Validation of an Elliptical Anthropometric Model to Estimate Visceral Compartment Area

Validation of an Elliptical AnthropometricModel to Estimate Visceral Compartment AreaQing He,* Ellen S. Engelson,* Jack Wang,† Sonjia Kenya,* Gabriel Ionescu,* Steven B. Heymsfield,† andDonald P. Kotler*

AbstractHE, QING, ELLEN S. ENGELSON, JACK WANG,SONJIA KENYA, GABRIEL IONESCU, STEVEN B.HEYMSFIELD, AND DONALD P. KOTLER. Validationof an elliptical anthropometric model to estimate visceralcompartment area. Obes Res. 2004;12:250–257.Objective: The visceral compartment is a surrogate forvisceral adipose tissue. Cross-sectional visceral compart-ment area (VCA) has been approximated from waist cir-cumference using a circular model. However, the two-dimensional shape of the abdomen is rarely circular. Thisstudy validated an elliptical model of cross-sectional totalabdominal area (TAA), subcutaneous adipose tissue (SAT)area, and VCA at the L4–L5 level.Research Methods and Procedures: We analyzed magneticresonance images (MRIs) at the level of the L4–L5 inter-vertebral space from 35 subjects with a wide range ofabdominal adiposity. Waist circumference, abdominalthickness (midline sagittal diameter), abdominal width(coronal diameter at one-half of abdominal thickness), andabdominal SAT thickness at four sites (front, back, right,and left) were measured from MRI images using an imageanalysis software. The same anatomical regions were alsoestimated from anthropometrics purely by geometric formu-lae of circular and elliptical models. A simple linear regres-sion model was used to interpret the association strengthbetween anthropometric estimates and MRI measures.Results: Estimated TAA by either model was strongly re-

lated to MRI TAA (r2 � 0.98, p � 0.0001). The SAT andVCA by MRI analysis showed a stronger association withcalculation from an elliptical model (r2 � 0.95 and 0.88,respectively; p � 0.001) than a circular model (r2 � 0.69and 0.25, respectively; p � 0.001). The absolute predictionresiduals and variances were significantly smaller with anelliptical model than a circular model (p � 0.0001).Discussion: An elliptical anthropometric model might besuperior to a circular model to estimate abdominal SAT andVCA.

Key words: body composition, magnetic resonance im-aging, subcutaneous adipose tissue, visceral adipose tis-sue, anthropometrics

IntroductionA large body of evidence has established associations

among abdominal fat content, diabetes, and cardiovasculardisease (1–3). Although studies have suggested differentialstrength of associations between various abdominal adiposetissue subcompartments and cardiovascular risk (4–6), theexact biological roles of various fat depots remain uncertain.Subcutaneous adipose tissue (SAT)1 and visceral adiposetissue (VAT) are anatomically recognized, metabolicallydistinct subdivisions in the abdominal region. Determina-tion of total abdominal adiposity and its distribution mighthelp in risk stratification.

Waist circumference (WC) has long been used as a sur-rogate measure of total abdominal adiposity without thedifferentiation of SAT from VAT. WC is a direct measureof length rather than of area or volume. Defining fat distri-bution in the abdominal region based on WC requires trans-formation of length into separate area or volume. Othermodels, such as the use of sagittal diameter as a surrogate

Received for review June 2, 2003.Accepted in final form December 10, 2003.The costs of publication of this article were defrayed, in part, by the payment of pagecharges. This article must, therefore, be hereby marked “advertisement” in accordance with18 U.S.C. Section 1734 solely to indicate this fact.*Division of Gastroenterology and †Body Composition Unit, Obesity Research Center,Department of Medicine, St. Luke’s-Roosevelt Hospital Center, College of Physicians andSurgeons, Columbia University, New York, New York.Address correspondence to Donald P. Kotler, Division of Gastroenterology, Rm. S & R1301, St. Luke’s-Roosevelt Hospital Center, 1111 Amsterdam Avenue, New York, NY10025.E-mail: [email protected] © 2004 NAASO

1 Nonstandard abbreviations: SAT, subcutaneous adipose tissue; VAT, visceral adiposetissue; WC, waist circumference; TAA, total abdominal area; VCA, visceral compartmentarea; MRI, magnetic resonance imaging; SLRHC, St. Luke’s-Roosevelt Hospital Center; CI,confidence interval.

250 OBESITY RESEARCH Vol. 12 No. 2 February 2004

measure of VAT, have been proposed to achieve this goal(7). However, WC and sagittal diameter are one-dimen-sional variables and are not complete models for a two-dimensional variable such as cross-sectional area or a three-dimensional variable such as volume (8).

