Related papers: Mathematical modeling of the vascular system
We survey systemic risks to financial markets and present a high-level description of an algorithm that measures systemic risk in terms of coupled networks.
Mathematical modeling is an important theoretical tool which provides researchers with quantification of the permeability of dialyzing systems in renal replacement therapy. In the paper we provide a short review of the most successful…
The use of nanoparticles for targeted drug delivery, especially in diseased arteries, is a novel procedure. We are incorporating nanoparticles into blood vessels using a catheter, which could potentially deliver drugs precisely to affected…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…
We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thin vascular structure (treated as a co-dimension two…
Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…
We discuss a formal system of mathematics. We use it to construct the natural numbers.
We present and critically discuss five commonly used mathematical models of the meal glucose rate of appearance in humans. Such models are key to simulation of the metabolism in healthy people, people with diabetes, and obese people, and…
Based on a simple example, it is explained how the homological analysis may be applied for modeling of the electric circuits. The homological branch, mesh and nodal analyses are presented. Geometrical interpretations are given.
The human body is a complex organism whose gross mechanical properties are enabled by an interconnected musculoskeletal network controlled by the nervous system. The nature of musculoskeletal interconnection facilitates stability, voluntary…
The aim of this chapter is to convey the importance and usefulness of mathematical modelling as a tool to achieve a deeper understanding of stem cell biology. We introduce key mathematical concepts (random walk theory, differential…
In this paper, an approach to facilitate the treatment with variabilities in system families is presented by explicitly modelling variants. The proposed method of managing variability consists of a variant part, which models variants and a…
In this paper, an approach to facilitate the treatment with variabilities in system families is presented by explicitly modelling variants. The proposed method of managing variability consists of a variant part, which models variants and a…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
Atherosclerosis is one of the principle pathologies of cardiovascular disease with blood cholesterol a significant risk factor. The World Health Organisation estimates that approximately 2.5 million deaths occur annually due to the risk…
In this work we propose a mathematical model that describes the orientation of ventricular cardiac fibers. These fibers are commonly computed as the normalized gradient of certain harmonic potentials, so our work consisted in finding the…
Stochastic fluid-fluid models (SFFMs) offer powerful modeling ability for a wide range of real-life systems of significance. The existing theoretical framework for this class of models is in terms of operator-analytic methods. For the first…
There has been a consistent growth in research involving imaging of microvasculature over the past few decades. By 2008, publications mentioning the microcirculation had grown more than 2000 per annum. Many techniques have been demonstrated…
In this paper, we are concerned with the simulation of blood flow in microvascular networks and the surrounding tissue. To reduce the computational complexity of this issue, the network structures are modeled by a one-dimensional graph,…