Numerical Modeling of COVID-19 Neurological Effects: ODE/PDE Analysis in R

The book focuses on modeling the dynamics of blood flow along the brain capillaries and tissue using ordinary and partial differential equations (ODE/PDEs). It presents a basic one-PDE model for O2 concentration in the brain capillary blood, a two-PDE model for O2 concentration in the brain capillary blood and brain tissue, and an extended three-PDE model to include the brain functional neuron cell density. The computer-based implementation of the example models is presented in R, a quality, open-source scientific computing system. The PDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The routines are available for download, allowing the example models to be executed without prior knowledge of numerical methods and computer coding.

\n Format: Hardback
\n Length: 188 pages
\n Publication date: 27 December 2021
\n Publisher: Taylor & Francis Ltd
\n

Covid-19 primarily affects the respiratory system, leading to impaired oxygenation of blood. This oxygen-deficient blood circulates throughout the body, with a particular focus on its passage to the brain. In this book, the study revolves around the dynamics of blood flow within the brain capillaries and surrounding tissue, which are modeled using systems of ordinary and partial differential equations (ODE/PDEs).

The ODE/PDE methodology is introduced through a series of examples. These examples encompass:

1. A basic one-PDE model for oxygen concentration in brain capillary blood.
2. A two-PDE model that accounts for oxygen concentration in brain capillary blood and brain tissue, considering the transport of oxygen across the blood-brain barrier (BBB).
3. An extension of the two-PDE model to incorporate the brain functional neuron cell density.

Reduced neuron cell density in both time and space within the brain, resulting from lowered oxygen concentration (hypoxia), can lead to cognitive impairment.

To facilitate the computer-based implementation of these example models, routines coded in the R programming language are presented. R is a widely accessible and reputable open-source scientific computing system available on the Internet. Formal mathematics is kept to a minimum, with a focus on providing detailed examples that can be executed on modest computers. The PDE analysis is based on the method of lines (MOL), a well-established general algorithm for PDEs, implemented with finite differences.

These routines are made readily available through a download link, allowing users to execute the example models without prior knowledge of numerical methods and computer coding. Once the routines are understood, they can be applied to variations and extensions of the blood/brain hypoxia models, such as modifying the ODE/PDE parameters or altering the form of the model equations.

By employing the ODE/PDE methodology and the provided example models, researchers, analysts, and practitioners can gain insights into the complex dynamics of blood flow. This knowledge can contribute to developing effective treatments and interventions for conditions related to brain hypoxia, such as Covid-19 and other respiratory diseases.

\n Weight: 436g\n
Dimension: 160 x 240 x 19 (mm)\n
ISBN-13: 9781032152110\n \n