A two-dimensional, circular model is typically used toestimate cross-section abdominal VAT area from WC{�[(WC/� � X)/2]2; where X denotes skinfold thickness atthe front of abdomen} (9). This model is based on twoassumptions: 1) the cross-section of a human abdomen is acircle, and 2) the visceral compartment (peritoneal cavityand its muscle wall) and the surrounding SAT layer consti-tute two concentric circular areas. However, the cross-sectional shapes of the typical abdomen and, especially, thevisceral compartment are ellipses rather than circles (Figure1A), even in obese subjects. As the rule of geometry dic-tates, the area surrounded with a fixed circumference on aplane reaches its maximum when circumference forms acircle (see Appendix). Thus, the circular model might over-estimate total abdominal cross-sectional area (TAA). Theoverestimation might have consequences for the estimationof inner visceral compartment area (VCA) and, by exten-sion, VAT, because of the close dependence of two estima-tions described below.

The assumption that VCA and SAT are concentric sug-gests that the diameter of the inner visceral compartmentcan be calculated by subtracting skinfold thickness from theouter diameter of TAA. However, the inner visceral com-partment and outer contour are not concentric, in that SATthickness is not uniform in the abdomen. In general, fourcurrently used WC-measurement sites fall in a narrow in-terval of abdominal segment between the lowest rib andiliac crest (10). Within this window, posterior-lateral SAT isthicker than that in the front, because a large portion of deepsubcutaneous adipose tissue compartment tapers off fromthe gluteal adipose tissue compartment (Figure 1A). How-ever, skinfold thickness in the anterior abdomen, but notposterior skinfold thickness, is typically measured both clin-ically and in clinical studies. Inclusion of the biased anteriorskinfold thickness into the circular model would introduceanother source of error.

The purpose of this study was to develop an ellipticalmodel to estimate VCA and SAT independently. The ratio-nale of this model is straightforward. The cross-section of atypical human visceral compartment appears to be an el-lipse. Two geometrical variables, long axis (a) and shortaxis (b), are needed to determine the area (i.e., �ab/4, of anellipse) (Figure 1B). Thus, the key to the application of anelliptical anthropometric model for the human abdomen isto measure the long and short axes.

In this retrospective study, we validated an ellipticalmodel to estimate TAA, VCA, and SAT (TAA � VCA) byreferencing direct magnetic resonance imaging (MRI) andsimulating anthropometric measurements over abdominalMRI images at the level of the L4–L5 intervertebral space.MRI images were obtained from three completed clinicalstudies, including a wide range of SAT and VAT contents.In addition, TAA and VCA were also estimated using acircular model, as reported previously, with WC and ante-rior abdominal SAT thickness. The estimates of area werecorrelated to direct MRI-measured areas of the same ana-tomical region. The strength of correlation offered a gaugeof precision of the estimations, whereas the prediction re-siduals from the model gave a gauge of accuracy of theestimates. We looked at cross-sectional data, as well as alongitudinal subgroup with duplicate measurements. Directanthropometric measurements, as opposed to MRI simula-tion, on a few human subjects were made for further vali-dation.

Research Methods and ProceduresSubjects

This study included pooled data from volunteers in threeseparate clinical studies at St. Luke’s-Roosevelt HospitalCenter (SLRHC). All were approved by the SLRHC Insti-tutional Review Board, and subjects in each study signed aninformed consent form. Total body MRI was part of the

Figure 1: (A) T1-weighted MRI axial images at the level of L4–L5

intervertebral space showing an elliptical shape of a supine ab-dominal cross-section. Note the thicker SAT in the posterior-lateral aspect. (B) Schematic ellipse covers almost whole area ofvisceral compartment, with its long (a) and short axis (b) indicated.

Elliptical Model of the Visceral Compartment, He et al.

OBESITY RESEARCH Vol. 12 No. 2 February 2004 251

body composition measurement in these studies. Ten sub-jects were taken from a study that investigated the effect ofrecombinant growth hormone on HIV-infected patients withexcessive VAT (11); eight had follow-up measures, and thissubgroup was characterized by large VAT and small SATcontents. Twelve HIV-uninfected controls were includedfrom a cross-sectional study that investigated adipocytemetabolism in controls and subjects with HIV lipodystro-phy. This group was characterized by normal VAT and SATcontents. Thirteen subjects were taken from a study lookinginto the effect of diet and exercise on insulin resistance inHIV-infected obese women, eight of whom had follow-upmeasures. The subgroup was characterized by large SATand relatively small VAT contents.

