J Med Syst (2017) 41:5 DOI 10.1007/s10916-016-0636-9
TRANSACTIONAL PROCESSING SYSTEMS
What kind of Relationship is Between Body Mass Index and Body Fat Percentage? Aleksandar Kupusinac1 · Edita Stoki´c2 · Enes Suki´c3 · Olivera Rankov2 · Andrea Kati´c1
Received: 30 November 2015 / Accepted: 12 October 2016 © Springer Science+Business Media New York 2016
Abstract Although body mass index (BMI ) and body fat percentage (BF %) are well known as indicators of nutritional status, there are insuficient data whether the relationship between them is linear or not. There are appropriate linear and quadratic formulas that are available to predict BF % from age, gender and BMI . On the other hand, our previous research has shown that artificial neural network (ANN) is a more accurate method for that. The aim of this study is to analyze relationship between BMI and BF % by using ANN and big dataset (3058 persons). Our results show that this relationship is rather quadratic than linear for both gender and all age groups. Comparing genders, quadratic relathionship is more pronounced in women, while linear relationship is more pronounced in men. Additionaly, our results show that quadratic relationship is more pronounced in old than in young and middle-age men and it is slightly more pronounced in young and middle-age than in old women. Keywords Artificial neural networks · Big data · Body mass index · Body fat percentage · Obesity This article is part of the Topical Collection on Transactional Processing Systems Aleksandar Kupusinac
[email protected] 1
Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovi´ca 6, 21000 Novi Sad, Serbia
2
Medical Faculty, University of Novi Sad, Hajduk Veljkova 3, 21000 Novi Sad, Serbia
3
Faculty of Electronic Engineering, University of Niˇs, Aleksandra Medvedeva 14, Niˇs 18000, Serbia
Introduction BMI and BF % are well known indicators of nutritional status. While BMI is general indicator of nutritional status, BF % is better predictor of visceral fat mass and independent risk factor for cardiovascular diseases, diabetes and metabolic disorders. BMI is defined as the ration of body mass and the square of body height. The values of BMI over 25 kg/m2 correspond to the overweight, and values over 30 kg/m2 correspond to obesity [1]. BMI is not measure of body fat mass. The process of aging is characterized by decreasing body height and increasing fat mass with redistribution of fat tissue mostly as a visceral fat deposition, even if body weight and BMI are maintained [2, 3]. On the other hand, during the entire adult life span the BF % of females is significantly higher than that of males with the same BMI [4, 5]. Based on that, the relationship between BF % and BMI is age- and gender-dependent [6, 7]. A healthy range of body fat for women is 20-25 %, while it is 10-15 % for men [8]. Differences between body fat percentages can be describe by influences of hormones, hormone receptors and enzyme concentration. Higher concentration of lipoprotein lipase in women, differences in the type and number of receptors for epinephrine in genders, may be only some explanations for different body fat percentage in genders [9]. Beside that, estrogen in women is response for reduction in postprandial fatty acid oxidation, increase insulin resistance, and higher leptin level, that can closely explain higher body fat percentage in women [10]. There is uncertainty and some controversy as to whether the relationship between BMI and BF % is linear or curvilinear [7, 11]. There are appropriate linear and quadratic formulas based on coefficients previously determinated by
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using statistical methods. These formulas are all fairly similar and frequently used to predict body fat percentage (BF %) from gender (GEN), age (AGE) and body mass index (BMI ): –
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Deurenberg et al. formula [12] BF % = 1.20 ∗ BMI − 0.23 ∗ AGE − 10.80 ∗ GEN − 5.40, Deurenberg et al. formula [13] BF % = 1.29 ∗ BMI − 0.20 ∗ AGE − 11.40 ∗ GEN − 8.00, Gallagher et al formula [4] BF % = 1.46 ∗ BMI − 0.14 ∗ AGE − 11.60 ∗ GEN − 10.00, Jackson and Pollock formula [14, 15] BF % = 1.61 ∗ BMI − 0.13 ∗ AGE − 12.10 ∗ GEN − 13.90, Jackson et al. formula [5] BF % = 1.39 ∗ BMI − 0.16 ∗ AGE − 10.34 ∗ GEN − 9.00, Sun et al. [16] BF % = −0.030 ∗ BMI 2 + 0.033 ∗ AGE ∗ GEN − 0.001∗AGE ∗BMI −0.006∗AGE +12.409∗GEN + 3.306 ∗ BMI − 32.515.
