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

---

FLEXURAL RIGIDITY OF NEW LABORATORY AND SURGICAL SUBSTITUTES
FOR HUMAN FIBULAR BONE GRAFTS

A. Heiner ¹ , R. Poggie ² , T. Brown ^1,3
Departments of Orthopaedic Surgery ¹ and Biomedical Engineering ³
University of Iowa, Iowa City, IA 52242
² Implex Corp., 80 Commerce Drive, Allendale, NJ 07401

INTRODUCTION

The purpose of this study was to measure flexural rigidity of two synthetic fibular graft substitutes, and compare these data to the flexural rigidity of natural human fibulas. These substitutes were composite fiberglass surrogate fibulas, to be used in laboratory experimental studies, and porous tantalum rods, being researched as a bone graft substitute. Ten fiberglass surrogate fibulas and 13 porous tantalum rods were tested in a 4-point bending fixture. Both fibular graft substitutes had flexural rigidities comparable to natural human fibulas. The surrogate fibulas and porous tantalum rods had much less inter-specimen variability in flexural rigidity than did the natural fibulas.

REVIEW AND THEORY

The fibula is a preferred source for cortical bone graft to be used in musculoskeletal reconstructive surgery. Often, the fibula is employed in bending-dominated applications, such as a structural support graft for femoral head osteonecrosis (Urbaniak et al., 1995). The purpose of this study was to measure flexural rigidity of two synthetic fibular graft substitutes, one intended for physical laboratory study and one intended as a surgical implant, and to compare these data to the flexural rigidity of natural human fibulas.

Mechanically realistic composite fiberglass surrogate analogs of the femur and tibia (Sawbones, Pacific Research Laboratories, Inc., Vashon, WA) are in widespread use for testing implants and prostheses. Advantages of these surrogates over cadaver bones are less variability, ready availability, and ease of handling; they also do not degrade (Cristofolini et al., 1996). The overall stiffnesses of composite fiberglass surrogate femurs under axial, bending, and torsional loading are within the range of human cadaver femurs, as are the dimensions (Cristofolini et al., 1996). A composite fiberglass surrogate fibula would have obvious application to laboratory studies of segmental fibular grafting, such as in femoral head osteonecrosis.

A highly porous tantalum material (Hedrocelâ, Implex Corp., Allendale, NJ), being researched as a bone ingrowth material and bone graft substitute, could replace a (nonvascularized) fibular graft, thus eliminating donor-site morbidity. The porosity of this material is typically 80%, can be intentionally varied between 90 - 50%, and has shown excellent bone ingrowth capability (Stackpool et al., 1996). The stiffness and strength of porous tantalum increases with increasing density, which can be controlled by the manufacturing process (Implex Corp., 1997).

PROCEDURES

Ten composite fiberglass surrogate fibulas and 13 porous tantalum rods were tested in a 4-point bending fixture built according to ASTM Specification F383. The geometry of the surrogate fibulas was based on the left fibula of a 890 N, 183 cm tall male. Only the central 20 cm of the fibula was fabricated. The surrogate fibulas were tested such that the longitudinal midstation of the fibula was centered within the 4-point bending fixture. The fibulas were tested in each of four anatomic directions: anterior, posterior, medial and lateral. The porous tantalum rods had a nominal length of 152 mm and a nominal diameter of 12.5 mm. The density of the rods was intentionally varied between 19% and 28%.

Loading was applied using an MTS 858 Bionix (MTS, Eden Prairie, MN). All specimens were loaded at 0.025 mm/sec to 200 N. Five replicate trials were conducted for each loading configuration. Load and deflection were measured by the MTS load cell and LVDT (compensating for the tare displacement of the fixtures and load frame), respectively. The load-deflection slope (N/mm) was calculated by linear regression, and converted to flexural rigidity EI, by the formula:

where E = elastic modulus, I = moment of inertia, P/y = slope of load-deflection curve, and c = distance between inner and outer supports of the bending fixture.

For the fiberglass surrogate fibulas, the anterior and posterior values were pooled to obtain one A-P direction value, and the medial and lateral values were pooled to obtain one M-L direction value. All flexural rigidity values obtained were compared to values from the longitudinal midstation of fresh-frozen human fibulas (Heiner et al., submitted). A 2-tailed t-test determined if values from the fiberglass surrogates and human fibulas were significantly different (a = 0.05).

RESULTS AND DISCUSSION

The coefficients of variation for the fiberglass surrogates were much less than corresponding values for natural human fibulas (Table 1). Small inter-specimen variability is one of the major advantages of using anatomic surrogates rather than natural bones in laboratory biomechanical testing (Cristofolini et al., 1996).

The fiberglass surrogates had a modestly higher flexural rigidity than previously measured for natural human fibulas in the A-P direction (p=0.017), but had an equivalent stiffness in the M-L direction (Table 1). The ratio of A-P direction to M-L direction flexural rigidity was equivalent (p=0.647) between the surrogate fibulas and the natural fibulas. This type of surrogate fibula, therefore, seems appropriate for use in laboratory experimental studies of fibular grafts which will undergo bending, including studies sensitive to the effect of circumferential orientation of the graft at the host site.

The flexural rigidity of the porous tantalum rods increased with the 1.2 power of relative density (Figure 1), as per the relationship noted for the stiffness vs. density of cellular solids (Gibson et al., 1988). The rods with the higher relative densities had flexural rigidities comparable to those of natural human fibulas. Density and rod diameter can be varied, within limits, to obtain a porous tantalum rod of desired flexural rigidity.

Direction	Fiberglass surrogate	Natural fibula	Surrogate/ Natural
A-P	20.1 (6%)	16.5 (36%)	1.21
M-L	11.1 (10%)	10.9 (52%)	1.02
A-P/M-L	1.81	1.72	1.05

Table 1. Flexural rigidity (EI, N-m²) of composite fiberglass anatomic surrogate fibulas (n=10) and natural human fibulas (n=10) (Heiner et al., submitted). Coefficients of variation (S.D./Avg) are in parentheses.

Figure 1. Flexural rigidity (EI) of porous tantalum rods vs. 1.2 power of density.

REFERENCES

Cristofolini L. et al. J Biomech 29(4): 525-535, 1996.

Gibson L., Ashby M. Cellular Solids: Structure & Properties, Pergamon Press, 1988.

Implex Corp., Unpublished product literature, 1997.

Heiner A.D. et al. J Musculoskeletal Res (submitted).

Stackpool G., et al. Trans Orthop Res Soc 42:524, 1996.

Urbaniak J., Coogan P. J Bone Jt Surg 77- A:681-694, 1995.

ACKNOWLEDGMENTS

The authors wish to thank Douglas R. Pedersen, M.S. and Forrest Miller for helpful suggestions and technical assistance. Financial support was provided by NIH AR35788. The porous tantalum rods were donated by Implex Corp.