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.Inspec keywords: medical control systems, diseases, microorganisms, cellular biophysics, drugs, patient treatment, Lyapunov methods, switching systems (control)Other keywords: control process, switching control strategy, human immunodeficiency virus infection, healthy cells, immune cells, viruses, drug treatment design, HIV dynamic system model, unmeasurable CD8 + T cell count, switching form, drug therapies, Lyapunov function theory     

艾滋病毒感染后疾病进展和治疗的数学模型及其动力学性态(英文)

本文是对个体被艾滋病毒感染后的数学模型及动力学性态研究情况的简单综述。介绍了CD4~+ T细胞、病毒颗粒和药物治疗相互作用的艾滋病数学模型的研究结果,主要是用常微分方程、时滞方程、积分微分方程和脉冲微分方程来描述艾滋病感染后疾病进展和治疗的模型理论研究和数值模拟结果。我们收集了这些模型中基本参数值的取值范围,将其整理成一个表格放在附录中以便读者参考。     

Robust control of HIV infection by antiretroviral therapy: a super‐twisting sliding mode control approach

Acquired immune deficiency syndrome is an epidemic infectious disease which is caused by the human immunodeficiency virus (HIV) and that has proliferated across worldwide. It has been a matter of concern for the scientific community to develop an antiretroviral therapy, which will prompt a rapid decline in viral abundance. With this motivation, this study proposes the design of a robust super twisting sliding mode controller based on output information for an uncertain HIV infection model. The control objective is to decrease the concentration of infected CD4+ T cells to a specified level by drug administration using only the output information of the uncertain HIV infection model which is total CD4+ T cell concentration. The robust output‐feedback controller has been developed in combination with a robust exact differentiator, functioning as an observer. The reported analysis demonstrates that the approach proposed here is capable of ensuring robust performance under several operating conditions, measurement and modelling error, parametric uncertainties and external disturbances and the simulation results prove the proficiency of the controller proposed.Inspec keywords: control system synthesis, observers, robust control, drugs, medical control systems, diseases, uncertain systems, variable structure systems, patient treatment, feedback, cellular biophysics, microorganismsOther keywords: robust control, antiretroviral therapy, sliding mode control approach, acquired immune deficiency syndrome, epidemic infectious disease, human immunodeficiency virus, scientific community, robust super, mode controller, output information, uncertain HIV infection model, control objective, infected CD4, total CD4, T cell concentration, robust output‐feedback controller, robust exact differentiator, robust performance     

On the design of human immunodeficiency virus treatment based on a non‐linear time‐delay model

Mathematical modelling and methods from control theory can be employed to find appropriate drug regimens in human immunodeficiency virus (HIV) treatment. In this study, using a non‐linear time‐delay model, the authors design some suboptimal highly active antiretroviral therapy (HAART) [http://www.en.wikipedia.org/wiki/Protease_inhibitor_%28pharmacology%29] regimens for patients with HIV. The non‐linear delayed model is used to describe the dynamical interactions between HIV and human immune system in the presence of HAART. Based on the model, a set point tracking problem is defined in order to set the number of susceptible CD4⁺ T cells to a desired value. To solve this set point tracking problem in a suboptimal way, the authors introduce a new method which is able to consider constraints on the amount of drug dosage. It is proved that the proposed method is able to set the number of susceptible CD4⁺ T cells to the desired value. Simulation results confirm that the method is efficient even in the presence of parametric uncertainties.Inspec keywords: control theory, delays, diseases, patient treatmentOther keywords: human immunodeficiency virus treatment design, nonlinear time delay model, control theory, HIV treatment, suboptimal highly active antiretroviral therapy, suboptimal HAART, human immune system, set point tracking problem, CD4+T cells, drug dosage     

Binding of HIV-1 gp120 glycoprotein to silica nanoparticles modified with CD4 glycoprotein and CD4 peptide fragments

An important step in human immunodeficiency virus infection involves the interaction between the viral envelope glycoprotein gp120 and the human host cell surface receptor CD4. Herein, we describe a CD4-functionalized mesoporous silica-based system to selectively capture HIV-gp120 with high binding efficiency. Using a protection-deprotection strategy developed recently by our group, the external surface of the mesoporous particles was selectively functionalized with soluble CD4 ("sCD4") or an 18-peptide fragment mimicking the gp120 binding region. Confocal microscopy confirmed the CD4 locations and showed that the internal pores can be made accessible after external modification in a controlled manner. An evaluation of the ability of an 18-peptide CD4 fragment versus amide-immobilized sCD4 and sCD4 immobilized through its glycosidic group indicated that while all peptides were selective, the latter method was clearly best, with nearly complete removal of whole gp120 from solution. This study shows, for the first time, that sCD4 bound to mesoporous silica particles actively recognizes and retains high binding affinity for HIV-gp120. It is anticipated that, by proper modification of the accessible internal pores, our methodology can be adopted to develop porous platforms for HIV diagnosis, imaging, drug delivery, and vaccine development.     

