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CHAPTER 6/SPINAL INSTRUMENTATION / 83
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51. Heth JA, Hitchon PW, Goel VK, et al. A biomechanical comparison between anterior and transverse interbody fusion cages. Spine 2001;26:E261–E267.
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54. Kim Y. Prediction of mechanical behaviors at interfaces between bone and two interbody cages of lumbar spine segments. Spine 2001 26(13):1437–1442.
55. Volkman T, Horton WC, Hutton WC. Transfacet screws with lumbar interbody reconstruction: biomechanical study of motion segment stiff­ness. J Spinal Disord 1996;9(5):425–432.
56. Shirado O, Zdeblick TA, McAfee PC, et al. Quantitative histologic study of the influence of anterior spinal instrumentation and biodegradable polymer on lumbar interbody fusion after corpectomy— a canine model. Spine 1992;17:795.
57. Smith KR, Hunt TR, Asher MA, et al. The effect of a stiff spinal implant on the bone mineral content of the lumbar spine in dogs, J Bone Joint Surg Am 1991;73:115.
58. Spivak JM, Neuwirth MG, Labiak JJ, et al. Hydroxyapatite enhance­ment of posterior spinal instrumentation fixation. Spine 1994;19:955.
59. McAfee PC, Farey ID, Sutterlin CE, et al. The effect of spinal implant rigidity on vertebral bone density: a canine model. Spine 1991;16: S190.
60. Penta M, F raser RD. Anterior lumbar interbody fusion—a minimum 10 year follow-up. Spine 1997;22:2429.
61. Kanayama M, Cunningham BW, Sefter JC, et al. Does spinal instru­mentation influence the healing process of posterolateral spinal fusion? An in vivo animal model. Spine 1999;24(11):1058–1065.
62. Eric H, Ledet MS, Sachs BL, et al. Real-time in vivo loading in the lumbar spine. Part 1. Interbody implant: load cell design and prelimi­nary results. Spine 2000 25(20):2595–2600
63. Rohlmann A, Bergmann G, Graichen F. A spinal fixation device for in vivo load measurement. J Biomech 1994;27:961.
64. Rohlmann A, Graichen F, Weber U, et al. Biomechanical studies mon­itoring in vivo implant loads with a telemeterized internal spinal fixa­tion device. Spine 2000;25(23):2981–2986.
65. Rohlmann A, Calisse J, Bergmann G, et al. Internal spinal fixator stiff­ness has only a minor influence on stresses in the adjacent discs. Spine 1999;24(12):1192.
66. Rohlmann A, Bergmann G, Graichen F, et al. Influence of muscle forces on loads in internal spinal fixation devices Spine 1998;23(5): 537–542.
67. Szivek JA, Roberto RF, Slack JM, et al. An implantable strain mea­surement system designed to detect spine fusion preliminary results from a biomechanical in vivo study. Spine 2002;27(5):487–497.
68. Goel VK, Lim TH, Gilbertson LG, et al. Clinically relevant finite ele­ment models of a ligamentous lumbar motion segment. Semin Spine Surg;1993;5:29.
69. Goel VK, Lim TH, Gwon J, et al. Effects of rigidity of an internal f ix­ation device—a comprehensive biomechanical investigation. Spine 1991;16:S155.
70. Goel V, Konz R, Chang H-T, et al. Hinged dynamic stability as com­pared to dynamic rigid device. Paper presented at the 45th Annual Meeting of the Orthopaedic Research Society; Feb. 1–4, 1999; Ana­heim, CA.
71. Scifert J, Sairyo K, Goel VK, et al. Stability analysis of an enhanced load sharing posterior fixation device and its equivalent conventional device in a calf spine model. Spine 1999;24:2206–2213.
72. Hitchon PW, Goel VK, Rogge T, et al. Biomechanical studies of a dynamized anterior thoracolumbar implant. Spine 2000;25(3):306–309.
73. Dooris AP. Experimental and theoretical investigations into the effects of artificial disc implantation on the lumbar spine [PhD disser tation]. Iowa City, IA: University of Iowa; 2001.
