Deformation and stress in the vertebral endplate and outer annulus fibrosus.

Spinal motion segments consisting of two vertebral bodies and the disc in between were loaded in compression, and the deformation of the annulus fibrosus and vertebral endplate were measured to determine the relative contributions of each of these structures to the strain of the motion segment. Volume changes were calculated from the results using a geometric model, and the tensile stress developed in the endplate was estimated by applying the theory of plates from solid mechanics. Further testing examined the indentation stiffness of the outer annulus to complement the findings on annular bulge. Deformation of the endplate increased from the periphery to the center, indicating curvature and disproving claims that displacement transducers reflect only vertebral strain artifact remote from the interface with the disc. The shape of the deformed endplate deviated from axisymmetric with its highest point located in the posterior aspect. Characterization of the load-displacement behavior determined that endplate deformation occurs early in the loading event, indeed displaying its highest compliance in the first 500 N of load. Thus, its contribution to shock absorption is immediate rather than successive to disc deformation. Annular bulge was highest in the posterolateral disc, consistent with the site of most herniations. Statistically derived bulge contours showed a local minimum in the region of the posterior longitudinal ligament, corroborating its perceived role in preventing disc prolapse directly posteriorly. Indentation stiffness of the annulus was not affected by load, suggesting that little of the intranuclear pressure developed under compression is transmitted to the periphery of the disc. Only half the disc volume corresponding to the loss of height of the loaded motion segment was redistributed into annular bulge and endplate deformation. The remaining half is believed to represent volume strain of the disc, measuring about 8% of the initial volume. The solid-mechanics model of endplate stresses concluded that curvature is caused by less than 5% of the applied load being converted effectively to bending load through inhomogeneities in the reactive stress of both the vertebra and disc. These results improve the understanding of how compressive load is reacted through the spine and why the disc and endplate fail. They represent the behavior of the spine under the fundamental component of all loading conditions associated with injury. Secondary modes of loading, especially bending, likewise are of critical importance and must be added to the protocols developed in this thesis to complete the characterization of the mechanical response of the spinal motion segment. Future work may use these methods to determine the effects of age and degeneration on the integrity of the spine and to recommend limits on activity for those at risk.

DEFORMATION AND STRESS OF THE VERTEBRAL ENDPLATE AND OUTER ANNULUS FIBROSUS Karl H. Wenger A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Bioengineering The University of Utah June 1995 TABLE OF CONTENTS INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 . 1 Dissertation Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3 1 .2 Literature Review . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . •• 4 1.2.1 Architecture and. Constituents of the Intervertebral Disc and Vertebral Endplate ............•.............•• 5 1.2.2 Biomechanics of the Spinal Motion Segment ....•....• 9 1.3 Introduction of the Experiments . . . . . . . . . . . . . . . . . . . . . . . . .. 16 1 .3. 1 Annular Bulge .............................. 17 1.3.2 Annular Indentation Stiffness. . . . . . . . . . . . . . . . . . .. 19 1.3.3 Endplate Deformation ....................•.... 20 TRANSDUCER QUALIFICATION, FIXTURE DESCRIPTION, AND SPECIMEN SELECTION ....................................•...... 23 2. 1 Overview of Experiments .............................. 23 2.2 Transducer Qualification ................. . . . . . . . . . . . . .. 24 2.2.1 Linear Displacement Potentiometers . . . . . . . . . . . . . .. 26 2.2.2 Indentation Load Cell ......................... 28 2.2.3 Camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28 2.3 Fixture Description . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . .. 29 2.4 Specimen Selection .................................. 30 EXPERIMENTAL FINDINGS ON ANNULAR BULGE .................... 33 3.1 Introduction........................................ 33 3.2 Methods .......................................... 35 3.3 Results ............................... . . . . . . . . . . .. 38 3.4 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 EXPERIMENTAL FINDINGS ON ANNULAR INDENTATION STIFFNESS ...... 42 4.1 Introduction........................................ 42 4.2 Methods .......................................... 44 4.3 Results ............... . . . . . . . . . . . . . . . . . . . . . . . . . . .. 47 4.4 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 48 EXPERIMENTAL FINDINGS ON ENDPLATE DEFORMATION. . . . . . . . . . . . .. 51 5.1 Introduction........................................ 51 5.2 Methods .......................................... 53 5.3 Results ........................................... 56 5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 57 ANALYSIS OF VOLUME CHANGES OF THE DISC AND TENSILE STRESSES OF THE VERTEBRAL ENDPLATE UNDER COMPRESSIVE LOAD. . . . . . . . .. 60 6.1 Disc Volume Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 60 6.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 60 6.1.2 Undeformed Volume and Cylindrical Portion of Deformed Volume. . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. 62 6.1.3 Annular Bulge Volume . . . . . . . . . . . . . . . . . . . . . . . .. 63 6.1.5 Calculations and Volume Relationships ............. 67 6.2 Development of Endplate Tensile Stress Equations. . . . . . . . . . . .. 71 SUMMARY AND DIRECTION OF FUTURE RESEARCH ................. 84 7.1 Summary of Experimental Findings and Analyses: Introduction .... 86 7.2 Endpfate Deformation Study ............................ 88 7.3 Annular Indentation Stiffness Study .. . . . . . . . . . . . . . . . . . . . .. 90 7.4 Annular Bulge Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 92 7.5 Volume Analysis .................................... 94 7.6 Stress Analysis ..................................... 95 7.7 Direction of Future Studies ............................. 96 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 ABSTRACT Spinal motion segments consisting of two vertebrae and the disc inbetween were loaded in compression and the deformation of the annulus fibrosus and vertebral endplate were measured to determine the relative contributions of each these structures to the strain of the motion segment. Volume changes were calculated from the results using a geometric model and the tensile stress developed in the endplate was estimated by applying the theory of plates from solid mechanics. In addition, further testing examined the indentation stiffness of the outer annulus to complement the findings on annular bulge. It was established that deformation of the endplate is not vertebral strain artifact remote to the. interface with the disc, as has been suggested, since an array of transducers produced a range of displacements indicative of curvature. Characterization of the load-displacement behavior determined that end plate deformation occurs early in the loading event, indeed displaying its highest compliance in the first 500 N of load. Deformation deviates from axisymmetric, being highest in the posterior aspect. Annular bulge was highest in the posterolateral disc, the site of most herniations. Statistically derived bulge contours showed a local minimum in the region of the posterior longitudinal ligament, consistent with its perceived role in preventing disc prolapse directly posteriorly. Indentation stiffness of the annulus was not affected by load, suggesting that little of the intra-nuclear pressure developed under compression is transmitted to the periphery of the disc. The loss of disc height, and the corresponding volume change from an assumed~cylindrical to a bulged shape was not entirely accounted for by annular bulge and endplate deformation; half the volume change was not redistributed. This is believed to be an indication of volume strain of the disc, measuring about 8% of the initial volume. The solid-mechanics model of end plate stresses concluded that curvature is caused by a small fraction of the applied load being converted effectively to bending stress through inhomogeneities in the reactive stress of both the vertebra and disc. These results provide a basis for comparing the mechanical behavior of these specific structures under different loading conditions, notably bending, in which the disc assumes a greater role. Compressive loading is an especially useful model for studying bony failure of the spine, so future work can apply the methods developed in this thesis for determining the effects of age, disease, and degeneration on the strength of the spine. 3 CHAPTER 1 INTRODUCTION 1 . 1 Dissertation Overview The spine has a unique bending function in the body which necessitates that its tissues withstand large deformations when loaded. This makes it uniquely vulnerable to injury under relatively benign circumstances. In bending, most of the deformation takes place in the soft tissues that comprise the disc. The intuitive deduction from this understanding is that the bony vertebrae serve only a structural support role in the spine and do not deform. However, the vertebral bodies which overlie the disc consist almost entirely of trabecular, or spongy, bone, unlike most of the skeleton which is primarily cortical, or compact, bone. Trabecular stiffness is less than one-tenth that of cortical stiffness. If, instead of bending, the spine performs a task like lifting in the upright position, then the disc assumes a smaller proportion of the deformation and the strain of the soft and bony tissues is not so clearly divided. This roading condition of pure compression has become the focus of studies investigating the relative strains of the disc and vertebra and how they interact in injury mechanisms. This dissertation examines the deformation of the disc and vertebra together under compression, coordinating the results to determine the relative contribution of each to volume changes in the spine. Also, stresses developed in the vertebral endplate, which separates the vertebral body from the disc, are analyzed using the theory of plates from the field of solid mechanics. To complement the disc 4 deformation data, stiffness of the outer annulus fibrosus of the disc is directly measured before and after loading to determine whether compressive stresses are transmitted to the periphery of the disc. These experiments and analyses provide a new level of detail and original insights regarding the transmission of load in the spine, in some instances conflicting qualitatively with established concepts of spine biomechanics. The organization of this dissertation begins with a review of the spine literature, concentrating on the biomechanics of the spinal motion segment, the common in vitro testing sub-unit of the spine consisting of a disc and the two vertebrae it joins. The literature review is followed by an introduction to the experiments. In Chapter 2, the transducers and apparatus used in the experiments are described and qualified. Chapters 3, 4, and 5 are essentially independent manuscripts of the three experimental studies of the dissertation. Chapter 6 contains the two analyses of volume changes and end plate tensile stress. And Chapter 7 summarizes the experimental and analytical results and their relationship to existing concepts of spine biomechanics. The direction of future studies finishes the work. 1 .2 Literature Review Understanding the function of the spine and disc requires considerable knowledge of at feast two fields of basic science-- biomechanics and biochemistry. Biomechanics describes how the tissue structures of the spine respond to loading, and how aging, disease, degeneration, and clinical treatments affect its mechanical response. Biochemistry describes the molecular, cellular, and microstructural constituents of the 5 spine and how the above conditions and treatments affect their presence and viability. Since this dissertation concerns biomechanical studies, the biochemical review, which mostly follows the reviews of others, will necessarily be of a general descriptive nature, without critical comment, and the biomechanicalliterature wHl be treated with a more probing and relevant perspective. An especially important consideration that ties together the biomechanics of this dissertation and the body of work in the biochemistry field is the effect of degeneration on the concentrations and functions of the complex substances comprising the tissues of the disc. Failure of the end plate or annulus violates an otherwise avascular and mostly aneural structure. With the inner disc exposed to blood and other bodily fluids, a cascade of potentially damaging and pain-producing events occurs.42 These will be discussed in various sections of the review. Architecture and Constituents of the Intervertebral Disc and Vertebral Endplate The disc is composed of three parts (Figure 1.1). The nucleus toward the center of the disc is a gel consisting primarily of a well hydrated matrix of collagen and proteoglycan. It takes up about half the disc volume. Surrounding the nucleus is the annulus fibrosus, which is organized in rings, or lamellae, of collagen fibers oriented in sequentially alternating oblique angles to the axis of the spine. As in the nucleus, the collagen is integrated in a matrix of proteoglycans. The fibers of the annulus attach above and below to the vertebral end plate which is a transitional structure between the disc and vertebra, and which is best described as a composite of the two tissue-types it joins. On the disc side is a layer of cartilage with essentially the same endplate NP endplate Figure 1. 1 The disc consists of the nucleus pulposus (NP) gel located centrally and the annulus fibrosus (AF) surrounding it in layers of oblique fibers. Vertebral endplates separate the disc from the vertebral bodies above and below. 6 constituents as the annulus and nucleus, and on the vertebra side is a layer of subchondral (below-cartilage) bone, somewhat like cortical, or compact, bone. Following is a description of the two main constituents of the disc, collagen and proteoglycans. Collagen fibrils are built up from smaller micro-fibrils aligned along an axis in staggered, parallel order and cross-linked together ,67 similar to the general architecture of muscle. In tendons, undulating collagen and straight elastin form a composite which has an elastic quality in the initial range of stretch that strains only the elastin, and a stiff quality beyond the point where the collagen fibers are straightened out. In the disc, however, only trace amounts of elastin are observed,67 suggesting that the function of the disc, being dominated by stiff collagen fibers, is not in fact an elastic one. The small micro-fibrils formed from procollagen are triple left-handed helices consisting of chains of amino acid residues.43 This is a defining quality of the family of collagens, which has been divided into at least 12 types. 36 Another defining feature is the presence of hydroxyproline, which serves as the binding site for cross-linking chains. The fibrils of collagen in the nucleus are referred to as Type II and are thinner and less organized than those in the annulus, which are of Type I. They merge at the interface of the two tissues, providing attachment for the nucleus gel. Actually, the collagen fibrils of the annulus follow a gradient of mostly Type II in the inner lamellae to mostly Type I in the medial and outer lameJlae.13 Collagen accounts for 50% of the dry weight of the annulus and 20-30% of the nucleus. 