Research Report
䢇
Upper-Extremity Volume
Measurements in Women with
Lymphedema: A Comparison of
Measurements Obtained Via Water
Displacement With Geometrically
Determined Volume
ўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўўў
Background and Purpose. Upper-extremity (UE) swelling following
breast cancer treatment is a frequent manifestation of lymphedema. In
order 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 determining UE volumes with water displacement methods. Subjects. The
edematous hand, forearm, and upper arm of 50 women with UE
swelling secondary to lymphedema were measured. Methods. Upperextremity volumes were determined by water displacement using arm
and hand volumeters. Displaced water was weighed to determine
volume. Circumferential girth measurements were taken. Width and
depth measurements of the hand were taken with a tension-controlled
caliper. Geometric volume formulas for a cylinder, frustum, rectangular solid, and trapezoidal solid were used to calculate volumes of the
arm and hand at different measurement intervals. Results. Intraclass
correlation coefficients [2,1] for interrater and intrarater reliability of
all water and geometric measurements of the arm and hand were .91
to .99 and .92 to .99, respectively. Water displacement correlated with
geometric measurements in the arm (r ⫽.97–.98) and in the hand
(r ⫽.81–.91). The limits of agreement (LOA) indicated that water and
geometric measurements of arm volume differed by 479 to 655 mL.
Scatterplots of the LOA data indicated in that geometric volumes were
either larger or smaller than water volumes. The smallest standard error
of measurement for the arm measurements was for the 6-cm frustum
method at 115 mL; for the hand measurements, the smallest standard
error of measurement was for the frustum method at 16 mL. Discussion
and Conclusion. Volume of an edematous UE calculated by geometric
formulas correlated strongly with volume determined by water displacement. Although strongly correlated, the measurements obtained by the 2
methods did not agree. [Sander AP, Hajer NM, Hemenway K, Miller AC.
Upper-extremity volume measurements in women with lymphedema: a
comparison of measurements obtained via water displacement with
geometrically determined volume. Phys Ther. 2002;82:1201–1212.]
Key Words: Arm and hand volume, Edema, Lymphedema, Measurement.
ўўўўўўўўўў
Antoinette P Sander, Nicole M Hajer, Kristie Hemenway, Amy C Miller
Physical Therapy . Volume 82 . Number 12 . December 2002
1201
P
rimary lymphedema is caused by impaired
lymph vessel or lymph node development, and
secondary lymphedema results from damage to
the lymphatic structures.1 Women who have
had surgical removal of axillary lymph nodes in the
treatment of breast cancer are at risk for the development of secondary lymphedema.2 The prevalence of
lymphedema in the population of women treated for
breast cancer has been estimated to be 25% to 28%,3 but
its prevalence is difficult to determine due to variability
in the definition of lymphedema and in the methods of
measuring swelling.
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
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 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.
This article was submitted March 6, 2002, and was accepted May 31, 2002.
1202 . Sander et al
Physical Therapy . Volume 82 . Number 12 . December 2002
ўўўўўўўўўўўўўўўўўўўўўўўўўўў
reviewed, the volume determined from water displacement was consistently larger than cylinder volume.12,13
Researchers evaluating the effects of lymphedema treatment have often used UE volume measurements to
determine treatment outcomes. Bunce et al17 measured
girth 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 determine
volume in 10-cm segments in 38 patients with either arm
or leg lymphedema. Zanolla et al19 measured circumference at 7 predetermined points on the arm and calculated changes in girth at these points. Sitzia 20 argued for
use of a simplified frustum formula to calculate UE
volume based on the shape of the arm more closely
resembling a frustum than a cylinder. Because of the
variations in the methods used, we believe a reliable
method of measuring swelling that includes measurements of both the arm and the hand is needed to
document outcomes and to compare interventions.
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 triangulartrapezoidal 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.
Method
Subjects
The subjects in this study were 50 women with a diagnosis of primary or secondary lymphedema and observable
swelling any place in the involved upper extremity. To
avoid a type II error, a preliminary power analysis
(power⫽0.80, effect size⫽0.35) determined a sample
size of 50 for this method-comparison study. This effect
size was chosen because it yielded a realistic sample
size,21 not because we determined any change as being
clinically meaningful. Self-report of length of time that
subjects had swelling ranged from 3 months to 37 years,
with a mean of 5 years (SD⫽6.25). The age of the
women ranged from 25 to 85 years, with a mean age of
56 years (SD⫽13.3). Subjects were recruited from Y-Me
Support groups and from physical therapy clinics in the
Chicago area. All subjects signed an informed consent
form, and the rights of subjects were protected.
