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Mechanical Characterization of the Human Lumbar Intervertebral Disc Subjected
to Impact Loading Conditions
A Thesis
Submitted to the Faculty
of
Drexel University
by
David Jamison, IV
in partial fulfillment of the
requirements for the degree
of
Doctor of Philosophy
August 2013
© Copyright 2013
David Jamison, IV. All Rights Reserved.
ii
Dedication
This work is dedicated to my mother, Devra Jamison. Without her unconditional love and support
and nurturing of my God-given abilities, I would not be where I am today. I am forever grateful.
iii
Acknowledgements
I would like to first thank my advisor, Dr. Michele Marcolongo. She took me in her lab
and immediately gave me meaningful work. Her unwavering confidence in my abilities provided
me the intellectual freedom to pursue the research questions I had (when funds allowed, of
course!). Most of all, she is the kindest and most supportive advisor I could have ever hoped for.
She truly is an advisor, not merely a PI who demands data to be churned out.
Dr. Marco Cannella, who showed me some no-nonsense, tough love in the beginning
stages of my graduate career. His tutelage enabled me to use the Instron – with which I quickly
developed a love-hate relationship – and develop my critical thinking skills.
To Dr. Chris Massey, who took lots of time out of his busy schedule to show me how to
build models in ABAQUS. He also provided me with plenty of laughs and some advice on
navigating the “new professor” landscape.
Of course, the members of the Biomaterials Laboratory – past and present – deserve
recognition: Sumona Sarkar, Nandita Ganesh, Rob Yucha, Katsiaryna Prudnikova, and Rob
Yucha. Thank you for the laughs, the stories, the random lunch truck trips, the happy hours, and
for listening to my relatively frequent rants.
Last and certainly not least, I must thank my love and my partner, Veronica Miller. I
could not have asked for a better mate with which to take this journey, and you kept me focused
and positive the whole time. Words can’t express how much your continual support means to me.
iv
Table of Contents
List of Figures ............................................................................................................................ vi
List of Tables ............................................................................................................................ viii
Abstract ....................................................................................................................................... ix
1. Introduction ......................................................................................................................... 1
2. The Intervertebral Disc ..................................................................................................... 2 2.1. Functional Anatomy .............................................................................................................. 2 2.2. Mechanics ................................................................................................................................. 3
2.2.1. Static Loading ................................................................................................................................... 4 2.2.2. Quasistatic Loading ........................................................................................................................ 5 2.2.3. Dynamic and Impact Loading ..................................................................................................... 6
3. Naval High Speed Boats .................................................................................................. 15 3.1. General Description and Impact Events ........................................................................ 15 3.2. Injury Assessment ............................................................................................................... 16 3.3. Current Metrics for Shock Mitigation ........................................................................... 16
4. Review of Dynamic Loading Literature: Experimental Studies ........................... 22
5. Review of Relevant Finite Element Literature .......................................................... 30 5.1. Advancements in IVD Finite Element Modeling ......................................................... 30 5.2. Finite Element Models of Impact Loading .................................................................... 32
6. Project Objective and Specific Aims ............................................................................ 36
7. Aim 1: A Comparison of the Human Lumbar Intervertebral Disc Mechanical
Response to Normal and Impact Loading Conditions..................................................... 38 7.1. Introduction .......................................................................................................................... 38 7.2. Methods ................................................................................................................................. 39 7.3. Results .................................................................................................................................... 42 7.4. Discussion .............................................................................................................................. 43
8. Aim 2: The Effect of Creep on Human Lumbar Intervertebral Disc Impact
Mechanics ................................................................................................................................... 50 8.1. Introduction .......................................................................................................................... 50 8.2. Methods ................................................................................................................................. 51 8.3. Results .................................................................................................................................... 53 8.4. Discussion .............................................................................................................................. 53
9. Aim 3: Development and Validation of a Poroelastic Lumbar Disc Finite
Element Model for Impact Mechanical Response Analysis ........................................... 65 9.1. Introduction .......................................................................................................................... 65 9.2. Methods ................................................................................................................................. 68
9.2.1. Model Geometry and Material Properties ............................................................................. 68 9.2.2. Model Validation ........................................................................................................................... 69 9.2.3. Loading and Boundary Conditions .......................................................................................... 70
9.3. Results .................................................................................................................................... 71 9.4. Discussion .............................................................................................................................. 72
v
10. Discussion ........................................................................................................................... 81 10.1. Limitations ............................................................................................................................ 83
11. Conclusions ........................................................................................................................ 86 11.1. Novel Contributions ............................................................................................................ 87 11.2. Future Work and Direction .............................................................................................. 88
List of References ..................................................................................................................... 90
Vita ........................................................................................................................................... 106
vi
List of Figures
Figure 2.1. A schematic of the skull and entire spinal column, showing the different
regions of the spine. (Adapted from Penn Medicine website.) .......................................... 8
Figure 2.2. A schematic of the lumbar intervertebral disc, showing its structural
components [14]. ............................................................................................................................. 9
Figure 2.3. A schematic showing the molecular structure of aggrecan [44]. ....................... 10
Figure 2.4. A close-up schematic of the cartilaginous endplate. Arrows indicate
nutritional pathways into and within the disc [14]. ............................................................ 11
Figure 2.5. A Schematic of a typical diurnal (24-hr loading) cycle on the disc. Creep
response to static load can be seen here during both the "loading" and "recovery"
phases. ............................................................................................................................................. 12
Figure 2.6. A schematic showing the hysteresis in a stress-strain curve of a typical
viscoelastic tissue. ........................................................................................................................ 13
Figure 2.7. Typical stress-strain curve of a biological soft tissue such as the IVD, with
tow and linear regions of the curve [44]................................................................................ 14
Figure 3.1. A schematic showing the local coordinate system of a HSB crew member in
seated orientation. ........................................................................................................................ 19
Figure 3.2. Axial acceleration over time on an HSB during an at-sea test [56]. ................. 20
Figure 3.3. A breakdown of the most typical injury sights among HSC crew members
[61]. .................................................................................................................................................. 21
Figure 4.1. Representation of selected dynamic studies. Most fall outside of the desired
impact loading range for this study......................................................................................... 29
Figure 5.1. Finite element mesh of osmo-poro-viscoelastic model from Schoeder et al.
[100]. Analysis used only ¼ of the whole disc, since it is symmetric about the
transverse and mid-sagittal planes. ......................................................................................... 35
Figure 7.1. Representative acceleration waveforms in x, y, and z directions on a high
speed craft. The z-axis accelerations are generally an order of magnitude higher than
x and y. Top insert: coordinate axis for this system. Bottom insert: sample impact
magnified for clarity. ................................................................................................................... 47
Figure 7.2. Comparison of load-displacement curves between 80ms and 1000ms (top),
along with results for k (middle), and ΔE (bottom). Values are normalized to the
baseline 1000ms impact (represented by dashed lines). Error bars indicate standard
error. **: p < 0.01, ***: p < 0.001. ......................................................................................... 48
Figure 7.3. Representative impact event (top) and its corresponding frequency spectrum
(bottom). The signal consisted of high frequencies at 10-15 Hz and 20-30 Hz, which
were below noise frequencies (< 50 Hz). Frequency analysis was performed via fast
Fourier transform with a custom-written code in MATLAB. ......................................... 49
vii
Figure 8.1. X-ray of disc (sagittal section) showing measurements of anterior, middle,
and posterior heights. The radiopaque object at the left is a reference metal rod with
a diameter of 2.8 mm. ................................................................................................................. 57
Figure 8.2. Schematic of a 1000-ms impact event showing calculation methods for NZ,
ΔE, ktoe, and klin. ........................................................................................................................... 58
Figure 8.3. Axial strain versus tcreep. Results showed a strong positive correlation between
the two parameters. ...................................................................................................................... 59
Figure 8.4. Neutral zone (NZ) was positively correlated with (A) tcreep (some time points
omitted for clarity) and negatively correlated with (B) timp. ............................................ 60
Figure 8.5. Energy dissipation (ΔE) was positively correlated with both (A) tcreep (some
time points omitted for clarity) and (B) timp. ........................................................................ 61
Figure 8.6. Toe-region stiffness (ktoe) was negatively correlated with both (A) tcreep (some
time points omitted for clarity) and (B) timp. ........................................................................ 62
Figure 8.7. Linear-region stiffness (klin) was positively correlated with (A) tcreep (some
time points omitted for clarity) but showed no strong correlation with (B) timp. ....... 63
Figure 8.8. NZ showed a negative correlation with both (A) ΔE and (B) ktoe. .................... 64
Figure 9.1. Axisymmetric model of lumbar intervertebral disc consisting of nucleus,
annulus, and superior and inferior endplates and vertebrae. ........................................... 75
Figure 9.2. FE model validation data, showing an acceptable fit in both loading and
unloading for impact durations below 320 ms. ................................................................... 76
Figure 9.3. Stress response in the disc, showing maximum Savg for the NP, AF, and EC
(top) along with stress distribution profiles of the NP and AF for both 40 and 200 ms
(bottom). Both contour plots are displaying t = . ................................................. 77
Figure 9.4. Pore pressure response in the disc. Maximum ΔPOR averaged across the
nodes in each disc component are given (top) along with POR distribution profiles
of the disc for the 40 and 200 ms impact events (bottom). Both contour plots are
displaying t = . ................................................................................................................ 78
Figure 9.5. Percent change in Vfluid over time for the NP and AF at 40 and 200 ms. Fluid
loss was negligible during impact events. ............................................................................. 79
viii
List of Tables
Table 4.1. Summary of selected literature on spine dynamic loading. .................................. 26
Table 9.1. Finite element model material properties. .................................................................. 80
ix
Abstract
Low back pain is a large and costly problem in the United States. Several working
populations, such as miners, construction workers, forklift operators, and military personnel, have
an increased risk and prevalence of low back pain compared to the general population. This is due
to exposure to repeated, transient impact shocks, particularly while operating vehicles or other
machinery. These shocks typically do not cause acute injury, but rather lead to pain and injury
over time. The major focus in low back pain is often the intervertebral disc, due to its role as the
major primary load-bearing component along the spinal column. The formation of a reliable
standard for human lumbar disc exposure to repeated transient shock could potentially reduce
injury risk for these working populations. The objective of this project, therefore, is to
characterize the mechanical response of the lumbar intervertebral disc subjected to sub-traumatic
impact loading conditions using both cadaveric and computational models, and to investigate the
possible implications of this type of loading environment for low back pain.
