Physical Sciences and Mathematics Commons^™

Mathematical Modeling And Analysis Of Inflammation And Tissue Repair: Lung Inflammation And Wound Healing In Corals Under Stress, Quintessa Hay

Theses and Dissertations

A variety of insults, including tissue injury and/or exposure to pathogen, elicit an immune response in many organisms. An improperly regulated immune response can result in deleterious effects to the organism. Here we present models for lung injury in young and old mice and models for wound healing in coral reefs.

It is well known that the immune response becomes less effective in older individuals. This is of particular interest in pulmonary insults such as ventilator induced lung injury (VILI) or lung infection. We extended a mathematical model for the inflammatory response to VILI and used experimental data to select …

Mathematical Modeling Of Diabetic Foot Ulcers Using Optimal Design And Mixed-Modeling Techniques, Michael Belcher

Mahurin Honors College Capstone Experience/Thesis Projects

A mathematical model for the healing response of diabetic foot ulcers was developed using averaged data (Krishna et al., 2015). The model contains four major factors in the healing of wounds using four separate differential equations with 12 parameters. The four differential equations describe the interactions between matrix metalloproteinases (MMP-1), tissue inhibitors of matrix metalloproteinases (TIMP-1), the extracellular matrix (ECM) of the skin, and the fibroblasts, which produce these proteins. Recently, our research group obtained the individual patient data that comprised the averaged data. The research group has since taken several approaches to analyze the model with the individual …

Applications Of Latin Hypercube Sampling Scheme And Partial Rank Correlation Coefficient Analysis To Mathematical Models On Wound Healing, Hannah M. Pennington

Mahurin Honors College Capstone Experience/Thesis Projects

Latin hypercube sampling and Partial Rank Correlation Coefficient procedure (LHS/PRCC) can be used in combination to perform a sensitivity analysis that assesses a model over a global parameter space. Through this analysis, the uncertainty of the parameters and therefore the variability of the model output in response to this uncertainty can be observed. Latin hypercube sampling divides the parameter space into equiprobable regions and sample without replacement, producing a global, unbiased selection of parameter values. For montonic, non-linear relationships, the correlation between the outputs and parameters can be understood by performing a Partial Rank Correlation Coefficient procedure. This sensitivity analysis …

A Simplified Model For Growth Factor Induced Healing Of Wounds, F. J. Vermolen, E. Van Baaren, J. A. Adam

Mathematics & Statistics Faculty Publications

A mathematical model is developed for the rate of healing of a circular or elliptic wound. In this paper the regeneration, decay and transport of a generic 'growth factor', which induces the healing of the wound, is taken into account. Further, an equation of motion is derived for radial healing of a circular wound. The expressions for the equation of motion and the distribution of the growth factor are related in such a way that no healing occurs if the growth factor concentration at the wound edge is below a threshold value. In this paper we investigate the influence of …

The Effect Of Surface Curvature On Wound Healing In Bone, J. A. Adam

Mathematics & Statistics Faculty Publications

The time-independent nonhomogeneous diffusion equation is solved for the equilibrium distribution of wound-induced growth factor over a hemispherical surface. The growth factor is produced at the inner edge of a circular wound and stimulates healing in regions where the concentration exceeds a certain threshold value. An implicit analytic criterion is derived for complete healing of the wound. (C) 2001 Elsevier Science Ltd. All rights reserved.

Healing Times For Circular Wounds On Plane And Spherical Bone Surfaces, J. A. Adam

Mathematics & Statistics Faculty Publications

A mathematical model is developed for the rate of healing of a circular wound in a spherical "skull". The motivation for this model is based on experimental studies of the "'critical size defect" (CSD) in animal models; this has been defined as the smallest intraosseous wound that does not heal by bone formation during the lifetime of the animal [1]. For practical purposes, this timescale can usually be taken as one year. In [2], the definition was further extended to a defect which has less than ton percent bony regeneration during the lifetime of the animal. CSDS can "heal" by …

A Simplified Model Of Wound Healing - Ii: The Critical Size Defect In Two Dimensions, J. S. Arnold, John A. Adam

Mathematics & Statistics Faculty Publications

Recently, a one-dimensional model was developed which gives a reasonable explanation for the existence of a Critical Size Defect (CSD) in certain animals [1]. In this paper, we examine the more realistic two-dimensional model of a circular wound of uniform depth to see what modifications are to be found, as compared with the one-dimensional model, in studying the CSD phenomenon. It transpires that the range of CSD sizes for a reasonable estimate of parameter values is 1 mm-1 cm. More realistic estimates await the appropriate experimental data.

A Simplified Model Of Wound Healing (With Particular Reference To The Critical Size Defect), J. A. Adam

Mathematics & Statistics Faculty Publications

This paper is an attempt to construct a simple mathematical model of wound healing/tissue regeneration which reproduces some of the known qualitative features of those phenomena. It does not address the time development of the wound in any way, but does examine conditions (e.g., wound size) under which such healing may occur. Two related one-dimensional models are examined here. The first, and simpler of the two corresponds to a "swath" of tissue (or more realistically in this case, bone) removed from an infinite plane of tissue in which only a thin band of tissue at the wound edges takes part …