Validation of an Elliptical Anthropometric Model to Estimate Visceral Compartment Area Qing He,* Ellen S. Engelson,* Jack Wang,† Sonjia Kenya,* Gabriel Ionescu,* Steven B. Heymsfield,† and Donald P. Kotler*
Abstract HE, QING, ELLEN S. ENGELSON, JACK WANG, SONJIA KENYA, GABRIEL IONESCU, STEVEN B. HEYMSFIELD, AND DONALD P. KOTLER. Validation of an elliptical anthropometric model to estimate visceral compartment area. Obes Res. 2004;12:250 –257. Objective: The visceral compartment is a surrogate for visceral adipose tissue. Cross-sectional visceral compartment area (VCA) has been approximated from waist circumference using a circular model. However, the twodimensional shape of the abdomen is rarely circular. This study validated an elliptical model of cross-sectional total abdominal area (TAA), subcutaneous adipose tissue (SAT) area, and VCA at the L4–L5 level. Research Methods and Procedures: We analyzed magnetic resonance images (MRIs) at the level of the L4–L5 intervertebral space from 35 subjects with a wide range of abdominal adiposity. Waist circumference, abdominal thickness (midline sagittal diameter), abdominal width (coronal diameter at one-half of abdominal thickness), and abdominal SAT thickness at four sites (front, back, right, and left) were measured from MRI images using an image analysis software. The same anatomical regions were also estimated from anthropometrics purely by geometric formulae of circular and elliptical models. A simple linear regression model was used to interpret the association strength between anthropometric estimates and MRI measures. Results: Estimated TAA by either model was strongly re-
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 page charges. This article must, therefore, be hereby marked “advertisement” in accordance with 18 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 and Surgeons, Columbia University, New York, New York. Address correspondence to Donald P. Kotler, Division of Gastroenterology, Rm. S & R 1301, St. Luke’s-Roosevelt Hospital Center, 1111 Amsterdam Avenue, New York, NY 10025. E-mail:
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lated to MRI TAA (r2 ⫽ 0.98, p ⬍ 0.0001). The SAT and VCA by MRI analysis showed a stronger association with calculation from an elliptical model (r2 ⫽ 0.95 and 0.88, respectively; p ⬍ 0.001) than a circular model (r2 ⫽ 0.69 and 0.25, respectively; p ⬍ 0.001). The absolute prediction residuals and variances were significantly smaller with an elliptical model than a circular model (p ⬍ 0.0001). Discussion: An elliptical anthropometric model might be superior to a circular model to estimate abdominal SAT and VCA. Key words: body composition, magnetic resonance imaging, subcutaneous adipose tissue, visceral adipose tissue, anthropometrics
Introduction A large body of evidence has established associations among abdominal fat content, diabetes, and cardiovascular disease (1–3). Although studies have suggested differential strength of associations between various abdominal adipose tissue subcompartments and cardiovascular risk (4 – 6), the exact biological roles of various fat depots remain uncertain. Subcutaneous adipose tissue (SAT)1 and visceral adipose tissue (VAT) are anatomically recognized, metabolically distinct subdivisions in the abdominal region. Determination of total abdominal adiposity and its distribution might help in risk stratification. Waist circumference (WC) has long been used as a surrogate measure of total abdominal adiposity without the differentiation of SAT from VAT. WC is a direct measure of length rather than of area or volume. Defining fat distribution in the abdominal region based on WC requires transformation of length into separate area or volume. Other models, such as the use of sagittal diameter as a surrogate
1 Nonstandard abbreviations: SAT, subcutaneous adipose tissue; VAT, visceral adipose tissue; WC, waist circumference; TAA, total abdominal area; VCA, visceral compartment area; MRI, magnetic resonance imaging; SLRHC, St. Luke’s-Roosevelt Hospital Center; CI, confidence interval.