74. Dooris A, Hudgin G, Goel V, et al. Restoration of normal multisegment biomechanics with prosthetic intervertebral disc. Paper presented at the 48th Annual Meeting of the Orthopedic Research Society; Februar y 10–13, 2002; Dallas, TX.
75. Yamashita H, Dijke PT, Heldin CH, et al. Bone morphogenetic protein receptors. Bone 1996;19:569.
76. Grauer JN, Patel TC, Erulkar JS, et al. 2000 Young Investigator Research Award Winner: Evaluation of OP-1 as a graft substitute for intertransverse process lumbar fusion. Spine 2001;26(2):127–133.
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78. Magin MN, Delling G. Improved lumbar vertebral interbody fusion using rhOP-1: a comparison of autogenous bone graft, bovine hydrox­ylapatite (Bio-Oss), and BMP-7 (rhOP-1) in sheep. Spine 2001;26(5): 469–478.
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79. Sandhu HS, Toth JM, Diwan AD, et al. Histologic evaluation of the efficacy of rhBMP-2 compared with autograft bone in sheep spinal anterior interbody fusion. Spine 2002;27(6):567–575.
80. Klara PM, Ray CD. Artificial nucleus replacement clinical experience. Spine 2002;27(12):1374–1377.
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CHAPTER 7

Fracture and Repair of Lumbar Vertebrae

Tony S. Keller, Victor Kosmopoulos, and Thomas Steffen
The lumbar spine, located between the sacrum and tho­racic regions of the vertebral column (the lower back), typically consists of five vertebrae. These five vertebrae generally increase in size from the superior to the infe­rior lumbar spine and are larger than both the cervical and thoracic vertebrae. Similar to size, the weight-bear­ing ability of lumbar vertebrae is often greater, resulting in a higher incidence of pain following injury. From a mechanical point of view, the weight-bearing or struc­tural capacity (force at failure) of the vertebrae depends on both material properties (bone mineral content, tra­becular bone tissue density, and apparent density) and geometric properties (size, orientation, and connectivity of bone elements). A close association between bone mineral loss due to osteoporosis and the risk of fracture has been clearly established. Skeletal structures such as the vertebral bodies, which are comprised primarily of trabecular bone, are particularly at risk. The purpose of this chapter is to discuss the mechanics of vertebral compression fractures and trabecular bone damage. An understanding of microdamage and microfracture of vertebrae is used to facilitate discussions of cement repair strategies.
STRUCTURAL AND MECHANICAL BEHAVIOR OF LUMBAR VER TEBRAE
Mechanical properties not only vary from vertebra to vertebra or level to level, but also can vary dramatically within a given vertebral body. Trabeculae tend to be denser, rodlike structures in the inferior and superior sections in contrast to the less dense, platelike trabecu­lae that are associated with the central region of the lumbar vertebral centrum (1). Studies that have exam­ined the physical and mechanical properties of lumbar vertebral trabecular bone have also shown that trabecu­lar bone underlying the normal intervertebral disc nucleus is significantly stronger, stiffer, and denser in comparison to trabecular bone underlying the disc annu-
bone properties have been attributed, in part, to adapta­tion to the heterogeneous pressure distribution within the normal intervertebral disc (4). Namely, the pressur­ized disc nucleus exerts higher stresses on the underly­ing end plate and trabecular bone compared to pressure transmitted by the disc annulus. Keller et al. (2,4) also noted that disc degeneration reduces intravertebral vari­ations in trabecular bone-apparent stiffness, strength, and density in regions adjacent to the end plate, which presumably reflects a more uniform or homogeneous distribution of pressure and stress within the degener­ated disc.
