# [abstract] MATHEMATICAL DESCRIPTION ON THE RELATIONSHIP BETWEEN TWO DIFFERENT FUNCTIONS DERIVED FROM DIFFUSION-BASED DECOMPRESSION THEORY.

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 Title: [abstract] MATHEMATICAL DESCRIPTION ON THE RELATIONSHIP BETWEEN TWO DIFFERENT FUNCTIONS DERIVED FROM DIFFUSION-BASED DECOMPRESSION THEORY. Author: Ashida, H; Ikeda, T; Tikuisis, P; Nishi, RY Abstract: BACKGROUND: Hempleman's diffusion-based decompression theory yields two different functions; one is expressed by a root function (root model) and the other by a series function (series model). Although both models coincide very well within an elapsed time of 100 minutes, no clear mathematical explanations have been published which describe the relationship between the two models. ASSUMPTIONS: When C(x,t) denotes the concentration of inert gas in tissue at the time t and distance x from the interface, the amount of inert gas transferred into the tissue is obtained by integrating C(x.t) by x. The root model is derived by assuming that the tissue has infinite thickness and gas moves from the blood with a boundary condition C(x,0)=C(,t)=0 when x greater than 0, and C(0,t) (C is constant). The series model is obtained by assuming that the tissue of the finite thickness 2b is bounded on its both sides by a permeable wall which separates the blood from the tissue. The boundary condition is set as C(x,t)=C when x=0 or x=2b, C(x,0)=0 when 0 less than x less than 2b. RESULTS and CONCLUSION: With these assumptions, the amount of gas transferred in the root model becomes infinite at saturation since the thickness is infinite, and that in the series model reaches a fixed value in equilibrium with C. When t is sufficiently short, however, the mass of gas moved beyond the thickness b in the root model becomes negligible. Thus, meaningful gas movement of the root model occurs within the confined space of thickness b as in the series model. In other words, gas in the root model accumulates similarly in the series model over short times. This is the mathematical description of the gas movement in the root model which is almost identical to that in the series model when t is limited. Description: Undersea and Hyperbaric Medical Society, Inc. (http://www.uhms.org ) URI: http://archive.rubicon-foundation.org/953 Date: 2001

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• UHMS Meeting Abstracts
This is a collection of the published abstracts from the Undersea and Hyperbaric Medical Society (UHMS) annual meetings.