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Figure 1: (A) T1-weighted MRI axial images at the level of L4–L5 intervertebral space showing an elliptical shape of a supine abdominal cross-section. Note the thicker SAT in the posteriorlateral aspect. (B) Schematic ellipse covers almost whole area of visceral compartment, with its long (a) and short axis (b) indicated.
measure of VAT, have been proposed to achieve this goal (7). However, WC and sagittal diameter are one-dimensional variables and are not complete models for a twodimensional variable such as cross-sectional area or a threedimensional variable such as volume (8). A two-dimensional, circular model is typically used to estimate cross-section abdominal VAT area from WC {[(WC/ ⫺ X)/2]2; where X denotes skinfold thickness at the front of abdomen} (9). This model is based on two assumptions: 1) the cross-section of a human abdomen is a circle, and 2) the visceral compartment (peritoneal cavity and its muscle wall) and the surrounding SAT layer constitute two concentric circular areas. However, the crosssectional shapes of the typical abdomen and, especially, the visceral compartment are ellipses rather than circles (Figure 1A), even in obese subjects. As the rule of geometry dictates, the area surrounded with a fixed circumference on a plane reaches its maximum when circumference forms a circle (see Appendix). Thus, the circular model might overestimate total abdominal cross-sectional area (TAA). The overestimation might have consequences for the estimation of inner visceral compartment area (VCA) and, by extension, VAT, because of the close dependence of two estimations described below.
The assumption that VCA and SAT are concentric suggests that the diameter of the inner visceral compartment can be calculated by subtracting skinfold thickness from the outer diameter of TAA. However, the inner visceral compartment and outer contour are not concentric, in that SAT thickness is not uniform in the abdomen. In general, four currently used WC-measurement sites fall in a narrow interval of abdominal segment between the lowest rib and iliac crest (10). Within this window, posterior-lateral SAT is thicker than that in the front, because a large portion of deep subcutaneous adipose tissue compartment tapers off from the gluteal adipose tissue compartment (Figure 1A). However, skinfold thickness in the anterior abdomen, but not posterior skinfold thickness, is typically measured both clinically and in clinical studies. Inclusion of the biased anterior skinfold thickness into the circular model would introduce another source of error. The purpose of this study was to develop an elliptical model to estimate VCA and SAT independently. The rationale of this model is straightforward. The cross-section of a typical human visceral compartment appears to be an ellipse. Two geometrical variables, long axis (a) and short axis (b), are needed to determine the area (i.e., ab/4, of an ellipse) (Figure 1B). Thus, the key to the application of an elliptical anthropometric model for the human abdomen is to measure the long and short axes. In this retrospective study, we validated an elliptical model to estimate TAA, VCA, and SAT (TAA ⫺ VCA) by referencing direct magnetic resonance imaging (MRI) and simulating anthropometric measurements over abdominal MRI images at the level of the L4–L5 intervertebral space. MRI images were obtained from three completed clinical studies, including a wide range of SAT and VAT contents. In addition, TAA and VCA were also estimated using a circular model, as reported previously, with WC and anterior abdominal SAT thickness. The estimates of area were correlated to direct MRI-measured areas of the same anatomical region. The strength of correlation offered a gauge of precision of the estimations, whereas the prediction residuals from the model gave a gauge of accuracy of the estimates. We looked at cross-sectional data, as well as a longitudinal subgroup with duplicate measurements. Direct anthropometric measurements, as opposed to MRI simulation, on a few human subjects were made for further validation.