Hollow ZnO Nanospheres Enhance Anticancer Immunity by Promoting CD4+ and CD8+ T Cell Populations In Vivo

Appropriate adjuvant aiding in generating robust anticancer immunity is crucial for cancer immunotherapy. Herein, hollow ZnO (HZnO) nanospheres are synthesized by a facile method using carbon nanospheres as the template. The HZnO nanospheres significantly promote the cellular uptake of a model antigen, and cytokine secretion by antigen‐presenting cells in vitro. HZnO loaded with ovalbumin and polyinosinic‐polycytidylic acid (poly(I:C)) inhibits cancer growth and metastasis to inguinal lymph node in a cancer cell challenge model. Moreover, HZnO loaded with autologous cancer antigens inhibits cancer cell growth in a cancer cell re‐challenge model. HZnO nanospheres significantly improve the CD4⁺ and/or CD8⁺ T cell population in splenocytes of mice in both cancer cell challenge model and re‐challenge model. The HZnO nanospheres can be used for cancer immunotherapy as adjuvant.     

Prediction of the containment of HIV infection by antiretroviral therapy – a variable structure control approach

It is demonstrated that the reachability paradigm from variable structure control theory is a suitable framework to monitor and predict the progression of the human immunodeficiency virus (HIV) infection following initiation of antiretroviral therapy (ART). A manifold is selected which characterises the infection‐free steady‐state. A model of HIV infection together with an associated reachability analysis is used to formulate a dynamical condition for the containment of HIV infection on the manifold. This condition is tested using data from two different HIV clinical trials which contain measurements of the CD4+ T cell count and HIV load in the peripheral blood collected from HIV infected individuals for the six month period following initiation of ART. The biological rates of the model are estimated using the multi‐point identification method and data points collected in the initial period of the trial. Using the parameter estimates and the numerical solutions of the model, the predictions of the reachability analysis are shown to be consistent with the clinical diagnosis at the conclusion of the trial. The methodology captures the dynamical characteristics of eventual successful, failed and marginal outcomes. The findings evidence that the reachability analysis is an appropriate tool to monitor and develop personalised antiretroviral treatment.Inspec keywords: microorganisms, patient treatment, drugs, parameter estimationOther keywords: HIV infection, antiretroviral therapy, variable structure control theory, human immunodeficiency virus, antiretroviral drugs, multipoint identification method, parameter estimation, reachability analysis     

Si4+离子对Y3+:PbWO4晶体闪烁性能及辐照硬度的影响

Y³⁺离子掺杂钨酸铅晶体特殊的低剂量率辐照行为一般在晶体顶端表现更为明显,以往研究认为该现象起因于晶体中有效分凝系数<1的Na⁺、K⁺和Si⁴⁺等杂质在顶端的富集.本文研究了Si⁴⁺掺杂的Y³⁺:PWO晶体,对晶体顶端和晶种端的分段晶体测试了退火温度对晶体透过率和辐照硬度的影响,结果发现:在实验所涉及的掺杂浓度范围内,Si⁴⁺离子杂质对Y³⁺:PWO晶体的辐照硬度及透过率无影响,可以认为Y³⁺:PWO晶体特殊的低剂量率辐照行为和晶体中的Si⁴⁺离子含量无关.     

Occurrence of HIV eradication for preexposure prophylaxis treatment with a deterministic HIV model

The authors examine the human immunodeficiency virus (HIV) eradication in this study using a mathematical model and analyse the occurrence of virus eradication during the early stage of infection. To this end they use a deterministic HIV‐infection model, modify it to describe the pharmacological dynamics of antiretroviral HIV drugs, and consider the clinical experimental results of preexposure prophylaxis HIV treatment. They also use numerical simulation to model the experimental scenario, thereby supporting the clinical results with a model‐based explanation. The study results indicate that the protocol employed in the experiment can eradicate HIV in infected patients at the early stage of the infection.Inspec keywords: diseases, numerical analysis, drugs, patient treatmentOther keywords: preexposure prophylaxis HIV treatment, antiretroviral HIV drug, pharmacological dynamics, deterministic HIV‐infection model, early infection stage, virus eradication, mathematical model, human immunodeficiency virus, HIV eradication     

Global stability of infection‐free state and endemic infection state of a modified human immunodeficiency virus infection model

