by [TC]²
A New Method of Classifying Adiposity Using Height, Volume and Surface Area
Introducing the Barixsm
David Stefan
President, Novaptus Systems, Inc.
David Gilbert, M.D.
Vice President, Medical Research
The Barix, Barix Trajectory, Barix Rate of Change, The Optimal Barix Range, The Generalized Barix Scale and Specialized Barix Scales described within are service marks of Novaptus Systems, Inc.
The information contained within this document is patent pending.
Copyright 2005, Novaptus Systems, Inc. All rights reserved.
A New Method of Classifying Adiposity Using Height, Volume and Surface Area
Introducing the Barixsm
Introduction
It has always been difficult to quantify the shape of the body. Known methods of categorization can be misleading. For example, the Body Mass Index, or BMI, can falsely categorize a bodybuilding athlete as obese. Various other ratios have also been employed to give an indication of the general shape of the body. The waist-to-hip ratio is one such common calculation. In general, it is thought that a waist-to-hip ratio of less than 1 indicates a favorable shape, the lower the number, the more ideal the shape. Thus an obese person with a waist-to-hip ratio of 0.70 could be thought to be more ideal than a person of shapely frame with a waist-to-hip ratio of 0.80. One reason for misclassification is that these traditional calculations do not take into account the subject's volume and surface area information.
The search for a “universal” value that quantifies and classifies a subject's general level of adiposity has been uncovered with the help of modern 3D body scanning technology. It is well known within the medical community that the shape of the torso is an excellent proxy for the overall shape of a subject. This new technique utilizes the subject's torso height, torso volume and torso surface area to calculate a dimensionless value known as the Barixsm. A subject's Barixsm can be compared to the Generalized Barix Scalesm to determine where the subject's Barixsm falls within the general population. The Generalized Barix Scalesm classifies the degree of adiposity for the general adult population. Moreover, by monitoring the changes to the subject's Barixsm, known as the Barix Trajectorysm and the Barix Rate of Changesm, medical, fitness or nutrition professionals can determine the direction and pace of weight loss or weight gain over a period of time.
Medical disciplines can use Specialized Barix Scalessm to classify the degree of adiposity for particular subjects of interest. Specialized Barix Scalessm include but are not limited to The Bariatric Index, The Pediatric Index, The Obstetric Index, The Geriatric Index, The Diabetic Index and the Anorexic Index. Monitoring the changes to the Barix, Barix Trajectories and Barix Rates of Change of subjects within a Specialized Barix Scale can assist the medical professional in determining whether the subject is experiencing a normal growth pattern, a normal aging pattern or help understand when a subject has responded to surgery or treatments to such a degree that the subject has moved out of a Specialized Barix Scale and into the Generalized Barix Scale.
Another practical use of the Barix, Barix Trajectory and Barix Rate of Change is to help monitor the recovery progress of subjects that have undergone a surgical procedure affecting general body contours. Examples of such surgical procedures include bariatric surgery, as well as aesthetic contouring procedures such as breast augmentation, breast reduction/reconstruction, abdominoplasty and lipoplasty.
To understand the Barix, one must move beyond common circumferential measurements such as waist, hips, bust and chest, measured in centimeters into the realm of squared centimeters and cubic centimeters.
Surface area measurements are made in centimeters, squared (cm2), volume measurements are made in centimeters, cubed (cm3). It is important to note that there is no direct relationship between volume and surface area. As an example, a sheet of paper has a large surface area, but because it is thin, it occupies a correspondingly small volume.
The formula for calculating the Barix is:
The (torso volume/torso surface area) product reduces to centimeters in the denominator. The torso height units are in centimeters, which cancels the centimeters in the denominator, leaving a dimensionless value.
The Barix is a descending value, the smaller the Barix, the greater the subject's degree of adiposity.
Before calculating the Barix values for particular subjects, it is appropriate to understand how the Barix changes for a simple shape.
The examples below begin with a simple cylinder closed at each end. The cylinder height, volume and surface area are calculated using tools within a 3D CAD program.
The Barix is calculated for this initial cylinder. Using tools in the CAD program, the cylinder was gradually shaped into the form of a torso.
The Barix, volume and surface area for each example were then tabulated.
From these examples, one can see that the Barix increases as the torso begins to take shape. It can also be seen that the volume and surface area change at different rates with respect to each other.
