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2002; 82:1201-1212.PHYS THER.and Amy C MillerAntoinette P Sander, Nicole M Hajer, Kristie HemenwayDetermined VolumeObtained Via Water Displacement With GeometricallyWith Lymphedema: A Comparison of MeasurementsUpper-Extremity Volume Measurements in Women

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Upper-Extremity VolumeMeasurements in Women withLymphedema: A Comparison of

Measurements Obtained Via WaterDisplacement With GeometricallyDetermined Volume

Background and Purpose. Upper-extremity (UE) swelling followingbreast cancer treatment is a frequent manifestation of lymphedema. Inorder to document outcomes from lymphedema treatments, reliable,

valid, and practical measurements of UE swelling are necessary. The

purpose of this study was to compare geometric methods of determin-ing UE volumes with water displacement methods. Subjects. Theedematous hand, forearm, and upper arm of 50 women with UEswelling secondary to lymphedema were measured. Methods. Upper-extremity volumes were determined by water displacement using armand hand volumeters. Displaced water was weighed to determine

volume. Circumferential girth measurements were taken. Width anddepth measurements of the hand were taken with a tension-controlledcaliper. Geometric volume formulas for a cylinder, frustum, rectangu-lar solid, and trapezoidal solid were used to calculate volumes of thearm and hand at different measurement intervals. Results. Intraclasscorrelation coefficients [2,1] for interrater and intrarater reliability of

all water and geometric measurements of the arm and hand were .91to .99 and .92 to .99, respectively. Water displacement correlated withgeometric measurements in the arm (r.97.98) and in the hand(r.81.91). The limits of agreement (LOA) indicated that water andgeometric measurements of arm volume differed by 479 to 655 mL.Scatterplots of the LOA data indicated in that geometric volumes wereeither larger or smaller than water volumes. The smallest standard errorof measurement for the arm measurements was for the 6-cm frustummethod at 115 mL; for the hand measurements, the smallest standarderror of measurement was for the frustum method at 16 mL. Discussionand Conclusion. Volume of an edematous UE calculated by geometricformulas correlated strongly with volume determined by water displace-

ment. Although strongly correlated, the measurements obtained by the 2methods did not agree. [Sander AP, Hajer NM, Hemenway K, Miller AC.Upper-extremity volume measurements in women with lymphedema: acomparison of measurements obtained via water displacement withgeometrically determined volume.Phys Ther. 2002;82:12011212.]

Key Words: Arm and hand volume, Edema, Lymphedema, Measurement.

Antoinette P Sander, Nicole M Hajer, Kristie Hemenway, Amy C Miller

Physical Therapy . Volume 82 . Number 12 . December 2002 1201

Resea

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Report

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Primary lymphedema is caused by impairedlymph vessel or lymph node development, andsecondary lymphedema results from damage tothe lymphatic structures.1 Women who have

had surgical removal of axillary lymph nodes in thetreatment of breast cancer are at risk for the develop-ment of secondary lymphedema.2 The prevalence of

lymphedema in the population of women treated forbreast cancer has been estimated to be 25% to 28%,3 butits prevalence is difficult to determine due to variabilityin the definition of lymphedema and in the methods ofmeasuring swelling.

Stanton et al4 reviewed noninvasive methods of assessinglymphedema. Limb volume has been determined by avariety of sophisticated methods, including a computer-ized limb volume measurement system (CLEMS),5

computer-aided design/computer-aided manufacturing(CAD/CAM),6 infrared optoelectronic perometer tech-nique,7 multiple-frequency bioelectrical impedance,8,9

and computed tomography.4 All of these methodsrequire equipment that is not commonly available inclinics due to cost and the need for specialized training.

Two common methods of determining volume in clini-cal practice are water displacement and circumferentialmeasurements. Water volume is considered by someauthors4,10 as the gold standard for volumetric mea-surements and provides a way of including volumetricmeasurements of the hand or foot in the total limbvolume measurement. Boland and Adams11 found anintraclass correlation coefficient (ICC [2,1]) of .99 for

reliability of measurements of the volume of the hand

and forearm in 16 women and 7 men without swelling.Their method detected a change in volume as small as10 mL. Water temperatures from 20 to 32C did notaffect the volume of the segments measured. However,the water volume method of measurement provides noinformation about the shape of the extremity, cannot beused with open wounds, and can be time-consuming and

cumbersome to perform. In addition, Boland andAdams studied what we would consider a clinicallyirrelevant sample because the subjects did not haveswelling.