Axial, compressive impact loading events on Naval high speed boats were simulated in
the laboratory and applied to human cadaveric specimen. Disc stiffness was higher and hysteresis
was lower than quasi-static loading conditions. This indicates a shift in mechanical response
when the disc is under impact loads and this behavior could be contributing to long-term back
pain.
Interstitial fluid loss and disc height changes were shown to affect disc impact mechanics
in a creep study. Neutral zone increased, while energy dissipation and low-strain region stiffness
decreased. This suggests that the disc has greater clinical instability during impact loading with
progressive creep and fluid loss, indicating that time of day should be considered for working
populations subjected to impact loads.
x
A finite element model was developed and validated against cadaver specimen subjected
to impacts in the laboratory. Analysis showed greater total von Mises stress and pore pressure in
the components of the disc under transient shocks compared to static or quasi-static loading.
These findings support the idea that impact shocks cause a change in mechanical response and are
potentially damaging to the disc in the long term.
1
1. Introduction
Low back pain is a large and costly problem in the United States. It is estimated that 15 to
20% of the adult American population seek medical attention for low back pain annually [1, 2].
The yearly cost of treatment for lower back pain – ranging from short-term to chronic – is
estimated at $50 Billion dollars in the U.S. alone [3]. The major focus in low back pain is often
the intervertebral disc, due to its role as the major primary load-bearing component along the
spinal column. Low back pain can also be an indication of precursor to disc injury, such as
herniations causing impingement of the spinal cord.
In addition to back pain caused by daily, physiologic loading, there are several working
populations who have an increased risk and prevalence of low back pain compared to the general
population. This is due to exposure to transient impact shocks, particularly while operating
vehicles or other machinery [4]. Experimental studies and accident reports have shown increased
injury risk due to impact shocks in miners [5], race car drivers [6], tractor drivers [7, 8], and
military personnel [9, 10]. It should be noted, however, that most of these studies and reports do
not attempt to make a distinction between transient shocks and whole body vibration.
Additionally, though epidemiological reviews [11] have shown a link between impact exposure
and low back pain, little investigation has been done to understand the underlying mechanics of
the spine or lumbar disc during occupational hazardous loading. A better understanding of disc
mechanical response to impacts is needed; this could lead to the development of more effective
exposure limits to this type of loading. The formation of a reliable standard for human exposure
to repeated transient shock could potentially reduce the injury risk for the previously mentioned
working populations. Thus, it is clear that a characterization of lumbar intervertebral disc
mechanical response to transient impact shocks is needed.
2
2. The Intervertebral Disc
2.1. Functional Anatomy
The human spine is responsible for transferring loads of the head and trunk, along with
any externally applied forces, to the pelvis. It also is important for movement and flexibility of
the upper body, and critical in the protection of the spinal cord from injury due to trauma and
excessive motion [12, 13]. The spinal column consists of 24 bony elements, or vertebrae, and is
divided into three distinct regions – cervical (seven vertebrae), thoracic (12 vertebrae), and
lumbar (five vertebrae). Both the cervical and lumbar regions have a kyphotic curve while the
thoracic spine has a lordotic curve, both of which are visible in the sagittal plane Figure 2.1. There
is also a sacral region, consisting of five fused vertebrae, and well as the vestigial coccyx region.
Along the spinal column, adjacent vertebrae are linked via an intervertebral disc (IVD),
the exceptions being the fused sacral and coccyx regions as well as C1-C2. The IVD is the
primary load-bearing component of the spine. It serves to distribute and dissipate intrinsic loads
while also allowing for flexibility of the spinal column in lateral bending, flexion/extension, and
torsion [13, 14]. In the lumbar region, discs are approximately 7-10 mm in height and 40-50 mm
in diameter [15, 16]; size dimensions of the more inferior discs (e.g.: L4-L5) are slightly larger
than the superior ones (e.g.: T12-L1). Figure 2.2 shows the basic structure of the IVD. The disc
has three regions: the nucleus pulposus (NP), annulus fibrosus (AF), and cartilaginous endplates.
The cell density in the disc is low – it comprises only 0.25% of tissue volume [17], or
approximately 4e6 cells/cm3 [18]. The extracellular matrix plays a large role in determining disc
function and mechanical properties.
The nucleus is located centrally in the disc along the transverse plane. It is a gelatinous
structure made mostly of water – nearly 80% of the wet weight [14, 19-21]. The NP extracellular
3
matrix is comprised chiefly of proteoglycans, which are large, negatively-charged molecules,
comprising 14% of disc’s wet weight. Aggrecan, the major proteoglycan of the disc [22], helps
maintain tissue hydration via osmotic pressure provided by the negatively charged condroitin and
keratin sulfate side chains [23]. The molecular structure of aggrecan can be seen in Figure 2.3. As
aging progresses, these molecules are continually enzymatically digested into smaller fragments,
which can leach from the tissue [14, 18]. Loss of proteoglycans is the most significant
biochemical change that occurs in the process of disc ageing and degeneration [24]. Collagen and
elastin fibers are also embedded in the matrix, providing tensile strength to the tissue. This fibril
network makes up 20% of the dry weight of the NP [25].
The annulus fibrosus surrounds the NP and is made up of the same constituents, though
collagen represents a much larger portion of its dry weight (50-70%) [26]. Water content in the
AF is lower overall than the NP, and decreases as you move radially outward [21]. The AF is
organized in concentric rings called lamellae. Type I collagen fibers line up parallel within each
lamella and are arranged in alternating ±30 degree angles between lamellae [27]. Elastin fibers
have a radial orientation within the AF, in order to help the structure return to its original shape
after it has been strained [14].
The cartilaginous endplates lie between the disc and their adjacent superior and inferior
vertebral bodies. It is a thin layer of permeable hyaline cartilage – less than 1 mm in thickness
[28]; this is illustrated in Figure 2.4. The IVD is the largest avascular tissue in the body, and the
majority of nutrient supply and metabolic waste removal is achieved via diffusion through the
endplate [13, 29]. Fluid flow into and out of the disc is also primarily through the endplates; the
secondary source of fluid flow is through the annulus itself.
2.2. Mechanics
4
The lumbar intervertebral disc supports axial loads from the head and trunk, transmitted
along the long axis of the spine. The IVD works to dissipate these loads, distributing it to the
vertebral bodies. The fluid-filled NP deforms and expands radially upon axial loading and
behaves like a pressurized fluid, generating radial stresses on the AF. This results in subsequent
tensile forces on AF collagen fibers within the lamellae [30, 31]. The low modulus in the NP
contributes to overall disc compressibility and radial expansion properties. Flexion-extension,
torsion, and lateral bending, are the other loading modes typically experienced by the IVD [32].
These loading modes introduce bending moments, torque, and also shear forces to the disc tissue.
However, as the IVD is the principal compressive load-bearing component of the spine, our
discussion will be limited to the mechanical properties of the tissue in axial compression.
2.2.1. Static Loading
The IVD exhibits a linear elastic and time-dependent mechanical response under static
loading. Young’s Modulus, E, and Poisson’s Ratio, ν, are the two parameters necessary to define
a linear elastic material property [33]. Young’s modulus is the ratio of uniaxial stress to strain,
while ν is defined as the ratio of lateral strain to axial strain. Time-dependency of IVD
mechanical response can be modeled using poroelastic material properties and the biphasic theory
[34]. This constitutive model assumes a porous medium that is filled with fluid. The two material
parameters needed to define a poroelastic material are permeability and void ratio. Permeability
describes the ability for fluid to flow through the material, while void ratio is the proportion of
void (pore) volume to solid material volume.
During a 24-hour diurnal cycle, the IVD will experience approximately 16 hours of heavy
loading due to physiologic activity. A substantial volume of fluid (up to 20%) leaves the disc
during this period [35-37], primarily through the endplates [38, 39]. Each disc can lose 1-2mm of
5
height during the day due to this expulsion of fluid from the discs [35]. The loss of fluid is due to
increased pressure in the NP. The driving force for the flow of fluid is the change in pressure
[11]:
(2.1)
If ΔP is greater than zero, a net expulsion of water occurs. Conversely, during the approximately
eight hours of the diurnal cycle when an individual is asleep and the spine is in the supine
position and under reduced load, ΔP becomes negative and water is drawn back into the disc. The
osmotic pressure is what determines the final hydration level in the disc. Thus, the mechanical
behavior of the disc is dictated to a large extent by its proteoglycan content [40].
While under a static compressive load, the IVD responds with continuous displacement –
known as creep – resulting in decreased hydrostatic pressure in the NP and an increase in
compressive stiffness [41, 42] and radial bulging [42, 43]. This change in disc height arise from
both creep deformation of the solid phase as well as fluid exchange between the IVD and its
environment [42]. Figure 2.5 depicts typical creep response over time for a step-wise applied load.
The disc will continue to creep until it reaches equilibrium, that is, when ΔP reaches zero.
2.2.2. Quasistatic Loading
Although the poroelastic model is effective in modeling the intervertebral disc as a fluid-
filled porous solid, one limitation of this material model is that it treats the solid phase as a linear
elastic material. However, stress-strain curves from quasistatic (QS) tests show that the disc still
exhibits non-linear elastic behavior event though the effects of interstitial fluid movement on IVD
mechanics are not as dominant, due to the shorter time duration of such tests. QS loads are
6
dynamic, however, the loading rate is low enough where inertial effects may still be ignored.
Thus, while considering of the influx and efflux of fluid under this type of loading is not as
important for modeling disc mechanics, a linear elastic model is insufficient for describing IVD
response. Viscoelastic material models are typically used to describe IVD mechanics in this
regime. Viscoelasticty incorporates both elastic and viscous components for a material. As such,
viscoelastic materials exhibit latency in response during unloading, forming a hysteresis in the
stress-strain curve, as can be seen in Figure 2.6. The hysteresis is directly related to the amount of
viscous damping (energy dissipation) in the material. Several studies have shown that hysteresis
decreases along with fluid loss in the IVD [42].
During the loading phase, the IVD exhibits the characteristic stress-strain response as
other biological soft tissues, with a toe and linear region (Figure 2.7). In the toe (low strain)
region, the applied pressure in the NP increases, and it begins to expand and push radially on the
annulus. In the linear (high strain) region of the curve, the reduced disc height and radial bulging
of the NP cause higher stresses in the AF. The collagen fibers, which exhibit linear elastic
behavior once fully recruited as they would be in this scenario, are put into tension and take on
most of the applied load [25, 44], which explains why this portion of the curve has a nearly linear
stress-strain relationship.