Figure 1
Closed Cylinder, Dimensions, Volume and Surface Area
Note that the volume of the cylinder is 678.8 cm3 and the surface area is 457.9 cm2.The Barix for this cylinder is (15 cm/(678.8 cm 3 /457.9 cm2 )), or 10.119.
Figure 2 depicts the creation of a “waist” in the middle of the cylinder.
Figure 2
Creating a “waist” in the middle of the cylinder
In this case, the volume changed from 678.8 cm3 to 657.6 cm3, a difference of 22.2 cm3. The surface area changed only slightly from 457.9 cm2 to 456.4 cm2.
The Barix for this example is (15 cm/(657.6 cm3 /456.4 cm2 )), or 10.411.
The Barix has increased from 10.119 to 10.411, indicating an improving “shape”.
Figure 3 depicts shaping the “waist” of the cylinder further.
Figure 3
Further Shaping of the Cylinder's “Waist”
In this case, the volume changed from 657.6 cm3 to 645.7 cm3, a difference of 9.9 cm3. The surface area changed from 456.4 cm2 to 451.6 cm2.
The Barix for this example is (15 cm/(645.7 cm3 /451.6 cm2 )), or 10.491.
This is an improvement from a Barix of 10.411 to 10.491.
Figure 4
Shaping the Cylinder Further by Introducing a “Bust”
In this case, the volume changed from 645.7 cm3 to 639.5 cm3, a difference of 6.2 cm3. The surface area changed from 451.6 cm2 to 451.4 cm2.
The Barix for this example is (15 cm/(639.5 cm3 /451.4 cm2 )), or 10.590.
This is an improvement from a Barix of 10.491 to 10.590.
Figure 5
The Cylinder Formed into a Torso
In this case, the volume changed from 639.5 cm3 to 595.9 cm3, a difference of 44.6 cm3. The surface area changed from 451.4 cm2 to 432.4 cm2.
The Barix for this example is (15 cm/(595.9 cm3 /432.4 cm2 )), or 10.884.
This is an improvement from a Barix of 10.590 to 10.884.
Table 1
Tabulating the Cylinder Examples
| Description | Volume | Surface Area | Barix |
| Cylinder | 678.8 | 457.9 | 10.119 |
| Cylinder/Waist 1 | 657.6 | 456.4 | 10.411 |
| Cylinder/Waist 2 | 645.7 | 451.6 | 10.491 |
| Cylinder Waist/Bust | 639.5 | 451.4 | 10.590 |
| Cylinder as Torso | 595.9 | 432.4 | 10.884 |
Close examination of Table 1 indicates that there is no direct (linear) relationship between the volume and surface area of the cylinder as the cylinder undergoes transformation. In each successive example, the Barix of the cylinder is increasing as the cylinder is transformed from its original shape to a shape resembling a torso.
This is an important concept to understand when calculating the Barix of a particular subject.
In general, obese people have a larger (torso volume/torso surface area) product than thinner people.
Put another way, obese people have a larger torso volume relative to their torso surface area and thinner people have a larger torso surface area relative to their torso volume.
Barix Calculation Examples:
The following are examples of calculating the Barix . There are five examples in total. The first example details the determination of the torso, the torso height value, and how the torso surface area and torso volume are calculated. Other Barix calculations are made for a morbidly obese subject, an endomorphic body type, a mesomorphic body type and an ectomorphic body type.
Figure 6 depicts views of a three-dimensional scan image. This scan image was produced by a [TC]² white light scanner, provided by Novaptus Systems, Incorporated. The calculations and statistical computations were also provided by Novaptus Systems, Incorporated.
Figure 6
Composite Images of Subject's Three Dimensional Scan Shown in “Surface” Mode
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Linear and circumferential measurements as well as measurement height locations can be extracted from the 3D scan image by applying a programmable measurement-specific Measurement Extraction Profile (MEP) to the scan image. In this fashion, hip, waist, abdomen, chest, bust circumferential among other measurements can be automatically extracted and documented. For further information on Measurement Extraction Profiles applied to particular surgical procedures, refer to www.novaptus.com.
A Measurement Extraction Profile file has been programmed to determine the torso height, torso surface area and torso volume.
For Barix calculation purposes, the torso is defined to be between the front of the neck location and slightly under the buttocks, known as the crotch point. This torso definition excludes the head, arms, hands, leg and feet, but includes the entire buttocks area.
