Abstract
Background: Body mass index (BMI) is a squared-height power function. Nevertheless, some studies show a significant exponential weight-height correlation. Objectives: To demonstrate that the weight-height relationship from 2 to 20 years of age is better expressed by an exponential function. Design: 5th, 50th and 85th percentile weight-height curves according CDC 2000 Growth Charts. A theoretical curve was created with the data on the 50th percentiles of weight and height for each age, equivalent to the 50th percentile of the weight-for-height curve. The statistical analysis was performed applying regression analysis of the curve estimation in the power and exponential models. Results: The exponential model correlation coefficient is higher than the power model. The exponential model variable (1.9 in boys, 2 in girls) was standardized to 2 to establish the body mass exponential index (BMEI): weight/exp(2*height). Weight-for-age and exponential height-for-age fiftieth percentile curves show a stable age-independent ratio near 2. These ratios are 1.5 and 2.5 for the 5th and 85th percentiles, respectively. The shape of the well-known curve BMI-for-age is due to the disparity between a exponential curve and a power curve. Conclusions: An exponential function expresses the weight-height relationship during growth better than a power function. A BMEI of 2 with limits of 1.5 and 2.5 is useful for screening nutritional status during growth, and the weight-for-height chart is an ideal substitute for the BMI-for-age chart. The BMI-for-age curve shape and the disproportional BMI in taller children are mathematical artifacts without biological meanings.
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