2.2.3. Dynamic and Impact Loading
The mechanical behavior of the intervertebral disc is not only time-dependent, but also
frequency-dependent. It has been shown that disc compressive stiffness increases and energy
damping decreases with increasing loading frequency [45-52]. At greater loading rates, the disc
takes on more force with the same level of displacement, while being less able to dissipate that
7
energy. This change in mechanical response has implications in both vibrational and impact
loading scenarios.
Poroelastic and viscoelastic behaviors are still present in the tissue at high frequencies,
however, these diminish and are dominated by elastic material behavior, particularly for small
displacements [45]. Movement of interstitial fluid in and out of the IVD is limited at loading rates
shorter than on the order of minutes [53]; therefore, permeability effects on mechanics in this
loading regime become negligible. The disc is still not a linearly elastic material, however, and
should not be modeled as such. Few attempts to assign a different constitutive model for the IVD
under higher frequency loads have been made. Of those that have, several have employed a
hyperelastic material model [54, 55]. A hyperelastic material is one that is defined by the strain
energy density function and can be suitable for the disc since it maintains non-linear elasticity.
Although the changes in some mechanical response parameters with loading rate have
been highlighted as indicated above, the overall mechanical behavior of the IVD under fast-rate
loads is still not well understood. Furthermore, though some studies have examined the disc under
catastrophic impacts – which will be highlighted in a later section – the transition from static and
QS load behavior to impact behavior – and at which point this transition takes place – is also
unknown. This work will expand on some of these questions.
8
Figure 2.1. A schematic of the skull and entire spinal column, showing the different regions of the spine.
(Adapted from Penn Medicine website.)
9
Figure 2.2. A schematic of the lumbar intervertebral disc, showing its structural components [14].
10
Figure 2.3. A schematic showing the molecular structure of aggrecan [44].
11
Figure 2.4. A close-up schematic of the cartilaginous endplate. Arrows indicate nutritional pathways into
and within the disc [14].
12
Figure 2.5. A Schematic of a typical diurnal (24-hr loading) cycle on the disc. Creep response to static load
can be seen here during both the "loading" and "recovery" phases.
13
Figure 2.6. A schematic showing the hysteresis in a stress-strain curve of a typical viscoelastic tissue.
14
Figure 2.7. Typical stress-strain curve of a biological soft tissue such as the IVD, with tow and linear
regions of the curve [44].
15
3. Naval High Speed Boats
3.1. General Description and Impact Events
The United States Navy and Special Operations Command (SOCOM) often employ
small, high-speed boats (HSB) for Navy SEAL missions out on open waterways. Two commonly
used HSBs are the Rigid Inflatable Boat (RIB) and the Mark V (MkV). These crafts may carry up
to 16 SEALS, in the case of the MkV. They can attain speeds of 40 knots or higher, often
navigating through rough sea states.
Small swift boats operating in the open ocean – particularly during rough sea states – can
generate high shocks, due to the boat pitching after hitting a wave, then quickly coming into
contact with the ocean surface. HSB personnel are typically subjected to large magnitude shocks
in the axial direction as the vehicles pitch and crash into the water (Figure 3.1). Accelerations of
these shocks can be upwards of 10 G [56, 57], and are typically less than one second in duration.
A shock, or impact, is defined as a distinct event resulting from the boat slamming into the water,
where acceleration pulses are less than 200 ms [56]. These impact events usually occur multiple
times throughout a single ride on an HSB (Figure 3.2).
Lighter and less rigid hulls have since been designed for some HSBs in an attempt to
stem this problem. For example, the Mark V.1 hull consists of a carbon fiber composite with
Kevlar and a foam core. It is unclear, however, how effective these newer designs are in
mitigating shock.
16
3.2. Injury Assessment
In 2000, the Naval Health Research Center conducted a survey of self-reported injuries
among a selected group of special boat operators [10]. This study found that 18% of injuries
requiring medical attention were related to operations in an HSB, specifically arising from
exposure to impacts and vibrations while on the boat during sea states. This rate of injury was
behind only those considered “mission related.” Of these injuries, nearly 34% were at the lower
back, with a high percentage of them being specifically related to disc problems (Figure 3.3). All
disc related problems resulted in the individuals seeking medical attention, which led to limited
duty status. A significant correlation (r = 0.39, p < 0.05) was found between years served in a
Special Boat Unit and prevalence of injury, indicating that consistent exposure to impacts can
lead to a greater risk of injury.
3.3. Current Metrics for Shock Mitigation
To address the issue of boat ride-related injuries sustained to HSB personnel, numerous
manufacturers have designed various passive and active suspension seats to be fitted onto these
boats. The most widely used standard for assessing the efficacy of shock mitigating seats in the
HSB environment is ISO 2631-5 (2004) [58]. This International Standard addresses human
exposure to shock and whole body vibration, particularly as it pertains to the lumbar spine; its
purpose is to effectively quantify shock-containing vibrations. The standard describes how to
calculate an effective “acceleration exposure dosage” at the lumbar spine for a seated individual,
using accelerometer data collected during the event in question. The lumbar spine response model
assumes the individual is in an upright position and does not have any additional movement
relative to the seat pad.
17
This exposure dosage is determined by summing the number of acceleration peaks from
an accelerometer data set from a boat ride. The accelerometer to be analyzed is typically placed
on the back of the seat or the seat pad. The equation for daily equivalent compression dose, Sed,
is:
[∑ ( )
] ⁄ (3.1)
where mk is a constant and Dk is expressed as:
[∑
]
⁄
(3.2)
and
tdj is the duration of daily exposure
tmj is the period over which Dkj has been measured.
The parameter Dkd is in units of acceleration (m/s2) and Sed is in units of stress (MPa). The
acceptable Sed limit for d = 8 hrs was established to be 0.8 MPa, based on subsequent predictive
calculations of health effects of shock exposure. Seats that were manufactured to this
specification do help to mitigate shock. However, the reduction in shock appears to be
insufficient, as the prevalence of injury to special boat operators is still high. Thus it is necessary
to refine the standard to which most current shock mitigation technologies are set.
There are several limitations in the usage of this ISO standard and the Sed exposure
criteria. First, accelerations at the lumbar spine level are estimated from the actual accelerations
measured at the seat pad. This is done by use of a recurrent neural network [59]. Second, Sed only
accounts for the magnitude of impacts and not the duration or time history, which is an important
18
factor for determining impact tolerance and injury thresholds [60]. For two impact events of equal
acceleration magnitude, the event with the shorter time duration would surely impart more power
to the system than the longer one. However, Sed is not able to account for this. These limitations
could in part be the cause for current HSB seat designs that are not fully effective against limiting
impact loading injury on the lumbar spine, even though they meet current ISO exposure rate
criteria. A better understanding of a broad spectrum of impact events (particularly with regard to
event duration) may lead to a reconsideration of the current standard and metric for shock
mitigation technologies.
19
Figure 3.1. A schematic showing the local coordinate system of a HSB crew member in seated orientation.
20
Figure 3.2. Axial acceleration over time on an HSB during an at-sea test [56].
21
Figure 3.3. A breakdown of the most typical injury sights among HSC crew members [61].
22
4. Review of Dynamic Loading Literature: Experimental Studies
Dynamic loads are, by definition, those which are not static. Impact loads certainly fit
within this broad definition, as do many other types of cyclic or rate-varying conditions. There
have been numerous studies in the literature that examined dynamic loading of some sort on the
spine. This section highlights several of those studies, while also pointing out the differences
between them and the HSC loading environment being analyzed in this work. A summary of
these and other selected studies is available in Table 4.1.
Several studies have analyzed dynamic loads that are outside the range of high speed
craft impact events, in either frequency (impact duration) or resultant force. Hansson and
colleagues [62] applied axial compressive loads in a physiologic range (0.5 Hz) and found that
disc stiffness at equilibrium was higher than the initial stiffness prior to loading. Kasra [63]
showed that viscous damping in the disc decreases with increasing frequency. These tests were
performed on human tissue in the frequency range of 0-50 Hz; however, the load amplitude was
only 20 N. Rostedt [64] applied impacts of 40 ms in duration to IVDs and investigated the change
in resonant frequency and transmissibility, but the force range was only 30-100 N.
Many other studies that have looked at dynamic loading instead had frequencies or loads
that were far too high to be comparable to HSB impacts, often resulting in failure of the spinal
motion segment. Canine lumbar discs were loaded to failure at rates up to 500 mm/min in a study
by Cassidy [21], which found that compressive modulus and maximum stress increased with
loading rate. Duma [65] analyzed failure mechanisms in the lumbar spine subjected to loads as
high as 12 kN and applied at 1 m/s. The study found that the endplate was the most typical failure
site. Pintar and colleagues [66] studied injury threshold and how it was affected by age, gender,
and loading rate. The latter parameter lowered the injury threshold. However, these tests were
23
done on head-neck complexes and loaded up to 8 m/s. Ranu [67] demonstrated that intradiscal
pressure within the lumbar disc increases linearly with increased load, but these loads went up to
30 kN. Yingling and colleagues [50] investigated the effect of loading rate on compressive
mechanics in the disc. This group had similar conclusions to other studies; however, their
methods are not relevant to the proposed work here because it was performed on cervical discs to
failure at a maximum loading rate of 16 kN/s.
Several studies have examined impact loading on the spine, but with limited analysis of
IVD mechanical response. A computational model was developed by Bazrgari [68] to estimate
trunk muscle forces, spinal loads, and stability under a 4 G impact event at two different
frequencies (4 and 20 Hz). Gatt and colleagues [69] estimated compressive and shear forces in the
lumbar disc arising from performing a football “sled blocking” technique via a previously
established method [70-72]. They found that maximum compressive loads were nearly 8700 N in
some cases, and were applied over a duration of 0.67 s. Pankoke [73] also used a model to
estimate loads on the lumbar disc of a seated subject, this time via vibration cases. They also
measured transmissibility of forces from the seat to L4. Rukuiza [74] analyzed the effect of seat
pad stiffness on lumbar spine loads during an impact event (1 G impulse for 1 s), and found that
maximum applied forces decreases 1.4 times when seat stiffness is reduced by a factor of 3.5.
Though all of these studies measured or estimated forces in the lumbar IVD, no attempt was
made to characterize the overall mechanical response to these loading scenarios.
