Biomechanics of the cervical spine Part 2. Cervical spine soft tissue responses and biomechanical.pdf

Clinical Biomechanics 16 (2001) 1±27

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Review paper

Biomechanics of the cervical spine Part 2. Cervical spine soft tissue

responses and biomechanical modeling

Narayan Yoganandan a,b, * , Srirangam Kumaresan a,b , Frank A. Pintar a,b

Biomedical Engineering, Department of Neurosurgery, Medical College of Wisconsin, 9200 West Wisconsin Avenue, Milwaukee, WI 53226, USA

Department of Veterans Aairs Medical Center, Milwaukee, WI, USA

Received 7 February 2000; accepted 21 September 2000

Abstract

Objective. The responses and contributions of the soft tissue structures of the human neck are described with a focus on

mathematical modeling. Spinal ligaments, intervertebral discs, zygapophysial joints, and uncovertebral joints of the cervical spine

are included. Finite element modeling approaches have been emphasized. Representative data relevant to the development and

execution of the model are discussed. A brief description is given on the functional mechanical role of the soft tissue components.

Geometrical characteristics such as length and cross-sectional areas, and material properties such as force±displacement and stress±

strain responses, are described for all components. Modeling approaches are discussed for each soft tissue structure. The ®nal

discussion emphasizes the normal and abnormal (e.g., degenerative joint disease, iatrogenic alteration, trauma) behaviors of the

cervical spine with a focus on all these soft tissue responses. A brief description is provided on the modeling of the developmental

biomechanics of the pediatric spine with a focus on soft tissues.

Relevance

Experimentally validated models based on accurate geometry, material property, boundary, and loading conditions are useful to

delineate the clinical biomechanics of the spine. Both external and internal responses of the various spinal components, a data set

not obtainable directly from experiments, can be determined using computational models. Since soft tissues control the complex

structural response, an accurate simulation of their anatomic, functional, and biomechanical characteristics is necessary to un-

derstand the behavior of the cervical spine under normal and abnormal conditions such as facetectomy, discectomy, laminectomy,

and fusion. Ó 2001 Published by Elsevier Science Ltd.

Keywords: Finite element modelling; Pediatric spine; Validation; Injury

1. Introduction

connection is interrupted where the anulus is disrupted

by transverse clefts that traditionally, but mistakenly,

have been regarded as forming uncovertebral joints [2].

These soft tissues render the cervical spine compliant in

that they allow for movement between the cervical ver-

tebrae. However, they are also responsible for limiting

the range of many movements under normal conditions.

In the face of external (e.g., traumatic) loading, they are

critical to maintaining the integrity of the cervical spine

[1,3±7].

While sharing the general functions of enabling and

limiting movement, the soft tissues of the cervical spine

dier in structure and contribute dierently to these

functions. Ligaments consist of various amounts of

collagen and elastin, arranged in essentially a uniaxial

manner so as to resist tension. In contrast, the inter-

vertebral discs consist of a proteoglycan nucleus de-

signed to sustain compression loads, surrounded by a

The osseous elements of the cervical vertebral column

are connected by a variety of structures that collectively

are known as the soft tissues of the cervical spine [1].

Ligaments of various types connect the vertebral bodies

and the posterior elements of the cervical vertebrae, and

span one or more segments, depending on the type of

ligament and vertebral level. Fibrous capsules connect

the articular processes of the synovial joints of the neck.

At each segmental level, the anulus ®brosus of the in-

tervertebral discs binds the adjacent vertebral bodies.

Posteriorly, in the region of the uncinate processes, the

Corresponding author.

E-mail address: yoga@mcw.edu (N. Yoganandan).

0268-0033/01/$ - see front matter Ó 2001 Published by Elsevier Science Ltd.

PII: S 0 2 6 8 - 0 0 3 3 ( 0 0 ) 0 0 074-7

N. Yoganandan et al. / Clinical Biomechanics 16 (2001) 1±27

collagenous anulus ®brosus designed to resist tension,

shear, and torsion [7±10].

