A Nonlinear Contact Algorithm Predicting Facet Joint

A NONLINEAR CONTACT ALGORITHM PREDICTING FACET JOINT

CONTRIBUTION IN THE LUMBAR SPINE

A Thesis

Presented in Partial Fulfillment of the Requirements for the

Degree Master of Science in the

Graduate School of The Ohio State University

Kimberly Anne Vandlen, B.S.

Industrial and Systems Engineering

*******

The Ohio State University

2009

Master’s Examination Committee

Dr. William S. Marras, Advisor

Dr. Daniel A. Mendelsohn

ABSTRACT

It is hypothesized that the facet joints may play an important role in the causality

behind back pain. Previous biomechanical models lack detailed facet geometry and

contact modeling, the inclusion of cartilage, and the modeling of the full lumbar spine.

The objective of this study was to more realistically assess facet loading in an existing

low back biomechanical model. The second objective of this study was to demonstrate

how the model including facets reports load distribution in pushing and pulling tasks.

Several new components were added to an existing biomechanical model: realistic

geometry (based on CT & MRI), more accurate facet radii of curvature, articular cartilage

thickness, and contact algorithms which defined the contact between each lumbar spine

facet. Trials were run once with facets turned on, and repeated with facets turned off.

Resultant disc loads were lower in the model with facets. The model clearly

showed facet to lamina contact for many of the trials studied. Facets at L4/L5 and L5/S1

bore about 40% of the total load through those segments.

The nonlinear model performed well. The facets bear a large portion of the load though the lumbar spine. Load transmission percentage results with the facet model are comparable to previous studies. The facets bore a greater amount of load in pushing tasks than in pulling tasks. The direction of the offloading of the intervertebral discs is not as straightforward as previously hypothesized. Including realistic facets in the model does

ii not necessarily result in decreased anterior-posterior shear loads within the disc under these loading conditions.

iii

ACKNOWLEDGEMENTS

I would like to extend a special thank you to my advisor, William Marras, for his support while I have worked in the lab and during the thesis journey. He pushed me to challenge myself in ways that I hadn’t done before, and I am stronger for it. Thanks also to the second member of my committee, Dan Mendelsohn, who lent his expertise and his time for many question-filled meetings.

Thank you to my cohorts in the Biodynamics Lab, especially the modeling team. Greg, Cliff and Peter contributed a tremendous amount of knowledge and time to aid in my understanding of the whole system. Thanks also to Greg for reviewing my thesis. The working environment I was surrounded with could not have been more pleasant.

Finally, thank you to my family. My parents have supported me throughout. All of my gratitude goes to my husband Jeff, whose patience and encouragement kept me strong.

VITA November, 6 1983 …………………………….. Born - Hillsdale, MI, U.S.A.

2006 .………………………………………….. B.S. Mechanical Engineering

Hope College, Holland, MI

2006-Present …………………………………… Research Assistant

The Biodynamics Laboratory

The Ohio State University

FIELDS OF STUDY

Major Field: Industrial and Systems Engineering

TABLE OF CONTENTS

Page

Abstract ………………………………………………………ii

Acknowledgements ………………………………………………………iv

Vita ……………………………………………………….v

List of Tables ……………………………………………………..viii

List of Figures ………………………………………………………ix

Chapters:

1. Introduction …………………….…………………………1 1.1 Anatomy …………….…………………………2 1.2 Potential Pain Pathways ………….…………………………4 1.3 Facet Modeling …………….…………………………5 1.4 Biomechanical Model …….…………………………9 2. Methods ………………………………………………………11 2.1 Overview ………………………………………11 2.2 Modeling Software Overview ………………………13 2.3 Material Properties ………………………………13 2.4 Lumbar Spine Geometry ………………………………14 2.5 The Articular Facets ………………………………………17 2.6 Model Building ………………………………………21 2.7 Experimental Conditions ……………………………....23 3. Results ………………………………………25 4. Discussion ………………………………………41 5. Conclusions and Future Work ………………………………………51 5.1 Conclusions ………………………………………51 vi

2.2 Future Work ………………………52 Bibliography ………………………………………………………54

vii

LIST OF TABLES

Table Page

1.1 Percentages of total sample (n=25) population…………………………………..4

1.2 Previous spine FEM and contact models………………………………………...8

2.1 Model material properties………………………………………………………13

2.2 Anthropometric data of test subject…………………………………………….15

2.3 Constants for ADAMS IMPACT function……………………………………..21

3.1 Conditions tested in facet model………………………………………………..25

3.2 Percentage of max contact load relative to max resultant load without facets….40

4.1 Facet static load transmission literature………………………………………....48

viii

LIST OF FIGURES

Figure Page

1.1 Facet joint capsule……………………………...………………………………..3

2.1 Methods flowchart…………………….………………………………………..12

2.2 Lumbar spine model with facet contacts..………………………………………16

2.3 Overlap of contacting bodies……..…………………………………………….18

2.4 Problem description, contact with coated bodies...……………………………..19

2.5 Force-displacement curves for L4/L5…………………………………………..20

2.6 Graphical representation of facet contact……………………………………….22

3.1 Percent difference (pushing, heavy load)………………………………….……28

3.2 Percent difference (pushing, light load)……………………………....………...28

3.3 Percent difference (pulling, heavy load)………………………………….….…29

3.4 Percent difference (pulling, light load)……………………………....………....29

3.5 Average of resultant disc loads, facets on…………………………….………...32

3.6 Average of resultant disc loads, facets off…………………………….………..32

3.7 Left and right resultant contact forces………………………………….……….33

3.8 Pushing, superior disc loads with and without facets…………………..…….....34

3.9 Pulling, superior disc loads with and without facets…………………..………..34

3.10 Pushing, inferior disc loads, with and without facets…………………..……...36

3.11 Pulling, inferior disc loads, with and without facets…………………..………36

3.12 Pulling/50% handle height/light – disc & facet loads L4/L5……………………..38

3.13 Pulling/50% handle height/light – disc & facet loads L5/S1……………………..38

3.14 Pushing/50% handle height/heavy – resultant loading comparison………………39

3.15 Comparison of load born by facets with different stiffness values……………….40

4.1 Graphical example of facet to lamina contact……………………………………...42

CHAPTER 1

INTRODUCTION

The study of the causality behind low back pain is an ongoing one in the world of biomechanics because of the number of people who experience back pain. Approximately

80% of Americans will experience some type of back pain during their lifetime[1]. It is estimated that every year in the United States almost 600,000 people take time away from work to treat or recover from musculoskeletal pain or functional loss [2]. The significance of this problem should not be underestimated. A common speculation as to the causality behind low back pain is disc and facet joint degeneration[3]. As the intervertebral discs deteriorate, the zygapophyseal (facet) joints are consequently called upon to bear a greater load. The facet surfaces degenerate via ossification and the deterioration of the surrounding cartilage. The aim of this study is to develop a more realistic representation of the forces occurring in the facet joints, in order to better understand their role in spinal loading possibly leading to low back pain.

