Presented at NACOB 98: North American Congress on Biomechanics Canadian Society for Biomechanics - American Society of Biomechanics University of Waterloo Waterloo, Ontario, Canada August 14-18, 1998

---

A SYNTHETIC MATERIAL MIMICKING THE FRAGMENTATION OF BONE

C. Beardsley ¹ , J.L. Marsh ² , T.D. Brown ^1,2
Departments of ¹ Biomedical Engineering and ² Orthopaedic Surgery
University of Iowa, Iowa City, IA 52242

INTRODUCTION

Fracture patterns are studied and classified in orthopaedic trauma because the mechanism and energy that produce an injury are considerations in treatment. Biological variation can be a confounding issue in research, and cadaveric studies often mandate a large number of specimens in order to obtain statistical significance. This suggests a need for a surrogate material that responds to impact in a manner comparable to bone. While some artificial materials are commonly used in orthopaedic research based on their ability to duplicate the behavior and properties of bone in some respects, they do not shatter into fragments on impact. For example, mechanical properties of Sawbones® (Pacific Research Labs, Vashon, WA) have been used in place of bone in compressive and four-point bend tests, and one grade of Last-A-Foam® (General Plastics Manufacturing Co., Tacoma, WA) is currently under consideration as an ASTM standard material for tests of screw purchase.

REVIEW AND THEORY

Bone is a viscoelastic material, and, as such, its properties are dependent on loading rate. Figure 1 shows two distal tibial pilon fractures. The curved surfaces and large fragments in the first photograph (a) are indicative of a lower energy insult as compared with the second (b) in which there are many more small, sharp fragments.

Figure 1a, and 1b: Two tibial pilon fractures with different fracture patterns.

Attempts have been made to describe the intuitive differences between the two fractures above. In the Ruedi and Allgower classification system, forces of impact are greater as one progresses from Type I to Type III (Bourne et al., 1983). The classification system devised by the Orthopaedic Trauma Association (J. Orthop Trauma, 1996), in part, stipulates the number of fragments created by the injury. Trumble et al. also presented an injury score system in which the number of fracture fragments correlated most closely with the outcome of several classification systems which they examined.

PROCEDURES

Prelimary impact tests were conducted on six different grades of Last-A-Foam®, which varied in both density and composition. Most rejected candidate materials were deemed undesirable either because they produced substantial "powder" when crushed or because it was evident from their fracture surfaces that they had deformed considerably before failing. Last-A-Foam® is a polyether urethane resin with methyl diphenyl diisocyanate; the foam's cell size and texture are controlled with a silicon surfactant. Grade FR3740 foam has a density of 40 lb/ft ³ , and its polymeric precursor material is glucose-based.

Uniform hollow cylinders (19.69 mm OD, 11.11 mm ID, 69.22 mm height) were machined from grade FR3740 foam. Specimens were divided into groups of three, and each group was subjected to a vertical drop test utilizing a particular mass and drop height. This produced four distinct energy levels (approx. 20 to 108 J). The number of identifiable fragments was counted manually for each specimen.

RESULTS

The average number of fragments liberated is plotted as a function of the kinetic energy developed in the drop test in Figure 2. Figure 3 shows one typical fractured specimen from each group.

Figure 2: Mean fragmentation by group. Fragmentation increases monotonically with energy.

Figure 3a-d: Representative fractured specimens from each of the four groups. Input energy progressively rises from (a) to (d).

DISCUSSION

As with bone, the foam material used in this experiment produced varying degrees of comminution when fractured. Although it is not possible to precisely count the number of fragments produced by each specimen, especially at higher energies when the sample is pulverized to a greater extent, the plot in Figure 1 clearly illustrates that as more energy was imparted to the FR3740 foam, more pieces resulted. There are also observable qualitative differences between each group. As shown in Figure 3, fragment size diminished from lowest to highest energy. Additionally, at the lowest energy, the fracture pattern can be compared to that shown in Figure 1a, whereas the highest energy specimen and Figure 1b are analogous.

Clinically, assessment of bone fractures depends upon x-ray or CT examination. One obvious factor that would improve comparison of FR3740 foam to clinical results would be radiographic equivalence. Future work will aim to develop a system for doping this material with inorganic salts in order to produce such equivalence.

A fundamental tenet of engineering fracture mechanics theory (Anderson, 1995) is that the energy absorbed in propagating a crack through a solid medium is equal to the material's fracture energy per unit surface area, times the total fragment surface area liberated. Pending development of CT-based image analysis routines (ongoing work), we are not yet in a position to formally quantitate the interfragmentary surface area in these foam specimens. However, a first-order approximation of this surface area can be made with the simplifying assumption of identical size and nominally spherical morphology for the foam fragments produced by each specimen. Re-plotted in that idealized manner, pilot data in Figure 4 are reasonably consistent with the theoretically suggested linear proportionality between energy and interfragmentary surface area.

Figure 4: Estimated interfragmentary surface area increases with input energy.

REFERENCES

Anderson, TL, Fracture Mechanics - Fundamentals and Applications, CRC Press, 1995.

Bourne, RB et al, J. Trauma, 23, 591-596, 1983.

Cristofolini, L et al, J. Biomechanics, 29, 525-535, 1996. J. Orthop Trauma, 10 Suppl 1, v-ix, 1-154, 1996.

Trumble, TE et al, J. Hand Surg., 19A, 325-340, 1994.

ACKNOWLEDGMENTS

Foam samples were provided by General Plastics Manufacturing Co.