This study proposes a modified human immunodeficiency virus (HIV) infection differential equation model with a saturated infection rate. This model has an infection‐free equilibrium point and an endemic infection equilibrium point. Using Lyapunov functions and LaSalle’s invariance principle shows that if the model’s basic reproductive number R ₀ < 1, the infection‐free equilibrium point is globally asymptotically stable, otherwise the endemic infection equilibrium point is globally asymptotically stable. It is shown that a forward bifurcation will occur when R ₀ = 1. The basic reproductive number R ₀ of the modified model is independent of plasma total CD4⁺ T cell counts and thus the modified model is more reasonable than the original model proposed by Buonomo and Vargas‐De‐León. Based on the clinical data from HIV drug resistance database of Stanford University, using the proposed model simulates the dynamics of two group patients’ anti‐HIV infection treatments. The simulation results have shown that the first 4 weeks’ treatments made the two group patients’ R′ ₀ < 1, respectively. After the period, drug resistance made the two group patients’ R′ ₀ > 1. The results explain why the two group patients’ mean CD4⁺ T cell counts raised and mean HIV RNA levels declined in the first period, but contrary in the following weeks.Inspec keywords: microorganisms, cellular biophysics, differential equations, Lyapunov methods, blood, drugs, patient treatment, RNAOther keywords: global stability, infection‐free state, endemic infection state, modified human immunodeficiency virus infection model, HIV, differential equation model, saturated infection rate, infection‐free equilibrium point, endemic infection equilibrium point, Lyapunov functions, LaSalle invariance principle, forward bifurcation, plasma total CD4⁺ T cell counts, HIV drug resistance database, mean HIV RNA levels     

Study on UV excitation properties of Y2O3:Ln3+ (Ln = Eu3+ or Tb3+) luminescent nanomaterials

Y2O3:Ln3+ (Ln = Eu or Tb) nanocrystals with different Ln3+ doping concentrations and average sizes were prepared by chemical self-combustion. The corresponding bulk materials with various doping concentrations were obtained by annealing the nanomaterials at high temperature. The emission spectra, excitation spectra, and X-ray diffraction spectra were used in this study. It was found that the charge transfer band of Y2O3:Eu3+ red-shifted as particle size decreased, and the charge transfer band in the 5-nm particles obviously broadened toward the long wavelength. It was also found that the profile of excitation spectra corresponding to the 4f5d (4f8 --> 4f(7)5d1) transition changed a lot with the variation of the particle size. The dependence of the excitation spectra of Y2O3:Ln3+ on particle size was investigated.     

BCP coatings on pure titanium plates by CD method

Ca–P coatings on pure titanium plates were precipitated in this work by a cathode deposition (CD) method and showed several differences from other reported works. The fast calcification solution (FCS) and revised simulation body fluid (R-SBF) were used as electrolytes. A significant difference in sizes of crystals and thickness of the precipitated coatings was observed between the bioactive calcium phosphate (BCP) coatings precipitated from FCS and from R-SBF. The possible reason of this difference was ascribed to that the ion concentrations of Ca²⁺ and HPO₄²⁻ and some inhibitors of Ca–P crystals growth such as Mg²⁺ and CO₃²⁻ ions and pH of electrolytes. The crystalline structure and composition of BCP coatings are of special importance to applications of the BCP coatings. The characterization has been fulfilled by the use of XRD, FTIR, SEM and TEM. The results of this study made it clear that the precipitates on the Ti plates by cathode deposition method in different electrolytes were not the hydroxyapatite (HA) but octacalcium phosphate (OCP) and some carbonate-containing amorphous calcium phosphate apatite, and a few of precipitates changed to needle-like HA after immerged in a 0.1 M NaOH solution at 60 °C for 48 h. The present study confirms that CD method is a more convenient and fast way to prepare BCP coatings on titanium implants than the reported works.     

Efficiency dependence on the Tm3+ and Al3+ concentrations for Tm3+-doped silica double-clad fiber lasers

We present measurements of the slope efficiency and the pump power at threshold for a number of Tm3+-doped silica double-clad fiber lasers that incorporate fibers that have a range of Tm3+ concentrations. We obtain a slope efficiency for the approximately 2-microm 3H4 --> 3H6 laser transition that is greater than the Stokes efficiency limit for a Tm3+ concentration as low as 1.3 wt. %. These results indicate that the cross relaxation process, 3F4, 3H6 --> 3H4, 3H4, has a significant effect on the efficiency of the laser despite the relatively short lifetime of the 3F4 energy level. Energy migration of the excitation at the 3F4 level through the process 3F4, 3H6 --> 3H6, 3F4 may be enhancing the cross-relaxation mechanism. We also show the importance of reducing the level of clustering of the Tm3+ ion when it is doped into silica by use of appropriate amounts of Al3+ codopant. For Tm3+ concentrations of >1 wt. %, Al3+/Tm3+ concentration ratios of > 10 are recommended forreducing scattering losses, quenching the lifetime, or both.     

