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Research Reports |
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 (t-sander{at}northwestern.edu). 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
Submitted March 6, 2002;
Accepted May 31, 2002
 | Abstract |
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Key Words: Arm and hand volume • Edema • Lymphedema • Measurement
| Introduction |
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 TopAbstract Introduction MethodResultsDiscussionConclusionReferences |
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Stanton et al4 reviewed noninvasive methods of assessing lymphedema. Limb volume has been determined by a variety of sophisticated methods, including a computerized limb volume measurement system (CLEMS),5 computer-aided design/computer-aided manufacturing (CAD/CAM),6 infrared optoelectronic perometer technique,7 multiple-frequency bioelectrical impedance,8,9 and computed tomography.4 All of these methods require equipment that is not commonly available in clinics due to cost and the need for specialized training.
Two common methods of determining volume in clinical practice are water displacement and circumferential measurements. Water volume is considered by some authors4,10 as the "gold standard"; for volumetric measurements and provides a way of including volumetric measurements of the hand or foot in the total limb volume measurement. Boland and Adams11 found an intraclass 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 as 10 mL. Water temperatures from 20° to 32°C did not affect the volume of the segments measured. However, the water volume method of measurement provides no information about the shape of the extremity, cannot be used with open wounds, and can be time-consuming and cumbersome to perform. In addition, Boland and Adams studied what we would consider a clinically irrelevant sample because the subjects did not have swelling.
Girth measurements can be obtained in clinical practice, and volume can be calculated by using geometric formulas for a cylinder or a frustum (a truncated cone). The swollen extremity can be visualized as a series of cylinders or frustums, and total volume is determined by summing the volumes of individual segments (Fig. 1A). Volumetric measurements obtained with water displacement have been compared with cylinder or frustum volumes in the lower extremity12–15 and the upper extremity (UE).13 Although the foot was sometimes included in the volume calculations,12,14 we did not find any reports in which geometric volume of the hand was included in the total arm volume measurement. Studies have included people with12,14 and without13,15 swelling. Several authors12,14,15 found correlations between the methods analyzed. Sukul et al15 compared water, cylinder, and frustum volumes in the lower extremity using the limits of agreement (LOA).16 They found that water volume and cylinder volume were interchangeable, but not water volume and frustum volume. In the studies we reviewed, the volume determined from water displacement was consistently larger than cylinder volume.12,13
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A comparison of volume determined with water displacement and volume calculated with a geometric formula for the UE of people with swelling that includes both arm and hand measurements has not been done. We believe that the shape of the hand is similar to both a rectangular solid and a triangular trapezoidal solid. We calculated the following geometric volumes: (1) cylinder and frustum volumes for the arm (Fig. 1A), which included 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 the intrarater and interrater reliability of UE volume measurements determined from water displacement and from geometric formulas, (2) to determine the relationship between water volume and geometric volume measurements, and (3) to determine whether water volume and geometric volume measurements are interchangeable.
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TopAbstractIntroductionMethodResultsDiscussionConclusionReferences |
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Evaluators
One physical therapist and 3 physical therapist students participated in the data collection. Through a pilot study of 10 subjects without swelling, we developed a protocol for data collection. Evaluators practiced together to develop the method and then followed a written protocol for data collection for each subject. The same evaluator or different evaluators, providing data for both intrarater and interrater analyses, made all measurements twice. When 2 evaluators were involved, 1 evaluator obtained the measurements, and the other evaluator recorded the data. When only 1 evaluator was involved, the first set of measurements was covered while recording the second set. Second evaluators were not blinded to data obtained by the first evaluator.
Water Displacement Volume
Subjects arrived and sat in the study room for 30 minutes prior to the investigators taking any measurements. This was done in an effort to stabilize skin temperature with room temperature.22 In our study, room temperature ranged from 20° to 27°C, but could not be set to a constant temperature. All compression bandages, compression sleeves, and jewelry were removed from the edematous UE during this time.
Both an arm volumeter* (19 x 20 x 76 cm) and a hand volumeter (10 x 14x 28.5 cm) were used in this study to measure water volume of the arm and hand. The procedures for water displacement volume of the arm and the hand were demonstrated and practiced by the subject before water was added to the volumeter. For the arm measurements, subjects were instructed to lower the arm slowly into the volumeter and to stop when the top of the volumeter came in contact with the axilla. At this point, a rod was placed at the level of the second and third finger web space. This rod became the stopping point that determined the depth of immersion for repeated measurements. Hand volumeters have a fixed, nonadjustable rod. For the hand measurements, subjects were instructed to hold the hand with the palm facing medially, to straddle the rod between the second and third fingers, and to stop when the tip of the thumb reached the preset rod. Using the thumb rather than the web space as the contact stopping point allowed us to include more of the forearm in the arm calculations rather than in the hand calculations because the hand was not submerged as deeply (Fig. 2).
