Generation of a 3-D Parametric Solid Model of the Human Spine Using

GENERATION OF A 3-D PARAMETRIC SOLID MODEL OF THE HUMAN SPINE USING

ANTHROPOMORPHIC PARAMETERS

A thesis presented to

the faculty of

the Fritz J. and Dolores H. Russ College of Engineering and Technology

of Ohio University

In partial fulfillment

of the requirements for the degree

Master of Science

Douglas P. Breglia

June 2006

This thesis entitled

GENERATION OF A 3-D PARAMETRIC SOLID MODEL OF THE HUMAN SPINE USING

ANTHROPOMORPHIC PARAMETERS

DOUGLAS P. BREGLIA

has been approved for

the Department of Mechanical Engineering

and the Russ College of Engineering and Technology by

Bhavin Mehta

Associate Professor of Mechanical Engineering

R. Dennis Irwin

Dean, Russ College of Engineering and Technology

Abstract

BREGLIA, DOUGLAS P., M.S., June 2006. Mechanical Engineering

GENERATION OF A 3-D PARAMETRIC SOLID MODEL OF THE HUMAN SPINE USING

ANTHROPOMORPHIC PARAMETERS (98 pp.)

Director of Thesis: Bhavin Mehta

It has been shown that there is a correlation between stature and the dimensions of the vertebra in humans [1]. The objective of this thesis is to create a computer model of the vertebra that is personalized based on external metrics. To accomplish this, a parametrically linked solid model of the vertebrae is linked to the height, sex, and ethnicity of an individual.

Vertebral morphologies presented in the literature are used to create geometric primitives of each bone.

Relationships from forensic science are used to relate an individual’s stature to the heights of each of the

vertebrae. Also, relationships between the vertebral height and the other dimensions of the vertebra are derived.

These together can be used to create a model of each vertebra that is modified according to external human parameters. This model creates a simple and fast tool for the creation of personalized vertebral models.

Approved:

Bhavin Mehta

Associate Professor of Mechanical Engineering

Table of Contents Page

Abstract ...... 3 List of Tables ...... 6 List of Figures...... 7 1. Introduction...... 8 1.1. The Human Body and Bio-Engineering ...... 8 1.3. The Spine: Anatomy and Function ...... 11 1.3.1. Sections of the Spine...... 12 1.3.2. The Vertebra ...... 14 1.4. Forensic Osteology ...... 18 1.5. Medical Imaging ...... 18 1.6. Statement of Thesis...... 20 1.7. Thesis Objectives...... 20 2. Literature Review...... 22 2.1. Modeling the Spine and Vertebrae ...... 22 2.1.1. Whole Spine Models...... 22 2.1.2. Vertebral Models ...... 23 2.1.3. Intervertebral Disc, Lumbar, and Cervical Models ...... 24 2.1.4. Spinal Mobility - Condition and Instrumentation...... 26 2.2. Methods to Obtain a Model ...... 26 2.3. External/Internal Parameter Matching...... 28 3. Methodology...... 32 3.1. Software ...... 32 3.2. Obtaining Data...... 32 3.3. Determination of Spinal Parameter Relationships...... 38 3.3.1. Spinal Curve...... 38 3.3.2. Spinal Height and Vertebral Body Heights ...... 40 3.3.3. Disc Heights...... 41 3.4. Determination of Vertebral Parameter Relationships...... 43 3.4.1. Distance Method & Area Method...... 45 3.4.2. Angular Parameters...... 45 3.4.2.1. Endplate Inclination...... 45 3.4.2.2. Articular Facet Angles ...... 47 3.4.2.3. Pedicle Inclination ...... 48 3.4.3. Poor Correlation Parameters...... 49 3.5. Creating a Solid Model of a General Vertebra ...... 52 3.5.1. Vertebral Body Model ...... 54 3.5.2. Vertebral Arch Model...... 56 3.6. Spinal Curve Model ...... 64 3.7. Final Assembly of the Model...... 67 4. Results and Conclusions ...... 70 5

4.1. The Spinal Model...... 70 4.2. Conclusions...... 75 References...... 77 Appendix A...... 84 Appendix B ...... 85 Appendix C ...... 86 Appendix D...... 87 Appendix E ...... 88 Appendix F...... 89 Appendix G...... 90 Appendix H...... 91 Appendix I ...... 92 Appendix J ...... 93 Appendix K...... 94 Appendix L ...... 95 Appendix M ...... 96 Appendix N...... 97 Appendix O...... 98 6

List of Tables Page

Table 3-1 Abbreviations for dimensions...... 37 Table 3-2 Spinal length coefficients ...... 40 Table 3-3 Vertebral height as percentage of spinal length, modified from Tibbetts ...... 41 Table 3-4 Lumbar disc height determination modified from Shao...... 42 Table 3-5 Disc height percentages for male and female subjects...... 43 Table 3-6 Parameter linear regressions on vertebral body height...... 44 Table 3-7 Comparison of distance method and area method of parameter prediction ...... 45 Table 3-8 Linear regression parameters of inferior card angles on superior card agles...... 48 Table 4-1 Parameter prediction formulas ...... 73 7

List of Figures Page

Figure 1-1 Example of a Solid Model Application...... 10 Figure 1-2 Traverse, Frontal and Sagital planes ...... 12 Figure 1-3 Segments of the Spine...... 13 Figure 1-4 C6 Vertebra ...... 15 Figure 1-5 T8 Vertebra ...... 16 Figure 1-6 L3 Vertebra ...... 17 Figure 2-1 Examples of Whole Spine Models...... 23 Figure 2-2 Examples of Vertebral Models...... 24 Figure 2-3 FFD of a Vertebra Using Control Points...... 28 Figure 3-1 Cervical Vertebra Dimensions ...... 33 Figure 3-2 Thoracic Vertebra Dimensions ...... 34 Figure 3-3 Lumbar Vertebra Dimensions...... 35 Figure 3-4 Vertebral Facet Dimensions, Front View...... 36 Figure 3-5 Spine Coordinate Data and Trend Line Fit ...... 39 Figure 3-6 Illustration of Endplate and Disc Inclination Determination ...... 47 Figure 3-7 Spinal Canal Area by Segment Vs. Vertebral Body Height ...... 49 Figure 3-8 Transverse Process Width by Segment Vs. Vertebral Body Height...... 50 Figure 3-9 Superior Inter-Facet Width by Segment Vs Vertebral Body Height ...... 51 Figure 3-10 Superior Facet Area Vs. Inferior Facet Area ...... 52 Figure 3-11 Example of the Difference Between Global Anatomic Planes and Local Element Planes...... 54 Figure 3-12 Vertebral Body Model...... 55 Figure 3-13 Pedicle Model...... 57 Figure 3-14 Illustration of Spinous Process Angle on T8 Vertebra...... 58 Figure 3-15 Pedicle and Lamina...... 59 Figure 3-16 Pedicle, Lamina and Transverse Process ...... 60 Figure 3-17 Complete Vertebral Arch Model...... 61 Figure 3-18 Superior Articular Process Model...... 62 Figure 3-19 Inferior Articular Process Model ...... 63 Figure 3-21 Sagittal View of Spinal Curve Model ...... 65 Figure 3-22 Spine Curve Model ...... 66 Figure 3-23 Assembled Spine Model Using Distance Method ...... 68 Figure 3-24 Comparison of Spine Models for Subjects Using the Distance Method...... 69 Figure 4-1 Diagram of Spine Height Calculation from Input Parameters...... 70 Figure 4-2 Diagram of Vertebral Body Height and Disc Height Calculation ...... 71 Figure 4-3 Diagram of Spine Curve Model Creation ...... 72 Figure 4-4 Diagram of Vertebral Model Creation ...... 74 Figure 4-5 Diagram of Final Assembly of Spine Model ...... 75

1. Introduction

1.1. The Human Body and Bio-Engineering

The human body is an amazing and complex system whose function involves every aspect of modern

engineering. Long ago, the fathers of modern medicine were often inventors, engineers, and artists as well.

The ability to look at the human body as a machine seems to be universal in the early pioneers of anatomy and

function of the body.

“Bioengineering integrates physical, chemical, mathematical, and computational sciences and

engineering principles to study biology, medicine, behavior, and health” [2]. Bioengineering is playing an ever

increasing role in the development of medical devices and the understanding of the functioning of the human body. Bioengineering started in the 1930’s with the development of the diagnostic X-ray. Through the application of science and engineering principles, doctors were able to see inside the body without surgery for the first time. Now the field has expanded to encompass almost every engineering field and area.

The applications in bio-engineering today are numerous and growing. From environmental engineering

and other broad based disciplines that involve the effects on humans and other living organisms to specific

applications such as engineering drugs to be delivered only to specific sites or cells, the range of bioengineering is enormous. Understanding of engineering concepts is required to make new and innovative treatments and techniques to improve the health and care of each one of us. Fluid mechanics is a must for everything from understanding why plaques accumulate on arterial walls to understanding how cancer cells migrate through the body and metastasize. Mechanical behavior of tissues and bones is essential for the design of medical devices both in and out of the body. Understanding the electrical impulses and signals that control

every movement and thought we have and how these are distributed and affected can unlock the deepest

mysteries of muscular disorders like Parkinson’s disease or psychiatric ones such as Alzheimer’s disease. 9

In short, bio-engineering plays an absolutely vital role in the future of medicine and mankind. Through the understanding of engineering and science, we can bring about new cures and affect countless lives to ease pain, bring relief, and improve life.

