Body Mass Exponential Index: An Age-Independent Anthropometric Nutritional Assessment

DOI: 10.4236/oalib.1101943   PDF   HTML   XML   1,421 Downloads   1,949 Views   Citations


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.

Share and Cite:

Cidrás, M. (2015) Body Mass Exponential Index: An Age-Independent Anthropometric Nutritional Assessment. Open Access Library Journal, 2, 1-8. doi: 10.4236/oalib.1101943.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Keys, A., Fidanza, F., Karvonen, M.J., Kimura, N. and Taylor, H.L. (1972) Indices of Relative Weight and Obesity. Journal of Chronic Diseases, 25, 329-343.
[2] Must, A., Dallal, G.E. and Dietz, W.H. (1991) Reference Data for Obesity: 85th and 95th Percentiles of Body Mass Index (wt/ht2) and Triceps Skinfold Thickness. The American Journal of Clinical Nutrition, 53, 839-846.
[3] Klein, J.D., Sesselberg, T.S., Johnson, M.S., et al. (2010) Adoption of Body Mass Index Guidelines for Screening and Counseling in Pediatric Practice. Pediatrics, 125, 265-272.
[4] Centers for Disease Control and Prevention (2014) Overweight and Obesity.
[5] World Health Organization (2014) Obesity and Overweight. Fact Sheet No. 311.
[6] James, W.P.T. and Lobstein, T. (2009) BMI Screening and Surveillance: An International Perspective. Pediatrics, 124, S42-S49.
[7] Flegal, K.M., Kit, B.K., Orpana, H. and Graubard, B.I. (2013) Association of All-Cause Mortality with Overweight and Obesity Using Standard Body Mass Index Categories: A Systematic Review and Meta-Analysis. JAMA, 309, 71-82.
[8] Ogden, C.L., Carroll, M.D., Kit, B.K. and Flegal, K.M. (2014) Prevalence of Childhood and Adult Obesity in the United States, 2011-2012. JAMA, 311, 806-814.
[9] Quetelet, L. (1832) Recherches sur le poids de l’homme aux different ages. Nouv Mem l’Academie R Des Sci B-Lett Bruxelles, t. VII.
[10] Quetelet, L. (1994) A Treatise on Man and the Development of His Faculties. Obesity Research, 2, 72-85.
[11] Burton, R.F. (2013) Adolphe Quetelet and the BMI: Fact, Fiction, and Childhood Growth. Obesity, 21, 6.
[12] Hammer, L.D., Kraemer, H.C., Wilson, D.M., Ritter, P.L. and Dornbusch, S.M. (1991) Standardized Percentile Curves of Body-Mass Index for Children and Adolescents. American Journal of Diseases of Children, 145, 259-263.
[13] WHO (2000) Obesity: Preventing and Managing the Global Epidemic. Report of a WHO Consultation, World Health Organization Technical Report, Series 894, I-XII, 1-253.
[14] Ogden, C.L., Kuczmarski, R.J., Flegal, K.M., Mei, Z., Guo, S., Wei, R., Grummer-Strawn, L.M., Curtin, L.R., Roche, A.F. and Johnson, C.L. (2002) Centers for Disease Control and Prevention 2000 Growth Charts for the United States: Improvements to the 1977 National Center for Health Statistics Version. Pediatrics, 109, 45-60.
[15] Cole, T.J., Flegal, K.M., Nicholls, D. and Jackson, A.A. (2007) Body Mass Index Cut Offs to Define Thinness in Children and Adolescents: International Survey. BMJ, 335, 194.
[16] De Onis, M., Onyango, A.W., Borghi, E., Siyam, A., Nishida, C. and Siekmann, J. (2007) Development of a WHO Growth Reference for School-Aged Children and Adolescents. Bulletin of the World Health Organization, 85, 660-667.
[17] Leung, S.S., Lau, J.T., Tse, L.Y. and Oppenheimer, S.J. (1996) Weight-for-Age and Weight-for-Height References for Hong Kong Children from Birth to 18 Years. Journal of Paediatrics and Child Health, 32, 103-109.
[18] Kragelund, C. and Omland, T. (2005) A Farewell to Body-Mass Index? The Lancet, 366, 1589-1591.
[19] Plachta-Danielzik, S., Bosy-Westphal, A., Kehden, B., et al. (2013) Adiposity Rebound Is Misclassified by BMI Rebound. European Journal of Clinical Nutrition, 67, 984-989.
