title: [The theoretical analysis of Fick's equation. On the centennial of the use of Fick's principle in physiology].
abstract: In the first section Adolf Fick's outstanding scientific performances are pointed out in their historical sequence, particularly the derivation of the laws of diffusion (1855) and the basic equation for determining the heart-minute-volume (Fm) by O2-absorption per time (V02) and arteriovenous O2-difference (AVD), known as Fick's Principle. The latter was derived theoretically in 1870 by Fick, but it found it practical employment by other investigators, in dog not before 1886 and in man not earlier than 1930. In the following two sections the universality of Fick's Principle is shown by explaining its internal relation 1. to Fick's first law of diffusion and 2. to the general law of solution. This is done by mathematical transformation of the relations (formulas)of the physical resp. the physiological standards (parameters). By analyzing the diffusion of a substance into a streaming fluid according to the first diffusion law, perfectly isomorphic equations to Fick's Principle (No. 7 and No. 9) are obtained by what Fick's formula as a determinant of the heart-minute-volume is just proved to be derivable from Fick's first diffusion law. Furthermore by transforming the trivial formula for the determination of substance concentration in a fluid provement is given, that Fick's Principle may be considered a variant of the solution theory. By this the internal relation of the so-called dilution respectively indicating methods depending on the Stewart-Hamilton-Principle to the original Fick's Principle is made visible. In the last section an attempt is made to produce a relation to 1. the so-called physical methods determining the minute volume which primarily are known as a measurement for stroke volume and frequency, and, besides that, 2. to Vierordt's equation, by which the heart-minute-volume is determinable from circulating blood volume and circulation time. This trial is made by equating the value of the minute volume given by Fick's Principle (VO2/AVD) with the product from stroke volume and beating frequency, and on the other hand by equating it with the quotient from circulating blood volume Qc and complete circulation time Tc (Qc/Tc). Finally, physiological arguments are derived from these relations, allowing an evaluation of the relative proportions in circulation adaption during muscular work of the magnitudes of changes in stroke volume, beating frequencies, or the O2-pulse.
mesh_terms: D001692:Biological Transport; D002302:Cardiac Output / Q000379:methods*; D005858:Germany; D049672:History, 19th Century; D006801:Humans; D008433:Mathematics; D010101:Oxygen Consumption; D010827:Physiology / Q000266:history
vernacular_title: Die theoretische Analyse der Fickschen Gleichung Zur Jahrhundertfeier der Anwendung des Fickschen Prinzips in der Physiologie