1.2. Solid Modeling and the Human Body

Solid modeling is an area of computer aided design (CAD) where an object is represented as a three-

dimensional (3-D) solid on a computer. Primary uses of solid modeling are for computer aided engineering

(CAE), engineering analysis, computer graphics and animation, rapid prototyping, medical testing, product visualization, and visualization of scientific research [3].

Solid models are developed in numerous ways based on different theories and mathematical

representations of the solid. This project uses parametric feature based modeling because of its unique abilities.

Parametric feature based modelers allow for features to be created and defined by variables or parameters. The

parameters can then be linked together and linked to mathematical formulas to determine an optimal size or

create a family of similarly shaped parts, each with uniquely shaped geometries. This ability makes parametric

feature based modelers ideal for the project at hand, since the vertebrae all contain similar features with unique

sizes and characteristics.

Solid modeling is applied to the human body in three primary areas: visualization, design, and

investigation of function. In the arena of visualization, imaging modalities such as computed tomography (CT) and magnetic resonance imaging (MRI) are used to obtain 3-D data about the internal structure of the body

which is segmented into various structures. These can be visualized together or separately to identify healthy or

diseased tissues, identify injuries, and dysfunctions. Visualization is applied in the developing field of virtual 10 surgery, where the graphical solid models are used to create an artificial environment where procedures can be practiced and perfected prior to actual surgery to increase surgeon skill and planning.

The design applications of human solid modeling encompass the design of both implants and prosthetic devices and the way they fit and interact with the human body. Many external devices are tested with a solid model of a “virtual human” for ergonomic concerns and fit. Rapid prototyping is often used in conjunction with solid modeling to design or fit devices to patient specific geometry; for example creating a prosthetic to exactly fit a missing portion of a patient’s skull so that the patient can regain a normal appearance.[4].

B A

Figure 1-1 Example Of A Solid Model Application A) A Solid Model Of A Skull Is Made And Used To Create A Rapid Prototype Of The Skull With Defect. B) A Prosthesis Is Made To Fit The Exact Contours Of The Defect [4]

Finally the investigations of function using solid modeling often involve the use of design tools to evaluate different treatments, therapies, or traumas to the human body. Solid models are used in conjunction with finite element analysis software to evaluate the stresses induced by a treatment, the likely injury from an impact, or the likely effect of a device on the body. For example, researchers have evaluated the effectiveness 11 of scoliosis treatments like the Boston brace using finite element analysis and solid models of the spine and rib cage. [5]

The advantage of solid modeling is that experiments that would be impossible to run on live patients can be performed hundreds of times controlling all the necessary variables in a relatively short time. The simulations performed also result in much more detailed information being gathered with the ability to pinpoint localized stresses and optimize locations for application. The cost savings solid models can realize can be significant in terms of time and money as well as reduced risk of patient injury.

1.3. The Spine: Anatomy and Function

The mature human vertebral column usually consists of 24 presacral vertebrae, the remainder being

arranged into five fused sacral vertebrae and three to four coccygeal vertebrae. [6] in addition to the bony

structures there are 23 intervertebral discs between each vertebra, and associated ligaments, muscles, and

tendons. This thesis focuses on the osseous or bony spine which will be discussed in detail.

Before continuing, some basic anatomical terms must be addressed. There are three primary planes used

and numerous directional terms referenced to a body in anatomical position (Figure 1-2). The planes are referred to as the transverse or horizontal plane, the frontal or coronal plane, and the median sagittal or median plane as. The transverse plane divides the body into upper and lower or superior and inferior parts. The median

plane divides the body into left and right portions. The body has a single median plane and many sagittal planes

that are parallel to the median plane. The anatomical term medial means closer to the median plane, while

lateral means farther from the median plane. Finally the coronal or frontal plane divides the body in to front

and rear portions, where anterior is towards the front or face and posterior is toward the rear or back. 12

Figure 1-2 Traverse, Frontal And Sagital Planes.[7]

Other common terms used are proximal, which is toward the center of the body, and distal, which is away from the center of the body. Some terms not involved with direction are foramen, which is a hole or opening, and tubercle, which is a protuberance.

1.2.1. Sections of the Spine

The spine is divided into five sections: the cervical, thoracic, lumbar, and sacral and coccygeal spine, as seen in Figure 1-3. 13

A B

Figure 1-3. Segments Of The Spine A) Medial View. B) Frontal View Adapted From Atlas Of Anatomy [8] 14

The cervical is spine is the most superior section, which means it is closest to the head, and the coccygeal spine is the most inferior, or closest to the feet. The cervical section of the spine is comprised of the seven neck bones. Next is the thoracic spine which is the 12 bones of the chest to which the ribs attach. Then the lumbar spine made of five bones in the lower back. Next is the sacral spine which is a single bone made from five fused sacral segments attached to the pelvis, and finally the coccygeal spine.

As seen in Figure 1-3, there are three primary curves of concern in the medial plane of the spine. The cervical and lumbar sections have a lordosis, or a curve that is convex toward the posterior. The thoracic spine has a kyphosis, or a curve convex towards the anterior of the body.

This project focuses on the vertebrae that have very similar geometry. This includes the cervical spine, excluding the atlas and axis (the two superiormost vertebra), the thoracic, and the lumbar segments.

1.2.2. The Vertebra

Each vertebra has a unique geometry, but is closely related to the other vertebrae of its spinal segment

with few exceptions. Each vertebra is usually referred to with the first letter of the spinal section in which it is

contained and numbered from superior to inferior. For example the most superior cervical vertebra, labeled

atlas in Figure 1-3, is C1. L5 is the lowest lumbar vertebra.

The basic geometry of the vertebra is illustrated in Figure 1-3, Figure 1-4, and Figure1-5.

Superior Articular Superior End Plate Groove of the Spinal Processes Nerve

Transverse Process

A Inferior Articular Process Vertebral Body

Superior Articular Processes

Spinal Canal

Pedicle B

Figure1-4 C6 Vertebra – A) Frontal View B) Axial View Adapted From Atlas Of Anatomy [8]

Superior Articular Facet Costotransverse Facet

Pedicle

Costovertebral Facet

A Vertebral Body Costovertabral Facet

Spinous Process

Lamina

Transverse Process Costotransverse Facet

Superior Articular Process Pedicle

Costovertebral Facet

Superior End Plate

Figure 1-5 – T8 Vertebra – A) Transverse View B) Axial View Adapted From Atlas Of Anatomy [8] 17

Superior Articular Facet Pedicle

Vertebral Body Transverse Process

Spinous A Process Inferior Articular Facet

Spinous Process

Inferior Articular Facet

Spinal Canal Superior Articular Facet

Transverse Process Pedicle

Superior End Plate B

Figure 1-6 – L3 Vertebra – A) Transverse View B) Axial View Adapted From Atlas Of Anatomy [8]

1.3. Forensic Osteology

Forensic science is the application of a field of science to the facts related to criminal and civil litigation.

Forensic osteology is an area of forensic science concerned with the study of bones to determine relevant

identifying characteristics of an individual from their bones [9]. Often, the determination of stature and sex of a

given set of bones is the first task of a forensic osteologist. Though a spine does not typically hold enough sex

distinguishing features, there are published correlations relating different spinal and vertebral dimensions to

stature. [10-12]

Forensic osteology is concerned with taking measurements of a bone and estimating an external stature

of the body. In this application the roles of the variables are reversed so that the known stature can be used to

calculate the internal unknown dimensions.

1.4. Medical Imaging

There are many imaging modalities used in modern medicine. X-ray, computed tomography, and

magnetic resonance are often used to diagnose spinal problems and used by spinal researchers to investigate many pathological and non-pathological conditions and treatments.

X-ray images are obtained by passing ionizing radiation through the body to either a film or electronic

detector. X-ray images are able to distinguish bone, soft tissue, and gas in the human body.

Computed tomography (CT) is a more modern technology, developed in the early 1970’s. CT scans

work by rotating an X-ray source and detector around the body and measuring the different densities that are

encountered in the path of the x-ray beam. This information is then passed to a computer that calculates a two-

dimensional (2-D) image or slice of the scanned area. Many of these slices can be taken and a 3-D image can

be extrapolated from the 2-D data obtained. 19

Magnetic resonance imaging (MRI) was developed in the late 1970’s and relies not on ionizing radiation to pass through the body, but very powerful magnets to detect hydrogen atoms in the body. By creating a very powerful and uniform magnetic field, the spin axis of hydrogen atoms can be aligned with the main magnetic field. Radio frequency pulses of energy are then directed at the target area in order to knock a few hydrogen atoms to a new alignment. The radio frequency energy is then turned off and the hydrogen atoms can slowly return to their previous alignment and give off the energy gained from the initial radio frequency exposure.

This energy release is then detected and fed into a computer. The computer is able to then calculate the density of hydrogen in the target area which is used to differentiate tissues. Through a number of scans a 3-Dimage of the cross-section of the body can be constructed.

X-ray images are useful in imaging bones, but each image is a 2-D shadow of the entire bone which introduces the possibility of image distortion. The uses for x-ray in imaging soft tissues is limited but can be accomplished better with the aid of a contrast agent to highlight specific structures. CT images can obtain lots of 3-D information about bones and soft tissues. CT bone images are typically very bright and clear. CT is the most often used modality for obtaining high resolution surface images of bones in research. The soft tissue imaging with CT is limited in structure differentiation among tissues with similar density. This lack of differentiation can be resolved with the use of a contrasting agent applied to the structure of interest. MRI imaging is the best of the three modalities for soft tissue imaging. MRI is the only modality that does not use ionizing radiation, so use it is only limited by the presence of unsecured magnetic material in the body of the imaging subject. MRI, however, is at present very expensive and time consuming.