There are a number of studies that looked at dynamic loading on the spine, but in
different loading conditions or modes, and applied to the cervical spine. Both Nightingale [75]
and Pintar [76] looked at dynamic loads on head-neck complexes; the former investigated drop
tests while the latter looked at whiplash injuries. A study by Nuckley [77] showed that stiffness
and ultimate stress in the baboon cervical spine increased as a function of loading rate; however,
these tests were performed in tension, not compression.
24
Some investigations of dynamic loading and its effects on the disc have focused on gene
expression or cell viability, rather than mechanical response. MacLean and colleagues [78]
analyzed the effect of dynamic compression at 0.2 Hz on rat caudal discs and found a
downregulation of anabolic genes and an upregulation of catabolic genes for both aggrecan and
collagen. Wuertz [79] also utilized a rat model and found that expression of aggrecan and
collagen increased when loaded with physiologic dynamic loads (1 MPa at 1 Hz) for up to eight
weeks. Illien-Junger [80] looked at the effects of nutrition (low and normal glucose
concentration) and cyclic loading rate (0.2 and 10 Hz) on IVD cell viability. The results showed
that the high frequency tested groups saw significantly less cell viability, and this effect was more
pronounced on NP cells than AF cells.
Also of interest are studies investigating whole body vibrations (WBV) and their effects
on the lumbar spine and causation of low back pain. A comprehensive review by Lings and
Leboeuf-Yde [11] concluded that WBV do indeed have an association with low back pain.
Another review by Bovenzi [81] also points to several clinical and radiological studies that show
a link between WBV and low back pain, particularly in occupations such as truck drivers,
construction workers, and forklift operators. The review also notes the usage of ISO 2631-1 [73]
for determining an exposure threshold for WBV, just as part 5 of the standard is used for impact
shocks. While literature on WBV does provide a good framework and motivation for our work on
high-impact loading, the vibration loads investigated were low in amplitude and thus do not
adequately represent the loading profiles we wish to subject to the disc.
As the comprehensive review by Waters and colleagues [82] noted, while many studies
have looked at the link between WBV and low back pain, very few have analyzed WBV
combined with transient shocks. In addition to affecting HSB personnel, these transient shocks
also affect other working populations, such as tractor drivers, construction equipment operators,
coal miners, and other military populations. Moreover, Waters points out that most of the studies
that examined populations experiencing WBV and transient shocks only reported injury types and
25
rates or performed an epidemiological study, rather than make an attempt to understand the
underlying injury mechanisms or characterize disc mechanics during such shocks or the impacts
themselves. The only quantitative study to consider the effects of impact loads on the lumbar
spine was performed by Brinckmann [4]. This work used radiographs of the thoracolumbar spine
to show a significant decrease in disc height following miners’ exposure to mechanical shocks
while on the job. However, even this work does not make an attempt to measure the VD
mechanical response to transient shocks. The review by Waters even concludes that an evaluative
framework for mechanical affects from impact exposure is needed.
One study is most relevant to the types of loads and speeds of impacts present in HSB
environments. Kemper and colleagues [49] tested human lumbar functional spinal units in
compression at 6.8 sec-1
(0.5 mm displacement) and 13.5 sec-1
(1 mm) strain rates. The
compressive tests were non-destructive, that is, the discs were not loaded to failure. The results
showed that compressive stiffness increases with loading rate.
Numerous studies over the last several decades have analyzed dynamic loading on the
intervertebral disc in some fashion. However, there still exists a gap in the literature in
examination of fast, yet non-destructive impact events and their effect on IVD mechanical
response both in the short and long term. Figure 4.1 shows the loading regimes of several of the
studies highlighted in this section, and illustrates how they fall outside of the desired loading
range for sub-traumatic impacts.
26
Table 4.1. Summary of selected literature on spine dynamic loading.
Author Focus
Loading
profile(s) Anatomy
Measurements/
Calculations Findings
Deng (1987)
Physical model of head/neck/torso
subjected to
dynamic loads in sagittal plane
Sled tests at
23.6, 52.7, and 75.3 m/s2
Model of
head, neck and torso
disc pressure,
muscle strain,
accelerations at the head, etc
Head needed 300-
400ms to reposition; disc pressure increase
in T11-T12 40.8 kPa
with pulse duration of 200-300ms; certain
muscles may have
exceeded injury threshold
Yoganandan (1989)
stiffness and strain
energy to define
injury threshold in disc
axial
compression, 2.54mm/s
Human lumbar FSUs
Load, stiffness,
energy at trauma initiation
All measured values
higher for normal discs vs degenerated ones
Cassidy (1990)
response of
structural components to
uniaxial compression
uniaxial
compression (0.005, 0.05,
0.5, 5, 50, and 500mm/min)
thoracolumb
ar and lumbar
ACUs (canine)
toe-strain intercept,
modulus, maximum stress
t-s intercept
unchanged, modulus and max stress
increase as loading rate increases
Broman (1991)
impact response of
a seated subject not sure, 3.9J
lumbar
(specifically
L3)
transmissibility
and attenuation
peaks
Different postures
affect dynamic
response, as measured
by transmissibility and attenuation peaks;
trunk activation causes
stiffening effect
Kasra (1992)
dynamics of lumbar
IVD: experimental
and FE
axial
compression (5-50Hz) at 20N,
with differing
preloads
experimental: human
thoracolumb
ar ACUs and FSUs;
model: L2-
L3 ACU
frequency response,
compliance,
stiffness, hysteresis,
resonant
frequency (see paper)
Nightingale (1996)
axial impact loading
on head and neck
(does inertia of the
head constrain head motion)
drop test at avg 3.2m/s
human
cadaver
cervical
spine and head
force at failure
(If applicable),
type of failure,
impulse, momentum
inertia of the head
constrains motion,
cervical spine loading
due to head rebound is significant
27
Yingling (1997)
dynamic loading
effects on cervical spine
load to failure
at 100, 1000,
3000, 10000, and 16000N/s
Porcine
cervical spine, 2-disc
segments
(C2-C4, C5-C7)
displacement and
load at failure, stiffness
all factors are affected
by loading rate, however, not as much
difference shown when
loading rates are much higher than quasi-static
Pintar (1998)
effects of loading
rate, age, and
gender on force at failure for cervical
spines
head-neck
loaded at 0.25cm/s up to
800cm/s (this
was a part of a previous study,
this study is
simply a statistical
analysis)
Human head
and neck failure load
all factors had
significant effect
Lee (2000)
Effect of impact
duration on lumbar spine (FE model)
axial compression
with dt = [2.5 -
200]ms, Load = 3kN
Human
lumbar ACU (FE)
stiffness, energy absorption (see paper)
Keller (2002)
what's the force-
deformation response of the
lumbar spine in the sagittal plane, a
mathematical model
impulse applied
in posteroanterior
direction; ~100N, 5ms;
applied to L3
Human thorax to
pelvis
axial and PA
displacement (see paper)
Izambert (2003)
dynamic stiffness and damping under
oscillatory displacement
axial
compression ([5:5:30]Hz),
accel at 0.5 m/s2
human
lumbar ACUs
stiffness and damping from
frequency-gain data
stiffness increases, damping decreases
with higher frequencies
MacLean (2005)
effects of short-term
load on metabolic gene expression in
the disc
1MPa
amplitude at 1Hz for 0.5h
and 4h rat tail
disc height,
strain, mRNA levels, disc
thickness
cellular responses vary
based on exposure time and location
within the disc
Duma (2006)
disc response to dynamic
compression
dynamic, 1m/s
to failure
Human
lumbar (whole and
FSUs)
compressive stiffness, load at
failure
loading modes,
stability important;
reports failure loads for lumbar spine and
lumbar FSUs
Elias (2006)
effect of loading
rate on compressive mechanics
5, 50, 500, 5000
mm/s;
compression to 60% strain
multi-
segmented
cervical
FSUs (baboon)
stiffness; load
and displacement at failure
loading rate important,
but only to a certain
point (agreement with
Yingling and Elias studies)
Kemper (2007)
strain rate effect on
compressive stiffness
Dynamic,
0.5mm @
0.1m/s and 1mm at 0.2m/s
Human lumbar FSUs
compressive stiffness
stiffness increases with loading rate
28
Bazrgari (2008)
WBV and high
accel on seated
subjects
vibration
profile from Robinson
(2009) with 4
and 20Hz impact at 4G;
actual values
were 5Hz (3.5G) and
16Hz (1.4G) at
L4
whole lumbar spine
(mathematic
al model)
acceleration at disc level,
muscle
activation, disc compression/she
ar; values
reported at L5-S1
disc loads greater at lower frequency,
critical muscle
stiffness higher; accelerations at freq
near resonance are
worse
C. Bass (2008)
impact tolerance of
the spine
drop test on dorsal side of
intact spine
(avg: 4.1m/s)
in-vivo thoracic and
lumbar spine
(porcine)
injury from radiographs;
reaction force,
loading rate (see paper)
Costi (2008)
frequency dependence of IVD
to 6 DOF dynamic
loading
axial
compression
and rotation:
0.001Hz (2
cyc), 0.01Hz (5
cyc), 0.1Hz (10 cyc), 1Hz
(10cyc); +/-
0.25mm
Human
lumbar
ACUs
stiffness and phase angle (a
measure of
hysteresis)
stiffness increased
with frequency, phase
angle decreased
29
Figure 4.1. Representation of selected dynamic studies. Most fall outside of the desired impact loading
range for this study.
30
5. Review of Relevant Finite Element Literature
5.1. Advancements in IVD Finite Element Modeling
Cadaveric or animal model testing of the lumbar spine has been employed extensively in
the literature, and is useful in many ways. There are, however, some intrinsic disadvantages to
this kind of testing, such as the interspecimen and intersegmental variability in geometry and
biomechanical response. It is also quite difficult to maintain disc health when using cadaveric
specimen, and long-term testing is often impossible. In light of these limitations, the development
of IVD finite element (FE) models has increased over the years. The advancement of these FE
models is highlighted here.
Some of the earliest models of the intervertebral disc used linear elastic material
properties to describe the various components. Belytschko and colleagues were one of the first to
use an FE model to analyze IVD mechanics [83]. In their model, the anterior column was
assumed to be axisymmetric, and the annulus was modeled as a linear elastic isotropic material.
The group further advanced their model to make the annulus an orthotropic, non-linear elastic
material [84]. Both FE models assumed the NP was an incompressible, hydrostatic material, and
simulated it by applying a hydrostatic pressure to the interior walls of the annulus. This approach
was also used by Kurowski and Kubo [85], who were analyzing disc injury mechanisms under
various conditions.