Our goal is to consider specifics of the relationship between BMI and BF % by using artificial neural network (ANN), as a well-known method of machine learning. ANNs have been extensively used in numerous clinical fields since they are suitable for complex realworld problems, particularly for non-linear or incomplete models [17]. They recognize complex patterns between inputs and outputs and than apply this knowledge on unknown data [18, 19]. Our previous research has shown that feedforward ANN with back-propagation as the training algorithm is a more accurate solution for estimating BF % based on AGE, GEN and BMI [20]. Additionaly, we have considered single-layer feedforward ANNs and determinated the optimal number of hidden neurons. In this paper, we will analyze the relationship between BMI and BF % by using larger dataset and optimal ANN architectures that achieve the highest average accuracy on testing set.
Table 1 Characteristics of dataset Minimum
Average
Maximum
Females (N = 1483) AGE [y] BMI [kg/m2 ] BF % [%]
18 16.58 7.40
40.09 30.18 37.16
88 63.73 71.80
Males (N = 1575) AGE [y] BMI [kg/m2 ] BF % [%]
18 17.21 3.70
39.25 27.07 24.04
86 64.62 64.00
Diabetes and Metabolic Disorders of the Clinical Centre of Vojvodina in Novi Sad (Serbia) in accordance with the Declaration of Helsinki. Harpenden anthropometer was used for measuring body height (BH ) with the precision of 0.1 cm. Body mass (BM) was measured using balanced beam scale with the precision of 0.1 kg. By definition, BMI was calculated as the ration of BM and the square of BH . Tanita Body Composition Analyzer BC-418 MA III (Tanita Corporation, Tokyo, Japan) was used for measuring body fat percentage BF %. The subjects were given instructions to undertake the measurement in a state of normal hydration - no eating or drinking at least 4 h, no exercise in the preceding 12 h, no alcohol/caffeine consumption in the preceding 48 h, empty the bladder 30 min before measuring, no taking diuretics in the preceding seven days and detailed instructions about electrode placements according to the manufacturer’s manual were also provided. The relationship between BMI and BF % from our dataset is depicted in the Fig. 1, separately for women and men. In this research, the feedforward ANN with backpropagation as the training algorithm has been applied to simulate the relationship between BMI and BF% in MATLAB (Neural Network Toolbox). The ANN input values are vectors: X(i) = [AGE(i), GEN(i), BMI (i)], while the output values are:
Materials and methods The group inquired consisted of 3058 subjects (1483 women and 1575 men) aged 18 to 88 y, with BMI values between 16.58 and 64.62 kg/m2 and with BF % values between 3.7 % and 71.8 %. In the Table 1 are shown the minimal, average, and maximal values, separately for women and men. The respondents volunteered in the research and all the inquires were taken at the Department of Endocrinology,
Y (i) = BF %(i), where i = 1, 2, . . . , 3058. Based on our previous results given in [20], we will use ANN architectures with one hidden layer and 25 hidden neurons as optimal (Fig. 2). The dataset is randomly divided into three parts (training, validation and testing sets) with the proportion 70:15:15, by using function dividerand. As a network training function we have used trainlm that is often the fastest backpropagation algorithm in the MATLAB neural network toolbox
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Fig. 1 The relationship between BMI and BF % from dataset
and highly recommended as a first-choice supervised algorithm. During the training phase, we have used the following values of training parameters: min grad = 10−10 , mu = 10−3 , mu dec = 0.3, mu inc = 3 and mu max = 1010 . We have used tansig neural function (hyperbolic tangent sigmoid transfer function) in hidden layers and purelin neural function (linear transfer function) in output layer. In the test phase, ANN estimates BF % based on given AGE, GEN and BMI and the estimation accuracy is: ACT S [%] = 100 %[1 −
|BF %∗ − BF %| ], BF %
where BF % is the measured value and BF %∗ is the value estimated by ANN. ANN architectures that achieve the highest average accuracy on testing set (e.g. ACT S > 80) will be asked to estimate BF % for appropriate values for AGE, GEN and BMI . Based on that, we will discuss
Fig. 2 The optimal ANN architecture
whether the relationship between BMI and BF % is linear or quadratic.
