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2017 | OriginalPaper | Buchkapitel

4. Extracorporeal Blood Ultrafiltration

verfasst von : Antonio Fasano, Adélia Sequeira

Erschienen in: Hemomath

Verlag: Springer International Publishing

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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.

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Vorheriges Kapitel Blood Filtration in Kidneys

Nächstes Kapitel Extracorporeal Blood Oxygenation

The estimated number of patients whose life depends on dialysis is one million (of course in the countries where the treatment is available!). Useless to say, in old times a widespread remedy for dropsy (the old name for edema) was bloodletting.

Cellophane was invented in 1908 by the Swiss chemist Jacques Edwin Brandenberger (1872–1954). Owing to its fragility it is easily imagined how difficult was to manage that early machine.

After his death he received the title of Righteous Among the Nations.

In 1957 he implanted a machine in a dog, which worked for 90 min. In 1967 he started the Division of Artificial Organs at the University of Utah. The project for developing a new artificial heart was given to the graduate student Robert Jarvik (b.1946). In 1982 the machine perfected by Jarvik and William De Vries (called Jarvik 7) was implanted by Kolff and his team in the chest of Barney Clark, a retired dentist, who survived 112 days. The operation had an impressive resonance. We will briefly return to this subject in the next chapter.

The Romans used hot baths for extracting toxins from the body. In a sense this was a sort of dialysis performed through sweat, though with very limited effect.

Also known for his law on gas effusion.

Graham estimated that application of his discovery to blood treatment would have taken 60 years: excellent guess! Abel pumped the dog’s blood in a tube made with a membranous material. However, he observed that the blood kept clotting. Indeed it was not until the discovery of heparin (1918, see the chapter on blood coagulation) that dialysis became actually feasible. Abel and colleagues (Rowntree, Turner) used hirudin (see the chapter on blood coagulation) as anticoagulant, but their machine (which they called artificial kidney) was never used on humans.

Today a natural shunt is obtained by connecting directly an artery to a vein in the forearm by minor surgery (radio-cephalic fistula).

This principle was already used by Kolff in his early machine, to enhance the cross flow, since the cellophane membrane could bear only a very limited pressure.

The first treatment with the introduction of liquids in the abdomen was reported by Christopher Warrick in 1744. He injected a mixture of water and wine in the abdomen of a patient as a treatment of her ascites, using a leather tube [48].

The single fiber approach was used long ago in the paper [27] in a different context. We will return to it in the next chapter.

It is clearly desirable to have the largest possible exchange surface area, taking thinner and more numerous fibers. However a thinner fiber produces a larger wall shear stress, with the risk of damaging RBCs.

In the present framework these concentrations are supposed to be known. Actually, they vary in consequence of the migration of the respective substances from blood. Here we are supposing that variations can be neglected, thanks to efficient convection. There are treatments in which some concentrations in dialyzate are prescribed as functions of time. Then the procedure is called Profiled Dialysis (PD).

This result is equivalent to the so-called Starling law [44] we have used in the previous chapter, and it has been derived here from the basic principles, with no ad hoc assumption.

Hematocrit changes do occur if water extraction is fast enough (see e.g. [26]). The present assumption is acceptable in the case of frequent dialysis sessions.

We are assuming that all fibers work identically. We recall that this is not always the case. See Remark 4.2.1.

In view of the cost of albumin we can think of an alternative molecule of similar molecular weight.

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Titel: Extracorporeal Blood Ultrafiltration
verfasst von: Antonio Fasano
Adélia Sequeira
Verlag: Springer International Publishing
Buch: Hemomath
Print ISBN: 978-3-319-60512-8

Electronic ISBN: 978-3-319-60513-5

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-319-60513-5_4

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