Mathematical biosciences
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Mathematical biosciences · Dec 2014
Oxygen transport in a cross section of the rat inner medulla: impact of heterogeneous distribution of nephrons and vessels.
We have developed a highly detailed mathematical model of oxygen transport in a cross section of the upper inner medulla of the rat kidney. The model is used to study the impact of the structured organization of nephrons and vessels revealed in anatomic studies, in which descending vasa recta are found to lie distant from clusters of collecting ducts. Specifically, we formulated a two-dimensional oxygen transport model, in which the positions and physical dimensions of renal tubules and vessels are based on an image obtained by immunochemical techniques (T. ⋯ The model represents oxygen diffusion through interstitium and other renal structures, oxygen consumption by the Na(+)/K(+)-ATPase activities of the collecting ducts, and basal metabolic consumption. Model simulations yield marked variations in interstitial PO2, which can be attributed, in large part, to the heterogeneities in the position and physical dimensions of the collecting ducts. Further, results of a sensitivity study suggest that medullary oxygenation is highly sensitive to medullary blood flow, and that, at high active consumption rates, localized patches of tissue may be vulnerable to hypoxic injury.
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Mathematical biosciences · Jun 2014
On heart rate variability and autonomic activity in homeostasis and in systemic inflammation.
Analysis of heart rate variability (HRV) is a promising diagnostic technique due to the noninvasive nature of the measurements involved and established correlations with disease severity, particularly in inflammation-linked disorders. However, the complexities underlying the interpretation of HRV complicate understanding the mechanisms that cause variability. Despite this, such interpretations are often found in literature. ⋯ In total, our work illustrates how conventional assumptions about the relationships between autonomic activity and frequency-domain HRV metrics break down, even in a simple model. This underscores the need for further experimental work towards unraveling the underlying mechanisms of autonomic dysfunction and HRV changes in systemic inflammation. Understanding the extent of information encoded in HRV signals is critical in appropriately analyzing prior and future studies.
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Mathematical biosciences · Feb 2014
Estimation of kinetic parameters in an S-system equation model for a metabolic reaction system using the Newton-Raphson method.
Metabolic reaction systems can be modeled easily in terms of S-system type equations if their metabolic maps are available. This study therefore proposes a method for estimating parameters in decoupled S-system equations on the basis of the Newton-Raphson method and elucidates the performance of this estimation method. ⋯ The method is also applied to time course data with noise and found to estimate parameters efficiently. Results indicate that the present method has the potential to be extended to a method for estimating parameters in large-scale metabolic reaction systems.
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Mathematical biosciences · Jun 2011
Comparative StudyThe role of optimal control in assessing the most cost-effective implementation of a vaccination programme: HPV as a case study.
Vaccination against the human papillomavirus (HPV) is a recent development in the UK. This paper uses an optimal control model to explore how best to target vaccination. ⋯ Extending the model to include male vaccination, we find that including males in a vaccination strategy is cost-effective. We compare the optimal control solution to that from a constant control model and show that the optimal control model is more efficient at forcing the system to a disease-controlled steady state.
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Mathematical biosciences · Sep 2010
An exact solution for the modified nonlinear Schrödinger's equation for Davydov solitons in alpha-helix proteins.
The solitons in alpha-helix proteins that are governed by the nonlinear Schrödinger's equation is investigated in presence of perturbation terms in this paper. The integration of this perturbed nonlinear Schrödinger's equation is carried out. The solitary wave ansatz is used to carry out the integration and the parameter domain is identified.