A Review of Computational Spinal Injury Biomechanics

Research and Recommendations for Future Efforts

by Reuben H. Kraft and Samantha L. Wozniak

ARL-TR-5673 September 2011

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ARL-TR-5673 September 2011

A Review of Computational Spinal Injury Biomechanics

Research and Recommendations for Future Efforts

Reuben H. Kraft and Samantha L. Wozniak

Weapons and Materials Research Directorate, ARL

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ARL-TR-5673

Approved for public release; distribution is unlimited.

November 2010-April 2011

A Review of Computational Spinal Injury Biomechanics Research and

Recommendations for Future Efforts

W911QX-09-0057

Reuben H. Kraft and Samantha L. Wozniak AH80

U.S. Army Research Laboratory

ATTN: RDRL-WMP-B

Aberdeen Proving Ground, MD 21005-5066

Author email: reuben.h.kraft.civ@mail.mil

Developing an understanding of the high rate injury biomechanics associated with blast-induced loading to the

spine, lower extremities, central nervous system, and peripheral nervous system is critical to optimize protective

equipment for Soldiers. Computational methods and high performance computing are an essential part of the

toolset needed to develop the understanding of spinal injury caused by high strain rate loading. These methods

provide a wealth of information that otherwise may not be available. While the research area of computational

spinal injury biomechanics has received much attention in the past with regard to low strain rate degenerate effects,

there are significant opportunities to enhance the state of knowledge of spinal injury in the area of high strain rate

military loading. Through this literature review and careful contemplation, a list of six recommendations for future

research directions has been developed.

spinal injury, computational modeling, finite element analysis, explosion, blast

UU 48

Reuben H. Kraft

Unclassified Unclassified Unclassified 410-278-6142

ii
Contents

List of Figures iv

List of Tables v

Preface vi

1. Introduction 1

1.1 Anatomy of the Spine ................................................................... 2

1.2 Osseous, Soft Tissue, and Neurological Injury ...................................... 5

2. Computational Spinal Injury Biomechanics 11

2.1 Models of the Vertebra .................................................................. 15

2.2 Models of the Intervertebral Disc...................................................... 16

2.3 Segment Models.......................................................................... 16

2.4 System Models ........................................................................... 18

2.5 Failure Models............................................................................ 18

2.6 Uncertainty Quantification ............................................................. 20

3. Conclusion and Recommendations 21

4. References 25

Appendix A. Verification, Sensitivity and Validation 35

Distribution List 36

iii
List of Figures

Figure 1. Bony anatomy of the (a) spinal column and (b) vertebra. Netter illustration from

www.netterimages.com. 
c Elsevier Inc. All rights reserved. ............................... 3

Figure 2. Time scales associated with the loading process in the human body inside a vehicle due to mine detonation (17). Figure courtesy of the NATO Research and Technology

Organization/Human Factors and Medicine Panel. . ......................................... 6

Figure 3. Principal applied loading mechanisms that may lead to spinal injury (21). Reprinted

with permission from Springer Science + Business Media...................................... 7

Figure 4. (a) Drawings show the grading of wedge vertebral fractures. The approximate

degree of height reduction determines the assignment of grade to the fractured vertebra (reproduced with permission of Mary Ann Liebert, Inc.). (b) Lateral radiograph

of lumbar spine shows a mild wedge fracture (grade 1) of L3 vertebra. (c) Lateral radiograph of lumbar spine shows moderate wedge fracture (grade 2) of L3 vertebra and

moderate crush fracture (grade 2) of L2 vertebra. (d) Lateral radiograph of thoracic

spine shows severe wedge fracture (grade 3) of T7 vertebra (31). Figures b through d

reprinted with permission from the American Journal of Roentgenology. . ................. 9

Figure 5. (a) Patterns of the retropulsed fragment. (b) Sagittal and (c) axial CT scans of

the thoracolumbar spine demonstrates an L4 burst fracture with retropulsion of bone

into the spinal canal (as shown by arrows) (32, 33). Reprinted with permission from

the American Journal of Roentgenology and Neurosurgical Focus. . ....................... 10

Figure 6. Variations of Chance-type flexion-distraction spinal injuries include (a) classic

Chance fracture, (b) fulcrum fracture, and (c) pure soft-tissue flexion-distraction injury. (d) Lateral radiograph shows a classic Chance fracture that extends horizontally

through the pedicle (right arrow) and into the vertebral body. There is an anterosuperior wedge-shaped compression fracture (left arrow) in the same vertebral body (36).

Reprinted with permission granted from The Radiological Society of North America

and author. . .................................................................................... 11

iv
List of Tables

Table 1. Compilation of various constitutive models and parameters found in recent computational models of the spine.1

. .............................................................. 14

v
Preface

Since this is a joint publication between a government employee and a government

contractor, a break down of the report is offered to show that it is in the best interest of

the government to have a combined government/contractor report. This review article

was designed by Reuben Kraft to offer a precise overview of a subtopic within the large

research field of spinal injury biomechanics, namely computational spinal injury

biomechanics. Samantha Wozniak, a Bowhead, Inc. contractor, significantly

contributed to the authorship as she gathered references and wrote summaries for

targeted research topics dictated by Kraft. Kraft and Wozniak worked closely to shape

this report each making many modifications of their own. If asked to divide the report

into ”who did what,” it would be extremely difficult but would look close to the

following:

• Introduction: Kraft and Wozniak

• Anatomy Section: Wozniak

• Injury Section: Kraft and Wozniak

• Vertebra Models Section: Wozniak

• Intervertebral Disc Models Section: Wozniak

• Segment Models Section: Wozniak

• System Models Section: Kraft

• Failure Models Section: Kraft

• Uncertainty Quantification Section: Kraft

• Conclusion and Recommendations Section: Kraft

vi
1. Introduction

The incidence of spine injuries among American military personnel is currently

estimated to be at its highest in comparison to the last 60 years (1). While injuries to the

neck and spine only account for 5% of the total injuries seen in the current conflicts,

these injuries are commonly the most debilitating and costly for the warfighter (2).

Spinal injuries that result in spinal cord impingement are of particular concern because

they may result in paralysis, loss of bowel and bladder function, inability to regulate

automatic functions of the body, and many other complications.