The architectural design or structure of bone in human vertebrae and elsewhere in the body is very complex ranging from a very porous solid (trabecular bone) to a very dense solid (compact bone). The anterior column, or centrum, of human vertebrae is comprised of only a very thin cortical shell (less than 2 mm), which is virtually indistinguishable from the trabeculae that comprise the bulk of the vertebral centrum (Fig. 7-1). Silva et al. (5) performed a f inite element analysis of an idealized lum­bar vertebrae, and reported that the cortical shell’s contri­bution was only 10% of the total vertebral strength, thus making the trabecular centrum the main load-bearing structure. Using anatomically accurate microstructural finite element simulations, the authors estimate that removal of the trabecular centrum, leaving only the ver­tebral shell, results in ov er an eightfold decrease in appar­ent stiffness compared to the intact vertebrae (having both the vertebral shell and centrum) (Fig. 7-2). Finite element analysis of vertebral mechanics is covered in more detail in later sections of this chapter.
Given the porous nature of bone, the relati ve amount of bone tissue is described histologically using apparent density (ρ bone tissue present within a given volume. Clinically, estimates of bone mass are most commonly obtained using dual energy X-ray absorptiometry (DEXA). This
). Apparent density is defined as the mass of
a
85
86 /SECTION I/BASIC SCIENCE
FIG. 7-1. Volume rendering of microcomputed tomography scan image of T10 osteopenic ver tebral body (1.8-mm thick section). (From Keller TS, Kosmopoulos V, Liebschner MAK. Modeling of bone loss and fracture in osteoporosis.In: Gunz­burg R, Szpalski M, eds.Vertebral osteoporotic compression fractures. Philadelphia: Lippincott Williams & Wilkins, 2002: 35–50.)
low-radiation method provides measures of the bone mineral content (BMC, g/cm) and bone mineral density
2
(BMD, g/cm
) distributions within the body (6).
Although BMC and BMD are not true volumetric mea­sures of tissue mass or apparent density, both have been shown to be useful predictors of bone fragility (2,7–9). Hansson (8) performed in vitro mechanical compression tests on 109 intact L1-L4 vertebral centrum specimens from subjects spanning five decades in age (31 to 79 years). In this test series, the BMC ranged from 1.44 g/cm to 6.39 g/cm (mean 3.33 g/cm), and the compressive force at failure F
ranged from 1,520 Newtons (N) to
ult
10,987 N (mean 3,850 N). From this data the following linear correlations are obtained (10):
F
= 1,535 BMC 1,258 (R2= 0.74)
ult
= 75 AGE + 8,199 (R2= 0.30)
F
ult
Examination of these relationships indicates that the compressive strength of the lumbar vertebral centrum is strongly and positively correlated to BMC, but is weakly and negatively correlated to subject age. After age 30, lumbar vertebral compressive strength is pre­dicted to decrease 750 N per decade, declining to 1,500 N at 89 years of age. When the lumbar vertebral strength decreases to 1,500 N or lower, failure of the vertebral structures can occur under postural loads imposed by the weight of the body above the vertebrae (10,11).
From a mechanical point of view, ultimate force is a structural property that is dependent upon both the size
A B
FIG. 7-2. Finite element microstr uctural models used to simulate experimental compression of (A) just the cortical shell (without the trabecular centrum) and (B) of the complete vertebral body (cortical shell and trabecular centrum).
CHAPTER 7/FRACTURE AND REPAIR OF LUMBAR VERTEBRAE / 87
(geometry) and composition (material) of the tissue. Thus, one cannot directly compare the ultimate force of vertebrae from different regions in the spine because the size of the cervical, thoracic, and lumbar vertebrae varies appreciably from each other and from one level to the next. For this reason, material property measurements, such as stress or force/area are often preferred, since they account for geometry variations of different size struc­tures. An estimate of the apparent stress at failure (σ
6
MPa or 10 dividing the ultimate force (F area (mm
N/m2) can be obtained for Hansson’s data by
, N) by the cross-sectional
2
) reported for the vertebral end plate. The
ult
ult
apparent stress at failure of the lumbar vertebrae is found to range from 0.95 to 4.95 MPa (mean 2.29 MPa). Here apparent stress refers to the fact that we still have not accounted for the porosity of the vertebral centrum. Namely, two similar size vertebrae can have very differ­ent structural properties if their porosity or apparent den­sity differs appreciably.