Research Methods and Procedures Subjects This study included pooled data from volunteers in three separate clinical studies at St. Luke’s-Roosevelt Hospital Center (SLRHC). All were approved by the SLRHC Institutional Review Board, and subjects in each study signed an informed consent form. Total body MRI was part of the OBESITY RESEARCH Vol. 12 No. 2 February 2004
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body composition measurement in these studies. Ten subjects were taken from a study that investigated the effect of recombinant growth hormone on HIV-infected patients with excessive VAT (11); eight had follow-up measures, and this subgroup was characterized by large VAT and small SAT contents. Twelve HIV-uninfected controls were included from a cross-sectional study that investigated adipocyte metabolism in controls and subjects with HIV lipodystrophy. This group was characterized by normal VAT and SAT contents. Thirteen subjects were taken from a study looking into the effect of diet and exercise on insulin resistance in HIV-infected obese women, eight of whom had follow-up measures. The subgroup was characterized by large SAT and relatively small VAT contents. Measurements MRI. 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 described in a previous report (12). Total body MRI images consist of ⬃40 slices of 10 mm thickness with 40-mm spaces between slices. We selected the level at L4–L5 intervertebral space for analysis because it was used as a reference that was consistently provided by the scanning protocol, guaranteeing easy identification with MRI. The level of L4-L5 intervertebral space for the circumference is also close to the WC measurement site recommended by the NIH (13), and the circumference was assumed to represent WC in this study. The analyses were performed on a personal computer (Gateway, Inc., North Sioux City, SD). We used three measurement tools provided by the MRI image analysis software (SliceOmatic, Version 4.0; Tomovision, Montreal, Canada) to simulate anthropometric measurement. A freehand measurement tool for a region of interest was used to determine circumference of an abdominal slice, the distance measurement tool was used to quantify the abdominal thickness and width, and the caliper measurement tool was used to measure SAT thickness (Figure 2). In such a way, WC, abdominal thickness (DAP, the sagittal diameter at the midline), abdominal width (DRL, the coronal diameter at the midlevel of thickness), and four SAT thicknesses [in the front (TF), back (TB), right (TR), and left (TL)] at the locations of diameter measuring sites were determined. (Epidermis has an insignificant signal on MRI image and was, in fact, excluded from SAT thickness.) The TAA and VCA were calculated with corresponding formulas as dictated in geometry. The calculation of the former was based on DAP and DRL, whereas calculation of the latter was based on determination of axes by subtracting right (TR) and left (TL) SAT thickness from DRL and subtracting front (TF) and back (TB) SAT from DAP. Finally, the area of SAT was obtained by subtracting VCA from TAA. The areas of the same anatomical regions were determined by an independent surfaces/volumes measurement function of the soft252
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Figure 2: A representative MRI image with three measurement tools of analysis software, a free-hand measurement tool to determine circumference (A), a distance measurement tool to determine diameters (B), and a caliper measurement tool to determine SAT thickness (C).
ware, which determined the area by counting the number of color-encoded pixels in the region. Anthropometrics. To further validate the estimation of VCA as based on anthropometric measurements using MRI analysis software, direct anthropometric measurements were performed on four standing volunteers in hospital gowns. The L4–L5 level was determined during anthropometric measurement by identifying the midpoint of a line connecting posterior iliac spines on both sides. The diameters were taken with a large ruler. The skinfolds at diameter measurement sites (at the front, back, and right) were determined with a Lange skinfold caliper (Beta Technology Inc., Cambridge, MD), and waist circumference at the same level was measured with a plastic fiber tape measure (PrymDritz USA; Spartanbrug, SC). All measurements were performed by an expert (J.W.) in the Body Composition Unit of SLRHC. The subjects also had total body MRI scans. Data Analysis and Statistics Using 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 elliptical model: the TAA was estimated as DAPDRL/4, and the VCA was estimated as (DAP ⫺ TF ⫺ TB)(DRL ⫺ TR ⫺ TL)/4. A simple linear correlation model was used to examine the association strength between MRI areas and estimated areas by each model. Paired Student’s t tests were used to compare anthropometric- and MRI-measured VCA. Bland-Altman analysis was performed to evaluate the prediction bias of VCA in an elliptical model. Data analyses
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Table 1. Estimation and MRI-measured area of abdominal compartments
2
TAA (cm ) VCA (cm2) SAT (cm2)
Circular model
Elliptical model
MRI measure
780.90 ⫾ 207.54* 534.44 ⫾ 143.48 246.46 ⫾ 151.38
680.67 ⫾ 167.24 454.37 ⫾ 106.49 226.30 ⫾ 148.64
723.52 ⫾ 188.38 406.17 ⫾ 104.29 315.35 ⫾ 186.24
* Mean ⫾ SD.
were performed with SAS statistical software (Version 8; SAS Institute, Cary, NC). The significance level was set at p ⬍ 0.05.