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 ⫻ 20 ⫻ 76 cm) and a hand
volumeter* (10 ⫻ 14⫻ 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
* AliMed Inc, 297 High St, Dedham, MA 02026.
Physical Therapy . Volume 82 . Number 12 . December 2002
Sander et al . 1203
Figure 2.
Arm and hand water displacement: (left) demonstrates rod placement in
the empty arm volumeter, (right) demonstrates hand position for hand
water displacement.
rather than in the hand calculations because the hand
was not submerged as deeply (Fig. 2).
Water displacement for the arm was measured first. The
volumeter was filled with water to the level of the
overflow spout, and the water was allowed to stabilize11
prior to reading the water temperature and beginning
the immersion. Water temperature for both arm and
hand measurements was maintained between 28° and
32°C throughout the study, with temperature for
repeated measurements varying by a maximum of 2°C.
King23 found that volume measurements did not change
with water temperatures that varied from 20° to 35°C.
The subject immersed the arm into the volumeter,
stopping at the preset rod, and the water level on the
upper arm was marked with nonallergic tape. Ink was
used in lieu of tape to mark the water level when a
subject self-reported allergies to adhesives or tape. This
tape or mark became the upper arm point for the girth
measurements. The displaced water was collected in a
beaker and weighed (in kilograms) on a calibrated
benchtop scale (Acculab Bench Scale†). 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.
Figure 1.
Geometric volumes: (A) Geometric volume was calculated in the arm using
cylinder and frustum shapes. (B) Geometric volume was calculated in the
hand using cylinder, frustum, rectangular, and trapezoidal shapes.
1204 . Sander et al
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
†
Precision Weighing Balances, 10 Peabody St, Bradford, MA 01835-7614.
Physical Therapy . Volume 82 . Number 12 . December 2002
ўўўўўўўўўўўўўўўўўўўўўўўўўўў
Figure 3.
Figure 4.
Subject position for arm girth measurement. Subject was seated at a
table with the shoulder at 90 degrees of flexion and comfortable
horizontal abduction and the arm resting on a T square calibrated in
centimeters, with the end of the middle finger aligned at the zero
marking.
Dial caliper and tape measure: (top) dial caliper used for width and
depth hand measurements; (bottom) spring-loaded tape measure used
for arm and hand girth measurements.
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.
Girth measurements were taken of the hand and the arm
using a spring-loaded tape measure (Gulick anthropometric tape*) (Fig. 4) to maximize accuracy within and
between examiners. Hand measurements were taken at
the 3-cm markings up to the level of the hand water
displacement tape at the wrist. Arm measurements
began at this same level and continued at 3-cm segments
to the tape marking on the upper arm. The centimeter
markings on the T square were used to position the tape
measure at 3-cm segments along the arm. The final
segment length sometimes was less than 3 cm, and the
actual segment length was used in the data analysis. By
this method, the same total mass was used to calculate
water and geometric volumes. The girth measurements
in both the hand and the arm were used to calculate the
cylinder and frustum volumes.
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
‡
Physical Therapy . Volume 82 . Number 12 . December 2002
Enco Dial Calipers, 400 Nevada Pacific Hwy, Fernley, NV 89408.
Sander et al . 1205
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:
Vcylinder ⫽
(1)
1
4␲
冘 LC
n
i
2
i⫽1
where n ⫽ the number of segments, L ⫽ length of each
segment, and C ⫽ circumference of segment i.
The formula used to calculate the frustum volume was:
(2)
Vfrustum ⫽
1
12 ␲
冘 L(C
n
i
2
⫹ CiCi⫺1 ⫹ Ci⫺12)
i⫽1
where n⫽the number of segments, L⫽length of each
segment, and Ci and Ci-1⫽circumference at each end of
segment i.
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:
冘 LW D
n
Vrectangle ⫽
(3)
i
i
i⫽1
where n⫽the number of segments, L⫽length of each
segment, Wi⫽width of segment i, and Di⫽depth of
segment i.
The formula used to calculate the trapezoid volume was:
(4)
1
Vtrapezoid ⫽
4
冘 L (W ⫹ W
n
i
i⫺1)
共Di ⫹ Di⫺1兲
i⫽1
where n⫽the number of segments, L⫽length of each
segment, Wi and Wi⫺1⫽width at each end of segment i,
and Di and Di⫺1⫽depth at each end of segment i.