Shiradi-Adl and colleagues made a more realistic FE model by representing the AF as a
fiber-reinforced composite (collagen fibers embedded in ground substance) and the NP as an
incompressible fluid [86]. This model does raise concerns; however, since the NP is not an
incompressible fluid. A viscoelstic model was developed by Lu et al. [87] to analyze bending,
31
twisting, and diurnal fluid changes in the disc; however, only the annulus fibers and ligaments
were modeled as viscoelastic. The other disc and bony elements were represented as isotropic
linear elastic except the nucleus, which was also modeled as an incompressible fluid. The FE
model developed by the Schroeder group [55, 88, 89] uses the Mooney-Rivlin material law to
simulate the fluid-like behavior of the NP and AF ground substance. This model, however,
ignores the presence of actual interstitial fluid. The approaches thus far to modeling the nucleus
present oversimplifications that can compromise the accuracy of the model.
More recent models have incorporated the biphasic theory [34] to obtain a better
representation of the intervertebral disc. The previous models do not differentiate between the
solid and fluid phases of the constituents of the disc, and thus cannot accurately model the time-
dependent nature of disc mechanics. These biphasic models use a pore fluid inside a porous solid;
the solid is generally modeled as linear or non-linear elastic. They will allow for the movement of
interstitial fluid, which is important for accurately modeling disc behavior, particularly for creep
response. Simon and colleagues [90] were some of the first to develop a poro-elastic model of the
spinal motion segment. In this and other similar models [91, 92], externally applied loads cause a
reduction in volume of the solid phase, which in turn makes the fluid-filled voids smaller, causing
an efflux of interstitial fluid. The influx of fluid during relaxation of applied load was not
accurately predicted in these models, however. To improve the simulations, the application of an
external pore, or swelling, pressure was applied, effectively forcing water back into the disc
during relaxation [58, 93-95].
As noted previously, the presence of proteoglycans and their fixed charges is important in
disc biomechanics because of their contribution to osmotic pressure, allowing the tissue to hold
water against externally applied loads. More recently, FE models are being developed to account
for these fixed charges and IVD osmotic pressure. The behavior of biological soft tissues such as
cartilage has been described by the mechano-electrochemical theory, derived by Lai et al. [96] for
small deformations and later extended to finite deformations by Huyghe and Janssen [97]. This
32
theory has been incorporated into finite element models for the study of biological tissues by
several investigators over the last decade [69, 93, 98]. The drawback, however, is that these
models are complex and computationally expensive.
Wilson and colleagues modified the standard biphasic theory model in order to simplify
the mechano-electrochemical model [99]. Using an assumption by Lanir that the effect of time on
ionic concentration, and therefore osmotic pressure, is negligible, Wilson hypothesized that the
swelling behavior of biological soft tissues can be described by adding a strain-dependent
pressure term to the biphasic model. In essence, intervertebral disc behavior can be fully
described by mechanical load, osmotic potential and strain-dependent permeability. A model was
developed and compared with the full mechano-electrochemical model by Frijins [98] and was
shown to be a suitable alternative and simplification. A lumbar disc model was further developed
[100] in ABAQUS using three primary material types: viscoelastic collagen structure, elastic non-
fribrillar solid matrix and osmotically prestressed fluid. The nucleus of the disc contained the
latter 2 material types, while the annulus contained all three, in varying amounts. The model was
further validated with experimental results [101, 102]. However, the lack of endplates or vertebral
bodies was a shortcoming in the model.
5.2. Finite Element Models of Impact Loading
Just as there are few experimental studies that focus on sub-traumatic IVD impact
loading, there, too, is little in the literature that focuses on FE analysis of this loading
environment. Most FE studies deal with injury mechanisms [87, 103], creep and stress relaxation
responses [48, 84, 92], or changes due to degeneration [72, 85, 104-106] or morphology [32, 66,
107]. This section will highlight the most relevant finite element analyses of IVD impact
mechanics.
33
Lee and colleagues [76] developed a poro-elastic model of the L3-L4 disc and L3
vertebra for the FE analysis of IVD impact response. Their model consisted of a porous nucleus
and annulus matrix, along with annulus fibers. The vertebral elements were made up of a porous
endplate and trabecular bone along with cortical bone. The solid sections of all constituents were
defined as linear elastic and defined with Young’s modulus and Poisson’s ratio. Neither swelling
pressure nor initial disc pressure were considered in this model. A triangular waveform axial
impact load was applied to the superior face of L3 with a variable duration (∆t = 1 – 200 ms). The
maximum compressive force was set to be 3000 N. Their results showed an increase in pore
pressure, dynamic stiffness, and stress with faster impacts.
Wang et al. [108] developed a three-dimensional FE model of a complete L2-L3 motion
segment – including facet joints – to analyze the mechanical response of the lumbar spine to
dynamic loading. The model was considered viscoelastic, in that the material properties of the
annulus fibers were defined by a Zener model, while the annulus and nucleus matrices were
defined using the Prony series. The rest of the model components were considered linear elastic.
The motion segment was given a preload consisting of 600 N axial and 60 N anterior shear. The
dynamic loading was simulated by applying a final net force of 2000 N axial, 200 N shear, and a
10º-flexion angle. These loads were applied at 0.3, 1, and 3 seconds. Higher intradiscal pressure,
posterior longitudinal ligament, and annulus matrix and fiber stresses were reported for the fastest
loading rate.
El-Rich and colleagues also used an L2-L3 full motion segment model of the disc [109],
this time to analyze load sharing and injury risk during rapid sagittal movements as seen in frontal
or rear impacts (e.g.: car crashes). Vertebral components were defined via a visco-plastic material
law, ligaments were viscoelastic, and the disc components were governed by the Mooney-Rivlin
hyperelastic material model. Five degrees of flexion were applied on the superior face of L2, at
rates of 0.05, 0.5, and 5 º/ms. Their study found that stresses in the ligaments and intradiscal
34
pressure both increased with rotation rate. Yield and ultimate stresses were also surpassed in the
5 º/ms rate case.
Through all three studies highlighted here provide great insight into disc and spinal
motion segment response to impact loading conditions, they are not without limitations. Wang
notes that the loading rates presented in their work are more reflective of daily living activities
and cannot be applied to sudden loading conditions such as expected impact. The Wang and El-
Rich studies do not apply axial, purely compressive impact loads on the disc; this only occurs in
the Lee paper. While other loading modes (shear and flexion-extension) are certainly important,
they are not indicative of the highest magnitude loads imposed on HSBs.
The chief limitation of all three studies is the method in which the models are validated.
Lee compares ramp load data to a vertebral body FE model study by Hakim and King [110] as
well as creep data to another experimental study. The Wang model was validated by comparison
with experimental data from literature of cyclic and constant compressive strain rate loading. The
El-Rich group validated their model with cadaveric samples subjected to quasistatic loading
conditions (1.267 mm/s) to failure. None of these studies validated their FE model with actual
impact loading (sub-traumatic or traumatic), let along the type seen on HSBs.
35
Figure 5.1. Finite element mesh of osmo-poro-viscoelastic model from Schoeder et al. [100]. Analysis used
only ¼ of the whole disc, since it is symmetric about the transverse and mid-sagittal planes.
36
6. Project Objective and Specific Aims
The literature on dynamic loading and the mechanical response of the spine to such loads
is extensive. However, there is still little analysis of lumbar intervertebral disc biomechanics
under sub-traumatic, axial impact loads, particularly the type that affects the Naval HSB and
other similar working populations.
Developing a set of experimental and computational human IVD models that simulate the
dynamic impact loads imposed during HSB operations can provide a better understanding of
internal disc mechanics and, potentially, lumbar spine pain and injury patterns observed in HSB
personnel. This work will fill a void in the literature in understanding impact loading on the
lumbar intervertebral disc. The methods and findings from this work may be extended to non-
traumatic impact loading scenarios in other occupational environments (e.g.: pilots, astronauts,
and construction workers) and repeated loading conditions at lower frequencies [69, 81, 111,
112].
Therefore, the objective of this project is to characterize the mechanical response of the
lumbar intervertebral disc subjected to sub-traumatic impact loading conditions using both
cadaveric and computational models, and to investigate the possible implications of this type of
loading environment for low back pain. This will allow us to gain more insight into the changes
in mechanical behavior of disc tissue under impact loading (compared to static or quasistatic),
and ultimately use this information to inform updates and improvements to the guiding standards
on shock mitigation and exposure thresholds, such as ISO 2631-5.
To achieve the aforementioned objective, the following specific aims have been
proposed:
Specific Aim 1: Simulate HSC impact rates in the laboratory on a human, cadaveric,
lumbar IVD model, and effectively characterize the mechanical response of the lumbar
37
intervertebral disc subjected to impact loading conditions and observe the transition from
quasi-static to dynamic behavior. Data has previously been recorded from accelerometers placed
on various Naval HSBs during trial runs at sea. This data has been collected and processed, the
information being used to model a singular compressive impact event on the intervertebral disc.
Cadaveric specimens were obtained and subjected to impact load waveforms via a servohydraulic
mechanical testing apparatus. The stiffness and energy dissipation of the samples were calculated
and compared with values for normal loading conditions.
Specific Aim 2: Investigate the effects of disc creep displacement and corresponding
fluid loss on the mechanical response of the tissue to impact loading. Though the effects of
creep on IVD mechanics and the response to fast-rate loading have been investigated separately,
we were interested in the effect of tissue dehydration after creep on the impact response of the
disc, as this could have implications for changes in injury intolerance due to the time of day in
which transient shocks occur. We varied lengths of time of creep, and looked at the effect of fluid
and disc height loss, as seen during daily activity in a diurnal cycle, on disc compressive impact
mechanics.
Specific Aim 3: Develop and validate a Finite Element (FE) model of the
intervertebral disc to determine internal disc mechanics during impact loading. A poro-elastic
FE model of the intervertebral disc has previously been developed in our laboratory [105]. We
modified this preexisting model to enable investigation into disc biomechanics under impact
loading. Specifically, the model allows for the analysis of responses that are not possible with a
cadaveric system such as intradiscal pressure, interstitial fluid velocities, and stress distributions
in the various sub-structures of the disc. The model will be validated using experimental data
from simulated HSB impacts.
38
7. Aim 1: A Comparison of the Human Lumbar Intervertebral Disc Mechanical
Response to Normal and Impact Loading Conditions
The information contained in this chapter has been accepted for publication by the Journal of
Biomechanical Engineering, and will appear in the September 2013 issue.