Girth measurements can be obtained in clinical practice,and volume can be calculated by using geometric for-mulas for a cylinder or a frustum (a truncated cone).The swollen extremity can be visualized as a series ofcylinders or frustums, and total volume is determined bysumming the volumes of individual segments (Fig. 1A).Volumetric measurements obtained with water displace-ment have been compared with cylinder or frustumvolumes in the lower extremity1215 and the upperextremity (UE).13 Although the foot was sometimesincluded in the volume calculations,12,14 we did not findany reports in which geometric volume of the hand wasincluded in the total arm volume measurement. Studieshave included people with12,14 and without13,15 swelling.Several authors12,14,15 found correlations between themethods analyzed. Sukul et al15 compared water, cylin-der, and frustum volumes in the lower extremity usingthe limits of agreement (LOA).16 They found that watervolume and cylinder volume were interchangeable, butnot water volume and frustum volume. In the studies we

AP Sander, PT, MS, CLT- LANA, is Assistant Professor of Clinical Physical Therapy, Department of Physical Therapy and Human Movement

Sciences, The Feinberg School of Medicine, Northwestern University, 645 N Michigan Ave, Suite 1100, Chicago, IL 60611

([email protected]). Address all correspondence to Ms Sander.

NM Hajer, PT, MPT, is Registry Physical Therapist, MacNeal Hospital, Berwyn, Ill, and Rehabilitation Institute of Chicago, Chicago, Ill.

K Hemenway, PT, MPT, is Staff Physical Therapist, Westlake Hospital, Melrose Park, Ill.

AC Miller, PT, MPT, CLT-LANA, is Staff Therapist, The Moorings, Arlington Heights, Ill.

All authors provided data collection and consultation (including review of manuscript before submission). Ms Sander and Ms Hajer provided

concept/idea/research design. Ms Sander and Ms Hemenway provided writing and data analysis. Ms Sander and Ms Miller provided subjects. Ms

Sander provided project management and fund procurement. Ms Hemenway provided clerical support.

This study was conducted as an elective for Ms Hajers, Ms Hemenways, and Ms Millers Master of Physical Therapy degree at Northwestern

University.

This study was approved by the Institutional Review Board of Northwestern University.

Financial support for this study was provided by the Section on Womens Health, American Physical Therapy Association.

This article was adapted from a presentation given at the American Physical Therapy Association Combined Sections Meeting; February 16, 2001;

San Antonio, Tex.

This article was submitted March 6, 2002, and was accepted May 31, 2002.

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reviewed, the volume determined from water displace-ment was consistently larger than cylinder volume.12,13

Researchers evaluating the effects of lymphedema treat-ment have often used UE volume measurements todetermine treatment outcomes. Bunce et al17 measuredgirth in 10-cm segments from the ulnar styloid process

and calculated volume using the formula for a cylinder.They did not include any measurement of the hand.Boris et al18 used the frustum formula to determinevolume in 10-cm segments in 38 patients with either armor leg lymphedema. Zanolla et al19 measured circumfer-ence at 7 predetermined points on the arm and calcu-lated changes in girth at these points. Sitzia 20 argued foruse of a simplified frustum formula to calculate UEvolume based on the shape of the arm more closelyresembling a frustum than a cylinder. Because of thevariations in the methods used, we believe a reliablemethod of measuring swelling that includes measure-ments of both the arm and the hand is needed todocument outcomes and to compare interventions.

A comparison of volume determined with water displace-ment and volume calculated with a geometric formulafor the UE of people with swelling that includes botharm and hand measurements has not been done. Webelieve that the shape of the hand is similar to both arectangular solid and a triangular trapezoidal solid. Wecalculated the following geometric volumes: (1) cylinderand frustum volumes for the arm (Fig. 1A), whichincluded the forearm and the upper arm, and (2)cylinder, frustum, rectangular, and triangular-

trapezoidal volumes for the hand (Fig. 1B).

The purposes of our study were (1) to determine theintrarater and interrater reliability of UE volume mea-surements determined from water displacement andfrom geometric formulas, (2) to determine the rela-tionship between water volume and geometric volumemeasurements, and (3) to determine whether watervolume and geometric volume measurements areinterchangeable.

Method

SubjectsThe subjects in this study were 50 women with a diagno-sis of primary or secondary lymphedema and observableswelling any place in the involved upper extremity. Toavoid a type II error, a preliminary power analysis(power0.80, effect size0.35) determined a samplesize of 50 for this method-comparison study. This effectsize was chosen because it yielded a realistic samplesize,21 not because we determined any change as beingclinically meaningful. Self-report of length of time thatsubjects had swelling ranged from 3 months to 37 years,

with a mean of 5 years (SD6.25). The age of thewomen ranged from 25 to 85 years, with a mean age of56 years (SD13.3). Subjects were recruited from Y-MeSupport groups and from physical therapy clinics in theChicago area. All subjects signed an informed consentform, and the rights of subjects were protected.