Results There were 35 subjects in the sample (19 men and 16 women). Ages ranged from 20 to 58 years old, and BMIs ranged from 20.7 to 37.8 kg/m2. Calculated and MRImeasured TAA, VCA, and SAT are shown in Table 1. There was a strong simple linear association between TAA estimated by the circular model and MRI-determined TAA (r2 ⫽ 0.98, p ⬍ 0.001, Figure 3A). The 95% confidence interval (CI) of the slope was 0.85 to 0.94 for TAA by circular model regressed on MRI TAA. Paired Student’s t test showed that TAA estimated with a circular model was significantly larger that MRI-derived TAA (p ⬍ 0.0001). A similarly strong association existed between TAA estimated with an elliptical model and MRI-derived abdominal area (r2 ⫽ 0.98, p ⬍ 0.001, Figure 3B). The 95% CI of the slope was 1.06 to 1.17 for TAA by elliptical model regressed on MRI TAA. A paired Student’s t test showed that estimated TAA by an elliptical model was significantly smaller than MRI TAA (p ⬍ 0.0001). It was evident that the trend line in a circular model was below the line of equality, whereas the trend line in an elliptical model was above the line of equality. The estimated SAT at L4–L5 was significantly associated with MRI SAT area using either model. However, the coefficient of determination of the regression model was stronger in an elliptical model (r2 ⫽ 0.97, p ⬍ 0.001, Figure 4A) than in a circular model (r2 ⫽ 0.72, p ⬍ 0.001, Figure 4B). The absolute prediction residue in the elliptical model was significantly smaller than that in the circular model by paired Student’s t test (p ⬍ 0.0001), and the variance of prediction residuals was significantly smaller in the elliptical model by a variance ratio F test (p ⬍ 0.0001). The 95% CI of slope for SAT by an elliptical model regressed on MRI SAT was 1.16 to 1.31. The corresponding 95% CI by a circular model was 0.81 to 1.27. The associations between the MRI-derived VCA and estimated VCA in both models were significant. Once again, the relationship was much stronger in an elliptical
Figure 3: Simple linear regression models showing the associations between estimated TAA and MRI determined areas in both the circular (A) and elliptical models (B). The lines of identity are also shown for reference.
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Figure 4: Simple linear regression models showing the associations between estimated SAT area and MRI SAT area in both the elliptical (A) and circular models (B). The lines of identity are also shown for reference.
model (r2 ⫽ 0.95, p ⬍ 0.001, Figure 5A) than in a circular one (r2 ⫽ 0.31, p ⬍ 0.001, Figure 5B). The absolute prediction residuals of SAT in a linear model were significantly smaller in an elliptical model than in a circular model by paired Student’s t test (p ⬍ 0.0001), and the variance of prediction residuals was significantly smaller than that in a circular model, as judged with a variance ratio F test (p ⬍ 0.0001). The 95% CI of slope of VCA in an elliptical model regressed on MRI VCA was 0.87 to 1.03, whereas the corresponding 95% CI in a circular model was 0.19 to 0.62. Bland-Altman analysis showed that there was a systematic offset by ⫹40 mm2 in the elliptical model to estimate VCA in reference to MRI VCA. However, there 254
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Figure 5: Simple linear regression models showing the associations between estimated VCA and MRI VCA in both the elliptical (A) and circular models (B). The lines of identity are also shown for reference.
was no estimation bias related to the magnitude of tested VCA, because the correlation between the average and the difference was not significant (r2 ⫽ 0.0079, p ⫽ 0.61, Figure 6). A similar Bland-Altman analysis showed that there was an estimation bias for VCA in a circular model, because the association between average and difference was significant (r2 ⫽ 0.132, p ⫽ 0.032). Of note, the trend line for VCA in a circular model deviated from the line of equality, whereas there was no such overt discrepancy in an elliptical model. In a pooled cohort sample of 16 subjects, which consisted of 8 subjects finishing 12 weeks of recombinant human growth hormone therapy and another 8 obese women com-
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Figure 6: The Bland-Altman analysis showing the limit of agreement between estimate of the VCA by an elliptical model and MRI-measured VCA.
pleting 12 weeks of a diet and exercise weight-loss program, the change in VCA estimated with an elliptical model was strongly related to change in MRI-detected VCA (r2 ⫽ 0.90, p ⬍ 0.001, Figure 7). In contrast, the change estimated using a circular model was moderately associated with MRI result (r2 ⫽ 0.43, p ⫽ 0.0056). The variance of prediction residue of a linear model in an elliptical model was significantly smaller than that in a circular model (p ⫽ 0.0007). Anthropometric measurements performed in four subjects and localized likewise to the MRI images showed similar
Figure 7: A simple linear relationship between change of VCA estimated with an elliptical model and MRI-detected change.