All the imaging modalities discussed are important to medical science and engineering, but involve the use of expensive specialized equipment and trained technicians to run. One of the goals of the project is to obtain the internal information desired without the expense or side effects of using these imaging modalities. 20

1.5. Statement of Thesis

External parameters such as stature, gender, and ethnicity can be used to determine the geometry of a subject’s vertebrae and subsequently be used to create a 3-dimensional solid model of the spine.

1.6. Thesis Objectives

This study is directed at the creation of a realistic model that has the ability to closely model a subject’s spinal anatomy with minimal data input. Being able to create a model without the need for expensive, invasive, and time-consuming data collection is seen as a great advantage to someone who does not require exacting conformity to a specific subject’s anatomy, as in surgical planning. A more general model such as this one can aid designers and researchers in many fields and applications. As improvements are made to this model, a greater understanding of the driving factors behind human development and the changes across gender and other genetic lines can be achieved.

This model is intended to be used as a tool to understand the complex nature of the spine and its relation to biomechanics and overall health. One of the motivations behind this project was to create a first attempt at a subject specific “ideal” spine. If the model is able to tell a researcher or clinician what the ideal configuration of the spine should be for a given individual, then a comparison to that subject’s actual anatomy might be of use as a diagnostic tool. Though this is one of the motivations behind the project, there are other applications for this model.

A research group at Ohio University is working to create a virtual reality interface in order to better train medical students in the palpatory diagnosis of the human back.[13] A model such as this one may aid in the development of future back models, or in the visualization of the vertebrae in a proper location. The simplicity 21 of the input data and the fast model update make it easy to integrate this model into many applications where realism is needed, but extensive time and effort to create an exact anatomical match are not.

The ability to use very simple inputs is a great advantage for engineers in crash safety. Using this model would allow them to create realistic virtual crash simulations on numerous realistic subjects without the need for extensive data collection, or to generalize the subject to an average of all people. The increase in the level of specificity in the creation of virtual crash test dummies may allow engineers to make design decisions that improve safety for specific subsets of the population. 22

2. Literature Review

2.1. Modeling the Spine and Vertebrae

Numerous models of the spine and vertebrae have been developed and are in use in research today to investigate almost every physical movement or spinal pathology. There are many types of models used based on what type of investigation is being performed and the level of detail needed from the collected data. These models can be categorized into six types of models:

1. Whole Spine (simple) 2. Vertebral Body 3. Intervertebral disc/motion segment 4. Lumbar spine 5. Cervical spine 6. Spinal mobility – condition and instrumentation [14]

2.1.1. Whole Spine Models

Full spine simplified models are the first type of spinal models developed. The first model simplified the spine to a single element along with a lumped mass for the human head and simulated pilot ejection from an aircraft [14]. In the early types of these spine models, the spine is reduced to just a few elements, usually one or three, representing the full spine or spinal segments. Often a simple spring mass configuration is used. Other simple whole spine models attempt to model the spine as either a column or an arch [15].

Modern whole spine models utilize 3-D elements in a finite element environment to obtain more detailed results. Often the vertebrae are considered rigid elements, cable elements for ligaments, and spring elements represent the inter-vertebral discs. One such model utilized simplified 3-D elements of vertebra, discs, ribs, ligaments, and the pelvis to investigate vertebral displacements due to manipulative forces [16] Another assigned more complicated disc geometry and properties along with rigid vertebra to investigate forces and 23

stress for different spinal positions [17]. These studies provide insight into the basic biomechanics of the

complicated spine system and give clues to injury and treatment mechanisms.

Many other similar models involving the whole spine are concerned with the investigation of a specific

spinal condition such as scoliosis and are categorized with spinal mobility models [14].

B A Figure 2-1 Examples Of Whole Spine Models A) Ribs, Spine And Pelvis For Investigation Of Manipulative Force And Displacements [16] B) 2-D Model Modeling Spine As An Arch [15]

2.1.2. Vertebral Models

Vertebral models tend to focus on the stress behavior of each vertebra or sections of vertebrae separately

and the mechanics and strength under various loadings.

Vertebral models are more complex models where each vertebra is modeled as 3-D solid with detailed

geometry. The anatomical features are more accurately captured using various imaging methods or

measurements to create a model. Multiple finite elements are used on each component in these models, which

provide much more information to the stress and displacement reactions of the model. Vertebral models

typically exhibit a much more complex behavior. 24

Although it is important to accurately capture the vertebral geometry, according to Fagan [14]:

“…the dimensions of much of the vertebrae are not critical to most modeling applications, provided that

the primary features reliably reflect their function and properties. Although the secondary features must

still be similar if the attachment and action of the muscles and ligaments are to be reasonable.”

So there is a measure of generality that can be achieved in modeling of each vertebra.

A B

Figure 2-2 Examples Of Vertebral Models A) Geometrically Accurate Lumbar Vertebra B) Finite Element Model Of The First Cervical Vertebra (Atlas) Developed By Direct Measurement Of A Cadaveric Specimen And Used To Examine Fracture Mechanisms. [14]

2.1.3. Intervertebral Disc, Lumbar, and Cervical Models

The next three categories of models have very specific uses and developmental concerns which are generally outside the focus of this project and will be dealt with in a simple overview.

Intervertebral disc/motion segment models are primarily focused on the behavior and failure of discs and

the effects of loading on a set of vertebrae and the discs between them. Investigations into the loading of

intervertebral discs have shown that in simple compression, vertebral endplates will fail before failure of the

annulus fibrosis. [18] there have been many investigations into the material properties of the intervertebral discs

[19-23]. The non-linear properties of the outer ring of the intervertebral disc, called the annulus fibrosis, have 25 made modeling the disc a particular challenge. The complex nature of the interaction of the vertebra, the annulus fibrosis, and the nucleus pulposis, the liquid filled interior structure at the center of the intervertebral disc, has created a need for many analyses and investigations with increasing degrees of complication. Spiker

[24] laid ground work in the field by creating a very simplified parametric model with linear isotropic material properties. He was able to determine the geometric and material properties with the most significant effect on the disc’s response to compression. Significant contributions were made by Shirazi-Adl and colleagues [25] in creating a model with non-linear finite element model with non linear geometry and material properties. More recently, Kong [26] has done research to show that intra-discal pressure is reduced by muscle action under load.

This increases facet load-bearing in the spinal motion segment, and can lead to better realism in biomechanical modeling of disc failures.

Lumbar spinal models have been used to study the biomechanics, movement, and stability of the lumbar section under various loadings, with a focus on the investigation of the causes and treatment of low back pain.

Industrial concerns over lifting and prevention of worker injury are strongly prevalent [27, 28]. A finite element model based on the one developed by Shirazdi et al. [25] has been the basis of many lumbar models used to investigate many aspects of the biomechanics of the lumbar spine [29-34].

Cervical spine models are mostly focused on the behavior of the cervical spine as it relates to cervical spinal cord injuries such as whiplash. There have been much fewer efforts expended on modeling the cervical spine than there has been on the lumbar segment of the spine [14]. Panjabi and colleagues have done a number of studies involving automotive crash simulations and cervical spine injury, specifically looking at ligamentous injury, disc injury and whiplash. [35-39] Maurel’s parametric study [40] focused on the function and importance of the posterior articular facets and their variability between individuals. 26

2.1.4. Spinal Mobility – Condition and Instrumentation

Apart from using models to broaden knowledge of the component function of the spine, models can also

be applied to study and simulate different spinal conditions and treatments, as well as aid in the design and

analysis of new instrumentation and medical devices. Currently there are very few patient or subject specific

models [14]. However, there is a growing shift and technological expansion towards patient specific models to

explore better fitting, more effective, and safer treatments for spinal conditions. [41]

Many models investigate surgical procedures that alter some aspect of the spine such as facetectomy

(partial or complete removal of an articular facet), laminectomy (removal of all or part of the vertebral arch), laminoplasty (the addition of material to the vertebral arch to decompress the spinal canal), and scoliotic treatments such as Harrington rods and Cotrel-Dubousset instrumentation have been examined. Also studies have investigated the effects of muscle dysfunction in the lumbar spine and the roles of the ligaments and facets on lumbar spinal stability [14].

Many of these studies used models were detailed but of only certain spinal segments or that were

simplified and included multiple spinal segments.

2.2. Methods to Obtain a Model

The vertebral geometry is typically obtained from either from 3-D digitizers or CT scans. 3-D digitizers

collect 3-D coordinates from a touch probe. They are used on prepared cadaver vertebra, recording coordinates

at certain marked landmarks. The coordinate data obtained is then fed into a computer. With proper user

guidance the points are connected to create an outline of a solid. The method relies on accurate sample preparation and a large number of input points to obtain a solid.

Touch probes have been used to generate quantitative data of vertebral dimensions in a number of

studies of vertebral landmarks, the most comprehensive of which was performed by Panjabi and colleagues in a 27 series of articles describing the cervical [42], thoracic [43], lumbar [44] spinal segments and the articular facets of the entire spine [45]. These measurements are used to create geometric primitives in this project.