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). The scale had a tare ability that provided for subtraction of the weight of the empty beaker. The kilogram weight was converted to milliliters using the standard conversion of 1 kg=1,000 mL. This computation gave an accurate measurement of the water displaced. Water displacement for the hand was measured next and followed a similar procedure. Following immersion, the water level at the wrist was marked with nonallergic tape or ink. This mark became the proximal end point for the hand girth measurements and the distal arm point for the arm girth measurements. The displaced water was collected in a beaker, weighed in kilograms, and converted to milliliters.
Hand water volume was a direct measurement of the water displaced. Arm water volume, which included the forearm and the upper arm extending from the wrist to the shoulder, was a derived measurement that was determined by subtracting the hand water displacement value from the arm water displacement value.
Geometric Volume
The distance between girth measurements determines the length of the segment that is used in the calculation of geometric volume. This segment length has not been standardized, with variations of 3 cm,15 4-cm,20 and 10-cm8,17,24 reported in the literature. An arm with swelling does not have a true cylinder or frustum shape because the location of the swelling is variable. In order to measure these variations in swelling, we theorized that using the smallest segment length reported in the literature would give the most accurate geometric volume measurement, so we measured in 3-cm segments.
Each subject was seated at a table with the shoulder at 90 degrees of flexion and comfortable horizontal abduction and with the arm resting on a T square calibrated in centimeters, with the end of the middle finger aligned at the zero marking (Fig. 3). The hand was marked in 3-cm segments along the third ray from the tip of the middle finger to the tape marking the level of the hand water displacement. The length of the last segment was sometimes less than 3 cm due to the size of the hand, and this actual segment length was used in the data analysis. A dial caliper
was modified with a spring load for accuracy of tension within and between examiners (Fig. 4). This caliper was used to measure the depth and the width of the hand at the 3-cm markings. The hand was positioned on the ulnar border for the depth measurements; for the width measurements, the elbow was bent to 90 degrees with the hand in the air. The thumb was held in anatomical position and included in the third 3-cm segment measurement. These depth and width measurements were used to calculate the geometric rectangular and trapezoidal volumes.
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Data Analysis
Girth measurements of the arm were taken at 3-cm segments, and geometric volume using formulas for a cylinder and a frustum were calculated for 3-, 6-, and 9-cm segments. We wanted to determine an optimal length of segments for use in clinical practice because this affects the time for taking measurements. We had 7 methods 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 the volumes of the geometric segments. The formula used for calculation of the cylinder volume was:
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| (1) |
The formula used to calculate the frustum volume was:
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| (2) |
We used 5 methods for computing hand volume: water volume, cylinder volume, frustum volume, and rectangle and trapezoid volumes. The cylinder and frustum volumes were calculated from the same formulas that were used for the upper arm, but the segment length was always 3 cm unless the last segment was less than 3 cm. We theorized that because the hand is small, variations in swelling might be missed if a larger segment length were used. Total hand volume was the sum of the volumes of the geometric segments. The formula used to calculate rectangle volume was:
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| (3) |
The formula used to calculate the trapezoid volume was:
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| (4) |
An analysis of variance for repeated measures and the ICC (2,1) were used to determine intrarater and interrater reliability for each method of computing water volume and geometric volume for both the arm and the hand. The relationship between measurements obtained with the water volume and geometric volume methods was analyzed using the Pearson product moment correlation coefficient. To determine whether the 2 methods of measuring UE volume are interchangeable, we used the LOA.16,25–27 We calculated the standard error of measurement (SEM)21 for each of the arm and hand volumes to further evaluate the measurements.
The LOA procedure involves computing the mean difference between all pairs of measurements for 2 methods. The standard deviation of the differences also is calculated. If the difference between the 2 methods is normally distributed, then 95% of the differences will lie between ±2 standard deviations from the mean difference, representing the "limits of agreement." The magnitude of difference between 2 methods of measurement that is acceptable is a clinical decision rather than a statistical decision.16 If a difference of ±2 standard deviations from the mean difference is clinically acceptable, the 2 methods can be used interchangeably.