EvaluatorsOne physical therapist and 3 physical therapist studentsparticipated in the data collection. Through a pilot studyof 10 subjects without swelling, we developed a protocolfor data collection. Evaluators practiced together todevelop the method and then followed a written proto-col for data collection for each subject. The sameevaluator or different evaluators, providing data for bothintrarater and interrater analyses, made all measure-ments twice. When 2 evaluators were involved, 1 evalua-tor obtained the measurements, and the other evaluatorrecorded the data. When only 1 evaluator was involved,the first set of measurements was covered while record-ing the second set. Second evaluators were not blindedto data obtained by the first evaluator.

Water Displacement VolumeSubjects arrived and sat in the study room for 30 minutesprior to the investigators taking any measurements. Thiswas done in an effort to stabilize skin temperature withroom temperature.22 In our study, room temperatureranged from 20 to 27C, but could not be set to aconstant temperature. All compression bandages, com-pression sleeves, and jewelry were removed from theedematous UE during this time.

Both an arm volumeter* (19 20 76 cm) and a handvolumeter* (10 14 28.5 cm) were used in this studyto measure water volume of the arm and hand. Theprocedures for water displacement volume of the armand the hand were demonstrated and practiced by thesubject before water was added to the volumeter. For thearm measurements, subjects were instructed to lower thearm slowly into the volumeter and to stop when the topof the volumeter came in contact with the axilla. At thispoint, a rod was placed at the level of the second andthird finger web space. This rod became the stopping

point that determined the depth of immersion forrepeated measurements. Hand volumeters have a fixed,nonadjustable rod. For the hand measurements, subjectswere instructed to hold the hand with the palm facingmedially, to straddle the rod between the second andthird fingers, and to stop when the tip of the thumbreached the preset rod. Using the thumb rather than theweb space as the contact stopping point allowed us toinclude more of the forearm in the arm calculations

* AliMed Inc, 297 High St, Dedham, MA 02026.

Physical Therapy . Volume 82 . Number 12 . December 2002 Sander et al . 1203

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rather than in the hand calculations because the handwas not submerged as deeply (Fig. 2).

Water displacement for the arm was measured first. Thevolumeter was filled with water to the level of theoverflow spout, and the water was allowed to stabilize11

prior to reading the water temperature and beginningthe immersion. Water temperature for both arm andhand measurements was maintained between 28 and32C throughout the study, with temperature forrepeated measurements varying by a maximum of 2C.King23 found that volume measurements did not change

with water temperatures that varied from 20 to 35C.The subject immersed the arm into the volumeter,stopping at the preset rod, and the water level on theupper arm was marked with nonallergic tape. Ink wasused in lieu of tape to mark the water level when asubject self-reported allergies to adhesives or tape. Thistape or mark became the upper arm point for the girthmeasurements. The displaced water was collected in abeaker and weighed (in kilograms) on a calibratedbenchtop scale (Acculab Bench Scale). The scale had atare ability that provided for subtraction of the weight ofthe empty beaker. The kilogram weight was converted to

milliliters using the standard conversion of 1 kg1,000mL. This computation gave an accurate measurement ofthe water displaced.

Water displacement for the hand was measured next andfollowed a similar procedure. Following immersion, thewater level at the wrist was marked with nonallergic tapeor ink. This mark became the proximal end point for thehand girth measurements and the distal arm point forthe arm girth measurements. The displaced water was

Precision Weighing Balances, 10 Peabody St, Bradford, MA 01835-7614.

Figure 1.Geometric volumes: (A) Geometric volume was calculated in the arm usingcylinder and frustum shapes. (B) Geometric volume was calculated in thehand using cylinder, frustum, rectangular, and trapezoidal shapes.

Figure 2.Arm and hand water displacement: (left) demonstrates rod placement inthe empty arm volumeter, (right) demonstrates hand position for handwater displacement.



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collected in a beaker, weighed in kilograms, and con-verted to milliliters.

Hand water volume was a direct measurement of thewater displaced. Arm water volume, which included theforearm and the upper arm extending from the wrist tothe shoulder, was a derived measurement that wasdetermined by subtracting the hand water displacementvalue from the arm water displacement value.

Geometric VolumeThe distance between girth measurements determinesthe length of the segment that is used in the calculationof geometric volume. This segment length has not beenstandardized, with variations of 3 cm,15 4-cm,20 and10-cm8,17,24 reported in the literature. An arm withswelling does not have a true cylinder or frustum shapebecause the location of the swelling is variable. In orderto measure these variations in swelling, we theorized thatusing the smallest segment length reported in the liter-ature would give the most accurate geometric volumemeasurement, so we measured in 3-cm segments.