The state of the art has definitely shifted to the use of high resolution models obtained directly from CT images because of the ability to better capture fine geometric details and re-create the bone surfaces and internal structure [14]. Because of the complex geometry of vertebra there is difficulty in automatically sectioning and creating solids of the vertebra as has been done with other long bones such as the femur. Currently, there are many semi-automatic tools to aid in segmentation and registration of CT images using specialized software [46

- 48].

CT scanning has one very large drawback of imparting a large dose of ionizing radiation to a subject.

This limitation has become the impetus for some researchers to develop methods that combine a model built from existing CT models with data from other sources that have a lower radiation exposure. These methods rely on interpolation algorithms to morph key landmarks on the existing CT vertebrae model to corresponding new ones on the target subject’s vertebrae.

Canadian and French researchers among others have developed an approach that uses stereo- radiography to take simultaneous x-rays from 2 or more positions around a subject [49 - 55]. (Figure 2-3)

Landmarks on all the images that correspond with each other as well as unique landmarks are identified on the images. The landmark coordinates are calculated and used to modify existing CT solids using a free form deformation (FFD) algorithm. The new landmark positions are used to calculate a displacement for each of the remaining surface points to create a model that is personalized to the patient with minimally invasive data collection. Results of this technique have an accuracy of 3.3mm+3.8mm. Although this is sufficient for

orthopedic simulation, it is far less accurate than the 1.1mm+0.8mm obtained from direct CT imaging.[49] 28

A B

Figure 2-3 FFD of a Vertebra Using Control Points. A) Anatomical primitive with the original control points. B) Modeled vertebra with control points modified by new patient geometry. [49].

The implication of these studies is a reasonably accurate model of the vertebrae can be obtained using a few key control points or parameters. The researchers using either the stereo-corresponding points or non- stereo corresponding methods and FFD method described above have to manually identify the landmarks and control points on a target subject. This thesis aims to eliminate the need to have an x-ray taken or even have an actual physical subject. In this way a designer can have a realistic model that can be made to fit a variety of subjects or a subset of the population with the desired characteristics. The control points needed for a model can be predicted from the desired external metrics.

2.3. External/Internal Parameter Matching

Although there have been some parametric models of the spine developed, none of these models have

linked the parameters of each vertebrae together or to an external easily measurable source. The more complex

parametric model which defined 60 parameters per vertebra taken from a single spine was developed by

Stepney [56]. Two more simplified parametric models were developed by Lavaste[57] and Robin[58] using 29 only 6 parameters per vertebra. A parametric study of the lower cervical spine by Maurel[40] was also performed and focused on the effects of the posterior articular facets.

One study by Klinich and colleagues linked external parameters of stature, age, and gender to dimensions of the cervical spine [59]. The study was based on an analysis of lateral x-rays taken of 180 subjects representing both genders, three stature groups (short, medium, tall), and three age groups (young, mid- age, old). The study was conducted using a cascading regression where an adjacent vertebral measurement could be dependant on a previous one. The advantages of this method should make the set of vertebra more congruent with each other however it may result in the propagation of an error through the set of vertebra. This work was done with the aim of better modeling different age, gender and stature groups for automotive crash simulation. The accuracy of such models needs a much lower threshold than would a medical application.

One of the main objectives of the Klinich study was to properly determine the position and curvature of the cervical spine in a neutral seated position. Through the analysis of the many lateral x-rays, correlations to age, sex and stature to the curvature of the cervical spine were determined and modeled using Bezier splines.

This finding is very important to the future success of parametric models as it can provide detailed spinal level information about the likely position of the vertebrae and curvature of the spine.

Another study [1] simply looked at linking relationships between internal and external measurements of the human body. Sixty-four subjects of the three basic morphotypes had numerous internal and external measurements taken which were statistically analyzed for correlations. The conclusion came that 10 easily measured external parameters could be used to create a personalized 189 personalized anthropomorphic measurements to define a model of the whole human. Most applicable to the vertebrae was the finding of a correlation (R2 = 0.66) between the height of an individual and the inferior width of the vertebral body of L2. 30

Klinich [59] was able to correlate vertebral body heights of the cervical spine with age, gender and stature of an individual (age coefficient = .01, stature coefficient.= .1, gender coefficient = 1.27). The rest of the cervical spinal measurements become dependant on this initial measurement makes it difficult to compare the overall dependence of the entire spine with each exterior parameter. Both Klinich and Bertrand’s studies have a similar design to link a few external parameters to a small number of internal parameters and then link the internal parameters to other internal parameters.

Other sources for information linking external and internal body measurements come from the field of forensic science. There have been a few studies to link spinal column length to stature [10-12] in various racial groups. Tibbetts [12] related the height of each individual vertebra as a percentage of the whole as well as relating the stature of an individual to various segments of the spine in American blacks. Terazawa [11] related the length of the lumbar segment to stature in Japanese subjects.

Jason and Taylor [10] performed the most widespread analysis of American whites and blacks separating by race and gender to obtain quantitative spinal measurements of spinal segments and the column as a whole. After attempts to use Terazawa’s [11] published formulas, it was found that stature estimation formulas could not be accurately applied across racial borders. Age was found to be significant in the lumbar spine of white males. White males were the only group with a large enough sample to make this determination, and the resulting relationship was only really significant in the lumbar spinal section. What was not discussed was whether the change in the segment length was due to disc compression over time or loss of vertebral body height.

There are other articles that discuss other variations between the sexes [60, 61] and the effects of age on various body segments [9]. The discussions of the changes in the vertebra and spinal column with age are more qualitative than quantitative. It shows there is a definite effect of age on the vertebra in males on certain 31 parameters. Rühli [62] performed a study that showed the pedicle height, endplate width and depth increased with increasing age in males. The majority of the assessed measurements showed no change (77 out of 94) on male subjects and females showed no significant correlation with age. The correlations published are too specific for inclusion at this level of model development (only apply to L1 right pedicle height and C7 end plate width). However future work in model development should investigate the effect of aging on both the vertebral dimensions as in Rühli [62] and the age effects on the spinal curvature as in Klinich. [59]

Other studies [63, 64] show there is a definite increase in intervertebral disc height in the lumbar spine with increasing age. Frobin [63] found that in both males and females the disc height increased with age and concavity of the vertebraql endplates also increased with age. Shao [64] also found similar increases in disc height and endplate concavity. Frobin[63] also found a decrease in anterior vertebral body height for males with increasing age, but not for females.

The effects on the full spinal system and the curves composing the spine are not dealt with quantitatively in these studies; however there seem to be consensus that intervertebral disc height increases linearly until the

5th or 6th decade and decreases thereafter [64, 65].

3. Methodology

3.1. Software

Of the various software packages available to complete this project, two primary packages were used to

complete the tasks of calculation of vertebral parameters and creations of a solid model. Microsoft Excel, a

spreadsheet software package, was used for calculation and data manipulation purposes. This software was

chosen because of its ability to dynamically link to the parametric solid modeler used, to create a real-time

updateable model. Solid edge was used as the solid modeling program both for the linking capabilities and the

availability of the software due to college site licensing.

3.2. Obtaining Data

Data were needed to complete two tasks: first the calculation of relationships between the internal

parameters of the vertebrae, and then the creation of a generic solid model. The most complete collection of

quantitative data was found in the series of Panjabi et al. articles [42-45], the compilation of this data can be found in the Appendix. Figures 3-1, 3-2, 3-3, & 3-4 show graphically what the dimensions describe. Table 3-1 shows the nomenclature used in the tabulation of data. 33

Figure 3-1 – Cervical Vertebra Dimensions In Three Orthogonal Views (Front Side, Top) And Isometric View Showing Coordinate System Used.[42]

Figure 3-2 – Thoracic Vertebra Dimensions In Three Orthogonal Views (Front Side, Top) And Isometric View Showing Coordinate System Used. [43]

Figure 3-3 – Lumbar Vertebra Dimensions In Three Orthogonal Views (Front Side, Top) And Isometric View Showing Coordinate System Used. [44]

Figure 3-4 – Vertebral Facet Dimensions, Front View. [45] 37

Table 3-1 Abbreviations for dimensions [42-45] Body Part Mnemonic Dimension Vertebral Body EPW End Plate Width EPD End Plate Depth EPI End Plate inclination EPA End Plate Area VBH Vertebral Body Height Spinal Canal SCW Spinal Canal Width SCD Spinal Canal Depth SCA Spinal Canal Area Pedicle PDW Pedicle Width PDH Pedicle depth PDA Pedicle Area PDI Pedicle Inclination Spinous Process SPL Spinous Process Length SPI Spinous Process Inclination Transverse Process TPW Transverse Process Width TPI Transverse Process Inclination Facet FCH Facet Height FCW Facet Width IFH Interfacet Height IFW Interfacet Width FCA Facet Area CAX Card Angle About X CAY Card Angle About Y

Suffixes a anterior p posterior f frontal s sagittal (or superior depending on context) t transverse u upper l lower (or left depending on context) r right i inferior

The measurements in the study were taken from a sample of 12 spines from subjects that are intended to be an approximate average for all non-pathological human spines. Panjabi fit geometric shapes to various parts of the vertebrae in order to facilitate mathematical modeling. Ellipses and triangles were fit to the areas of the end plates, spinal canal, and pedicle cross-section based on the measured widths and heights or depths. Panjabi found that the elliptical approximations fit best, with an area overestimation of 10%, while the triangular 38 approximation underestimated by 40% [42-45]. Therefore, ellipses are used throughout the model generation to approximate vertebral shapes.