Torso height is calculated by finding the back of neck height point and the crotch point as measured from the floor.
Figure 7
Composite Images of the Subject's Torso
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The MEP file slices the torso into 1 cm “segments”. Each segment is integrated around its surface contour by using a finite triangular summation to calculate the surface area of each segment. Each slice segment is then closed on the top and bottom, treated as a solid, and integrated within to calculate the volume of each segment.
Figure 8
The torso sliced into 1 cm segments.
The output of this Measurement Extraction Profile consists of the height of the torso segments, along with each segment's surface area and volume.
The overall torso height is calculated by determining the difference, in centimeters between the crotch point and the back neck point. The total torso surface area is calculated by summing each segment's surface area value. The total torso volume is calculated by summing each segment's volume value.
Table 2
Subject's Torso Height Segments and Associated Volume and Surface Area
| Units = centimeters, volume in CC | ||
| Torso | ||
| Height | Volume | Surface Area |
| 69 | 265.5 | 63.9 |
| 70 | 642.9 | 111.3 |
| 71 | 680.2 | 109.9 |
| 72 | 697.2 | 108.3 |
| 73 | 709.5 | 106.3 |
| 74 | 721 | 105.2 |
| 75 | 722.2 | 104.3 |
| 76 | 721.6 | 103.4 |
| 77 | 719 | 102.4 |
| 78 | 713.2 | 101.7 |
| 79 | 708.4 | 101.7 |
| 80 | 708.5 | 100.7 |
| 81 | 716.2 | 100.2 |
| 82 | 722 | 100 |
| 83 | 719.8 | 99.3 |
| 84 | 712.4 | 98.6 |
| 85 | 697.7 | 97.4 |
| 86 | 679.3 | 96.3 |
| 87 | 660.8 | 95.1 |
| 88 | 639.6 | 93.7 |
| 89 | 614.8 | 92.1 |
| 90 | 587.4 | 90.1 |
| 91 | 555.9 | 87.3 |
| 92 | 526 | 84.4 |
| 93 | 507.6 | 82.6 |
| 94 | 500 | 81.8 |
| 95 | 492.1 | 81 |
| 96 | 485.2 | 80.3 |
| 97 | 476.6 | 79.4 |
| 98 | 465.7 | 78.5 |
| 99 | 460.1 | 78 |
| 100 | 458.6 | 77.9 |
| 101 | 462.8 | 80.5 |
| 102 | 499.7 | 88.3 |
| 103 | 517.1 | 93.8 |
| 104 | 539.3 | 96.1 |
| 105 | 629.6 | 99 |
| 106 | 645.1 | 99.8 |
| 107 | 660.4 | 100.1 |
| 108 | 675.1 | 100 |
| 109 | 676.1 | 99.4 |
| 110 | 672.8 | 98 |
| 111 | 664.3 | 96.6 |
| 112 | 654.9 | 95.6 |
| 113 | 649 | 94.9 |
| 114 | 641.8 | 94.5 |
| 115 | 632.6 | 93.9 |
| 116 | 626.5 | 93.2 |
| 117 | 611 | 92 |
| 118 | 595.9 | 91.2 |
| 119 | 581.5 | 90.5 |
| 120 | 562.5 | 89.6 |
| 121 | 536.6 | 88.1 |
| 122 | 513.3 | 87.3 |
| 123 | 481.8 | 85.3 |
| 124 | 454.8 | 84.2 |
| 125 | 424.1 | 82.7 |
| 126 | 395.3 | 81.2 |
| 127 | 360.9 | 79 |
| 128 | 327 | 77.4 |
| 129 | 286.1 | 74.4 |
| 130 | 233.2 | 68 |
| 131 | 170.6 | 55.4 |
| 62 | 36068.7 | 5743.1 |
The last row indicates that the subject's torso height is 62 cm, the subject's torso volume is 36068.7 cubic centimeters and the subject's torso surface area is 5743.1 centimeters, squared. The crotch point is located 69 cm from the floor, and the back neck point is located 131 cm from the floor, for a difference of 62 cm.
The Barix is calculated using the formula:
Accordingly, the subject's Barix is (62)/(36068/5743), or 9.872. The Barix is a dimensionless quantity.
September 2005