Results and discussion The optimal ANN architectures with one hidden layer and 25 hidden neurons were trained, validated, and tested one hundred times. After every testing, ANN architecture with average accuracy on testing set ACT S > 80 % was asked to estimate BF % for the following six cases: 1. AGE = 25, GEN = F emale and BMI {15, 16, . . . , 65}, 2. AGE = 25, GEN = Male and BMI {15, 16, . . . , 65}, 3. AGE = 45, GEN = F emale and BMI {15, 16, . . . , 65}, 4. AGE = 45, GEN = Male and BMI {15, 16, . . . , 65}, 5. AGE = 65, GEN = F emale and BMI {15, 16, . . . , 65}, 6. AGE = 65, GEN = Male and BMI {15, 16, . . . , 65}.
= = = = = =
In the Fig. 3 are depicted ANN outputs for cases 1 and 2. Cases 3 and 4 are shown in the Fig. 4 and cases 5 and 6 in the Fig. 5. In general, we conclude that BF % is higher in women than in men and this is in accordance with [7, 11]. Additionaly, we conclude that BF % has positive trend in order to BMI , i.e. BF % increases with BMI increase, independently of age and gender. In order to analyze whether the relationship between BMI and BF % is
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Fig. 3 ANN outputs for cases: AGE = 25, GEN = F emale and BMI = {15, 16, . . . , 65} and AGE = 25, GEN = Male and BMI = {15, 16, . . . , 65}
linear or quadratic, we approximate obtained ANN outputs given in the Figs. 3, 4 and 5 with linear and quadratic polynomials and consider mean square error (MSE). Approximations are done in MATLAB by using polyf it function and obtained the following approximative functions:
2. For AGE = 25 and GEN = Male
1. For AGE = 25 and GEN = F emale
3. For AGE = 45 and GEN = F emale
– –
linear: BF % = 0.8585 ∗ BMI + 9.6576 quadratic: BF % = −0.0174 ∗ BMI 2 + 2.2526 ∗ BMI − 14.4480
Fig. 4 ANN outputs for cases: AGE = 45, GEN = F emale and BMI = {15, 16, . . . , 65} and AGE = 45, GEN = Male and BMI = {15, 16, . . . , 65}
– –
– –
linear: BF % = 0.9136 ∗ BMI − 2.4337 quadratic: BF % = −0.0078 ∗ BMI 2 + 1.5377 ∗ BMI − 13.2260
linear: BF % = 0.7327 ∗ BMI + 14.7823 quadratic: BF % = −0.0150 ∗ BMI 2 + 1.9356 ∗ BMI − 6.0172
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Fig. 5 ANN outputs for cases: AGE = 65, GEN = F emale and BMI = {15, 16, . . . , 65} and AGE = 65, GEN = Male and BMI = {15, 16, . . . , 65}
4. For AGE = 45 and GEN = Male – –
linear: BF % = 0.6884 ∗ BMI + 7.3733 quadratic: BF % = −0.0024 ∗ BMI 2 + 0.8806 ∗ BMI − 4.0491
5. For AGE = 65 and GEN = F emale – –
linear: BF % = 0.6603 ∗ BMI + 17.2159 quadratic: BF % = −0.0168 ∗ BMI 2 + 2.0032 ∗ BMI − 6.0044
6. For AGE = 65 and GEN = Male – –
linear: BF % = 0.6805 ∗ BMI + 8.3138 quadratic: BF % = −0.0096 ∗ BMI 2 + 1.4519 ∗ BMI − 5.0241
In the Table 2 are given the mean square error MSEL for linear and MSEQ for quadratic approximations. Based
Table 2 Mean square errors for linear (MSEL ) and quadratic (MSEQ ) approximations AGE
Females (N = 1483) MSEL MSEQ
Males (N = 1575) MSEL MSEQ
25 45 65 AV ERAGE
11.85 8.88 11.20 10.64
3.83 1.08 3.86 2.92
0.46 0.40 0.63 0.50
1.54 0.86 0.37 0.93
on that, we conclude that the relationship between BMI and BF % is rather quadratic than linear for both genders and all age groups and this is in accordance with [7]. In our study both genders have similar average age, but average BF % is higher in women than in men, and that is in accordance with [11]. Republic of Serbia, expecially its north part (AP Vojvodina), is well known as country with a warning high percent of obese people. Pathophysiological obesity increases insulin secretion, decreases insulin sensitivity and number and sensitivity of insulin receptors at target cells and in liver, which causes higher body fat mass [21]. Higher body fat percentage in women is effect of higher level of estrogen and his influence on insulin and leptin level and resistance [22]. Higher leptin level is documented in literature - this can be crucial base for higher body fat percentage in women [23]. Lower level of estrogen in younger and postmenopausal women than in women in generative period explains lower quadratic relationship in this age groups [24]. MSEQ decreases by aging in men, what means that quadratic relationship is more pronounced in old than in young and middle-age men. On the other hand, in women MSEQ slowly increases by aging, what means that quadratic relationship is slightly more pronounced in young and middle-age than in old women. Average MSEL and MSEQ are given in separate rows, respectively for women and men. Since average MSEQ = 0.50 in women and average MSEQ = 0.93 in men, quadratic relationship is more pronounced in women than men. On the other hand, since average MSEL = 2.92 in men and average MSEL = 10.64 in women, linear relationship is more pronounced in men than women.