7.1. Introduction
The United States Navy employs lightweight, low-occupancy, high-speed craft (HSC) for
missions on the open seas. While operating HSCs, occupants are frequently subjected to large-
magnitude accelerations that can be upwards of ten times the acceleration due to gravity, and are
typically less than 200 ms in duration [113]. These high-magnitude, high-speed impacts present a
great health risk to HSC occupants. A survey of self-reported injuries among special boat
operators [114] found that 95% of injuries requiring medical attention occurred on the job, while
performing functions pertaining to HSC operation. Of these, nearly 34% were lower back
injuries, many of them related specifically to the intervertebral disc (IVD). This is considerably
high when compared to 15 to 20% of adults in the general population who experience low back
pain and require medical attention annually [2, 23, 115]. It is believed that the high incidence of
lower back/discogenic pain stems in part from riding on rough seas and being subjected to
multiple impacts as the boats pitch and crash into the water [116]. Though these impact loads are
generally sub-traumatic, they are thought to cause cumulative damage and injury to the lumbar
spine [117].
Many ex vivo studies of dynamic loading on human and animal spines have been
analyzed in the context of pure axial compression. Cassidy and colleagues [21] and Lee and Kim
[76] demonstrated that the lumbar disc behaves with an increased stiffness and pore pressure
39
under fast-rate loading, representing a more glassy material than when subjected to more
moderate loading conditions. The dynamic loading frequencies of Costi [45] ranged from 0.001
to 1 Hz and are outside the range of those imposed on small high-speed craft, while the 20-N
amplitude of Kasra and colleagues [48] is below the magnitudes seen on HSCs. Experiments by
Elias [46], Pintar [118], Nightingale [75], and Yingling [50] examined the dynamics of cervical
discs, which exhibit different mechanics due to a smaller size and greater range of motion.
Developing a human, cadaveric experimental model of the lumbar IVD under the unique
operating conditions of HSCs will allow a better understanding of the spinal injury patterns
observed in HSC personnel. The aims of this study are twofold: (1) to simulate HSC impact rates
in the laboratory on a human cadaveric lumbar IVD model, and (2) to effectively characterize the
mechanical response of the lumbar intervertebral disc subjected to impact loading conditions and
observe the transition from quasi-static to dynamic behavior. We hypothesize that there is a
transition point for impact duration, where disc impact mechanical response moves from quasi-
static to dynamic behavior, and that it lies within the range of event durations experienced on
HSCs.
7.2. Methods
Impact Event Analysis
Data collected from four HSC test rides along various seaways were obtained for
characterization of typical high-speed boat impacts. Maximum boat speeds typically reached 30
knots. Most HSC personnel are in the seated position while the boat is navigating through
seaways, so data from a three-axis accelerometer, placed on the back of the seated boat operator,
was utilized. Only the z-direction (axial) data was used to simulate impact events in the
laboratory, as an initial assessment showed that accelerations in the horizontal (x-y) plane were
40
often an order of magnitude lower than the axial direction (Figure 7.1), which is consistent with a
previous analysis of HSC impacts [113]. Data was collected at 750 Hz and post-processed with a
250-Hz anti-aliasing filter.
Inspection of accelerometer data confirmed that typical impact events were between
50 ms and 200 ms in duration, in agreement with [113]. Impact events were modeled with a
triangular waveform for the simplicity of testing in the laboratory. Since force data was not
captured on any test runs, it was determined that the laboratory testing device would be operated
in displacement control during testing. As the transmissibility between the seat and the lumbar
disc could not be determined, physiologic displacements to yield forces that were sufficiently
high but would not result in traumatic injury to the disc were determined empirically.
Sample Preparation
Fresh-frozen, human cadaveric lumbar spines were obtained from an approved source
(NDRI, Philadelphia, PA) from donors whose death did not stem from any spinal pathology.
Tissues were visually assessed using fluoroscopic images (FluoroScan Imaging Systems,
Northbrook, IL) to ensure the discs were healthy and free of any herniations, osteophytes, or other
structural abnormalities. Five disc samples were obtained (average age: 64.6 ± 11.4, range: 59-
85) by removing all connecting muscles and ligaments. Posterior elements of the spine were
removed as well, yielding an anterior column unit (ACU), comprised of the disc along with its
intact adjacent superior and inferior vertebrae. This allowed for isolated analysis of intervertebral
disc mechanics, without factoring in the contribution of surrounding hard and soft tissues [45, 47,
77, 101, 119]. The free ends of the vertebral bodies were potted using Smooth Cast 300 (Smooth-
On, Inc, Easton, PA) to ensure the longitudinal axis of the ACU would be collinear with the
loading axis, simulating a follower load Samples were frozen at -20 °C until testing. Once
thawed, the samples were then placed into a custom fixture on a biaxial servohydraulic
mechanical testing system (Model 8874, Instron Corp., Norwood, MA).
41
Impact Sequence and Data Collection
To ensure discs remained hydrated throughout testing, they were sprayed periodically
with 0.01M phosphate buffered saline. Each sample was first subjected to a preconditioning
loading sequence (50 cycles, -50 N to -150 N compression, havertriangle waveform, 1Hz) to
eliminate any potential superhydration effects and restore normal disc mechanics [119, 120].
Each specimen then underwent an impact loading sequence while under a 50-N
compressive preload. These sequences consisted of a succession of impacts with duration, Δt (80,
160, 300, 400, 600, 800, and 1000 ms). This Δt range was chosen to incorporate impact events
within and above that seen on HSCs. The 1000-ms duration was used as the baseline for normal
loading in this experiment, as 1 s represents physiologic walking speeds [45]. Inertial properties
of the testing frame were accounted for by the Instron software. The sequence was randomized
for each sample, and each impact event within the sequence was separated by 3 s, to ensure the
disc had enough time to recover to its initial displacement and preload between events. Each disc
underwent a total of three impact sequences, varying the level of displacement with each run (0.2,
0.5, 0.8 mm). Input and output signals for each impact event were compared to each other and the
normalized root mean square error (RMSE) for each pair was calculated, to confirm the
capabilities of the loading frame in achieving the desired waveforms. The loading frame tended to
undershoot the desired displacement, particularly for the lowest displacement and faster impact
durations. However, no error for any impact event was above 7.5%, indicating a good fit between
input and output. The highest in displacement were seen at 0.2 mm (RMSE = 5.2 ± 1.8%), while
the largest errors among impact durations occurred at 80 ms (RMSE = 6.8 ± 0.6%). This was
deemed acceptable to perform the proposed study.
Data was collected at 5 kHz, and axial compressive stiffness, k, and energy dissipation,
ΔE – derived from the load-displacement data as the tangent at maximum load and the area
42
within the curve, respectively – were calculated using custom-made code written with MATLAB
software (version R2010b, The Mathworks, Natick, MA).
Compressive stiffness and ΔE for all impact events were normalized to the baseline
(Δt = 1000 ms) for their respective sample and level of displacement. ΔE was also normalized to
the achieved displacement. A repeated-measures two-way ANOVA and Bonferroni post hoc tests
were performed to analyze differences in the mechanical responses due to Δt and displacement
level. All statistical analyses were performed using GraphPad Prism (version 5.0, GraphPad
Software, La Jolla, CA) and significance was set at the 5% level.
7.3. Results
Peak axial loads on the disc averaged from 150 N at 0.2 mm to 700 N at 0.8 mm, which
are below failure loads, as desired. These loads did not vary significantly across Δt. Stiffness for
the baseline impact events ranged from nearly 500 N/mm (0.2 mm) to 850 N/mm (0.8 mm), and
values in this study fell within range of those seen in other published studies [31, 77, 121-124].
ΔE varied from 50 mJ at the smallest displacement up to 420 mJ at the largest. Impact duration
(p < 0.001) and displacement (p < 0.05) were shown to be a statistically significant source of
overall variation for the reported compressive stiffness values. Both parameters were also a
significant source of overall variation (p < 0.0001 for each) for IVD energy dissipation.
Normalized stiffness and hysteresis values for all impact scenarios are shown in Figure
7.2. There was a decreasing trend in dynamic stiffness as Δt increased, approaching baseline
compressive stiffness values. There was statistical significance at 0.5 mm for k between 80 ms
and the baseline (p < 0.01). Energy dissipation per unit displacement in the disc increased as Δt
increased. Statistical differences were shown between 80 ms and the baseline at 0.5 mm
(p < 0.05) and 0.8 mm (p < 0.001). At 80 ms, ΔE dropped 3-7% from the baseline for all three
displacement groups.
43
There was a rather large deviation in stiffness data at 0.2 mm displacement. This is likely
due to errors in achieved displacement from the mechanical tester, as discussed earlier, as well as
possible large variances in low-strain stiffness for discs of different initial hydration level.
Compressive stiffness at 800 ms was not closest to the baseline at 0.2 mm as expected. This is
also likely a result of the errors in achieved output at this displacement level; however, the exact
reason for this is unclear.
7.4. Discussion
The objectives of this study were to simulate the HSC impact loading environment on an
ex vivo model in the laboratory, investigate intervertebral disc mechanics, and determine if a
transition point between quasi-static and dynamic behavior exists under these unique loading
conditions. Additionally, the degree of axial displacement and its effect on IVD mechanical
response during impact was analyzed. Non-linearity can be seen at 0.5 and 0.8 mm, though not at
0.2 mm. This difference is likely due to the larger displacements providing more distinct toe and
linear regions on the load-displacement curve. Impact events were simulated at 80 and 160 ms,
and a range of longer durations at or near a more physiologic level were added for comparison.
HSC impacts adversely affect the IVD, as evidenced by prior work by the authors [125] as well as
the reported high incidence of lower back and discogenic pain among HSC operators [114].
Results from this ex vivo study show that between 80 and 160 ms, there is a distinct change in
mechanical response of the disc for the two larger displacement groups, particularly in energy
dissipation. This is in agreement with work by Kasra and colleagues [48] who concluded that
loads with duration above approximately 120 ms were not considered impact. While ΔE remains
at or near the baseline level for Δt above 160 ms, there is a significant decrease of 3-7% below
this value. These findings suggest that when the disc is subjected to impact loads faster than
44
160 ms in duration, the shock absorbing capabilities are significantly reduced, coupled with a
more modest increase in compressive stiffness. This change in disc mechanics occurs at Δt
coincident with HSC impacts. The disc transitions from viscoelastic behavior under moderate
loading conditions [94, 101, 126-128] to a more glassy material behavior. This phenomenon
likely results in a greater transmission of forces to the endplates, vertebral bodies, and
surrounding tissues, and can potentially explain the cause of lower back pain under these loading
conditions. The precise determination of this transition point is left for future studies. If a solution
can be developed to actively dampen impacts by slowing their duration to a range above that of
the transition point, the disc can still exhibit viscous damping as it would under normal activity.
