CGM Metrics Identify Dysglycemic States in Participants From the TrialNet Pathway to Prevention Study.

OBJECTIVE: Continuous glucose monitoring (CGM) parameters may identify individuals at risk for progression to overt type 1 diabetes. We aimed to determine whether CGM metrics provide additional insights into progression to clinical stage 3 type 1 diabetes. RESEARCH DESIGN AND METHODS: One hundred five relatives of individuals in type 1 diabetes probands (median age 16.8 years; 89% non-Hispanic White; 43.8% female) from the TrialNet Pathway to Prevention study underwent 7-day CGM assessments and oral glucose tolerance tests (OGTTs) at 6-month intervals. The baseline data are reported here. Three groups were evaluated: individuals with 1) stage 2 type 1 diabetes (n = 42) with two or more diabetes-related autoantibodies and abnormal OGTT; 2) stage 1 type 1 diabetes (n = 53) with two or more diabetes-related autoantibodies and normal OGTT; and 3) negative test for all diabetes-related autoantibodies and normal OGTT (n = 10). RESULTS: Multiple CGM metrics were associated with progression to stage 3 type 1 diabetes. Specifically, spending ≥5% time with glucose levels ≥140 mg/dL (P = 0.01), ≥8% time with glucose levels ≥140 mg/dL (P = 0.02), ≥5% time with glucose levels ≥160 mg/dL (P = 0.0001), and ≥8% time with glucose levels ≥160 mg/dL (P = 0.02) were all associated with progression to stage 3 disease. Stage 2 participants and those who progressed to stage 3 also exhibited higher mean daytime glucose values; spent more time with glucose values over 120, 140, and 160 mg/dL; and had greater variability. CONCLUSIONS: CGM could aid in the identification of individuals, including those with a normal OGTT, who are likely to rapidly progress to stage 3 type 1 diabetes.

Modeling adaptive regulatory T-cell dynamics during early HIV infection.

Regulatory T-cells (Tregs) are a subset of CD4(+) T-cells that have been found to suppress the immune response. During HIV viral infection, Treg activity has been observed to have both beneficial and deleterious effects on patient recovery; however, the extent to which this is regulated is poorly understood. We hypothesize that this dichotomy in behavior is attributed to Treg dynamics changing over the course of infection through the proliferation of an 'adaptive' Treg population which targets HIV-specific immune responses. To investigate the role Tregs play in HIV infection, a delay differatial equation model was constructed to examine (1) the possible existence of two distinct Treg populations, normal (nTregs) and adaptive (aTregs), and (2) their respective effects in limiting viral load. Sensitivity analysis was performed to test parameter regimes that show the proportionality of viral load with adaptive regulatory populations and also gave insight into the importance of downregulation of CD4(+) cells by normal Tregs on viral loads. Through the inclusion of Treg populations in the model, a diverse array of viral dynamics was found. Specifically, oscillatory and steady state behaviors were both witnessed and it was seen that the model provided a more accurate depiction of the effector cell population as compared with previous models. Through further studies of adaptive and normal Tregs, improved treatments for HIV can be constructed for patients and the viral mechanisms of infection can be further elucidated.

Translating glucose variability metrics into the clinic via Continuous Glucose Monitoring: a Graphical User Interface for Diabetes Evaluation (CGM-GUIDE©).

BACKGROUND: Several metrics of glucose variability have been proposed to date, but an integrated approach that provides a complete and consistent assessment of glycemic variation is missing. As a consequence, and because of the tedious coding necessary during quantification, most investigators and clinicians have not yet adopted the use of multiple glucose variability metrics to evaluate glycemic variation. METHODS: We compiled the most extensively used statistical techniques and glucose variability metrics, with adjustable hyper- and hypoglycemic limits and metric parameters, to create a user-friendly Continuous Glucose Monitoring Graphical User Interface for Diabetes Evaluation (CGM-GUIDE©). In addition, we introduce and demonstrate a novel transition density profile that emphasizes the dynamics of transitions between defined glucose states. RESULTS: Our combined dashboard of numerical statistics and graphical plots support the task of providing an integrated approach to describing glycemic variability. We integrated existing metrics, such as SD, area under the curve, and mean amplitude of glycemic excursion, with novel metrics such as the slopes across critical transitions and the transition density profile to assess the severity and frequency of glucose transitions per day as they move between critical glycemic zones. CONCLUSIONS: By presenting the above-mentioned metrics and graphics in a concise aggregate format, CGM-GUIDE provides an easy to use tool to compare quantitative measures of glucose variability. This tool can be used by researchers and clinicians to develop new algorithms of insulin delivery for patients with diabetes and to better explore the link between glucose variability and chronic diabetes complications.