2 It has a characteristicly resilient quality, exhibiting little change with aging and degeneration. 1 It has been shown that the fiber angle in the annulus changes from 62 0 off the vertical axis at the 7 periphery to 45 0 at the margin of the nucleus, and that the collagen fibrils have a planar crimped morphology In the endplate, the collagen fibrils lie parallel to the endplate toward the osseous side, then transition to an almost vertical orientation on the disc side in order to bind with the fibers of the annulus. In this way, an encircling chamber of collagen fibrils is formed around the nucleus.27 Proteoglycan, with its ability to dramatically alter the character of a soft tissue, is a more complex and subtle substance. Sometimes thought of as the ground substance of the disc, it is formed by the attachment of glycosaminoglycans (GaG's) onto a protein core (Figure 1.2). GaG's were first isolated from disc tissue by Hirsch et al. in 1951 .22 Hansen et al. 19 showed that GaG's are synthesized at the junction of the nucleus and annulus. Multiple protein cores, or proteoglycan monomers, aggregate onto a chain of hyaluronic acid. The concentration of proteoglycans helps determine the fixed charge density of the tissue in which it resides, which together with the osmotic pressure determines the ability of the tissue to imbibe and bind water.57 Water can be considered the third substance of the disc, and the proportion of the disc it occupies is correlated with age. At birth, the water content of the nucleus is 88%, and at 77 years, it is reduced to 69%.49 The two GaG's that appear on the proteoglycan monomer are keratin sulfate and chondroitin sulfate. Keratin sulfate is smaller and occupies the proximal position toward the hyaluronic acid chain when the proteoglycans aggregate. Chondroitin sulfate is larger and resides distally from the aggregation binding site. The ability of a proteoglycan-containing tissue to imbibe water is more a function of the density of keratin sulfate chondroitin sulfate protein core ~ hyaluronic acid Figure 1 .2 The ground substance of the disc consists of proteoglycans, or, glycosaminoglycans (GaG's) bound to protein cores, which aggregate onto chains of hyaluronic acid. The GaG content determines the hydration capacity of the disc, and the amount of aggregation determines whether the tissue is cartilage, fibrocartilage, or gel. 8 the proteoglycans than their ability to aggregate, although this helps determine how easily the hyaluronic acid chain can escape from the matrix. 67 However, their ability to aggregate is critical to the consistency and thus the function of the tissue. For instance, the aggregation fraction in the nucleus is 15%, in the annulus, 40%, and in acetabular articular cartilage, 80%.37 The density of proteoglycans, like collagen type, follows a gradient through the disc, being more concentrated toward the nucleus. Thus, the lamellae of the annulus are less distinct centrally.57 This effect is compounded by the influence proteoglycans appear to have on the synthesis of collagen fibrils; so the collagen type and the density of proteoglycans seem to be in a singular balance.59 In degeneration, the larger chondroitin sulfates are broken down preferentially to the keratin sulfates, and the proteoglycans demonstrate less ability to aggregate.57 The reduced density of proteoglycans leads to less binding of water (dehydration).67 The end plate is a two-layered structure, the layer toward the disc being cartilaginous and the layer toward the vertebra being subchondral bone. Together, these give the endplate a thickness of about 1 mm. Brodin9 demonstrated the flow of solutes across the end plate in 1955 and Kramer31 quantified this semi-permeable membrane function as allowing molecules up to 400 Daltons to pass through without loading. Since proteins larger than this are observed in the disc, loading may be important for augmenting the transport capacity of the endplate. When the endplate fails in fracture, it no longer cordons off the disc from the vasculature. Failure brings on granulation tissue, fibroblasts, and other material normally foreign to the disc.42 The disc is largely aneural except in its posterior third, where it is innervated by 9 dorsal rami of the spinal nerves.5, 28,55 As one possible contributor to low-back pain, these nociceptors are thought to be activated when unmyelinated portions are depolarized by mechanical forces. 1.2.2 Biomechanics of the Spinal Motion Segment This portion of the review highlights the historical works which helped to shape the scientific and clinical communities' perception of how the disc responds to load and how degeneration and aging affect its response. Details are further explored in the separate introductions of each chapter on experimental findings, which critically examine the methods and results of previous studies in the given area. The organization of the review is essentially chronological with occasional deviations where work in specific areas has spanned the decades. The concept of the motion segment, consisting of a disc and the two vertebrae it joins, was introduced by Schmorl and Junghanns58 in their seminal work of the 1930's. They described the spine as a series of three-joint complexes-- the disc and a laterally syrnmetric pair of facets-- defining each level. To analyze the subtle behavior of the spine, it seemed logical to break it into its functional sub-units. This movement followed the earliest body of work normally cited in the spine biomechanics literature which comes from their fellow German colleagues. In 1904, Fick14 noted the swelling properties of the disc with imbibition and Gocke later quantified that finding with the result that in normal adults, the disc imbibes 50% of its weight, and in the aged, only 25%. Probably the most consequential report of the first half of the century was by Mixter and Barr ,39 who in 1934 first made the connection between herniation of the 10 disc and back pain. Just prior to that, Petter48 had reported a method for determining the intrinsic load on the disc due to the pre-load of the ligamentum flavum and longitudinal ligaments. Markers were placed on the vertebral bodies before sectioning out a motion segment, then, after sectioning, the segment was placed into a load­transducing vice and compressed until the the markers on the segment returned to their unsectioned separation. Mechanical testing in general, however, did not proliferate for two more decades. Between the time of Petter in the early 30's and Hirsch in the early 50's, spine studies concentrated on elucidations of pathology. One study in 1951 by Virgin,58 who perhaps first described the disc as "viscous elastic," hinted at the emergence of a biomechanical emphasis, but many of the conclusions of that work proved premature. Likely the first report of the pressure within the nucleus-- broadly referred to as intradiscal pressure-- came in an article by Hirsch and Nachemson in 1954.21 Using a fluid-filled catheter, it was shown that the pressure developed in the nucleus under load was about 1.5 times the applied force divided by the disc area. Nachemson4o • 41 followed that study with in vivo measurements, which since have assumed the status of a gold standard in the spine biomechanics database. Due to the invasiveness of the procedure, it is no ronger approved, and thus Nachemson's data is virtually all that is available of direct in vivo measurements of reactive stresses in the disc. As with other investigators at the time, Nachmeson concluded that the load-relieving function of the neural arch and articular processes was minimal. In the 1950's, a Swedish journal, Acta Orthopaedica Scandinavica, became the leading journal in spine biomechanics partly because it published the doctoral theses and extended studies of clinicians working in the basic sciences. This drew many of 11 the world's most ambitious young spinal orthopedic surgeons, headed by Swedes themselves, to Goteborg and Stockholm to do some of the most widely cited work on spine biomechanics. perey47 completed the first exhaustive study of endplate fractures, classifying them into central, peripheral, and transverse types. It was found that specimens over 40 years old averaged 425 kg to failure and those under 40, 780 kg. This was one of the first demonstrations of the effects of age on the mechanical properties of the motion segment. In the United States, Brown et al. 10 demonstrated the advantages of combining clinical and mechanical expertise through a collaboration between Massachusetts General Hospital and Massachusetts Institute of Technology in 1957. One component of the study was annular bulge, which was shown to be greatest under bending loads on the anterior side. With high frequency loading, a horizontal tear was achieved through the annulus, perhaps the first report of in vitro herniation which still remains essentially irreproducible. Hardy20 had a similar finding. Using a very slow strain ratel. it was possible to demonstrate that part of the reduction in the volume of the disc under load was due to collapse of voids and fluid losses through the endplate. Roaf52 extended this concept to state that, since the annulus bulges very little in compression, the true shock absorber of the spine is the vertebra, which is capable of communicating with its surroundings more readily than the disc. No references have been found since Roaf that address this possibility. Rather, the spine community appears fixed on its intuitive sense that the annulus is the shock absorber of the spine. By coordinating the results of the experiments in this dissertation (Chapter 6). the possibility that the vertebra may playa role in shock absorption of the spine is re­examined. Roaf also may have been the first to observe that when the nucleus has 12 "lost its turgor, abnormal mobility" results and that instead of bulging outwardly, the annulus bulges inwardly. The next milestone work was by Galante in 1967,17 again a lengthy discourse published as an Acta supplement. This is perhaps the most widely cited work in the spine biomechanics literature owing to a section in which a disc degeneration grading system was proposed that has since become a standard for in vitro reporting. More importantly for this dissertation, it determined that the tensile properties of the annulus vary regionally, being more compliant in the posterior aspect. This has important implications for annular bulge, end plate deformation, and indentation stiffness. Other important results of the work included: (1) samples recovered their tensile properties after unloading, thereby justifying multiple tests on single specimens; (2) exposure of the specimens to air was limited to 10 min intervals, setting a standard for dehydration care; (3) freezing and thawing did not affect tensile properties-- a very important demonstration for all biomechanical testing (Smeathers60 and Flynn et al.16 found similar results for whole motion segments later); (4) annulus stiffness was greatest when pulled at horizontal angles and least vertically; (5) annulus was stiffer above and below, where it merges with the end plate, than centrally; (6) degeneration increased the energy dissipation of the tissue; (7) however, age did not affect tensile properties beyond 26 years old; and (8) annulus did not resist angular motion, but was highly resistant to shear. Markolf,35 in a thorough study of the repsonse of the motion segment to bending loads, described its non-linearity represented by stiffening at higher loads. It was also found that the disc was at least two times stiffer in compression than in tension, highlighting the mechanical pivot role of the nucleus. Following this basic science work, mathematical modeling began to emerge from 13 increasing collaborations between clinicians and mechanicists. The modeling process grew up with electromyographic (EMG) signals, which helped to determine the amount of load contributed by each muscle group in the spine. Simple equilibrium equations were overwhelmed by the number of variables introduced by the various muscles in the spine, so optimization schemes were applied using computational techniques to reduce the set of equations down to a statically determinate problem. Schultz,57 working at the University of Illinois with Galante, proposed perhaps the most widely used model which started with simple groupings of muscles in an early orthopedic use of free-body diagrams to estimate the load on the spine in different activities like lifting in a flexed position. Some representative values resulting from the early work ascribed a load of 400 N on the disc to standing and 4000 N to exercise. Andersson et al.3 provided EMG data to drive the model, finding that pressure in the nucleus was higher in unsupported sitting postures than in standing. Basic science progressed concurrently with modeling. Jayson et al.29 found by overpressurizing the nucleus that degenerated nuclei could be forced out of the annulus. Fiorini et al. 15 measured the pressure in the facets, finding as expected a low proportion of compressive and flexion loads resisted by the facets, but due to their size, a similar resultant stress to that seen in the disc at higher loads. By contrast, Shah et al.58 found with strain gauges placed throughout the vertebra that the maximum compressive strain occurred in the pedicles, pointing to a more prominent role for the facets and neural arch. Shah et al. also measured the tangential strain in the longitudinal ligaments, observing an increase in the ligament away from the bending center. The implication of this finding is that it lends credence to the theory that the nucleus shifts away from the bending center, loading the longitudinal ligament 14 opposite. Others have stated otherwise. 10 Tencer et al.65 found further evidence to suggest that the disc is the primary load-bearing tissue in compression, flexion, and lateral and anterior shear, and that the mechanical role of the facets is best realized in posterior shear and axial torque. Degeneration was found by Panjabi46 to have minimal effect on range of motion. By contrast, Lindh34 has reported that aging effects are substantial, with range of motion being reduced by 50% between youth and old age. Sonnerup,61 working with Nachemson, first reported pressure readings from within the annulus. Reactive stresses in the annulus up to that time had only been estimated from nuclear pressures. By introducing a series of semi-conductor pressure probes on a large-bore needle into the annulus, simultaneous readings of the pressure at various points was possible. The results showed a gradient of pressure from the junction of the nucleus and annulus to the margin of the annulus. This corroborated Nachemson's calculated results at least qualitatively. Recently, a variation on this method was reported with different results. McNally et al.38 found a fairly uniform pressure distribution up to within a few millimeter of the periphery of the disc. It is difficult to know to what extent degeneration may have compromised the results, since this condition is known to produce such an effect. About the same time, Ordway et al.44 found variations in the annular pressure following in vitro discectomy. Ranu et al.50 also found by direct measurement that degeneration produced an uneven pressure distribution. Lin et aI., 33 using models, systematically determined the material properties for the tissues of the disc, including the elastic and shear moduli. The vertebral body was found to have an elastic modulus in the axial direction of about 1 GPa, very close to that of trabecular bone and thus highlighting its predominance in the vertebral body. 15 The modulus of the annulus, by contrast, was 22 MPa. Edwards12 showed that the apparent density of bone varied through the mid-plane of the vertebral body, necessitating a range rather than a fixed value to accurately describe its stiffness. Likewise, Horst and Brinckmann25 demonstrated similar variations in the axial reaction stress of the endplate, emphasizing that the variability depended on the state of degeneration. Lin et al.,32 in a separate study, also showed that most disc bulge occurs early in the loading event and that degeneratives bulge more than normals. Near failure, specimens showed high yielding in their bony structures. The results of Stokes,62. 