The classifications of spinal injuries are related to the abnormal forces acting on the

central axial spinal pillar and the accompanying exaggerated movements that cause

spinal instability. The magnitude and type of injuries produced by an explosion are a

result of many factors including the type and amount of explosive material, delivery

method, the surrounding environment, and the distance between the victim and the

blast. Injuries induced by explosions can be divided into four classes: primary,

secondary, tertiary, and quaternary blast injury. Primary blast injury is a result of the

sudden increase in air pressure after the blast while secondary blast injury is due to

projectiles from the blast. Tertiary blast injury is due to the thrust of the victim against

stationary objects or wind disruption, and quaternary blast injury is a result of fire and

heat generated by the explosion, toxic effects, or post-incident risks (3, 4).

A study published in 2010 characterized combat-related spinal injuries sustained by a

Brigade Combat Team (BCT), the basic deployable unit in the U.S. Army (1). The BCT

involved in this study participated in The Iraq War Troop Surge of 2007, a major operation

of the Iraq conflict. Twenty-nine of the 4,122 Soldiers deployed for 15 months sustained

combat spine injuries (1). Twenty-three (74%) of these injuries were from improvised

explosive devices. Four spine injuries were due to vehicular accidents and a gunshot

wound led to one spinal injury. Specific spinal injuries sustained by these service

members include lumbar burst fractures, compression fractures, nondisplaced type III

fracture of the odontoid, traverse process fractures, and a flexion-distraction injury.

Seven Soldiers were considered polytraumas, including one who experienced neurologic

compromise due to a burst fracture.

1
The purpose of this report is to review recent literature on computational spinal injury

biomechanics modeling for high strain rate loading, identify gaps in the research, and

formulate recommendations for future efforts. This review does not aim to be an

exhaustive list of papers that use finite computational techniques to analyze the spine,

but rather focuses on current state-of-the-art techniques with regard to high rate injury

and failure modeling. Models of the spine range from the sub-micron scale of vertebral

bone to models of the whole spine and surrounding structures. This review focuses on

models of individual spinal components and small segments of the spine at the macro

scale. First, in sections 1.1 and 1.2, we present the spinal anatomy and a biomechanical

description of spinal injuries sustained by Soldiers during combat, including the length

and time scales associated with blast-induced spinal injury. Next, in section 2, a brief

history of spine modeling is discussed, followed by a more in depth review of vertebra,

intervertebral disc, segment, and full spine finite element models. In addition, section 2

includes a discussion of computational approaches for modeling spinal injury

mechanisms, such as fracture and various techniques for handling uncertainty

quantification. Finally, in section 3 we conclude with a summary of the state-of-the-art

finite element model techniques and suggest recommendations for future research.

1.1 Anatomy of the Spine

The spine has many functions including to protect the spinal cord and associated nerves,

allow for movement, support the body frame in an upright position, allow for flexibility,

provide a structural foundation for the shoulder and pelvic girdles, prevent and absorb

shock, and provide a structural base for rib attachments which protect the heart and

lungs. The spinal column is an intricate structure, comprised of vertebrae and cartilage

discs, known as intervertebral discs, stacked alternatively on top of each other. The

column starts at the base of the skull and continues to the pelvis. As seen in figure 1a,

the spine is divided into five regions: the cervical spine, the thoracic spine, the lumbar

spine, the sacrum, the coccyx. Each individual vertebra is named by referring to the first

letter of the region (e.g., “L” for lumbar), and, starting with the most superior vertebra in

that region, numbered consecutively until the most inferior vertebra in the region has

been named.

2
Figure 1. Bony anatomy of the (a) spinal column and (b) vertebra. Netter illustration from

www.netterimages.com. 
c Elsevier Inc. All rights reserved.

Vertebrae differ in size and shape between regions and also within a region. For

example, the 12 vertebrae in the thoracic spine (commonly referred to as T1-T12) each

have two thoracic facet joint sets– one set on the top and one set on the bottom– which

are responsible for providing the middle back with the flexibility and strength it needs.

A typical vertebra consists of two main parts: an anterior vertebral body and posterior

vertebral arch. As seen in figure 1b, the lumbar vertebral arch is formed by a pair of

pedicles, and laminae and supports seven processes: four articular, two transverse, and

one spinous (note that T1-T12 have six articular processes). The principal biomechanical

function of the vertebral body is to support the daily loads of the spine. Accordingly,

the vertebral bodies graduate in size from the cervical to the lumbar region. The

microstructure of the vertebral body is comprised of highly porous trabecular bone and

a thin, dense cortical shell. The trabecular bone supports the majority of the vertical

3
compressive loads while the outer cortical shell helps resist torsion and shear forces (5).

A thin layer of semi-porous subchondral bone forms a boundary layer between the

cancellous (synonymous with trabecular bone) core of the vertebral body and the

intervertebral disc, known as the vertebral end-plate. The end-plates of a healthy disc

prevent the highly hydrated nucleus from bulging into the adjacent vertebral bone, while

simultaneously absorbing hydrostatic pressure that results from mechanical loading of

the spine (6). In many respects the structure is similar to that of articular cartilage, and

while the end-plate cartilage is not connected directly to the bone of the vertebral bodies,

it does have direct connections with the disc through the lamellae of the inner (medial)

annulus fibrosus (7). In the adult disc the end-plates typically are less than 1 mm thick,

and although this varies considerably across the width of any disc, there is a tendency

for the end-plate to be thinnest in the central region adjacent to the nucleus pulposus (8).

Intervertebral discs lie between adjacent vertebrae and form a cartilaginous joint that

allows for motion between the vertebrae. These structures help absorb compression

forces, support bending loads and resist rotation, tension, and shear (9). Discs are

complex structures made up of an outer ring of fibrous cartilage (type I and II), also

known as the annulus fibrosus, and an inner gelatinous core termed the nucleus

pulposus. The nucleus pulposus contains randomly organized collagen fibers and

radially organized elastin fibers (10). The annulus fibrosis is comprised of alternating

layers of type I (outer annulus) and type II (inner annulus) collagen at 30◦ angles to the

end-plate. This arrangement leads to an anisotropic and inhomogeneous material. In

addition, the orientation of the collagen fibers makes the structure nonlinear (11).

Another load-bearing junction between the vertebrae is the zygapophysial joint

(zygapophyseal, or facet joint). This joint is formed between the superior articular

process of one vertebrae and the inferior articular process of the vertebrae directly above

it as schematically depicted in figure 1b. In each spinal segment there are two facet

joints, which, in combination with the disc, allows for motion including flexion,

extension, rotation, and lateral bending. These joints also may restrict movement

depending on their orientation; they limit flexion in the thoracic spine and rotation in the

lumbar spine (12). Similar to other joints in the body, each facet joint is surrounded by a

capsule of connective tissue and covered by articular cartilage. Within the joint capsule,

the joint is lined by a membrane known as the synovium. Synovial fluid surrounds the

joint and is compromised of hyaluronic acid, lubricin, proteinases, and collagenases.