The internal response of the tissue during HSC impact events is not known, and cannot be
ascertained with the results from this study. However, a study by Wuertz and colleagues [79]
revealed evidence of anabolic remodeling, minimal changes in disc structure, and increased
glycosaminoglycan content in the nucleus pulposus (NP) for physiologic levels of dynamic
compression. Repeated impact events on the IVD may therefore result in greater degradation
changes to disc structure, especially in the NP and the endplates, which are thought to be most
affected by this type of loading.
Determination of a constitutive model of the altered disc mechanical response to impact
loads is not attempted here and is saved for future investigation; however, it is worth noting
possible material models to consider. A hyperelastic model is appropriate for compressible, non-
linear elastic, fluid-filled tissues such as the IVD. The phenomenological Mooney-Rivlin model
can potentially provide a good description of the observed impact behavior. Hyperelastic models
are limited, however, in that they do not account for strain-rate dependency. A viscoplastic model
may also provide a good quantitative description of impact phenomena, in that it includes rate-
dependent behavior and is useful in systems subjected to high strain rates. The Johnson-Cook
model is worthy of consideration for this system; however, only the inelastic behavior is modeled
as strain-rate dependent.
45
HSCs and other vehicles also introduce whole body vibrations, and it is known that
operators of vibrational mechanical vehicles suffer from low back pain and accelerated disc
degeneration as well [129-132]. To our knowledge, however, there are few studies in the
literature [68] that investigate the effect of impact events on the IVD when combined with whole
body vibrations. A frequency analysis of HSC accelerometer data showed that many of the
impact events contain frequencies up to 30 Hz (Figure 7.3). Through modal analysis in both
experimental and finite element studies, Kasra and colleagues have reported the resonant
frequency of lumbar spine motion segments under axial loads from 20-25 Hz at a 50-N preload
[48]. Thus, it is possible that HSC impact events could be imparting further damage to the disc
via resonant disturbance.
Limiting factors of this study include the inherent variability of human cadaveric
specimens. Several aspects, including donor history and condition of the discs, could not be
controlled. The degenerative grade of the samples was not determined in this study; therefore, a
correlation between disc degeneration and the results could not be drawn. A bone-disc-bone
anterior column unit was used rather than a full motion segment. The rationale was to isolate IVD
mechanics during impact loading, as this is the area of focus for HSC personnel injury. It should
be noted; however, that the facet joints do play an important role in spinal mechanics [133, 134],
as they share 16% of the compressive load in a standing posture [135]. Different spinal levels
from several spines were used and, as a result, may have had different native biomechanical
properties. A matched comparison statistical analysis was used to account for these variances.
The specimen donor age range is higher than that of the at-risk HSC population. It is possible that
younger or less degenerated discs would require greater displacements or faster impacts in order
to see an adverse mechanical response. Though impact events were modeled with as much
fidelity as possible, the exact behavior could not be achieved in the laboratory setting. This is due
to several reasons: (1) the authors used a triangular waveform to model impact events; (2) there is
a lack of actual disc displacement data from HSC trial runs, as well as an explicit transfer
46
function relating boat seat displacements or forces to lumbar disc displacement or forces; (3) it
was unknown during the test runs whether the seat harnesses effectively eliminated decoupling of
the occupants from their seats, which could alter accelerations and forces at the disc level; and (4)
the exclusion of loading modes other than axial compression. The acceleration profiles in the
horizontal plane (x and y axes) were not used in this study due to their relatively low magnitude
compared with axial accelerations. However, inclusion of a 3-D acceleration profile may be
helpful in future studies for a full understanding of disc impact mechanics in the HSC
environment. IVD mechanical behavior was analyzed only in the context of single impacts. It
would be beneficial to explore the mechanical effects of repeated impact loading and recovery on
overall disc mechanics.
The findings in this study on disc biomechanics can be used to further inform and
reassess injury tolerance criteria on high speed craft. Currently, the most widely used standard to
address this occupational hazard is ISO 2631-5 [116]. This standard is limited, however, because
it only accounts for magnitude and number of impact events, not the frequency or duration.
In summary, the observed response of the lumbar intervertebral disc suggests the
mechanical behavior of this viscoelastic soft tissue is adversely affected under impact loading
conditions. Specifically, the IVD reacts with higher stiffness and lower ΔE, compared with
physiologic loads. This results in the disc losing its ability to dissipate energy and act as a shock
absorber for the spine, which may exacerbate abnormal loading on the surrounding hard and soft
tissues, and can help begin to explain the high incidence of low back pain and accelerated disc
degeneration among HSC operators and other individuals who typically experience similar
loading environments. In this study, a transition range between quasi-static and impact behavior
has been suggested, and can be useful in providing specific design criteria for the development of
active damping mechanisms in shock mitigating systems for HSCs and other similar vehicles.
47
Figure 7.1. Representative acceleration waveforms in x, y, and z directions on a high speed craft. The z-
axis accelerations are generally an order of magnitude higher than x and y. Top insert: coordinate axis for
this system. Bottom insert: sample impact magnified for clarity.
48
Figure 7.2. Comparison of load-displacement curves between 80ms and 1000ms (top), along with results
for k (middle), and ΔE (bottom). Values are normalized to the baseline 1000ms impact (represented by
dashed lines). Error bars indicate standard error. **: p < 0.01, ***: p < 0.001.
49
Figure 7.3. Representative impact event (top) and its corresponding frequency spectrum (bottom). The
signal consisted of high frequencies at 10-15 Hz and 20-30 Hz, which were below noise frequencies (< 50
Hz). Frequency analysis was performed via fast Fourier transform with a custom-written code in
MATLAB.
50
8. Aim 2: The Effect of Creep on Human Lumbar Intervertebral Disc Impact
Mechanics
The information contained in this chapter is in revision for publication in the Journal of
Biomechanical Engineering.
8.1. Introduction
The intervertebral disc (IVD) can be modeled as a biphasic tissue, with both a solid and a
fluid phase [34, 99, 136]. The nucleus pulposus (NP) and annulus fibrosus (AF) contain a
significant amount of water, comprising 80% and 70% of tissue wet weight, respectively [23].
Aggrecan, the major proteoglycan in the disc [22], is responsible for maintaining tissue hydration
via osmotic potential generated by its charged glycosaminoglycan side chains [137]. This high
molecular weight molecule is found primarily in the NP and significantly contributes to
intradiscal pressure and equilibrium elastic modulus [138] as well as time-dependent behavior in
the disc [42, 45, 119, 127]. The poroelasticity and osmotic potential result in the ability for fluid
to flow into and out of the disc; these properties are directly related to IVD deformation [139].
During daily loading, a substantial volume of fluid leaves the disc [35, 140, 141], predominantly
through the endplates [29]. While under a static compressive load, the IVD responds with
continuous creep displacement resulting in decreased pressure in the NP, and an increase in
compressive stiffness [42].
The mechanical response of the IVD at different loading rates has been studied
extensively [66, 109, 127, 142, 143]. Due to the viscoelastic behavior of the tissue, the disc
compressive stiffness increases with loading rate. Increased tensile stiffness was observed in
individual lamellae, with increasing strain rate [27]. The compressive stiffness of bovine [127]
51
and human discs [49] were found to increase with loading rate, up to 73% strain/s. High
frequency or impact loading on the lumbar disc results in higher stiffness and lower energy
dissipation [144] while pore pressure in an FE model was shown to be relatively independent of
loading rate [76].
Though the effects of creep on IVD mechanics and the mechanical response to fast-rate
loading have been investigated separately, we were interested in the effect of tissue dehydration
after creep on the impact response of the disc. Therefore, we have performed an ex vivo study to
investigate the effects of disc creep displacement and corresponding fluid loss on the mechanical
response of the tissue to impact loading. Injury due to impact loading may ultimately be related to
the dehydration level of the disc.
8.2. Methods
Fresh-frozen human lumbar spine segments from 11 donors with no history of spinal
injury were obtained from an approved source (NDRI). Individual discs were dissected with their
adjacent vertebrae intact and posterior elements were removed, yielding anterior column units
(ACU) for testing (age: 56.7 ± 8.8, n=24, male and female; Table 1). This allowed for isolated
analysis of intervertebral disc mechanics, without factoring in the contribution of surrounding
hard and soft tissues [45, 47, 77, 101, 119].
Prior to testing, each sample was submerged in a fluid bath of phosphate-buffered saline
(PBS) and protease inhibitors overnight under a 50N load at 4°C, in order to equilibrate the
hydration level [2, 145]. Samples were imaged with fluoroscopy (FluoroScan Imaging Systems,
Northbrook, IL) and the initial disc height was calculated from the sagittal plane image as the
average of the anterior, middle, and posterior heights (Figure 8.1). Discs were randomly assigned
to one of six testing groups (n=4 per group), corresponding to the amount of time in which
52
samples would be subjected to a static 400N load and undergo creep (tcreep = 0, 3, 6, 9, 12, 15 h).
The 400-N load signifies moderate daily activity [47, 48, 89]. A group assignment algorithm was
implemented such that no group could have more than one disc from the same donor spine. Tests
were administered in a bath of PBS and protease inhibitors at room temperature, which was fixed
to a custom-made jig on a servohydraulic mechanical testing device (Instron 8874, Norwood,
MA).
At the end of tcreep, each sample was subjected to an impact loading sequence, consisting
of singular impact events with varying duration (timp = 80, 160, 320, 400, 600, 800, 1000ms; 1mm
amplitude; 3s apart). The order of the impacts was randomized for each sample. Preliminary work
showed a 2.6% RMSE between the input and output displacement signals, indicating the testing
apparatus was successful in achieving the desired impacts. Impacts transmitted loads up to
4000 N in compression, which is in the physiological range [135], and included a small amount of
tension, up to 150 N.
Parameters indicating mechanical response were calculated for each impact within the
sequence (Figure 8.2). The neutral zone (NZ) has been defined by White and Panjabi [121] as a
measure of relative instability of the tissue. NZ was calculated as the change in displacement at
zero load [146]. Hysteresis (ΔE) is a measure of energy dissipation. The toe region (low strain)
compressive stiffness (ktoe) and linear region (high strain) compressive stiffness (klin) were also
calculated.