3.3. Determination of Spinal Parameter Relationships

3.3.1. Spinal Curve

The spinal curve used in this project is an estimation obtained from a single subject. The curve was

obtained from a 3-D picture of a male back from the VHB project. The subject was male, white, approximately

6ft. tall in the prone position. The contour of the midline of the back was isolated and 3-D point information

exported to Excel. The deviation from the median plane was considered negligible; therefore the data in the

medial lateral directions was ignored. The anterior-posterior coordinates were graphed against the superior-

inferior coordinates. A sixth-order polynomial trend line was fit to the data using Excel (Figure 3-5). It is

important to note that the curve obtained is the curve associated with the spinous processes of the vertebra. This

curve is transferred to the vertebral body center for assembly purposes. There is some error in the shape of the

curve introduced in this move. The actual curve associated with the vertebral body centerline would require a

more invasive procedure to obtain. 39

Spinal Curve

y = 6.09823E-15x6 - 1.25181E-11x5 + 1.12818E-08x4 - 6.72949E-06x3 + 40 2.39912E-03x2 - 3.31650E-01x + 2.17857E+01 R2 = 9.97313E-01 30

0 0 200 400 600 800 1000

-10

Anterior/Posterior Displacement (mm) -20

-30

-40 Superior displacement (mm)

Figure 3-5 Spine Coordinate Data And Trend Line Fit.

This data was used as the basis for all spinal curves. When a new subject is modeled, the spinal length of the new subject is compared to this original spine length to obtain a scaling factor. This scaling factor is used to scale both original coordinates to obtain a new 6th order polynomial spinal curve. This new curve is used to assemble the desired subject’s vertebrae and determine certain vertebral parameters, as described below. 40

3.3.2. Spinal Height and Vertebral Body Heights

The spinal level parameters (length of the cervical-thoracic-lumbar segments, and spinal curve)

determine how the vertebrae fit together. These can then be used to provide the base for calculation of the

vertebral level parameters, which are the dimensions of the individual vertebra bones and intervertebral discs.

This step is necessary at this point in model development because no external internal parameter equation has been found or determined without this intermediary step. The stature equations from Jason and Taylor [10] are used.

The following equations for the determination of the combined cervical-thoracic-lumbar spine length

(C-T-L) are used

= ( )+−− bLTCastature Equation 3-1

Where a & b are given by Table 3-2.

Table 3-2 Spinal length coefficients [10] White Male White Female Black Male Black Female a (C-T-L regression Coeffcient) 2.069 2.334 2.42 1.661 b (C-T-L regression Constant) 47.258 29.735 29.395 70.336 r2 0.768 0.72 0.809 0.806 SE 5.29 5.32 5.09 3.62

Solving for (C-T-L) yields:

( − bstature ) ()LTC =−− Equation 3-2 a

The resulting C-T-L length (in mm) cannot be used directly in the next set of calculations yet. Because this relationship was derived from fresh cadaveric specimens without the removal of the intervertebral discs, the disc height must be accounted for. According to White and Panjabi’s Clinical Biomechanics of the Spine [66], the intervertebral discs account for between 22 and 30% of the total spinal column length. Without quantitative 41 studies of the disc heights of the entire spine the upper bound was chosen for this model. After subtraction of the disc height, Table 3-3 from Tibbetts [12] was used to determine the individual vertebral heights.

Table 3-3 Vertebral height as percentage of spinal length, modified from Tibbetts [12] Cumulative Percentage Vertebra Individual Percentage From Superior End From Inferior End Male Female Male Female Male Female C2 7.7 7.64 7.7 7.64 100 100 C3 2.81 2.70 10.51 10.33 92.3 92.365 C4 2.72 2.63 13.23 12.96 89.49 89.67 C5 2.64 2.61 15.87 15.57 86.77 87.04 C6 2.67 2.66 18.54 18.23 84.13 84.43 C7 2.94 2.91 21.48 21.14 81.46 81.77 T1 3.42 3.36 24.9 24.50 78.52 78.86 T2 3.7 3.62 28.6 28.12 75.1 75.5 T3 3.8 3.73 32.4 31.85 71.4 71.88 T4 3.83 3.79 36.23 35.64 67.6 68.15 T5 3.93 3.89 40.16 39.53 63.77 64.36 T6 4.07 4.02 44.23 43.55 59.84 60.47 T7 4.17 4.12 48.4 47.66 55.77 56.455 T8 4.26 4.21 52.66 51.87 51.6 52.34 T9 4.36 4.34 57.02 56.21 47.34 48.13 T10 4.61 4.59 61.63 60.80 42.98 43.79 T11 4.94 4.90 66.57 65.70 38.37 39.2 T12 5.28 5.27 71.85 70.97 33.43 34.3 L1 5.55 5.59 77.4 76.56 28.15 29.03 L2 5.6 5.77 83 82.33 22.6 23.44 L3 5.66 5.89 88.66 88.22 17 17.67 L4 5.63 5.87 94.29 94.09 11.34 11.78 L5 5.71 5.91 100 100 5.71 5.91

3.3.3. Disc Heights

Determining the height of the discs is important so the vertebrae are properly spaced and intervertebral disc can be modeled for future finite element analysis. Information regarding quantitative disc height reference values has not been accurately compiled [64]. However Shao and colleagues [64] have done preliminary work to create an accurate method to determine lumbar disc height and describe its variability with age. Shao determined a formula to create a non-dimensional disc height, which allowed for comparison of discs among 42 individuals of different heights. This non-dimensional number is a ratio of disc height to the depth of the endplate on the superior side of the disc of interest.

The overall change in disc height over the age range defined in Shao [64], 20 to 67, is about 2%. Since the accuracy of the predictions of this model are expected to be well above that, a single age will be applied in a test case to determine average disc height values for both male and female subjects. The test case consists of male and female subjects, both white, with a height of 65 inches and an age of 43 years. Gender and age are required for the Shao equations; height and race are required to determine the endplate depth of the adjacent superior vertebra. Using Shao’s method, the disc heights of the lumbar vertebra of a test case were determined.

(Equations 3-3, Table 3-4)

DiscHeight = 0+ 1× AgeAA Equation 3-3

Table 3-4 Lumbar disc height determination modified from Shao [64] Male Male Female Female Disc Disc Rank A0 A1A0A1 T12-L1 18 0.519 0.004903 0.433 0.00484 L1-L2 19 0.68 0.006201 0.627 0.004771 L2-L3 20 0.832 0.006687 0.817 0.004982 L3-L4 21 1.105 0.005455 0.985 0.005052 L4-L5 22 1.076 0.006952 1.051 0.005979 L5-S1 23 0.973 0.00863 0.926 0.00817

By multiplying the non-dimensional disc height from Shao’s method by the endplate depth of the

adjacent superior vertebra, an actual disc height is calculated. This disc height is converted to a percentage of

total disc height for the test spine. The cervical discs are assigned a disc height of 1% each. The remainder of

the thoracic discs are assigned an equal portion of the remaining percentage of disc height. The resulting disc

height percentages are shown in Table 3-5 43

Table 3-5 Disc height percentages for male and female subjects Male Female Disc % total disc height % total disc height C3-C4 1.00% 1.00% C4-C5 1.00% 1.00% C5-C6 1.00% 1.00% C6-C7 1.00% 1.00% C7-T1 1.00% 1.00% T1-T2 1.94% 2.54% T2-T3 1.94% 2.54% T3-T4 1.94% 2.54% T4-T5 1.94% 2.54% T5-T6 1.94% 2.54% T6-T7 1.94% 2.54% T7-T8 1.94% 2.54% T8-T9 1.94% 2.54% T9-T10 1.94% 2.54% T10-T11 1.94% 2.54% T11-T12 1.94% 2.54% T12-L1 8.97% 7.88% L1-L2 12.35% 10.85% L2-L3 15.07% 13.88% L3-L4 18.41% 16.52% L4-L5 18.83% 17.92%

3.4. Determination of Vertebral Parameter Relationships

For this model, the quantitative morphology data collected by Panjabi [42-45] is used to determine relationships between various parameters and the vertebral height. Linear regression is used to determine the relationship between the parameter of interest and the vertebral height.