63 who introduced stereophotogrammetric methods into the study of bulge, concluded in contrast to Lin et al.33 that annular bulge was a linear function with segment displacement, a slightly non-linear function itself. Tamaki and Panjabi64 more fully described this behavior analytically using a linear Kelvin model in series with a non-linear spring. One of the most significant works relative to this dissertation during that period from the mid-70's to the mid-80's was the pioneering end plate study of Rolander and Blair. 53,54 A displacement transducer was inserted through the vertebral body onto the osseous surface of the endplate and load was applied. This stimulated other investigations using similar protocols. Together with earlier results, it was concluded that annular bulge dominated the volume change of the disc early in the loading event, but that at higher loads, endplate deformation caught up to it. Reuber et a).51 demonstrated similar results in an integrated study of endplate deformation and annular bulge. In that study, it was shown that removal of the posterior elements did not affect the bulge results. This is an important finding for justifying the method used in the annular bulge experiment reported in this dissertation. Later, Holmes et al.24 16 showed that the specimens that had failed in that end plate study had lower rigidity of the end plate and underlying bone than those that did not. In a follow-up study, it was shown that the creep of the endplate represented about 10% of the total displacement.23 The study of annular bulge continued through the 80's. Klein et al.30 showed that the profile of the bulge assumed a reasonably circular shape, allowing the determination analytically of the amount of volume change of the annulus redistributed to annular bulge. Consistent with other calculation methods applied to the analysis of bulge, an assumption was made about the conservation of volume, implying zero strain of the disc. Researchers appear hesitant to allow the possibility of disc strain in the characterization of disc behavior under load. Brinckmann et al.7 , 8 found that bulge increased with injury and discectomy and decreased with injection. In a later study it was concluded that high intradiscal pressure is a prerequisite for the mechanical function of the disc.7 1.3 Introduction of the Experiments The literature contains conflicting results regarding how tissues deform and how load is transmitted in the spine. Part of the reason for this is that most of the studies have examined just one parameter like annular bulge. Developing an integrated description of the deformation of the spinal motion segment requires merging the data of different studies which used different specimens and varying techniques. With multiple investigators and laboratories involved in the science, this is to some extent unavoidable. The experiments of this dissertation have the advantage that the sample 17 of specimens for the three tests are drawn from a single population or macro-sample. Due to testing failure of a few specimens and as-delivered compromise of a few others in regions pertinent to a particular experiment, the samples are not quite identical as orginally intended. But they are at least highly overlapping. In preparing the specimens, care was taken in particular not to damage the anterior and posterior longitudinal ligaments since they appear to contribute substantially to the mechanical properties of the disc. Otherwise, the spines were cleaned of all surrounding soft tissue. It is important for preserving the properties of the specimen to avoid drying them out by overexposure during preparation and testing. To this end, saline mist was applied as needed. The tests were performed in the order of least to most invasive; annular bulge was studied first, indentation stiffness second, and endplate deformation, which required drilling holes vertically through the vertebra, third. The protocols are summarized below. 1 .3. 1 Annular Bulge An open load frame was fabricated with an acrylic load plate at its base. The frame was secured to the crosshead of an Instron mechanical test frame. In an Instron, the crosshead is moved up and down on screw-driven rails to either side by a computer-controlled motor and a load cell mounts to the crosshead. The fixtures in turn mount to the load cell so that the applied force transmitted through the loading apparatus is transduced onto a strip chart recorder or into a computer-based data­acquisition system. The internal load frame was just large enough in cross-section to fit a 35 mm 18 camera which then looked directly down on the motion segment. Because vertebrae splay toward their ends, it was necessary to section the specimens just below the end external to the motion segment to avoid obstructing the view of the camera. Sectioning already was required to provide even, parallel surfaces of the vertebrae for loading fidelity; simply removing the external, or upper and lower, discs of the vertebrae and keeping the vertebral body intact would have resulted in the applied loading favoring the thin cortex since the vertebral body is slightly concave through the end plate. This raised the concern that with a disrupted, open vertebra blood may be lost during compression through the artificial opening rather than through sinuses in the body. However, with trial specimens this effect was shown to be negligible; the residue on the load plate was a thin layer of viscous marrow and fat. A length standard was placed in the field of view to determine the magnification in the resulting photographs. The outermost part of the disc was digitized around its periphery to determine the· bulge. The contour resulting from the image of the unloaded state was taken as a baseline. The difference between it and the contour from the fully loaded state represented the annular bulge. (In this theisis, the term "unloaded" embodies a slight pre-load which was necessary to define a consistent start point for the tests. The term "unloaded" is preferred to communicate the difference with full load more readily.) Full load was 2500 N, about the average minimum failure of motion segments reported in the literature. It was important not to exceed the expected ultimate load since the specimens were to be used in more experiments. This turned out to be a safe load. Annular bulge in clinically relevant regions were compared. Since herniations most often occur in the posterolateral region, bulge was expected to be highest there. 19 A local difference in the region of the longitudinal ligaments also was hypothesized. 1.3.2 Annular Indentation Stiffness As a fibrous structure, deformation of the annulus does not necessarily indicate stress in the collagen fibers, which can accomodate shape changes with very little actual stretching. Annular bulge measurements suggest where the reactive stress at the periphery may be greatest, but only by inference. More directly, they indictate how the disc tissue may be interfering with nerve roots as they exit the foramen. To gain insight into the actual stress state of the outer annulus, an indenting apparatus was constructed using a small load cell connected to a micrometer advance mechanism on one end and an indenting probe on the other. Measurements were made at anterior, posterior, and lateral locations. The anterior and posterior regions corresponded to the centers of the longitudinal ligaments. Three load states were tested: unloaded, axially loaded to 2500 N, and axially loaded with 7.5 N-m of torsion added. Maximum indentation was 4 mm. Beyond this depth, the outer annulus fibers can develop a concave tension. Conveniently, the load limit for maintaining a workable level of friction within the micrometer screw mechanism was about 100 N, which often occurred close to the indentation limit of 4 mm. If the compressive and torsional stresses applied to the motion segment are transmitted to the outer annulus, they will increase the pressure within those lamellae and the indentation stiffness will increase, just as it becomes harder to sQueeze a bicycle tire as it is pumped up. One limit in the interpretation of these results is that the two sources of stress-- direct compression of the annulus by the vertebrae and hydrostatic pressure transmitted radially from the nucleus-- cannot be distinguished in 20 this measurement. A change of indentation stiffness could be attributed to either. Another result concerns the stiffness specifically in the regions of the longitudinal ligaments. It is difficult to compare the effects of the two longitudinal ligaments from general bending tests since the center of rotation of the motion segment influences the moment arm each acts through in flexion or extension. The method used in this experiment is a more direct measurement of their effects in situ. The ligaments have been studied thoroughly ex vivo, but in situ measurements have been of a more congolomerate nature. 1.3.3 Endplate Deformation The annular bulge data indicates the radial deformation of the disc but does not by itself allow the volume change of the disc to be determined. This is because the endplate deforms around the disc and into the vertebral body, allowing for some of the disc volume lost to overall motion segment compression to be redistributed underneath the endplate. To accurately assess the volume strain of the disc, this endplate deformation volume must be accounted for. Endplate deformation data is vital unto itself for modeling the tensile stresses in this structure which is prone to at least micro-failure non-traumatically even in young, healthy specimens. It is interesting from a basic science standpoint, as well, because the development of curvature under load can only occur when resultant bending loads exist. Since this phenomenon is observed in pure compression of the disc, an inhomogeneity in the reaction stresses through the plane of the disc and/or the plane of the vertebra must exist. The potential factors include higher stress in the nucleus than in the annulus, a higher stress at the margin of the vertebral body in the region 21 of the thin cortex than centrally, and variations in the stiffness of the trabecular bone matrix in the vertebra. An analytical model is used to determine what proportion of applied load is converted through these potential inhomogeneities into effective bending load. With the range of possible bending loads established, the tensile stresses which cause failure of the endplate can be estimated. These values result from the model as well. The method involves drilling a set of five holes vertically into the superior vertebra from above the load plate. These correspond to left and right anterior, left and right posterior, and central locations within the end plate. The load plate is essentially a copy of the annular bulge acrylic load plate with the addition of holes drilled through to allow the stylus extensions on the linear displacement transducer shafts to pass through the plate, into the vertebral body, and onto the osseous surface of the endplate. As load is applied and the end plate deforms the styluses drive the shafts deeper into the transducer bodies to register the displacement at the five points. Previously, only one, central location has been studied. By taking data at a number of intervals, characteristic load-deformation behavior is revealed, improving on the popularly reported maximum values. These three experiments improve on the understanding of deformation and stress of the annulus and end plate, using a few innovative methods while expanding others. The application of analytical techniques to determine the inhomogeneities in the distribution of reactive stresses within the disc and vertebra lays a foundation for improving numerical techniques which can accomodate the organic morphology and material complexity of the spine in determining its stress-strain characteristics. CHAPTER 2 TRANSDUCER QUALIFICATION, FIXTURE DESCRIPTION, AND SPECIMEN SELECTION 2. 1 Overview of Experiments 22 Three experiments were performed. The first was a study of annular bulge. To record the bulge continuously around the periphery of the disc, an SLR camera was mounted inside a custom four-post load frame with an acrylic load plate forming the base of the fixture. The load frame attached to the crosshead of an Instron 1125 mechanical tester, which applied compression. Axial photographs (in the direction of the loading) were taken in the unloaded and loaded states. The prints represented about 3x scale and the peripheries of the discs were traced on an Ortho-Graphics ™ digitizing tablet to obtain the bulge. The second study examined the indentation stiffness of the outer lamellae of the annulus at anterior, lateral, and posterior points. A miniature, low-load mechanical tester (indentation tester) was fabricated using a micrometer, load cell, and indenting probe secured as a subassembly to one of three mechanical tester bases located in the regions of the test points. Known displacements of the indenting probe were applied in the plane of the disc, transverse to the axis of the spine, and the reactive force was measured with the small load cell. Torsion was applied manually through the base fixture using a torque wrench. Compression was applied through the load frame described in the first study. 23 The third study examined deformation of the vertebral end plate using displacement transducers passing from above the specimen on the load plate through the upper vertebral body of the motion segment and onto the inferior osseous endplate of the upper vertebra. Collars were fabricated to secure the transducers onto the load plate. A second acrylic load plate was machined with datum recesses and tap holes specific to the collar configuration. 2.2 Transducer Qualification Figure 2. 1 is a block diagram showing the schematic configuration of the test apparatus. Compressive load was applied in the lnstron 1125. A strip chart recorder integrated with the control panel registered load. The signals from either the displacement transducers or the small load cell in the indentation tester were ampli"fied and low-pass fiftered on a multiplexing terminal board (EXP-16, Computer Boards, Inc., Mansfield, MA). The multiplexing feature was unnecessary and unwanted but unavoidable. This feature makes it difficult to directly monitor and troubleshoot the output of the board, requiring instead an inseparable link with a data acquisition software program. The 5-V power supply leads connected to the first channel of the terminal board, then jumper wires connected the first channel to the + terminal on each of the other channels. Shielded leads connected the transducers from the Instron to the terminal board, and a shielded cable connected the board to the 12-bit AID card (DASH-8 PGA, Keithley-MetraByte, Inc., Taunton, MA) in the 486-class computer. It was important, therefore, to provide a good earth ground at the point of the terminal board where the Instron Controlier I strip chart recorder data acquisition program Instron 1125 load frame transducers power supply terminal board I I-- wi signal condo I--~ 486 computer wi 12-bitND spreadsheet analysis I Figure 2. 