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2017 | Book

Hemorheology and Hemodynamics Read chapter Read first chapter

Hemomath

The Mathematics of Blood

Authors: Dr. Antonio Fasano, Adélia Sequeira

Publisher: Springer International Publishing

Book Series : MS&A

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This book illustrates applications of mathematics to various processes (physiological or artificial) involving flowing blood, including hemorheology, microcirculation, coagulation, kidney filtration and dialysis, offering a historical overview of each topic. Mathematical models are used to simulate processes normally occurring in flowing blood and to predict the effects of dysfunctions (e.g. bleeding disorders, renal failure), as well as the effects of therapies with an eye to improving treatments. Most of the models have a completely new approach that makes patient-specific simulations possible. The book is mainly intended for mathematicians interested in medical applications, but it is also useful for clinicians such as hematologists, nephrologists, cardio-surgeons, and bioengineers. Some parts require no specific knowledge of mathematics. The book is a valuable addition to mathematics, medical, biology, and bioengineering libraries.

Table of Contents

Frontmatter
Chapter 1. Hemorheology and Hemodynamics
Abstract
In this first approach to the subject we start describing a few basic facts about blood composition and about the circulatory system. Such notions will be enriched in the rest of the book, when needed. Concerning modeling, this chapter is devoted to the debatable question of the rheological properties of blood and to the various ways the circulatory system has been described in a mathematical way, both at the scale of main vessels and at the level of microcirculation. The peculiar phenomenon of vessels oscillation (vasomotion) will be considered briefly, and the literature on the mathematical modeling of diseases like atherosclerosis, affecting blood flow through arteries, will be illustrated.
Antonio Fasano, Adélia Sequeira
Chapter 2. Blood Coagulation
Abstract
This chapter is devoted to the description and modeling of the process of blood coagulation which is crucial for life and is the result of an intricate sequence of chemical reactions, involving an active role of platelets and of a surprisingly large number of blood born massive molecules performing a sequence of operations aimed at the formation of the clot and at its subsequent dissolution. Due to such a complexity there is an enormous variety of conditions leading to insufficient or excessive coagulation. We will discuss also the biological and mathematical aspects regarding these pathologies.
Antonio Fasano, Adélia Sequeira
Chapter 3. Blood Filtration in Kidneys
Abstract
Kidneys are organs performing a number of fundamental operations of great complexity which involve a delicate combination of fluid dynamics and chemistry whose aim is not only to purify blood, but also to regulate blood pressure. In this chapter we will concentrate on modeling their filtrating action, which is made possible thanks to the admirable structure of the capillaries in the filtration units (the nephrons), provided with fenestrations calibrated in such a way to allow the passage of molecules not exceeding a certain size, so to prevent proteins loss.
Antonio Fasano, Adélia Sequeira
Chapter 4. Extracorporeal Blood Ultrafiltration
Abstract
In the present chapter and in the one which follows we are going to deal with treatments performed on blood while circulated out of the patient’s body. It is obvious that such procedures invariably require sophisticated techniques, so it is not surprising that mathematics comes into play in a massive way. Having just described the physiology of kidneys it is rather natural to start with hemodialysis, i.e. blood filtration (or more precisely ultrafiltration) which saves the life of people affected by renal dysfunction. We will describe how to model the modern hemofilter, consisting of a bundle of very thin hollow fibers, and how the treatment interacts with the equilibrium of water and other substances in the patient’s organism. Such a device is certainly a prodigious and hardly improvable technological achievement, but comparing it with the natural system we realize how the latter is inimitably efficient.
Antonio Fasano, Adélia Sequeira
Chapter 5. Extracorporeal Blood Oxygenation
Abstract
Respiration is a complex vital process taking place in the lungs. Deoxygenated blood reaches the right atrium through the venae cavae (superior and inferior), is transferred to the right ventricle through the tricuspid valve, from which it is pumped to the lungs trough the two pairs of pulmonary arteries (left and right). The gas exchange between blood and air occurring in pulmonary alveoli is described in mathematical terms. Besides this aspect, in this chapter we will deal with machines helping or replacing the natural respiratory function with external blood oxygenation. These are the heart-lung machine for cardiopulmonary bypass used in particularly long and complex surgical operations, the extracorporeal membrane oxygenation (ECMO) or the alternative intravenous membrane oxygenator (IMO, or IVOX), and the newly developed machines combining an oxygenator (with the main task of removing CO 2) with a hemofilter.
Antonio Fasano, Adélia Sequeira
Chapter 6. Blood and Heat Transfer
Abstract
Circulating blood has an important role in achieving tissues thermal equilibrium. Such an action has to be taken into account when modeling treatments involving the transfer of a substantial amount of heat. Warming up or cooling down parts of the body have become important procedures in many kinds of therapies, either in a relatively mild form or by raising or lowering the temperature of targeted tissues to extreme values with the purpose of inducing massive cells destruction (ablation). Heat can be delivered in various ways (radio frequency sources, laser, focused ultrasounds), while cryoablation is performed by means of tips or balloons in which a very cold gas is circulated. In all such procedures it is very important to predict the thermal field generated in order to confine tissue damage to the targeted area. In this chapter we will examine models that have been formulated with this aim for various treatments involving heat transfer within the body. Of course we will also describe the corresponding clinical background.
Antonio Fasano, Adélia Sequeira
Chapter 7. Thermal Ablative Procedures in the Treatment of Heart Arrhythmia
Abstract
There are several pathological conditions producing alterations of the normal heart rhythm. One of the most common, affecting millions, is atrial fibrillation, due to abnormal (ectopic) electrical stimuli frequently originating in the region where pulmonary veins empty into the left atrium. When the disease is drug resistant the remedy is to perform a tissue ablation in those sites, either by delivering radiofrequency power, or by cryoablation. In this chapter we will describe the important role of mathematics in mapping the thermal field around the heat or cold sources, whose knowledge is essential to prevent serious damages to important organs. It will also be a great opportunity to illustrate the birth of electrophysiology and to summarize its fantastic development.
Antonio Fasano, Adélia Sequeira
Chapter 8. Blood and Cancer
Abstract
In this chapter we will deal with the aspects which are specific to blood cancer, avoiding to broaden our analysis to the general area of modeling tumor growth and therapy, which is huge, though it includes many subjects involving blood too (like angiogenesis and tumors perfusion, drugs delivery to tumors, etc.) which occupy a large space in the literature of mathematical modeling of tumors. Even the restricted field of modeling leukemic disorders is extremely large for the great variety of the subjects and of the approaches that have been adopted in the literature. The reader will realize the impressive complexity of the present topic already from the sketchy classification of leukemic disorders in Sect. 8.2.
Antonio Fasano, Adélia Sequeira
Backmatter
Metadata
Title
Hemomath
Authors
Dr. Antonio Fasano
Adélia Sequeira
Copyright Year
2017
Electronic ISBN
978-3-319-60513-5
Print ISBN
978-3-319-60512-8
DOI
https://doi.org/10.1007/978-3-319-60513-5

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