Keller (12) published empirical relationships from in vitro mechanical tests that can be used to calculate the compressive apparent strength (ρ
σa= 97.8 ρ
, MPa) of vertebral bone:
a
2.30
a
where ρais the apparent density (0.05 < ρa< 0.30 g/
3
). Note that the approximately square exponent
cm means that a relative reduction in apparent density of one half will produce a corresponding relative reduction in compressive apparent strength of one fourth. In older adults (more than 70 years), the apparent density of human vertebral trabecular bone can be as low as 0.05
3
, which corresponds to an ultimate compressive
g/cm strength of only 0.05 MPa. Stresses much greater than
0.05 MPa are produced in vertebrae when subjected to compressive forces associated with weight bearing in upright postures (10).
OSTEOPOROSIS
Osteoporosis is a skeletal disorder distinguished by weakened skeletal architecture caused by suboptimal bone development or a reduction in bone mass. It is a dis­ease that weakens the structural properties of bone in both men and women, and results in fracture when loads applied to bone exceed the bone’s ability to support those loads. Thus, osteoporosis is a significant risk factor for
,
fracture and its incidence increases with age. In the United States, 10 million individuals have been diag­nosed with osteoporosis and another 18 million have low bone mass, which places them at increased risk for osteo­porosis and fracture. Treatment of osteoporotic fracture is estimated to be as high as $15 billion annually (13).
Osteoporosis is accompanied by reduced bone strength, and has been clinically characterized using non­invasive radiographic measures such as BMD, BMC, and apparent density (ρ
). The standard diagnosis for osteo-
a
porosis is 2.5 standard deviations or more below the mean BMD (or BMC) for an average 30-y ear -old adult of the same sex. Osteoporosis affects bone quality, which refers to bone architecture, rate of adaptation/remodeling, level of mineralization, and damage accumulation (13).
In osteoporosis perforations exist within the structure causing increased fragility (Fig. 7-3). One reason for this fragility increase is due to the replacement of the plate­like closed cell trabecular structures by open cell rodlike structures, resulting in an increasingly porous appear­ance. Mechanically, trabecular-buckling strength is de­pendent on the diameter, length, distance between cross­links, and the material properties of individual trabeculae. In osteoporosis the vertebral trabeculae become thinner and cross-linking continuity with hori­zontal trabeculae is reduced without compensation by the vertebral shell. Throughout the progression of this dis­ease, deterioration of the trabecular structure induces the
FIG. 7-3. Volumetric rendering of a 2.56 mm × 2.56 mm × 2.56 mm region of trabecular bone from the human lumbar vertebral centrum. The panels (from left to right) illustrate progressive and uniform bone loss resulting in a decrease of the bone volume fraction from 15.3% to 11.1% to 7.66%. Note that there is significant loss of trabecular connectivity following the simulated bone loss. The 20 µm voxel (volume pixel) images were reconstructed from a histologic specimen using a quantitative serial imag­ing and marching cubes algorithm. (From Saxena R, Keller TS. Computer modeling for evaluating tra­becular bone mechanics. In: An YH, Draughn RA, eds.Mechanical testing of bone and the bone-implant interface. Boca Raton, FL: CRC Press, 1999:407–436.)
88 /SECTION I/BASIC SCIENCE
reduction in bone mass (and thus density) ensuring an increased rate of fracture.
VERTEBRAL FRACTURE
Approximately 700,000 osteoporotic vertebral frac­tures occur per year in the United States with 230,000 resulting in chronic disabling pain (13,14). Vertebral frac­tures alter force transmission to the vertebral body seg­ments, lead to vertebral body collapse, increase fracture risk (fivefold) to neighboring vertebrae (15), and result in progressive spinal deformity (e.g., kyphosis) (16).
Vertebral fracture may occur as a result of a traumatic force exceeding the load-bearing capacity of the verte­bral body, or by the accumulation of trabecular tissue­level damage (microdamage) from repeated (fatigue), uniform and nonuniform, everyday subfailure-type pos­tural loading (no trauma) (10,11,17). A traumatic force can result from high-impact falls to normal lifting and bending (13).
