Center for Limb Loss and MoBility

Introduction

To calculate the material properties from mechanical testing data, the length and cross-sectional area of the object are needed. Measuring the cross-sectional area is simple for items such as metal rods, but it is not as straightforward for soft tissues. While the standard for determining the length continues to be calipers, there is no equivalent standard for the cross-sectional area.

Many techniques have been used to find the cross-sectional area of ligaments and tendons. However, since foot and ankle ligaments are often short, have concavities, and are located between oddly shaped bones, many techniques would be difficult to perform without damage to the ligament. Thus, a suitable molding and casting technique (i.e., nondestructive, no applied force, and no shrinkage) is the best option for determining the cross-sectional area of such ligaments. Previous researchers have used molding techniques on ligaments and tendons that were validated by comparing cross sections of the molds or castings to metal rods.^1,2 Our study developed a molding and casting technique that could accurately capture the odd shapes and concavities of foot and ankle ligaments. Materials were optimized so that the mold could be used for multiple castings and so the castings would not shrink and add error to the system. The materials were also chosen for the special application of foot ligaments with concavities and small clearances between bones, necessitating a molding material with low viscosity prior to curing that is very elastic after curing. The casting material was also chosen to capture the fine details by flowing well into tight spaces without creating air bubbles.

Methods

Metal Rod Validation. Brass rods of 1.62 mm, 2.90 mm, and 3.18 mm in diameter, and a steel rod of 9.43 mm in diameter were cut to approximately 75 mm in length. The diameters of the rods were chosen for comparison to previous studies and to cover the size range from the average cross-sectional area of the foot and ankle ligaments to the smallest details found on the ligaments. One end of each rod was held vertically in place with a chemistry stand, while a second stand held a tongue depressor vertical approximately 1 cm away. The two were placed in a small paper cup so that the tip of each touched the bottom of the cup and then potted in 100 cc of polymethylmethacrylate (PMMA). The PMMA served as a stand to hold the rod and tongue depressor in a fixed position for the subsequent modeling. Upon curing of the PMMA, the cup was removed, and the resulting construct was placed in the bottom of a 473 cc paper cup and molded with 240 cc of liquid silicone rubber (Smooth-On Oomoo 25). Upon curing, the specimen was removed by pulling it out of the bottom of the cup-shaped mold. The mold was placed back into the paper cup, and a casting was made of each rod. The void left by the tongue depressor in the mold acted as an air vent during casting, allowing small diameter rods to be cast without air bubbles. Each rod casting required approximately 15 cc of liquid polyurethane (Smooth-On SmoothCast 305). The cast specimen was removed in the same manner as the original specimen. A section of the rod was removed from the casting by using a hacksaw with 32 teeth per 2.54 cm such that the cut was perpendicular to the length of the rod. The cross-section was colored with a black permanent marker to enhance the contrast from the white casting. The rod cross-section was then photographed with the cross-section perpendicular to the camera lens and a ruler in the same plane as the cross section. ImageJ, a public domain program developed at the National Institutes of Health, was used to determine the cross-sectional area of each photographed cross section.

Once a satisfactory casting and image were taken, a slit was cut in the original molds to mimic the slit required to remove a bone-ligament-bone specimen. The cut molds were carefully realigned and placed back into the paper cup, and another casting was made, sectioned, and photographed. This study would help determine the effect of cutting the silicone.

Another set of molds and castings were made in the same fashion as the original with the exception that the metal rods were sprayed with saline just prior to pouring the liquid silicone rubber. This study would help determine any effect on the curing of the silicone rubber and the determination of cross-sectional area due to the presence of saline.

One image of each rod was opened five times, and the cross-sectional area was measured using ImageJ. The five areas found for each rod were averaged. The percent difference was calculated by comparing the average ImageJ cross-sectional area with the average cross-sectional area from ten measurements of the diameter of each metal rod using calipers. The reported standard deviation signifies the repeatability of using ImageJ to find the cross-sectional area of a single rod. An overall root mean square (RMS) error was also calculated.

To validate the camera system, two tests were done. The cross-sectional areas of the actual metal rods were found from photographs, and an RMS error was calculated for comparison to the calculated rod areas from the diameter measurements with calipers. In addition, graph paper (6.35 × 6.35 mm²) was photographed to determine lens distortion.