The lubricin found in the synovial fluid allows the cartilage to move with very little

friction. The coefficient of friction for synovial joints in humans has been estimated to

4
be 0.01 for static friction and 0.003-0.0057 for kinetic friction (13, 14).

Excessive movement of the spinal components is limited by the spinal ligaments.

Ligaments, in combination with muscles and tendons, help preserve the natural

articulation of the spine and stabilize the components. There are two primary ligament

systems in the spine: the intersegmental and intrasegmental systems (15). The

intrasegmental system holds individual vertebrae together and is made up of the

ligamentum flavum, interspinous ligament, intertransverse ligament, and facet capsule.

The intersegmental system holds many vertebrae together and includes the anterior

longitudinal ligament, posterior longitudinal ligament, and supraspinous ligament.

Within the vertebral canal is the spinal cord, which is protected by three tissue layers,

known as meninges. Beginning as a continuation of cranial dura mater, the outer

protective membrane, spinal dura mater, extends to the level of the second sacral

vertebra (16). Between the dura mater and the vertebrae is a space, known as the

epidural space, filled with adipose tissue and a network of blood vessels. The middle

layer, or arachnoid mater, is separated from the inner layer (pia mater) by the

subarachnoid space which contains cerebrospinal fluid.

1.2 Osseous, Soft Tissue, and Neurological Injury

It is important to understand the length and time scales associated with blast-induced

spinal injury. In vehicle mine blasts, tertiary blast effects tend to be the most common

injury mechanism (4). Within 0.5 ms of the initiation of the explosion, a shock wave hits

the bottom plate of the vehicle and causes a large peak in pressure. This pressure results

in local acceleration and subsequent deformations of the plate, which apply significant

axial loads to the Soldier and may result in spinal, pelvic, and lower limb fractures (17).

In 2007, the North Atlantic Treaty Organization (NATO) published a technical report,

Test Methodology for Protection of Vehicle Occupants against Anti-Vehicular Landmine Effects,

which provided information about the process of vehicular mine blasts (17). As

described in the report, as the blast wave reflects under the vehicle, a pressure force acts

on the bottom of the vehicle and causes it to lift off the ground. The acceleration of the

vehicle and the collisions that follow are a significant source of injury, especially if the

Soldier is not properly restrained. As seen in figure 2 (reprinted from the NATO

technical report), the body is subjected to both the local effects (caused by shock and

high rate deformation of the vehicle) and global effects (vehicle motion over time) of the

vehicle mine detonation process. Drop-down effects and subsequent events, such as

5
rollover, are not considered due to a high variability in boundary conditions.

Figure 2. Time scales associated with the loading process in the human body inside a vehicle

due to mine detonation (17). Figure courtesy of the NATO Research and Technology

Organization/Human Factors and Medicine Panel.

Spinal injury in Soldiers is often caused by high accelerative loading and may result

from explosions and vehicular accidents. Mechanisms of spinal injury include axial

deformation (compression or tension); torsion or axial rotation; segmental translation

(shear); and simultaneous or successive combination of the previous three mechanisms

(18). Principal applied loading mechanisms that may lead to spinal injury are shown in

figure 3. The thoracolumbar junction (TLJ), T12-L2, is a common site of traumatic

injuries, accounting for 30–60% of all spinal injuries (19). However, in current military

operations, for spinal injury cases involving underbelly blast to a vehicle, the common

site of burst fractures is mid-lumbar. This is unusual for spinal fractures which tend to

happen at C7-T1 and T12-L1. This difference may be due to rate of loading, posture, and

armor load on the Solider (12, 20).

6
Figure 3. Principal applied loading mechanisms that may lead to spinal injury (21). Reprinted

with permission from Springer Science + Business Media.

Trauma to the spine may result in vertebral fractures, degenerative disc disease, spinal

cord contusions, lesions of connecting ligaments, and other disabilities. Some common

disabilities include protrusions of cartilage of the intervertebral disc through the

vertebral body endplate into the adjacent vertebra (Schmol’s nodes); degenerative

osteoarthritis of joints between the spinal vertebrae and neural foraminae (spondylosis,

narrowing of space between vertebrae); and anterior displacement of vertebra in relation

to the vertebrae below (spondylolisthesis) (22). Among adults, the most common

injuries are vertebral column fractures and fracture dislocations (23).

Aside from visible injuries to the spinal cord, such as fractures and crushing, Soldiers can

also experience damage to the nerve roots or myelinated fiber tracts that are responsible

for carrying signals to and from the brain. Injuries to the neck (C1-C7) tend to be more

life-threatening since they may affect the phrenic nerve, a nerve originating from the

cervical spine that is responsible for the movement of the diaphragm (17). There is also

increasing evidence that the central nervous system may be damaged as a direct effect of

primary blast (24, 25). Systemic acute gas embolism, a result of pulmonary disruption

from the blast wave, may result in occluded blood vessels in the brain or spinal cord (24).

The spine is capable of withstanding large amounts of pressure (spinal injuries typically

do not develop below accelerations of 20–25 G) and the construction of the neural arch in

the vertebrae provides significant resistance to forward shear (26, 27). However, as the

lateral trunk velocity increases, the lateral shear forces increase proportionally and more

intensely than other spinal forces (27). Compression forces also increase as velocity

increases, and thus when the combination of lateral shear and compression forces are too

great for the vertebra to withstand, fractures may occur in the pedicle, lamina,

transverse, or spinous process; facet; or vertebral body (17). The severity of these

7
fractures will depend on the structure stability of the fracture, i.e., whether or not the

bony and ligamentous integrity is compromised such that free movement can occur.

Even with a stable fracture, the spine is still capable of carrying and distributing a

person’s weight. Unstable fractures involve an abnormal motion of the fracture site,

which could potentially impinge the spinal cord or its vascular supply, resulting in pain

or loss of neurological function. Neurologic deficit is present in 10–30% of all spinal

column injuries (23, 28). Typically, the degree of associated neurological injury is

correlated with the extent of the vertebral column fracture and any accompanying

dislocation or subluxation.