Apparent density and its clinical counterpart BMD pro­vide good estimates of bone mechanical properties but are not definitive in predicting vertebral strength (12). The load-bearing capacity of the lumbar vertebrae (structural characteristics) coupled with the applied loads (magnitude, duration, rate) determine fracture risk (Fig. 7-4). Vertebral
fracture is about four times more common in women than in men, and the risk for a vertebral fracture has been found to increase almost exponentially with age. The frequency of osteoporotic vertebral fracture also increases during menopause in women and continues to steadil y increase in frequency throughout the remainder of life. Furthermore, depending on the age groups studied (40 years to more than 80 years), the prevalence of osteoporotic vertebral fractures varies from around 5% to somewhat over 50% (18–21).
Compression Fracture Classification
Vertebral compression fractures are primarily caused by excessive axial loads that may result in vertebral body height reductions, and in the more extreme cases, defor­mities. The axial failure loads for lumbar vertebrae have been estimated and classified by age. In general, a force of approximately 4,200 N produces fracture in individu­als over the age of 60, whereas under the age of 40, an increased load of approximately 7,600 N causes fracture (22,23). As we noted earlier, however, the compressive strength of lumbar vertebrae is closely dependent on the size and quality of the segment, and, in the case of osteo­porosis, can be substantially lower than 4,200 N.
Different postural loading conditions (e.g., uniform and nonuniform) endured by the vertebral body result in dif­ferent vertebral fracture geometries at failure. In the most general case, postural loads are greatest on the anterior aspect of the vertebral body resulting in what is known as anterior wedge-type compression fractures. Anterior com­pression fractures have been classified into four subtypes (22): (a) both end plates are damaged; (b) only the superior end plate is damaged (most common); (c) only the inferior end plate is damaged; and (d) both end plates are intact but anterior cortical shell is damaged.
In the least severe case, hairline fractures to the corti­cal shell or the vertebral end plate may occur . These types of hairline fractures are difficult to diagnose and may plague the patient with pain. End-plate damage can occur in the central regions, periphery regions, or as transverse cracks across the end plate (22). End-plate damage has been proposed to be the initial stage of more severe ver­tebral compression fractures (1,24,25). Burst fractures are the most severe and can range from an end-plate frac­ture resulting in disc intrusion into the vertebral body (22) to complete shattering of the vertebral body. Burst fractures occur at axial loads ranging from 6,000 to 10,000 N (26).
FIG. 7-4. Vertebral material, geometry, and structure are biomechanical determinants of fracture risk. Loading charac­teristics (magnitude, profile, duration, and rate) also influ­ence fracture risk.
Clinical Definition of Vertebral Fracture
Radiographic detection of vertebral compression frac­tures is often the confir mation of the presence of osteo­porosis or bone fragility. Without any known patho­morphologic aberrations distinguishing osteoporotic
CHAPTER 7/FRACTURE AND REPAIR OF LUMBAR VERTEBRAE / 89
bone from nonosteoporotic bone tissue, the fracture itself defines pathology. Since the occurrence of a fracture is not only the result of the mechanical properties of the bone, but is also a function of the fracturing trauma, both factors must be considered when defining osteoporosis. In the presence of a patient with a recent fracture, know­ing nothing or very little about the patient’s bone quality or the forces involved in the trauma, the most practical way for clarifying whether a fracture is osteoporotic or not is Harold Frost’s criterion of the “everyday trauma.” Frost stated that a fracture occurring because of an every­day trauma indicates that the patient has osteoporosis or bone fragility. Even if current technology allows us to determine, for example, the amount of bone mineral in different parts of the human skeleton, we still lack practi­cal techniques for measuring the fracture-generating forces. Therefore the “e veryday trauma” definition is still a practical measure for estimating bone fragility (27). Hence, development of models that can simulate both the loading and structural (trabecular) damage behavior of vertebral bodies are important for understanding clinical pathologies (e.g., osteoporosis) and for predicting bone fragility and its risk for fracture.