The parameters in Table 3-6 show the results of the linear regressions of parameter against the vertebral body height. 44

Table 3-6 Parameter linear regressions on vertebral body height sorted by correlation coefficient (R2) 2 Parameter Coefficient Constant R Linear Parameters EPWu 1.6836 -1.598 0.9525 EPWl 1.7618 -0.7654 0.9374 EPDu 1.2326 2.838 0.9234 EPDl 1.1348 5.3909 0.8868 IFHa 1.0397 3.7644 0.8728 SPL 2.0017 13.823 0.774 PDH 0.5528 2.0493 0.7669 PDW 0.3683 1.2182 0.4611 TPW 1.4069 36.851 0.4002 IFWs -0.2873 36.603 0.1687 IFWi -0.2373 34.805 0.1149 SCW 0.0905 16.553 0.1041 SCD 0.1216 17.777 0.0244 Area Parameters EPSAl 64.922 -538.2 0.962 EPSAu 64.184 -581.56 0.9605 PDA 5.5432 -47.409 0.7339 FCAs 4.6258 15.739 0.4444 SCA 4.8481 146.53 0.3321 FCAi 4.0778 33.253 0.2394 Angular Parameters EPItu 0.3944 -8.415 0.7835 CAYs 2.0263 -18.202 0.7656 CAXs 2.0895 30.144 0.7322 CAYi 2.0726 -15.354 0.5576 CAXi 1.6088 39.103 0.4966 PDIs -1.2456 46.075 0.4403 EPItl 0.1184 -2.1698 0.0626 PDIt 0.0422 4.683 0.0013

It is important to remember that each of these regressions are intended to be used as predictors of new vertebra geometry as the vertebral body height varies according to the height, gender, and ethnicity of the desired subject. In order to be a good predictor of new geometry, a reasonable level of correlation is important; however there are many other considerations. If the correlation coefficient (R2) was lower than 0.4 or the coefficient was negative, alternate ways of predicting the parameter were analyzed. 45

3.4.1. Distance Method & Area Method

There is enough information provided by the Panjabi database to create a model with two methods. The first method uses linear regressions of distance parameters such as endplate width and depth (EPW, EPD) directly to predict the dimensions of a subject. The second method employs the linear regressions of area parameters such as the endplate surface area (EPSA) and the original ratio of endplate width to depth

(EPW/EPD) along with the equation for area of an ellipse. Both methods are presented and compared.

The first method yields greater differences between subjects as stature increases, as seen in Table 3-7.

The two methods also show a significant difference in the magnitude of change from cervical to lumbar on a single subject.

Table 3-7 Comparison of distance method and area method of parameter prediction Distance Method Distance Method % increase Area Method Area Method % increase Subject 1 Subject 2 Subject 1-2 Subject 1 Subject 2 Subject 1-2 C3 EPDu 17.84 22.03 23.47% 9.36 12.00 28.23% T8 EPDu 27.60 33.88 22.73% 15.16 17.85 17.72% L5 EPDu 39.46 48.27 22.32% 17.10 19.59 14.60%

% increase C3-L5 121.16% 119.10% 82.74% 63.32%

Subject 1 - White Male 60" tall Subject 2 - White Male 72" tall

Future work will be needed to determine whether one method provides a better prediction than the other

3.4.2. Angular Parameters

3.4.2.1. Endplate Inclination

Angular parameters such as endplate inclination of both the upper and lower end plates should be reasonably related to the vertebral body height, however they must also be closely tied to the spinal curve since 46 the end plate inclination along with the wedge shape of the intervertebral disc is what causes the spinal curve.

The combination of both of these factors would be necessary to create a predictor that yielded a reasonable approximation of the end plate inclination that would be congruous with the spinal curve. Since the spinal curve is being specified, and the vertebral body heights and disc heights have been specified, it will be assumed that the intervertebral disc inclination and the adjacent endplate inclination will be equal. Therefore the inclination on both the endplate and the disc will each be half of the difference between the angles of the centerlines of the vertebral body and the disc.

To obtain EPIu a calculation using some basic geometry is required. To illustrate refer to Figure 3-6.

EPIu for the first vertebral body , VB(1), is obtained from the slope of VB(1) and the slope of Disc(2). By taking the inverse tangent of both slopes, the angle with respect to the axis label Y is obtained. By subtracting these two angles and multiplying by ½, the Endplate inclination is found. To find EPIl for the vertebral body labeled VB(3), the slope of Disc(2) and VB(3) are compared in the same manner.

Figure 3-6 Illustration Of Endplate And Disc Inclination Determination

3.4.2.2. Articular Facet Angles

The facet orientation card angles (CAX and CAY) for the superior articular processes show good correlation with vertebral height, however, inferior processes angulations do not. As a side note, the card angle 48 is described in Panjabi [45], and refers to the angle needed to rotate a playing card from the origin planes to be parallel to the facet. In order to have a realistic, congruous set of articular facets, it makes sense to relate the superior facet orientation to the inferior facet orientation. The inferior card angle correlation to the superior card angle will be used to predict the inferior card angle using the linear regression relationship parameters in

Table 3-8

Table 3-8 Linear regression parameters of inferior card angles on superior card angles 2 Parameter Coefficient Constant R CAXi 0.8584 9.7198 0.8432 CAYi 0.9452 4.8383 0.622

In reality, the articular process dimensions and facet angles are very closely tied to many variable factors including the spinal curvature, vertebral orientation, the geometry of the articular processes, and the amount of mobility and movement in that spinal region. A better definition of the variability and the factors affecting articular facet orientation will have to be undertaken in future research.

3.4.2.3. Pedicle Inclination

The pedicles are inclined in two planes, sagittal and transverse. Both parameters poorly correlate with vertebral body height. Regressions against other likely parameters also show low correlations.

This poor correlation with the given data set probably points to dependence on some other factors that were not studied. It may be that the angulations seen vary with muscle cross-sectional area adjacent to the vertebra, or be associated with muscular or ligamentous attachment area needed. Association with some measure of spinal curvature may also be useful. Future work will be required to definitively associate these 49 parameters with changes in gender, stature, and ethnicity, or to establish that there is no significance to the variations observed.

For the purposes of this model, the average values obtained by Panjabi [42-44] will be used.

3.4.3. Poor Correlation Parameters

The parameters defining the dimensions of the spinal canal show a poor correlation (R2<0.4) to the vertebral body height. Though there is a low correlation with vertebral body height, each spinal segment shows a grouped cluster of data points.(Figure 3-7) Therefore the data for each segment will be averaged and set to a constant .

Spinal Canal Area by Segment 350 330 310 SCA-C 290 SCA-T 270 SCA-L 250 230 210

190 Spinal Canal Area (mm^2) Area Canal Spinal 170 150 0 5 10 15 20 25 30 35 Vertebral Body Height (mm)

Figure 3-7 Spinal Canal Area By Segment Vs. Vertebral Body Height

The area of the neural opening probably has quite a bit of dependence on the spinal cord and other neural structures which run through it. Based on the anatomy of the spinal cord itself, one would expect the cervical, lower thoracic and upper lumbar sections have larger openings and the upper thoracic section to be somewhat smaller, to mirror the bulges at the upper and lower ands of the spinal cord.

Transverse process width was another parameter that showed a marginal correlation with vertebral body height. TPW does group together well by segment (Figure 3-8), so the same technique of creating an average for each segment will be employed.

Transverse Process Width by Segment

100 90 80 70 60 50 TPW-C 40 TPW-T 30 TPW-L 20 10 Transverse Process Width (mm) 0 0 5 10 15 20 25 30 35 Vertebral Body Height (mm)

Figure 3-8 Transverse Process Width By Segment Vs. Vertebral Body Height

Another parameter that shows poor correlation with vertebral body height definite segment dependence is the inter-facet width (Figure 3-9). Again, a segment average will be used for the model. 51

Superior Inter-facet Width by Segment

25 IFWs-c IFWs-t 20 IFWs-L 15

Inter-facet Width (mm)Inter-facet Width 10

0 0 10203040 Vertebral Body Height (mm)

Figure 3-9 Superior Inter-Facet Width By Segment Vs Vertebral Body Height

Finally, the inferior articular facet area shows a poor vertebral body height correlation. However, when the inferior facet area is compared to the superior facet area, the correlation s greater (R2 = 0.5634).(Figure 3-

10) Therefore, the superior facet area will be used to predict the inferior facet area, using the trend line equation from Figure 3-10. 52

Articular Facet Area y = 1.1425x - 1.5249 250 R2 = 0.5634

200

150 FCA_ave_i Linear (FCA_ave_i) 100

50 Facet area inferior (mm^2) inferior Facet area 0 0 50 100 150 200 Facet area superior (mm^2)

Figure 3-10 Superior Facet Area Vs. Inferior Facet Area

3.5. Creating a Solid Model of a General Vertebra

In order to reduce the size of linking tables within Solid Edge and improve memory usage, the vertebra was created in four separate sections: the vertebral body, the pedicle and vertebral arch, the superior facet and the inferior facet. Because of the creation in separate parts, some assembly features were added to aid in the assembly of the final model, and will be identified in the following sections.

Each section is created as a separate file in Solid Edge. Each section’s file is then linked to cells in an

Excel file, which holds all the personalized parameter data. The link table in Solid Edge is modified so that a separate file for each vertebra is created. For example, to create the vertebral body for C3 the link table for the general vertebral body is opened. All the links in the table are modified such that the pointer variable points to the column of data in Excel for the C3 vertebral body. The C3 vertebral body model is saved with a unique 53 name (VB_C3.par). The general model (VB.par) is then modified such that the pointers in the link table point to the next column of Excel data, the data for C4.

By the repetition of this process, a distinct file for each section of the vertebra and for each vertebra is created. With 22 vertebrae modeled (C3-L5 - 5 cervical, 12 thoracic, 5 lumbar) and 4 sections per vertebra, there are a total of 88 files.

Each group of vertebral section files are then assembled in Solid Edge to create an assembly file containing a single vertebra. The assembly file is given a name based on the vertebra it represents (e.g. vertebra_T6.asm for the assembly of the vertebral body, vertebral arch, superior and inferior articular processes models for T6).

Each of the vertebral model sections will be discussed below. The files are built using a local coordinate system to simplify the creation of each element. In general the planes referred to in construction are similar to the anatomical planes of the body. The y-z plane used in model construction is a sagittal plane of the body and the terms are interchangeable. All other planes are locally defined as is the local coordinate system. In general the x-y plane is closest to the transverse plane, and the x-z plane is closest to the frontal plane (see Figure 3-11).

