Biological modelling and computational implementation using the finite elements method

Acosta, Juan Carlos Vanegas; Garzón‐Alvarado, Diego Alexander

doi:10.1007/s40314-013-0085-8

Cited by 6 publications

(1 citation statement)

References 15 publications

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“…PDEs are solved almost exclusively numerically [41]. The three most common approaches are the Finite Element Method (FEM), the Finite Difference Method (FDE), and the Finite Volume Method (FVM) [42][43][44][45]. These methods discretize the problem by subdividing it into smaller parts.…”

Section: Partial Differential Equationsmentioning

confidence: 99%

Model-Based Hypothesis Testing in Biomedicine : How Systems Biology Can Drive the Growth of Scientific Knowledge

Johansson¹

2017

Linköping Studies in Science and Technology. Dissertations

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The utilization of mathematical tools within biology and medicine has traditionally been less widespread compared to other hard sciences, such as physics and chemistry. However, an increased need for tools such as data processing, bioinformatics, statistics, and mathematical modeling, have emerged due to advancements during the last decades. These advancements are partly due to the development of high-throughput experimental procedures and techniques, which produce ever increasing amounts of data. For all aspects of biology and medicine, these data reveal a high level of inter-connectivity between components, which operate on many levels of control, and with multiple feedbacks both between and within each level of control. However, the availability of these large-scale data is not synonymous to a detailed mechanistic understanding of the underlying system. Rather, a mechanistic understanding is gained first when we construct a hypothesis, and test its predictions experimentally. Identifying interesting predictions that are quantitative in nature, generally requires mathematical modeling. This, in turn, requires that the studied system can be formulated into a mathematical model, such as a series of ordinary differential equations, where different hypotheses can be expressed as precise mathematical expressions that influence the output of the model.Within specific sub-domains of biology, the utilization of mathematical models have had a long tradition, such as the modeling done on electrophysiology by Hodgkin and Huxley in the 1950s. However, it is only in recent years, with the arrival of the field known as systems biology that mathematical modeling has become more commonplace. The somewhat slow adaptation of mathematical modeling in biology is partly due to historical differences in training and terminology, as well as in a lack of awareness of showcases illustrating how modeling can make a difference, or even be required, for a correct analysis of the experimental data.In this work, I provide such showcases by demonstrating the universality and applicability of mathematical modeling and hypothesis testing in three disparate biological systems. In Paper II, we demonstrate how mathematical modeling is necessary for the correct interpretation and analysis of dominant negative inhibition data in insulin signaling in primary human adipocytes. In Paper III, we use modeling to determine transport rates across the nuclear membrane in yeast cells, and we show how this technique is superior to traditional curve-fitting methods. We also demonstrate the issue of population heterogeneity and the need to account for individual differences between cells and the population at large. In Paper IV, we use mathematical modeling to reject three hypotheses concerning the phenomenon of facilitation in pyramidal nerve cells in rats and mice. We also show how one surviving hypothesis can explain all data and adequately describe independent validation data. Finally, in Paper I, we develop a method for model selection and discri...

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Section: Partial Differential Equationsmentioning

confidence: 99%