The role of soft tissues in the biomechanics of the

human cervical column can be assessed by investigating

the external and internal responses of the spine. External

responses can be de®ned as measurable parameters of

the spinal structure (segment or column) under an ex-

ternally applied load. For example, sagittal rotation

under ¯exion-moment loading, i.e., moment-rotation

curve is an external response. Similarly, compressive

displacement under axial loading, i.e., force±deforma-

tion curve is an external response. These types of re-

sponses can be directly measured using experimental

models such as a human cadaver spine segment [11±14]

or spinal column [15,16]. In contrast, internal responses

can be de®ned as the intrinsic parameter(s) of the spinal

structure under externally applied load(s). For example,

tensile stress in the intervertebral anulus ®bers due to

compressive loading is an internal response. Not only by

de®nition but also because of the complex nature of

spinal architecture, internal responses are not direct

measurable quantities in an experiment.

Laboratory-driven experimental studies can delineate

the external responses of the spine by studying isolated

components (ligaments, etc.), segmented units (motion

segments for disc evaluation, etc.) entire ligamentous

cervical columns (evaluation of eects of spinal levels,

injury, etc.), intact head±neck complexes (which includes

passive musculature), and intact (whole body) human

cadavers [13±27]. However, these studies are primarily

limited in the sense that internal responses such as load

sharing by the disc, and stresses and strains in the soft

tissues cannot be determined. Mathematical analogues

such as ®nite element models provide a unique oppor-

tunity to not only determine the external responses

(verify/validate with experimental data), but they can

also determine a number of internal responses (stresses,

strains, strain energy density, etc.) [28±33]. Thus, ®nite

element models serve as an adjunct to experimental

models (external responses) and also complement ex-

periments to determine internal responses. Furthermore,

because of absolute repeatability and reproducibility,

parametric studies are possible using ®nite element

models.

Regardless of the type of response, internal or ex-

ternal, both the soft tissue and bony components con-

tribute to spine biomechanical behavior. However,

because of the signi®cant dierences in the mechanical

properties of the soft tissues compared to the bony ele-

ments (hard tissues), the roles contributed by the various

soft tissue structures (e.g., ligaments, discs, facet and

uncovertebral joints) are dierent. Studies have clearly

demonstrated that soft tissues govern the biomechanical

responses of the cervical spine under external loading

[34]. Therefore, it is important to delineate the charac-

teristics and responses of the soft tissues of the spine.

With the above background, this review focuses on

soft tissue structural responses with an emphasis on ®-

nite element mathematical models. The soft tissue

structures included are the ligaments, intervertebral

discs, zygapophysial joints, and uncovertebral joints.

Speci®cally, each type of soft issue structure is discussed

in terms of the following:

· its individual functional mechanical role,

· geometrical characteristics,

· material property, and

· modeling procedures.

Subsequent to these discussions, in a separate section,

the eects of these individual soft tissue responses on the

normal and abnormal (due to degenerative disorder,

trauma, or iatrogenic alteration) behaviors of the cer-

vical spine are discussed from a modeling perspective

using representative ®nite element models. At the outset,

it should be emphasized that signi®cant dierences exist

in the anatomy and function, and mechanisms of load

transfer and injury between the well-studied lumbar

spine and relatively less-researched cervical spine. This is

particularly true from a mathematical modeling per-

spective. Because of characteristic dierences, a direct

comparison/extrapolation from the low back to the neck

should not be made.

2. Ligaments

2.1. Role

As stated earlier, ligaments are uniaxial structures

that resist only tensile or distractive forces [7]. How-

ever, some ligaments are capable of resisting tensile

forces in a range of directions because of their orien-

tation. Since more than one type of ligament span ad-

jacent vertebrae, their response is dependent on the

nature of the external load vector. The anterior longi-

tudinal ligament is most eective under an extension

bending moment [35]. Interspinous ligaments are ef-

fective under a ¯exion moment. Depending on the se-

verity, i.e., magnitude and application of the load

vector, internal forces resisted by the various ligaments

dier. Ligaments such as the posterior longitudinal

ligament, which lie close to the center of rotation, re-

spond with less force resistance than the anterior lon-

gitudinal ligament or the interspinous ligament.