1. 1 Anatomy

The facet joints are within the posterior elements of the spine, which are the bony processes that engage when the spine is extended or in torsion. The surfaces that touch between the upper and lower posterior elements are called articular facets, which are a part of the facet joint. These joints are reported to transmit anywhere between 2-59% of the load through the spine[4-7]. The facets are also richly innervated with branches of the spinal nerves[8]. The facet joints are so close to the intervertebral foramina, the area through which the spinal nerves pass from the vertebral canal, that it is easy for the facets to cause irritation if they are pushed beyond their physical limits via extreme torsion or bending.

The facet joints are paired synovial joints that join the vertebral arch of one vertebra to the arch of the next vertebra[9]. The facet surface lies between the superior and inferior processes of a vertebra. The facet joint is the only synovial joint in the spine, and it consists of hyaline cartilage that overlies subchondral bone, with a synovial membrane and a joint capsule (Figure 1.1, [10]). The articular cartilage surrounding the bony portion of the facets is covered with a film of synovial fluid which facilitates in the gliding movement between the articular processes and to consequently reduce friction[11]. The joint is encapsulated, and the amount of space in the joint capsule has a synovial fluid capacity of approximately 1-2 mL [12], while larger facets are more likely to carry a wider capsule[13]. Finally, the outer layer of this facet capsule is known as the capsular ligament [14]. The capsular ligaments provide joint stability and act as a form of mechanical support throughout facet contact and separation.

Figure 1.1: Facet joint capsule. IAP, inferior articular process; SAP, superior articular process; cart, articular cartilage; men, meniscus[10].

It has been shown that the curvature of the articular facet surfaces varies both by the level of the spine as well as between subjects. Horwitz et al. [15] performed a roentgenographic study of the lumbar spine on a population of 25 human cadaveric spines (Table 1.1). Samples from the population of facets were categorized as curved or flat and are shown as percentage of the total sample population in Table 1.1. This study found that in the lower levels of the lumbar spine, the facets are more likely to have a flat, planar surface. In the higher levels of the spinal column, especially L2/L3 and L3/L4, facets tend to have more of a curved surface. In an anatomical study, Bogduk [11] also concluded that the facets may be planar or curved, but went on to describe the curvature of the facets as either C-shaped or J-shaped. C-shaped facets, then, have a larger surface area which faces posteriorly and can afford greater resistance to motion. J-shaped facets have only a small portion of their articular surfaces facing posteriorly, and therefore offer less resistance than C-shaped facets. The fact that shapes of the facet surfaces can change both between subjects and between levels of the spine becomes very important when modeling the facet contact interaction at all spinal levels.

Table 1.1: Percentages of total sample (n=25) population [15]

Level Flat Curved L1/L2 44 56 L2/L3 21 79 L3/L4 19 81 L4/L5 51 49 L5/S1 86 14

1.2 Potential Pain Pathways

There are different hypotheses for facet pain, ranging from that which is related to the facet anatomy just described to pain sensing via the Neuroanatomic system. One potential source of pain occurs when a superior facet bottoms out on the lamina of the inferior vertebral body[7] Because the facets are so richly innervated, this type of irritation is thought to be a potential source for back pain. Secondly, when facets are injured or deteriorating, the related spinal nerves are also affected and this is hypothesized to be a significant cause of low back pain [9, 10, 16]. A common method of diagnosing facet joint pain is through controlled diagnostic blocks[11]. One study used these injections to investigate predictors of low back pain due to the facet joints [17]. The investigators found that though facet joint pain is not uncommon, there are no clinical indicators for this type of pain. Some studies have come to similar conclusions [18], while still others have been able to identify origins of facet joint pain [19, 20]. Therefore, the pain-producing mechanisms in the facet joint cannot be described solely on the basis of anatomic compromise[21].

Neuroanatomic studies take a deeper look into the causes of low back pain. The peripheral nerve endings within the facets can become sensitized by chemical mediators

4 which are released when the tissue is damaged and inflamed [16]. These inflammatory mediators produce a continuous background discharge in the sensory nerves of the joints, which causes the nerves to be extremely sensitive to mechanical stress. Therefore, when these chemical mediators are present, fibers in the facets that would otherwise fire only when the mechanical stress was clearly noxious will instead fire at a much lower state of stress. Another inflammatory mediator is substance P, which is a neurotransmitter that resides in sensory nerves. As previously indicated, the facets are richly innervated and contain open nerve endings, which possess substance P [22]. Substance P causes vasodilation, plasma extravasation, and a release of histamine from mast cells [23]. These are an integral part of the inflammatory cascade, which is a source of prolonging pain.

The development of a more accurate model with precise geometry and a nonlinear contact definition will allow a greater understanding of the mechanisms causing facet pain. If we can come to an understanding about the types of loads born by the facets, we may be able to indicate where degeneration will start to occur. This would indicate where the spinal nerves will start to be irritated and pain could occur. By creating an anatomically accurate facet model, and by facilitating the output of loads at each individual facet at all levels of the lumbar spine, attempts can be made to better understand facet pain.

1.3 Facet Modeling

Biomechanical modeling is one method used in research to better understand facet contact. In the late-1980’s, researchers modeling the spine began integrating a representation of the posterior elements into Finite Element Models (FEM) of the spine

[4-6, 24-31]. Shirazi-Adl et al. [32] assumed that the material properties of the facet joint lie somewhere in between those of spinal cortical and cancellous bone, and those homogeneous material properties were used for all of the posterior elements in their model. Each FEM model of the posterior elements since then has made this same assumption. In a recent study modeling the knee joint contact, researchers modeled the bone with a cancellous core, cortical shell and cartilage layer and found that the cancellous core played little mechanical role in cartilage contact stresses[33]. For this reason, the bone will be represented using only cortical bone material properties in the current model. Finally, the geometry for the facets is primarily generated from CT scans, and the preferred element types are isoparametric solid elements. The facet contact force has been chiefly represented by gap (contact) elements, which provide a restoring force when two surfaces approach each other, and removes the contact force when the two surfaces separate.

Very few models have accounted for the synovial fluid, possibly because of the complexity involved. Kumaresan et al. [34] compared four different types of FEM contact model approaches in the cervical spine that each included a representation of synovial fluid. The authors suggest that a representation of the synovial fluid medium is a primary step in understanding human cervical spine biomechanics. In the hyperelastic model (HE), synovial fluid was simulated by eight-noded incompressible hyperelastic solid elements and the gap between the cartilages was filled with synovial fluid. In the fluid model, synovial fluid was modeled by hydrostatic incompressible fluid elements. In the contact surface model, the contact interaction was achieved by defining a contact plane between the inferior surface of the superior cartilage and the superior surface of the

6 inferior cartilage. This study found that material properties of the articular pillar, synovial fluid/membrane, articular cartilage and the friction coefficient between the cartilages does not affect the force transmitted through the joint. It is also important to note that these authors chose to represent friction in the contact interaction.

A summary of some of the aforementioned studies can be found in Table 1.2.

Though these models have accounted for the posterior elements or the facet joints specifically, the anatomical description of the facet joints is not thorough in many of them. There are no models in this list that consider the system behavior of the synovium, the cartilage on the facets, and the spinal ligaments. The majority of models are built via the Finite Element method, which can be computationally intensive and is not a desirable addition to the current model in this study. The FE models primarily use gap elements, which estimate contact stiffness properties based on material properties of surrounding elements and do not take into account facet geometry. Other models are static and they usually do not include muscles. Also, much of the geometry in existing models do not come from the same subject as the motion or loading data that is run through them. It is certain that there are limitations to the previous literature that call for the improvements made in the current study.

