# 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

#### Figures, Tables, and Topics from this paper

Determination of the Area Under a Curve
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
Modeling Metabolic Curves
• Medicine
• Diabetes Care
• 1994
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
• Medicine
• Clinical chemistry and laboratory medicine
• 2006
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
Using Glucose Tolerance Tests to Model Insulin Secretion and Clearance
The purpose of the studies described in this paper is to develop theoretically and to validate experimentally mathematical compartment models which can be used to predict plasma insulin levels inExpand
A non-linear mixed-effects model to describe the effect of acarbose intake on postprandial glycaemia in a single rat
• Medicine
• 2017
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
Comparison of various simple insulin sensitivity and beta-cell function indices in lean hyperandrogenemic and normoandrogenemic young hirsute women.
• Medicine
• Fertility and sterility
• 2003
Lean hyperandrogenemic hirsute women have insulin resistance and increased beta-cell function and the HOMA-IR may be a proposed global test for insulin resistance. Expand
Diastolic function and insulin resistance in essential hypertension.
• Medicine
• International journal of cardiology
• 1998
It is found that E/A ratio is negatively correlated to insulin concentrations at 120 min and to AUC-I in hyperinsulinemic subgroup of subjects (fasting insulin> 10). Expand
Effect of Different Insulin Response Patterns During Oral Glucose Tolerance Test on Glycemia in Individuals with Normal Glucose Tolerance.
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
Prehypertension is associated with insulin resistance.
• Medicine
• QJM : monthly journal of the Association of Physicians
• 2009
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
• Diabetes Care
• 1994
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

#### References

SHOWING 1-8 OF 8 REFERENCES
How Important is Prediction of Glycemic Responses?
It has been assumed that the glycemic response to a food is related linearly to the amount of carbohydrate ingested, but Gannon et al. conclude that the net glucose response area to the oral glucose dose is best described by a secondor third-order polynomial. Expand
The glycemic index: methodology and clinical implications.
• Medicine
• The American journal of clinical nutrition
• 1991
In long-term trials, low-GI diets result in modest improvements in overall blood glucose control in patients with insulin-dependent and non-insulin-dependent diabetes and the ability of low- GI diets to reduce insulin secretion and lower blood lipid concentrations in patientswith hypertriglyceridemia is of greater therapeutic importance. Expand
ORAL SODIUM TOLBUTAMIDE AND GLUCOSE TOLERANCE TESTS.
• Medicine
• Archives of internal medicine
• 1965
This oral test, in which 2.0 gm of sodium tolbutamide are administered orally in rapidly dissolving tablets along with sodium bicarbonate, gave results comparable to the intravenous test with a lag of about ten minutes. Expand
Meal size and frequency: effect on the thermic effect of food.
• Biology, Medicine
• The American journal of clinical nutrition
• 1991
It is concluded that the temporal pattern in which a mixed caloric load is eaten affects the thermogenic response and may be an important determinant of energy balance after a meal. Expand
Effect of exercise on thermic effect of food (TEF) in lean (L) and obese (O) women (Abstract)
• Int J Obesity 1L461A,
• 1987
Alder I: A New Look at Geometry
• 1966
Pi-Sunyer EX Meal size and frequency: effect on the thermic effect of food Alder I: A New Look at Geometry
• Am] Clin Nutr
• 1966