A New Method of Classifying Adiposity Using Height, Volume and Surface Area

Introducing the Barix^sm

Continued...

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page 1,2,3,4,5

Barix Calculation for a Typical Mesomorph Body Shape:

Figure 14 depict a scan image of a mesomorph body type. A mesomorphic build is generally muscular.

 Figure 14
Scan Image of Example Mesomorph Body Type

 

Figure 15 depicts the torso of the mesomorphic body type example. It is to be noted that the head is not included in the torso height, surface area and volume calculations.

Figure 15
Torso of the Mesomorphic Body Type Example

 

Table 5 depicts the torso height segments, and long with each segment's surface area and volume calculations.

Table 5
Mesomorph Example Torso Height Segments with Associated Volume and Surface Area

Units = centimeters, volume in CC
Torso
Height	Volume	Surface Area
80	307.9	70.3
81	741.4	117.4
82	798	113.7
83	830.8	112.7
84	854.5	112.2
85	871.2	112
86	882.3	111.8
87	886.9	111.6
88	886.4	111
89	879.1	110.3
90	869.1	109.5
91	856.1	108.7
92	841	107.6
93	828.7	106.7
94	819.5	106
95	812.3	105.2
96	807.6	104.6
97	806.7	104.1
98	807.3	103.8
99	805.3	103.5
100	800.6	103.1
101	789.8	102.3
102	769.1	101
103	757.6	100.3
104	749.9	99.9
105	735.7	98.6
106	720	96.9
107	710.2	96.1
108	705.7	96.4
109	710.4	97.7
110	718.5	97.6
111	719.6	98
112	714.5	98
113	716.7	98.1
114	721.8	98.5
115	731.8	99.4
116	741.7	100
117	752.4	100.9
118	763.6	101.8
119	778	103
120	800.9	104.9
121	820.1	106.2
122	837.1	107.4
123	851.5	108.8
124	866.1	110
125	884	111.2
126	910.3	113.3
127	939.9	115.9
128	968.3	118.1
129	997.2	120.3
130	1024.7	121.8
131	1051.4	123.5
132	1069.9	124.4
133	1081.7	125
134	1090.2	125.5
135	1092.4	125.7
136	1093.7	125.7
137	1076.9	124.7
138	1055.2	123.4
139	1036.9	122.3
140	1014.7	121.3
141	992.2	120.4
142	963.6	118.8
143	936.7	117.5
144	892.4	115.2
145	844.9	113.1
146	792.8	110.8
147	729.8	107.5
148	660.7	103.2
149	580.8	97.6
150	496.4	90.4
151	428.2	83.1
152	374.7	76.5
153	325.8	71.1
154	274.9	65
155	247.9	63.8
156	237.6	64.2
157	222.4	59.6
77	61564.6	8187.5

The mesomorph body type example's Torso Height is 77 cm, the Torso Volume is 61565 cubic centimeters (cc), and the Torso Surface Area is 8188 centimeters squared (cm²).

The mesomorph body type example's Barix is 77/(61565/8188) or 10.241.

As an aside, the mesomorphic example subject's height is 5' 11” and his weight at the time of the scan was 225 lbs. The traditional BMI calculation for this subject is 32. A BMI of 32 is considered to be obese.

Figure 16 depict a scan image of an endomorph body type. An endomorphic build is generally disposed toward greater adiposity.

Figure 16
Scan Image of Endomorphic Body Type Example

Figure 17 depicts the torso of the endomorphic body type example. It is to be noted that the head is not included in the torso height, surface area and volume calculations.

Figure 17
Torso of the endomorphic Body Type Example

 

Table 6 depicts the torso height segments, and long with each segment's surface area and volume calculations.

Table 6
Endomorph Example Torso Height Segments with Associated Volume and Surface Area

