Link to Figures Show Figures
	Article Text Figures References
	Send Link Send HTML Article

Three-Dimensional Lower-Extremity Residua Measurement Systems Error Analysis

Michael W. Vannier, MD
Paul K. Commean
Kirk E. Smith

ABSTRACT

Accurate and reproducible geometric measurement of lower-extremity residua is required for custom prosthetic socket design. The authors compared three-dimensional electromagnetic point digitizer, spiral X-ray computed tomography (SXCT) and three-dimensional optical surface scanning (OSS) with caliper measurements and evaluated the precision and accuracy of each system.

Digitizer, SXCT and OSS were used to measure lower-limb residuum geometry of 13 transtibial adult amputees. Six markers were placed on each subject's residuum and corresponding positive plaster models, and distance measurements were taken to determine precision and accuracy for each system.

The digitizer, SXCT and OSS measurements were precise within 1 percent in vivo and 0.5 percent on positive plaster models. When compared with caliper measures, these measures were within 2 percent in vivo and 1 percent on positive plaster models.

SXCT and three-dimensional optical surface-imaging systems, which are feasible for capturing the comprehensive three-dimensional surface geometry of transtibial residua, provide distance measurements statistically equivalent to calipers. In addition, SXCT can readily distinguish internal soft tissue and bony structure of the residuum.

Key Words: Lower-Limb Prosthetics, Anthropometry, Spiral/Helical Computed Tomography, Surface Digitization.

Introduction

Lower-limb amputations are common; approximately 60,000 occur each year in the United States (1). Postamputation quality of life and potential for return to work are influenced significantly by the quality of lower-limb prosthesis fit (2). The authors studied the performance of a three-dimensional electromagnetic point digitizer, three-dimensional optical surface scanner (OSS) and spiral X-ray computed tomography (SXCT) imaging applied to the measurement of lower-limb residua geometry. These systems were selected for evaluation since they may facilitate custom prosthesis production by providing accurate noncontact limb remnant measurements.

Measurement techniques for residuum surface geometry should be accurate, reproducible and time efficient. Traditionally, measurement of the subject's residuum has been made in one and two dimensions by rulers, tape measures and calipers. The three-dimensional surface shape of the residuum is conventionally captured in a negative plaster impression of the residuum. Major limitations to traditional measuring devices and methods include 1) operator idiosyncrasies in performing measurements; 2) surface data cannot be stored for future socket modification; 3) once the prosthetist modifies the positive plaster model to form the socket, the original shape information is lost; and 4) only measurement of external surfaces is possible.

Three-dimensional OSS overcomes two of these limitations of traditional measuring attempts since, with OSS, the external surface can be captured repeatedly and stored for later use in check socket fabrication. However, three-dimensional optical surface scans do not contain internal residual-limb structural information.

Limitations of surface scanning are overcome with spiral volumetric CT scanning as it provides comprehensive surface and subsurface information. CT data can be registered with three-dimensional optical surface data for comparison when nonchanging landmark locations are used in the registration process. The optical surface scanner can be used for longitudinal examination, thereby limiting the subject's exposure to X-radiation. More recently, SXCT has become available (3) and is capable of scanning a subject in seconds as compared to minutes with conventional CT.

Shape information obtained from an optical surface scanner and SXCT along with the measurements can be used to customize the fit of prosthetic devices fabricated with CAD/CAM systems (4). Before new three-dimensional measuring devices are adopted for prosthetic fitting, they should be validated on both subjects and their plaster models with known precision and repeatability (5). The authors developed methods to measure and model lower-extremity residua and performed a study to demonstrate the validity of the proposed method. Precision and accuracy of the new devices were determined and proven suitable for measurement of lower-extremity residua morphology.

While many subjects can be successfully fitted with only a few check sockets, many subjects remain inaccurately fitted by currently available methods, causing them to seek other employment (2). Subjects' potential for recovery and reintegration into the work force (performing their original jobs following the prosthesis fitting process) may be greatly improved by application of more sophisticated data-capture techniques and better fitting methods to eliminate the pain or complications associated with improper fit. The clinical significance of noncontact modalities, which automatically capture both external and internal information for use in the complex fitting procedure, can be substantial.