Axial compressive loads commonly cause compression, burst, or chance fractures. A

wedge compression fracture occurs when there is a combination of a flexion bending

moment and compressive loading, crushing the anterior aspect of the vertebra and

forming a wedge shape (figure 4). Three subtypes of wedge fractures can be defined

based on the height reductions in the anterior, middle, and posterior dimensions of the

vertebra (29). The anterior column includes the anterior longitudinal ligaments and

anterior one third of the vertebral body. The middle column consists of the posterior

longitudinal ligament and posterior two thirds of the vertebral body. The posterior

column is comprised of the facets, spinous processes, pedicles, and posterior

ligamentous complex (19, 30). In a grade 1 fracture, only the anterior column is crushed

(stable fracture). In a grade 2 fracture, the anterior column is crushed and the posterior

column ligaments fail (potentially unstable fracture). The loss of anterior vertebral body

height is typically <50%. Figures 4b and 4c, show a grade 1 and 2 fracture, respectively,

of the L3 vertebra. In a grade 3 fracture, all three columns fail, leading to an unstable

fracture. The loss of anterior vertebral body height is usually >50%. A lateral

radiograph of a grade 3 wedge fracture of the T7 vertebra can be seen in figure 4d.

8
(a) (b) (c) (d)

Figure 4. (a) Drawings show the grading of wedge vertebral fractures. The approximate degree of height reduction determines the assignment of grade to the fractured vertebra

(reproduced with permission of Mary Ann Liebert, Inc.). (b) Lateral radiograph of

lumbar spine shows a mild wedge fracture (grade 1) of L3 vertebra. (c) Lateral radiograph of lumbar spine shows moderate wedge fracture (grade 2) of L3 vertebra and

moderate crush fracture (grade 2) of L2 vertebra. (d) Lateral radiograph of thoracic

spine shows severe wedge fracture (grade 3) of T7 vertebra (31). Figures b through d

reprinted with permission from the American Journal of Roentgenology.

Burst fractures are typically associated with high energy trauma and are most commonly

found between T5 and T8 and the TLJ (29). However, as mentioned earlier, in current

military operations, for spinal injury cases involving underbelly blast to a vehicle, the

common site of burst fractures is mid-lumbar. They are characterized by the crushing of

the anterior and middle aspects of the vertebral body (figure 5). The state of the

posterior elements determines whether the fracture is stable or unstable. Displacement

of posterior elements and/or vertebral body or facet dislocation or subluxation define an

unstable burst fracture (29). Sagittal and axial computed tomography (CT) scans of the

thoracolumbar spine, seen in figures 5b and 5c, demonstrates an L4 burst fracture with

retropulsion of bone into the spinal cord. Displacement of bone fragments may lead to

life-threatening injuries if they penetrate into the spinal canal and cause loss of spinal

cord function (17). While burst fractures only account for 15% of spinal injuries, patients

with burst fractures can reach up to 50–60% neurological deficit from their pre-injured

state (19).

9
(a) (b) (c)

Figure 5. (a) Patterns of the retropulsed fragment. (b) Sagittal and (c) axial CT scans of the

thoracolumbar spine demonstrates an L4 burst fracture with retropulsion of bone into

the spinal canal (as shown by arrows) (32, 33). Reprinted with permission from the

American Journal of Roentgenology and Neurosurgical Focus.

While experimental studies have identified sites of failure initiation in burst loading

within the literature, there is a lack of consensus to which region fails first. Several

authors believe that the initial fracture occurs in the vertebral body, which leads to

expulsion of bone and fluid into the spinal canal. This results in reduced support of the

endplates, continuing their exposure to compression and eventually forcing them to

crack (34). Others report that an increase in pressure within the nucleus pulposus

causes the endplates to bulge and crack (19). Hongo et al. found high compressive and

tensile strains at the base of the pedicle of T10, L1, and L4, indicating that the base of the

pedicle is the site of burst fracture initiation (35).

Flexion-distraction thoracolumbar spine fractures, also known as Chance fractures,

commonly occur at the thoracolumbar junction and tend to be the result of violent

forward flexion (bending), which causes a distraction injury (pulling apart) to the

posterior elements of the vertebra. Chance fractures occur when the anterior portion of

the vertebral body is minimally compressed and there is a transverse fracture through

the posterior elements of the vertebra and posterior portion of the vertebral body (2).

Several subtypes of flexion-distraction thoracolumbar spine fractures exist, including a

classic Chance fracture, fulcrum fracture, and pure soft-tissue flexion-distraction injury

as seen in figures 6a, 6b, and 6c, respectively. The pathophysiology of each fracture

depends on the axis of flexion.

10
(a) (b) (c) (d)

Figure 6. Variations of Chance-type flexion-distraction spinal injuries include (a) classic Chance

fracture, (b) fulcrum fracture, and (c) pure soft-tissue flexion-distraction injury. (d)

Lateral radiograph shows a classic Chance fracture that extends horizontally through

the pedicle (right arrow) and into the vertebral body. There is an anterosuperior

wedge-shaped compression fracture (left arrow) in the same vertebral body (36).

Reprinted with permission granted from The Radiological Society of North America

and author.

2. Computational Spinal Injury Biomechanics

Biomechanical models of the human body have the aptitude to support advancements in

many fields including medicine, biology, and engineering. Over the past 60 years, a

substantial effort has been dedicated to modeling the human body. An assortment of

models that vary in fidelity have been developed and range from having one degree of

freedom to models with millions of degrees of freedom. The spine is a complex

component of the human skeleton, consisting of many intricate components with

diverse material properties. Modeling of the spine provides opportunities to gain more

understanding and a detailed description of temporal and spatial deformation

processes, including failure of the intervertebral discs and vertebrae.

In general, research groups started with relatively simple models of individual

components of the spine and eventually developed models that represented larger

sections of the spine and surrounding anatomy. Latham (1957) is considered the first to

have developed a mathematical model of the spine; focused on studying pilot ejection,

he used a one-degree-of-freedom model consisting of two masses, representing the body

and ejection seat, interconnected by a spring to represent the response of the spine to

vertical acceleration (37–40). In Payne’s (1961) subsequent model, the head and upper

11
torso were modeled as a rigid body and the spine was represented by a spring-dashpot

in a parallel system (38). Liu and Murray (1966) contributed to the modeling approach

by proposing a mathematical model that consisted of a uniform rod and a rigid

end-mass, representing the spinal column and head, respectively (41).