Ligaments. After obtaining Institution Review Board approval from the University of Washington, ligaments were dissected from fresh frozen cadaveric feet in the form of bone-ligament-bone specimens by using standard surgical equipment. The ligaments studied were the:

• Short plantar ligament (SPL)
• Inferior calcaneonavicular (ICN) ligament
• Interosseous second cuneiform-third cuneiform (IC2C3) ligament
• Interosseous fourth metatarsal fifth metatarsal (IM4M5) ligament

Five specimens of each ligament type were used. Bones were trimmed as necessary by using a bone saw Stryker Corp. Model 5100-34 TPS Sagittal Saw). Each bony end was potted in 74 cc of PMMA using a previously made silicone mold of the clamps used for the mechanical testing (Figure 1a). A tongue depressor was taped spanning the potted ends while the ligament was suspended (Figure 1b). The tongue depressor not only created an air vent for casting, but also kept the ligament from twisting during molding. The ligament was kept moist by spraying it with saline prior to molding. It took approximately 473 cc of silicone rubber for molding in a specially made molding box (Figure 1c). The ligament specimen was removed by slicing the mold by using a scalpel (Figure 1d). The mold was held together with rubber bands, and approximately 120 cc of liquid polyurethane was used for the casting. The finished castings were sectioned with the hacksaw, and the cross section was colored with a permanent marker and then photographed in the same manner as the metal rods. Due to the short nature of most foot ligaments and the presence of overhanging bones, the castings were sectioned as close to the midpoint of the ligament length as possible. ImageJ was then used again to find the cross-sectional area for each specimen. Due to the high repeatability found during the metal rod validation of using ImageJ to find the cross-sectional area for each area, the area was found only once for each ligament.

Figure 1: Molding preparation and procedure: a) potting bony ends in PMMA, b) suspended specimen with tongue depressor attached ready for molding, c) finished mold, and d) ligament removal with scalpel and retractor.

The length of each ligament was measured by using calipers with extensions. On longer ligaments (SPL and ICN), Verhoff’s stain was used to mark the ligament insertions. If ligament insertions were over a wide area, the center of the insertion site was marked. If the insertion site was not perpendicular to the ligament length, the length was measured at the center of the insertion. The stain was 1–2 mm thick; so to be consistent, the calipers were placed in the same position for each ligament such that the entire stained portion was included in the length measurement. For short ligaments (IC2C3 and IM4M5), stain could not be applied because the ligaments were deep between bones. The insertions of these ligaments were generally perpendicular to the length, and thus, the distance between the bones at the insertions was measured. When each length was measured, a weight was suspended from the lower PMMA block such that the total weight was 5 N, which would match the preload applied during mechanical testing. Three measurements were taken and averaged to determine the length of each ligament.

Results

Figure 2: Casting of the calcaneofibular ligament from a single foot. Left is the lateral view, and right is the medial view: a) fibular insertion, b) calcaneal insertion, c) trabecular bone of calcaneus exposed with bone saw, and d) ligament midsubstance showing fiber orientation

All metal rod sizes were successfully molded and cast. A positive number in the “difference from rod” category indicates the overall expansion, where a negative number indicates the overall shrinkage. Only one condition (1.62 mm rod, uncut with saline) was greater than a 1.8% error. The overall RMS error was 0.334 mm² or 0.97% of the area. When comparing photographs of the metal rods to areas calculated from diameter measurements, the RMS error was 0.071 mm² or 0.86% of the area. Within an ellipse that is centered in the viewfinder with major and minor diameters of 82.6 mm and 63.5 mm, respectively, there was no camera distortion, as determined from the images of the graph paper.

Castings showed clear details of the ligaments and bones (Figure 2). Ligament fibers were visible along with cartilaginous surfaces and bony detail including trabecular bone exposed by the bone saw. The cross-sections of foot ligaments were complex with many concavities, varying cross-sectional shapes, and even with different numbers of fiber bundles (Figure 3). Cross-sectional areas were also varied within each type of ligament and across all specimens.

Figure 3: Ligament cross sections from castings for all 20 ligaments tested in this study. Cross sections taken from the center of each ligament. Images are not all in the same anatomical orientation because left and right feet were used. Nevertheless, the broad range of cross-sectional areas and shapes are demonstrated.

Overhanging bony protrusions and tight spaces did not pose a problem for molding, casting, and sectioning (Figure 4). This IM4M5 ligament measured 4.37 mm in length. In this case, the base of the metatarsals created an overhanging bone (Figure 4a). Resection of the bone for improved line of sight to the ligament would be difficult without damaging the ligament, but the molding (Figure 4b) and casting (Figure 4c) technique successfully captured the detail and cross-sectional shape (Figure 4d).

Figure 4: Example with overhanging bones and small clearances: a) interosseous fourth metatarsal fifth metatarsal (IM4M5) bone-ligament-bone specimen with overhanging bone, b) mold of IM4M5 showing cross-section of ligament, c) casting of IM4M5 specimen, and d) cross-section of IM4M5 casting.

Conclusion

We have developed a method of measuring ligament cross-sectional area that overcomes the limitations of other area measurement techniques while accounting for the complicated anatomy of the bones of the foot. The method was validated by using metal rods of known diameters and by analyzing representative sets of foot ligaments (N = 20).

To read the full project description, please see:

Quantifying Ligament Cross-sectional Area via Molding and Casting. Schmidt KH, Ledoux WR. J Biomech Eng. 2010 Sep;132(9):091012. PMID: 20815646.

Acknowledgements

The research reported here was supported by Department of Veterans Affairs, Rehabilitation Research and Development Service under Grant Nos. A2661C and A4843C.

Research Team

Kelly H. Schmidt, M.S.
William R. Ledoux, Ph.D.

References