Each subject was seated at a table with the shoulder at 90degrees of flexion and comfortable horizontal abductionand with the arm resting on a T square calibrated incentimeters, with the end of the middle finger aligned atthe zero marking (Fig. 3). The hand was marked in 3-cmsegments along the third ray from the tip of the middlefinger to the tape marking the level of the hand waterdisplacement. The length of the last segment was some-times less than 3 cm due to the size of the hand, and thisactual segment length was used in the data analysis.

A dial caliper was modified with a spring load foraccuracy of tension within and between examiners(Fig. 4). This caliper was used to measure the depth andthe width of the hand at the 3-cm markings. The handwas positioned on the ulnar border for the depthmeasurements; for the width measurements, the elbowwas bent to 90 degrees with the hand in the air. Thethumb was held in anatomical position and included inthe third 3-cm segment measurement. These depth andwidth measurements were used to calculate the geomet-ric rectangular and trapezoidal volumes.

Girth measurements were taken of the hand and the armusing a spring-loaded tape measure (Gulick anthropo-metric tape*) (Fig. 4) to maximize accuracy within andbetween examiners. Hand measurements were taken atthe 3-cm markings up to the level of the hand waterdisplacement tape at the wrist. Arm measurementsbegan at this same level and continued at 3-cm segmentsto the tape marking on the upper arm. The centimetermarkings on the T square were used to position the tapemeasure at 3-cm segments along the arm. The finalsegment length sometimes was less than 3 cm, and theactual segment length was used in the data analysis. By

this method, the same total mass was used to calculatewater and geometric volumes. The girth measurementsin both the hand and the arm were used to calculate thecylinder and frustum volumes.

Data AnalysisGirth measurements of the arm were taken at 3-cmsegments, and geometric volume using formulas for acylinder and a frustum were calculated for 3-, 6-, and9-cm segments. We wanted to determine an optimal

Enco Dial Calipers, 400 Nevada Pacific Hwy, Fernley, NV 89408.

Figure 3.Subject position for arm girth measurement. Subject was seated at atable with the shoulder at 90 degrees of flexion and comfortablehorizontal abduction and the arm resting on a T square calibrated incentimeters, with the end of the middle finger aligned at the zeromarking.

Figure 4.Dial caliper and tape measure: (top) dial caliper used for width anddepth hand measurements; (bottom) spring-loaded tape measure usedfor arm and hand girth measurements.


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length of segments for use in clinical practice becausethis affects the time for taking measurements. We had 7methods for computing arm volume: water volume,cylinder volume (3, 6, and 9 cm), and frustum volume(3, 6, and 9 cm). Total arm volume was the sum of thevolumes of the geometric segments. The formula usedfor calculation of the cylinder volume was:

(1) V cylinder1

4i1

n

LCi2

where n the number of segments, L length of eachsegment, and C circumference of segment i.

The formula used to calculate the frustum volume was:

(2) V frustum1

12

i1

n

L(Ci2 CiCi1 Ci1

2)

where nthe number of segments, Llength of eachsegment, and Ciand Ci-1circumference at each end ofsegment i.

We used 5 methods for computing hand volume: watervolume, cylinder volume, frustum volume, and rectangleand trapezoid volumes. The cylinder and frustum vol-umes were calculated from the same formulas that wereused for the upper arm, but the segment length wasalways 3 cm unless the last segment was less than 3 cm.We theorized that because the hand is small, variationsin swelling might be missed if a larger segment lengthwere used. Total hand volume was the sum of thevolumes of the geometric segments. The formula used tocalculate rectangle volume was:

(3) V rectangle i1

n

L WiD i

where nthe number of segments, Llength of eachsegment, Wiwidth of segment i, and Didepth ofsegment i.

The formula used to calculate the trapezoid volume was:

(4) V trapezoid1

4

i1

n

L (Wi Wi1) Di Di1

where nthe number of segments, Llength of eachsegment, Wiand Wi1width at each end of segment i,and Diand Di1depth at each end of segment i.

An analysis of variance for repeated measures and theICC (2,1) were used to determine intrarater and inter-rater reliability for each method of computing watervolume and geometric volume for both the arm and thehand. The relationship between measurements obtainedwith the water volume and geometric volume methodswas analyzed using the Pearson product moment corre-

lation coefficient. To determine whether the 2 methodsof measuring UE volume are interchangeable, we usedthe LOA.16,2527 We calculated the standard error ofmeasurement (SEM)21 for each of the arm and handvolumes to further evaluate the measurements.