MeasurementsMRI. The MRI scans were obtained in a 1.5-Tesla whole

body scanner (Signa LX; General Electric, Milwaukee, WI).The protocol to obtain T1-weighted images has been de-scribed in a previous report (12). Total body MRI imagesconsist of �40 slices of 10 mm thickness with 40-mmspaces between slices. We selected the level at L4–L5 in-tervertebral space for analysis because it was used as areference that was consistently provided by the scanningprotocol, guaranteeing easy identification with MRI. Thelevel of L4-L5 intervertebral space for the circumference isalso close to the WC measurement site recommended by theNIH (13), and the circumference was assumed to representWC in this study. The analyses were performed on a per-sonal computer (Gateway, Inc., North Sioux City, SD). Weused three measurement tools provided by the MRI imageanalysis software (SliceOmatic, Version 4.0; Tomovision,Montreal, Canada) to simulate anthropometric measure-ment. A freehand measurement tool for a region of interestwas used to determine circumference of an abdominal slice,the distance measurement tool was used to quantify theabdominal thickness and width, and the caliper measure-ment tool was used to measure SAT thickness (Figure 2). Insuch a way, WC, abdominal thickness (DAP, the sagittaldiameter at the midline), abdominal width (DRL, the coronaldiameter at the midlevel of thickness), and four SAT thick-nesses [in the front (TF), back (TB), right (TR), and left (TL)]at the locations of diameter measuring sites were deter-mined. (Epidermis has an insignificant signal on MRI imageand was, in fact, excluded from SAT thickness.) The TAAand VCA were calculated with corresponding formulas asdictated in geometry. The calculation of the former wasbased on DAP and DRL, whereas calculation of the latter wasbased on determination of axes by subtracting right (TR) andleft (TL) SAT thickness from DRL and subtracting front (TF)and back (TB) SAT from DAP. Finally, the area of SAT wasobtained by subtracting VCA from TAA. The areas of thesame anatomical regions were determined by an indepen-dent surfaces/volumes measurement function of the soft-

ware, which determined the area by counting the number ofcolor-encoded pixels in the region.

Anthropometrics. To further validate the estimation ofVCA as based on anthropometric measurements using MRIanalysis software, direct anthropometric measurementswere performed on four standing volunteers in hospitalgowns. The L4–L5 level was determined during anthropo-metric measurement by identifying the midpoint of a lineconnecting posterior iliac spines on both sides. The diame-ters were taken with a large ruler. The skinfolds at diametermeasurement sites (at the front, back, and right) were de-termined with a Lange skinfold caliper (Beta TechnologyInc., Cambridge, MD), and waist circumference at the samelevel was measured with a plastic fiber tape measure (Prym-Dritz USA; Spartanbrug, SC). All measurements were per-formed by an expert (J.W.) in the Body Composition Unit ofSLRHC. The subjects also had total body MRI scans.

Data Analysis and StatisticsUsing a circular model, the TAA was estimated as WC2/

4�, and the inner VCA was estimated as �(WC/2� �TF)2.TAA and VCA were also calculated using an ellipticalmodel: the TAA was estimated as �DAPDRL/4, and theVCA was estimated as �(DAP � TF � TB)(DRL � TR �TL)/4. A simple linear correlation model was used to exam-ine the association strength between MRI areas and esti-mated areas by each model. Paired Student’s t tests wereused to compare anthropometric- and MRI-measured VCA.Bland-Altman analysis was performed to evaluate the pre-diction bias of VCA in an elliptical model. Data analyses

Figure 2: A representative MRI image with three measurementtools of analysis software, a free-hand measurement tool to deter-mine circumference (A), a distance measurement tool to determinediameters (B), and a caliper measurement tool to determine SATthickness (C).



were performed with SAS statistical software (Version 8;SAS Institute, Cary, NC). The significance level was set atp � 0.05.

ResultsThere were 35 subjects in the sample (19 men and 16

women). Ages ranged from 20 to 58 years old, and BMIsranged from 20.7 to 37.8 kg/m2. Calculated and MRI-measured TAA, VCA, and SAT are shown in Table 1.

There was a strong simple linear association betweenTAA estimated by the circular model and MRI-determinedTAA (r2 � 0.98, p � 0.001, Figure 3A). The 95% confi-dence interval (CI) of the slope was 0.85 to 0.94 for TAA bycircular model regressed on MRI TAA. Paired Student’s ttest showed that TAA estimated with a circular model wassignificantly larger that MRI-derived TAA (p � 0.0001). Asimilarly strong association existed between TAA estimatedwith an elliptical model and MRI-derived abdominal area(r2 � 0.98, p � 0.001, Figure 3B). The 95% CI of the slopewas 1.06 to 1.17 for TAA by elliptical model regressed onMRI TAA. A paired Student’s t test showed that estimatedTAA by an elliptical model was significantly smaller thanMRI TAA (p � 0.0001). It was evident that the trend line ina circular model was below the line of equality, whereas thetrend line in an elliptical model was above the line ofequality.