It wasn’t until the late 1960s that segmentation of vertebrae and intervertebral discs were

incorporated into models. Toth (1966) developed an eight-degree-of-freedom model in

which vertebrae were modeled as rigid masses interconnected by springs and dampers,

simulating the action of discs (42). A mathematical model developed by Orne and Liu

(1971) took into account the curvature of the spine as well as inertial properties of the

vertebral bodies and axial shear and bending stiffness were introduced (43). The

interaction between the spine and the torso, however, were not considered. Prasad and

King (1974) further developed this model to include the interactions of the articular

facets (44).

Up until this point, models did not take the rib cage or viscera into account. Belytschko

et al. (1976) developed the first three-dimensional representation of the entire spine and

several other models with increasing complexity (45). These finite element models

consisted of the head, vertebrae (lumbar, thoracic, and cervical), ribs from T1 to T10,

intervertebral discs, articular facets, ligaments, muscle, connective tissue, upper and

lower viscera, and the pelvis. Skeletal components were modeled as rigid masses,

intervertebral discs as beam elements, ligaments as spring elements, and articular facet

interactions as hydrodynamic elements (38, 40, 46).

Finite element modeling continues to be popular in spinal research. When constructing

a finite element model, three primary areas need to be addressed: geometric

representation including segmentation of spinal components; constitutive models and

corresponding material properties of the components; and boundary conditions used to

apply loading and constraints. More recently, model components are developed with

geometries that match that of a specific in vitro specimen or that represent an average

vertebra. It is important to define the geometry of the structure as accurately as possible

because it greatly influences deformation (47–49). Generic models are developed from

anatomical measurements while specific geometries can be formed from CT and

magnetic resonance imaging (MRI) scans. Software packages convert data obtained

from these images into a format that can be interpreted by solid modeling software and

then input into finite element software. Wilcox et al. (2007) found that finite element

results demonstrated a greater agreement with previous experimental results when the

12
models were morphologically accurate as opposed to generic models (47). It should be

noted, however, that the accuracy of image-based models is affected by the original

resolution of the medical image (50).

Constitutive models and their parameters are also a critical aspect of developing a finite

element model. Determining the properties of hard and soft tissues, and fluids, as well

as discovering their complex interactions and changes over time, are a new set of

challenges currently facing researchers. To date, a wide range of material values have

been used in finite element models of the spine due to the large assortment of

measurement techniques, testing strain rates, and sample preparation (table 1). The

verification of mesh and boundary conditions and the sensitivity of results to material

properties, however, has been limited (47) .

13
Table 1. Compilation of various constitutive models and parameters found in recent computational models of the spine.1

Anatomic Component Material

Model

Material Properties References

Vertebra

Trabecular

bone

Plastic with

kinematic

yield,

Poroelastic

E = 0.1-2.2 GPa

v = 0.2

σY = 42-110 MPa

(34, 51–56)

Cortical

bone

Plastic with

kinematic

yield,

Elastic

E = 5-22 GPa

v = 0.3

σY = 132 MPa

(34, 52–55)

Posterior

elements

Elastic E = 1000-3500 MPa

v = 0.25

(52–55, 57)

Cartilaginous

endplates

Poroelastic E = 20-25 MPa

v = 0.1-0.4

(34, 53, 54)

Facet

cartilage

Elastic E = 11 MPa

v = 0.4

(53)

Intervertebral disc Nucleus

pulposus

Poroelastic,

Hyperelastic

K = 1.667 GPa

E = 0.15-4 MPa

v = 0.4999

(34, 52–55, 57, 58)

Annulus

fibrosis

Orthotropic

elastic,

Hyperelastic,

Poroelastic

E = 2-450 MPa

v = 0.3-0.45

(51, 53–55, 58, 59)

Ligaments

Anterior

longitudinal

ligament

Hyperelastic σY = 22.5 MPa

εY = 0.2

E = 7.8-20 MPa

v = 0.3

(54, 60, 61)

Posterior

longitudinal

ligament

Piecewise

linear,

Hyperelastic

σY = 16-20 MPa

εY = 0.3-0.45

E = 10-20 MPa

v = 0.3

(34, 52, 54, 60, 61)

Supraspinous

ligament

Hyperelastic,

Nonlinear

elastic

E = 3.4-15 MPa

v = 0.3

(54, 55, 61)

Spinal cord Elastic E = 0.26-1.3 MPa

v = 0.35-0.49

(34, 62)

Dura mater Anisotropic

elastic

Err = Eθθ = 142 MPa

Ezz = 0.7 MPa

(34)

1Not all parameters are listed for each constitutive model. Furthermore, not all spinal components are

listed. E is the Young’s Modulus, ν is Poisson’s ratio, σY is the yield strength, Y is the yield strain, and

K is the bulk modulus. The symbols rr, θθ, and zz denote directions in the polar coordinate system.

14
2.1 Models of the Vertebra

The vertebral body have several features that should be considered in the development

of its simulation. The vertebral body is comprised mainly of porous cancellous bone,

with denser cortical bone at the periphery (11). Several groups have shown that varying

material properties of the cancellous and cortical bone that make up the vertebral body,

as well as changes to the material properties of the cartilaginous endplates, do not result

in a significant change in biomechanical response (11, 51). However, these studies did

not consider high-rate failure where fracture may be sensitive to inhomogeneous

material properties. Thus, it may be important to consider in the future. Another

important feature of vertebrae are their complex posterior geometry, which presents a

challenge when meshing that area. Some researchers have simplified the geometry by

developing models that exclude posterior elements and focus solely on the vertebral

body (47, 58, 63–66).

Computational models of isolated single vertebrae allow researchers to investigate the

natural properties of the vertebra, without having to take into consideration soft tissue

or ligament interactions. The principal clinical application for detailed modeling of a

single vertebra is to provide insight into the loading regime within the spine. Current

models are able to accurately predict compressive strength and are typically validated

through direct validation by comparing model predictions with stiffness and strength

values measured in vitro (see the appendix for a review on computational model

verification, sensitivity and validation) (54). Single vertebrae models have also been

developed to study the effects of metastatically compromised vertebral segments (58, 67)

as well as simulate the presence of bone cement after a vertebroplasty procedure

(65, 66, 68, 69).

