection, and we therefore propose new mathematical models of HIV infection. In the modeling, we have paid attention to the nonlinear relations between stimuli and responses (i.e., when responses are plotted against the logarithm of stimuli, a sigmoid curve is obtained), and to lymphoid organs which seem more important than the blood compartment (i.e., lymphoid organs are major reservoirs of HIV virions and contain most of the lymphocytes). Using the models, we have found that viral antigenic mutation plays an important role in the slow progression in the chronic phase of HIV infection. We have also found that viral antigenic mutation can cause relapse of HIV infection when the inhibition rate of anti-HIV drugs is low and that viral antigenic mutation cannot cause relapse when the inhibition rate is high.

Feedback control of a biodynamical model of HIV-1

We describe a continuous differential equation model of the interaction dynamics of HIV-1 and CD4 and CD8 lymphocytes in the human body. We demonstrate several methods of stable control of the HIV-1 population using an external feedback control term that is analogous to the introduction of a therapeutic drug regimen. We also show how the immune system components can be bolstered against the virus through a feedback control approach.