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A Mathematical Model of Tracer Distribution

Frederick Finseth, MD; Mojmir Mazur, PhD; Arthur Baue, MD; John F. Burke, MD

AMA Arch Surg. 1973;106(1):68-71.

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.

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).

Footnotes
Accepted for publication June 6, 1972.

Reprint requests to General Surgical Services, Massachusetts General Hospital, Fruit St, Boston 02114 (Dr. Finseth).

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