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.㛳
Results
Arm Data
Seven methods of obtaining volume measurements for
the arm were analyzed: water volume; cylinder 3-cm,
6-cm, and 9-cm volumes; and frustum 3-cm, 6-cm, and
9-cm volumes. The ICC (2,1) for interrater reliability for
water volume and all geometric cylinder and frustum
volumes was .99 (Tab. 1). The ICC (2,1) for intrarater
reliability from both evaluators for water and all geometric volumes also was .99 (Tab. 1). Water volume mea-
§
㛳
1206 . Sander et al
SPSS Inc, 233 S Wacker Dr, Chicago, IL 60606.
Microsoft Corp, One Microsoft Way, Redmond, WA 98052-6399.
Physical Therapy . Volume 82 . Number 12 . December 2002
ўўўўўўўўўўўўўўўўўўўўўўўўўўў
Table 1.
Intraclass Correlation Coefficients (ICC [2,1]) for Intrarater and Interrater Reliability With 95% Confidence Intervals (95% CI) for Arm Volume
Determined by Water and Geometric Methods
a
Method
Sample
Size
Intrarater
ICC
95% CI
Sample
Size
Interrater
ICC
95% CI
SEMa
Water
Cylinder, 3 cm
Cylinder, 6 cm
Cylinder, 9 cm
Frustum, 3 cm
Frustum, 6 cm
Frustum, 9 cm
25
25
25
25
25
25
25
.99
.99
.99
.99
.99
.99
.99
.96–.99
.98–.99
.98–.99
.97–.99
.98–.99
.98–.99
.97–.99
19
19
19
19
19
19
19
.99
.99
.99
.99
.99
.99
.99
.99–.99
.99–.99
.99–.99
.98–.99
.99–.99
.99–.99
.99–.99
117
120
124
130
115
114
116
SEM⫽standard error of measurement (in milliliters).
Table 2.
Arm Correlations (r), Limits of Agreement (LOA), and Percentage of
Variation Between Water and Geometric Methodsa
a
b
Method
r
LOA (mL)
% Variationb
Cylinder, 3 cm
Cylinder, 6 cm
Cylinder, 9 cm
Frustum, 3 cm
Frustum, 6 cm
Frustum, 9 cm
.98
.97
.97
.98
.98
.97
513
577
655
479
497
506
15
17
19
19
15
15
All methods are compared with water volume.
% variation⫽LOA/mean of water and geometric method.
surements correlated highly with all cylinder and frustum volume measurements (r ⫽.97–.98, P ⬍.01)
(Tab. 2). A high correlation between 2 methods of
measuring volume does not mean that the methods are
interchangeable.26
Table 2 shows the LOA for the water and geometric
volumes of the arm that were calculated to determine
whether water volume and geometric volumes are interchangeable.16,25–27 Table 2 indicates that the range of
the LOA for the arm data was 479 to 655 mL. We
calculated the percentage variation of the LOA from the
mean of the 2 methods being compared. The range of
this percentage was from 15% to 19% (Tab. 2), which is
another indication of the amount of variation in the
methods.
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
Physical Therapy . Volume 82 . Number 12 . December 2002
than the water volume. Figure 5C indicates that the
cylinder 9-cm volume was larger than the water volume.
Scatterplots were created comparing water volume measurements with all of the geometric volume measurements for the arm (cylinder 3-cm, 6-cm, and 9-cm
volumes and frustum 3-cm, 6-cm, and 9-cm volumes) to
determine both the LOA and the bias. Each of the
scatterplots indicated a bias. The frustum 3-cm, 6-cm,
and 9-cm volume measurements and the cylinder 3-cm
measurements were consistently smaller than the water
volume measurements. The cylinder 6-cm and 9-cm
volume measurements were larger than the water volume measurements.
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).
The LOA data for the hand volume methods are shown
in Table 4, indicating a range from 108 to 152 mL. We
Sander et al . 1207
calculated the percentage of variation of the LOA from
the mean of the 2 methods being compared. The
percentages of variation ranged from 18% to 24%
(Tab. 4), which is another indication of the amount of
variation in the measurements obtained with the different methods.
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.
The SEM calculations for the hand data are shown in
Table 3. The range of SEM values for the hand was 16 to
33 mL, with the frustum method of determining hand
volume having the smallest SEM at 16 mL.
Figure 5.
Scatterplots of limits of agreement for methods of arm volume measurement: (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 the
2 methods being compared is plotted against the difference between
the 2 methods. All measurements are in milliliters. Scatterplots indicate
the wide variation between the 2 methods and the bias.