The LOA procedure involves computing the mean dif-ference between all pairs of measurements for 2 meth-ods. The standard deviation of the differences also iscalculated. If the difference between the 2 methods isnormally distributed, then 95% of the differences will liebetween 2 standard deviations from the mean differ-ence, representing the limits of agreement. The mag-nitude of difference between 2 methods of measurementthat is acceptable is a clinical decision rather than astatistical decision.16 If a difference of 2 standarddeviations from the mean difference is clinically accept-able, the 2 methods can be used interchangeably.

Data from all 50 subjects, which were collected by the 4evaluators, were used to compute the Pearson correla-tion, the LOA, and the SEM. Data from a subset of 19subjects that were collected by 2 evaluators who eachmeasured the subjects once were used in determiningthe interrater reliability. Two evaluators contributed to

the analysis of intrarater reliability. One evaluator mea-sured 17 subjects twice, and the other evaluator mea-sured 8 subjects twice, for a total of 25 subjects contrib-uting to the analysis of intrarater reliability. Data for 6subjects were not used in the reliability analysis becausethe combination of raters did not give a sufficientnumber of subjects for analysis. Analysis was performedusing SPSS 8.0 statistical software for Windows and anExcel spreadsheet.

Results

Arm DataSeven methods of obtaining volume measurements forthe arm were analyzed: water volume; cylinder 3-cm,6-cm, and 9-cm volumes; and frustum 3-cm, 6-cm, and9-cm volumes. The ICC (2,1) for interrater reliability forwater volume and all geometric cylinder and frustumvolumes was .99 (Tab. 1). The ICC (2,1) for intraraterreliability from both evaluators for water and all geomet-ric volumes also was .99 (Tab. 1). Water volume mea-

SPSS Inc, 233 S Wacker Dr, Chicago, IL 60606. Microsoft Corp, One Microsoft Way, Redmond, WA 98052-6399.



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surements correlated highly with all cylinder and frus-tum volume measurements (r.97.98, P.01)(Tab. 2). A high correlation between 2 methods of

measuring volume does not mean that the methods areinterchangeable.26

Table 2 shows the LOA for the water and geometricvolumes of the arm that were calculated to determinewhether water volume and geometric volumes are inter-changeable.16,2527 Table 2 indicates that the range ofthe LOA for the arm data was 479 to 655 mL. Wecalculated the percentage variation of the LOA from themean of the 2 methods being compared. The range ofthis percentage was from 15% to 19% (Tab. 2), which isanother indication of the amount of variation in themethods.

A scatterplot graph of the mean of the 2 methods plottedagainst the difference between the 2 methods provides avisual representation of the LOA. Figure 5 illustratestypical graphs of the LOA found for the arm methods.Figure 5 also provides information about how onemethod may give results consistently larger or smallerthan the results obtained with the other method basedon the distribution of data points above and below thezero line. In Figures 5A and 5B, the majority of the datapoints fall above the zero line, indicating that thefrustum 3-cm and frustum 6-cm volumes were smaller

than the water volume. Figure 5C indicates that thecylinder 9-cm volume was larger than the water volume.

Scatterplots were created comparing water volume mea-surements with all of the geometric volume measure-

ments for the arm (cylinder 3-cm, 6-cm, and 9-cmvolumes and frustum 3-cm, 6-cm, and 9-cm volumes) todetermine both the LOA and the bias. Each of thescatterplots indicated a bias. The frustum 3-cm, 6-cm,and 9-cm volume measurements and the cylinder 3-cmmeasurements were consistently smaller than the watervolume measurements. The cylinder 6-cm and 9-cmvolume measurements were larger than the water vol-ume measurements.

If the methods are not interchangeable, the methodwith the least variability might be the most desirable

method. We calculated the SEM, which is the standarddeviation of error distribution.21 Changes in swellingbetween treatment sessions, we believe, need to be largerthan 1.96 SEM to indicate changes in swelling and nota measurement error.21 Table 1 indicates that the rangefor the SEM for the arm data was 114 to 130 mL. Thefrustum volume calculated in 6-cm segments had thesmallest SEM at 114 mL.

Hand DataFive methods of obtaining volume measurements for thehand were analyzed: water volume and cylinder, frus-

tum, rectangle, and trapezoid volumes. Table 3 indicatesa range of ICCs for interrater reliability from .91 to .98.We pooled the data from the 2 evaluators who measuredeach subject twice to give a sample data set of 25 subjectsfor the intrarater reliability analysis, with ICCs thatranged from .92 to .99 (Tab. 3). Water volume measure-ments correlated highly with all of the geometric volumemeasurements for the hand (r.81-.91, P.01)(Tab. 4).