Ligaments are most eective when distracted along the

direction of the ®bers [35]. Thus, although ligaments

are uniaxial mechanically, because of their complex

anatomy, they respond under varying nature of exter-

nal loads. Their internal response (strain or stress)

secondary to loading is dependent on the mechanical

properties of the particular ligament which, in turn, is a

function of the constituents. Since elastin contributes to

a more mechanical elastic behavior than collagen, lig-

N. Yoganandan et al. / Clinical Biomechanics 16 (2001) 1±27

aments with a higher proportion of elastin are more

elastic (e.g., ligamentum ¯avum) [36,37].

adopt an approach parallel to and consistent with the

mathematical model. For example, the anterior and

posterior longitudinal ligaments, because of their con-

tinuous nature in the human spinal column (traverse

from upper cervical spine to sacrum), should be treated

to span from mid-height of caudal vertebral body to

mid-height of adjacent cephalad body at the speci®c

vertebral level. This allows for a ``continuous'' ligament

when longer column models are constructed. Re-

searchers have identi®ed this ligament to span the two

neighboring endplates for determining length-related

mechanical properties [40]. While this is acceptable from

an experimental standpoint, use of this de®nition poses

diculties in a mathematical model as the portion of the

ligament superior to the cephalad endplate and inferior

to the caudal endplate cannot be simulated. Thus, cau-

tion is needed to de®ne ligaments based on experiments

which provide such information.

Ligament length and area de®nitions useful in

mathematical modeling studies are as follows. As stated

above, for length purposes, the longitudinal ligaments

span the mid-height of adjacent vertebrae; ligamentum

¯avum and interspinous ligaments span the superior and

inferior points of attachment of the two vertebrae; and

joint capsules span from the superior tip of the caudal

facet articulation to the inferior tip of the cephalad facet

articulation [37]. For cross-sectional area purposes,

maximum areas generally occur at mid-capsule height

for joint capsules; locations midway between the adja-

cent spinous processes for interspinous ligaments; and

mid-disc height for the two longitudinal ligaments [44].

Table 1 provides geometrical data, i.e., length and cross-

sectional area of major cervical ligaments.

2.2. Geometrical characteristics

In order to investigate the role of spinal ligaments

and to model cervical spine behavior, it is important to

quantify their geometry (origin and insertion/length and

cross-sectional area) and material properties (stiness,

force±de¯ection, stress±strain). Radiographs can be

used as an initial tool, although accuracy cannot be

assured due to the integrated (e.g., one lateral view) and

inferential nature of the imaging process. Computed

tomography (CT) permits a higher level of geometrical

measurement due to multiplanar (sagittal, axial) and

multisectional (in a given plane) imaging ¯exibility.

However, this method is also inferential with respect to

soft tissue de®nitions [38]. Magnetic resonance imaging

(MRI) is not routinely performed in a laboratory envi-

ronment due to cost considerations. Furthermore, im-

ages with this technique for frozen human cadaver

specimens is not a preferred methodology. Resolution of

X-ray, CT, and MRI is also a factor for determining the

geometry, i.e., length and cross-sectional areas of the

ligaments.

Researchers have attempted to measure ligament ge-

ometry during gross dissection procedures [39]. How-

ever, signi®cant diculties are often encountered due to

the presence of intervening tissues and body ¯uids.

Other methods to obtain the geometry of anterior and

posterior longitudinal ligaments of the mid-lower cer-

vical spine have included the use of electromagnetic

digitizer and laser micrometers [40], and micro dissec-

tion approach [41]. However, the ecacy of these sys-

tems has not been demonstrated to obtain data for

upper cervical and internal ligaments. Cryomicrotomy

techniques have been used to quantify ligament geom-

etry [17,42]. Although this technique is destructive, it has

been found to be superior because of its ability to obtain

sequential images in a predetermined plane at very close

intervals (of the order of a few microns, 1 mm 1000 lm),

thus describing the three-dimensional geometry. Cryo-

microtomy techniques allow the specimen to be frozen

in an undeformed, speci®c anatomic state (e.g., neutral

alignment), thus preserving the in situ features of the

spinal column. Because no dissection is done and the

tissues can be frozen in their natural state, the anatomic

integrity of the various hard and soft tissue structures

and their relative position are not compromised [43].