The authors compared anthropometric measurements of transtibial residua obtained using calipers, three-dimensional electromagnetic digitizer, three-dimensional OSS and SXCT scanner in a population of transtibial amputees (see Figure 1a , Figure 1b , and Figure 1c ). Precision and accuracy of the digitizer, OSS and SXCT were compared with direct manual caliper results from each subject's residuum and corresponding positive plaster model replica. The plaster model is not subject to change due to edema and motion artifact when testing the measuring devices.

The authors previously reported on repeatability and precision of residual-limb measurement systems, which included data from both measurement sessions for all subjects who participated in the study (6). The caliper and SXCT measurement precision was found to be less than 1 mm. The measurement deviations for the SXCT, digitizer (DIG) and OSS measurement devices, when compared to the caliper measurements, were found to be 3.48 mm, 2.11 mm and 1.86 mm, respectively (6). A separate analysis was performed on the 13 subjects who attended the first measurement session to find the source of the larger (3.48-mm) error in SXCT measurements on the subject's residuum as compared to the digitizer and OSS errors.

The results from the analysis presented in this article indicate the SXCT measurements made in the axial direction (long axis of the tibia) of the residuum deviated less than the crosswise measurements and the soft-tissue envelope thickness (STET), normal to the tibia, measurements on the residuum, when compared to the caliper measurements. The larger measurement deviations in the STET and cross measurements are attributed to the subject's recumbent posture, with the residuum lying relaxed on the SXCT table versus being tensed while suspended in air when the caliper, digitizer and OSS measurements were taken. Therefore, the SXCT scanner provides measurements equivalent to the digitizer and OSS measurements if adjusted for postural change.

Two additional subjects have been SXCT scanned with their residual limbs suspended in air and the measurements compared to those obtained by calipers. The results indicate these SXCT cross and STET measurement deviations were reduced to a level consistent with the axial measurements on the SXCT data in the initial 13-subject study.

Methods

Equipment

A three-dimensional electromagnetic point digitizer was used to measure the distances between points on the subject's residuum. This digitizer was proved to provide precise and repeatable measurements when compared to caliper measurements for measuring human skulls (7).

The authors developed and tested a three-dimensional optical surface scanner (OSS) to acquire, process and display the human head surface (8-10). The OSS technology was adapted for noncontact lower-extremity residua measurement by designing a new system employing four integrated stationary sensors positioned to cover the entire limb remnant surface (11). This scanner is capable of digitizing a subject's residuum in 0.75 seconds, followed by surface reconstruction and display on a graphics workstation.

The three-dimensional OSS system used in this study employs a stationary (10), multiple-sensor, fixed geometry (see Figure 1b) . The camera/projector sensors are arranged to view the residual-limb surface in overlapping segments. The stationary sensors eliminate mechanical motion required by some sensors, and 360-degree coverage is achieved in 0.75 seconds. The multiple sensors can be positioned to reach portions of the residuum surface, such as the distal end, which perhaps is not viewable by other scanning methods. The number of sensors chosen (i.e., four) was based on the surface complexity, thus matching the system to the problem.

The OSS consists of four cameras and three projectors, which were arranged (see Figure 1b) around a cubic metal frame to capture a 38-cm cube enveloping either the subject's transtibial or transfemoral residuum. The instrument and its operation are similar to the Cencit human head scanner and are described in detail in previous publications (8-10).

In making use of computed tomography, the authors found the advantages of spiral CT (which has been available for experimental and clinical use for several years) over conventional CT are considerable reduction in radiation dosage and scan time as well as improved definition of soft tissues. These advantages allowed the authors to perform a measurement study on the subjects' residua in a more complete and precise manner without subjecting the patients to unnecessary additional radiation exposure.