The LOA data for the hand volume methods are shownin Table 4, indicating a range from 108 to 152 mL. We

Table 1.Intraclass Correlation Coefficients (ICC [2,1]) for Intrarater and Interrater Reliability With 95% Confidence Intervals (95% CI) for Arm VolumeDetermined by Water and Geometric Methods

MethodSampleSize

IntraraterICC 95% CI

SampleSize

InterraterICC 95% CI SEMa

Water 25 .99 .96.99 19 .99 .99.99 117Cylinder, 3 cm 25 .99 .98.99 19 .99 .99.99 120

Cylinder, 6 cm 25 .99 .98.99 19 .99 .99.99 124Cylinder, 9 cm 25 .99 .97.99 19 .99 .98.99 130Frustum, 3 cm 25 .99 .98.99 19 .99 .99.99 115Frustum, 6 cm 25 .99 .98.99 19 .99 .99.99 114Frustum, 9 cm 25 .99 .97.99 19 .99 .99.99 116

a SEMstandard error of measurement (in milliliters).

Table 2.Arm Correlations (r), Limits of Agreement (LOA), and Percentage ofVariation Between Water and Geometric Methodsa

Method r LOA (mL) % Variationb

Cylinder, 3 cm .98 513 15Cylinder, 6 cm .97 577 17Cylinder, 9 cm .97 655 19Frustum, 3 cm .98 479 19Frustum, 6 cm .98 497 15Frustum, 9 cm .97 506 15

aAll methods are compared with water volume.b % variationLOA/mean of water and geometric method.




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calculated the percentage of variation of the LOA fromthe mean of the 2 methods being compared. Thepercentages of variation ranged from 18% to 24%(Tab. 4), which is another indication of the amount ofvariation in the measurements obtained with the differ-ent methods.

Scatterplots were drawn of the mean of the water volumemeasurements and the measurements obtained for eachgeometric volume against the difference between thewater volume measurements and the measurementsobtained for each geometric volume to visually representthe LOA and the bias. Figure 6A illustrates the compar-ison of the water volume and rectangle volume measure-ments for the hand, and Figure 6B illustrates the com-parison of the water volume and frustum volumemeasurements for the hand. In our study, the geometriccylinder, frustum, and rectangle volume measurementswere consistently larger than the water volume measure-ments, whereas the trapezoid volume measurement wassmaller.

The SEM calculations for the hand data are shown inTable 3. The range of SEM values for the hand was 16 to33 mL, with the frustum method of determining handvolume having the smallest SEM at 16 mL.

DiscussionWe found what we consider to be high interrater andintrarater reliability (ICC [2,1].91.99) for both waterand geometric volume methods using a large sample ofpeople with swelling. We found the high reliability

reported previously for water displacement methods.11Apotential limitation of our study was the lack of blindingfor the second examiner, which may have contributed tothe high reliability ratings. Although the second exam-iner had recorded the first set of data, it is unlikely thatthe examiner would remember specific numbers,because measurements were taken in 3-cm increments,resulting in a total of 16 to 24 measurements per UE,depending on the length of the limb. Measuring limbswith edema is different from measuring limbs withoutedema because of the tissue texture changes that accom-pany swelling, such as pitting and fibrosis. Both pitting

and fibrosis can respond to external pressure on the skinthat may alter the accuracy of girth measurements.Because we studied women with swelling, our results canbe generalized to a patient population. The ICC21

reflects both the degree of correspondence and agree-ment among ratings. By choosing the ICC model 2, wecontend that results can be generalized to other raterswith similar characteristics, such as knowledge, training,and experience. The high interrater and intraraterreliability we found supports the premise that the sameand different evaluators can reliably obtain the measure-ments if they train together with an established protocol.

Figure 5.Scatterplots of limits of agreement for methods of arm volume measure-ment: (A) water volume method and frustum 3-cm volume method,(B) water volume method and frustum 6-cm volume method, and (C)water volume method and frustum 9-cm volume method. The mean of the2 methods being compared is plotted against the difference betweenthe 2 methods. All measurements are in milliliters. Scatterplots indicatethe wide variation between the 2 methods and the bias.

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For the geometric measurements, we believe this proto-col should include patient position, a predeterminedlength of segment, and a tape measure that includes aspring that standardizes how tightly the tape is pulled.

The correlation between the water volume and geomet-

ric volume methods was strong, indicating a strongrelationship between the 2 methods of measuring vol-ume. Some authors5,12,14 have considered this strongcorrelation as an indication that the methods are inter-changeable. Altman and Bland25,26 discussed the pitfallsof assuming agreement from correlations. As long as thecovariation between values is uniform, the coefficient rwill remain high, even when direct agreement betweenvalues is low.27 The LOA is the statistic of choice inmethod-comparison studies,25 and this analysis is one ofthe strengths of our study.

