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Abstract
To develop a mathematical model for the determination of total areas under curves
from various metabolic studies.
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 area under the curve. Validity of the model is established by comparing total
areas obtained from this model to these same areas obtained from graphic method (less
than +/- 0.4%). Other formulas widely applied by researchers under- or overestimated
total area under a metabolic curve by a great margin.
Tai's model proves to be able to 1) determine total area under a curve with precision;
2) calculate area with varied shapes that may or may not intercept on one or both
X/Y axes; 3) estimate total area under a curve plotted against varied time intervals
(abscissas), whereas other formulas only allow the same time interval; and 4) compare
total areas of metabolic curves produced by different studies.
The Tai model allows flexibility in experimental conditions, which means, in the case
of the glucose-response curve, samples can be taken with differing time intervals
and total area under the curve can still be determined with precision.