Table 1.2: Previous spine FEM and contact models

Facet Location Synovial Facet Facet Reference Type Geometry (Spinal Levels) Fluid Cartilage Articulation Kumaresan et al, 1999 [35] FEM CT C4-C6 YES -- -- Teo & Ng, 2001 [36] FEM 3D digitization C4-C6 -- -- Contact elements Kumaresan et al, 1998 [34] FEM From literature C1-C7 -- YES Slideline elements Rohlmann et al, 2006 [25] FEM CT scans and literature L3/L4 -- -- 0.5 mm gap Williams et al, 2007 [37] FEM CT L4/L5 -- -- Contact elements Calisse et al, 1999 [38] FEM X-Ray and CT L1-L5 ------Kuroki et al, 2002 FEM CT L4/L5 -- -- Gap elements

Goel et al, 1993 [26] FEM and optimization CT L3/L4 -- YES Gap elements

8 Goel et al, 1994 [27] FEM CT L4-S1 -- -- Gap elements Teo et al, 2003 [4] FEM Multi-axis digitizer L2/L3 -- YES Contact elements Natarajan et al, 1999 [29] FEM CT L3/L4 -- YES Gap elements Guo et al, 2007 [5] FEM Flexible digitizer L3-L5 -- -- Gap elements Schmidt et al, 2007 [24] FEM CT L4/L5 -- -- Contact elements Schmidt et al, 2008 [31] FEM CT L4/L5 -- -- Contact elements Kim et al, 1991 [6] FEM CT L3-L5 -- -- Gap elements Shirazi-Adl et al, 1986 [32] FEM in vitro measurements L2/L3 -- -- 1 mm gap Extension of Hertz Hertz model Eberhardt et al, 1990 [39] theory Coated sphere in spherical cavity -- YES YES Mathematical contact Mathematical Blankevoort et al, 1991 [40] model From literature Knee joint -- YES model Based on Rigid Body Articular surfaces determined either RBSM An et al, 1990 [41] Spring Model mathematically or numerically Elbow joint YES -- Simplified RBSM, modified Rigid Body Spring Coated sphere in contact with articular joint Hertz, elasticity Li et al, 1997 [42] Model and others hemispherical layer model -- YES theories Eberhardt et al, 1991 [43] Elasticity theories Sphere to sphere contact Patella -- YES Elasticity theories

1.4 Biomechanical Model

The foundation for the modified facet model is an established electromyography(EMG)-assisted model developed and validated by Marras et al.[44-

48]. This biologically assisted model was developed in order to represent spine loading under dynamic, three-dimensional motion conditions [46]. In doing so, the researchers were able to more accurately represent dynamic industrial tasks via the model, rather than simplifying a complex dynamic task into a static representation. This model has evolved over the past 25 years to include inputs that together predict the loading on the spine at each vertebral level of the lumbar spine.

The current biomechanical model of the whole lumbar spine does not contain a

representation of the contact forces between the facet joints. At first some rough

approximations for the contact force stiffness and damping coefficients were developed.

The contact stiffness was estimated based on the Hertz theory of elastic contact, which

estimates that locally near the contact each contacting body is an elastic half-space

loaded over a small region in its surface, and where the contact area between two

surfaces is assumed to be elliptical[49]. This theory assumes that the two contacting

surfaces contact initially at only one point and takes into account the actual relative

curvatures of the two contacting bodies. The material properties of cortical bone were

determined from the literature[50], and were assumed to be the same for both the

inferior and superior facets. A single resultant contact force for one facet pair was

assumed and an average radii of curvature was calculated over the entire facet surface.

This way of modeling facet contact forces does not provide realistic contact force values

for the following reasons: some facets are planar while other are curved, and the Hertz

assumptions do not hold true for all of these facet surface geometries; also, this facet

contact description does not account for the cartilage and synovium which surround the

posterior elements. Furthermore, this approximation does not allow for multiple discrete

contacts that can occur at different points (with different local curvatures) on the facet-

pair surfaces at the same time. Also, the average curvatures used over an entire facet

surfaces make no sense when applied to actual local simultaneous point to point

contacts. Hence, the much refined model described in this thesis was developed.

The objective of this study is to more realistically assess loading in magnitude and direction in the existing low back injury risk model. With modifications, the model will include a more accurate representation of the forces occurring between facet joints in the spine during engaged facet contact. The model will be tested on data collected from a lab study investigating spinal loads during pushing and pulling[51]. The second objective of this study is to demonstrate whether the model with updated facets will show a difference in facet loads between these two types of industrial tasks.

CHAPTER 2

METHODS

2.1 Overview

A summary of the modeling process used in this study is found in Figure 2.1. This model is unique because it uses an accurate description of the anatomy of the facet. The model includes: the material properties of the bone and cartilage, the radius of curvature of each individual facet, and it also accounts for articular cartilage while considering the synovial fluid’s properties that make the joint frictionless. Though a physical representation of the capsular ligament is still under development, the support provided by all of the spinal ligaments is embedded in the stiffness parameters chosen for the discs in the model.

Figure 2.1: Methods flowchart

2.2 Modeling Software Overview

The modeling software used for the current model is the MSC ADAMS

(Automatic Dynamic Analysis of Mechanical Systems) rigid body modeling software package. ADAMS can simulate the reaction of modeled bodies to motions, forces, and other test data while accounting for momentum and gravitational effects. The updates to the facets were also completed in the ADAMS software environment. To “Setup” the model in ADAMS, each vertebral body was imported into a single database. The cartilage layers were joined to each facet as a solid part.

2.3 Material Properties

The next step in updating the facet model was to choose material properties for model elements. The facet joints in the model were assumed to be comprised of the homogenous properties of cortical bone covered with a homogenous cartilage layer. The material properties of the cartilage were taken from Kumaresan et al.[34], and were used for cartilage layers on both facets at each lumbar vertebral level. See Table 2.1 for the material properties for all of the important elements in this model.

Table 2.1: Model material properties

Material Young’s Poisson’s Density Reference Modulus Ratio (kg/mm^3) (MPa) Cortical bone 12,000 0.3 1.76E-6 [27] Cartilage 10,400 0.4 1.1E-6 [52]

The intervertebral discs were represented by multidimensional spring-dampers calculated with translational and torsional stiffness and damping parameters found in literature. Gardner-Morse and Stokes[53] determined stiffness values of the L2/L3 and

L4/L5 motion segments via cadaveric testing. Since the values they presented were determined from motion segments with the ligaments and the facets intact, the values used in the current model were reduced slightly to account for the stiffness from all of the spinal ligaments (including capsular ligaments) but to ignore the stiffness due to facet contact.