The angular relationships between the local vertebral planes and the anatomic planes change for every vertebral level and the degree and direction of spinal curvature. 54

Figure 3-11 Example Of The Difference Between Global Anatomic Planes And Local Element Planes. Sagittal View Of L5 Vertebral Body Model

3.5.1. Vertebral Body Model

The vertebral body was created in Solid Edge v14. The first parameter defined in the building process is the posterior vertebral height. A plane parallel to the x-y plane is offset to create 2 parallel planes with the 55 distance between them defined as VBHp. Since the vertebrae are all slightly wedge shaped, planes for the end plates are inclined, defined by the parameters EPIu and EPIl. Next, an ellipse is sketched on the upper and lower endplate planes. A guideline is drawn between the centers to be an anchor point for proper constraint of the shape of the vertebral body. The parameters of the end plate width and depth for both end plates are defined. The sketches for upper and lower end plates are lofted to form a solid, constituting the vertebral body.

For assembly purposes, a sketch of the pedicles is made at the center of the vertebral body on the x-z plane. A path is defined by a guide curve, consisting of a line angled in both the x-y and y-z planes according to the parameters PDIs and PDIt. The pedicle outline is then cut out of the vertebral body along the guide curve path. This hole will be filled with the pedicle portion of the model during assembly. Two more holes are cut from the vertebral body along a line connecting the centers of the upper and lower endplate ellipses. These two holes are used to locate the completed vertebra along the spinal curve when assembling the full spine model.

The completed model is seen in Figure 3-12.

Spinal Curve Holes Pedicle Outline

Pedicle Guide Curve

Figure 3-12 Vertebral Body Model Isometric View

3.5.2. Vertebral Arch Model

The posterior elements created in this section include: the pedicles, the laminae, the transverse processes, and the spinous process. The spinal canal and vertebral arch are created by default during the process. The posterior elements are modeled using symmetry along the median plane. The right half of the model is built then reflected about the median plane. To accommodate the left and right dimensions recorded in

Panjabi’s research [42-44], averages of the left and right dimensions of the pedicles were used.

First, an ellipse is sketched on the x-z plane to represent the outline of the pedicle. The major and minor axes of the ellipse are linked to the pedicle height and width. The ellipse center is determined by offsetting from the origin by half of the spinal canal width added to half of the pedicle width, ensuring the spinal canal will be of proper size. A guide curve to determine the path of the pedicle is then sketched on the x-y plane. The length of the line is linked to both the end plate depth and the spinal canal depth, to ensure the pedicle solid will preserve the spinal canal dimensions and fill the associated space removed from the vertebral body for assembly. The pedicle outline ellipse is then protruded along the guide curve. (Figure 3-13) 57

Pedicle Guide Curve

Pedicle Outline

Figure 3-13 Pedicle Model

Next the lamina is created. A plane is angled from the x-y plane to create the downward slope observed in the vertebrae, which extend down along the spinous process. This downward slope will be referred to as the spinous process angle, as the angle is maintained from the laminae to the end of the spinous process. (Figure 3-

14) 58

Figure 3-14 Illustration Of Spinous Process Angle On T8 Vertebra. The Top Line Is Drawn Across The Top Of The Pedicle; The Bottom Line Is Drawn Across The Top Of The Spinous Process And The Laminae. Modified From Atlas Of Anatomy[8]

This angle is not defined in the literature, and is set according to measurements taken on vertebra obtained from cadaveric specimens. None of the driving parameters (sex, height, etc.) were obtained to match to the measurements, and measurements were taken from a single spine. The values set in this model do not change with the driving parameters. Future investigation will be required to quantitatively determine this parameter and its change with the driving parameters.

Another ellipse is sketched with its center anchored to the spinous process angle plane. The depth of the spinal canal is used to determine the depth of the sketched ellipse. The Pedicle outline and this new ellipse are lofted together to create the vertebral arch. See Figure 3-15. 59

Spinal Canal

Lamina Outline Figure 3-15 Pedicle And Lamina

Next the transverse process is created. A circular cross-section is assumed for the transverse process.

Panjabi only provides the width of the transverse process from the tip of one to the tip of the other. It is observed that there is a general posterior sweep of the transverse process. Therefore a sketch is made of a circle that has been rotated about the z-axis. The parameter of transverse process angle is created and given an arbitrary value. A guide curve is drawn along this angle normal to the circular sketch, whose length is defined by half the TPW. Another circular cross-section is defined at the end of the guide curve and the transverse process is lofted (Figure 3-16). 60

Transverse process base

Transverse process tip

Figure 3-16 Pedicle, Lamina And Transverse Process

Finally, the spinous process is created. A sketch is made on the medial plane of the outline of the process. The sketch is angled down parallel to the plane made for the vertebral arch. Though the spinous process length is defined in Panjabi, the length of the process in the model is as of now arbitrary, due to the lack of a spinous process angle definition. The outline of the spinous process is protruded.

All the elements, including the spinous process are now mirrored about the median plane to create the completed pedicle/vertebral arch seen in Figure 3-17. 61

Figure 3-17 Complete Vertebral Arch Model

3.5.3. Articular Process Models

The articular facets were created separately to facilitate easier assembly. Again, symmetry was used to simplify the creation of the models about the median plane. To accommodate the left and right dimensions in the Panjabi data [45], averages of the left and right articular process were used as parameters.

The faces of the articular facets are not regular shapes, therefore, to simplify the model a circle of equivalent surface area was used. The model was created by first creating two guide curves in the x-y plane and the y-z plane. The curves were defined by a line with an angle set according to the Panjabi data for card angle.

In the x-y plane, the angle in set from the x-axis, in the y-z plane the angle is set from the y-axis. The end points from these two lines define the facet face. A circle is sketched at the center of the face guide curves. To connect the facet face to the rest of the vertebral structures another sketch was placed. For the superior facet, an assembly sketch was placed along the coronal mid-plane of the pedicle. For the inferior facet, an assembly 62 sketch identical to the vertebral arch cross section was used. A solid was lofted from the face circular sketch to the assembly sketch, and then mirrored along the medial plane of the vertebra. (Figures 3-18 and 3-19).

Figure 3-18 Superior Articular Process Model. Isometric, Rear And Side Views

Figure 3-19 Inferior Articular Process Model. Iso Metric, Front, And Side Views

The fully assembled vertebral model is seen in Figure 3-20 64

Figure 3-20 – Vertebral Model, Two Isometric Views

3.6. Spinal Curve Model

In order to simplify the assembly process, two solids are created that follow the spinal curve. The solids consist of straight segments whose end points are attached to the spinal curve. There is a line segment for each vertebral body and a segment for each intervertebral disc. The end points of each segment are defined by the vertebral body height or disc height and the equation for the spinal curve derived above. The end points are 65 calculated in Excel and imported in Solid Edge using the CurveByKeypoints tool. The option for create a curve by straight segments is selected and Solid Edge creates a sketch of the desired curve. A circular sketch is placed on a plane normal to the lumbar end of the spine curve. This circular cross section is then protruded along the path created by the straight segments of the spine curve. (Figure 3 21)

B A

Figure 3-21 Sagittal View Of The Spine Curve Model. A) Full Spine B) Close-Up Of Inferior End.

This solid is then reflected about a sagittal plane to create two solids that both follow the desired spine curve. There are two solids so that the pitch, roll, yaw, and translation in two directions of the vertebra are 66 constrained when the axes of the segment and the vertebral body holes are aligned during assembly.(Figure 3-

22)

Figure 3-22 Spine Curve Model. Isometric And Side View

3.7. Final Assembly of the Model

To complete the model assemble each vertebra is brought into the Solid Edge assembly environment and has three assembly relationships defined. The first two relationships are axial alignments between the holes in the vertebral body to the corresponding cylinder on the spinal curve model. Finally the superior endplate has a planar alignment relation ship placed between the spinal curve segment end and the upper vertebral endplate..

This completes the assembly of the spine model. (Figure 3-23,3-24) 68

Figure 3-23 Assembled Spine Model Using Distance Method. Isometric AND RIGHT VIEWS. Subject: White Male 65” TALL.

A B C D

E F G H

Figure 3-24 - Comparison Of Spine Models For Subjects Using The Distance Method. A) Black Female 65” Tall B) Black Female 72” C) White Female 65” D) White Female 72” E) Black Male 65” F) Black Male 72” Tall G) White Male 65” H) White Male 72”. Scale Displayed Next To Each Model Represents 100 Mm. 70

4. Results and Conclusions

4.1. The Spinal Model

The spinal model is created in a number of steps and calculations. First a user inputs the driving parametric data about a subject: height, gender, ethnicity, and age. Height, gender and age are used to calculate a spinal height using the information from Table 3-2. (Figure 4-1)

Figure 4-1 Diagram Of Spine Height Calculation From Input Parameters

The spine height is used to determine the individual vertebral and disc heights. The vertebral height is calculated by taking 70% of the spine height and applying the individual vertebral heights from Tibbetts [12] seen in Table 3-3. The disc heights are calculated by taking the remaining 30% of the spine height and applying the individual disc height percentages determined in Section 3.3.3. seen in Table 3-5. (Figure 4-2). 71

Figure 4-2 Diagram Of Vertebral Body Height And Disc Height Calculation

These three sets of data are used along with the original spine curve are used to create a spine curve model in Solid Edge. The spine height is used to scale the original spine curve coordinates. These new coordinates are fit with a sixth-order polynomial to determine the equation for the personalized spine curve.