In the future, researchers would like to use these finite element models to predict

fracture risk in vivo (54). The ability to non-invasively assess vertebral strength is

critical for the diagnosis and management of osteoporosis. The current clinical standard

to predict vertebral strength is to perform a bone mineral density (BMD) assessment

through the use of dual energy x-ray absorptiometry (DXA) (70). Finite element models

derived from quantitative computed tomography (QCT) scans, however, have been

shown to better predict the vertebral bone strength than BMD techniques due to their

ability to assess geometry and include heterogeneous mechanical properties of the bone

(70–72). Several groups have loaded vertebral specimens at strain rates up to 0.5% until

failure and then analyzed finite element models under matching conditions. The

15
models were able to predict yield loads, strain values, and stiffness values, which can be

used to predict fracture sites. Model predictions were found to correlate with

experimentally measured values and fracture sites (71–74).

2.2 Models of the Intervertebral Disc

Similar to vertebral simulations, one major reason for developing finite element models

of the disc is to study the diseased state. Unlike vertebral modeling, which tends to

focus on predicting fracture risk, intervertebral disc research has focused on

understanding the process of degeneration and its biomechanical effects on the tissue

(54). Some research groups have also investigated treatments for degenerative disc

disease including replacement materials for the nucleus pulposus (75) and total disc

replacement implants (76).

Generally the geometry of intervertebral disc finite element meshes are simplified.

Many researchers, for instance, assume the structure to be axisymmetric (11, 75, 77–81)

or exhibit symmetry in the sagittal (80) or transverse planes (77). In addition, cranial

and caudal surfaces of the disc are often assumed to have a flat surface although some

groups are incorporating more realistic curvatures into their models (81). Recently,

increasingly complexity has been incorporated into material models of the intervertebral

disc tissue, including ways to represent fluid content and flow, osmotic forces, and

anisotropy (77, 78).

Validation of intervertebral disc model predictions often presents as a challenge due to

the difficulties in taking in vivo measurements and preserving a realistic tissue

environment in vitro. Single studies are often used for indirect validation, however,

there tend to be large standard deviations in experimental data. It is often the case that

reasonable agreement can be found but not quantified (54).

2.3 Segment Models

The motion segment, or functional spinal unit, is comprised of two adjacent vertebra, the

interconnecting intervertebral disc, facet joint, and associated spinal ligaments. Since

the spine may be considered a structure composed of several motion segments

connected in series, motion segments are often used to study the biomechanical behavior

of the spine. The functional spinal unit, along with larger spinal segments, can be used

to simulate different spinal conditions and assist in the design and analysis of new

spinal instrumentation, including pedicle screws, Harrington rods, and interbody cages.

16
In addition to modeling the vertebral and disc components, these models incorporate

the facet joints and spinal ligaments and therefore present additional challenges beyond

those seen in the previous two sections due to the limited experimental data available

for characterization and the need to incorporate contact.

Due to limited experimental data on the behavior of the facet joint, researchers have

developed a number of approaches to model facet interactions. Some groups have

incorporated material properties through the use of gap elements that adjust the force

transferred across the joint based on the gap size (55, 82), while others included and

assigned properties to a cartilage layer (53). The articular facets surfaces are generally

assumed to be frictionless (53, 57, 83) or a low coefficient of friction has been applied

(84). In general, researchers have depended on indirect validation to provide evidence

of their model accuracy. A few authors, however, have directly compared their model’s

results with tests on cadaveric specimens (51, 52, 55, 59, 85). All these studies, however,

compare a generic model with experiments as opposed to a direct subject-specific

segment model validation (54).

Advanced models are now beginning to incorporate poroelastic characteristics to

simulate the fluid flow between the intervertebral disc and cancellous core. This

complex interaction is believed to play a major role in absorbing impact energy and may

be partially responsible for a perceived rate-dependency of spinal component response.

In a poroelastic model, the disc is modeled as having two distinct phases: a fluid phase

and a permeable solid phase. Simon and Wu were among the first to include poroelastic

behavior in a finite element segment model (86). From short- and long-term creep

analyses, they found that failure is likely to be initiated in the endplates or in the

cancellous bone adjacent to the endplate. Wu and Chen created a similar model that

incorporated posterior elements and found that under long-term creep loading their

model demonstrated similar results as Simon and Wu (87). A poroelastic finite element

model of the L3-L4 segment developed by Lee et al. (described in section 2.5) also

supported Simon and Wu’s results (88). In 2007, Natarajan et al. developed a poroelastic

model that incorporated physiological parameters, such as the change in permeability in

the disc due to strain, in order to predict the failure initiation and progression in a

lumbar disc due to cyclic loads. The model accurately predicted change in disc height

during loading and unloading that was comparable to in vivo experiments (86).

Many of the finite element models of the spine often assume a simplified geometry due

to the complex nature of the vertebra and intervertebral disc. Facet joints and spinal

17
ligaments may also be disregarded even though these structures have an important

influence on motion segment behavior (67). In addition, trunk muscles are often not

included in finite element models even though they are known to be primary stabilizers

in the spine (19). Muscle forces have a strong influence on spinal load and stresses in

the intervertebral discs and, in their absence, the applied stress distribution in the discs

differs greatly (85). This elimination and simplification of geometry may influence

which area will fail first under dynamic loading, altering the mechanism of failure. It is

therefore essential that future efforts include the complex geometry of the vertebra and

intervertebral discs, as well as the ligaments and muscles.

2.4 System Models

System level models of the spine include lumbar, thoracic, and cervical spine sections, as

well as coupling to other body regions that have an influence on the loads transmitted to

the spine, such as the torso. Developing a high-resolution finite element model of the

entire human spine and its connected anatomy is computationally expensive and is

difficult to validate. In the past, full models of the spine were referred to as simple

models because they lacked a high degree of anatomic fidelity– many use just a few

(usually one or three) elements to represent each motion segment. Many of these efforts

were reviewed in the beginning of section 2. Now, with the advances in high

performance computing, it is becoming easier to incorporate more accurate geometry

and improved material constitutive models. However, from the published literature, it

seems that there are limited high-resolution full spine models that capture the effects of

high strain rate loading regimes. Nevertheless, there are a few research groups making

significant progress achieving this goal, for example the Southwest Research Institute

(89) and the Spine Research Center at Walter Reed Medical Center (20).

