Muscular dystrophy describes generalized progressive muscular weakness due to the wasting of muscle fibers. The progression of the disease is affected by known immunological and mechanical factors, and possibly other unknown mechanisms. This article introduces a new mathematical model, the FRiND model, to further elucidate these known immunological actions. We will perform stability and sensitivity analyses on this model. The models time course results will be verified by biological studies in the literature. This model could be the foundation for further understanding of immunological muscle repair.
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http://dx.doi.org/10.1007/s11538-019-00635-8 | DOI Listing |
Bull Math Biol
October 2019
University of Texas, San Antonio, San Antonio, TX, 78249, USA.
Muscular dystrophy describes generalized progressive muscular weakness due to the wasting of muscle fibers. The progression of the disease is affected by known immunological and mechanical factors, and possibly other unknown mechanisms. This article introduces a new mathematical model, the FRiND model, to further elucidate these known immunological actions.
View Article and Find Full Text PDFGround Water
May 2018
Department of Geology and Geological Engineering, Université Laval, 2325 Rue de l'Université, Ville de Québec, QC, G1V 0A6, Canada.
The delineation of wellhead protection areas (WHPAs) under uncertainty is still a challenge for heterogeneous porous media. For granular media, one option is to combine particle tracking (PT) with the Monte Carlo approach (PT-MC) to account for geologic uncertainties. Fractured porous media, however, require certain restrictive assumptions under this approach.
View Article and Find Full Text PDFJ Contam Hydrol
December 2016
Institute for Modelling Hydraulic and Environmental Systems (LS(3))/SimTech, Pfaffenwaldring 5a, D-70569 Stuttgart, University of Stuttgart, Germany. Electronic address:
This study addresses the delineation of areas that contribute baseflow to a stream reach, also known as stream capture zones. Such areas can be delineated using standard well capture zone delineation methods, with three important differences: (1) natural gradients are smaller compared to those produced by supply wells and are therefore subject to greater numerical errors, (2) stream discharge varies seasonally, and (3) stream discharge varies spatially. This study focuses on model-related uncertainties due to model characteristics, discretization schemes, delineation methods, and particle tracking algorithms.
View Article and Find Full Text PDFJ Contam Hydrol
May 2013
Department of Earth and Environmental Sciences - University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
Uncertainty is a pervasive but often poorly understood factor in the delineation of wellhead protection areas (WHPAs), which can discourage water managers and practitioners from relying on model results. To make uncertainty more understandable and thereby remove a barrier to the acceptance of models in the WHPA context, we present a simple approach for dealing with uncertainty. The approach considers two spatial scales for representing uncertainty: local and global.
View Article and Find Full Text PDFJ Contam Hydrol
January 2013
University of Waterloo, Department of Earth and Environmental Sciences, Waterloo, Ontario, Canada.
In contaminant travel from ground surface to groundwater receptors, the time taken in travelling through the unsaturated zone is known as the unsaturated zone time lag. Depending on the situation, this time lag may or may not be significant within the context of the overall problem. A method is presented for assessing the importance of the unsaturated zone in the travel time from source to receptor in terms of estimates of both the absolute and the relative advective times.
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