[Skip to Content]
Sign In
Individual Sign In
Create an Account
Institutional Sign In
OpenAthens Shibboleth
[Skip to Content Landing]
Article
January 1973

The Extracellular Fluid SystemA Mathematical Model of Tracer Distribution

Author Affiliations

St. Louis, Mo; Boston
From the General Surgical Services, Massachusetts General Hospital, Boston (Drs. Finseth and Burke); the Shriners Burns Institute, Boston (Drs. Mazur and Burke); the Jewish Hospital and the Washington University School of Medicine, St. Louis, Mo (Dr. Baue); and the Department of Surgery, Harvard Medical School, Boston (Dr. Burke).

Arch Surg. 1973;106(1):68-71. doi:10.1001/archsurg.1973.01350130070015
Abstract

This paper proposes a mathematical model for the volume of distribution and kinetics of tracer dilution in the mammalian extracellular fluid system. Analogy to certain simple mechanical and electrical physical systems suggests an exponential decay formulation for the time course of tracer distribution, y = A(1−e −Bt) + Ct. This hypothesis is supported by the successful optimal curve fitting of the model to experimental data on 35SO4 and thiocyanate distribution in the extracellular fluid. Nonlinear regression analysis is performed by computer, utilizing techniques devised for exponential functions. The parameters of the equation suggest a correspondence to and an interpretation of the descriptive physical properties of the extracellular fluid system as discerned by tracer dilution.

References
1.
Bassingthwaighte JB:  Blood flow and diffusion through mammalian organs . Science 167:1347-1353, 1970.Article
2.
Breckenridge IM, Digerness SB, Kirklin JW:  Validity of concept of increased extracellular fluid after open heart surgery . Surg Forum 20:169-171, 1969.
3.
Crystal RG, Baue AE:  Influence of hemorrhagic hypotension on measurements of the extracellular fluid volume . Surg Gynecol Obstet 129:576-582, 1969.
4.
Mathews RE, Douglas GJ:  Sulphur-35 measurements of functional and total extracellular fluid in dogs with hemorrhagic shock . Surg Forum 20:3, 1969.
5.
McNeill IF, Williams JP, Moore, FD:  The effects of hemorrhage and hormones on the partition of body water . J Surg Res 3:322-331, 1963.Article
6.
Middleton ES, Mathews R, Shires GT:  Radiosulphate as a measure of the extracellular fluid in acute hemorrhagic shock . Ann Surg 170:174-186, 1969.Article
7.
Moore FD, Dagher FJ, Boyden CM, et al:  Hemorrhage in normal man: I. Distribution and dispersal of saline infusions following acute blood loss . Ann Surg 163:485-504, 1966.Article
8.
Shires GT, Broun FT, Canizaro PC, et al:  Distributional changes in extracellular fluid during acute hemorrhagic shock . Surg Forum 11:115-117, 1960.
9.
Grodins FS:  Basic concepts in the determination of vascular volumes by indicator-dilution methods . Circ Res 10:429-471, 1962.Article
10.
Zierler KL:  Theoretical basis of indicator-dilution methods for measuring flow and volume . Circ Res 10:393-407, 1962.Article
11.
Crystal RG, Baue AE:  Kinetics of monovalent and divalent anion distribution in hemorrhagic hypotension and hypoxemia . Ann Surg 170:720-730, 1969.Article
12.
Douglas GJ, Shiscar JO, Forstner GG, et al:  Evaluation of radiosulfate as a measure of functional and total extracellular fluid . Surg Forum 20:34-36, 1969.
13.
Flexner LB, Gellhorn A, Merrell M:  Studies on rates of exchange of substances between the blood and extracellular fluid . J Biol Chem 144:35-40, 1942.
14.
Walser M, Sledin DW, Grellman A:  An evaluation of radiosulfate for the determination of the volume of extracellular fluid in man and dogs . J Clin Invest 32:299-311, 1953.Article
15.
Zierler KL:  Tracer-dilution techniques in the study of microvascular behavior . Fed Proc 24:1085-1093, 1965.
16.
Gellhorn A, Merrell M, Renkin R:  The rate of transcapillary exchange of sodium in normal and shocked dogs . Am J Physiol 142:407-427, 1944.
17.
Newton WT, Pease HD, Butcher HR:  Sodium and sulphate distributions in dogs after hemorrhagic shock . Surg Forum 20:1-2, 1969.
18.
Eder HA: Determination of thiocyanate space, in Methods in Modern Research . Visscher MB (ed.): Chicago, Year Book Medical Publisher Inc, 1951.
×