The LOA16,2527 is a direct comparison of the resultsobtained from each method of measurement and pro-vides information about the magnitude of the disagree-ment between methods and the bias. The LOA statisticrequires good reliability for each method for the differ-ences between the methods to be demonstrated. Ifclinicians find the difference between the measurementsobtained by the 2 methods acceptable, then the methodsmay be used interchangeably. Although the volumeamount varied with the different methods that we com-pared, we believe that all of the differences for themethods were too large for the methods to be consid-ered interchangeable. The difference approached 19%

of the mean arm volume and 24% of the mean handvolume, differences that we believe are unacceptable.We argue that the LOA were too large to be acceptablefor practice and that the water and geometric methodsof measuring arm and hand volume are notinterchangeable.

Our results differed from those of Sukul et al,15 whocompared water displacement measurements and cylin-der and frustum volume measurements of the lowerextremity of 20 men without swelling. They used 3-cmsegments for the cylinder calculations and judged thecylinder and water displacement methods to be inter-changeable using the LOA, with a 156-mL differencebetween the 2 methods. To calculate the frustum vol-umes, they used only 2 circumferences, 1 at the ankleand 1 at the calf. They did not find this frustum volumemethod to be interchangeable with the water volumemethod, with a 1,042-mL difference between the 2

methods. Perhaps Sukul et al15 would have found thefrustum volume and water volume methods to be inter-changeable if they had calculated frustum volume in3-cm segments as was done for the cylinder volume. Wereplicated the 3-cm segments and used this segment sizefor calculation of both cylinder and frustum volumes of50 people with swelling. Swelling in a limb introducesvariables such as pitting and fibrosis that cannot beassumed when measuring people without swelling. Inaddition, in the absence of swelling, measurements mayhave less variability.

Consistent with other studies,10,12,13 we found variabilityin the bias of our methods, with some geometric volumemeasurements being larger and some smaller than watervolume measurements. This variation in bias is interest-ing because the same girth, depth, and width measure-ments were used to calculate all of the geometric vol-umes, with only the segment length varied in the armcalculations. In the arm, all of the frustum (3-, 6-, and9-cm) volume measurements and the 3-cm cylindervolume measurements were smaller than the water vol-ume measurements, with the cylinder 6- and 9-cm vol-ume measurementsbeing larger.

Table 3.Intraclass Correlation Coefficients (ICC [2,1]) for Intrarater and Interrater Reliability With 95% Confidence Intervals (95% CI) for Hand VolumeDetermined by Water and Geometric Methods

MethodSampleSize Intrarater 95% CI

SampleSize Interrater 95% CI SEMa

Water 25 .97 .94.98 19 .97 .91.98 22Cylinder 25 .99 .98.99 19 .98 .94.99 17

Frustum 25 .99 .98.99 19 .98 .94.99 16Rectangle 25 .92 .83.96 19 .92 .76.96 33Trapezoid 25 .93 .85.97 19 .91 .74.97 33

a SEMstandard error of measurement (in milliliters).

Table 4.Hand Correlations (r), Limits of Agreement (LOA), and Percentage ofVariation Between Water and Geometric Methodsa

Method r LOA (mL) % Variationb

Cylinder .86 133 21%Frustum .81 152 24%Rectangle .91 108 18%Trapezoid .89 118 20%

aAll methods are compared with water volume.b % variationLOA/mean of water and geometric method.




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In our study, the longer segmentschanged the bias from smaller to largerwhen using the cylinder formula forvolume. In the hand, cylinder, frustum,and rectangle volume measurementswere larger than water volume mea-surements, with only the trapezoid vol-

ume measurements being smaller. Thisvariation in hand bias is likely due tothe different formulas used to calculatethe geometric volumes. Stanton et al4

reported that serial circumferencemeasurements have an inherent ten-dency to overestimate, so a consistentbias in the geometric volume measure-ments being larger than water volumemeasurements might be expected.Because we used a spring-loaded tapemeasure and measured people withswelling, it is possible that the skin wascompressed during the girth measure-ments, which could result in circumfer-ences being smaller than they actuallywere. If so, tissue compression wouldlead to volume measured by girth beingsmaller than volumes measured withwater.

The truncated cone shape of the frus-tum appears to more accurately repre-sent the shape of the arm than thecylinder shape. Our data showed that as

the cylinder segment becomes longer(6 and 9 cm), the tendency to overesti-mate volume increases. We believe thatclinicians need to recognize bias inusing geometric measurements, andthe fact that a bias is present supportsthe conclusion that the methods arenot interchangeable.