The authors generated three-dimensional reconstructions of residua from an isotropic data volume synthesized from continuous two-dimensional spiral X-ray CT slices. SXCT's dimensional determinations were validated to evaluate SXCT's potential for development of new prosthetic fitting methods (12-14). Spiral CT enables volumetric imaging with markedly reduced scan time (32 seconds) compared to conventional step and shoot CT (30 minutes) (3).

Experimental Design

The experimental design (see Figure 2) for a single measurement session consisted of enrolling the subject in the prosthetic fitting system project and obtaining informed consent.

Second, the subject's prosthesis was removed and volume measurements obtained by applying Archimedes' principle of weighing the volume of displaced water.

Next, calipers were used to obtain distance measurements between all possible combinations of six marks placed on the subject's residuum (i.e., 15 total measurements). An electromagnetic point digitizer was employed to obtain the three-dimensional coordinates of the six marker locations. The subject was seated in the optical surface scanner, and scans were taken to allow measurements between the dots to be obtained from the surface data.

A negative plaster impression was made of the subject's residuum to enable a positive plaster model to be made for comparing measurements of the model to the subject's residuum.

Finally, SXCT scans were taken of the subject's residuum to allow measurements between the markers to be acquired from the three-dimensional volumetric data.

To determine error due to subject movement during scan acquisition and marker movement (due to soft tissue shape change) between measurement systems, positive plaster models of the subjects' residua also were evaluated as an independent standard. Each marker location was transferred to the plaster positive from the subject's residuum during the negative plaster impression process. The positive plaster model was scanned twice using the OSS and SXCT. The plaster positives allowed the authors to eliminate changing variables and obtain the best possible precision and accuracy when using precision digital calipers^c, point digitizer, three-dimensional optical surface scanner and SXCT scanner.

Transtibial Residua Marker Measurements

To determine the measurement locations for the transtibial residuum, the subject's residuum was immersed and positioned in a water bath (used to measure residuum volume) to a point approximately in the middle of the patellar tendon. Three marks were placed on the residuum using a permanent ink marker at the water level: The first mark (labeled marker 3 in Figure 3 ) was placed at the approximate center of the patellar tendon, with two additional marks (labeled markers 1 and 2 in Figure 3 ) located approximately 120 degrees on either side of the first. After the volume of the subject's residuum was determined using Archimedes' principle of weighing the volume of water displaced by the subject's residuum, three additional marks were placed distally (from the first three) along the length of the residuum after the subject removed his or her limb from the water bath.

Distance measurements were repeated twice using calipers (see Figure 1a) between the various pairwise combinations of the six marker centers located on the subject, which produced two distance measurement sets of 15 measurements each for the calipers. Repeated measurements of each marker location pair on the residuum were required to estimate measurement error introduced by the operator. The point digitizer was positioned in the center of each marker location, and the three-dimensional coordinates were obtained for all six markers. The six measurements were repeated a total of four times to produce four measurement sets. The distance between the various combinations of three-dimensional coordinates for the six markers were calculated to produce four sets of 15 distance measurements each for the point digitizer. This measurement process also was repeated for each plaster positive.

After measuring the residua using the point digitizer, 0.635-cm-diameter colored dots were applied to the permanent marker locations. The dots were required for making measurements with the three-dimensional optical surface scanner. Subjects were scanned twice using the prosthetic three-dimensional optical surface scanner without moving the dots (see Figure 1b) . The three-dimensional surface data for each of the two scans were processed and measured using a program written with the PV-Waved (15) command language. The center of each dot was located and digitized using a point-and-click computer mouse. The PV-Wave software automatically calculated the distances between dots. Measurements were performed twice to determine error introduced during landmark digitization for each surface data set.

Upon completion of the surface scans, conventional radiography/CT markerse containing 1.5-mm-diameter spheres located in the center of the radiographic markers were centered on the colored 0.635-cm dots. The prosthetist then placed a thin sock on the subject's residuum and marked the sphere locations on the sock with a transferable ink. The negative plaster impression was made with minimal application of pressure except in the patellar tendon region, which assisted in model orientation during subsequent measurements. When the positive plaster model was made, the ink marks and sphere locations were visible on the model.