2.5 Failure Models

An adequate comprehension of fracture mechanisms is essential for effective prevention,

mitigation and treatment. Predicting vertebral fractures, however, continues to be a

challenge due to the complex and elaborate geometry of the vertebra and the different

material properties of the vertebral components. While a number of researchers have

studied the instability, spinal canal impingement, and treatment methods of vertebral

fractures produced by spinal trauma, there is still a lack of knowledge on the internal

transient change of the vertebral bodies during fracture (19). Lee et al. used a

three-dimensional, poroelastic finite element model of the L3-L4 segment to predict

18
changes in biomechanical parameters such as dynamic stiffness, intradiscal pressure,

stress in the endplates, and the shock-absorbing mechanism of the spine under different

impact durations and loading rates (88). Additionally, the authors analyzed the relation

between the loading rate and the potential of vertebral body fracture. It was found that

short-duration loading has a strong effect of initiating fractures in the endplates or the

posterior wall of the cortical shell. The authors also concluded that pressure in the

nucleus is independent of the impact duration and depends on the magnitude of the

impact force.

To date, very little research has been performed to analyze the mechanism of fracture,

especially on a predictive basis. Qiu et al. developed a finite element model of the

thoracolumbar junction and subjected it to dynamic vertical impacts in order to

investigate the vertebral burst fracture process (19). The authors found that an increase

in pressure inside the nucleus forces each endplate to bulge towards the cancellous core

of the vertebral body. When the endplates fail, the nucleus material is able to enter the

vertebral body, pressurizing it more. This increase in pressure squeezes the contents of

the vertebral body, including fat and marrow, out of the cancellous bone. When the

nucleus material enters the vertebral body faster than the rate at which fat and marrow

are being expulsed, a burst fracture is said to occur. Fracture sites predicted in this

study were consistent with other studies as well as identical to the medical definition of

burst fractures (19). Teo et al., developed a finite element model of the human atlas (C1)

and were also able to accurately predict failure sites in comparison to experimental

results (90).

In 2009, El-Rich et al. developed a finite element model of the L2-L3 spinal segment that

analyzed the response of the bony structures and soft tissues to five degrees of sagittal

rotation at different rates until fracture occurred. The model allowed for a detailed

evaluation of failure occurrence and propagation over the bone. Results showed that

the endplate, pedicle, and facet surface were the weakest regions when subjected to

rapid movement in the sagittal plane and spinal injuries resulted from a sagittal

rotational velocity exceeding 0.5◦/ms (56). Segments subjected to the highest velocity

resulted in a more severely damaged structural response compared to those subjected to

the low and intermediate velocities, confirming that rapid movements increase the risk

of injury (91). Under the highest velocity the model exhibited a considerable increase in

intradiscal pressure in the nucleus and the stresses over the rest of the structures while

there was only slight changes under lower and intermediate loading rates.

19
The spinal cord may be injured through various injury patterns; however, the

relationship between spinal column injury pattern and spinal cord damage is not well

understood. Greaves et al. developed a finite element model of the cervical spine and

spinal cord in order to compare spinal cord distributions between three different injury

mechanisms (62). Their model predictions showed that strain that induces distraction

injuries were uniformly distributed lengthwise throughout the spinal cord, while

dislocation injuries and contusion injuries (such as a burst fracture) led to focal strains.

A biomechanical description of the injury process can help predict subsequent acute and

chronic pathophysiology of spinal cord trauma. Li et al. developed a finite element

model of the cervical spinal cord to simulate the complex injury mechanism of a

hyperextension injury (92). The results of their hyperextension injury simulation

showed high localized stress at the anterior and posterior horn in the gray matter of the

spinal cord. It is believed that these stresses account for the predominance of hand

weakness in patients with central cord injury (92).

2.6 Uncertainty Quantification

Probabilistic analysis methods provide a tool in which the biomechanical response due

to characteristic uncertainties and variations in biological structures can be studied. The

uncertainty of these values lead to an associated degree of uncertainty in the results (93).

In order to improve the precision of computer models, probabilistic models, in which

uncertainties and natural variations are incorporated into the model, have been

developed. The fundamental concept of this method is that the input parameters are

defined by an appropriate statistical distribution, not a single value (93, 94). A Normal

or Gaussian distribution is commonly used in probabilistic models and defines the input

variables by a mean and standard deviation. The values of each input parameter are

sampled at random from the distribution and used in the model. The model can then be

solved multiple times, allowing researchers to develop an indication of the range of the

results that can be found.

To date, this methodology has been used to study the influence of variations in material

properties and geometry on spinal behavior (95–97). In 2005, the U.S. Naval

Bio-dynamics Laboratory/U.S. Naval Air Warfare Center Aircraft Division used

NESSUS, a computer software system that combines finite element methods with

advanced reliability methods in order to model uncertainties in geometries, material

properties, and other variables, to evaluate the risk of cervical spine injury from

20
maneuvers experienced during flight, high speed ejection, and crashes (97). The group

incorporated mechanical and geometric data in order to develop, verify, and validate a

parameterized probabilistic spinal injury prediction model. In order to simulate

heterogeneous and nonlinear materials the group defined the mechanical characteristics

of vertebrae, discs, ligaments and muscles through data collected from QCT, bone

mineral density data, and cryomicrotomy (98).

In addition, probabilistic models have been developed to study the impact spinal

procedures, such as vertebroplasty and the implantation of spinal stabilization devices

including artificial discs and pedicle screws, have on spinal functions (94, 99, 100).

Progress in probabilistic biomechanics will depend upon the identification of injury

modes, data collection, and the development of validated models (39). Additional

research is necessary to integrate random loading schemes and random representations

of geometric variations. As Thacker et al. (101) point out, uncertainty and error

quantification play a key role in model verification and validation. Uncertainties

associated with the model input parameters include material behavior, geometry, loads,

initial conditions, and boundary conditions. Ideally, each input parameter would be

varied according to statistically significant data obtained from experiments.

3. Conclusion and Recommendations

Developing an understanding of the high rate injury biomechanics associated with

blast-induced loading to the spine, lower extremities, central nervous system, and

peripheral nervous system is critical to optimize protective equipment for Soldiers.

Finite element analysis is an essential part of understanding the biomechanics of spinal

injury. These models provide a wealth of information that otherwise may not be

available. While the research area of computational spinal injury biomechanics has

received much attention in the past with regard to low strain rate degenerative effects,

there are significant opportunities to enhance the state of knowledge of spinal injury in

the area of high strain rate military loading. Through this literature review and careful

contemplation, a list of six recommendations for future research directions has been

developed. Future research concerning the finite element model of the spine should

focus on the following aspects:

21
• Develop high-resolution anatomic finite element models that capture the

geometric complexity of the spine in a probabilistic manner. Models should be

three-dimensional and include all anatomic components of the spine necessary to

capture the physics of interest, namely, injury mechanisms such as fracture and

ligament rupture. Models should be constructed directly from high-resolution

medical data such as x-rays, CT scans and MRI that enable individual-to-individual

variations of the geometric representation. Finite element studies should use a

probabilistic approach to include the variation of geometry ranges that are typical

during postural changes, movement, gravity, aging, and extrinsic loading.