We demonstrated that the methods arenot interchangeable, but this analysiscannot indicate which method is pref-

erable. High correlation as a measureof validity and low SEM could be usedto determine a preferable method. Cor-relation may be seen as a measure ofconcurrent validity if one of the mea-sures is considered a gold standard.21

We did not consider water volume agold standard in our study, and this ledto the method-comparison analysis.We used the SEM to make a clinicalrecommendation about volumemeasurement.

Figure 6.Scatterplots of limits of agreement for methods of hand volume measurement: (A) water volumemethod and rectangle volume method, (B) water volume method and frustum volume method.The mean of the 2 methods being compared is plotted against the difference between the 2methods. All measurements are in milliliters. Scatterplots indicate the wide variation betweenthe 2 methods and the bias.

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The SEM reflects the extent of expected error in differ-ent raters scores. Difference in measurement betweentreatment sessions that are not greater than 1.96 SEMmay be due to measurement error and may not reflectchanges in the patient. We believe that therapists shouldchoose the clinical measurement method with the small-est SEM. Table 1 indicates that, in the arm, the frustum

volumes had the smallest SEM. The variation in thefrustum volume measurements (115 mL for the 3-cmsegment, 114 mL for the 6-cm segment, and 116 mL forthe 9-cm segment) was small, so the decision of thesegment length to use becomes a clinical one based onefficiency and the best representation of the swellingthat is present in each patient. One of the advantages ofusing geometric volume measurements is that segmentalchanges in swelling can be monitored. The larger 9-cmsegment will require fewer measurements and be mostefficient to use if it provides the clinician with the bestdata on segmental swelling.

Hand edema traditionally has been measured by waterdisplacement for gross volume measurements and bygirth measurements for individual digits.28,29We studieda new way of calculating hand volume and found that ithas what we consider acceptable reliability and does nottake a lot of time to obtain the measurements. Table 3indicates the frustum and cylinder volumes had thesmallest SEM (16 and 17 mL, respectively). We hadhypothesized that a geometric shape such as a rectangleor trapezoid that more closely represents the shape ofthe hand would give a volume that would be inter-changeable with water volume. We found that all the

geometric volumes varied from water volume enoughthat the measurements obtained could not be inter-changed and that simple girth measurements can beused to calculate a hand volume with a small measure-ment error. We recommend that the frustum formula beused to calculate volume in both the arm and the hand.The frustum formula can be entered into a spreadsheetfor ease of calculation.

Although the water volume method has been consideredagold standardin volumetric measurements, we foundthat this method did not have the smallest measurement

error for either the arm or the hand. The standardprocedure is to collect the water in a graduated beakerand then visually determine the amount of water dis-placed.30 We weighed the displaced water rather thanusing a visual reading in an effort to reduce measure-ment error. Because of the difficulties in doing waterdisplacement on a regular basis, and because the geo-metric frustum volume had the smallest SEM in both thearm and the hand, we recommend using a frustumvolume calculation with measurements in 3-cm segmentsfor the hand and either 6-cm or 9-cm segments for thearm. Changes in total volume of the arm and the hand

between treatment sessions need to be greater than 130mL if using a 6-cm arm segment and greater than 132mL if using a 9-cm arm segment to reflect changes in thepatients swelling and not measurement error.21 Ourresults support other authors,20,24,31 who recommendedthe use of a frustum volume method for UE swelling.

ConclusionWe compared measurements obtained with a watervolume method with calculations determined using geo-metric formulas in the UEs of women with swelling. Weexamined arm volumes and hand volumes separately,and we examined geometric formulas for hand volumebecause measurement properties of different geometrieshave not been reported in the literature. We had asample size of 50 subjects. We found strong interraterand intrarater reliability (ICC [2,1].91.99) for bothwater and geometric volumes. Volume of an edematousUE calculated by geometric formulas correlates stronglywith volume determined by water displacement (r.81.98, P.01). In our view, however, the differencesbetween the methods are too large to substitute mea-surements made with one method for the other. Geo-metric volume measurements had a bias of being largeror smaller than water volume measurements. We recom-mend that the geometric formulas for calculating frus-tum (truncated cone) volume be used, with the handmeasured in 3-cm segments and with the arm measuredin either 6-cm or 9-cm segments. Reliable measurementsof swelling are necessary to document change as a resultof interventions or disease progression.

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2002; 82:1201-1212.PHYS THER.and Amy C MillerAntoinette P Sander, Nicole M Hajer, Kristie HemenwayDetermined VolumeObtained Via Water Displacement With GeometricallyWith Lymphedema: A Comparison of MeasurementsUpper-Extremity Volume Measurements in Women

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