TRABECULAR BONE DAMAGE
Trabecular bone is a porous structure (Figs. 7-1 to 7-4), which behaves similarly to typical engineering materials (and cortical bone) in compression until the ultimate stress is reached. The mechanical behavior in trabecular bone shows a relatively linear or elastic response for deformations less than 1% (Fig. 7-5). The point at which the mechanical behavior becomes nonlinear (strain increasing at a greater rate than the stress) is def ined as the yield strain and permanent or inelastic deformation and damage occurs beyond yield. The yield point of ver-
tebral trabecular bone is similar for both compression and tension: 0.84% and 0.78% indicate compressive and ten­sile yield strain, respectively, for vertebral trabecular bone specimens (28). However, beyond yield the com­pressive load capacity of trabecular bone does not go to zero as would be expected. Instead the load is maintained or may even show a slight increase compared to the pre­viously recorded ultimate load (Fig. 7-5B.).
Physically this behavior can be explained by under­standing the compressive mechanics of porous structures. As the pore spaces begin to collapse, the trabeculae col­lide and compress into each other increasing the trabecu­lar bone-volume fraction (bone volume/combined bone and pore space volume) of the specimen. This reduction in pore space and consequent increase in volume fraction results in a temporary load tolerance by the trabecular structure. Thus, the load-carrying capacity of trabecular bone is still quite substantial following compression frac­ture, and results in a large post-yield stress-strain re­sponse (28). This behavior is similar to elastoplastic materials having large post-yield regions and therefore can be modeled as such. In contrast, during tensile load­ing the load-carrying capacity of trabecular bone is min­imal resulting in a smaller post-yield region and abrupt failure. Note that in studying the mechanics of porous structures it is often useful to clarify between whole spec­imen properties (e.g., vertebral body) by referring to them as “apparent” and site-specific properties of the individual constituents (e.g., trabeculae) by referring to them as “tissue.”
Stress-Strain Behavior
The inelastic stress-strain behavior of bone is mainly a result of cracks, plasticity, and viscous creep. Cracks degrade stiffness, strength, and other material properties
A
FIG. 7-5. Experimental stress-strain cur ve displaying the load-unload-reload mechanical behavior (A) and post-yield mechanical behavior (B) of an osteoporotic ver tebral body.
B
90 /SECTION I/BASIC SCIENCE
because of the imposed material discontinuities. The complex strain behavior of vertebral trabecular bone and other porous materials is a result of the cumulative ef fects of the elastic strain, inelastic strain due to damage accu­mulation, plastic strain, and anelastic (viscous) strain (29). Such strain behavior can be differentiated using a load-unload-reload protocol. After unloading from a damaging event, the stress-strain behavior of bone (tra­becular and compact) is similar to that of composites (30). Namely, bone recovers approximately three-fourths of the total inelastic strains (29). Damaged bone shows relativel y small changes in its elastic modulus or stiffness during the initial onset (at low strain levels) of a reload. As loads are increased (relativel y high strain levels) how­ever, cracks propagate, and residual stresses are relieved resulting in a curvilinear stress-strain behavior (Fig. 7-5) (31). This c yclic load-unload-reload beha vior in time pro­duces bone fatigue, which in turn reduces bone strength and stiffness (32–36). Bone damage resulting from fa­tigue or creep can occur under elastic conditions (pre­yield loading) and has been accepted as a normal physio­logic process (37–39).
Damage Mechanics
A microstructural reduction in tissue mechanical prop­erties (e.g., strength, stiffness) is often referred to as microdamage. The accumulation of microdamage, microfracture, leads to local tissue discontinuities within a single trabecula and a decrease in apparent vertebral bone strength. Both microdamage and microfracture are load-dependent, although bone microdamage occurs at a higher incidence than microfracture (40). Microdamage or microfracture may act as a precursor for bone remod­eling (41–44). The resorption phase of bone remodeling can in turn induce further microdamage (45,46) by increasing pore size. This increase in pore size (decrease in apparent density and volume fraction) consequentially reduces the apparent modulus, increases the tissue strain, and results in a temporary increase in bone fragility and osteoporotic fracture risk (39,47–50). Gross vertebral fracture can be a result of extensive microdamage or microfracture accumulation to the trabecular structure (47,51,52).