2.4 Lumbar Spine Geometry

The geometry for the lumbar spinal segment used in this model was obtained via

computed tomography (CT) in vivo with 0.625 mm slices . The subject was a 24-year-old

male with no previous history of low back pain. Anthropometric data for this subject can

be found in Table 2.2. The CT scans were compiled to create a three-dimensional model

of the lumbar spine from T12/L1 to L5/S1. Figure 2.2 is an image of the detailed model

created from the CT scans. The detailed geometry of the CT scans allow for extraction

of radii of curvature of the individual facets. According to the literature, cartilage

thickness ranges from 0.2 mm [4, 54, 55] to 3.02 mm[56]. Since cartilage degenerates

with time[57], the cartilage thickness chosen for this study was on the lower end of that

range. An estimate of 0.5 mm was made for the thickness of the cartilage surrounding

the bony facet joints[29]. This value was chosen as a realistic approximation for the

amount of cartilage in an adult, given that there is definite deterioration of cartilage over

time. It was also determined upon inspection of this subject’s CT scan that the cartilage

had to be less than 1 mm.

Table 2.2: Anthropometric data of test subject

Age (years) 24 Subject Weight (kg) 74.84 Stature (cm) 178.99 Xyphoid Breadth (cm) 29.39 Xyphoid Depth (cm) 23.39 Illiac Breadth (cm) 27.71 Illiac Depth (cm) 18.21 Spine Length (cm) 57.0 Torso Circumference (cm) 86.0 Subscapular Skinfold (mm) 11.0

Figure 2.2: Lumbar spine model with facet contacts

2.5 The Articular Facets In order to determine the components of the force equation describing facet contact in ADAMS, the following assumptions were made.

1. The cartilage layer was a continuous thickness of 0.5 mm over the entire facet

surface.

2. The material properties of the bone and the cartilage were linear and isotropic.

3. The synovial fluid, which serves the purpose of lubricating the joint, enforces

the condition of zero friction during the contact.

4. One facet in each contact location has a much larger radius of curvature which

is considered infinite in calculating stiffness constants.

The radius of curvature for each contact surface was determined by fitting a surface to the face of each of the facet surfaces. After observing small areas where the contacts occur, patches were selected and a radius of curvature was measured for each patch. The equivalent radius of curvature for that portion of the facet face was determined by averaging the radii of each patch.

The contact force uses the ADAMS IMPACT function, where the contact force is described as:

F = k*(distance) n (6)

where k is the material stiffness, n is the force exponent, and the distance is the total

distance between the centroid of the intersection volume the closest point on each of the

intersecting bodies (Figure 2.3).

Figure 2.3: Overlap of contacting bodies

To represent the contact between two articulating facets, several studies using mathematical descriptions of contact force were reviewed. Some of these papers describe contacting bodies but do not include a coating on the bodies[58, 59] which was needed in this model to represent the cartilage. Other contact models focused primarily on contact between a sphere and a spherical cavity[39, 41, 42, 60, 61], which does not apply to the current model because it is conformal contact and does not represent the point contact occurring between facets. After this review, an extension of the Hertzian contact theory model was chosen[61]. The Hertz equations are commonly used in the fields of contact and engineering mechanics to describe circular and elliptical point contact. The purpose of this extension model was to predict contact approach, contact radius, and maximum contact pressure for both circular and elliptical contact problems of coated bodies. This extension applied to the facet model because it describes the contact of coated bodies: in the facet contact problem, the bone of the articulating facets was considered to be the substrate of the coated body and the cartilage was the coating. Figure 2.4 displays the current contact problem description, where both bodies are coated. In Figure 2.4 the first body is a sphere and the second contacting body is a plate. The current model solutions

18 designate Body 1 as a sphere (which represents the curved superior facet surface) and

Body 2 as a coated plate (the inferior facet surface).

Figure 2.4: Problem description, contact with coated bodies

Given a substrate of cortical bone and a coating of articular cartilage, several equations were adapted from Liu et al[61]. First, the non-dimensional coating thickness is defined as a ratio of the cartilage thickness (h) to the contact radius ( : ͕*. ʛ

H = # (1) *. The following equations were also employed:

• Total equivalent radius,

ͥ ͥ ͥ (2) Ɣ ƍ u v • Total equivalent modulus,

v v ͥ ͥͯ1u + ͥͯ1v (3) ǳ Ɣ u v • Contact radius,

w ao= ͧ (4) ǯ ͨǳ • Contact approach or rigid body motion,

w v δo = ͭ (5) ǯͥͪǳv

The next steps in model building were to use the given information about the specific facets (material properties, cartilage thickness and radii of curvature) to solve for force constants to be used in the ADAMS contact force definition. First, a range of reasonable loads born by the facets was determined from the literature. The range is anywhere from 2-59% of the total load on the spine[4-7], so a range of W from 2-900 N was used in these solutions. By solving Equation 5 for the contact approach ( δo ) over the

range of applied loads (W), a force-displacement curve could be determined (Figure 2.5).

Figure 2.5 shows two force-displacement curves, one at the L4/L5 right facet and one at

the L4/L5 left facet with a cartilage thickness of 0.5 mm.

Figure 2.5: Force-displacement curves for L4/L5

The force-displacement relationship used in ADAMS was then fit to the curve determined from the modified Hertzian solutions. In doing so, an individual stiffness (k) and force exponent (e) value was found for each of the facet contacts in the lumbar spine

(Table 2.3).

Table 2.3: Constants for ADAMS IMPACT function

LEVEL LEFT RIGHT Radius(m) k e Radius(m) k e T12_L1 0.0092 1.85E+08 2.253 0.0078 1.47E+08 2.249 L1_L2 0.0043 6.23E+07 2.225 0.006 1.01E+08 2.24 L2_L3 0.007 1.26E+08 2.245 0.0086 1.68E+08 2.251 L3_L4 0.0135 3.07E+08 2.258 0.0094 1.90E+08 2.253 L4_L5 0.0108 2.30E+08 2.256 0.0304 8.49E+08 2.257 L5_S1 0.0151 3.56E+08 2.259 0.0129 2.91E+08 2.258

2.6 Model Building

The cartilage is represented in the model by a 0.5 mm shell placed around the outside of the articular portion of the facet surface. Both the inferior and superior facet surfaces of facets in the lumbar vertebrae have this layer. The layer representing the cartilage was created in the Rapidform XOR (Inus Technology) solid modeling program, and then imported and joined to the ADAMS rigid body of the facet at the layer’s center of mass. An ADAMS contact force was created between the layered articulating surfaces.

The layer of articular cartilage can be found in Figure 2.6 (see the portion encircled in black), a snapshot of the facet model during a trial simulation. The added depth from the 0.5 mm cartilage layer is shown by the darker portion in this posterior view. Also in this figure are arrows representing the depiction of the discs (yellow), the muscles (red) and the facet contact (blue).

Figure 2.6: Graphical representation of facet contact

2.7 Experimental Conditions

In order to show the feasibility of the modified facet model, a demonstration subject was chosen from a study previously performed in the lab assessing the current biomechanical model for pushing and pulling tasks[51]. This was one of three pushing and pulling studies assessing the complex loads occurring on the spine that differentiate themselves from traditional lifting tasks[51, 62, 63]. Results showed that lumbar lordosis was maintained during pushing, whereas the subject tended to flex their spine during pulling[51]. Part of this was due to the fact that the subject was encouraged to keep their upper torso vertical during the tasks. One would consequently expect prolonged contact between facets during pushing tasks and intermittent contact (disengaged facets) during pulling tasks. This study also found significant shear loading at the upper levels of the lumbar spine that are expected to load the facets.