The subjects were transported to the SXCT scanner and scanned with the radiographic CT markers in place (see Figure 1c) . The subjects would lie supine on the SXCT table as shown in Figure 1c , and a topogram was taken as shown in Figure 3 . The topogram allowed the SXCT operator to position the table so the SXCT scan would begin several millimeters below the distal end of the residuum enabling the entire residuum volume to be captured. Approximately 256 mm of the subject's residuum was scanned using 8 mm/second table feed over a continuous 32-second scan period. Scans were repeated to aid in error determination. The SXCT scanning parameters were collimation of 8 mm, table feed of 8 mm/second 120 kVp, 210 mAs, gantry tilt of 0 degrees, and maximum scan time of 32 seconds. The raw three-dimensional image data were stored on a write-once, read-many (WORM) optical diskf and processed on a satellite evaluation consoleg. The three-dimensional voxel images were read into ANALYZE? (16-20) software. The coordinates of the six 1.5-mm sphere locations were identified and the distances between the markers calculated.

The plaster positive model for each subject was measured and scanned using the same procedure described above. During the OSS and SXCT scans, the model was scanned twice without moving the model, ideally guaranteeing the two data sets would be automatically superimposed.

Population

Thirteen adult amputees were recruited to participate in this transtibial study (nine males and four females between 31 and 76 years old, average age of 49.15 years and a median age of 49). The authors obtained the subjects' informed consent approved by the Institutional Review Board of Washington University. Since St. Louis and the surrounding area are populated predominantly by Caucasians and African-Americans, the authors included only these two racial groups in this study. Three of the 13 subjects were African-Americans (two females and one male).

Results

The OSS and SXCT cannot directly measure the distance between the marker locations; the operator in this study used a "point-and-click" method to identify and locate the six marker locations (digitize) for the OSS and SXCT scan data sets displayed on a graphics monitor. A surface measurement program developed using PV-Wave was employed to compute the three-dimensional coordinates directly from the OSS data for each marker and automatically calculate the measurement distances between the various pairwise combinations of markers. ANALYZE was used to determine the three-dimensional coordinates directly from the SXCT data (see Figure 4) .

Precision

Precision is the closeness of repeated measurements of the same quantity. The 15 unique distances between six operator-selected markers comprise a complete measurement set. The operator digitized the six markers for a single scan twice to produce two separate sets of 15 measurements. These measurement sets are labeled "1A" and "1B," the "direct measurements" shown in Figure 5 . The second surface scan of the same residuum was digitized twice and the measurement sets labeled "2A" and "2B." The distance measurements between 1A and 1B were compared by determining the absolute difference between homologous marker positions. These 15 absolute differences for a single subject were averaged to produce a single average difference for scan 1; this process was repeated for scan 2. The analysis of both scans of each subject averaged for all subjects in the study is shown in Table A , which indicates the measure of error due to the operator's digitizing process at the "direct measurement" level. The average distance measurements at the measurement level for all subjects in the study are shown in Table B .

Second, the direct measurements labeled 1A and 1B were averaged, and 2A and 2B distances were averaged; as a result, two indirect scan measurements, labeled 1 and 2, respectively, were produced. The indirect scan measurements were compared by calculating the absolute difference between homologous markers taken between scans 1 and 2. These 15 absolute differences for a single subject were averaged to produce a single average difference at the indirect scan measurement level. The scan analysis for all subjects in the study is shown in Table C , which indicates the measure of error due to the operator's digitizing process and the measurement device. The average distance measurements at the scan level are shown in Table D .

Accuracy

Accuracy is the closeness of a measured or computed value to its true value. The authors considered caliper measurements were "truth" in this investigation. Accuracy (measurement deviation for the digitizer, OSS and SXCT as compared to calipers) was determined by taking the absolute difference of distance measurements between homologous marker positions for each measurement device (digitizer, OSS or SXCT) and the physical caliper measurements. These 15 absolute differences for a single subject were averaged to produce a single average difference for each measurement acquired on scan 1. This process was repeated for scan 2. The analyses of both scans for each subject averaged for all subjects in the study are shown in Table E , which indicates the measure of error due to the operator's digitizing process at the direct measurement level.