1 Block diagram of the general test apparatus. An Instron mechanical test frame applies load to the specimen and a series of transducers provide signals which are signal conditioned en route to AID conversion and storage in the computer. 24 electronics were not formally shielded. Figure 2.2 shows three high-magnification plots of a nominally steady voltage processed by the terminal board. Full scale is .025 V, which is roughly 10 increments of resolution of the 12-bit AID board set for a simulated test range of 0-10 V. The option was avaifable on each channel to solder across a break in a parallel capacitance circuit which provided a 7-Hz corner frequency low-pass filter for the incoming signal. As seen in the second panel of Figure 2.2, the filter function appeared to be ineffective against the primary component of noise which was closer to 5 Hz. A custom shielding box was fabricated for the board to reduce noise. The third panel of Figure 2.2, showing the combined effects of shielding and filtering, appears less contaminated than the second panel, which shows the effect of filtering alone, but not substantially different than the first panel, which shows the supplied voltage without shielding or filtering. Both were chosen to be used during testing since they did not compromise the fidelity of the signal or the utility of the apparatus and may have offered stabilizing effects obscured in these pilot investigations. Data were collected using LabTech Notebook Pro software from Laboratory Technologies Corp. (Wilmington, MA). In this program, virtual instruments are connected to icons which control real-time display and data storage. Within the virtual instrument the programmer establishes the channel of the AID output to be read, the sampling frequency and duration, the range of input voltage to the AID card from the terminal board, and a series of preference parameters. no shield, no filter 4.15 4.145 tCDn 4.14 .5 ">0 4.135 4.13 2 tI 10 12 14 16 18 20 time (sec) no shield, filtered 4.15 4.145 tCDn 4.14 .5 ">'6 4.135 4.13 4.125 0 2 tI 10 12 14 16 1t1 20 time (.ec) shielded, filtered 4.15,.-----------------, 4.145 & 4.14 .5 "'6 > 4.135 4.13 10 12 14 16 1t1 20 time (sec) Figure 2.2 Shielding and low-pass filtering had minimal effect on reducing noise. Signal averaging was used to obtain higher accuracy of the transducer readings. 25 2.2.1 Linear Displacement Potentiometers Figure 2.3 is a photo of one linear pot (MLT, Data Instruments, Acton, MA) with an extension stylus, 50 mm long and 1 mm in diameter, attached to the shaft. The stroke of the linear pots was 12.5 mm, the shortest range readily available using this technology. With an expected displacement of the endplate of only 0.20 mm, this was well beyond the range needed and thus less precise than desired. However, qualification of the linear pots in the lab, as described below, showed them to be acceptably accurate. The term potentiometer means that the device is simply a voltage divider. In the case of linear pots, the shaft makes contact with quasi-discrete points along a resistor inside the body of the transducer. The configuration of transducers in the endpJate deformation protocol was mostly defined by the diameter of the body of the linear pots. Again, the ML T had the smallest diameter readily available at 10 mm. With this dimension and the thickness added by the supporting collars, a reasonable limit of five linear pots could be used: two in the anterior region, one centrally, and two posteriorly. A sixth linear pot was mounted to the side of the acrylic load plate, contacting the base fixture to measure overall motion segment displacement. Without sophisticated signal conditioning circuitry, it was necessary to perform signal averaging to obtain reliable data. Figure 2.4 shows the signal recorded at sampling rates of 1, 10, and 20 Hz. The left panels are the raw data of the output signal as a function of transducer displacement. The right panels are the corresponding averages of the sets of points from each transducer position. With each sampling rate, two consecutive tests to 100 microns in 10-micron steps were performed. The calibration fixture is shown in Figure 2.5a. The potting fixture is Figure 2.3 Linear displacement transducer using potentiometer technology. A stylus screwed onto the transducer shaft to probe the end plate. 10-polnt: 1 Hz, 10 sec 1-Hz Average 3.99 3.98 3.98 3.97 3.96 3.96 !! !! 3.95 '0 3.94 '0 > > 3.94 3.92 3.93 3.92 3.9 3.91 3.68 3.9 0 50 100 150 200 250 0 50 250 pOints microns 10-polnt: 10 Hz, 1 sec 10-Hz Average 3.99 3.98 3.98 3.97 3.96 3.96 3.95 !! !! '0 3.94 '0 3.94 > > 3.93 3.92 3.92 3.9 3.91 3.9 3.8s 0 50 100 150 200 250 SO 100 150 200 250 points microns 20-polnt: 20 Hz, 1 sec 20-Hz Average 401 3.99 3.98 399 3.98 3.97 !! 3.97 '" 3.96 '0 3.96 :a > > 3.95 3,95 3.94 3.94 3,93 3.93 3.92 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 points microns Figure 2.4 The effect of different sampling rates and periods. Linearity was not improved by increasing the sampling rate. A frequency of 5 Hz over a period of 1 sec was chosen. 26 shown in Figure 2.5b. As can be seen from any of the three panels on the left in Figure 2.4, the noise in the system rendered any single data point unreliable. Averaging 10 points per position at either 1 Hz (10-sec duration) or 10Hz (1-sec duration) generated a similarly linear curve. The raw data signal at 20 Hz appeared noisier yet, and the average of 20 points (1-sec duration) did not improve the linearity of the response. Further testing of intermediate sampling rates indicated no detectable difference between averages of five points at 5 Hz and 10 points at 10Hz. Figure 2.6 shows the results of a test to 1000 microns (1 mm) using the 5-Hz, 1-sec sampling parameters. This was the expected range of overall motion segment displacement. For this qualification test of the linear pot, the terminal board was bypassed to eliminate its contribution to signal contamination. The flat trace in the upper panel is the power signal, which experienced deviations of only 2 increments of AID resolution from its nominal value. This quality of signal was achieved after placing 1000 pF capacitors between the + and - leads of the power supply and ground. Similarly, Figure 2.7 shows the results of a test to 200 microns, the expected maximum displacement of the endplate. The deviations from linearity of the transducer were considerably more evident at this magnification, representing less than 1/50th its operating range. Still, quantitatively, the standard deviation of the data points from the expected values of a least-squares fit curve was only 7 microns. This accuracy was accepted. The third panel in Figure 2.7 shows the repeatability of this result. The consistency of the traces indicated that operator error in dialing in the same displacement on the micrometer in each test was very small. This left open the possibility of micrometer inaccuracy, but with an acceptable accuracy for the transducer realized, the source of the slight deviations was not pursued further. Figure 2.5 a) Calibration fixture for qualifying linear potentiometers. Large-head micrometer provided accuracy of 3 microns. b) Potting fixture provided alignment of the specimen with anatomical axes. raw signal: 5 Hz, 1 sec, 1000 microns 4.S 4.4 4.3 4.2 4.1 ..t./.J, 0 4 > 3.9 3.8 3.7 3.6 3.S 0 SO 100 1S0 200 250 points averaged signal: 5 Hz, 1 sec 4.5 4.4 4.3 4.2 4.1 ..t./.J, 0 4 > 3.9 3.8 3.7 3.6 3.5 0 200 400 600 800 1000 1200 microns Figure 2.6 Accuracy of the linear potentiometers over a 1 mm range, using a 5-Hz, 1-sec average. Standard deviation was less than 10 microns. -II) '0 > .:2 '0 > 2 '0 > raw signal: 5 Hz, 1 sec, 200 microns 4.45.,.-------------------., 4.35 4.3 4.25 20 40 60 80 100 120 140 pOints averaged signal: 5 Hz, 1 sec 4.45.,.--------------------, 4.4 4.35 4.3 4.25 50 100 150 200 250 microns repeatability: 5 Hz, 1 sec 4.45 4.4 r : I I 4.35 j I I 4.3 { I I 4.25 J 42 0 50 100 150 200 250 microns Figure 2.7 Accuracy of the linear potentiometers over a 0.20 mm range, closer to the expected values of endplate displacement. The bottom panel shows the high degree of repeatability of the signal. 27 2.2.2 Indentation Load Cell Figure 2.8 is a photo of the indentation tester with the indenting probe screwed onto one end of the 250-lb load cell (model 31, Sensotec, Columbus, OH), and the micrometer shaft (model 262, Starrett Co., Athol, MA) screwed onto the other end via a coupler. The linearity of this device, as shown in Figure 2.9, was excellent over the 50-kg qualification range, producing an r2 of 0.99995. The low output of the load cell required the use of the 500x gain feature of the terminal board. 2.2.3 Camera In the study of annular bulge, a Konica Autoreflex A single-lens-reflex camera with a 55-mm, flat-field lens (Konica Macro-Hexanon AR) was mounted inside the custom load frame, pointing directly downward toward the top of the specimen. The accuracy of this method depended greatly on the optical quality of the camera and printing lenses, as well as the acrylic load plate, and how well they controlled distortion. Figure 2.10 is a print of a 3-mm calibration grid originally generated by a laser printer from a software drawing program. The image was taken with the Konica camera through the load plate. The distortion was found to be within the resolution of the Ortho-Graphics™ digitizing tablet (0.14 mm). With an expected average bulge of 1 mm and a magnification of 3x, the effective resolution of the digitizing tablet was about 1/20th the expected bulge. ' . . , . ~ : Figure 2.8 Indentation mechanical tester. The load cell lies between the indenter and the micrometer. A flange mounted to the micrometer housing is secured to fixtures on the base. 0.6 0.5 0.4 -en "0 0.3 > 0.2 0.1 0 0 0.6 0.5 0.4 -en "0 0,3 > 0.2 0.1 raw force sig nal: 5 Hz, 1 sec 20 40 60 80 100 points averaged force signal: 5 Hz, 1 sec 10 20 30 load (kg) 40 50 120 60 Figure 2.9 Load cell calibration. Its accuracy was excellent (r 2> 0.9999). I I I I I B ++ m -r-- I -- +ti .L I Htt a ! m ::= ~~ rl-;- :: I : I Figure 2.10 Photograph of a 3-mm-increment grid taken through the acrylic load plate used in the bulge experiment. With this line thickness, the combined distortion of the load plate and the camera and printing lenses was imperceptible to the digitizing tablet (resolution, 0.15 mm). 28 2.3 Fixture Description With a test load of 2500 N, most fixtures provided sufficient rigidity fabricated from aluminum; no steel was needed except for the load frame posts. The universal components of the test series are shown together in Figure 2.11 The four-post load frame, 180 x 1 50 mm in cross-section and 450 mm long, attached to the Instron crosshead. A pair of sliding, forked plates made of acrylic (Figure 2. 12) attached below the load plate. These abutted the top of the motion segment, wedging against screws placed in the vertebra at the same level anterolaterally and posterolateraJly. The specimen was potted with a low-melting-point alloy in a 75-mm inner-diameter cup (Figure 2.13). The cup fit into a shallow recess in the base fixture (Figure 2.14), which was elevated to aJlow a torque wrench underneath the specimen. A hole for the torque wrench was centered in the base fixture and a tapped hole for a bolt through which the torque was applied was centered in the specimen cup. The potting apparatus consisted of a base similar to the base fixture in the load frame. Four posts were press fit into the base to guide an acrylic alignment plate with holes matching those in the load plate (Figures 2.15, 16). In the end plate deformation study, extension styluses were made for the displacement transducers (Figure 2.17). A similar structure, but shorter and thicker, constituted the indenting probe in the annular indentation study. The indentation tester was held in place at various locations on the base fixture by two-piece stands which allowed vertical adjustment (Figure 2.18). Tangential adjustment was allowed by slotted channels in the base of the stand, and radial adjustment was allowed by the 40-mm flange which attached to the micrometer of the indentation tester and was held _';:. , __ - _ ~4_ , ~~'; - .- -- .... ..:. -~ r: - - ~ - Figure 2.11 The macro-apparatus consisted of a 450-mm long load frame and a standoff base which allowed a torque wrench below in the annulus indentation experiment. The linear potentiometers are shown here. The strain relief bar toward the top of the load frame held the camera in place in the annular bulge experiment. ~ ~ I----0oI ~ ~ ~ ........ 0. 'il Q. ~ ,. 1 0 i .:.J ..0 : !l..' :::) 't! <.J .'.C. i, \'Z!). ~ :51 ;:: ? ... .. lZIl / t) :: i !l.,,< \ I I " l I i , I I I I I I I -II I ~ :l -1 tl 1 I t .J 1 1: t\i) : :J is ::'. ~ ~ ~ .~~ ~ i C__ _____) C_ ____) ! J.I....--:"--~--+-----' I ~ I Figure 2.12 Dimensions of stabilizing plates mounted below the load plate. Figure 2.13 Dimensions of potting cup with through-tap in the base to allow the application of torque. ~ Q ~ i .OS"?' :. :!:! i \ I T ~ ~I \ll ~I Q<VIl 0 \0 ~! " \il 7.: 0. I 0:: \- ~I Q wi <L ---, ;rl a c ~ ".-. :i .<'S't '5 :i t'l: ~ .... ..a. "_ -.. -.c::: f ':i i. r- I I ! i I I I ~ wi , I :l IX. 5 .:.). gl ~ )( Ii: =1 s- ! Q. \ll ... i 0 Y) .. ~ ~~ ;! :::I .I) I) ~ 0 (,) 0 .:;, ~ :s Figure 2.14 Dimensions of base fixture. Figure 2.15 Dimensions of potting fixture. r-· ,I ~ II " I ~._ ~ I ~.- ~ I '-iJ ...--_______- .+,1~' •-•- ~ -- "-. }-- r-- I I 1-- I r- I I L. lor- ~ ~ (I ~ "- ~ ;. -- l:>- t - - - o d ~ 't ~ ....... ~ t( ~ ~ . o '2 ... 0 ~M is 0 < • c:x.t IU u Cl o 11. -r 7'71 I / ,J I-----"'----.J, / I I 'I ../.'..J.J..J 1----1 1... ·----11'1 ~ -t------------------------ --- ~.. ~ ~ I I I f j 11 01 ~I :1 ~I II o I ;1.-1 :'L ! '--------......j. ~ ;: ~lo.q i h"-" j ~ Figure 2. 16 Dimensions of load plate plus sketch of linear potentiometer collar stand which mounted above load plate. Figure 2.17 Dimensions of linear potentiometer extension stylus and indenting probe. I I ~ r- ~ r- III ';r: <I 'Z ~. « u: ct ~ I.Il ~I ~ 0 ct u :1i 1 i ~ j "'l 0 1:: I- ....-.I ~ ~ :s It :s '*' ~ ~ t; ~ ..... ~ ;- ... S .. § ~ .... ~' ~ ~. §: I ~I~ i \. 0'" -1 <:. -:. ~ "l ! 0 51 "( ~ ,) <:) .:;;: ~ .... ~,± I !! l,\J ! ~ VI 111 ct ... .,.J :5 ::- Q. 'I ~ ~ <: III ~ -:j ~I ~ ~ :I .... .., . () ':t ~ t ()t ~ () ::r .... -.. ,,~i~ :s §:'t' Figure 2. 18 Dimensions of indentation tester stands. A vertical and one horizontal degree of freedom were provided by the stand; the second horizontal degree of freedom was provided by the flange on the tester. Figure 2. 19 Dimensions of indentation tester flange and coupler guide. 29 to the stands with set screws (Figure 2.19). 2.4 Specimen Selection In spine testing, it is important to screen the specimens for excessive degeneration, osteoporosis, and spondylolisthesis, which can affect the mechanical properties of the tissue. Before sectioning into motion segments, each spine was x­rayed at 63 kVp and 4.0 mAs from a height of about 1 meter, both in the lateral and A-P (anterior-to-posterior) directions. Figures 2.20-22 each show a pair of x-rays for a set of specimens from the lateral perspective above and the A-P perspective below. John D. Schlegel, M.D., associate professor in the Department of Orthopedics, and Jason A. Smith, M.D., an orthopedic resident, evaluated the radiographs. Whole specimens or specific levels of a specimen were eliminated from the study series if a degeneration or spondylolisthesis grade of 2 or greater was observed, or if they were deemed osteoporotic. The clinicians' comments are listed in Table 2.1 below for each candidate lumbar spine. 