Because of the nature of this study, the data were chosen as a test bed for the biomechanical model with updated facet joints. The elements of the push-pull study give good examples of dynamic industrial tasks. Since there were distinct differences in the amount of facet contact between pushing and pulling, this data was an appropriate choice for demonstrating the ability of the modified facet model to decipher between contact force magnitudes in the facet joints.

The trials chosen to run in the model were from pushing and pulling tasks where very high and very low loads on the spine were determined[51]. The conditions chosen were at the heaviest load (40% of the subject’s weight, 29.9 kg), the lightest load (20% of the subject’s weight, 15.0 kg), at the highest handle height for pulling (80% of subject’s height, 143.2 cm) and at the lowest handle height for pushing (50% of subject’s height,

89.5 cm). There were four repetitions per condition. The specific tests of the model were: a) Comparing facet contact forces between a pushing and a pulling task and b)

Comparing spinal loads at each intervertebral level in a the lumbar spine model with modified facets to spinal loads in a model with the facet contact forces turned off. High shear loads are expected at upper levels of the spine at the 80% handle height for pulling and the 50% handle height for pushing.

CHAPTER 3

RESULTS

The conditions examined from the push-pull data have been laid out in the previous section. The actual conditions used for testing the model were slightly modified and can be found in Table 3.1. Pushing trials with the heaviest load at the 80% handle height were omitted. Upon inspecting that extreme condition, some of the equipment was out of its calibrated range, and therefore it was deemed invalid to examine these trials.

Table 3.1: Conditions tested in facet model

ACTIVITY HANDLE LOAD

Push 50% Heavy Pull 80% Heavy Pull 50% Heavy Push 80% Light Push 50% Light Pull 80% Light Pull 50% Light

Some noise was observed in the results from pulling the heavy load at the 80% handle height, and pushing the heavy load at the 50% handle height. These are the conditions in which the spine reached the most extreme extension and torsion. In excessive extension, the facets at L4/L5 and L5/S1 were in constant contact. The stiffnesses of the contact force at these levels were also higher, given that these facets

25 were more curved and therefore had higher radii of curvature. The stiffer contact caused some shifting of the vertebral bodies between the left and right facets, which can account for the noise in these two conditions. The peak disc and facet loads reported here were not affected by this noise.

The current facet model was created in such a way that the updated facets and their corresponding defined contact forces could be turned on or off. Each of the trials from the push-pull data was run through the model twice. First, the facets were turned on and the model was controlled by a torque. The intervertebral angular velocities were recorded and used to drive the motion in the second simulation with the facets turned off.

In this way, the motion was exactly the same between the two simulations and all changes could be contributed solely to the addition of the facet contact forces to the model.

The purpose of this study was to see how the model system would behave with

the addition of the facet joints and their load-sharing behavior in the lumbar spine.

Results will be interpreted via face validity since there is no way to really validate this

model in vivo. Overall, the model performed as expected. Allowing the facets to bear

load took a large portion of the load off of the discs at most of the vertebral levels of the

spine. Figures 3.1-3.4 show the percent difference (separated into pushing and pulling by

load, and the x-axis represents each trial at this condition) between the resultant disc

loads in the model with facets compared to the model without facets. Note that in Figure

3.1, levels T12/L1 to L2/L3 are all close to zero. A negative value indicates that the

resultant load in the model with facets was lower than the resultant load in the model

without facets, thereby signifying that the facets reduced the loading in the discs. The

26 load at the disc was reduced for all trials from levels L3/L4 to L5/S1, and for about 20% of the trials from T12/L1 to L2/L3. In most of the trials from T12/L1 to L2/L3 where the loading was not reduced by the facets, there was minimal difference between having the facets on or off.

0 1 2 3 -10

-20 L5/S1 -30 L4/L5 L3/L4 -40 L2/L3 -50 L1/L2

Percent DifferencePercent (%) T12/L1 -60

-70

-80

-90

Figure 3.1: Percent difference between facet and non-facet model prediction (pushing, heavy load)

0 1 2 3 4 5 6 7 -10

-20 L5/S1 -30 L4/L5 L3/L4 -40 L2/L3 -50 L1/L2

Percent DifferencePercent (%) T12/L1 -60

-70

-80

-90

Figure 3.2: Percent difference between facet and non-facet model prediction (pushing, light load)

0 1 2 3 4 5 6 7 -10

-20 L5/S1 -30 L4/L5 L3/L4 -40 L2/L3 -50 L1/L2

Percent DifferencePercent (%) T12/L1 -60

-70

-80

-90

Figure 3.3: Percent difference between facet and non-facet model prediction (pulling, heavy load)

0 1 2 3 4 5 6 7 8 -10

-20 L5/S1 -30 L4/L5 L3/L4 -40 L2/L3 -50 L1/L2

Percent DifferencePercent (%) T12/L1 -60

-70

-80

-90

Figure 3.4: Percent difference between facet and non-facet model prediction (pulling, light load)

The load-sharing between the discs and the facets was very complex. The facets were engaged most of the time during torsion and lateral bending, but this did not necessarily correspond to a decrease in lateral and AP (anterior-posterior) shear loading of the discs. Therefore, a resultant measure was created for both the disc and facet loads.

The resultant load on the disc was created using vector addition which combined the AP shear, lateral shear and compression. The resultant facet load for the left and right facets was calculated in Adams at each level. The peak resultant disc force and the peak contact force were calculated for each trial, and then averaged to obtain an overall value for both pushing and pulling. Figure 3.5 is a comparison between pushing and pulling of the disc loading during the trials with facets. As expected, the overall loading of the disc was lower during pushing where the spine was more lordotic and the facets were engaged, bearing some of the load for the disc. The disc loads were higher (~1600 N pulling and

~1200 N pushing) at the upper levels of the lumbar spine, which makes sense because the facets bore a greater load at the lower levels (~1200 N pulling and ~700 N pushing). It can be seen in Figure 3.6 that without the facets, the loading on the discs stayed fairly consistent at 1600 N pulling and 1200 N pushing through all the levels of the spine. It was expected that the magnitude would not change by level with the facets off; instead, the components of the force change by level because of spinal curvature. Again, the resultant disc load was higher in pulling than in pushing. Most studies report higher compression in pulling than in pushing, and the compression was the driving factor behind these resultant forces.

Figure 3.7 shows the left and right resultant loading at the facets. As expected, where the disc loads decreased from T12 to S1, the facet contact loads increased from

T12 to S1. At their peak, the right facet contact loads were just under 800 N. The only exception was for pushing at L4/L5, where the contact force was higher at L4/L5 than at

L5/S1. The contact load was greater in pushing than in pulling for all levels of the spine.