Continuum damage mechanics (CDM) is a rapidly developing area in the study of bone fracture. For a sim­ple isotropic or axisymmetric material, the presence of cracks or damage (D) can be expressed as a simple scalar representing the loss of load-carrying area (Fig. 7-6) (53). An effective modulus (E scaling the elastic modulus (E) by the damage parameter (D):
where D is continuous between zero (fractured material) and 1 (undamaged material).
) can then be determined by
EFF
E
= (E)(D)
EFF
FIG. 7-6. Schematic illustration of the isotropic damage con­cept defined by continuum damage mechanics.
To study vertebral trabecular bone damage a quasi­continuum CDM approach has been developed based on an empirical nonlinear stress-strain relationship (gener­alized tangent hyperbolic law) (54,55) and an elasto­plastic modulus reduction (EPMR) scheme (56,57). The latter assumes that the evolution of trabecular bone microdamage (D) can be modeled as a change in bone elastic modulus or stiffness, wherein the elastic modu­lus of bone is assumed to be proportional to the ap­parent density cubed (discussed earlier) (12,58). The EPMR scheme is easily implemented using the finite element method and can therefore be used to model the damage evolution behavior of complex material geome­tries. The following sections illustrate the use of CDM and the finite element method to study vertebral damage and cement repair.
Finite Element Damage Simulations
The finite element method is a numerical technique that provides approximations to theory. Finite element analysis is an efficient method used to solve differential equations over complex domains or structures. The structure is dis­cretized and represented by finite elements formed by nodes. Finite element modeling is especially attractive in the analysis of heterogeneous and anisotropic structures, such as trabecular bone, for which a closed form solution using analytic methods will be impossible. In recent y ears, anatomically accurate models of trabecular bone can and have been investigated (59–61). These microstructural finite element models are usually constructed from micro­computed tomography raster arrays at spatial resolutions of 150 µm or less for large volumes and 50 µm or less for
3
small volumes of bone (less than 50 mm
). Microstructural
CHAPTER 7/FRACTURE AND REPAIR OF LUMBAR VERTEBRAE / 91
finite element models enable calculation and visualization of internal tissue stresses and strains.
Damage simulations of complex structures, such as that of trabecular bone in the vertebral body, can be stud­ied using microstructural f inite element models. Contin­uum damage and EPMR approaches have been inte grated within the finite element numerical framework and used as a research tool to investigate existing or potential bone damage (56,57,62–65). Furthermore, finite element bone damage models can be used to study the mechanics of surgical repair. To date however, only a few studies have used finite element damage models to study the f ailure mechanisms (56,57,64–67) and surgical repair (vertebro­plasty) efficacy (56,64,67) of the vertebral body. Simula­tion of vertebral body damage using the finite element approach is presented in the following section, and repair simulations will be discussed later in this chapter.
Kosmopoulos and Keller (64) coupled the EPMR dam­age approach with an anatomically accurate two-dimen­sional (2D) microstructural finite element model of a midsagittal vertebral body section. Two vertebral loading postures were simulated by using a uniform loading pro­file and a nonuniform (ramped) loading profile. Com­pressive loads were applied incrementally over a stress range of 0 to 3 MPa. The experimentally validated (65) EPMR scheme and iterative finite element analysis resulted in a nonlinear stress-strain response (Fig. 7-5A) and a decrease in the apparent modulus of the vertebral body. At the highest stress the uniformly loaded model resulted in a total vertebral body apparent modulus reduction of 32%, while the ramp-loaded model resulted in a 95% apparent modulus reduction, compared to the initial undamaged vertebral body apparent modulus (E
0
444 MPa). Microdamage initiation (modulus reduction of 5%) was first apparent at an applied stress level of 1.5 MPa for both the uniform-loaded and ramped-loaded cases. At the maximum applied stress there was a trabec­ular bone modulus reduction of 40% or more in 10.4% and 15.9% of the total bone elements for the uniform­loaded and ramped-loaded microdamage models, respec­tively (Fig. 7-7). For the uniform-loaded vertebral body the distribution of highly stressed elements followed a column-wise (superior-inferior) pattern within the corti­cal shell and more centrally located trabeculae, in con­trast to the ramped-loaded case where the highly stressed elements were located on the posterior vertebral shell. The ramp-loaded model resulted in a substantially greater number of highly stressed bone elements (20.9% of bone elements with stress concentrations greater than 3) com­pared to the uniform-loaded model (4.2% of bone ele­ments with stress concentrations greater than 3).