30 Table 2.1 Clinician's Assessment of Candidate Specimens Figure Specimen Comments 2.20 716 degeneration grade 1 at L4-5; T12-L 1 degnerated-- segment excluded from study 936 T12 not available; slight osteophyte at L2-3, deemed biomechanically insignificant; radiolucencies in disc, but not indicative of degeneration 599 L4-5 possibly autofused, physical examination indicates palpably normal response to load-- L3-4 used in place of L4-5 940 spondylolisthesis grade 1 at L4-5-- segment retained 2.21 690 moderate fusion mass, L3-5; L2-3 retained, L4-5 relegated to trial specimen 696 degeneration grade 2 at T1 2-L 1-- segment excluded; L2-3, L4-5 slightly osteoporotic-- segments retained 297 degeneration grade 2 at T12-L 1-- segment excluded; others slightly osteoporotic-- segments retained 319 whole lumbar spine osteoporotic-- spine excluded 2.22 583 degeneration grade 3 at L4-5-- segment excluded, L3-4 used in place of L4-5; slight retrolisthesis at L 1-2, L2-3-- segments retained 564 possible Schmorl's nodes at T12-L 1-- segment excluded 230 appears normal 31 After resection of all non-ligamentous soft tissue, motion segments consisting of vertebrae pair and the disc inbetween were sectioned out of the spine using a horizontal milling shaft fitted with parallel saw blades (Figure 2.23). The sectioning strategy was to eliminate the ends of the vertebrae where splaying occurs, thereby minimizing the vertebral strain artifact. This left about two-thirds of the vertebra for the motion segment. Figures 2.24, 25 show the individual motion segments after sectioning. Between the radiographs and these photos, an informed opinion can be rendered regarding the viability of the specimens. Table 2.2 lists the specimens by their lab accession numbers and the specimen numbers assigned to them for each study, With this, the individual results reported in the following chapters can be referred back to the descriptive images in this chapter. Figure 2.20 Radiographs of four of the candidate spine specimens (Set A). Lateral view is above, anterior-posterior below. All four were admitted for the study with certain levels excluded. Figure 2.21 Radiographs of a second set of four candidate spine specimens (Set B). Lateral view is above, anterior-posterior below. The spine on the right was deemed osteoporotic and excluded from the experiments. , . , ,, • , ~ . ' ; ! . r Figure 2.22 Radiographs of three candidate spine specimens (Set C). Lateralview is above, anterior-posterior below. All were admitted for the study, although L4-5 of the left specimen was deemed degenerated and autofused and was excluded. --saw blades --- :111 1IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIlIII 111111:: .1111111111111111111111111111111111111111111111': :i~!~~~~::::::::':':':':':':'::::::::::::~:~~i~~~i~:. ~~~~~~:~::::::.:.:.:.:.:.:.:.:.::::::::::::~~~~~~~~:. ~"---- Figure 2.23 To section the specimens in parallel planes, a horizontal milling shaft was fitted with a pair of blades which could be set an adjustable distance apart. Figure 2.24 Six motion segment specimens. A high degree of variability is inherent in motion segment testing. Figure 2.25 A second set of six motion segment specimens. The bottom right image is the posterior view of Specimen 716 L2-3, showing the fanning out of the posterior longitudinal ligament in the region of the disc and narrowing along the vertebral body. ,I " 'I I I i ;, I , , ; " : , Figure 2.26 Four motion segment specimens. The upper right image is a posterior view of Specimen 936 L2-3, showing less dramatic fanning and narrowing of the longitudinal ligament than Specimen 716 L2-3 in Figure 2.25. Table 2.2 Age, Gender, and Cause of Death of Specimens; Indexing Study and Accession Numbers Lab Annular Annular Endplate Accession Bulge Indentation Deformation Number Exp't Exp't Exp't Level Age Gender Cause of Death ---------------------------------------------------------------------------------------------------------------------------------_ .. _---------- 230c 1.1 L4-5 42 M cardiopulmonary arrest 297c 1.1 1.1 2.1 L4-5 39 F disseminated intravascular coabulation 564b 2.1 2.1 3.1 L2-3 55 M cardiac arrest 564c 2.2 2.2 3.2 L4-5 583a 3.1 3.1 U-2 71 M myocardial infarction 583b 3.2 L3-4 599a 4.1 4.1 4.1 U-2 71 M cardiopulmonary arrest 599b 4.2 4.2 4.2 L3-4 685b 5.1 5.1 L2-3 61 M metastatic squamous cells 685c 5.2 5.2 L4-5 600b 6.1 L2-3 81 M peptic ulcer disease 696c 7.1 6.1 L4-5 67 M cerebral atherolsclerosis 714b 8.1 7.1 5.1 L4-5 65 M cardiopulmonary arrest 936a 9.1 L2-3 45 M motor vehicle accident 936b 9.2 8.1 6.1 L4-5 940b 10.1 9.1 7.1 L2-3 50 F cardiopulmonary arrest 940c 10.2 9.2 7.2 L4-5 32 CHAPTER 3 EXPERIMENTAL FINDINGS ON ANNULAR BULGE 3.1 Introduction Annular bulge and protrusion potentially effect low-back pain by causing nerve root impingement on the peri-foramenal structures. 21 Also, while much of the intervertebral disc is aneural, the annular periphery is innervated by branches of dorsal rami,5, 28. 55 With sufficient loading and a conducive fiber angle,SO pain may be induced directly in these nerve fibers by annular bulge. Brown et al. 1o examined annular bulge in 1957 using dial guages in contact with discrete points around the periphery of the disc. Restricted by a small sample size, conclusions were generalized to the trends observed, most notably that bulge increased on the concave side of a bending load. Later, Reuber et al.51 found that bulge decreased on the convex side in flexion-extension, even when corrected for posterior-to-anterior translation. This suggests that annular bulge in the posterior disc probably is greatest under axial compression, since the addition of flexion moments reduces posterior bulge, and loading in extension does not reach the levels experienced in the more functional positions of the spine. Since the posterior disc is the region of greatest clinical interest, this study focused on axial compression under the premise this loading mode would produce the most useful data. Different techniques for measuring annular bulge have evolved since Brown's study. In a report of the effects of discectomy and intradiscal injection on annular 33 bulge and loss of disc height, Brinckmann et al.7' a found that, under axial compression, bulge and height loss increased with discectomy and decreased with injection. In that study I they introduced a technique that allowed the bulge to be measured in fine increments around the entire periphery of the disc. This produced a bulge contour of spatially continuous data. As with other previous methods, 10,32,33,51.54 the technique involved contact between the transducer probe and the specimen. This condition can compromise the accuracy of data as it introduces uncertainties into the measurements due to the undetermined influence of the probe on the tissue. More recently I methods have been introduced using photographic techniques30. 62 to measure bulge. This study likewise used a photographic method. The data of these previous investigations vary regarding the region of the disc from which they were taken, the amount of bulge in regions common to some of the studies, and qualitative comparisons between regions. For instance, in a typical intact specimen, Brinckmann and Horst' found a fairly uniform bulge contour at 2000 N, increasing on average 0.14 mm from its value at 1000 N. Reuber et al.,51 however, found on average no change in bulge posteriorly between the unloaded state and 800 N, but, for a given specimen, posterolateral bulge was greater than posterior bulge. Lin et al. 32 found anterior bulge slightly greater than lateral bulge, and Stokes63 found anterior bulge to be twice that of posterolateral bulge. Shah,58 on the other hand, found greatest bulge posterolaterally. These inconsistencies could be improved upon perhaps with more thorough data. As previously described, measuring the full contour of the disc, for instance, provides continuous data from region to region, allowing comparisons with data from any similarly loaded specimen in other studies. Furthermore, using a photographic 34 technique to determine the bulge contour circumvents the problem of potential tissue disturbance by a mechanical probe. Averaging the data of the sample at defined intervals allows the construction of a characteristic contour of disc bulge. Thus, the goals of this study were to apply a non-contacting technique to the statistical measurement of the bulge contour around the disc, and to compare the results from clinically relevant regions in order to assess their implication in low-back pain. 3.2 Methods Specimen Prep Sixteen lumbar intervertebral discal motion segments consisting of vertebrae pairs with posterior elements resected and ligaments intact were obtained from 10 donors and stored in sealed plastic bags at -20°C until testing. Table 2.2 lists the level, age, gender, and cause of death of the specimens. To insure that the compressive load would be applied as evenly as possible and be oriented with the axis of the spine, the specimens were sectioned parallel to the mid-plane of the disc using a horizontal milling shaft fitted with two parallel circular saw blades (Figure 2.23). The separation distance of the blades was adjustable to allow the same proportion of vertebra to be retained in each motion segment. The sectioning strategy was to eliminate the part of the vertebra at the free end that showed pronounced splaying, thereby minimizing the potential for vertebral strain artifact in those regions and providing a mostly unobscured axial view to the disc. About two-thirds of the vertebra was retained. Apparatus The compressive load was applied through a four-post frame secured to the cross head of an Instron 1125 mechanical tester with a 10 ,OOO-kg load cell 35 (Figure 2.11). An SLR camera with a 55-mm, flat-field lens (Konica Macro-Hexanon AR) was mounted inside the 180 x 150 x 450 mm-Iong frame with 25-mm steel square-tube posts. Secured to the ends of the posts was a 25-mm-thick acrylic load plate with scored axes for reference. A pair of 6-mm plates with forked ends attached to either side of the bottom of the load plate. These abutted the specimen to prevent translation and rotation of the superior vertebra. A calibration grid of 3-mm increments was created to test the combined distortion of the camera and printing lenses and the load plate. A digitizing tablet (Ortho­Graphics ™, Salt Lake City, UT) with a resolution of 0.14 mm determined that the distortion was within its resolution. Experimental Protocol Specimens were thawed at ambient temperature within sealed bags for 3 hours, then placed in a 40 C refrigerator for 2-4 hours. A final warming period of 30 minutes occurred during potting with a low-melting-point alloy. The potted specimen was secured within a base fixture in the Instron and the forked plates on the load plate were brought in contact with the anterior and posterior aspects of the superior vertebra. A pre-load of 100 N was applied to assure full contact with the load plate. Three pre-cycles to the maximum test load of 2500 N were applied at a crosshead speed of 1 mm/min. The test load was chosen to be in the range of the minimum average failure for motion segments reported in the literature.624,54 Based on preliminary testing to failure, a specimen was eliminated if failure was observed either through the development of a constant force with continued crosshead displacement, or from an audible fracture. 10 , 32 During testing, the specimens were kept moist with saline mist applied as needed. Ambient air exposure time was about one hour per specimen, and the time under load was about three minutes. 36 Photographs were taken in the 100-N pre-loaded state and at 2500 N. From an axial view, the disc generally defines the periphery of the discal motion segment, although in lower lumbar segments, posterior slant of the vertebra caudally can produce a background for the posterior disc with more subtle distinguishing characteristics. The periphery of the image, except in the posterior portion, was taken to be the bulge of the annulus. AnalysiS Resulting photographs were enlarged to about 3x scale before digitizing (Figure 3.1). The exact magnification was determined by a length standard in the photographs. To standardize the analysis, a transparent radial grid was overlaid on the pre-loaded and fully loaded images, aligned consistently with the scored axes from the load plate. Annular bulge was measured every 5° in the photograph pair. Each image was traced three times and the results were averaged. Angular intervals of 10° each (3 data points), representing anterior, right and left lateral and posterolateral, and posterior regions of the disc were averaged to determine the characteristic bulge in those regions for each specimen. In the case of anterior, lateral, and posterior bulge, the interval was centered about anatomical axes (the scored lines in the load plate) originating in the center of the disc, and for posterolateral bulge the interval lay between 20-30 ° from the A-P axis. This corresponds qualitatively with the definition of posterolateral as "immediately lateral of the posterior elements." A Kruskal-Wallis ANOVA test for multiple comparisons was used to evaluate statistical significance in the comparison of annular bulge in the various regions. _ _ ~:t_ .., Figure 3.1 The disc is photographed from above and the periphery is digitized to determine annular bulge. A length standard references the magnification of the printing process. 37 3.3 Results Figure 3.2 shows the annular bulge contour generated by averaging the data of all specimens at 2500 N in each 50 interval. A generic shape represents the pre­loaded morphology. The results are amplified in Figure 3.3, in which the pre-loaded contour is plotted at 1/10th scale and the bulge is added to that at full scale. Maximum bulge occurs in the posterolateral regions with a local minimum at the site of the posterior longitudinal ligament. Figure 3.4 plots the bulge at 2500 N as a function of radial position, showing greater detail in the regional differences. Table 3.1 lists the regional data for each specimen. Blank entries indicate points at which data could not be obtained due to visual interference of the pedicles or overlying vertebrae, or to ambiguity in delineating the annulus edge. The mean anterior bulge was 0.37 mm (SD, 0.26; range, 0.07-0.91); left lateral, 0.65 mm (SD, 0.41; range, 0.09-1.29); right lateral, 0.54 mm (SD, 0.27; range, 0.11-1.13); left posterolateral, 0.98 mm (SO, 0.47; range, 0.35-1.98); right posterolateral, 0.88 mm (SD, 0.57; range, 0.18-1.87); and posterior, 0.76 mm (SD, 0.52, range, 0.21-1.82). The global average for all intervals was 0.61 mm (SD, 0.19; range, 0.36-1.10). The Kruskal-Wallis ANOVA test for multiple comparisons indicated statistically significant differences in annular bulge between the anterior region and all other regions. Every other comparison of region-pairs was not statistically significant. Table 3.1 Annular Bulge by Region (mm) Left Right Left Postero- Postero- Right .§Qecimen Anterior Lateral Lateral Posterior Lateral Lateral 1.1 0.143 0.271 1.355 0.891 1.655 0.293 2.1 0.887 1.058 0.789 0.208 0.698 0.634 2.2 0.180 0.922 1.439 1.458 1.406 0.709 3.1 0.908 0.300 0.544 3.2 0.121 0.092 1.980 1.818 1.872 0.537 4.1 0.269 0.876 0.646 0.387 0.243 0.203 4.2 0.286 0.578 0.487 0.335 1.035 0.297 5.1 0.416 0.294 0.326 5.2 0.127 0.206 0.310 0.423 0.532 6.1 0.074 0.946 0.701 0.262 0.299 0.768 7.1 0.170 1.187 1.349 1.159 0.987 0.107 8.1 0.683 1.006 0.985 1.179 1.564 0.503 9.1 0.466 1.287 0.519 0.292 9.2 0.191 0.184 0.720 0.794 1.243 1.130 10.1 0.544 0.984 0.354 0.280 0.253 0.892 10.2 0.415 0.153 0.176 0.871 mean 0.367 0.647 0.982 0.757 0.884 0.540 std dev 0.260 0.409 0.469 0.522 0.567 0.274 blank entries indicate obstruction of view to the edge of the annulus 40 30 20 ....... E ..E..... . 10 c 0 :e 0 0 0 D.. a. -10 ct -20 -30 -40 -50 -40 -30 -20 .. 10 0 10 20 30 40 50 lateral position (mm) Figure 3.2 True scale annular bulge, representing the difference between the contours generated by photographs in the unloaded and loaded state. 5-------------------------r----------------------~ ...... E E .s 2.5 c ;.:0:.; 0 Co 4t 9J 0 ~ .....a.. . c .2 :t: CI) 0 -2.5 Co a.. c( -5+----------------.