Units = centimeters, volume in CC
Torso
Height	Volume	Surface Area
72.8	380.1	54.8
73.8	780.8	109.1
74.8	804.2	108.7
75.8	829.7	108.4
76.8	864.1	109.7
77.8	881.9	110
78.8	894.2	110.2
79.8	901.5	110.5
80.8	907.9	110.8
81.8	908.7	110.7
82.8	913	110.7
83.8	912.8	110.5
84.8	908	110
85.8	903	109.5
86.8	900.6	109.5
87.8	904	110
88.8	909.4	110.5
89.8	914.5	110.6
90.8	919.5	110.6
91.8	920	110.3
92.8	920.4	110
93.8	921.8	109.8
94.8	921.1	109.8
95.8	919.1	109.5
96.8	920.2	109.5
97.8	920.7	109.6
98.8	926	109.9
99.8	924.6	109.9
100.8	919.9	109.6
101.8	916.7	109.3
102.8	912.3	108.8
103.8	906.6	108.3
104.8	898.8	107.6
105.8	890.2	106.8
106.8	889.5	106.8
107.8	896.6	107.3
108.8	902.8	107.8
109.8	909.4	108.2
110.8	922.2	109.5
111.8	946	112.9
112.8	973.2	117.3
113.8	1006.2	120.5
114.8	1033.2	124.1
115.8	1047.4	126.1
116.8	1069.9	129
117.8	1079.4	130.7
118.8	1078.7	131
119.8	1071	132.1
120.8	1044.7	130
121.8	1003	126.6
122.8	988	119.9
123.8	953.1	115
124.8	918	111.6
125.8	891.3	109.6
126.8	864	108.6
127.8	825.8	106.9
128.8	786	105.1
129.8	740.9	102.7
130.8	687.7	99.8
131.8	638.7	97.5
132.8	589	95.2
133.8	543.1	93.3
134.8	496.6	91.6
135.8	438.8	88.2
136.8	372.5	82.3
137.8	272.8	66.5
138.8	199.4	52.5
66	57155.2	7239.7

The endomorph body type example's Torso Height is 66 cm, the Torso Volume is 57155 cubic centimeters (cc), and the Torso Surface Area is 7240 centimeters squared (cm²).

The endomorph body type example's Barix is 66/(57155/7240) or 8.360.

Table 7 summarizes the Barix Calculations for the morbidly obese, endomorph, mesomorph and ectomorph body types.

Table 7
Summary of Example Barix Calculations for Body Types

	Morbidly Obese	Endomorph	Mesomorph	Ectomorph
Barix	7.159	8.360	10.241	11.331

Table 7 gives an indication of the descending nature of the Barix. The lower the Barix is, the greater the adiposity, or degree of the bariatric condition of the subject.

Interpretation of an Individual's Barix and the Generalized Barix Scale:

 The Barix is a dimensionless quantity that indicates the general adiposity of an individual. To fully understand the implication of this number, an individual's Barix must be interpreted against a Generalized Barix Scale . The preliminary Generalized Barix Scale is a scale that has been developed by calculating the Barix from a sample population of adult subjects.

The Generalized Barix Scale is a general scale taking in all adult body types. An individual's particular Barix can then be compared to the scale in order to understand what percentile the individual's Barix falls within.

The individual and/or the individual's physician can utilize this information to understand if any corrections in lifestyle are needed to improve the individual's Barix.

Specialized Barix Scales may be developed for pediatrics, geriatrics, obstetrics, the extreme morbidly obese, the anorexic as well as other medical disciplines. These Specialized Barix Scales categorize the degree of adiposity of specific subjects of interest within these particular medical disciplines. Specialized Barix Scales area needed because inclusion of the Barix numbers of the subjects within a Specialized Barix Scale would skew the Generalized Barix Scale.

It is important to note that a Specialized Barix Scale may or may not be a subset of the Generalized Barix Scale. The Pediatric Index, for instance, is not a subset of the Generalized Barix Scale as the Generalized Barix Scale is composed of Barix calculations for adults. The Bariatric Index is applied to morbidly obese subjects undergoing bariatric surgery. As they lose mass, the individuals that have undergone some form of bariatric surgery may move out of the Bariatric Index and into the Generalized Barix Scale. The Geriatric Index is a Specialized Barix Scale designed to interpret an elderly individual's Barix to elderly peers. The Anorexic Index is a Specialized Barix Scale designed to interpret an anorexic subject's Barix within a population of anorexic individuals.

All of the Specialized Barix Scales, with the exception of the Pediatric Index may be interpreted against the Generalized Barix Scale to gauge where the individual's Barix stands in comparison with the overall population sample.

The Development of Generalized Barix Scale:

A total of 200 adult subjects of various body types participated in a study to develop the preliminary Generalized Barix Scale. 200 samples appear to be enough to form the outline of a general scale. The Generalized Barix Scale will be calibrated as additional samples are added.

The main thrust of the Generalized Barix Scale is to derive the existence of certain cut-off points that categorize an individual's adiposity within the general population.

The Barix was calculated for each subject. Circumferential Waist and Hip measurements were extracted from each scan image and recorded. The waist-to-hip ratio was calculated, and the torso height was recorded.