Second, the direct measurements labeled 1A and 1B were averaged, and 2A and 2B were averaged; as a result, two indirect scan measurements labeled 1 and 2, respectively, were produced. These 15 absolute differences for a single subject were averaged to produce a single average difference at the indirect scan measurement level. The analyses for all subjects in the study were found to be similar to those shown in Table E , which indicates the measure of error due to the operator's digitizing process and the measurement device.

The accuracy of the SXCT for the 13 subjects obtained during a single measurement session was 3.59 mm, as compared to 2.29 and 2.41 mm for the digitizer and OSS, respectively. These errors were similar to those found when both measurement sessions were analyzed (7). The digitizer, OSS and SXCT data were analyzed by separating the 15 various measurements into three groups (called STET, axial and cross) to isolate the errors in measurement precision (see Figure 6) . The STET, axial and cross measurement mean accuracies were found to be 0.69 mm, 0.86 mm and 0.92 mm, respectively, on the positive plaster models as shown in Table F for SXCT measurement. The STET, axial and cross measurement mean differences as compared to caliper measurements were found to be 3.95 mm, 2.11 mm and 3.98 mm, respectively, on the subjects as shown in Table F for SXCT measurement. Therefore, the mean axial measurements (2.11 mm) on the subjects using the SXCT scan are smaller than the 2.5 mm recommended by Krouskop et al. (21) for making vertical measurements and are comparable to the 2.29-mm and 2.41-mm accuracy of the digitizer and OSS, respectively, as found in Table E . The SXCT, STET and cross measurement accuracy errors can be attributed to the subjects' residua changing shape while they lay relaxed on the SXCT table. The STET, axial and cross measurement accuracy errors for the model measurements are all approximately 1.0 mm or smaller.

Discussion

Using the previously described analysis method for each measurement device, we found the measurement and scan precision for the 13 subjects' residua and models measured with the calipers, digitizer, OSS and spiral X-ray CT (SXCT) scanner to be as shown in Table A and Table C . The measurement and scan accuracy for the digitizer, OSS and SXCT on the subjects' residua and models are shown in Table E . When performing the detailed accuracy analysis on the SXCT scan data, the individual measurements were grouped into three different categories depending on whether they were STET, axial or cross measurements (see Figure 6) .

The results shown in Table F indicate the large SXCT errors of 3.95 mm and 3.98 mm are in the STET and cross measures, respectively. This can be explained due to the subjects' residua lying flat on the SXCT table (the bottom of the residuum was flattened instead of being curved) instead of being suspended in air when the digitizer, OSS and caliper measurements were taken. The number of subjects shown in the tables is less than the number participating in the study for the following reasons: 1) For the OSS, dot locations could not be seen on some subjects so measurements were not taken on these markers, and the subjects' data were excluded; 2) For the digitizer, one subject was not measured four times, and one subject's data were lost; and 3) For the SXCT, one scan was not saved to disk for a single subject.

The positive plaster models were more precisely and accurately measured by each measurement method due to their rigidity and stability (nonmovement) when making measurements. Since the plaster models were solid, once the dots were placed on the plaster models they did not move, unlike the human subjects where muscle, fat and skin surface are more flexible.

When measuring the plaster model with calipers, the individual making the measurements could steady his or her arms and hands against the plaster model and the table to give a much more precise and accurate reading as compared to measuring the subject's residuum, which was suspended in air, allowing the limb to change shape. Also, the individual taking the measurements could not steady his or her arms and hands by touching the subject. To measure three of the 15 distances on the subject's limb, two individuals were required; one person could not see both dots simultaneously (which could add to the error on human subjects).