The estimated SAT at L4–L5 was significantly associatedwith MRI SAT area using either model. However, thecoefficient of determination of the regression model wasstronger in an elliptical model (r2 � 0.97, p � 0.001, Figure4A) than in a circular model (r2 � 0.72, p � 0.001, Figure4B). The absolute prediction residue in the elliptical modelwas significantly smaller than that in the circular model bypaired Student’s t test (p � 0.0001), and the variance ofprediction residuals was significantly smaller in the ellipti-cal model by a variance ratio F test (p � 0.0001). The 95%CI of slope for SAT by an elliptical model regressed onMRI SAT was 1.16 to 1.31. The corresponding 95% CI bya circular model was 0.81 to 1.27.

The associations between the MRI-derived VCA andestimated VCA in both models were significant. Onceagain, the relationship was much stronger in an elliptical

Figure 3: Simple linear regression models showing the associa-tions between estimated TAA and MRI determined areas in boththe circular (A) and elliptical models (B). The lines of identity arealso shown for reference.

Table 1. Estimation and MRI-measured area of abdominal compartments

Circular model Elliptical model MRI measure

TAA (cm2) 780.90 � 207.54* 680.67 � 167.24 723.52 � 188.38VCA (cm2) 534.44 � 143.48 454.37 � 106.49 406.17 � 104.29SAT (cm2) 246.46 � 151.38 226.30 � 148.64 315.35 � 186.24

* Mean � SD.



model (r2 � 0.95, p � 0.001, Figure 5A) than in a circularone (r2 � 0.31, p � 0.001, Figure 5B). The absoluteprediction residuals of SAT in a linear model were signif-icantly smaller in an elliptical model than in a circularmodel by paired Student’s t test (p � 0.0001), and thevariance of prediction residuals was significantly smallerthan that in a circular model, as judged with a variance ratioF test (p � 0.0001). The 95% CI of slope of VCA in anelliptical model regressed on MRI VCA was 0.87 to 1.03,whereas the corresponding 95% CI in a circular model was0.19 to 0.62. Bland-Altman analysis showed that there wasa systematic offset by �40 mm2 in the elliptical model toestimate VCA in reference to MRI VCA. However, there

was no estimation bias related to the magnitude of testedVCA, because the correlation between the average and thedifference was not significant (r2 � 0.0079, p � 0.61,Figure 6). A similar Bland-Altman analysis showed thatthere was an estimation bias for VCA in a circular model,because the association between average and difference wassignificant (r2 � 0.132, p � 0.032). Of note, the trend linefor VCA in a circular model deviated from the line ofequality, whereas there was no such overt discrepancy in anelliptical model.

In a pooled cohort sample of 16 subjects, which consistedof 8 subjects finishing 12 weeks of recombinant humangrowth hormone therapy and another 8 obese women com-

Figure 4: Simple linear regression models showing the associa-tions between estimated SAT area and MRI SAT area in both theelliptical (A) and circular models (B). The lines of identity are alsoshown for reference.

Figure 5: Simple linear regression models showing the associa-tions between estimated VCA and MRI VCA in both the elliptical(A) and circular models (B). The lines of identity are also shownfor reference.



pleting 12 weeks of a diet and exercise weight-loss program,the change in VCA estimated with an elliptical model wasstrongly related to change in MRI-detected VCA (r2 � 0.90,p � 0.001, Figure 7). In contrast, the change estimatedusing a circular model was moderately associated with MRIresult (r2 � 0.43, p � 0.0056). The variance of predictionresidue of a linear model in an elliptical model was signif-icantly smaller than that in a circular model (p � 0.0007).Anthropometric measurements performed in four subjectsand localized likewise to the MRI images showed similar

relationships between estimates of VCA by an ellipticalmodel and MRI measurement (Figure 8).

DiscussionThis study showed similarly strong associations between

MRI-measured TAA and calculated estimates using eithercircular or elliptical models. In addition to paired Student’st test, the overestimation by a circular model was alsoevidenced by 95% CI of slope for the simple linear corre-lation equation (Figure 1A), which was smaller than 1.0.This is consistent with forecasts by the geometrical rule thata circle covers a larger area than other possible optionsgiven a fixed circumference. On the other hand, the ellip-tical model gave smaller estimations, as shown by its 95%CI, which was larger than 1.0. The underestimation of TAAbased on an elliptical model might be because of the factthat portions of posterior-lateral fat were unlikely to becovered by an ellipse whose axes were determined bythickness and width. Nevertheless, the elliptical model al-lows estimation of TAA.