Dynamics of human complement-mediated killing of Klebsiella pneumoniae.

With an in vitro system that used a luminescent strain of Klebsiella pneumoniae to assess bacterial metabolic activity in near-real-time, we investigated the dynamics of complement-mediated attack in healthy individuals and in patients presenting to the emergency department with community-acquired severe sepsis. A novel mathematical/statistical model was developed to simplify light output trajectories over time into two fitted parameters, the rate of complement activation and the delay from activation to the onset of killing. Using Factor B-depleted serum, the alternative pathway was found to be the primary bactericidal effector: In the absence of B, C3 opsonization as measured by flow cytometry did not progress and bacteria proliferated near exponentially. Defects in bacterial killing were easily demonstrable in patients with severe sepsis compared with healthy volunteers. In most patients with sepsis, the rate of activation was higher than in normal subjects but was associated with a prolonged delay between activation and bacterial killing (P < 0.05 for both). Theoretical modeling suggested that this combination of accentuated but delayed function should allow successful bacterial killing but with significantly greater complement activation. The use of luminescent bacteria allowed for the development of a novel and powerful tool for assessing complement immunology for the purposes of mechanistic study and patient evaluation.

Delay differential equations via the matrix Lambert W function and bifurcation analysis: application to machine tool chatter.

In a turning process modeled using delay differential equations (DDEs), we investigate the stability of the regenerative machine tool chatter problem. An approach using the matrix Lambert W function for the analytical solution to systems of delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. The Lambert W function, known to be useful for solving scalar first-order DDEs, has recently been extended to a matrix Lambert W function approach to solve systems of DDEs. The essential advantages of the matrix Lambert W approach are not only the similarity to the concept of the state transition matrix in lin ear ordinary differential equations, enabling its use for general classes of linear delay differential equations, but also the observation that we need only the principal branch among an infinite number of roots to determine the stability of a system of DDEs. The bifurcation method combined with Sturm sequences provides an algorithm for determining the stability of DDEs without restrictive geometric analysis. With this approach, one can obtain the critical values of delay, which determine the stability of a system and hence the preferred operating spindle speed without chatter. We apply both the matrix Lambert W function and the bifurcation analysis approach to the problem of chatter stability in turning, and compare the results obtained to existing methods. The two new approaches show excellent accuracy and certain other advantages, when compared to traditional graphical, computational and approximate methods.

Modeling the mechanisms of acute hepatitis B virus infection.

Mathematical models have been used to understand the factors that govern infectious disease progression in viral infections. Here we focus on hepatitis B virus (HBV) dynamics during the acute stages of the infection and analyze the immune mechanisms responsible for viral clearance. We start by presenting the basic model used to interpret HBV therapy studies conducted in chronically infected patients. We then introduce additional models to study acute infection where immune responses presumably play an important role in determining whether the infection will be cleared or become chronic. We add complexity incrementally and explain each step of the modeling process. Finally, we validate the model against experimental data to determine how well it represents the biological system and, consequently, how useful are its predictions. In particular, we find that a cell-mediated immune response plays an important role in controlling the virus after the peak in viral load.

In vitro and in silico analysis of annexin V binding to lymphocytes as a biomarker in emergency department sepsis studies.

