The aim of the present experiments is to validate, in conscious dogs, the tracer infusion methods of measuring nonsteady turnover rates. This was done in nine experiments performed in four normal dogs by infusing isotopically labeled glucose (2-3H, 6-3H, 1-14C) and monitoring the concentrations of both the labeled and unlabeled substances. The validation is based on the observation that a high exogenous infusion of glucose will suppress endogenous glucose production and become the sole source of glucose in the body. By infusing glucose at a high, time-varying rate, calculating its rate of appearance, (Ra) and comparing it to the infused rate, the method can be verified. The calculations were based on: a) a single-compartment model with a modified volume of distribution; b) a two-compartment model; and c) a generalized dispersion model. The absolute values of the areas of the deviations of the calculated from the infused curves were found to be, respectively, 9.5, 8.4, and 7.8 percent of the total area under the infused curve. It was concluded that the tracer infusion method can reliably measure Ra of glucose when it is changing rapidly, and the system is out of steady state.

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The Weber fraction is treated as part of an information theoretical view of perception. In this theory of sensory perception, subjective magnitude is related to the information transmissible from stimulus to perceiver. The derived psychophysical law can be approximated as a power or logarithmic law, depending on conditions. The mathematical expression for the Weber fraction is obtained as a derivative of the psychophysical law. One of many interesting relationships derived here is that the product of the Stevens exponent with log,o stimulus range, for many sensory modalities, is equal to the maximum information transmitted per stimulus (in bits, measured in a test of categorical judgments) multiplied by 0.6. This number is a derived constant and is not measured from the data. 1978, 1981a, 1981b, 1982, 1983, 1984). The reader who is familiar with even the first and fourth of these papers may wish to proceed immediately to the section on Derivation of the Weber Fraction from the Psychophysical Law.Since the subject does not perform flawlessly, H. is not equal to the transmitted information, Hm , but must generally be diminished by the "stimulus equivocation," H•.The equivocation may be calculated from a generalization of Equation 1, which allows for the presence of conditional probabilities. Thus we have If H; is measured in bits of information, then 2 H .. gives us a measure of the maximum number of categories that can be identified without error. This value is largely independent of the number of categories (beyond a certain minimum) into which the'stimulus continuum was divided. Henceforth, we shall refer to H; as the "information content of the stimulus." H; was found to assume a relatively constant value across a number of sensory modalities. We shall take its mean value to be about 2.5 bits of information per stimulus. The Information Content of a Steady Stimulus From an Experiment on Categorical JudgmentsIt was not many years after the appearance of the seminal papers by Shannon (1948) that information theory was applied in the analysis of experiments on perception. Gamer and Hake (1951) demonstrated how to calculate H m , the maximum information transmissible by a steady stimulus, from the stimulus-response matrix generated when a subject makes categorical judgments of a number of stimuli.From the known probabilities, pi' governing the administration of stimuli in each category, the stimulus information, H., may be calculated from the equation In this paper, we shall develop a general theory of the Weber fraction. We shall obtain a mathematical expression for ..::lei> lei> that accounts for the observed shape of the curve in Figure 1; and we shall be able to predict the parameters of the curve on theoretical grounds. As an unexpected bonus from the theory, we shall be able to derive a general mathematical relationship connecting the Stevens exponent, n, with the range of physical magnitudes, eI>, spanned by a given modality. The theoretical function for the Weber fraction that we shall obtain is derived qu...

Despite important empirical findings, current models of the oral glucose tolerance test (OGTT) do not incorporate the essential contributions of the incretin hormones, glucagon-like peptide-1 and glucose-dependent insulinotropic peptide, to glucose-stimulated insulin secretion. In order to address this deficiency, a model was, therefore, developed in which the incretins, as well as a term reflecting net hepatic glucose balance, were included. Equations modeling the changes in incretins, hepatic glucose balance, insulin and glucose were used to simulate the responses to 50 and 100 g oral glucose loads under normal conditions. The model successfully captures main trends in mean data from the literature using a simple 'lumped-parameter,' single-compartment approach in which the majority of the parameters were matched to known clinical data. The accuracy of the model and its applicability to understanding fundamental mechanisms was further assessed using a variety of glycemic and insulinemic challenges beyond those which the model was originally created to encompass, including hyper- and hypoinsulinemia, changes in insulin sensitivity, and the insulin infusion-modified intravenous glucose tolerance test.

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To understand the relationships among 1) the dose of 25-hydroxyvitamin D [25(OH)D] in vivo, 2) the activity of 1-hydroxylase in renal mitochondria, and 3) the production of 1,25-dihydroxyvitamin D [1,25(OH)2D] in vivo, we gave rats different chronic or acute doses of 25-hydroxyvitamin D3 [25(OH)D3]. We followed the metabolism of intracardially administered [25-hydroxy-26,27-methyl-3H]cholecalciferol [25(OH)[3H]D3] for 24 h before killing by measuring extracts of serum by chromatography. Specific activity of 1-hydroxylase in kidney was measured at death. In rats given 0-2,000 pmol 25(OH)D3 chronically by mouth, there was a dose-dependent decline in the percent of serum radioactivity made up of 1,25-dihydroxy-[26,27-methyl-3H]cholecalciferol [1,25(OH)2[3H]D3] as well as a decline in mitochondrial 1-hydroxylase, and these correlated significantly (r = 0.83, P less than 0.001). Serum %1,25(OH)2[3H]D3 in this experiment ranged from 0.8 to 42%. A small part of this range could be accounted for by a faster metabolic clearance rate (MCR) of 1,25(OH)2D3 from rats supplemented with 25(OH)D3 (MCR, 2.12 +/- 0.10 ml/min) compared with rats restricted in vitamin D (MCR, 0.94 +/- 0.06 ml/min, P less than 0.001). The activity of 1-hydroxylase was by far the major factor determining serum %1,25(OH)2[3H]D3. When different acute doses of 25(OH)D3 were given to rats with identical specific activities of 1-hydroxylase, the resulting 1,25(OH)2D3 concentrations in serum correlated with the 25(OH)D3 dose (r = 0.99, P less than 0.001). We conclude that the behavior of 1-hydroxylase in vivo is analogous to the classic behavior in vitro of an enzyme functioning below its Michaelis constant (Km). The amount of 1-hydroxylase present in renal mitochondria determines the fraction (not simply the quantity) of 25(OH)D metabolized to 1,25(OH)2D3 in vivo.

A general method is advanced for measuring the rate of appearance (production) of a chemical substance in an intact physiological system when this rate is changing with respect to time. The method involves infusing an isotope of this substance at such a rate that specific activity remains constant in space and in time. The means of achieving this constancy are discussed, and the mathematical basis of the method is developed for a fairly general system. An. experiment is described in some detail to show how the rate of endogenous production of glucose in a dog may be calculated when this rate is changing quite rapidly.

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