The authors defined accuracy as the closeness of a measured value to its true value. The true value cannot be determined exactly on human subjects using calipers due to these measurement limitations. Therefore, measurement error likely exists in the authors' caliper measurements on human subjects, which the authors considered to be "truth." Caliper measurements were considered "truth" in this study since they typically are used by prosthetists for making measurements.

The OSS has several error-producing factors inherent in its design and configuration. To measure the 0.635-mm dots precisely, they must be easily seen, but this is not always the case. The following factors add to the difficulty of seeing the dots accurately: The OSS does not illuminate the entire surface of the residuum uniformly; shadows caused from the shape of the residuum can affect measurement; the skin sometimes curves away from being orthogonal to the camera sensor plane; and the camera pixel resolution can cause errors. Another source of error is the operator's ability to precisely locate the center of the dot using a mouse and crosshair on the computer screen; this source of error is not present in the caliper measurements because the operator can measure the distances directly from the center of the physical dots.

The precision of the SXCT scanner on subjects was 0.51 mm as compared to 1.04 mm, 0.58 mm and 0.83 mm for the digitizer, OSS and calipers, respectively. The subject's leg was recumbent (supine) on the table, where it was tensed and not supported when making the caliper, digitizer and optical surface scans. These processes allowed movement during measurement taking and acquisition of the scans. Since the subject's leg was supported on the SXCT table, the shape remained relatively constant between scans. Even though the scan time took up to 32 seconds, the subject was able to remain motionless during the two scans. Lying the subject's residuum on the table eliminated movement during the scan. If movement occurred during the scan, the authors could not easily register the data.

The authors previously reported on repeatability and precision of residual- limb measurement systems that included data from both measurement sessions for all subjects who participated in the study (6). The previously reported comparison of caliper measurements of subjects to other measurement types was found to be 3.48 mm for the SXCT data as compared to 2.11 mm and 1.86 mm for the DIG and OSS, respectively (6). A separate analysis was performed on the 13 subjects who attended the first measurement session to find the cause of the larger, 3.48-mm error in SXCT measurements on the subjects' residua as compared to the digitizer and OSS errors. The results from the analysis presented in this article indicate the measurements made in the axial direction of the residuum were more accurate than the cross and STET measurements on the residuum. The larger measurement errors in the STET and cross measurements are due to the subject's residuum lying relaxed on the SXCT table versus being tensed while suspended in air when the caliper, digitizer and OSS measurements were taken. Therefore, the SXCT scanner is equivalent to the digitizer and OSS measurements. Two additional subjects have been scanned with their residual limb suspended in air while being SXCT scanned; the resulting measurements were compared to caliper measurements. The results are similar to what the authors found when making the axial measurements on the SXCT data for the initial 13-subject study.

Conclusion

A new, lower-limb remnant three-dimensional optical surface scanner was built, tested and compared with digitizer and SXCT data-capturing modalities. The authors tested the newly designed optical surface scanner's and SXCT's abilities to precisely and accurately measure residua in transtibial amputees. The results demonstrate the precision and accuracy of the optical surface scanner and SXCT are sufficient for quantitative studies on the lower-extremity residua, and there is substantial equivalence of this method with others commonly used for residuum measurement--especially plaster casting. Distance measurements from three-dimensional spiral CT and an optical surface scanner were compared with caliper measurements. Both SXCT and OSS were found to have an accuracy within approximately 2 mm of the caliper values.

Acknowledgements

The original design concept of the Cencit Inc. scanning system is credited to Dr. John Grindon. This work was supported by the National Institutes of Health/National Center for Medical Rehabilitation Research grant RO1 HD30169. The authors wish to thank Universal Vision Partners, owners of the Cencit technology, for their support. The ANALYZE? software system was provided by Dr. Richard A. Robb and Dennis Hanson of the Mayo Biomedical Imaging Resource in Rochester, Minn. The authors appreciate the cooperation of James Weber, president; Gil Christley, CPO; and Marsha Klunk, CPO, of the Orthotic and Prosthetic Lab Inc. in St. Louis, Mo., for expert advice, referral of subjects and performing the plaster casting.