The heights of the vertebrae and discs are used to create a set of endpoints. The base of the model is considered to be the base of the L5 vertebral body (on the x-axis of spine curve). The successive heights of the vertebrae and discs are added to create the x-coordinates of the vertebral body endplates. These coordinates are evaluated using the personalized spine curve equation to obtain the endplate coordinates. These coordinates are used to create the solid model of the spine curve in Solid Edge. (Figure 4-3) 72

Figure 4-3 Diagram Of Spine Curve Model Creation

The coordinates of the endpoints of each segment that makes up the spinal curve are used to calculate the endplate inclination of the upper and lower endplates of each of the vertebrae. The remainder of the parameters defining the vertebral model are predicted using equations derived from relationships in the reference data set, obtained from Panjabi [42-45]. The reference data set is used to obtain linear regressions between vertebral body height and the parameter of interest. Each parameter and the formula obtained from the linear regression analysis are seen in Table 4-1. These parameters are used to create a set of the components of the vertebral model. 73

Table 4-1 Parameter prediction formulas Parameter Formula Used in EPWu =1.6836*VBH-1.598 Distance EPWl =1.7618*VBH-.7654 Distance EPDu =1.2326*VBH+2.838 Distance EPDl =1.1348*VBH+5.3909 Distance IFHa =1.0397*VBH+3.7644 Both SPL =2.0017*VBH+13.823 Both PDH =0.5528*VBH+2.0493 Distance PDW =0.3683*VBH+1.2182 Distance TPW C-52.26, T-60.1583, L-80.98 Both IFWs C-38.06, T-24.24, L-29.52 Both IFWi C-37.74, T-23.54, L-31.18 Both SCW C-16.92, T-18.64,L-18.6 Distance SCD C-24.56, T-16.16, L-24.86 Distance EPSAl =64.922*VBH-538.2 Area EPSAu =64.184*VBH-581.56 Area PDA =5.5432*VBH--47.409 Area FCAs =4.6258*VBH+15.739 Both SCA C-252.1, T-207.25,L-300.2 Area FCAi =1.1425*VBH - 1.5249 Both CAYs =2.0263*VBH-18.202 Both CAXs =2.0895*VBH+30.144 Both CAYi y = 0.9452x + 4.8383 Both CAXi y = 0.8584x + 9.7198 Both =1/2*(tan-1(slope of disc centerline)-tan-1(slope EPItl of VB centerline))(see 3.4.2.1) Both =1/2*(tan-1(slope of VB centerline)-tan-1(slope of disc centerline))(see 3.4.2.1) EPItu Both

Two methods are employed in model component generation, the distance method and the area method.

The two methods result in two models for each vertebral component and consequently each vertebra. These will be used to create two spines one based on each method.

The vertebral model components (vertebral body, vertebral arch, superior articular process, and inferior articular process) are then assembled into vertebral models of the vertebrae from C3 to L5. (Figure 4-4) 74

Figure 4-4 Diagram Of Vertebral Model Creation

The resulting 22 vertebrae models from the distance method and 22 vertebrae models from the area method are assembled along the spinal curve model to create 2 spine models, whose parameters are defined by a subject’s height, gender, and ethnicity. (Figure 4-5)

Figure 4-5 Diagram Of Final Assembly Of Spine Model

4.2. Conclusions

The solid models created in Chapter 3 model the human spine with variable geometry so that it can closely match the anatomy of many subjects in the population. Anthropomorphic parameters of gender, height, and ethnic background of a subject are used to vary the model’s geometry to match that of the desired subject.

Two methods have been developed to model the geometry of specific vertebrae, and are compared to each other. In the future, data collection and analysis of subjects will be able to discern the benefits and limitations on both methods and determine the accuracy of each model.

This model is a first attempt to link external, easily obtained, anthropomorphic parameters to the internal structure of the human spine. Many of the areas involved in the investigation of the relationships between external and internal parameters are poorly defined for this specific application. There are many areas where continued research will be very valuable to future developments to improve the accuracy and complexity of this model.

Research that better defines spinal curvature and its changes across the population will be required to further enhance the ability to model a subject-specific spine. The study of spinal curvature and a mathematical definition of the curvature and its ability to change lie at the center of optimizing this model as a diagnostic aide.

Also, there is a need to expand the scope of data collection to the muscular and ligamentous systems attached to and surrounding the vertebrae. The underlying reason behind the changes observed from one vertebra from to the next can only be discerned if a fuller understanding of the systems that react with and depend on the vertebrae is obtained. This understanding will lead to better identification of the key parameters 76 driving the changes observed. It also can lead to better relationships defining between the driving and driven dimensions of the vertebral parameters.

There are still some important geometric properties of the vertebrae that need to be defined. The ability to fully reproduce mathematical models of the vertebrae does not yet exist. Dimensions like the spinous process angle or transverse process angle have not been recorded in human morphological research, as they have been in the study of other animals [67, 68]. Geometric definitions of the articular processes are also sorely lacking.

The geometry and relationships between adjacent vertebrae also needs better definition and detail. 77

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Appendices

Appendix A

Average Card Angles for the Superior and Inferior Articular Facets

Panjabi, M. M., Oxland, T., and Takata, K., 1993, "Articular Facets of the Human Spine - Quantitative 3-Dimensional Anatomy," Spine, 18(10) pp. 1298-1310. 85

Appendix B

Means (and Standard Errors of the Mean) of the Superior and Inferior Articular Facet Surface Areas

Panjabi, M. M., Oxland, T., and Takata, K., 1993, "Articular Facets of the Human Spine - Quantitative 3-Dimensional Anatomy," Spine, 18(10) pp. 1298-1310. 86

Appendix C

Means (and Standard Errors of the Mean) of the Interfacet Distances

Panjabi, M. M., Oxland, T., and Takata, K., 1993, "Articular Facets of the Human Spine - Quantitative 3-Dimensional Anatomy," Spine, 18(10) pp. 1298-1310. 87

Appendix D

Cervical Vertebral Body Dimensions

Panjabi, M. M., Duranceau, J., and Goel, V., 1991, "Cervical Human Vertebrae - Quantitative 3-Dimensional Anatomy of the Middle and Lower Regions,"

Spine, 16(8) pp. 861-869 88

Appendix E

Cervical Spinal Canal Dimensions

Panjabi, M. M., Duranceau, J., and Goel, V., 1991, "Cervical Human Vertebrae - Quantitative 3-Dimensional Anatomy of the Middle and Lower Regions,"

Spine, 16(8) pp. 861-869 89

Appendix F

Cervical Pedicle Dimensions

Panjabi, M. M., Duranceau, J., and Goel, V., 1991, "Cervical Human Vertebrae - Quantitative 3-Dimensional Anatomy of the Middle and Lower Regions,"

Spine, 16(8) pp. 861-869

Appendix G

Cervical Spinous Process and Transverse Process Dimensions

Panjabi, M. M., Duranceau, J., and Goel, V., 1991, "Cervical Human Vertebrae - Quantitative 3-Dimensional Anatomy of the Middle and Lower Regions,"

Spine, 16(8) pp. 861-869 91

Appendix H

Thoracic Vertebral Body Dimensions

Panjabi, M. M., Goel, V., and Federico, D., 1991, "Thoracic Human Vertebrae - Quantitative 3-Dimensional Anatomy," Spine, 16(8) pp. 888-901. 92

Appendix I

Thoracic Spinal Canal Dimensions

Panjabi, M. M., Goel, V., and Federico, D., 1991, "Thoracic Human Vertebrae - Quantitative 3-Dimensional Anatomy," Spine, 16(8) pp. 888-901. 93

Appendix J

Thoracic Spinal Canal Dimensions

Panjabi, M. M., Goel, V., and Federico, D., 1991, "Thoracic Human Vertebrae - Quantitative 3-Dimensional Anatomy," Spine, 16(8) pp. 888-901. 94

Appendix K

Thoracic Pars Intra-Articularis, Spinous and Transverse Process Dimensions

Panjabi, M. M., Goel, V., and Federico, D., 1991, "Thoracic Human Vertebrae - Quantitative 3-Dimensional Anatomy," Spine, 16(8) pp. 888-901. 95

Appendix L

Lumbar Vertebral Body Dimensions

Panjabi, M. M., Goel, V., and Oxland, T., 1992, "Human Lumbar Vertebrae - Quantitative 3-Dimensional Anatomy," Spine, 17(3) pp. 299-306. 96

Appendix M

Lumbar Spinal Canal Dimensions

Panjabi, M. M., Goel, V., and Oxland, T., 1992, "Human Lumbar Vertebrae - Quantitative 3-Dimensional Anatomy," Spine, 17(3) pp. 299-306. 97

Appendix N

Lumbar Pedicle Dimensions

Panjabi, M. M., Goel, V., and Oxland, T., 1992, "Human Lumbar Vertebrae - Quantitative 3-Dimensional Anatomy," Spine, 17(3) pp. 299-306. 98

Appendix O

Lumbar Pars Interarticularis, Spinous Process, and Transverse Process Dimensions

Panjabi, M. M., Goel, V., and Oxland, T., 1992, "Human Lumbar Vertebrae - Quantitative 3-Dimensional Anatomy," Spine, 17(3) pp. 299-306.