VERTEBRAL REPAIR
Most compressive fractures do not affect the spinal cord, are relati v ely stab le, and are therefore asymptomatic
in nature. These types of fractures rarely require surgical intervention (68,69) and are treated using conservative nonsurgical approaches. These treatments often involve a short period of postural reduction (bed rest) directly after incidence, followed by external immobilization, and finally by gradual ambulation (16,70). Bed rest is usually recommended for the first 4 to 6 weeks followed by 6 to 12 weeks of bracing using a rigid orthosis. In severe cases of burst fractures, tissue fragments may enter the spinal canal and cause myelopathy (71). Fractures may lead to progressive deformity and instability, spinal stenosis, neurologic deficit, and pain requiring surgical interven­tion. The probability of fracture healing without surgery decreases as the severity or amount of tissue involved in the fracture increases (72).
Bone Cement Augmentation
Vertebroplasty and kyphoplasty are two recently de vel­oped minimally invasive repair techniques for the treat­ment of vertebral compressive fractures. Unlike tradi­tional treatments, these bone cement augmentation repair procedures help to restore spinal alignment and decrease chronic pain (73).
Vertebroplasty involves the forced injection, usually using either a parapedicular or transpedicular approach, of bone cement, usually polymethylmethacrylate (PMMA), through one (unipedicular) or two bone (bipedicular) biopsy needles into the closed space of a collapsed verte­bral body (16,73). The injections are performed under continuous fluoroscopic guidance, and for high-risk cases, computed tomography is also used (74,75). This technique
=
provides pain relief and stabilization, but typically does not restore the height of the collapsed vertebral body.
Kyphoplasty involves the insertion of a bone balloon into the vertebral body using biplanar fluoroscopic image guidance. The balloon is inflated causing the trabecular bone to compact, resulting in a suitable cavity to re­expand the vertebral body. In kyphoplasty, bone cement is injected with more control and with less pressure than during vertebroplasty. Another advantage of kyphoplasty is the restoration of vertebral body height and reduction of spinal deformity (16,73).
The main complication with each of these cement repair techniques is associated with the use of PMMA. In vertebroplasty cement, extravasation may occur since the PMMA is injected at much higher pressures. The rates of this occurrence have been reported to be as high as 40% when PMMA cement is used in the treatment of osteo­porotic compression fractures (15), and is greater when using higher injection volumes or less viscous cement (76). Another concern with PMMA is its high polymer­ization temperature. Polymerization has been reported to produce average peak cement core temperatures of 87°C and 108°C for small (approximately 14.9 cm
3
(approximately 27.6 cm
) cement volume fills (77).
3
) and larger
92 /SECTION I/BASIC SCIENCE
A
C
B
FIG. 7-7. Numer ical simulation of vertebral trabecular bone microdamage using the elastoplastic mod­ulus reduction finite element scheme. Four-node isoparametric elements were used to represent the vertebral body structure, which was assumed to have isotropic material properties. The applied com­pressive stress (3 MPa) corresponds to upright posture loads acting on the lumbar spine (10).Two ver­tebral loading postures were simulated by using a uniform (A, B) and a nonuniform or ramped (C, D) loading profile. In (A) and (C) the bone and marrow tissues are depicted as white and black elements, respectively, whereas bone tissue damage (modulus reduction of 40% or greater) is depicted by the dark gray elements. In (B) and (D), the gray scale intensity plots show the resulting stress concentra­tions (element axial stress/apparent stress, σ respectively. Highly stressed elements are depicted as lighter gray (max σ stressed elements as darker gray to black (min σ
) following the uniform and ramp loading profiles,
y/σa
y/σa
> 0).
< 6) and less severely
y/σa
D