Análisis dimensional de variables antropométricas y bioquímicas para diagnosticar el síndrome metabólico

  • Jesús Velásquez Universidad Simón Bolívar
  • Héctor Herrera Universidad Simón Bolívar
  • Lorena Encalada Universidad de Cuenca
  • Sara Wong Universidad de Cuenca
  • Erika Severeyn Universidad Simón Bolívar



Metabolic syndrome (MS) is a lifestyle-related condition, and it is linked to the development of diabetes and cardiovascular disease. There are numerous diagnostic criteria of MS; the most used is the diagnostic criterion according to NCEP-ATPIII. Although studies using body mass index and abdominal circumference have been performed to establish a cutoff point for the diagnosis of MS, there is no general index that establishes a cut-off point for this pathology diagnosis. The objective of this study is to propose a dimensionless index that can discriminate subjects with MS using biochemical variables (HDL, triglycerides) and anthropometric variables (weight, height, waist circumference). Three dimensionless indexes were designed and evaluated from the data obtained from the integration of three databases (n=829 subjects). By means of a simple correspondence analysis of the variables and a dimensional analysis based on the π Vaschy-Buckingham theorem, three dimensionless indexes were constructed: π1, π2 and π3. Performance was assessed using Receiver Operating Characteristic (ROC) curves. The index π1, constructed with the variables: Abdominal circumference, triglycerides, weight and height; was the one that obtained a better performance as classifier of MS, presenting an area under the ROC curve of 0.86, a sensitivity and specificity greater than 0.7 and an optimum detection point for the diagnosis of MS of π1<104.87. The π1 dimensionless index designed in this study is a simple method, which requires fewer variables than the NCEP-ATPIII criterion, to diagnose MS.

Keywords: Dimensional analysis, simple correspondence analysis, theorem π of Vaschy-Buckingham, metabolic syndrome, medical database, ROC curves.




El síndrome metabólico (SM) es una condición relacionada con el estilo de vida, y está vinculado al desarrollo de la diabetes y de enfermedades cardiovasculares. Existen numerosos criterios de diagnósticos del SM, el más usado es el criterio de diagnóstico según el NCEP-ATPIII. Aunque se han realizado estudios que usan el índice de masa corporal y la circunferencia abdominal para establecer un punto de corte para el diagnóstico del SM, no existe un índice general que establezca un punto de corte para esta patología. El objetivo de este estudio es proponer un índice adimensional que pueda discriminar sujetos con SM utilizando variables bioquímicas (HDL, triglicéridos) y antropométricas (peso, altura, circunferencia abdominal). Se diseñaron y evaluaron tres índices adimensionales a partir de los datos obtenidos de la integración de tres bases de datos (n=829 sujetos). Mediante un análisis de correspondencia simple de las variables y un análisis dimensional basado en el teorema π de Vaschy-Buckingham se construyeron tres índices adimensionales: π1, π2 y π3. El desempeño fue evaluado usando curvas Receiver Operating Characteristic (ROC). El índice π1 construido con las variables: circunferencia abdominal, triglicéridos, peso y altura; fue el que obtuvo un mejor desempeño como clasificador del SM, presentando un área bajo la curva ROC de 0.86, una sensibilidad y especificidad mayor de 0.7 y un punto de detección óptimo para el diagnóstico de SM de π1<104.87. El índice adimensional π1 diseñado en este estudio es un método simple, que requiere de menos variables que el criterio de la NCEP-ATPIII, para diagnosticar el SM.

Palabras clave: Análisis dimensional, análisis de correspondencias simples, teorema π de Vaschy-Buckingham, síndrome metabólico, bases de datos médicas, curvas ROC.


La descarga de datos todavía no está disponible.


Beltrán-Sánchez, H., Harhay, M. O., Harhay, M. M., & McElligott, S. (2013). Prevalence and trends of metabolic syndrome in the adult U.S. population, 1999-2010. Journal of the American College of Cardiology, (62), 697-703.

Bertrand, J. (1878). Sur l'homogénéité dans les formules de physique. Comptes Rendus, (15), 916-920.

Craig, C., Marshall, A., Sjöström, M., Bauman, A., Booth, M., Ainsworth, B., Pratt, M., Ekelund, U., Yngve, A., Sallis, J., & Oja, P. (2003). International physical activity questionnaire: 12-country reliability and validity. Medicine and Science in Sports and Exercise, 35(8), 1381-95.

Gozashti, M., Najmeasadat, F., Mohadeseh, S., & Najafipour, H. (2014). Determination of most suitable cut off point of waist circumference for diagnosis of metabolic syndrome in Kerman. Diabetes & Metabolic Syndrome: Clinical Research & Reviews, (8), 8-12.

Grundy, S. M., Cleeman, J. I., Daniels, S. R., Donato, K. A., Eckel, R. H., Franklin, B. A., Gordon, D. J., Krauss, R. M., Savage, P. J., Smith, S. C., Spertus, J. A., & Costa, F. (2005). Diagnosis and management of the metabolic syndrome: an American Heart Association/National Heart, Lung, and Blood Institute scientific statement. Circulation, 112(17), 2735–2752.