1800

1600

1400

1200

1000

800 Push Pull 600

400

Combined AP,Lat CombinedAP,Lat Shear & Compression(N) 200

0 L5/S1 L4/L5 L3/L4 L2/L3 L1/L2 T12/L1 Lumbar Level

Figure 3.5: Average of resultant disc loads, facets on

1800

1600

1400

1200

1000

800 Push Pull 600 Resultant Disc Loads (N) 400

200

0 L5/S1 L4/L5 L3/L4 L2/L3 L1/L2 T12/L1 Lumbar Level

Figure 3.6: Average of resultant disc loads, facets off

1000.00

800.00

600.00

Push - Left 400.00 Pull - Left Push - Right Facet LoadFacet (N) Pull - Right 200.00

0.00 L5/S1 L4/L5 L3/L4 L2/L3 L1/L2 T12/L1

-200.00 Lumbar Level

Figure 3.7: Left and right resultant contact forces

Figures 3.8-3.11 give the peak disc loads averaged over each condition. Figures

3.8 & 3.9 report the loads measured at the superior endplate of the disc while Figures

3.10 & 3.11 describe loads measured at the inferior disc endplate. The lateral shear indicates the direction of the lateral bending but for data clarity, the lateral shear data are presented here as absolute values. For the most part the loading at the inferior and superior endplates of the disc were nearly identical. The largest discrepancies between values at opposite endplates were seen at L3/L4, where the intervertebral angle is large and the load path changes the most. The differences between superior and inferior disc loads at the remaining levels were 15% or less, and the trends were the same at both endplates of each disc.

1700

1200

Lateral Shear - Facets 700 Compression - Facets AP Shear - Facets Lateral Shear - No Facets Load(N) 200 Compression - No Facets AP Shear - No Facets L5/S1 L4/L5 L3/L4 L2/L3 L1/L2 T12/L1 -300

-800

Figure 3.8: Pushing, superior disc loads with and without facets

1700

1200

Lateral Shear - Facets 700 Compression - Facets AP Shear - Facets Lateral Shear - No Facets Load(N) 200 Compression - No Facets AP Shear - No Facets L5/S1 L4/L5 L3/L4 L2/L3 L1/L2 T12/L1 -300

-800

Figure 3.9: Pulling, superior disc loads with and without facets

It can be noted in Figure 3.10 that in general, disc loads were higher in all directions at the upper levels of the spine and decreased going downward toward L5/S1.

From levels L3/L4 to L5/S1, where the highest facet contact was occurring, the compression on the disc was greater when the model had facets turned off. The AP shear, however, was lower when the facets were off at these same levels. This was one indication that the direction of the offloading of the disc may not be clear, and so it was beneficial to present a resultant disc load as in Figures 3.5 & 3.6. The lateral shear did not change much whether the facets were on or off, but the largest difference was found at

L5/S1 where the lateral shear was slightly higher with the facets turned on.

1700

1200

Lateral Shear - Facets 700 Compression - Facets AP Shear - Facets Lateral Shear - No Facets Load(N) 200 Compression - No Facets AP Shear - No Facets L5/S1 L4/L5 L3/L4 L2/L3 L1/L2 T12/L1 -300

-800

Figure 3.10: Pushing, inferior disc loads, with and without facets

1700

1200

Lateral Shear - Facets 700 Compression - Facets AP Shear - Facets Lateral Shear - No Facets Load(N) 200 Compression - No Facets AP Shear - No Facets L5/S1 L4/L5 L3/L4 L2/L3 L1/L2 T12/L1 -300

-800

Figure 3.11: Pulling, inferior disc loads, with and without facets

Figures 3.12 & 3.13 give a representation of one of the conditions with the lowest loading of the trials run in the facet model. Plots at L4/L5 and L5/S1 were chosen because these were the levels at which the greatest contact forces were observed. Figure

3.12 displays time-dependent, processed data at L4/L5 (including AP and lateral shears, and compression with and without facets as well as left and right facet resultant contact) from a pulling trial at the lowest handle height and with the lightest load. This figure shows the behavior of the model as the spine moved into a posture where the facets are in contact. As expected, the largest discrepancy between the disc loading in the trial with facets compared to the trial without facets occurred at the point in time where the facet contact load resultant was the highest. At approximately 93 seconds into this trial, the facets reached their highest contact loading and therefore offloaded disc L4/L5 the most.

The difference at this point between L4/L5 compression with facets and L4/L5 compression without facets was about 400 N. Figure 3.13 shows the same measures for this condition at L5/S1. At 277 seconds, the compression value with facets was almost identical to that without facets. Correspondingly it can be seen that the facet contact at that point in time was only about 50 N.

1.40E+03

L4/L5 Right Facet Contact 1.20E+03

L4/L5 Left Facet Contact 1.00E+03

L4/L5 Superior Lateral 8.00E+02 Shear L4/L5 Superior 6.00E+02 Compression L4/L5 Superior AP Shear

Load(N) 4.00E+02

L4/L5 Superior Lateral 2.00E+02 Shear (No Facets)

0.00E+00 L4/L5 Superior Compression (No Facets) 1 27 53 79 -2.00E+02 105 131 157 183 209 235 261 287 313 339 L4/L5 Superior AP Shear (No Facets) Trial Time (s) -4.00E+02

Figure 3.12: Pulling/50% handle height/light - disc & facet loads L4/L5

1.40E+03

1.20E+03 L5/S1 Left Facet Contact

1.00E+03 L5/S1 Right Facet Contact

8.00E+02 L5/S1 Superior Lateral 6.00E+02 Shear L5/S1 Superior 4.00E+02 Compression

2.00E+02 L5/S1 Superior AP Shear Load(N)

0.00E+00 L5/S1 Superior Lateral 1

27 53 79 Shear (No Facets)

-2.00E+02 105 131 157 183 209 235 261 287 313 339 L5/S1 Superior -4.00E+02 Compression (No Facets) L5/S1 Superior AP Shear -6.00E+02 (No Facets) Trial Time (s) -8.00E+02

Figure 3.13: Pulling/50% handle height/light - disc & facet loads L5/S1

A trial representative of the conditions with the highest spinal loading was chosen for Figure 3.14. The time-dependent loading is again shown for L4/L5 and L5/S1, but now the contact forces are shown relative to the resultant loads at the superior endplate of each disc rather than the directional loads. This comparison yields a percentage of the total load transmitted through the facets. For this representative trial, the percentage was calculated by dividing the maximum facet contact by the maximum resultant load from the simulation where the discs were the only method of load transmission. The resulting percentages are shown by level in Table 3.2. The facets bore the least amount of load at

L1/L2, accounting for only 0.54% of the total load through that motion segment. The lower levels, especially L4/L5 and L5/S1, accounted for around 40% of the load.

2500

2000

L5/S1 SUP - Facets L4/L5 SUP - Facets 1500 L4/L5 Right Facet Contact L4/L5 Left Facet Contact Load(N) 1000 L5/S1 Right Facet Contact L5/S1 Left Facet Contact L5/S1 SUP - No Facets 500 L4/L5 SUP - No Facets

0 1 30 59 88 117 146 175 204 233 262 291 320 349 378 407 436 Trial Time (s)

Figure 3.14: Pushing/50% handle height/heavy – resultant loading comparison

Table 3.2: Percentage of max contact load relative to max resultant load without facets

Level Percentage (%) T12/L1 1.05 L1/L2 0.54 L2/L3 0.70 L3/L4 15.0 L4/L5 39.55 L5/S1 43.14

Finally, an analysis was performed to determine the effects of changing the inputs into the modified Hertz equations. In Figure 3.15, a comparison of load transmission is made on a sample trial of pulling the light load. The percentage of total load born by

L5/S1 is 17% whether the cartilage thickness is 0.5 mm or 1 mm. At L4/L5, the facets bear 4.5% more load when the cartilage is thinner. The remaining levels of the spine did not show noteworthy changes based upon modifying cartilage thickness because there was little contact at these levels.