Dierences between the various structures are more

clearly perceptible since extravasation does not occur

immediately postmortem. Furthermore, the three-di-

mensional geometry of internal ligaments (ligamentum

¯avum) can be accurately obtained using this technique.

With regard to the de®nition of the speci®c ligament

for measuring geometry (e.g., length), it is necessary to

2.3. Material properties

From a mathematical modeling viewpoint, funda-

mental properties such as stiness (structural property)

or elastic modulus, a function of stress and strain (me-

chanical property), are generally required. These prop-

erties are obtained by subjecting the ligament under

consideration to tensile loading. Experiments conducted

with human cadaver cervical spine structures include

isolated ligament tests and in situ bone±ligament±bone

preparations [36,37,44,45]. Removal of the ligament

from the spinal column for testing often results in

damage to the structure and induces ®xation failures

[35]. In situ preparations have the unique advantage that

the ligament under test is not isolated from its sur-

roundings. In general, to perform these tests at a speci®c

vertebral level, all soft tissues are transected carefully

leaving the ligament under test to be the only structure

to resist the externally applied uniaxial tension. Ana-

tomical features are given importance during transection

procedures. For example, the anterior longitudinal lig-

ament is prepared by dierentiating its ®bers from the

N. Yoganandan et al. / Clinical Biomechanics 16 (2001) 1±27

Table 1

Length and cross-sectional area of cervical spine ligaments (Mean

(SD)) [37] a

loads [36]. These studies indicate the rate-dependent or

viscoelastic properties of the ligament structures. In

particular, the failure force, stiness, and energy have all

been reported to increase with rate of loading (Fig. 4).

For example, with increase in loading rate from 1.0 to

250 cm/s, the tensile failure load, stiness, and energy

for the anterior longitudinal ligament and ligamentum

¯avum of the cervical spine increased by a factor of 2±4.

However, the failure distraction did not show such in-

creasing tendencies with increasing loading rate. Similar

trends have been reported in torque and rotation at the

upper cervical joint with an increase in loading rate [59].

These results indicate that the spinal ligaments are de-

formation sensitive, i.e., once a stretch level is attained,

regardless of the loading rate, failure is imminent. This

property has also been observed in other soft tissue

structures (e.g., liver, kidney, and thoracolumbar discs

and ligaments) of the human body [60,61].

Area (mm 2 )

Length (mm)

C2±C5

ALL

11.1 (1.9)

18.8 (1.0)

PLL

11.3 (2.0)

19.0 (1.0)

46.0 (5.8)

8.5 (0.9)

ISL

13.0 (3.3)

10.4 (0.8)

C5±T1

ALL

12.1 (2.7)

18.3 (0.5)

PLL

14.7 (6.8)

17.9 (0.5)

48.9 (7.9)

10.6 (0.6)

ISL

13.4 (1.0)

9.9 (0.7)

ALL: anterior longitudinal ligament; PLL: posterior longitudinal

ligament; LF: ligamentum ¯avum; ISL: interspinous ligament.

anulus of the disc, i.e., noting that the ligament ®bers

traverse in a superior±inferior direction while the disc

anulus ®bers are oblique. Vertebrae above and below

the ligament under test are ®xed, and a load cell (pref-

erably six axis to insure uniaxial nature of force appli-

cation) is placed at the distal end (Fig. 1). The specimen

is subjected to axial tensile loading and the load-defor-

mation response is obtained. A representative tensile

force±de¯ection response is shown in Fig. 2 and dis-

cussed in detail in Appendix A [3±6,46]. Table 2 pro-

vides the failure force±deformation, energy, and stiness

for the various cervical spine ligaments in the upper

cervical spine. The above-described tensile force±dis-

placement response can be transformed into a stress±

strain curve using the length and cross-sectional area

geometrical parameters described in the earlier section.