Figure 8: The relationship between MRI VCA and VCA estimated in an elliptical model based on direct anthropometric measurement.
relationships between estimates of VCA by an elliptical model and MRI measurement (Figure 8).
Discussion This study showed similarly strong associations between MRI-measured TAA and calculated estimates using either circular or elliptical models. In addition to paired Student’s t test, the overestimation by a circular model was also evidenced by 95% CI of slope for the simple linear correlation equation (Figure 1A), which was smaller than 1.0. This is consistent with forecasts by the geometrical rule that a circle covers a larger area than other possible options given a fixed circumference. On the other hand, the elliptical model gave smaller estimations, as shown by its 95% CI, which was larger than 1.0. The underestimation of TAA based on an elliptical model might be because of the fact that portions of posterior-lateral fat were unlikely to be covered by an ellipse whose axes were determined by thickness and width. Nevertheless, the elliptical model allows estimation of TAA. More importantly, calculated SAT and VCA in the elliptical model had stronger associations with MRI-determined SAT and VCA than in a circular model. Its statistical validity was further demonstrated by the significantly smaller prediction residual and variance of prediction residual. The technique also allowed separate estimation of two compartments of TAA (i.e., SAT and VCA) to be made. Estimation of volume of visceral compartment carries important practical implications. It is a surrogate measurement of VAT. Whereas waist circumference is widely used, as evidenced by its application in the National Health and Nutrition Examination Survey and its recommendation by OBESITY RESEARCH Vol. 12 No. 2 February 2004
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the NIH to keep track of obesity (11), incorporation of this elliptical model might be more helpful because of its greater strength of association with the “criterion” value and, therefore, its stronger estimation power. The technique is inexpensive and, thus, feasible for large-scale applications. Because a single MRI slice has been reported to correlate well with total abdominal VAT, application of the elliptical model at a single anatomic site might be suitable for field application. An advantage of this study was that it avoided the error introduced during positional change between measurements by simulating the circumferences, diameters, and SAT thickness on MRI images, rather than on human subjects. This presented an ideal situation to show the power of the elliptical model. The results present the upper limit of accuracy that a true elliptical model could achieve. The relationship between direct anthropometric measurement and MRI determination remained strong (Figure 8). Of note, the subjects of direct anthropometrics had their MRI images scanned in a supine position, and the anthropometric measurements were performed on standing subjects for ease of measurement. Such a position change between measurements may introduce an error. Further refinement, taking into account the effect of position change during measurement, will be needed before the model can be applied for widespread use. The limitation of the model is that it does not differentiate among the contents inside the visceral compartment (i.e., VAT, visceral organ, abdominal muscle, and vertebrae). An additional difficulty in the clinical application of the elliptical model is in measurement of the skinfold at the back, because the skin tightly adheres to the longissimus muscle in some muscular subjects. One way to address this is to use a pointed caliper to measure the distance between the umbilicus and the point on the spine at the same horizontal level on standing subjects. This distance would serve as DAP of the inner visceral compartment ellipse. The rationale for this measurement is that the anterior skin at the umbilicus adheres to the linea alba and the posterior skin adheres to the supra-spinal ligament. At these sites, there is negligible SAT, so that the technique avoids having to measure the skinfolds directly. In summary, the application of an elliptical model to estimate SAT and VCA is more precise and accurate than using a circular model in both cross-sectional and longitudinal analyses under the condition of this study. The elliptical model requires simple measurements, such as thickness (midline sagittal diameter) and width (coronal diameter), for the outer ellipse and subtraction of SAT thickness from the outer diameters for the inner ellipse. An elliptical model takes the abdominal shape into account. It also takes lack of uniform distribution of SAT into account by quantifying SAT thickness at several sites. An elliptical 256
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model offers relative independence in the estimation of SAT and VCA.