Descriptive statistics were then calculated, including the arithmetic mean, median, standard deviation and variance.

Table 7
Descriptive Statistics for Preliminary
Generalized Barix Scale

Barix Sample Descriptive Statistics
Mean	9.670515
Standard Error	0.095358
Median	9.814
Mode	9.872
Standard Deviation	1.348573
Sample Variance	1.818648
Kurtosis	-0.46183
Skewness	-0.32477
Range	6.815
Minimum	5.781
Maximum	12.596
Sum	1934.103
Count	200

The arithmetic mean for this population is 9.671. The confidence level used to calculate the mean was 95%. The median is 9.814, meaning that half the sample population's Barix is above 9.814 and half is below.

The standard deviation is 1.349. In this case 63% of the population had a Barix of between 11.020 and 8.465. 18% if the population had a Barix above 11.02. 19% of the population had a Barix below 8.465. Those with a Barix higher than 11.02 were generally thin and/or physically fit. Those with a Barix below 8.465 were considered very obese to morbidly obese.

Only one of the samples was 2 standard deviations above the mean. Three of the samples were below 2 standard deviations from the mean.

To understand how an individual's Barix relates to this population, rank and percentile calculations were made.

Table 9 summarizes the preliminary Generalized Barix Scale:

Percentile	Barix	Indication
91 - 100	12.596	Problematically Thin
50 - 90	11.345	Proportionally Ideal to Thin
Below 50	9.814 (median)	Slightly Overweight
Below 40	9.470	Overweight
Below 30	8.944	Obese
Below 20	8.518	Extremely Obese
Below 10	7.783	Morbidly Obese

The Barix is designed to indicate the degree of adiposity in a subject, the lower the Barix, the greater the degree of adiposity. The Generalized Barix Scale emphasizes the percentiles below 50%. Individuals with a Barix that is near or above the median tend to appear fit or well proportioned. However, an extremely high Barix number could indicate a medical condition, such as anorexia. The anorexic individual's Barix would be interpreted against the Anorexic Index, which is a Specialized Barix Scale.

There exists an Optimal Barix Range for each individual, regardless of what category the individual is in. The Optimal Barix Range is defined as a narrow range of the highest feasible Barix values that an individual can obtain without generating medical risks (anorexia, anemia, etc.). The Optimal Barix Range can also be a useful indicator to track post-operative recovery from surgical procedures that affect contour changes in a subject's torso.

Medical or fitness professionals can assess the individual's Barix and body type and suggest lifestyle changes to help each individual towards their Optimal Barix Range.

Independencies and Dependencies of the Barix:

An individual's Barix has strong (negative) correlation to the individual's circumferential waist measurement and circumferential hip measurement, but weak correlation to the individual's waist-to-hip ratio (a traditional indicator) or the individual's torso height. In general, the smaller the waist and/or hip measurement, the larger the individual's Barix. This makes intuitive sense. Thinner individuals generally have a higher Barix.

The low degree of correlation (independence) between an individual's Barix and waist-to-hip ratio is beneficial since it has been shown that the waist-to-hip ratio can be a misleading aesthetic indicator.

The low degree of correlation (independence) between an individual's Barix and torso height is beneficial since many subjects may have the same torso height, but subjects with the same torso height are unlikely to have the same (volume/surface area) product.

Table 10 shows correlations between the Barix, Waist and Hip Measurements, Waist-to-Hip Ratio and Torso Height for the sample population.

Table 10
Correlation Values between the Barix, Waist and Hip Measurements, Waist-to-Hip Ratio and Torso Height for the Sample Population

	Waist	Hips	Waist-to-Hip Ratio	Barix	Torso Height
Waist	1
Hips	0.874692	1
Waist-to-Hip Ratio	0.735066	0.320518	1
Barix	-0.77236	-0.786	-0.41706861	1
Torso Height	0.264922	0.142504	0.342166981	0.307661	1

Table 10 indicates that the correlation between the Barix and the waist measurement is -0.772. The correlation between the Barix and the hip measurement is -0.786. These values indicate a high degree of negative correlation.

In contrast, the correlation between the Barix and the waist-to-hip ratio is -0.417. The correlation between the Barix and the torso height is 0.308. These values are insufficient to declare any dependencies.

Correlations between the Barix and other linear or circumferential measurements can be made as well. In addition, correlation between the Barix and a sample population's height, weight and BMI can be made.

 

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September 2005

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