Table 3 includes data for middle and lower cervical

spines, Fig. 3 illustrates the biomechanical responses,

and Table 4 provides a bilinear modulus of elasticity

data. In the interest of brevity, other data such as age,

gender and loading rate are not included in all tabular

data in this paper. The reader is referred to original

articles for such information. The eects of age, gender

and loading rate on cervical spine responses are reported

by Pintar et al. [47].

The above-described force, de¯ection, energy, sti-

ness, stress, and strain parameters are applicable to

(quasi) static tensile loading. In eect, these material

property variables are applicable during day-to-day

physiologic types of activities wherein the rate of load

application is slow, i.e., sucient time is allowed for the

ligament structure to react (process of gradual reorien-

tation of ®bers during loading). However, as indicated

in the introduction, the human body reacts and resists

external loads in a dynamic environment (e.g., motor

vehicle crashes, athletic activities) [27,47±58]. Ligament

tears have been documented during high rates of load-

ing; in contrast, avulsion of the ligament from the ad-

jacent vertebra has been identi®ed during slowly applied

2.4. Modeling

The above-determined geometrical and mechanical

properties of ligaments are being used in ®nite element

models of the cervical spine [30,31,62]. Because of a lack

of cervical ligament data, earlier researchers adopted

data from lumbar spine [63] and lower extremity (foot±

ankle) ligaments [64]. Varying assumptions have been

used for simulating ligaments. Element idealizations

have included spring or cable and membrane types.

Table 5 includes a summary of some recent approaches

used in modeling human cervical spine ligaments. Spring

elements use a force±de¯ection curve [28] or stiness as

material property input [65,66], whereas membrane

idealization uses a stress±strain curve [67] or modulus of

elasticity [31,62,68] as the input. Depending on the

complexity and need, ®nite element techniques allow the

¯exibility to choose linear, non-linear, and/or visco-

elastic approaches.

If the analysis is limited to the linear domain, only a

single number representing the linear stiness or

Young's modulus of elasticity is necessary and sucient

[30,32,69±71]. This approach has been shown to be ef-

®cacious at low-magnitude loading (e.g., 0.5 N m ¯ex-

ion±extension moment) to capture the spinal behavior.

In contrast, at higher levels of pure moment and com-

plex-eccentric loading, it is necessary to incorporate

non-linear force±de¯ection/stress±strain responses in

order to determine realistic spine behaviors [28,29].

Another important but frequently ignored issue is the

eect of ligament pre-stress on the internal and external

biomechanical responses of the spine. From functional

and anatomical perspectives, ligaments have varying

levels of pre-stress [45,72±74]. For example, the liga-

mentum ¯avum has more pre-stress than the anterior

longitudinal ligament. Only recently have ®nite element

studies begun to explore the eect of pre-stress [75].

N. Yoganandan et al. / Clinical Biomechanics 16 (2001) 1±27

Fig. 1. Schematic of an in situ bone±anterior longitudinal ligament±bone preparation for tensile tests. A six-axis load cell is placed below the

specimen to ensure the uniaxial nature of force application.

Both spring and truss element idealizations are capable

of simulating the initial pre-stress in the ligament. Pre-

stress increases the resting compression in the interver-

tebral disc and increases the overall structural stiness

[7]. Since ligaments are sensitive interconnecting struc-

tures, it is important to incorporate their complex (e.g.,

pre-stress, non-linear) characteristics to delineate accu-

rate biomechanical responses of the cervical spine. The

eects of the presence or absence of ligament structures

on the external and internal responses of the other soft

tissue structures (e.g., disc) are discussed in Section 6.

3. Intervertebral discs

3.1. Role

In contrast to ligaments which are uniaxial (tension),

intervertebral discs respond to or experience multiple

load vectors [7]. Under any external loading, with the

exception of direct uniaxial tension (e.g., airbag load-

ing), discs carry compressive forces in association with

other components [1]. During normal physiologic con-

ditions, the weight of the head places the C2±T1 discs in

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