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Limitations The relationship between BF % and BMI depends on race, ethnicity, and culture [25]. The dataset, that is used in this research, is limited to the Serbian population.
Conclusions This paper presented an analysis of the relationship between BMI and BF % based on ANN. The relationship is rather quadratic than linear for both gender and all age groups, but quadratic relationship is more pronounced in women than men and linear relationship is more pronounced in men than women. Quadratic relationship between BMI and BF % is more pronounced in old than in young and middle-age men and that quadratic relationship is slightly more pronounced in young and middle-age than in old women. While BMI is general indicator of nutritional status, BF % is better predictor of visceral fat mass and independent risk factor for cardiovascular diseases, diabetes and metabolic disorders. Since this study promotes an easy, non-invasive and low-cost analysis of relationship between BMI and BF %, the obtained results can be used in everyday clinical practice for recognition of high risk groups and their early and adequate cure to prevent mentioned disorders. Our future work will be directed toward the investigation of optimality of the numerous ANN types and architectures, use of different data mining and machine learning techniques, and development of population-specific models for BF %. Acknowledgments This work was partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia within the projects: ON 174026 and III 044006, and by the Provincial Secretariat for Higher Education and Scientific Research of the Autonomous Province of Vojvodina within the project: 114-451-2856/2016-03.
6. 7.
8.
9. 10.
11.
12.
13.
14.
15.
16.
17.
18.
References 19. 1. World Health Organization, Obesity: preventing and managing the global epidemic. Report of a WHO consultation. World Health Organ. Tech. Rep. Ser. 894:1–253, 2000. 2. Kuk, J.L., Lee, S., Heymsfield, S.B., and Ross, R., Waist circumference and abdominal adipose tissue distribution: influence of age and sex. Am. J. Clin. Nutr. 81:1330–1334, 2005. 3. Cartwright, M.J., Tchkonia, T., and Kirkland, J.L., Aging of adipocytes: potential impact of inherent, depot-specific mechanisms. Exp. Gerontol. 42:463–471, 2007. 4. Gallagher, D., Visser, M., Sepulveda, D., Pierson, R., Harris, T., and Heymsfield, S.B., How Useful is Body Mass Index for Comparison of Body Fatness across Age, Sex and Ethnic Groups? Am. J. Epidemiol. 143(3):228–239, 1996. 5. Jackson, A.S., Stanforth, P.R., Gagnon, J., Rankinen, T., Leon, A.S., Rao, D.C., Skinner, J.S., Bouchard, C., and Wilmore, J.H., The effect of sex, age and race on estimating percentage body fat
20.
21.
22.
