Tai M M
Obesity Research Center, St. Luke's-Roosevelt Hospital Center, New York, New York.
Diabetes Care. 1994 Feb;17(2):152-4. doi: 10.2337/diacare.17.2.152.
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.
建立一个用于确定各种代谢研究曲线下总面积的数学模型。
在泰氏模型中，曲线下的总面积通过将X轴（横坐标）上两个指定值之间的曲线下面积划分为小的部分（矩形和三角形）来计算，这些部分的面积可以根据各自的几何公式精确计算。这些单个面积的总和即代表曲线下的总面积。通过将该模型得到的总面积与通过图形法得到的相同面积进行比较（误差小于±0.4%）来确定模型的有效性。研究人员广泛应用的其他公式对代谢曲线下的总面积存在很大程度的低估或高估。
泰氏模型被证明能够：1）精确确定曲线下的总面积；2）计算可能与一个或两个X/Y轴相交或不相交的各种形状的面积；3）估计针对不同时间间隔（横坐标）绘制的曲线下的总面积，而其他公式只允许相同的时间间隔；4）比较不同研究产生的代谢曲线的总面积。
泰氏模型在实验条件上具有灵活性，这意味着，在葡萄糖反应曲线的情况下，可以采用不同的时间间隔采集样本，并且仍然能够精确确定曲线下的总面积。