References:

1. Walsh NE, Lancaster JL, Faulkner V, Rogers WE. A computerized system to manufacture prostheses for amputees in developing countries. JPO 1989;1:3:165-81.
2. Millstein S, Bain D, Hunter GA. A review of employee patterns of industrial amputees--factors influencing rehabilitation. Pros and Orth Intl 1985;9:69-78.
3. Kalender WA, Seissler W, Klotz E, Vock P. Spiral volumetric CT with single-breath-hold technique, continuous transport and continuous scanner rotation. Radiology 1990;176:181-3.
4. Faulkner VW, Walsh NE. Computer-designed prosthetic socket from analysis of computed tomography data. JPO 1989;1:3: 154-64.
5. Kohn LAP, Cheverud JM, Bhatia G, Commean PK, Smith KE, Vannier MW. Anthropometric optical surface imaging system repeatability, precision and validation. Annals of Plastic Surg 1995;34:362-71.
6. Commean PK, Smith KE, Cheverud JM, Vannier MW. Precision of surface measurements for below-knee residua. Arch Phys Med Rehab 1996,77:5:477-86.
7. Hildebolt C, Vannier M. Three-dimensional measurement accuracy of skull surface landmarks. Amer J Phys Anthrop 1988;76:497-503.
8. Vannier MW, Pilgram TK, Bhatia G, Brunsden B, Riolo J, Young LV. Quantitative three-dimensional assessment of face-lift with an optical surface scanner. Annals of Plastic Surg 1993:30:204-11.
9. Vannier MW, Pilgram TK, Bhatia G, Brunsden B, Commean PK. Facial surface scanner. IEEE Computer Graphics & Applications 1991;11:6:72-80.
10. Grindon JR. Noncontact three-dimensional surface digitization of the human head. NCGA Proceedings 1989;1:132-41.
11. Commean PK, Smith KE, Vannier MW. Design of a three-dimensional surface digitizer for lower-extremity prosthetics. J Rehab Res Devel 1996;33:3:267-78.
12. Commean PK, Smith KE, Bhatia G, Vannier MW. Validation of spiral-computed tomography and optical surface scanning for three-dimensional limb prosthesis design. IMAGE VII Conference, Image Society, Tucson, Ariz., June 1994, 12-17;369-81.
13. Vannier MW, Commean PK, Bhatia G, Smith KE. Validation of spiral CT and optical surface scanning for use in three-dimensional design of limb prosthesis. Radiology, 1993;189(P):218.
14. Smith KE, Vannier MW, Commean PK. Spiral CT volumetry of below-knee residua. IEEE Transactions on Rehabilitation Engineering 1995;3:3:235-41.
15. PV-Wave User's Manual, Version 3.0, Precision Visuals, Boulder, Colo.
16. Robb RA, Hanson DP, Karwoski RA, Larson AG, Workman EL, Stacy MC. ANALYZE?: a comprehensive, operator-interactive software package for multidimensional medical image display and analysis. Comput Med Imaging and Graph 1989;13:6:433-54.
17. Robb RA. Three-dimensional biomedical imaging: principles and practice. New York: VCH Publishers Inc. 1994.
18. Robb RA. A software system for interactive and quantitative analysis of biomedical images. In: Hohne KH, Fuchs H, Pizer SM, eds. Three-dimensional imaging in medicine. NATO ASI Series 1990; F 60:333-61.
19. Robb RA, Barillot C. Interactive display and rendering analysis of three-dimensional medical images. IEEE Transactions on Medical Imaging 1989;8:3:217-26.
20. Jiang H, Robb RA, Holton KS. A new approach matching to three-dimensional registration of multimodality medical images by surface matching. Proceedings of the Second Conference on Visualization in Biomedical Computing, Oct. 13-16, 1992, Chapel Hill, N.C., 196-213.
21. Krouskop TA, Muilenberg AL, Doughtery DR, Winningham DJ. Computer-aided design of a prosthetic socket for an above-knee amputee. J Rehab Res Devel 1987;24:2:31-8.