[20] Franklin, M.F. (1999) Comparison of Weight and Height Relations in Boys from 4 Countries. American Journal of Clinical Nutrition, 70, 157S-162S.
[21] Garn, S.M., Leonard, W.R. and Hawthorne, V.M. (1986) Three Limitations of the Body Mass Index. American Journal of Clinical Nutrition, 44, 996-997.
[22] Krebs, N.F., Himes, J.H., Jacobson, D., Nicklas, T.A., Guilday, P. and Styne, D. (2007) Assessment of Child and Adolescent Overweight and Obesity. Pediatrics, 120, S193-S228.
[23] Bellizzi, M.C. and Dietz, W.H. (1999) Workshop on Childhood Obesity: Summary of the Discussion. American Journal of Clinical Nutrition, 70, 173S-175S.
[24] Burton, R.F. (2007) Why Is the Body Mass Index Calculated as Mass/Height2, Not as Mass/Height3? Annals of Human Biology, 34, 656-663.
[25] Benn, R.T. (1971) Some Mathematical Properties of Weight-for-Height Indices Used as Measures of Adiposity. Journal of Epidemiology & Community Health, 25, 42-50.
[26] Chinn, S., Rona, R.J., Gulliford, M.C. and Hammond, J. (1992) Weight-for-Height in Children Aged 4-12 Years. A New Index Compared to the Normalized Body Mass Index. European Journal of Clinical Nutrition, 46, 489-500.
[27] Gayon, J. (2000) History of the Concept of Allometry. American Zoologist, 40, 748-758.[0748:HOTCOA]2.0.CO;2
[28] Huxley, J. and Teissier, G. (1936) Terminology of Relative Growth. Nature, 137, 780-781.
[29] Pasternack, B.S. and Gianutsos, R.R. (1969) Application of the Exponential and Power Functions to the Study of Allometric Growth, with Particular Reference to Doryline Ants. The American Naturalist, 103, 225-234.
[30] Henneberg, M., Hugg, J. and Townsend, E.J. (1989) Body Weight/Height Relationship: Exponential Solution. American Journal of Human Biology, 1, 483-491.
[31] Sargent, D.W. (1961) An Evaluation of Basal Metabolic Data for Children and Youth in the United States. US Department of Agriculture, Home Economics Research Report No 14.
[32] Sargent, D.W. (1963) Weight-Height Relationship of Young Men and Women. American Journal of Clinical Nutrition, 13, 318-325.
[33] Newens, E.M. and Goldstein, H. (1972) Height, Weight, and the Assessment of Obesity in Children. British Journal of Preventive & Social Medicine, 26, 33-39.
[34] Rolland-Cachera, M.F., Deheeger, M., Bellisle, F., Sempé, M., Guilloud-Bataille, M. and Patois, E. (1984) Adiposity Rebound in Children: A Simple Indicator for Predicting Obesity. American Journal of Clinical Nutrition, 39, 129-135.
[35] Billewicz, W.Z., Kemsley, W.F. and Thomson, A.M. (1962) Indices of Adiposity. British Journal of Preventive & Social Medicine, 16, 183-188.
[36] Fung, K.P., Lee, J., Lau, S.P., Chow, O.K., Wong, T.W. and Davis, D.P. (1990) Properties and Clinical Implications of Body Mass Indices. Archives of Disease in Childhood, 65, 516-519.
[37] Flegal, K.M., Wei, R. and Ogden, C. (2002) Weight-for-Stature Compared with Body Mass Index-for-Age Growth Charts for the United States from the Centers for Disease Control and Prevention. American Journal of Clinical Nutrition, 75, 761-766.
[38] Perrin, E.M., Flower, K.B. and Ammerman, A.S. (2004) Body Mass Index Charts: Useful Yet Underused. The Journal of Pediatrics, 144, 455-460.
[39] Davy-Jow, S.L., Lees, D.M.B. and Russell, S. (2013) Virtual Forensic Anthropology: Novel Applications of Anthropometry and Technology in a Child Death Case. Forensic Science International, 224, e7-e10.
[40] Hamill, P.V., Drizd, T.A., Johnson, C.L., Reed, R.B. and Roche, A.F. (1977) NCHS Growth Curves for Children Birth-18 Years: United States. Vital and Health Statistics, 11, 1-74.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.