BACKGROUND: Peripheral blood lymphocyte apoptosis is a recognized feature of serious infection and sepsis and can be easily quantified by flow cytometric measurement of annexin V binding to the cell surface. Use of apoptosis as a biomarker in emergency department (ED) studies of sepsis is potentially difficult because of sample processing requirements and limited availability of a research cytometer with which to measure patient samples. OBJECTIVES: To assess, in vitro and in simulation, the relationship between sample stability, timing of patient enrollment, and diagnostic performance of a flow cytometric assay for sepsis in patients evaluated in EDs. METHODS: Assuming any clinical trial would require daily sample batching, the authors measured the stability of lymphocyte samples over time, noting the rate at which annexin V-negative cells became positive as ED processing delays increased. With these data, they then optimized a study design that could evaluate lymphocyte apoptosis as a sepsis biomarker by using a series of Monte Carlo-based simulated clinical trials. RESULTS: The authors found that annexin V-negative lymphocytes become positive during storage delays that would be encountered in an ED sepsis trial. The extent of this deterioration was least among cells left as whole blood at room temperature until just before analysis or when lymphocytes were isolated early and stored in culture media at 4 degrees C until analysis. When the expected rate of sample deterioration was considered in simulated clinical trials, an inverse relationship was found between the rate at which patients are enrolled and the best achievable receiver operating characteristic curve a study could produce. CONCLUSIONS: Peripheral blood samples being analyzed for lymphocyte apoptosis degrade at a rate relevant to the design of ED trials of sepsis. Because of sample processing delays inherent in studying unscheduled septic patients, the performance of annexin V binding as a biomarker for sepsis can approach, but not be expected to exceed, its performance in a comparable intensive care unit-based study.

The role of cells refractory to productive infection in acute hepatitis B viral dynamics.

During acute hepatitis B virus (HBV) infection viral loads reach high levels ( approximately 10(10) HBV DNA per ml), and nearly every hepatocyte becomes infected. Nonetheless, approximately 85-95% of infected adults clear the infection. Although the immune response has been implicated in mediating clearance, the precise mechanisms remain to be elucidated. As infection clears, infected cells are replaced by uninfected ones. During much of this process the virus remains plentiful but nonetheless does not rekindle infection. Here, we analyze data from a set of individuals identified during acute HBV infection and develop mathematical models to test the role of immune responses in various stages of early HBV infection. Fitting the models to data we are able to separate the kinetics of the noncytolytic and the cytolytic immune responses, thus explaining the relative contribution of these two processes. We further show that we need to hypothesize that newly generated uninfected cells are refractory to productive infection. Without this assumption, viral resurgence is observed as uninfected cells are regenerated. Such protection, possibly mediated by cytokines, may also be important in resolving other acute viral infections.

An age-structured model of hiv infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells.

Mathematical models of HIV-1 infection can help interpret drug treatment experiments and improve our understanding of the interplay between HIV-1 and the immune system. We develop and analyze an age- structured model of HIV-1 infection that allows for variations in the death rate of productively infected T cells and the production rate of viral particles as a function of the length of time a T cell has been infected. We show that this model is a generalization of the standard differential equation and of delay models previously used to describe HIV-1 infection, and provides a means for exploring fundamental issues of viral production and death. We show that the model has uninfected and infected steady states, linked by a transcritical bifurcation. We perform a local stability analysis of the nontrivial equilibrium solution and provide a general stability condition for models with age structure. We then use numerical methods to study solutions of our model focusing on the analysis of primary HIV infection. We show that the time to reach peak viral levels in the blood depends not only on initial conditions but also on the way in which viral production ramps up. If viral production ramps up slowly, we find that the time to peak viral load is delayed compared to results obtained using the standard (constant viral production) model of HIV infection. We find that data on viral load changing over time is insufficient to identify the functions specifying the dependence of the viral production rate or infected cell death rate on infected cell age. These functions must be determined through new quantitative experiments.

Mathematical analysis of delay differential equation models of HIV-1 infection.

Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without delays. We develop and analyze a set of models that include intracellular delays, combination antiretroviral therapy, and the dynamics of both infected and uninfected T cells. We show that when the drug efficacy is less than perfect the estimated value of the loss rate of productively infected T cells, delta, is increased when data is fit with delay models compared to the values estimated with a non-delay model. We provide a mathematical justification for this increased value of delta. We also provide some general results on the stability of non-linear delay differential equation infection models.