1208 . Sander et al
Discussion
We found what we consider to be high interrater and
intrarater reliability (ICC [2,1]⫽.91–.99) for both water
and geometric volume methods using a large sample of
people with swelling. We found the high reliability
reported previously for water displacement methods.11 A
potential limitation of our study was the lack of blinding
for the second examiner, which may have contributed to
the high reliability ratings. Although the second examiner had recorded the first set of data, it is unlikely that
the 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 limbs
with edema is different from measuring limbs without
edema because of the tissue texture changes that accompany swelling, such as pitting and fibrosis. Both pitting
and fibrosis can respond to external pressure on the skin
that may alter the accuracy of girth measurements.
Because we studied women with swelling, our results can
be generalized to a patient population. The ICC21
reflects both the degree of correspondence and agreement among ratings. By choosing the ICC model 2, we
contend that results can be generalized to other raters
with similar characteristics, such as knowledge, training,
and experience. The high interrater and intrarater
reliability we found supports the premise that the same
and different evaluators can reliably obtain the measurements if they train together with an established protocol.
Physical Therapy . Volume 82 . Number 12 . December 2002
ўўўўўўўўўўўўўўўўўўўўўўўўўўў
Table 3.
Intraclass Correlation Coefficients (ICC [2,1]) for Intrarater and Interrater Reliability With 95% Confidence Intervals (95% CI) for Hand Volume
Determined by Water and Geometric Methods
a
Method
Sample
Size
Intrarater
95% CI
Sample
Size
Interrater
95% CI
SEMa
Water
Cylinder
Frustum
Rectangle
Trapezoid
25
25
25
25
25
.97
.99
.99
.92
.93
.94–.98
.98–.99
.98–.99
.83–.96
.85–.97
19
19
19
19
19
.97
.98
.98
.92
.91
.91–.98
.94–.99
.94–.99
.76–.96
.74–.97
22
17
16
33
33
SEM⫽standard error of measurement (in milliliters).
Table 4.
Hand Correlations (r), Limits of Agreement (LOA), and Percentage of
Variation Between Water and Geometric Methodsa
a
b
Method
r
LOA (mL)
% Variationb
Cylinder
Frustum
Rectangle
Trapezoid
.86
.81
.91
.89
133
152
108
118
21%
24%
18%
20%
All methods are compared with water volume.
% variation⫽LOA/mean of water and geometric method.
For the geometric measurements, we believe this protocol should include patient position, a predetermined
length of segment, and a tape measure that includes a
spring that standardizes how tightly the tape is pulled.
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%
Physical Therapy . Volume 82 . Number 12 . December 2002
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.
Sander et al . 1209
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.
Figure 6.
Scatterplots of limits of agreement for methods of hand volume measurement: (A) water volume
method 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 2
methods. All measurements are in milliliters. Scatterplots indicate the wide variation between
the 2 methods and the bias.
1210 . Sander et al
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.
Physical Therapy . Volume 82 . Number 12 . December 2002
ўўўўўўўўўўўўўўўўўўўўўўўўўўў
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
Physical Therapy . Volume 82 . Number 12 . December 2002
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
We compared measurements obtained with a water
volume method with calculations determined using geometric formulas in the UEs of women with swelling. We
examined arm volumes and hand volumes separately,
and we examined geometric formulas for hand volume
because measurement properties of different geometries
have not been reported in the literature. We had a
sample size of 50 subjects. We found strong interrater
and intrarater reliability (ICC [2,1]⫽.91–.99) for both
water and geometric volumes. Volume of an edematous
UE calculated by geometric formulas correlates strongly
with volume determined by water displacement (r ⫽.81–
.98, P ⬍.01). In our view, however, the differences
between the methods are too large to substitute measurements made with one method for the other. Geometric volume measurements had a bias of being larger
or smaller than water volume measurements. We recommend that the geometric formulas for calculating frustum (truncated cone) volume be used, with the hand
measured in 3-cm segments and with the arm measured
in either 6-cm or 9-cm segments. Reliable measurements
of swelling are necessary to document change as a result
of interventions or disease progression.
References
1 Weissleder H, Schuchhardt C, eds. Lymphedema Diagnosis and Therapy.
3rd ed. Cologne, Germany: Viavital Verlag GmbH; 2001.
2 Petrek JA, Pressman PI, Smith RA. Lymphedema: current issues in
research and management. CA Cancer J Clin. 2000;50:292–307.
3 Logan V. Incidence and prevalence of lymphoedema: a literature
review. J Clin Nurs. 1995;4:213–219.
4 Stanton AWB, Badger C, Sitzia J. Non-invasive assessment of the
lymphedematous limb. Lymphology. 2000;33:122–135.
5 Bednarczyk J, Hershler C, Cooper D. Development and clinical
evaluation of a computerized limb volume measurement system
(CLEMS). Arch Phys Med Rehabil. 1992;73:60 – 63.