Data from all 50 subjects, which were collected by the 4 evaluators, were used to compute the Pearson correlation, the LOA, and the SEM. Data from a subset of 19 subjects that were collected by 2 evaluators who each measured the subjects once were used in determining the interrater reliability. Two evaluators contributed to the analysis of intrarater reliability. One evaluator measured 17 subjects twice, and the other evaluator measured 8 subjects twice, for a total of 25 subjects contributing to the analysis of intrarater reliability. Data for 6 subjects were not used in the reliability analysis because the combination of raters did not give a sufficient number of subjects for analysis. Analysis was performed using SPSS 8.0 statistical software for Windows
and an Excel spreadsheet.||
| Results |
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TopAbstractIntroductionMethodResultsDiscussionConclusionReferences |
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A scatterplot graph of the mean of the 2 methods plotted against the difference between the 2 methods provides a visual representation of the LOA. Figure 5 illustrates typical graphs of the LOA found for the arm methods. Figure 5 also provides information about how one method may give results consistently larger or smaller than the results obtained with the other method based on the distribution of data points above and below the zero line. In Figures 5A and 5B, the majority of the data points fall above the zero line, indicating that the frustum 3-cm and frustum 6-cm volumes were smaller than the water volume. Figure 5C indicates that the cylinder 9-cm volume was larger than the water volume.
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If the methods are not interchangeable, the method with the least variability might be the most desirable method. We calculated the SEM, which is the standard deviation of error distribution.21 Changes in swelling between treatment sessions, we believe, need to be larger than ±1.96 SEM to indicate changes in swelling and not a measurement error.21 Table 1 indicates that the range for the SEM for the arm data was 114 to 130 mL. The frustum volume calculated in 6-cm segments had the smallest SEM at 114 mL.
Hand Data
Five methods of obtaining volume measurements for the hand were analyzed: water volume and cylinder, frustum, rectangle, and trapezoid volumes. Table 3 indicates a range of ICCs for interrater reliability from .91 to .98. We pooled the data from the 2 evaluators who measured each subject twice to give a sample data set of 25 subjects for the intrarater reliability analysis, with ICCs that ranged from .92 to .99 (Tab. 3). Water volume measurements correlated highly with all of the geometric volume measurements for the hand (r=.81–.91, P<.01) (Tab. 4).
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Scatterplots were drawn of the mean of the water volume measurements and the measurements obtained for each geometric volume against the difference between the water volume measurements and the measurements obtained for each geometric volume to visually represent the LOA and the bias. Figure 6A illustrates the comparison of the water volume and rectangle volume measurements for the hand, and Figure 6B illustrates the comparison of the water volume and frustum volume measurements for the hand. In our study, the geometric cylinder, frustum, and rectangle volume measurements were consistently larger than the water volume measurements, whereas the trapezoid volume measurement was smaller.
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| Discussion |
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TopAbstractIntroductionMethodResultsDiscussionConclusionReferences |
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The correlation between the water volume and geometric volume methods was strong, indicating a strong relationship between the 2 methods of measuring volume. Some authors5,12,14 have considered this strong correlation as an indication that the methods are interchangeable. Altman and Bland25,26 discussed the pitfalls of assuming agreement from correlations. As long as the covariation between values is uniform, the coefficient r will remain high, even when direct agreement between values is low.27 The LOA is the statistic of choice in method-comparison studies,25 and this analysis is one of the strengths of our study.
The LOA16,25–27 is a direct comparison of the results obtained from each method of measurement and provides information about the magnitude of the disagreement between methods and the bias. The LOA statistic requires good reliability for each method for the differences between the methods to be demonstrated. If clinicians find the difference between the measurements obtained by the 2 methods acceptable, then the methods may be used interchangeably. Although the volume amount varied with the different methods that we compared, we believe that all of the differences for the methods were too large for the methods to be considered interchangeable. The difference approached 19% of the mean arm volume and 24% of the mean hand volume, differences that we believe are unacceptable. We argue that the LOA were too large to be acceptable for practice and that the water and geometric methods of measuring arm and hand volume are not interchangeable.
Our results differed from those of Sukul et al,15 who compared water displacement measurements and cylinder and frustum volume measurements of the lower extremity of 20 men without swelling. They used 3-cm segments for the cylinder calculations and judged the cylinder and water displacement methods to be interchangeable using the LOA, with a 156-mL difference between the 2 methods. To calculate the frustum volumes, they used only 2 circumferences, 1 at the ankle and 1 at the calf. They did not find this frustum volume method to be interchangeable with the water volume method, with a 1,042-mL difference between the 2 methods. Perhaps Sukul et al15 would have found the frustum volume and water volume methods to be interchangeable if they had calculated frustum volume in 3-cm segments as was done for the cylinder volume. We replicated the 3-cm segments and used this segment size for calculation of both cylinder and frustum volumes of 50 people with swelling. Swelling in a limb introduces variables such as pitting and fibrosis that cannot be assumed when measuring people without swelling. In addition, in the absence of swelling, measurements may have less variability.
Consistent with other studies,10,12,13 we found variability in the bias of our methods, with some geometric volume measurements being larger and some smaller than water volume measurements. This variation in bias is interesting because the same girth, depth, and width measurements were used to calculate all of the geometric volumes, with only the segment length varied in the arm calculations. In the arm, all of the frustum (3-, 6-, and 9-cm) volume measurements and the 3-cm cylinder volume measurements were smaller than the water volume measurements, with the cylinder 6- and 9-cm volume measurements being larger.
