A mathematical and physiological model for early distribution of radioiodide in man

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Abstract
A model is proposed for the early distribution of radioiodide in man. This model is formalized as a set of eight simultaneous differential equations, each predicting the rate of change of radioiodide in a compartment. These equations have been fitted by numerical integration on a digital computer to plasma curves from sessions with and without aspiration of gastric contents, curves of the aspirated radioiodide, and thyroidal and renal plasma clearance rates. In this model, plasma radioiodide is distributed reversibly to the erythrocytes, interstitial fluid (space E) and a “slowly diffusible space” (space C). Distribution to the thyroid and kidney is irreversible. Radioiodide distributed to the salivary glands and gastric mucosa must pass through a gastrointestinal cycle before eventual reabsorption from the intestine. Successive compartments of this cycle are the “inaccessible gastric space” (space M), free gastric juice (space S) and the intestine (space D). All of the modes of distribution mentioned are governed by rate constants except for transfer from space S to space D, which occurs as a complete transfer at a fixed interval tau. gastrointestinal iodide cycle; pooling of radioiodide in gastrointestinal tract; plasma radioiodide curve; multicompartment model; iterative solution of mathematical model Submitted on September 28, 1964