10 h=0.5 mm, larger k 8 h=1 mm, smaller k

PercentageLoadBorn by Facets (%) 2

0 L5/S1 L4/L5 L3/L4 L2/L3 L1/L2 T12/L1 -2 Lumbar Level

Figure 3.15: Comparison of load born by facets with different stiffness values

CHAPTER 4

DISCUSSION

This facet model represents a very complex system, and it is appropriate to treat it

as such. Each element included in the model must work together with the others to

embody the complex movements of a human spine in vivo. The primary measures for the testing of the model were facet loads and intervertebral disc loads, but there are many components which can alter or account for these outputs.

There was one unexpected nuance observed while running data through the facet model. Measuring facet loads on the left and right sides of the vertebra proved to be very telling about where unbalanced loading occurred. At L4/L5 especially, the majority of the loads transferred through the facets followed the path on the right side of the joint (when looking at the posterior view of the spine). The magnitude of this contact force was also higher than at any other levels. The location of the contact could be pin-pointed through watching animations of the pushing trials where the facet loads were the highest. At the beginning of these trials, the right L4 inferior facet articulating surface was in contact with the right L5 superior facet surface. At the greatest point of extension in the trial the

L4 inferior facet slipped outside of the L5 articulating surface to come into contact with the L5 lamina (Figure 4.1). This contact continued throughout most of the remaining

41 length of the trial and was the source of the highest contact loads at this level.

Figure 4.1: Graphical example of facet to lamina contact The circumstance of a facet bottoming out on the lamina below is not a new discovery[7, 64]. Yang & King[7] cited this as a serious possible site for origination of back pain, given that this area is richly innervated and the contact might be irritating adjacent nerves or wearing away at the capsular ligament. However, the current model was not designed to account for cartilage to bone or bone to bone contact, but solely the cartilage to cartilage contact that occurs between two facet articulating surfaces. The material properties of the contacting bodies are integral in defining the stiffness coefficients of the contact force; therefore, they should be tailored to account for the cartilage to bone contact that is happening during facet to lamina contact. Though changing the stiffness values might affect the magnitude of the force at this location, it is still expected that the model will show similar facet to lamina contact behavior which

42 would therefore serve as an excellent indicator of what may be a very real source for low back pain.

One of the factors that seemed to have a great effect on loading patterns was the

initial orientation of the vertebrae. Lower concentrations of facet contact force were

observed at the upper levels of the spine. During model building, the spine was rotated

from the vertebral orientation with which it was built (from CT scans) to vertebral

orientations derived from an upright MRI. Scans from the upright MRI gave the benefit

of more realistic intervertebral angles since the subject was in a standing rather than a

supine posture. The rotation applied to the model to match the MRI angles decreased the

lordosis in this subject’s spine because in the supine CT scan a rolled towel had been

placed under the subject’s spine causing it to be more lordotic than was realistic in an

upright posture. The decrease in the lordotic curve caused the facets at the upper level of

the spine, especially T12/L1 and L1/L2, to separate and therefore come into contact less

throughout most of the trials than at lower spinal levels.

The results from the model give a good indication of the magnitude of the load

born by the facets. The highest concentration of contact force was found at L4/L5 and

L5/S1. This makes sense because these levels begin in contact and remain in contact

throughout a trial. Since a contact force was defined for both the left and right side of

each vertebra, this might indicate which portion of the disc is more likely to degenerate

first. In the instance of L4/L5, the right facet contact force was always much higher than

the left. This could mean that the right portion of the disc is offloading some of its force

to the facets, causing tension on the left side of that disc and creating a torque in the disc.

In the push-pull study from which the data run in this model was obtained[51], the researchers found values for AP shears at the upper levels of the lumbar spine that approached or exceeded a proposed safe limit of 1000 N[65]. The supposition was that the shears would not be that high if the facets were included in the model and were able to bear some of the load. The results for AP shears at these levels in the current model indicate that the offloading of the discs is more complex than was believed in the previous study. In many of the trials with the highest facet contact loads, the AP shears actually increased. In pushing, the average AP shear at L5/S1 of the peak values from all the trials increased from about 300 to 600 N and in pulling the difference was slightly greater, increasing from about 350 to 750N. It has been shown that the contact loading at

L5/S1 was also very high, at about 40% of the total load going through that level.

Therefore, it is possible that rather than the facets bearing some of the shear load on the disc, they are actually bearing more of the compressive force on the disc. In turn, the facets at L5/S1 were stiff enough that they actually generated shear forces by pushing the disc anteriorly or posteriorly. It should also be noted that using the current facet model based precisely on subject geometry, the shear loading never reached the same dangerous magnitude as in the previous study (whether the facets were on or off). The average AP shear values approached 800 N but never exceeded 1000 N.

Another possible explanation behind the shears at the upper levels being higher than expected with the facet model could be attributed to the spinal ligaments. Because the ligaments are still under development, they were not included in the model except for in slight modifications of the stiffness of the motion segment via the discs. There was very little facet contact at T12/L1 and L1/L2 (generally <50 N), indicating that the spine

44 at these levels was for the most part flexed during both pushing and pulling trials. During flexion, the capsular ligaments would have provided resistance to the motion and reduced the forward movement of these motion segments. Limiting their ability to flex forward would definitely reduce the AP shears at these levels and in turn pass on more of that force to the facets.

It was difficult to discern the precise direction of the load transmission through the facets and which disc loading components were affected the most. Consequently the resultant loading on the disc became an important measure. Though the average peak AP shear in both pushing and pulling was higher with the facets turned on, the average peak resultant disc loads were higher with the facets turned off. This indicates that the facets indeed play an integral role in the loading of the spine.

There are two sources of load transmission data available for comparison in the literature. The first type of study applies a static, compressive load, typically in an Instron machine, to a cadaveric single motion segment. The facet normal contact is then measured via a pressure sensitive film or a load cell. A representative sample of data from this type of study can be found in Table 4.1. The second type of study that can be used as a means for comparison typically uses cadaver data in an Instron machine as well, but the applied loading is an axial rotation or extension moment rather than static loads.

As a means of comparison to existing load transmission literature, a trial with the

highest spinal loading was chosen and the percentage of load transmitted through the

facet was calculated. At the point of maximum loading in this example trial, the facets

bore 39.55% of the loading through L4/L5 and 43.14% of the loading through L5/S1.

Lorenz and colleagues [66] found in their static loading test that the facets at L2/L3 bore

47% of an applied compressive load of 392.4 N and 57% of an applied load of 196.2 N.

The values in the current study are quite close to those found in the Lorenz study. A more fitting comparison might be to the findings of Sharma et al. [67] which are based on the

FEM analysis of an L3/L4 motion segment. The applied load in this study was a torque rather than an axial compression. An applied axial torque of 10 Nm yielded facet loads of

59% of the total applied load in this model. The data reported in these two studies serve as indication that the current model results fall into a believable range within the literature.