------~------~------~------~ -6 -4 -2 o 2 4 6 lateral position (bulge portion in mm) Figure 3.3 Annular bulge contour amplified ten times. The axes give the scale for the bulge portion. Bulge was greatest in the posterolateral region and local minima were seen in the region of the longitudinal ligaments, but these were not statistically different than the surrounding region. 1.5~------------------------------------------------' 1.25 ....... ..EE..... 1 G) !1) ..:a:.J. 0.75 ..!! ::J cc 0.5 cu 0.25 anterior lateral posterior lateral anterior o+-------~------~------~------~--------~----~ o 60 120 180 240 300 360 radial position (degrees) Figure 3.4 Annular bulge plotted as a function of circumferential (angular) position, highlighting the increase in the posterolateral region and the influence of the posterior longitudinal ligament. 38 3.4 Discussion The primary goal of this study was to compare annular bulge due to compressive loading in various regions of the disc using bulge contours generated by an axial photogrammetric technique. Bulge and protrusion are considered potential factors in nerve root impingement21 and nerve fiber stretching in the outer annulus,' although Klein et al.30 concluded from a model that fiber length remains fairly constant under load. Brinckmann and Horst8 introduced bulge contours using a position probe and presented their data individually for selected specimens. The contours reported here (Figures 3.4 and 3.5) represent an average of 16 specimens, providing a characteristic shape of disc bulge under axial compression. Annular bulge was greatest in the posterolateral region, averaging 0.93 mm at 2500 N. This is the region where herniations most frequently occur.21 These data differ at least qualitatively from the results of most previous investigations. Reuber et al.51 reported an average 0.55 mm bulge in the lateral region and 0.34 mm in the posterolateral region under 800 N. Brinckmann and HorstS reported a uniform increase in bulge in the typical specimen of 0.14 mm for a transition from simulated standing loads to lifting loads. The graphical data of Brown et al. 'O indicates a trend of greater anterior bulge than posterior. The data of Lin et al.32 shows an average anterior bulge of 0.51 mm and a posterolateral bulge of 0.41 mm. Corroborating the results of this study, on the other hand, Shah et al. 58 reported bulge to be greatest in the posterolateral region in a series of young spines. Generally, the differences between regions reported in the literature are slight and no statistical significance has been indicated. A possible explanation for the differences of this study's results with those 39 of previous studies is that the sample of specimens tested here included a higher proportion of L4-5 specimens than most. Brinckmann and Horst8 showed a trend toward uncharacteristic bulge behavior in L4-5 and L5-S 1 discal motion segments, and Brown et al. 'O showed that the L4-5 ultimate stress is much lower than that of L3-4. The cause of regional differences in annular bulge is not clear. One explanation may concern the proximity of the periphery of the annulus to the nucleus. In normals, compression of the disc causes the inner lamellae of the annulus to bulge outwardly. This bulge is resisted by the remaining thickness of the annulus. The thicker the annulus in a given region, the less the periphery will be strained. Thus, where the annulus is thickest-- in the anterior region-- bulge is the smallest. The next thickest area is the lateral region. From the results of this study, lateral bulge was greater than anterior bulge and less than posterolateral bulge, where annular thickness is the least. This is consistent with the annular thickness hypothesis. The longitudinal ligaments appear to have a restraining influence on bulge as seen especially in the region of the posterior longitudinal ligament. This is consistent with the small incidence of disc herniations seen directly posteriorly. Another consideration is the regional variations in mechanical properties of the annulus. Lin et al.32 reported that with posterior elements removed, bending stiffness was lower in extension than in flexion, implying a more compliant annulus in the posterior region. Evaluation of Protocol It was essential for viewing the posterior disc to remove the neural arch. Others32 • 51 reported little effect in axial compression from removing the posterior elements. However, Brown et al. 10 noted that this eliminates the tension provided by the ligamentum flavum in its unflexed state and widens the posterior disc. 40 The method used in this study reflects the individual advantages of various reported methods. In particular, the photographic aspect strongly enhances capabilities for discerning small changes in disc morphology. Especially in this application, which requires no markers, adequate enlargement of the images makes possible a considerably smaller resolution than typically is reported. Further studies, with technical improvements to this protocol, will be able to plot bulge contours as a function of load increments. Incremental photos taken in this study did not provide a level of accuracy sufficient to warrant load-vs.-bulge plots. When available, these could possibly corroborate the conclusions of Lin et al.32 that annular bulge primarily occurs early in the loading event. While this study focused on axial compression, the apparatus is adaptable for bending tests as well. Torsional effects previously were reported to be minimal,53 so the addition of axial moment loading as a separate test mode was excluded in this study. 41 CHAPTER 4 EXPERIMENTAL FINDINGS ON ANNULAR INDENTATION STIFFNESS 4. 1 Introduction As the spinal column is loaded, complex load-sharing develops within the facet joints and intervertebral disc. Under axial load, most of the stress occurs in the disc.15 This primary stress is shared between the nucleus gel and the annulus fibers. Early studies of disc mechanics21 • 40, 41 indicated that the pressure that develops in the nucleus generally is about 1.5 times the applied force divided by the disc area. Since the nucleus occupies about half the disc area, simple equilibrium calculations show that the stress in the annulus is about 0.5 times the applied stress, or about one-third the pressure in the nucleus. However I studies which have directly measured the pressure in the annulus show either a gradient of pressure from the inner lamellae to the outer lamellae61 or a constant pressure equal to that of the nucleus through all but the peripheral 2-3 mm of the annulus.38 Other studies have indirectly corroborated the latter result through measurement of the normal stress in the loaded endplate.25 These qualitatively conflicting results, some of which do not conform to equilibrium principles, confound the fundamental understanding of disc mechanics. In this study I a non-invasive method of indenting the annulus is introduced which indirectly provides insight into the stress state of the peripheral disc under load. If the high pressure developed in the nucleus extends nearly to the margin of the disc, indentation stiffness should increase with load. Otherwise, if most of the intra-nuclear 42 pressure is restrained by the inner lamellae, shielding the remaining annulus from hoop stress, indentation stiffness should remain fairly constant under load. This parameter can be determined for various regions of the disc. While not necessarily significant in its absolute value, it nonetheless may indicate potential differences in stress from one region to another and may help map the stress distribution around the periphery of the disc. Other non-invasive in situ tests of the mechanical properties of the disc have been limited to gross measurements of the whole disc. lo• 32, 35, 45, ss More detailed data regarding the pressure developed within the annulus have been obtained at the expense of the tissue. 3s , 44 To this point, such data have been available only by penetrating the annulus. The extent to which these data accurately reveal stresses in the fibers of the disc is uncertain. The method used in this study, on the other hand, maintains the integrity of the disc while examining its periphery. It was applied here to the loading modes of axial compression and axial torsion. Torsion is of interest in relation to this method because it alternately tightens and slackens the fibers of radially sequential lamellae. Presumably, this can affect the indentation stiffness, especially if the annular fibers experience true strain and not just straightening. The goals of this study were to establish the characteristics of indentation stiffness of the annulus and to determine the effect of compression and torsion on this parameter in clinically relevant peripheral regions of the disc. 43 4.2 Methods Specimens Thirteen lumbar discal motion segments were obtained from 9 donors and stored at -20°C until testing. A discal motion segment is defined here as a vertebrae pair with posterior elements resected and remaining ligaments intact. Table 2.2 lists the level, age, gender, and cause of death of the specimens. To insure that the compressive load would be applied as evenly as possible and be oriented with the axis of the spine, the specimens were sectioned parallel to the approximate mid-plane of the disc using a horizontal milling shaft fitted with two parallel circular saw blades (Figure 2.23). The separation distance of the blades was adjustable to allow the same proportion of vertebra, about two-thirds, to be retained in each motion segment. Apparatus The compressive load was applied through a plate mounted to the crosshead of an Instron 1125 mechanical test frame (Figure 2.11). Attached beneath the load plate were a pair of sliding plates with forked ends, which abutted the cephalic vertebra to provide restraint against translation and axial rotation. The caudal vertebra was fixed in a shallow cup with low-melting-point alloy. The base fixture was elevated so that a torque wrench could be connected to the specimen cup from below. The specimen cup fit inside a mating recess in the base fixture with a center hole for the torque wrench. In this way, biaxial loading was achieved, applied electro­mechanically in compression and manually in torsion. Indentation was applied through an aluminum probe, 5 mm in diameter and 13 mm long with a rounded tip (Figure 4.1). The base of the probe screwed onto a tension/compression load cell (Sensotec Model 31, Columbus, OH)' which in turn screwed into a coupler between the shaft of the micrometer advance mechanism , ' Figure 4. 1 Indentation was applied in the mid-plane of the disc. The indenter is advanced by the micrometer and the load cell transduces the reactive force of the outer annulus. 44 (Starrett Model 262, Athol, MA) and the load cell. This configuration constituted a miniature, low-load mechanical tester. Stands to hold the indentation apparatus, with adjustable height and horizontal position, were mounted to the base fixture in each of the three test regions-- anterior, lateral, and posterior. A linear displacement potentiometer (Data Instruments Model ML T, Acton, MA) was mounted vertically to the load plate to monitor crosshead displacement in lieu of analyzing the strip chart record. The standard deviation of its precision, as measured in the lab, is 0.007 mm. The data provided by the potentiometer was used in the calculation of the axial stiffness of the motion segment. This was determined for the cases of pure compression and added torsion. Experimental Protocol Specimens were thawed at ambient temperature within sealed bags for 3 hours, then placed in a 4 0 C refrigerator for 2-4 hours. A final warming period of 30 minutes occurred during potting. The specimen cup with the potted specimen was secured within the base fixture in the Instron and the forked plates beneath the load plate were brought into contact with the anterior and posterior aspects of the cephalic vertebra, then secured. A pre-load of 100 N was applied to assure full contact between the specimen and the load plate. Three pre-cylces to the maximum test load of 2500 N were applied at the test crosshead speed of 1 mm/min. The load of 2500 N approximates the minimum of the average failure load reported in previous investigations into the mechanical behavior of motion segments under compression.6, 24,54 In the pre-loaded state and at 2500 N of compression, the specimen was indented in 0.2 mm-increments in the anterior, lateral, and posterior aspects of the disc. The reactive force data were collected on a personal computer after AID conversion. The 45 test was stopped when either the indentation reached 4.0 mm or the reactive force reached 100 N. Preliminary testing suggested these thresholds for maintaining the integrity of the specimen. The height of each stand was adjusted such that the center of the indenter contacted the mid-plane of the disc. Following the pure compression tests, the load was reduced to the pre-load level of 100 N and the torque wrench was used to apply 7.5 N-m, which was maintained by securing the specimen cup to the base fixture at the desired torque. This cycle was repeated with a 30-second stress-relaxation period three times before re-applying 2500 N and repeating the indentation tests. Analysis The indentation stiffness of the specimen in each region under each load condition was determined by finding the points corresponding nominally to 20% and 80% of the maximum reactive force and dividing their difference by the difference of the displacements at those points. A Friedman two-way analysis of variance test for multiple comparisons was used evaluate the significance of the differences in each possible pair of load conditions. Each region constituted one test. The Friedman test is applicable when analyzing three or more related samples. A Kruskal-Wallis one-way analysis of variance test for multiple comparisons was used to evaluate the differences in each possible pair of regions. Each load constituted one test. The Kruskal-Wallis test is applicabl.e when analyzing three or more independent samples. A Wilcoxon matched-pairs, signed-ranks test was used to evaluate the significance of the difference between motion segment stiffness under pure compression and with torsion added. Non-parametric tests were chosen because of the small sample size and the acceptable power-efficiency of these tests, which for similar distribution functions is greater than 0.85 relative to their 46 parametric analog." The level of significance, alpha, was .05 in all tests. 4.3 Results Annular indentation stiffness results are summarized in Table 4.1. Mean indentation stiffness was virtually constant over the three load conditions for a given region. Consistentfy, the mean indentation stiffness was greatest in the posterior region (32.47 +/- 5.81 N/mm for the three loading conditions together), and least in the lateral region (26.06 + /- 2.97 N/mm); the anterior results fell between these (23.58 + /- 2.15 N/mm). The differences in each pair of loading conditions, for all regions, were not statistically significant. Conversely, the differences in each pair of regions, for all loading conditions, were statistically significant, with the exception of anterior versus lateral in the full load condition. Data points are missing for the anterior region of Specimen 1.1 and the posterior region of Specimens 3.1 and 5.2. In these cases, when the specimens were loaded, cuts were observed from the harvesting process in the regions of interest. Also, Specimen 9.2 did not yield torsion data due to technical compromises. Figures 4.2. a-f show characteristic indentation stiffness curves representing averages of the individual data records for the particular region or loading condition. Stiffness behavior is strongly linear over the range of displacement tested. The rippling evident toward the ends of the curves occurs because these are averages of individual tests, some of which reached the maximum allowable reactive force before reaching the maximum indentation and thus contributed incompletely to the averages. For a given specimen, the full-load and torsion curves often were near-duplicates of each Table 4.1 Annular Indentation Stiffness (N/mm) Pre-Load Full Load Torsion Specimen anterior lateral posterior anterior lateral posterior anterior lateral posterior _._---... --------------------------------_._-----------------------------------------------------------------------_ ... _------------------------------------.