More importantly, calculated SAT and VCA in the ellip-tical model had stronger associations with MRI-determinedSAT and VCA than in a circular model. Its statisticalvalidity was further demonstrated by the significantlysmaller prediction residual and variance of prediction resid-ual. The technique also allowed separate estimation of twocompartments of TAA (i.e., SAT and VCA) to be made.

Estimation of volume of visceral compartment carriesimportant practical implications. It is a surrogate measure-ment of VAT. Whereas waist circumference is widely used,as evidenced by its application in the National Health andNutrition Examination Survey and its recommendation by

Figure 6: The Bland-Altman analysis showing the limit of agree-ment between estimate of the VCA by an elliptical model andMRI-measured VCA.

Figure 7: A simple linear relationship between change of VCAestimated with an elliptical model and MRI-detected change.

Figure 8: The relationship between MRI VCA and VCA esti-mated in an elliptical model based on direct anthropometricmeasurement.



the NIH to keep track of obesity (11), incorporation of thiselliptical model might be more helpful because of its greaterstrength of association with the “criterion” value and, there-fore, its stronger estimation power. The technique is inex-pensive and, thus, feasible for large-scale applications. Be-cause a single MRI slice has been reported to correlate wellwith total abdominal VAT, application of the ellipticalmodel at a single anatomic site might be suitable for fieldapplication.

An advantage of this study was that it avoided the errorintroduced during positional change between measurementsby simulating the circumferences, diameters, and SATthickness on MRI images, rather than on human subjects.This presented an ideal situation to show the power of theelliptical model. The results present the upper limit ofaccuracy that a true elliptical model could achieve. Therelationship between direct anthropometric measurementand MRI determination remained strong (Figure 8). Of note,the subjects of direct anthropometrics had their MRI imagesscanned in a supine position, and the anthropometric mea-surements were performed on standing subjects for ease ofmeasurement. Such a position change between measure-ments may introduce an error. Further refinement, takinginto account the effect of position change during measure-ment, will be needed before the model can be applied forwidespread use.

The limitation of the model is that it does not differentiateamong the contents inside the visceral compartment (i.e.,VAT, visceral organ, abdominal muscle, and vertebrae). Anadditional difficulty in the clinical application of the ellip-tical model is in measurement of the skinfold at the back,because the skin tightly adheres to the longissimus musclein some muscular subjects. One way to address this is to usea pointed caliper to measure the distance between the um-bilicus and the point on the spine at the same horizontallevel on standing subjects. This distance would serve as DAP

of the inner visceral compartment ellipse. The rationale forthis measurement is that the anterior skin at the umbilicusadheres to the linea alba and the posterior skin adheres tothe supra-spinal ligament. At these sites, there is negligibleSAT, so that the technique avoids having to measure theskinfolds directly.

In summary, the application of an elliptical model toestimate SAT and VCA is more precise and accurate thanusing a circular model in both cross-sectional and longitu-dinal analyses under the condition of this study. The ellip-tical model requires simple measurements, such as thick-ness (midline sagittal diameter) and width (coronaldiameter), for the outer ellipse and subtraction of SATthickness from the outer diameters for the inner ellipse. Anelliptical model takes the abdominal shape into account. Italso takes lack of uniform distribution of SAT into accountby quantifying SAT thickness at several sites. An elliptical

model offers relative independence in the estimation of SATand VCA.

AcknowledgmentsThis study was supported in part by NIH Grant NIDDK-

42618. We thank Dr. Dympna Gallagher for providingsubjects for direct measurements.

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AppendixThe circumference of a circle with radius r is C � 2�r.The circumference of an ellipse with axes a and b is C �

2�[(a2 � b2)/8]1/2. (Note: this formula gives an approxi-mate circumference; the exact formula requires ellipticalintegrals).

If the circle and the ellipse have the same circumference,then

C � 2�r � 2�[(a2 � b2)/8]1/2

Therefore, r � [(a2 � b2)/8]1/2

�r2 � �(a2 � b2)/8

Note: (a � b)2 � 0 for all real a and b and a not equal to b:Or, a2 � 2ab � b2 � 0Or, a2 � b2 � 2abUsing this result gives

�r2 � �[(a2 � b2)/8) � �2ab/8 � �ab/4

The area of the circle is �r2, and the area of the ellipse is�ab/4, therefore,

Area of a circle (�r2) � area of an ellipse (�ab/4).



Validation of an Elliptical Anthropometric Model to Estimate Visceral Compartment Area

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