Acknowledgments This study was supported in part by NIH Grant NIDDK42618. We thank Dr. Dympna Gallagher for providing subjects for direct measurements. References 1. Ohlson LO, Larson B, Svardsudd K, et al. The influence of body fat distribution on the incidence of diabetes mellitus. 13.5 years of follow-up of participants of the study of men born in 1913. Diabetes. 1985;34:1055– 8. 2. Kannel WB, Cupples LA, Ramaswami R, Stokes J III, Kreger BE, Higgins M. Regional obesity and risk of cardiovascular disease: the Framingham Study. J Clin Epidemiol. 1991;44:183–90. 3. Rexrode RM, Carey VJ, Hennekens CH, et al. Abdominal adiposity and coronary heart disease in women. JAMA. 1998; 280:1843– 8. 4. Abate N, Garg A, Peshock RM, Stray-Gundersen J, Grundy SM. Relationships of generalized and regional adiposity to insulin sensitivity in men. J Clin Invest. 1995;96: 88 –98. 5. Kelley DE, Thaete FL, Troost F, Huwe T, Goodpaster BH. Subdivisions of subcutaneous abdominal adipose tissue and insulin resistance. Am J Physiol Endocrinol Metab. 2000;278: E941– 8. 6. Ross R, Freeman J, Hudson R, Janssen I. Abdominal obesity, muscle composition, and insulin resistance in premenopausal women. J Clin Endocrinol Metab. 2002;87:5044 –51. 7. Ohrvall M, Berglund L, Vessby B. Sagittal abdominal diameter compared with other anthropometric measurements in relation to cardiovascular risk. Int J Obes Relat Metab Disord. 2000;24:497–501. 8. van der Kooy K, Leenen R, Seidell JC, Deurenberg P, Visser M. Abdominal diameters as indicators of visceral fat: comparison between magnetic resonance imaging and anthropometry. Br J Nutr. 1993;70:47–58. 9. Wang J, Thornton JC, Russell M, Burastero S, Heymsfield S, Pierson RN Jr. Asians have lower body mass index (BMI) but higher percent body fat than do whites: comparisons of anthropometric measurements. Am J Clin Nutr. 1994;60:23– 8. 10. Wang J, Thornton JC, Bari S, et al. Comparisons of waist circumferences measured at 4 sites. Am J Clin Nutr. 2003;77: 379 – 84. 11. Engelson ES, Kotler DP, Tan Y, et al. Fat distribution in HIV-infected patients reporting truncal enlargement quantified by whole-body magnetic resonance imaging. Am J Clin Nutr. 1999;69:1162–9. 12. Ross R, Rissanen J, Pedwell H, Clifford J, Shragge P. Influence of diet and exercise on skeletal muscle and visceral adipose tissue in men. J Appl Physiol. 1996;81:2445–55. 13. National Institutes of Health. The Practical Guide Identification, Evaluation, and Treatment of Overweight and Obesity in Adults. Bethesda, MD: National Institutes of Health; 2000.
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Appendix
The circumference of a circle with radius r is C ⫽ 2r. The circumference of an ellipse with axes a and b is C ⫽ 2[(a2 ⫹ b2)/8]1/2. (Note: this formula gives an approximate circumference; the exact formula requires elliptical integrals). If the circle and the ellipse have the same circumference, then C ⫽ 2 r ⫽ 2[(a 2 ⫹ b 2)/8]1/2 Therefore, r ⫽ [(a2 ⫹ b2)/8]1/2
r 2 ⫽ (a 2 ⫹ b 2)/8 Note: (a ⫺ b)2 ⬎ 0 for all real a and b and a not equal to b: Or, a2 ⫺ 2ab ⫹ b2 ⬎ 0 Or, a2 ⫹ b2 ⬎ 2ab Using this result gives
r 2 ⫽ [(a 2 ⫹ b 2)/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).
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