-.. - .... _----------- 1.1 24.44 32.95 20.17 45.02 20.88 34.80 2.1 22.53 25.86 32.19 20.44 27.36 30.01 20.79 25.07 33.06 2.2 23.05 21.91 21.53 24.79 23.49 34.25 24.10 24.75 36.75 3.1 23.57 26.02 25.23 24.67 30.27 21.43 4.1 26.36 24.91 30.45 28.27 26.33 35.88 27.05 25.13 21.20 4.2 23.66 21.98 33.38 28.10 23.41 27.29 28.27 24.44 31.97 5.1 29.32 25.07 35.99 27.49 25.07 34.58 28.18 25.07 38.49 5.2 31.84 23.96 25.92 26.65 23.40 24.10 6.1 26.97 24.91 40.01 23.05 24.04 17.72 30.10 23.98 25.77 7.1 26.10 20.96 31.97 24.79 20.24 27.95 29.05 19.14 30.01 8.1 25.75 21.35 32.84 27.84 25.38 35.88 29.58 22.80 38.74 9.1 23.66 17.16 41.54 32.45 24.99 35.88 25.23 21.27 35.56 9.2 21.05 22.46 25.12 23.05 25.46 30.12 mean 25.32 23.15 32.54 25.95 24.41 32.24 26.91 23.17 32.63 std deY 2.93 2.40 5.48 3.01 2.11 6.58 2.97 1.94 5.36 ratio 0.12 0.10 0.17 0.12 0.09 0.20 0.11 0.08 0.16 anterior pre-load 100 100 80 80 ", ,,' ~ ~ " GI eo ",...~."'.' 0 /. ~' " JGI eo ,-~~ ~ <~ ~ /'.~~ "" "" ~ g "" 40 -= <40 ~ 0 ,. /?'" ~ ,.- ,. 20 ,,~ 20 g'" ,~1" i' #~ ••• * A ... ,'" 0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4 annulus indentation (mm) annulus indentation (mm) lateral full load 100 100 80 80 .......... '. ~ ~ .. ' " " GI 60 j 80 ~ Q) > ~ n 40 "" 40 ~ ~ 20 20 B 0.5 1 1.5 2 2.5 3 3.5 4 0.5 1 1.5 2 2.5 3 3.5 4 annulus indentation (mm) annulus indentation (mm) posterior torsion 100 100 p ..... IOfId 80 luI/load 80 ~ toralon ~ GI 60 GI 80 0 0 ~ ~ Q/ Q/ > > t; 40 :;:::I 0 40 ~ ~ 20 20 C 0.5 1.5 2 2.5 3 3.5 4 0.5 1.5 2 2.5 3 3.5 4 annulus indentation (mm) annulus indentation (mm) Figure 4.2 Averaged indentation-load behavior grouping the results by region in the left column (A-C), and by load in the right column (D-F). In a given region, loading did not affect indentation stiffness. While the differences between regions were slight, some were statistically significant. 0 an"rIot .... , .. podtriot E F 47 other, serving fortuitously as a check on individual repeatability of the indentation test. The effect of torsion on motion segment stiffness is shown in Figure 4.3 and Table 4.2. Torsion made the motion segment stiffness more linear and increased its value beyond 500 N in 12 of 13 specimens, 12% on average. 4.4 Discussion The goals of this study were to characterize annular indentation stiffness around the periphery of the disc and to determine whether location or load affects the stiffness. This information adds to the understanding of how the hydrostatic pressure developed in the nucleus under loading is transmitted throughout the annulus. Previous work examining mechanical properties of the intervertebral joint has concentrated on gross behavior of the whole disc. Internal studies of disc mechanics have measured intra-nuclear pressure and relied on modeling to suggest the stress state of the annulus. More recent work38 • 61 directly measuring intra-annular pressure has challenged the conclusions of these previous reports. One study suggests a relatively even gradient of pressure from the inner to outer lamellae.51 Another shows nearly constant pressure to within a few millimeters of the periphery.38 The data of this study do not support the latter finding. Typically, the specimens of this study were indented 4 mm and the stiffness did not change. A highly abrupt change in the stress state near the periphery of the annulus, as found in the one study, effectively constitutes a wall within the outer annulus, partitioning it into radially loaded and unloaded regions. The 4-mm indentation applied in this study produced substantial radial strains in the annulus matrix. The presence of a pressure partition close to the Table 4.2 Motion Segment Stiffness (kN/mm) Specimen 1.1 2.1 2.2 3.1 4.1 4.2 5.1 5.2 6.1 7.1 8.1 9.1 9.2 mean std dey ratio 2500 N Compression 1.72 1.42 1.17 1.34 1.50 1.93 1.25 1.17 1.26 1.25 1.45 1.23 1.60 1.41 0.22 0.16 7.5 N-m Added Torsion 1.59 1.47 1.30 1.43 1.93 2.05 1.49 1.23 1.53 1.41 1.72 1.52 1.86 1.58 0.24 0.15 ....... E E "..',- ' c G) E G) (J CG C. .!!! "..C, c (1) E en G) III 1.5 1.25 1 0.75 0.5 0.25 0 0 ,.. ' .' .' .•.. .' //// .,' " ., •••• p. re-Ioad = 100 N ...... " ....... "-,,."- , .. .,.., /-··<~:ion added .' 500 1000 1500 load (N) ........ -*,,-- 2000 ................... 2500 3000 Figure 4.3 Torsion has the effect of reducing the non-linearity in the behavior of the motion segment and slightly stiffening it beyond 500 N. 48 edge of the disc would increase the stiffness with increasing indentation since each successive increment of displacement represents a higher strain than the last. Therefore, these non-destructive data indirectly do not corroborate that earlier finding, and suggest alternatively that most of the nuclear pressure is restrained by the inner lamellae. Another result which supports this conclusion is that loading had no effect on indentation stiffness. The compressive test load of 2500 N approaches the reported in vitro failure loads of the discal motion segment. According to established concepts of disc mechanics, the intra-nuclear pressure increased substantially as a result of the applied load. Transmission of this pressure well into the annulus would effectively stiffen the partition between the radially loaded and unloaded regions, increasing the strain caused by a given increment of indentation. Also, the lack of change of the indentation stiffness with load suggests that the periphery of the annulus is largely shielded from the axial stress and that the radial stress predominates where it acts. The differences in indentation stiffness from one region to another may be due to various possibilities. One consideration is that the indentation occurred into the anterior longitudinal ligament in the anterior region, into the posterior longitudinal ligament in the posterior region, and directly into the annulus in the lateral region. Possibly, the different mechanical properties of these tissues affected the indentation stiffness. However, because the stiffness was nearly constant over the indentation range, presumably the fibers of the ligaments and annulus never reached the point of true strain but rather experienced only straightening. Another possibility is that the effective partition of the nucleus pressure recruits a uniform thickness of the inner annulus and that the variable radial thickness of the 49 annulus then establishes different radial strain relationships in different regions of the disc. Thus, where the distance between the nucleus and the margin of the disc is smallest-- in the posterior region-- the indentation stiffness may be expected to be greatest. This was the case in this study. However, that distance tends to be greatest in the anterior region, and the indentation stiffness, by contrast, was least in the lateral region. This may be explained by the effect of the anterior longitudinal ligament. This study focuses on inferences of the stress state only in the outer annulus. It does not provide data on the inner and medial annulus, which appear to be of more significance in the transmission of the pressure developed within the nucleus under load. Deeper indentation is not likely to yield substantially more data since at some point, the fibers of the outer annulus would become strained and prevent meaningful interpretation of the data beyond that point. The method introduced here may be useful in future studies for inferring the changes in the stress state of the outer annulus under bending loads like flexion, extension, and lateral bending. 50 CHAPTER 5 EXPERIMENTAL FINDINGS ON ENDPLATE DEFORMATION 5.1 Introduction Fracture of the vertebral endplate is the first occurrence of failure in both compression fracture and burst fracture and may be a source of low-back pain.18 Fractures can occur in the center of the disc, at the periphery, or as transverse fissures across most of the endplate.47 Understanding endplate deformation under load leads to an understanding of its stress state and modes of failure. Previous work has measured end plate deformation near the center of the disc6, 23, 24, 51, 53 under the implied assumption that the deformation is axisymmetric, meaning it assumes the shape of part of a sphere. This would be a reasonable assumption if the nucleus were not eccentrically located toward the posterior aspect of the disc.4 Nachemson's intra-nuclear pressure data4o,41 suggested that the pressure in the nucleus is three times that in the annulus, so by a theory of plate mechanics,66 its location substantially influences the location of greatest deformation of the endplate. The first reported intra-annular pressure study61 qualified this relationship by showing a declining gradient of pressure from the margin of the nucleus to the periphery of the annulus. The resultant of the pressure in the annulus likely approximated the calculated results of Nachemson. However, a recent study of intra-annular pressure indicated conversely that the pressure of the disc is fairly constant from the nucleus through most of the annulus. 38 An earlier study of 51 the axial stress of the endplate produced a similar finding. 25 If this is true, then the location of the nucleus is not a factor in the deformation of the endplate and axisymmetry is expected. This study measured endplate deformation at five locations to allow a three­dimensional interpretation of its behavior. The primary goal was to determine to what extent the mechanical behavior of the endplate deviates from being axisymmetric when loaded in compression, and thus to determine whether the underlying stresses in the disc are essentially uniform. Secondly, it has been stated in the literature6 that since the load path consists of a series of relatively stiff vertebrae and relatively compliant discs, the deformation of the spine must be dominated early in the loading event by the soft tissue, and deformation of the endplate and vertebral body must occur later. However, to the extent that the nucleus behaves as an incompressible fluid inside an inextensible chamber, there is considerable resistance to soft tissue deformation in that region. As the more compressible annulus deforms around the nucleus, the end plate is forced into the vertebral body. There is no evidence to suggest that this does not occur immediately. The secondary goal of this study, therefore, was to characterize the load­deformation behavior of the end plate with particular interest in determining at which stage of loading it deforms most easily. Figure 5.1 A set of five displacement transducers forming the pattern shown in Figure 5.2 were mounted to the load plate. Styluses threaded onto the shafts of the transducers passed through mating holes in the load plate, into holes drilled into the vertebral body, and onto the osseous surface of the end plate. Figun3 5.2 Axial radiograph of a motion segment showing the · configuration of the displacement transducers in left and right anterior and posterior plus central positions. The purpose of the screws is to restrain horizontal motion and axial twisting. 52 5.2 Methods Specimen Prep Ten lumbar discal motion segments consisting of vertebrae pairs with posterior elements resected and ligaments intact were obtained from 7 donors and stored in sealed plastic bags at -20°C until testing. Table 2.2 lists the level, age, gender, and cause of death of the donors. To insure that the compressive load would be applied as evenly as possible and be oriented with the axis of the spine, the specimens were sectioned parallel to the mid-plane of the disc using a horizontal milling shaft fitted with two parallel circular saw blades (Figure 2.23). The separation distance of the blades was adjustable to allow the same proportion of vertebra to be retained in each motion segment. The se~tioning strategy was to eliminate the part of the vertebra at the free end that showed pronounced splaying, thereby minimizing the potential for vertebral strain artifact in those regions. Apparatus Compressive load was applied through a four-post frame secured to the crosshead of an Instron 1125 mechanical tester with a 1 O,OOO-kg load cell (Figure 5.1). The frame was 180 mm x 150 mm x 450 mm long with 25-mm steel square tube posts and a 25-mm-thick acrylic load plate. Five holes, 6 mm in diameter, were drilled into the load plate, forming the pattern shown in Figure 5.2. The four outer holes formed a square, 14 mm on a side, and a fifth hole was located in the center. Five displacement transducers, 10 mm in diameter, were secured in cylindrical sleeves above the load plate. An extension stylus, 50 mm long and 1 mm in diameter, screwed onto the shaft of each transducer. A light spring between the transducer and stylus maintained a nominal extension force to overcome any aberrant friction. The positions of the transducers represented central, left and right anterior, and left and 53 right posterior positions within the vertebra. Due to space restraints in the chosen configuration, the center transducer mounted above the four outer transducers, and the base of its stylus was lengthened another 50 mm. The displacement transducers were linear potentiometers with a 12.5-mm stroke (model ML T, Data Instruments; Acton, MA). Generally, other investigators have used linear variable differential transformers (LVDTs). 24, 54 Calibration of the linear pots by the authors produced a standard deviation of 7 microns and an r2 > 0.99. The signals from the five transducers were multiplexed from a terminal board (ComputerBoards, Inc., Mansfield, MA) to an IBM 486-class PC with a 12-bit AID board (Keithley MetraByte, Inc., Taunton, MA). With a power supply of 5 V, the resolution of the system was 2.5 microns per increment of AID, or about one-third of a standard deviation of the accuracy of the transducers. Experimental Protocol Before testing, a specimen was thawed at ambient temperature within the sealed bag for 3 hours, then placed in a 45 0 refrigerator for 2-4 hours. A final warming period of 30 minutes was allowed during potting with a low­melting- point alloy. The specimen was positioned in the potting cup such that the center transducer would contact the approximate center of the endplate and the other four would lie square to the anatomical axes of the vertebra. The potted specimen was secured within a base fixture in the Instron and a pre-load of 100 N was applied to assure full contact with the load plate. The top of the specimen was secured with sliding, forked plates underneath the load plate which were brought into contact with the specimen then tightened. A surgical drill bit, 1.5 mm in diameter, was used with a hand drill to make the holes in the vertebra. It was aligned normal to the surface of the vertebra by placing 1. 