• Develop a multilevel approach to apply loading conditions to the spine.

Currently the direct loads, their distributions, and strain rate that the spine

experiences during a military underbelly blast event is unknown. There is detailed

understanding about the explosion and the loading to the vehicle, as well as the

spinal injury outcome observed from the field; however, little is known about the

processes in between these endpoints. It is critical to understand the process of

load transfer, injury initiation, and propagation. In addition to the complexity of

considering the spine itself, it is suspected that the lower extremity reactions to

underbelly blast and spinal injuries are coupled and cannot be considered isolated

systems. Also, as discussed in section 2.4, a coupling between the spine and the

torso exists. Thus, the coupled systems direct the research to face the challenging

task of considering a wide range of length and times scales. While on one hand

research must consider the large length scale (on the order of meters) for coupled

systems that include the lower extremities, spine, and torso, we must also consider

the smaller length scales (on the order of micrometers), such as the randomly

organized collagen fibers and radially organized elastin fibers found in the nucleus

pulposus, to understand the injury mechanisms. The military spinal injury

research community would benefit from a set of high strain rate military loading

paradigms for components (ligaments, processes), subassemblies (isolated

vertebral bodies and intervertebral discs), assemblies (motion segments consisting

of vertebral bodies, interconnecting ligaments, and intervertebral discs), and

system level (whole spine) models. Loading paradigms should include rate,

direction, and duration. Once again, finite element studies should use a

probabilistic approach to include the variation of loading that are typical.

22
• Develop, implement, and validate constitutive models for individual spinal

component materials at the appropriate strain rate conditions. As table 1

demonstrates, an abundance of literature sources describe a wide range of material

properties of spinal structures. This variation in material property values has

resulted in a substantial deviation of model predictions and results. Furthermore,

results currently obtained from finite element models are often limited by the

assumption of homogeneous, isotropic, and linear elastic material properties.

While these assumptions simplify the analysis, they do not capture the realistic

mechanical behavior of the spine (19, 84, 85, 92). Ultimately, models need to

incorporate the anisotropic, nonlinear, heterogeneous, and porous material

properties seen in the human spine. For example, we believe that a poroelastic

model is essential to characterize changes of the annulus matrix from a solid to

fluid phase during high-rate loading conditions. Recently, it has been shown that

standard high strain rate material characterization techniques are not adequate for

bones or soft tissues (102, 103). Additionally, standard gripping techniques for

dynamic tension tests do not work for biological materials, and material

inhomogeneity and anisotropy complicate the interpretation of measured stress

and strain data. New dynamic test methods and data analysis techniques are

needed to provide applicable high rate and failure data on spinal materials for

constitutive model development and calibration.

• Hierarchical verifications and validation. Computational models and results

should be compared at multiple length scales. Thacker et al. (101) provide a useful

hierarchical verification and validation scheme that decomposes the spine into

components (ligaments, processes), subassemblies (isolated vertebral bodies and

intervertebral discs), assemblies (motion segments consisting of vertebral bodies,

interconnecting ligaments and intervertebral discs), and system level (whole spine)

models. The process should start at smaller length scales such as the components

and progress to the last stage of system level models. This approach requires

simulations and experiments to be conducted at each level.

• Use novel computational approaches for capturing high strain rate compressive

failure. There are limited computational approaches to capture injury

mechanisms associated with accelerative loading to the human spine. Current

U.S. Army Research Laboratory (ARL) efforts are focused on using dynamic

insertion of rate-independent cohesive elements to capture fracture mechanisms.

The limitations of this approach are quickly being realized due to the large

23
fragmentation, finite element mesh dependency, and material interface

compatibility experienced during high rate accelerative loading. In addition,

computational approaches to model muscle rupture, tearing, and other failure

mechanisms are neither common nor validated within the tools used today. One

may think of cohesive elements as a traditional approach to modeling failure in the

computational setting. However, given the large deformations that biological

materials exhibit during accelerative loading and the complexity of the anatomic

geometry, cohesive approaches will only work within a limited regime of

deformation. Therefore, novel simulation capabilities should be pursued. The

Material Point Method (MPM) and the Extended Finite Element Method (XFEM)

are two methods that seem feasible.

• Integrate functional outcome predictions coupled with mechanical damage. It is

also important that computational models extend past mechanical descriptions to

include functional measures. A multidisciplinary approach combining

mechanics-based simulation and modeling with the clinical field to develop

computational approaches for modeling structural and functional deficits that may

arise from high strain rate spinal injuries is needed. The community should

develop time-evolving predictive models to understand musculoskeletal stability,

pain, and rehabilitation strategies.

At this time, the focus of numerous research groups is to develop a three-dimensional

model under a full range of loading schemes, while simultaneously considering

nonlinear material and geometry solutions. Current and past models are limited by

their selection of material models and simplified geometries that are unrealistic in

comparison to the human spine. With a full understanding of spinal injury

mechanisms, design criteria based on human injury, such as vertebral body fracture

tolerances, can be developed and implemented in order to develop spinal injury

mitigation strategies for the warfighter.

24
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34
Appendix A. Verification, Sensitivity and Validation

Models must establish credibility before clinicians and scientists can use the simulations

to extrapolate information and make decisions from information and results produced

by the model. Specifically, an analyst must (1) assess the numerical accuracy of the

underlying mathematical equations in the computation model, (2) evaluate the

sensitivity of the model results to the input parameters, and (3) validate that the model

results correspond to results of a real-world scenario (54, 104). Models are often

validated through one of two methods: direct or indirect validation. Direct validation

involves a comparison between a model’s prediction and an experimental test result.

Indirect validation compares model results to a physical case where it is not possible to

determine if conditions are the same. This includes comparisons between data from the

literature, clinical trial results, and historical medical data (54).

Since the first spinal finite element models were developed, significant advances have

been made. Through adequate considerations of model sensitivity and validation,

researchers have been able to develop more accurate and efficient simulations.

Generating a precise model that incorporates verification, analysis sensitivity, and

validation is a difficult task, especially for the complex spinal structure. However by

doing so, the gaps between clinical medicine, experimental biology, and computational

biomechanics will decrease.

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