Analysis of compartments-in-series models of liver metabolism as partial differential equations: the effect of dispersion and number of compartments.

Non-alcoholic fatty liver disease is the most common cause of chronic liver disease. Precipitated by the build up of extra fat in the liver not caused by alcohol, it is still not understood why steatosis occurs where it does in the liver microstructure in non-alcoholic fatty liver disease. It is likely, however, that the location of steatosis is due, at least in part, to metabolic zonation (heterogeneity among liver cells in function and enzyme expression). Recently, there has been an influx of computational and mathematical models in order to investigate the relationship between metabolic zonation and steatosis in non-alcoholic fatty liver disease. Of interest among these models are "compartments-in-series" models. Compartments-in-series models include the spatial distribution of metabolite concentrations via series of compartments that are connected through some representation of blood flow. In this paper, we analyze one such model, focusing specifically at how the number of compartments and inclusion of dispersion in the flow affect simulation results. We find the number of compartments to have a much larger effect than the inclusion of dispersion, however this is likely due to numerical artifacts. Overall, we conclude that considering partial differential equations that are equivalent to compartments-in-series models would be beneficial both in computation and in theoretical analyses.

Ecosystem function in predator-prey food webs-confronting dynamic models with empirical data.

Most ecosystem functions and related services involve species interactions across trophic levels, for example, pollination and biological pest control. Despite this, our understanding of ecosystem function in multitrophic communities is poor, and research has been limited to either manipulation in small communities or statistical descriptions in larger ones. Recent advances in food web ecology may allow us to overcome the trade-off between mechanistic insight and ecological realism. Molecular tools now simplify the detection of feeding interactions, and trait-based approaches allow the application of dynamic food web models to real ecosystems. We performed the first test of an allometric food web model's ability to replicate temporally nonaggregated abundance data from the field and to provide mechanistic insight into the function of predation. We aimed to reproduce and explore the drivers of the population dynamics of the aphid herbivore Rhopalosiphum padi observed in ten Swedish barley fields. We used a dynamic food web model, taking observed interactions and abundances of predators and alternative prey as input data, allowing us to examine the role of predation in aphid population control. The inverse problem methods were used for simultaneous model fit optimization and model parameterization. The model captured >70% of the variation in aphid abundance in five of ten fields, supporting the model-embodied hypothesis that body size can be an important determinant of predation in the arthropod community. We further demonstrate how in-depth model analysis can disentangle the likely drivers of function, such as the community's abundance and trait composition. Analysing the variability in model performance revealed knowledge gaps, such as the source of episodic aphid mortality, and general method development needs that, if addressed, would further increase model success and enable stronger inference about ecosystem function. The results demonstrate that confronting dynamic food web models with abundance data from the field is a viable approach to evaluate ecological theory and to aid our understanding of function in real ecosystems. However, to realize the full potential of food web models, in ecosystem function research and beyond, trait-based parameterization must be refined and extended to include more traits than body size.

Model validation for a noninvasive arterial stenosis detection problem.

A current thrust in medical research is the development of a non-invasive method for detection, localization, and characterization of an arterial stenosis (a blockage or partial blockage in an artery). A method has been proposed to detect shear waves in the chest cavity which have been generated by disturbances in the blood flow resulting from a stenosis. In order to develop this methodology further, we use one-dimensional shear wave experimental data from novel acoustic phantoms to validate a corresponding viscoelastic mathematical model. We estimate model parameters which give a good fit (in a sense to be precisely defined) to the experimental data, and use asymptotic error theory to provide confidence intervals for parameter estimates. Finally, since a robust error model is necessary for accurate parameter estimates and confidence analysis, we include a comparison of absolute and relative models for measurement error.

Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations.

In this paper we present new results for differentiability of delay systems with respect to initial conditions and delays. After motivating our results with a wide range of delay examples arising in biology applications, we further note the need for sensitivity functions (both traditional and generalized sensitivity functions), especially in control and estimation problems. We summarize general existence and uniqueness results before turning to our main results on differentiation with respect to delays, etc. Finally we discuss use of our results in the context of estimation problems.

A comparison of computational efficiencies of stochastic algorithms in terms of two infection models.

In this paper, we investigate three particular algorithms: a stochastic simulation algorithm (SSA), and explicit and implicit tau-leaping algorithms. To compare these methods, we used them to analyze two infection models: a Vancomycin-resistant enterococcus (VRE) infection model at the population level, and a Human Immunodeficiency Virus (HIV) within host infection model. While the first has a low species count and few transitions, the second is more complex with a comparable number of species involved. The relative efficiency of each algorithm is determined based on computational time and degree of precision required. The numerical results suggest that all three algorithms have the similar computational efficiency for the simpler VRE model, and the SSA is the best choice due to its simplicity and accuracy. In addition, we have found that with the larger and more complex HIV model, implementation and modification of tau-Leaping methods are preferred.

Nonlinear stochastic Markov processes and modeling uncertainty in populations.

We consider an alternative approach to the use of nonlinear stochastic Markov processes (which have a Fokker-Planck or Forward Kolmogorov representation for density) in modeling uncertainty in populations. These alternate formulations, which involve imposing probabilistic structures on a family of deterministic dynamical systems, are shown to yield pointwise equivalent population densities. Moreover, these alternate formulations lead to fast efficient calculations in inverse problems as well as in forward simulations. Here we derive a class of stochastic formulations for which such an alternate representation is readily found.

A comparison of nonlinear filtering approaches in the context of an HIV model.

In this paper three different filtering methods, the Extended Kalman Filter (EKF), the Gauss-Hermite Filter (GHF), and the Unscented Kalman Filter (UKF), are compared for state-only and coupled state and parameter estimation when used with log state variables of a model of the immunologic response to the human immunodeficiency virus (HIV) in individuals. The filters are implemented to estimate model states as well as model parameters from simulated noisy data, and are compared in terms of estimation accuracy and computational time. Numerical experiments reveal that the GHF is the most computationally expensive algorithm, while the EKF is the least expensive one. In addition, computational experiments suggest that there is little difference in the estimation accuracy between the UKF and GHF. When measurements are taken as frequently as every week to two weeks, the EKF is the superior filter. When measurements are further apart, the UKF is the best choice in the problem under investigation.

Using mathematical modeling and control to develop structured treatment interruption strategies for HIV infection.

The goal of this article is to suggest that mathematical models describing biological processes taking place within a patient over time can be used to design adaptive treatment strategies. We demonstrate using the key example of treatment strategies for human immunodeficiency virus type-1 (HIV) infection. Although there has been considerable progress in management of HIV infection using highly active antiretroviral therapies, continuous treatment with these agents involves significant cost and burden, toxicities, development of drug resistance, and problems with adherence; these latter complications are of particular concern in substance-abusing individuals. This has inspired interest in structured or supervised treatment interruption (STI) strategies, which involve cycles of treatment withdrawal and re-initiation. We argue that the most promising STI strategies are adaptive treatment strategies. We then describe how biological mechanisms governing the interaction over time between HIV and a patient's immune system may be represented by mathematical models and how control methods applied to these models can be used to design adaptive STI strategies seeking to maintain long-term suppression of the virus. We advocate that, when such mathematical representations of processes underlying a disease or disorder are available, they can be an important tool for suggesting adaptive treatment strategies for clinical study.