Cartilage thickness can vary between subjects and thin with deterioration, causing

the contact stiffness values to change. If the cartilage thins, the modulus of elasticity of

the bone increases, or the facet radii of curvature decrease, then the resulting contact

stiffness coefficients decrease. It was expected that a smaller contact stiffness value

would lead to lower loads through the facet. This was true in the comparison between a

pulling trial with cartilage thickness of 0.5 mm compared to 1 mm (Figure 3.15).

Other studies (Table 4.1) have yielded a wide range of percent load transmission

values in the literature. Results from the current study are generally on the higher end of

what has been found in previous studies. Differences between the current results and any

of these studies can be accounted for primarily by the different geometries of the tested

specimens. Segment stiffnesses can vary significantly between subjects as well as

between a spine in vivo and a cadaveric spine. Facet curvature is very specific to an

individual, and therefore could account for both the magnitude and direction of the load

going through the facet joints. Cartilage and bone thicknesses and material properties will

also change amongst different spines, both in vivo and in vitro . The cadaveric spines

46 might be older and therefore more likely to have loading influenced by the effects of spinal degeneration. Finally, most studies have tested only one or two motion segments.

The full lumbar spine model behaves as a system, each level having some influence on the next, therefore it is difficult to extrapolate comparable results from a study with a single motion segment. Because each model is geometry dependent, results should be taken to represent the loading for this individual and one should consider the observed trends rather than absolute magnitudes. However, it has been established that the current results match the values found in a few of these studies.

Table 4.1: Facet static load transmission literature

Static Compressive Facet contact Force % of applied axial Reference Load (N) (N) load Model Location Measurement Method 686.70 190.00 28.00 L2/L3 FEM 3D continuum surface-to-surface Teo et al. 2003[4] 1371.40 128.00 9.00 L2/L3 elements

196.20 111.80 57.00 L2/L3 392.40 184.40 47.00 L2/L3 Lorenz et al. 686.70 154.50 23.00 L2/L3 1983[66] 1371.40 119.30 9.00 L2/L3 Pressure sensitive film 196.20 59.00 28.00 L4/L5

48 392.40 37.60 10.00 L4/L5 Lorenz et al. 686.70 22.60 9.00 L4/L5 1983[66] 1371.40 112.20 8.00 L4/L5 Pressure sensitive film FEM 3D sliding surface Guo et al. 2007[5] 400.00 8.41 2.10 L3-L5 contact

1970.00 118.66 6.02 L3/L4

Kim et al. 1991[6] 1970.00 144.19 7.32 L4/L5 FEM gap elements 1000.00 283.25 28.33 L1/L2 1000.00 160.80 16.08 L3/L4 Intervertebral load cell Yang & King 1984[7] 1000.00 260.07 26.01 L4/L5 (IVLC)

It is interesting to note some results are in contrast with some previous research.

In earlier studies that tested more than one motion segment separately, the percentage of load supported by the facets increased in the direction going up the spine. In all of the trials run in the current facet model, the loading at the facets was higher at the lower levels of the lumbar spine. However, in the static tests that applied several loads to a motion segment, higher facet contact was seen when the applied load was smaller. This trend was less intuitive than the other trends observed here.

There are potential limitations to this study that should be mentioned. First, the data evaluated in the modified facet model came from only one subject. Since the particular geometry of this subject was a key factor behind loading results, it could be that other subject’s spinal geometry would change the amount of force offloaded through the facets. There was also no physical representation of the capsular ligament in this model. The geometry would be more complete with all of the spinal ligaments were included. The stability provided by these ligaments would surely affect both disc and facet loading. These ligament models are currently under development.

The modified Hertzian contact solution was found to be the best suited for this model, however a few assumption were made in obtaining solutions. Given the nature of the equations, it was assumed that the radius of curvature of the larger facet in a contact pair became infinite. Minor extrapolation was also necessary using some of the curves in the Liu paper[61]. Parameter studies were performed, and the aforementioned assumptions did not significantly affect the values of the chosen contact stiffnesses.

Finally, this was not a full validation study, rather an attempt at a better understanding of the load sharing between discs and facets based upon face validity.

Nonetheless, there are numerous advantages to this modified facet biomechanical model. First, the model accounts for specific, individual geometry of the spine because of the high resolution CT scans used to build the model. Because the realistic asymmetries of an individual’s spine indicate the uneven loading patterns on the facets, one can deduce a better idea of where degeneration is occurring both in the facets as well as in the adjacent intervertebral disc. Another advantage of this model is that it encompasses the whole lumbar spine. Of the previously reviewed FEM lumbar spine models with facet forces, only one evaluates more than two levels of the lumbar spine[38]. Finally, facet contact forces calculated in this model are more realistic than previous models because the model is biologically-driven and the data used to drive the model came from dynamic tasks in vivo. It has been shown that most previous facet models yield contact forces from a single load applied to a cadaveric spine. However, including facet loads at each level in a model which evaluates dynamic tasks will lead to a more accurate understanding of facet and disc degeneration and facet pain.

CHAPTER 5

CONCLUSIONS AND FUTURE WORK

5.1 Conclusions

The objective of this study was to more realistically assess loading in magnitude and direction in the existing low back injury risk model. Doing so would provide a more accurate representation of the load sharing between the facet joints and the intervertebral discs. The second objective of this study was to demonstrate whether the model with updated facets would show a difference in facet loads between these two types of industrial tasks. Conclusions from the current research are as follows:

1. The facets bear a large portion of the load though the lumbar spine, reaching 40%

or more at L4/L5 and L5/S1.

2. The direction of the offloading of the intervertebral discs is not as straightforward

as previously hypothesized. Having facets turned on in the model does not

necessarily mean that the anterior-posterior shear loads born by the disc decrease.

However, from L3/L4 to L5/S1, the resultant load was always lower through the

disc when the facets were turned on to provide an alternate load path.

3. Comparing the percentage of load transmission through the facet joints is

comparable with values reported in the literature for both static compressive load

testing as well as modeling techniques with moments applied.

4. The facets bore a greater amount of load in pushing tasks than in pulling tasks,

confirming that the spine was flexed more in pulling that in pushing in the

previous push-pull study.

5.2 Future Work

The possibilities for future work shown below would add to the strength of the current facet model.

1. An important area for future work would be to determine how the contact

definition would change for the areas in the lower lumbar levels where the

superior facet is contacting the lamina.

2. Once the development of the representations of the spinal ligaments has been

completed, especially the capsular ligament, these ligaments should be added

to the current facet model to enhance its realism.

3. In order to confirm the consistency in the results found in this model, the data

from multiple subjects should be evaluated.

4. In order to calculate the percentage of load transmission through the facets in

previous studies which have applied torques to their models, it would be

useful to apply these same torques to the current facet model and compare

resulting loading values.

5. A single cartilage thickness value was chosen for this study. It would be

useful to obtain results from the model at several different cartilage

thicknesses to simulate the degeneration and cartilage thinning that occurs as a

spine ages.

REFERENCES

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