Simulation of a detoxifying organ function: Focus on hemodynamics modeling and convection‐reaction numerical simulation in microcirculatory networks

International audienceWhen modeling a detoxifying organ function, an important component is the impact of flow on the metabolism of a compound of interest carried by the blood. We here study the effects of red blood cells (such as the Fahraeus-Lindqvist effect and plasma skimming) on blood flow in typical microcirculatory components such as tubes, bifurcations and entire networks, with particular emphasis on the liver as important representative of detoxifying organs. In one of the plasma skimming models, under certain conditions, oscillations between states are found and analyzed in a methodical study to identify their causes and influencing parameters. The flow solution obtained is then used to define the velocity at which a compound would be transported. A convection-reaction equation is studied to simulate the transport of a compound in blood and its uptake by the surrounding cells. Different types of signal sharpness have to be handled depending on the application to address different temporal compound concentration profiles. To permit executing the studied models numerically stable and accurate, we here extend existing transport schemes to handle converging bifurcations, and more generally multi-furcations. We study the accuracy of different numerical schemes as well as the effect of reactions and of the network itself on the bolus shape. Even though this study is guided by applications in liver micro-architecture, the proposed methodology is general and can readily be applied to other capillary network geometries, hence to other organs or to bioengineered network designs

The Physics Hypertextbook- Parametric Equations

This page offers a clear explanation of the equations that can be used to describe the one-dimensional, constant acceleration motion of an object in terms of its three kinematic variables: velocity, displacement, and time. A set of problems accompanies the text, giving students practice in conceptual, algebraic, calculus-based, and statistical questions. This is part of an online textbook in introductory physics

The Physics Hypertextbook- Equations of Motion

This page from The Physics Hypertextbook offers a clear explanation of the equations that can be used to describe the one-dimensional, constant acceleration motion of an object in terms of its three kinematic variables: velocity, displacement, and time. A set of problems accompanies the text, giving students practice in conceptual, algebraic, calculus-based, and statistical questions. This is part of an online textbook in introductory physics

Chaos Hypertextbook

High school teacher Glenn Elert wrote the original edition of the Chaos Hypertextbook for his M.S. degree in secondary science education at Teachers College, Columbia University. After graduation, Elert put the hypertext on the Internet for the benefit of people interested in mathematics, chaos, non-linear dynamics, and fractals. While the hypertext does require some mathematical knowledge, it is geared towards a wide audience. The hypertext addresses a variety of interesting topics including one-dimensional iterated maps; fractal construction; applications and definitions of dimension; and a comparison of non-linear and linear dynamics. The site also offers information about print, software, and Internet resources as well as a fun Eye Candy section. Site visitors can also link to other hypertexts by Elert including The Physics Factbook (an encyclopedia of scientific essays written by high school students), and the Physics Hypertextbook, which is currently under construction

The Physics Hypertextbook-Graphs of Motion

This is a very well-organized tutorial on how to read, construct, and interpret three basic kinematic graphs: Position vs. Time, Velocity vs. Time, and Acceleration vs. Time. It includes animated examples, links to five worksheets, and related problems for student exploration. This item is part of an online textbook in introductory physics

The Physics Hypertextbook

This online textbook by Glenn Elert contains explanations, examples, and practice problems for many topics in introductory physics. These topics include Mechanics, Matter, Thermal Physics, Waves & Optics, Electricity & Magnetism, and Modern Physics. This textbook is a work in progress and is not yet finished

Physics Hypertextbook: Energy in Collisions

This item is a high school-level assessment to gauge understanding of using diagrams to predict outcomes in systems set to collide. It is intended for use within a unit on the conservation of linear momentum. The one-page student assessment is printable, and an answer key is included. This resource is part of a larger online textbook designed for high school physics

The Physics Hypertextbook-Acceleration

This page from The Physics Hypertextbook offers support in understanding equations related to acceleration and includes several problems for numerical practice. Scroll to the bottom for a list of links to additional engaging and innovative activities for high school students. This is part of an online textbook in introductory physics