Günther, B., & León, B. (1966). An invariant and dimensionless number, which characterizes respiratory, haematic, circulatory and metabolic functions in mammals. Archives Biologica Medicina Experimental, (3), 1-6.

Herrera, H., Rebato, E., Arechabaleta, G., Lagrange, H., Salces, I., & Susanne, C. (2003). Body Mass Index and Energy Intake in Venezuelan University Students. Nutrition Research, 23(3), 389-390.

Lebert, A., & Piron, M. (2000). Statistique exploratoire multidimensionnelle (3rd ed.), pp. 344-346, Paris, France : Dunod Editions.

Motamed, N., Miresmail, S. J. H., Rabiee, B., Keyvani, H., Farahani, B., Maadi, M., & Zamani, F. (2016). Optimal cutoff points for HOMA-IR and QUICKI in the diagnosis of metabolic syndrome and non-alcoholic fatty liver disease: A population based study. Journal of Diabetes and its Complications, 30(2), 269-274.

National Cholesterol Education Program (NCEP) Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults (Adult Treatment Panel III). (2002). Third Report of the National Cholesterol Education Program Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults final report. Circulation, 106(25), 3143-421.

Parra, F., Andrade, D., Cruz, J., Solano-Quinde, L., Palacio-Baus, K., Encalada, L., & Wong, S. (2015). Plataforma basada en ecgML para el estudio de las complicaciones cardiovasculares en el adulto mayor con síndrome metabólico. Maskana, 6(Supl.), 157-164.

Prasad, D. S., Kabir, Z., Dash, A. K., & Das, B. C. (2012). Prevalence and risk factors for metabolic syndrome in Asian Indians: A community study from urban Eastern India. Journal Cardiovascular Disease Research, (3), 204-211.
Rayleigh, L. (1915). The principles of similitude. Nature, (95), 66-68.

Reitsma, J., Glasa, A., Rutjesa, A., Scholten, R., Bossuyta, P., & Zwindermana, A. (2005). Bivariate analysis of sensitivity and specificity produces informative summary measures in diagnostic reviews. Journal of Clinical Epidemiology, (58), 982-990.

Severeyn, E., Wong, S., Herrera, H., & Altuve, M. (2015) Anthropometric measurements for assessing insulin sensitivity on patients with metabolic syndrome, sedentaries and marathoners. Engineering in Medicine and Biology Society (EMBC), 2015 37th Annual International Conference of the IEEE. 4423-4426.

Sonin, A. A. (2004). A generalization of the π theorem and dimensional analysis. Proc. of the National Academy of Sciences of the United States of America, 101(23), 8525–8526.

Stahl, W. 1961. Dimensional Analysis in Mathematical Biology. Bulletin of Mathematical Biophysics, (23), 355-376.

Velásquez, J., Wong, S., Encalada, L., Herrera, H., & Severeyn, E. (2015). Lipid-anthropometric index optimization for insulin sensitivity estimation. Proceedings of SPIE - The International Society for Optical Engineering. 96810R1-96810R10.

Vishram, J. K., Borglykke, A., Andreasen A.H., Jeppesen J., Ibsen H., Jørgensen T., Palmieri, L., Giampaoli, S., Donfrancesco, C., Kee, F., Mancia, G., Cesana, G., Kuulasmaa, K., Salomaa, V., Sans, S., Ferrieres, J., Dallongeville, J., Söderberg, S., Arveiler, D., Wagner, A., Tunstall-Pedoe, H., Drygas, W., & Olsen, M. H. (2014). MORGAM Project. Impact of age and gender on the prevalence and prognostic importance of the metabolic syndrome and its components in Europeans. The MORGAM Prospective Cohort Project. PLOS One, (9), e107294.

Worachartcheewan, A., Dansethakul, P., Nantasenamat, C., Pidetcha, P., & Prachayasittikul, V. (2012). Determining the optimal cutoff points for waist circumference and body mass index for identification of metabolic abnormalities and metabolic syndrome in urban Thai population. Diabetes Research and Clinical Practice, (98), e16–e21.

Xi, B., He, D., Hu, Y., & Zhou, D. (2013). Prevalence of metabolic syndrome and its influencing factors among the Chinese adults: The China Health and Nutrition Survey in 2009. Preventive Medicine, (57), 867-871.

Zimmet, P., & Alberti, G. (2005). Una nueva definición mundial del síndrome metabólico por la federación internacional de diabetes: fundamento y resultados. Revista Española de Cardiología, 58(12), 1371-1376.
Resumen visto = 83 veces
PDF descargado = 51 veces
Cómo citar
Velásquez, J., Herrera, H., Encalada, L., Wong, S., & Severeyn, E. (2017). Análisis dimensional de variables antropométricas y bioquímicas para diagnosticar el síndrome metabólico. Maskana, 8, 57-67. Recuperado a partir de