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Full-Text Articles in Physical Sciences and Mathematics
Mathematical Modeling Of Diabetic Foot Ulcers Using Optimal Design And Mixed-Modeling Techniques, Michael Belcher
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
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 …