7-mm inner-diameter sleeves into the 6-mm holes in the load 54 plate. Following a method described by,23 contact of the drill bit with the endplate was noted by an increase in resistance of the drilled tissue. Lightly tapping on the specimen with the drill bit confirmed a transition onto a hard surface. Verification of contact between the transducer stylus and endplate was performed post-test using radiographs (Figure 5.3). Three pre-cycles to the maximum test load of 2500 N were applied at a crosshead speed of 1 mm/min before acquiring data. The test load was chosen to be in the range of the minimum average failure for motion segments reported in the Iiterature.6, 24, 54 During testing, the specimens were kept moist with saline mist applied as needed. Ambient air exposure time was about one hour per specimen, and the time under load was about three minutes. The displacement of the transducers was recorded at 500 N increments, as determined by the Instron strip chart recorder. Also, a transducer was placed between the top and bottom loading surfaces to accurately determine the amount of segment displacement. Previous work has plotted segment displacement, rather than load, as the abscissa6,24. 63 in its results. Based on preliminary testing to failure, a specimen was eliminated if failure was detected by either the development of a constant force reaction with continued crosshead displacement or the occurrence of an audible fracture. Statistical comparisons of anterior, center, and posterior results were made using a Kruskal-Wallis ANOVA test. Significance was defined at an alpha of .05. A non­parametric test was chosen in anticipation of a non-normally distributed data set. Figure 5.3 Lateral radiographs indicated the success of the vertebra drilling procedure by showing the proximity of the transducer stylus to the surface of the endplate. 55 5.3 Results Table 5.1 lists the maximum displacement at the five transducer locations for each specimen. The mean posterior displacement was 247 microns (SO, 87)' 65% greater than the mean anterior displacement of 149 microns (SO, 58)' and 24% greater than the mean center displacement of 200 microns (SO, 82). Figure 5.4 shows the consistency of this result. The anterior and posterior displacement data are normalized to the center displacement data, which are indicated for reference as a line at the ordinate value of 1.0. In all 10 specimens, the posterior displacement is greater than the anterior displacement (p < .01), and in 7 of 10 specimens, it is greater than the center displacement (p < .05). The difference between the means of the left and right displacements was 7% at the anterior location and 9% at the posterior location, indicating reasonable symmetry about the mid-sagittal plane. Overall, the standard deviation averaged 38 % of the mean. Figure 5.5 shows the characteristic load-displacement behavior of the endplates in the five locations. Note from the orientation of the axes that this is a graph of compliance rather than stiffness. The steeper slope in the first stage of loading indicates greater compliance at the onset of loading than at the maximum load of 2500 N. The specimens were not tested to failure, so the compliance cannot be characterized to the point of ultimate stress, but in this range of loading generally it follows an exponential function in the early stage and a stiffer linear function thereafter. Figure 5.6 shows the endplate behavior at the center as a function of segment displacement rather than load. The non-linearity of the motion segment stiffness is Table 5.1 Endplate Deformation (in microns) at 2500 N Right Left Right Left Specimen Anterior Anterior Posterior Posterior Center ---.. -... --------.. ------... --------------------------------... ----------------------------------------------------------------------- 1.1 119 101 249 354 166 2.1 113 100 253 326 172 3.1 80 114 115 145 108 3.2 92 93 111 109 109 4.1 255 211 259 246 259 4.2 139 156 154 159 82 5.1 298 232 262 284 291 6.1 138 188 284 246 204 7.1 157 100 411 354 296 7.2 146 137 254 362 317 mean 154 143 235 259 200 std dey 66 49 85 89 82 ... 2 .Q..). C 1 Q) U 0 1. ~ anterior .. posterior .... "t7 Q) .~ CU E... 0 .C... C Q) E Q) u .!! a.. :tg.n 0 >< CU E 1.1 2.1 3.1 3.2 4.1 4.2 5.1 6.1 7.1 7.2 specimen Figure 5.4 Anterior and posterior displacements (average of left and right) are normalized to the center displacement to indicate the relative behavior between those locations. Posterior displacement is greater than anterior in all specimens and greater than central in 7 of 10 specimens. ..ce..n. . 300 -ra-.n-t .0.. 250 ~ oS! E I ant ........ ..., 200 c -a- CED r post uCD 150 --s- C'CJ c.. I post .!! "C 100 ---- S center C'CJ c.. "C 50 C CD 0 0 500 1000 1500 2000 2500 load (N) Figure 5.5 Load-displacement behavior of the endplate, averaged from the sample of 10 specimens. Both left and right posterior displacement transducers produced the highest readings. 300 -In C .0.. ~ 250 ...E...... . c(1) 200 E (1) (,) ~ D.. 150 .!t! " .(.1.) a~.. 100 "c (1) S... 50 c (1) (,) 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 segment displacement (mm) Figure 5.6 Endplate displacement becomes a more linear function when plotted against motion segment displacement rather than load, suggesting that the non-linear behavior of the endplate and motion segment are comparable. 56 indicated two ways. First, the data points, which correspond to even intervals of load, occur successively at smaller increments of segment displacement. Second, the end plate displacement flattens out, indicating a dissimilarity between the two independent variables. (A 95% confidence interval is indicated by the thinner lines.) 5.4 Discussion The goals of this study were to determine to what extent the response of the end plate deviates from axisymmetric behavior under compressive load, and to characterize the load-deformation curve for the endplate. The first goal addressed the fundamental nature of the underlying stresses in the disc. It was found that the end plate deformed more in the posterior region than in the center. For an assumed uniform resistance within the trabecular matrix of the vertebral body, a relatively high reactive stress must exist in the posterior region. Since the location of the nucleus is somewhat posterior as well, this suggests that the pressure is higher in the nucleus than in the annulus, as concluded by Nachemson and Sonnerup.41,61 This conflicts with studies which report a fairly uniform pressure across all but the peripheral portion of the disc.25, 38 The second goal addressed the strain-sharing between the soft tissues of the annulus and the bony tissues of the vertebral body. Radial bulging of the annulus has been reported between 1 -2 mm for the level of loading applied in this study. 53, 63 This is an order of magnitude greater than the deformation of the end plate observed here and in other studies, leading to the perception that the soft tissue dominates the deformation of the motion segment. This has led several investigators to state without 57 statistical data that at small loads, deformation of the end plate is very slight, if measurable.5, 24,54 The accompanying graphs of the load-displacement behavior in their articles in fact can be interpreted quite differently. The intuitive extension of the prevailing hypothesis, together with the perception that it is the soft tissue of the disc that provides the shock-absorber mechanism in the spine, is that the annulus likely initiates the deformation of the whole motion segment. In this study, it is shown with statistical data that endplate deformation is no less remarkable at the onset of load than it is at high loads. In fact, it is in the first 500-N increment of load that the end plate displays its greatest compliance. This is consistent with the comments of Roaf52 who observed that in compression the vertebra bleeds, and proposed that this is the more active component of the dampening mechanism of the spine. These data support such an hypothesis, which requires the vertebra to develop strain through endplate and cortical deformation early in the loading event. The data in this study are consistent with those of previous investigators. Holmes found 0.14 mm of deformation at 1600 N;24 Brinckmann et aI., 0.17 mm at 3000 N;6 and Rolander and Blair, 0.22 mm at 2600 N.54 Data are still needed to fully characterize endplate deformation through its full range of function. Experimental Considerations This was a quasi-static test using a moderate strain rate of the vertebrae. Viscoelastic theory predicts that with a relatively slow loading rate, the tissue will withstand relatively high loads, and that the effect of the viscous component will be minimized. In a study using impulse loading of the vertebra, Holmes et a!. 23 demonstrated a relaxation period of about 2 seconds for the endplate, suggesting in this study that the specimens were adequately accomodated by the 1 mm/min crosshead speed. 58 Holmes et al. 24 also reported that some specimens failed not by fracture but by plastic deformation. It was evident in this study that no substantial plastic deformation occurred since the displacement transducers returned very close to their original readings as the specimens were unloaded following testing. Three specimens were retested one minute following unloading to characterize repeatability of the results. They demonstrated nearly identical load-displacement functions, differing only slightly in magnitude. Also, the effect of multiple drill holes in the specimen was investigated in the first motion segment tested. First, the center hole alone was drilled and the specimen loaded, then the remaining 4 holes were drifled and the specimen was loaded again. Endplate displacement at the center demonstrated similar results as the repeatability test. Future work will use these data and more extensive data from a complete range of loading conditions and specimen types as input to stress analysis models. Together with data from diseased specimens, this will help determine how much pathologic conditions compromise the ability of the spine to withstand loads corresponding to certain activities like lifting and will help clinicians recommend limits to those at risk. 59 CHAPTER 6 ANALYSIS OF VOLUME CHANGES OF THE DISC AND TENSILE STRESSES OF THE VERTEBRAL ENDPLATE UNDER COMPRESSIVE LOAD 6. 1 Disc Volume Analysis 6. 1.1 Introduction The results of the experiments confirm that when a spinal motion segment is compressed, the disc bulges radially and the endplate deforms axially. Various investigators6 . 54 have analyzed the redistribution of the disc volume under load, separating it into annular bulge and endplate deformation parts. Brinckmann et al.,E' using the data of other investigators, concluded that the annular bulge accounts for 20-50% of the cylindrical change of disc volume as calculated from the product of the cross-sectional area and the loss of height of the motion segment. From this, it was estimated that the endplate deformation volume accounts for 50% of the cylindrical volume change. A more precise value, it was explained, is precluded by the scatter in the reported data. The experiments from this dissertation, on the other hand, provide both endplate deformation and annular bulge data on the same sample of specimens, providing a matched basis for comparison. Rolander and Blair, 54 using extensometers spanning vertically from one vertebra to the next, suggested that annular bulge dominates the redistribution of the disc volume early in the loading event, but that at higher stages of loading, end plate deformation reaches a similar level. The assumption implied by the methods of both of these earlier studies is that disc volume is conserved under load. Researchers 60 apparently have reasoned intuitively that because the disc bulges radially and axially, its volume is not strained but rather redistributed. Conversely, the existence of a compressible trabecular matrix in the vertebra has prompted at least one estimate of the volume strain of the bony portion of the motion segment. Brinckmann et al.6 concluded that the strain of the vertebral body at 3000 N compression was 3% due to endplate deformation. This result, however, was compromised by the assumption of a cylindrical shape for the deformation. The purpose of the following volume analysis is to determine for an essentially matched sample the proportion of cylindrical disc volume loss redistributed as annular bulge and the proportion converted to vertebral strain through endplate deformation. Again, the calculated cylindrical volume loss is equal to the motion segment height loss times the area corresponding to the effective radius of the disc. Below is a symbols list for the analysis. Table 6.1 List of Symbols for Volume Analysis Vd undeformed disc volume V / deformed disc volume Vc' cylindrical portion of deformed disc volume loss (Ve O =Vd) Va annular bulge volume Ve endplate deformation volume a effective disc radius h undeformed disc height h' deformed disc height b d m Pa P. Pa P. annular bulge at the apex (averaged from contour) maximum end plate displacement coefficient of the parabolic curve describing annular bulge radius of curvature of annular bulge radius of curvature of deformed endplate angle scribing half-arc of curvature of annular bulge angle scribing half-arc of curvature of deformed end plate angle opposite aa; (2Ps + as = 180°) angle opposite a.; (2P. + a. = 180°) Undeformed Volume and Cylindrical Portion of Deformed Volume 61 For simplicity, the shape of the undeformed disc is taken to be a cylinder, approximating the disc radius as constant from end plate to endplate and the endplate shape as flat. Slight initial curvature is observed in the disc and end plate when working with motion segments, but geometric analysis of parabolas shows that for a consistent disc height, radius, and difference between the initial and deformed curves at the apex, the bulge or deformation cross-sectional area is constant regardless of the initial curvature. Therefore, error is not introduced into the analysis by assuming a flat volume initially, except that for normalizing functions, the initial disc volume is slightly underestimated. This simplification is intended to facilitate the visualization of the volume changes. The volume of the undeformed disc cylinder is simply Vd = Tta 2h The cylindrical portion of the deformed volume, in turn, is 62 1ta2 hi The difference of the two represents the disc volume deformation before correcting for annular bulge and end plate deformation volumes. v~ = 1ta 2 (h-hl) This expression for the cylindrical portion of the deformed disc volume of course makes the simplification that all the axial strain of the motion segment occurs in the disc. Reported values for the modulus of trabecular bone indicate that the strain of the vertebra may be as high as .004 at 2500 N, which for a vertebral height of 20-25 mm (after sectioning) accounts for about 0.1 mm of the motion segment displacement. In the experiments, 2500 N compressed the motion segment 1.7 mm on average, so that the axial vertebral strain constituted about 12% (two vertebrae per motion segment) of the motion segment strain. In the calculations section, h' is allowed to vary between the values it would assume with no vertebral strain and with 12% vertebral strain. 6. 1.3 Annular Bulge Volume The shape of the annular bulge profile has been described either as parabolic 6 or circular.30 In this analysis, both curve types are assumed and the results are compared. The case of a circular profile is treated first. Figure 6.1 diagrams the analysis for this profile. A circular function for the bulge cross-section generates a radius of curvature, Pa' This parameter was discussed qualitatively by Klein30 but not reported quantitatively. The radius of curvature is determined by fitting a curve to the three points defined by circle formed by radius of curvature h b disc center line i i i i i ! I ---'--~I ~ a deformed disc undeformed disc Figure 6.1 Diagram of analysis for circular bulge profile. Radius of curvature is determined from the bulge, b, and disc height, h. Initial disc volume is assumed cylindrical with radius, a. 63 the bulge-- the bulge point itself and the point to either side representing zero bulge. In the case of both annular bulge and endplate deformation the zero-bulge points correspond to the margin or periphery of the vertebral body. The angle, Pa, fo