# A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves

@article{Tai1994AMM, title={A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves}, author={M. M. Tai}, journal={Diabetes Care}, year={1994}, volume={17}, pages={152 - 154} }

OBJECTIVE To develop a mathematical model for the determination of total areas under curves from various metabolic studies. RESEARCH DESIGN AND METHODS In Tai's Model, the total area under a curve is computed by dividing the area under the curve between two designated values on the X-axis (abscissas) into small segments (rectangles and triangles) whose areas can be accurately calculated from their respective geometrical formulas. The total sum of these individual areas thus represents the total… Expand

#### 376 Citations

Determination of the Area Under a Curve

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What is exaggerately called "Tai's mathematical model" is nothing but a simple geometrical formula, well known for many years as the trapezoidal rule. Expand

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The T variate function cannot only be used to approximate the total area under the curve (AUC) but also to describe these curves functionally with estimates of their characteristic parameters and to separate their secretion and clearance phases. Expand

Comparability of indices for insulin resistance and insulin secretion determined during oral glucose tolerance tests

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The indices of Cederholm and Wibell and of Stumvoll et al. were found to be appropriate as diagnostic indicators of the pathogenesis of diabetic glucose tolerance and were more closely related to the glucose tolerance state than the other indices. Expand

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The proposed model showed great suitability, with inferences on the behavior of glucose levels in response to treatments and supplying a richer description than just the area under the curve, and acarbose significantly attenuates glycaemia after ingestion of starch. Expand

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Diastolic function and insulin resistance in essential hypertension.

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A delayed insulin pattern was associated with higher postprandial glucose levels and individuals with delayed and exaggerated insulin secretion may have a higher risk for glucose intolerance. Expand

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The data show that prehypertension is associated with IR, and it seems that the preHypertension group cannot handle oral glucose challenge as well as the normotension, probably a consequence of IR in prehyertension. Expand

Tai's Formula Is the Trapezoidal Rule

- Medicine
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The author says that the sample simplified formula in the 1991 paper is only appropriate for equal time intervals, and makes an error in assuming that readers would be able to modify it for different time intervals. Expand

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