6 Lilja M, Oberg T. Volumetric determinations with CAD/CAM in
prosthetics and orthotics: errors of measurement. J Rehabil Res Dev.
1995;32:141–148.
7 Tierney S, Aslam M, Rennie K, Grace P. Infrared optoelectronic
volumetry: the ideal way to measure limb volume. Eur J Vasc Endovasc
Surg. 1996;12:412– 417.
8 Cornish BH, Bunce IH, Ward LC, et al. Bioelectrical impedance for
monitoring the efficacy of lymphoedema treatment programs. Breast
Cancer Res Treat. 1996;38:169 –176.
9 Cornish BH, Chapman M, Hirst C, et al. Early diagnosis of lymphedema using multiple frequency bioimpedance. Lymphology. 2001;34:
2–11.
Sander et al . 1211
10 Perrin M, Guex JJ. Edema and leg volume: methods of assessment.
Angiology. 2000;51:9 –12.
20 Sitzia J. Volume measurement in lymphoedema treatment: examination of formulae. Eur J Cancer Care. 1995;4:11–16.
11 Boland R, Adams R. Development and evaluation of a precision
forearm and hand volumeter and measuring cylinder. Journal of Hand
Therapy. 1996;9:349 –358.
21 Welkowitz J, Ewen RB, Cohen J. Introductory Statistics for the Behavioral
Sciences. 3rd ed. San Diego, Calif: Harcourt Brace Jovanovich; 1982.
12 Pani SP, Vanamail P, Yuvaraj J. Limb circumference measurement
for recording edema volume in patients with filarial lymphedema.
Lymphology. 1995;28:57– 63.
13 Briele HA, Schneebaum S, Barnicle M, Briele CS. Method of
measurement for volume of an extremity. Surgery, Gynecology & Obstetrics. 1989;169:349 –351.
14 Cheah LH, Parkin A, Gilson P, et al. Limb volume measurements in
peripheral arterial disease. Clinical Physics & Physiological Measurement.
1989;10:75–79.
15 Sukul K, den Hoed PT, Johannes EJ, et al. Direct and indirect
methods for the quantification of leg volume: comparison between
water displacement volumetry, the disk model method, and the
frustum sign model method, using the correlation coefficient and the
limits of agreement. J Biomed Eng. 1993;15:477– 480.
16 Ottenbacher KJ, Stull GA. The analysis and interpretation of
method comparison studies in rehabilitation research. Am J Phys Med
Rehabil. 1993;72:266 –271.
17 Bunce IH, Mirolo BR, Hennessy JM, et al. Post-mastectomy lymphoedema treatment and measurement. Medical Journal of Australia.
1994;161:125–128.
18 Boris M, Weindorf S, Lasinski B, Boris G. Lymphedema reduction
by noninvasive complex lymphedema therapy. Oncology. 1994;8:
95–106.
19 Zanolla R, Monzeglio C, Balzarini A, Martino G. Evaluation of the
results of three different methods of postmastectomy lymphedema
treatment. J Surg Oncol. 1984;26:210 –213.
1212 . Sander et al
22 Rajapakse C, Grennan DM, Jones C, et al. Thermography in the
assessment of peripheral joint inflammation: a re-evaluation. Rheumatol
Rehabil. 1981;20:81– 87.
23 King T. The effect of water temperature on hand volume during
volumetric measurement using the water displacement method. Journal of Hand Therapy. July-September 1993:202–204.
24 Kosir MA, Rymal C, Koppolu R, et al. Surgical outcomes after breast
cancer surgery: measuring acute lymphedema. J Surg Res. 2001;95:
147–151.
25 Altman D, Bland J. Measurement in medicine: the analysis of
method comparison studies. The Statistician. 1983;32:307–317.
26 Bland JM, Altman DG. Statistical methods for assessing agreement
between two methods of clinical measurement. Lancet. 1986;1(8486):
307–310.
27 Ottenbacher KJ, Tomchek SD. Measurement variation in method
comparison studies: an empirical examination. Arch Phys Med Rehabil.
1994;75:505–512.
28 Bear-Lehman J, Abreu B. Evaluating the hand: issues in reliability
and validity. Phys Ther. 1989;69:1025–1033.
29 Sorenson M. The edematous hand. Phys Ther. 1989;69:1059 –1064.
30 Stanley BG, Tribuzi SM. Concepts in Hand Rehabilitation. Philadelphia, Pa: FA Davis Co; 1992.
31 Casley-Smith JR. Measuring and representing peripheral oedema
and its alterations. Lymphology. 1994;27:56 –70.
Physical Therapy . Volume 82 . Number 12 . December 2002