In our study, the longer segments changed the bias from smaller to larger when using the cylinder formula for volume. In the hand, cylinder, frustum, and rectangle volume measurements were larger than water volume measurements, with only the trapezoid volume measurements being smaller. This variation in hand bias is likely due to the different formulas used to calculate the geometric volumes. Stanton et al4 reported that serial circumference measurements have an inherent tendency to overestimate, so a consistent bias in the geometric volume measurements being larger than water volume measurements might be expected. Because we used a spring-loaded tape measure and measured people with swelling, it is possible that the skin was compressed during the girth measurements, which could result in circumferences being smaller than they actually were. If so, tissue compression would lead to volume measured by girth being smaller than volumes measured with water.
The truncated cone shape of the frustum appears to more accurately represent the shape of the arm than the cylinder shape. Our data showed that as the cylinder segment becomes longer (6 and 9 cm), the tendency to overestimate volume increases. We believe that clinicians need to recognize bias in using geometric measurements, and the fact that a bias is present supports the conclusion that the methods are not interchangeable.
We demonstrated that the methods are not interchangeable, but this analysis cannot indicate which method is preferable. High correlation as a measure of validity and low SEM could be used to determine a preferable method. Correlation may be seen as a measure of concurrent validity if one of the measures is considered a gold standard.21 We did not consider water volume a gold standard in our study, and this led to the method-comparison analysis. We used the SEM to make a clinical recommendation about volume measurement.
The SEM reflects the extent of expected error in different raters' scores. Difference in measurement between treatment sessions that are not greater than ±1.96 SEM may be due to measurement error and may not reflect changes in the patient. We believe that therapists should choose the clinical measurement method with the smallest SEM. Table 1 indicates that, in the arm, the frustum volumes had the smallest SEM. The variation in the frustum volume measurements (115 mL for the 3-cm segment, 114 mL for the 6-cm segment, and 116 mL for the 9-cm segment) was small, so the decision of the segment length to use becomes a clinical one based on efficiency and the best representation of the swelling that is present in each patient. One of the advantages of using geometric volume measurements is that segmental changes in swelling can be monitored. The larger 9-cm segment will require fewer measurements and be most efficient to use if it provides the clinician with the best data on segmental swelling.
Hand edema traditionally has been measured by water displacement for gross volume measurements and by girth measurements for individual digits.28,29 We studied a new way of calculating hand volume and found that it has what we consider acceptable reliability and does not take a lot of time to obtain the measurements. Table 3 indicates the frustum and cylinder volumes had the smallest SEM (16 and 17 mL, respectively). We had hypothesized that a geometric shape such as a rectangle or trapezoid that more closely represents the shape of the hand would give a volume that would be interchangeable with water volume. We found that all the geometric volumes varied from water volume enough that the measurements obtained could not be interchanged and that simple girth measurements can be used to calculate a hand volume with a small measurement error. We recommend that the frustum formula be used to calculate volume in both the arm and the hand. The frustum formula can be entered into a spreadsheet for ease of calculation.
Although the water volume method has been considered a "gold standard" in volumetric measurements, we found that this method did not have the smallest measurement error for either the arm or the hand. The standard procedure is to collect the water in a graduated beaker and then visually determine the amount of water displaced.30 We weighed the displaced water rather than using a visual reading in an effort to reduce measurement error. Because of the difficulties in doing water displacement on a regular basis, and because the geometric frustum volume had the smallest SEM in both the arm and the hand, we recommend using a frustum volume calculation with measurements in 3-cm segments for the hand and either 6-cm or 9-cm segments for the arm. Changes in total volume of the arm and the hand between treatment sessions need to be greater than 130 mL if using a 6-cm arm segment and greater than 132 mL if using a 9-cm arm segment to reflect changes in the patient's swelling and not measurement error.21 Our results support other authors,20,24,31 who recommended the use of a frustum volume method for UE swelling.
| Conclusion |
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TopAbstractIntroductionMethodResultsDiscussionConclusionReferences |
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| Footnotes |
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This study was conducted as an elective for Ms Hajer's, Ms Hemenway's, and Ms Miller's 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 Women's 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.
* AliMed Inc, 297 High St, Dedham, MA 02026. 
Precision Weighing Balances, 10 Peabody St, Bradford, MA 01835-7614.
Enco Dial Calipers, 400 Nevada Pacific Hwy, Fernley, NV 89408.
SPSS Inc, 233 S Wacker Dr, Chicago, IL 60606.
|| Microsoft Corp, One Microsoft Way, Redmond, WA 98052-6399.
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