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H T Banks

Publications and source records attributed to H T Banks.

9 recordsLinked to original sources
PubMed2007

Estimation and prediction with HIV-treatment interruption data.

We consider longitudinal clinical data for HIV patients undergoing treatment interruptions. We use a nonlinear dynamical mathematical model in attempts to fit individual patient data. A statistically-based censored data method is combined with inverse problem techniques to estimate dynamic parameters. The predictive capabilities of this approach are demonstrated by comparing simulations based on estimation of parameters using only half of the longitudinal observations to the full longitudinal data sets.

Antiretroviral Therapy, Highly Active↗
PubMed2006

A dynamic model for induced reactivation of latent virus.

We develop a deterministic mathematical model to describe reactivation of latent virus by chemical inducers. This model is applied to the reactivation of latent KSHV in BCBL-1 cell cultures with butyrate as the inducing agent. Parameters for the model are first estimated from known properties of the exponentially growing, uninduced cell cultures. Additional parameters that are necessary to describe induction are determined from fits to experimental data from the literature. Our initial model provides good agreement with two independent sets of experimental data, but also points to the need for a new class of experiments which are required for further understanding of the underlying mechanisms.

Butyrates↗
PubMed2005

Population dynamics models in plant-insect herbivore-pesticide interactions.

We consider several population dynamics models in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types (bare or weedy ground) and three levels of insecticide spray (no, light, or heavy spray). We carry out parameter estimation computations along with statistical analysis to compare autonomous versus non-autonomous model dynamics. We conclude with a brief discussion of some not-so-subtle pitfalls that can arise when using quantitative measures of model fit-to-data to make biological inferences as well as offer a positive example of how one might combine a priori biological hypothesis and intuition with rather sophisticated (from a field biology viewpoint) mathematical methodologies to suggest synergisms.

Animals↗
PubMed2004

Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model.

Population variability and uncertainty are important features of biological systems that must be considered when developing mathematical models for these systems. In this paper we present probability-based parameter estimation methods that account for such variability and uncertainty. Theoretical results that establish well-posedness and stability for these methods are discussed. A probabilistic parameter estimation technique is then applied to a toxicokinetic model for trichloroethylene using several types of simulated data. Comparison with results obtained using a standard, deterministic parameter estimation method suggests that the probabilistic methods are better able to capture population variability and uncertainty in model parameters.

Animals↗
PubMed2003

Incorporation of variability into the modeling of viral delays in HIV infection dynamics.

We consider classes of functional differential equation models which arise in attempts to describe temporal delays in HIV pathogenesis. In particular, we develop methods for incorporating arbitrary variability (i.e., general probability distributions) for these delays into systems that cannot readily be reduced to a finite number of coupled ordinary differential equations (as is done in the method of stages). We discuss modeling from first principles, introduce several classes of non-linear models (including discrete and distributed delays) and present a discussion of theoretical and computational approaches. We then use the resulting methodology to carry out simulations and perform parameter estimation calculations, fitting the models to a set of experimental data. Results obtained confirm the statistical significance of the presence of delays and the importance of including delays in validating mathematical models with experimental data. We also show that the models are quite sensitive to the mean of the distribution which describes the delay in viral production, whereas the variance of this distribution has relatively little impact.

Computer Simulation↗
PubMed2002

Physiologically based pharmacokinetic models for the transport of trichloroethylene in adipose tissue.

In this paper we present three physiologically based pharmacokinetic (PBPK) models for the systemic transport of trichloroethylene (TCE), with a focus on the adipose, or fat tissue. TCE is a widespread environmental contaminant, and has been shown to produce toxic effects in both animals and humans. A key characteristic of TCE is its tendency to accumulate in fat tissue, which has a major impact on the overall systemic disposition of TCE. Here we use PBPK models to predict the dynamics of TCE in the various tissues and organs, including the adipose tissue. The first model utilizes the standard 'perfusion-limited' compartmental model for the fat tissue, while the second model uses a 'diffusion-limited' model to describe the transport through the adipose tissue. Both of these ODE models are based on 'well-mixed' and rapid equilibrium assumptions, and do not take into account the specific and largely heterogeneous physiology of adipose tissue. The third model we discuss is a PBPK hybrid model with an axial-dispersion type model for the adipose tissue. This PDE-based model is designed to capture key physiological heterogeneities of fat tissue, including widely varying fat cell sizes, lipid distribution, and blood flow properties. Model simulations demonstrate that this model may be well-suited to predict the experimental behavior of TCE in adipose tissue using parameter estimation techniques.

Adipose Tissue↗
PubMed1983

Parameter estimation techniques for transport equations with application to population dispersal and tissue bulk flow models.

We developed techniques for estimating the coefficients, boundary data, and initial data associated with transport equations (or more generally, parabolic distributed models). Our estimation schemes are based on cubic spline approximations, for which convergence results are given. We discuss the performance of these techniques in two investigations of biological interest: (1) transport of labeled sucrose in brain tissue white matter, (2) insect dispersal that cannot be modeled by a random diffusion mechanism alone.

Animals↗