The Geometric Model and Fat Reduction

January 2013 | Volume 12 | Issue 1 | Original Article | 27 | Copyright © January 2013

Christopher B. Zachary FRCPa, Nazanin Saedi MDa, and John Allison PhDb

aDepartment of Dermatology, University of California, Irvine, Irvine, CA bMyoScience, Redwood City, CA

Background and Objective: Assessing the efficacy of noninvasive fat removal relies on measurements that are subject to error and subjective comparisons. Even the integrity of photographic comparisons, an accepted assessment tool, is difficult to control. With the emergence of noninvasive fat reduction technologies, there is a greater need for standardized assessments of efficacy.
Materials and Methods: A geometric model is described that correlates circumference and fat layer changes following noninvasive body contouring procedures. To validate the geometric model, abdominal measurements were taken with and without an artificial fat pad in place with: 1) a tape measure, 2) ultrasound, and 3) micrometer. The model was then used to analyze the published results of fat layer reduction and circumference changes following noninvasive body contouring procedures.
Results: While there was a high correlation (R2=0.8943) between our ultrasound method and the model with 6 subjects, the correlation between the tape measure method and the model was low (R2=0.0142).
Conclusion: Our results underscore the need for a highly accurate and standardized method for fat measurement. The efficacy in previous studies that had been assessed by tape measure in combination with ultrasound or computed tomography imaging does not conform to the model prediction, which leads us to conclude that the measurements used in those studies were not reliable. Studies reporting efficacy should use such a geometric model to ensure consistency between various measurement methods and to minimize errors due to weight change and measurement technique.

J Drugs Dermatol. 2013;12(1):27-34.


Standardized measurements are necessary to evaluate the plethora of new devices being developed for fat reduction. The efficacy of noninvasive fat removal techniques generally relies on measurements that might be criticized as being subjective and prone to error, such as 2-D photographic comparison, abdominal or thigh circumference measurements, and ultrasound imaging. In the best of circumstances, a photo comparison relies on a 2-D rendering of a 3-D effect, making accurate interpretation difficult. Circumferential tape measurements have been shown to be inaccurate, and even ultrasound fat layer measurements can be manipulated.1
In this paper, we develop a geometric model for predicting changes in torso circumference as the result of a known abdominal fat layer reduction. This validated geometric model is then used to analyze the published results of clinical studies demonstrating circumferential reduction after noninvasive fat reduction. This model demonstrated profound inconsistencies between the different measurement methods, resulting in widespread inaccuracies and exaggerations in some published reports.
With the emergence of new noninvasive fat reduction technologies, there is a need for standardized and reliable measures of efficacy that are credible. This geometric model will help to bring some order to the analysis and aid authors and journal reviewers in their interpretation and reporting of such results in the future.


Geometric Model

Since the circumference of a circle is directly related to its radius, one can use a geometric model to determine the relationship between changes in fat layer thickness and circumference. A reduction in the thickness of fat following a noninvasive fat reduction procedure will be reflected by a reduction in the abdominal circumference at that same location.
A cross-section of the human torso is approximately elliptical and can be modeled as an ellipse, where the perimeter is calculated from the major axis (a) and minor axis (b) as shown in Figure 1.

Perimeter ≈π√ 2(a2+b2)-(a-b)2/2 (Equation 1)
A quadratic formula may be used to approximate the perimeter of an ellipse (<1% error) as shown in Equation 1. To further simplify calculations, we modeled the human torso as a circle in cross-section (where a=b). Using a circular geometric model for the torso, Equation 1 is simplified to Equation 2, which is a familiar expression showing the circle circumference (C) is proportional to the radius (R).

C = 2π R (Equation 2)
This simplification is appropriate because it introduces an error of less than 1% when compared with an elliptical model. For