Dynamics of killer T cell inflation in viral infections

Upon acute viral infection, a typical cytotoxic T lymphocyte (CTL) response is characterized by a phase of expansion and contraction after which it settles at a relatively stable memory level. Recently, experimental data from mice infected with murine cytomegalovirus (MCMV) showed different and unusual dynamics. After acute infection had resolved, some antigen specific CTL started to expand over time despite the fact that no replicative virus was detectable. This phenomenon has been termed as "CTL memory inflation". In order to examine the dynamics of this system further, we developed a mathematical model analysing the impact of innate and adaptive immune responses. According to this model, a potentially important contributor to CTL inflation is competition between the specific CTL response and an innate natural killer (NK) cell response. Inflation occurs most readily if the NK cell response is more efficient than the CTL at reducing virus load during acute infection, but thereafter maintains a chronic virus load which is sufficient to induce CTL proliferation. The model further suggests that weaker NK cell mediated protection can correlate with more pronounced CTL inflation dynamics over time. We present experimental data from mice infected with MCMV which are consistent with the theoretical predictions. This model provides valuable information and may help to explain the inflation of CMV specific CD8+T cells seen in humans as they age.     

等价Ca、Sr离子固溶对CaTiO3:0.002Pr3+发光特性的影响

利用高温固相反应法,制备了不同Sr/Ca比的(Ca_1-xSr_x)TiO₃:0.002Pr³⁺(x=0-0.6)红色发光材料.荧光光谱与XRD测试结果表明:所有样品均发出源于Pr³⁺的¹D₂→³H₄跃迁的612m红色光;发光强度与晶胞a轴均随固溶取代量x改变而连续变化,并在x=0.15的出现极值:发光强度提高约三倍,a轴则最小.研究揭示除不等价离子取代产生的电荷缺陷外,等价离子取代导致的固溶结构变化也是改变发光强度的有效途径.     

Limitations to the use of Pr3+ as a sensitizer in luminescent Gd3+ compounds

Transfer phenomena which influence the energy transfer processes in Pr³⁺-sensitized Gd³⁺ compounds are discussed. Concentration quenching of the Pr³⁺ 4f5d emission at relatively low Pr³⁺ concentrations, and energy transfer from activator ions to Pr³⁺ limits strongly the use of Pr³⁺ as a sensitizer in the host lattice GdBO₃.     

A simultaneous confidence corridor for varying coefficient regression with sparse functional data

We consider a varying coefficient regression model for sparse functional data, with time varying response variable depending linearly on some time-independent covariates with coefficients as functions of time-dependent covariates. Based on spline smoothing, we propose data-driven simultaneous confidence corridors for the coefficient functions with asymptotically correct confidence level. Such confidence corridors are useful benchmarks for statistical inference on the global shapes of coefficient functions under any hypotheses. Simulation experiments corroborate with the theoretical results. An example in CD4/HIV study is used to illustrate how inference is made with computable p values on the effects of smoking, pre-infection CD4 cell percentage and age on the CD4 cell percentage of HIV infected patients under treatment.     

What is good about PD + HD combined therapy

It is known that β(2) -microglobulin (β(2) -MG) concentration in peritoneal dialysis (PD) patients is inversely correlated to the residual renal function (RRF). With decreasing RRF, some PD patients may necessarily be treated with hemodialysis (HD) once a week, not only for removing excess water and small solutes, but also for removing much larger solutes such as β(2) -MG. In this study, a kinetic model allowed us to show what is good about PD + HD combined therapy in long-term PD patients. A mathematical model was established based on a classic compartment theory for clinical use. Model validations were made by comparing calculated results with clinical data in order to specify what was good about PD + HD combined therapy (5-day PD?+?1-HD/week). Time-averaged concentration (TAC) for urea and creatinine decreased by 20% on the average by introducing PD+HD combined therapy no matter which dialyzers were used. TAC for β(2) -MG in PD+HD combined therapy, however, was strongly dependent upon the dialyzer clearance, and when a low flux dialyzer (clearance for β(2) -MG?=?10?mL/min under Q(B) =?200, Q(D) =?500?mL/min) was used, pre-dialysis β(2) -MG concentration may increase. Use of super high-flux dialyzers (clearance for β(2) -MG?=?60?mL/min under the same conditions) should greatly reduce the β(2) -MG concentration from 30 to 8?mg/L in 4-hr treatment. Then, when PD+HD combined therapy is introduced to a PD patient with diminishing RRF, use of super high-flux dialyzers may be strongly recommended in order not to increase concentrations of pre-dialysis β(2) -MG and/or even greater solutes. Use of super high-flux dialyzers is a key to the success of PD+HD combined therapy that could prevent concentrations of large solutes from increasing.