from body mass index: The Heritage Family Study. Int. J. Obes. 26:789–796, 2002. Forbes, G.B. Human body composition. New York: Springer Verlag, 1987. Meeuwsen, S., Horgan, G.W., and Elia, M., The relationship between BMI and percent body fat, measured by bioelectrical impedance, in a large adult sample is curvilinear and influenced by age and sex. Clin. Nutr. 29:560–566, 2010. Robergs, R.A., and Roberts S.O. Exercise physiology, Performance, and clinical Applications helah and disease. 2nd edn, pp. 61–82, 1997. Philadelphia. Blaak, E., Gender differences in fat metabolism. Curr. Opin. Clin. Nutr. Metab. Care 4(6):499–502, 2001. Lwin, R., Darnell, B., Oster, R., Lawrence, J., Foster, J., Azziz, R., and Gower, B.A., Effect of oral estrogen on substrate utilization in postmenopausal women. Fertil. Steril. 90(4):1275–1278, 2008. Ranasinghe, C., Gamage1, P., Katulanda, P., Andraweera1, N., Thilakarathne, S., and Tharanga, P., Relationship between Body mass index (BMI) and body fat percentage, estimated by bioelectrical impedance, in a group of Sri Lankan adults: a cross sectional study. BMC Public Health 13:797, 2013. doi:10.1186/1471-2458-13-797. Deurenberg, P., Weststrate, J.A., and Seidell, J.C., Body mass index as a measure of body fatness: age- and sex- specific prediction formulas. Br. J. Nutr. 65:105–114, 1991. Deurenberg, P., Yap, M., and van Staveren W.A., Body mass index and percent body fat, a meta analysis among different ethnic groups. Int. J. Obes. Relat. Metab. Disord. 22:1164–1171, 1998. Jackson, A.S., Research design and analysis of data procedures for predicting body density. Med. Sci. Sports Exerc. 16(6):616–620, 1984. Jackson, A.S., Pollock, M.L., and Ward, A., Generalized equations for predicting body density of women. Med. Sci. Sports. Exerc. 12(3):175–182, 1980. Sun, S.S., Chumlea, W.C., Heymsfield, S.B., Lukaski, H.C., Schoeller, D., Friedl, K., Kuczmarski, R.J., Flegal, K.M., Johnson, C.L., and Hubbard, V.S., Development of bioelectrical impedance analysis prediction equations for body composition with the use of a multicomponent model for use in epidemiologic surveys. Am. J. Clin. Nutr. 77(2):331–340, 2003. Kupusinac, A., Doroslovaˇcki R., Malbaˇski D., Srdi´c B., and Stoki´c E., A primary estimation of the cardiometabolic risk by using artificial neural networks. Comput. Biol. Med. 43(6):751–757, 2013. Abdul-Kareem, S., Baba, S., Zubairi, Y.Z., and Wahid, M.I.A., As a tool for medical prognosis. Health Inform. J. 6(3):162–165, 2000. Sheikhtaheri, A., Sadoughi, F., and Dehaghi, Z.H., Developing and Using Expert Systems and Neural Networks in Medicine: A Review on Benefits and Challenges. J. Med. Syst. 3(9):8:110, 2014. Kupusinac, A., Stoki´c, E., and Doroslovaˇcki R., Predicting body fat percentage based on gender, age and BMI by using artificial neural networks. Comput. Methods Programs Biomed. 113(2):610–619, 2014. Antuna-Puente, B., Feve, B., Fellahi, S., and Bastard, P., Adipokines: The missing link between insulin resistence and obesity. Diabetes Metab. 34(1):2–11, 2008. Blum, W.F., Englaro, P., Hanitsch, S., Juul, A., Hertel, N.T., Mller, J., Skakkebaek, N.E., Heiman, M.L., Birkett, M., Attanasio, A.M., Kiess, W., and Rascher, W., Plasma leptin level in healthy children and adolescents: Dependence ojn body mass index, body fat mass, gender, pubertal stage nad testosteron. J. Clin. Endocrinol. Metab. 82(9):2904–2910, 1997.
J Med Syst (2017) 41:5 23. Considine, R.V., Sinha, M.K., Heiman, M.L., Kriauciunas, A., Stephens, T.W., Nyce, M.R., Ohannesian, J.P., Marco, C.C., McKee, L.J., Bauer, T.L., and et al., Serum immunoreactive leptin concentations in normal weight and obese humans. N. Engl. J. Med. 334(5):292–295, 1996. 24. Elminger, M.W., Kuhnel, W., and Ranke, M.B., Reference ranges for serum concentrations of lutropin(LH), follitropin(FSH), estradiol(E2), Prolactin, progesterone, sex hormone-binding globulin (SHBG), dehydroepiandrosterone
Page 7 of 7 5 sulfate(DHEAS), cortisol and ferritin in neonates, children and young adults. Clin. Chem. Lab. Med. 40(11):1151–1160, 2002. 25. Caprio, S., Daniels, S.R., Drewnowski, A., Kaufman, F.R., Palinkas, L.A., Rosenbloom, A.L., and Schwimmer, J.B., Influence of Race, Ethnicity, and Culture on Childhood Obesity: Implications for Prevention and Treatment: A consensus statement of Shaping Americas Health and the Obesity Society. Diabetes Care 31(11):2211–2221, 2008. doi:10.2337/dc08-9024.