Statistical software (GraphPad Prism) was used to measure Pearson’s correlation between
the measured parameters and all values of tcreep and timp. For each mechanical parameter and time
variable pairing, the pooled correlation (rp) was used, which is defined as
[ ] (8.3)
where:
53
∑[( ) ]
∑( ) (8.4)
[
] (8.5)
and ni and ri are the number of samples and the correlation coefficient, respectively, for the ith
grouping [43].
8.3. Results
Axial strain increased with tcreep, up to 20% (r = 0.942, p < 0.01; Figure 8.3) which is
consistent with other published literature [35, 53, 105, 127, 141]. Deformation is coupled with an
increase in fluid loss from the disc due to its poroelastic nature [147], and prior studies have
shown that creep displacement correlates to water loss from the disc [119, 148].
Influence of tcreep and timp
As creep displacement increased, NZ increased as well (rp = 0.886, Figure 8.4a). This
parameter showed a negative correlation with timp (rp = -0.924, Figure 8.4b). There was a positive
correlation between ΔE and both tcreep and timp (rp = 0.930 and 0.826 respectively, Figure 8.5). A
decline was shown in ktoe as both tcreep and timp increased (rp = -0.954 and -0.742 respectively,
Figure 8.6). Data showed a positive correlation between klin and tcreep (rp = 0.788) but the linear-
region stiffness had no strong trend with impact duration (rp = 0.404, Figure 8.7). Linear region
stiffness values in this study fell within the upper end of the range seen in other published studies
[31, 77, 121-124].
8.4. Discussion
54
Our ex vivo investigation of creep and fluid loss demonstrated that IVD impact
mechanics are altered as the disc loses interstitial fluid. Low-strain mechanics of the disc are
primarily governed by the nucleus [149], which is the pressurized and highly hydrated portion of
the tissue. The NP has a high osmotic pressure due to the presence of proteoglycans in the
extracellular matrix, enabling the disc to retain water. As a result, the NP behaves like a semi-
incompressible fluid [150]. NP pressure increases during small deformations; however, this effect
is negated by loss of fluid during creep, which would reduce nucleus hydrostatic pressure [151].
This is supported by our findings, which showed that across all impact durations, ktoe decreased as
time of creep increased. These mechanical changes can lead to decreased mechanical stability and
potential low back pain [152, 153].
At higher strains, IVD mechanics are governed more by the annulus fibrosus (AF).
Increased compression causes the disc to bulge radially, as the NP pushes outward on the annulus
and puts the AF collagen fibers under greater stress. Though there is an overall positive
correlation between klin and tcreep, the linear-region stiffness actually begins to decrease slightly
after nearly 10 hours of creep deformation. We believe this is due to the countering effect of
decreased hydrostatic pressure in the NP over time caused by the loss of fluid leading to the
nucleus exerting less radial stress on the annulus. Because the loss of fluid and corresponding
decrease in NP pressure does not happen immediately, we suspect this explains the initial
increase and subsequent moderate decrease in AF stress as indicated by klin.
The NZ increased with tcreep, indicating the disc becomes increasingly compliant with
fluid loss. This finding is supported in previous literature showing that the disc is less clinically
stable after a period of loading, which would correspond to a higher NZ [77, 154]. Energy
dissipation is shown to increase with creep and loss of interstitial fluid. With reduced clinical
stability and stiffness due to fluid loss, the disc will deform and dissipate more under loading.
Depressurization in the nucleus is associated with increased stress distributions in the AF and
55
increased IVD deformation [77, 155], which supports the findings in this study of a positive
relationship between tcreep and both klin and ΔE.
Reported trends for measured parameters as a function of loading rate were as predicted
and agree with previous literature [45, 49, 50, 108, 125] with the exception of NZ. Slower
impacts allow for the time-dependent viscoelastic properties to take hold, while the fastest
impacts result in a more hyperelastic mechanical response, as evidenced by the trends for ΔE and
ktoe. Energy dissipation was shown to decrease ~15% with shorter impact durations, indicating the
mechanics of the disc are altered during fast-rate impact loading. As noted, NP interstitial fluid
dissipation is limited during fast-rate loading and this is also reflected in the positive correlation
between ktoe and timp. Since impact event strains were small (~ 10%), the stresses in the annulus
did not differ greatly among impact durations. This is seen in the relatively weak positive
correlation between klin and timp.
It was desired to assess the relationship between some of the measured parameters. The
authors assumed a positive relationship between energy dissipation and neutral zone. As the disc
becomes more unstable (higher NZ), energy dissipation should increase as well. Additionally, it
was expected that a more unstable disc would be correlated with decreased stiffness in the low-
strain region. We found a slight negative correlation between NZ and ΔE, contrary to our
hypothesis (r = -0.263, p < 0.001), while the relationship between NZ and ktoe agreed with our
prediction (r = -0.388, p < 0.001; Figure 8.8).
Limiting factors of this study include the inability to control for the inherent variability of
human cadaveric specimen in addition to donor history and level of degeneration of each of the
discs. Different spinal levels from several spines were used and may have had different native
biomechanical properties. The random assignment of discs to testing groups, ensuring there was
no more than one disc from each spine in each group, helped to mitigate these factors. Each
specimen was allowed to equilibrate in a saline bath prior to testing to ensure the discs were fully
hydrated; however, we were not able to ensure the discs were at steady state prior to testing.
56
Previous studies [119, 156] have shown that several diurnal cycles are required for an ex vivo disc
model to achieve steady state. It is therefore possible that some of the specimens used in this
study were over hydrated, which could alter the mechanics. This study also simplified the
analysis of disc biomechanical behavior by utilizing a vertebra-disc-vertebra ACU. Though the
removal of posterior elements allows for isolated study of disc tissue biomechanics [157], it
should be noted that the surrounding tissues of the lumbar spine – including facets, ligaments, and
musculature – do play a role in the overall mechanical response [133, 134]. Additionally, the
specimens were only loaded axially, ignoring any shear and torsional loading effects during
impact events.
This work suggests that fluid content in the disc is responsible for both creep and impact
mechanical responses. The higher instability and energy dissipation after longer periods of creep
may indicate that the risk of lower back injury due to discogenic pain increases later in the diurnal
cycle, when an individual has been actively loading their spine for several hours. Changes in
amount of interstitial fluid were achieved by way of creep displacement and loss of disc height,
which are associated with increases in hydrostatic pressure in the disc. Molecular changes to the
disc as a result of degeneration, such as the loss of proteoglycans, would also affect the fluid
content of the disc by way of a decrease in osmotic potential. Future work should include the
analysis of the effect of disc degeneration on impact mechanics.
57
Figure 8.1. X-ray of disc (sagittal section) showing measurements of anterior, middle, and posterior
heights. The radiopaque object at the left is a reference metal rod with a diameter of 2.8 mm.
58
Figure 8.2. Schematic of a 1000-ms impact event showing calculation methods for NZ, ΔE, ktoe, and klin.
59
Figure 8.3. Axial strain versus tcreep. Results showed a strong positive correlation between the two
parameters.
60
Figure 8.4. Neutral zone (NZ) was positively correlated with (A) tcreep (some time points omitted for clarity)
and negatively correlated with (B) timp.
61
Figure 8.5. Energy dissipation (ΔE) was positively correlated with both (A) tcreep (some time points omitted
for clarity) and (B) timp.
62
Figure 8.6. Toe-region stiffness (ktoe) was negatively correlated with both (A) tcreep (some time points
omitted for clarity) and (B) timp.
63
Figure 8.7. Linear-region stiffness (klin) was positively correlated with (A) tcreep (some time points omitted
for clarity) but showed no strong correlation with (B) timp.
64
Figure 8.8. NZ showed a negative correlation with both (A) ΔE and (B) ktoe.
65
9. Aim 3: Development and Validation of a Poroelastic Lumbar Disc Finite
Element Model for Impact Mechanical Response Analysis
9.1. Introduction
Low back pain is a problem that affects 15-20 % of adults in the United States [2,
115, 158]. Additionally, acute spinal injury due to vibration and high-rate impact
exposure has been shown among tractor drivers, construction workers, and other similar
working populations in several epidemiological studies [159-161]. Mechanics of the
lumbar spine have also been quantified under impact loading conditions. Canine lumbar
discs were loaded to failure at rates up to 500 mm/min in a study by Cassidy [162], which
found that compressive modulus and maximum stress increased with loading rate. Duma
[163] analyzed failure mechanisms in the lumbar spine subjected to loads as high as
12 kN and applied at 1 m/s. Pintar and colleagues [164] studied lumbar spine injury
threshold and how it was affected by age, gender, and loading rate, the latter causing a
reduction in injury threshold. These tests were done on head-neck complexes and loaded
up to 8 m/s. Ranu [67] used loads up to 30 kN and demonstrated that intradiscal pressure
within the lumbar disc increases linearly with increased load. Yingling and colleagues
[165] investigated the effect of loading rate on compressive mechanics in the disc at
loading rates up to 16 kN/s and came to similar conclusions as the other studies.
Non-traumatic, transient impact loading may also cause changes in disc
morphology and mechanics, and has been highlighted in several studies. A study by
Brinckmann [82] used radiographs to show a significant decrease in disc height following
miners’ exposure to mechanical shocks while on the job. Kemper and colleagues [166]
66
tested human lumbar functional spinal units in compression at 6.8 sec-1
(0.5 mm
displacement) and 13.5 sec-1
(1 mm) strain rates. The compressive tests were non-
destructive, that is, the discs were not loaded to failure. The results showed that
compressive stiffness increases with loading rate. Previous work by the authors [144] has
shown an increase by as much as 20% in stiffness and a 5% decrease in energy
dissipation in the disc as a function of faster impact events. These types of shocks may
lead to internal damage, injury, and even discogenic pain, as seen in a study by Ensign
[10], which showed the nearly 20% of injuries among U.S. Navy high speed boat
operators that required medical attention were related to operations on the craft itself.
These injuries, most of which were not acute damage from a severe shock, were caused
by the high-rate yet sub-traumatic impact events experienced when the craft pitched and
crashed in rough sea states.
Several investigators have used finite element (FE) models to analyze impact
loads on the lumbar spine. Lee and colleagues [167] developed a poro-elastic model of
the L3-L4 disc and L3 vertebra for the FE analysis of IVD impact response. Their model
consisted of a porous nucleus and annulus matrix, along with annulus fibers. The
vertebral elements were made up of a porous endplate and trabecular bone along with
cortical bone. The solid sections of all constituents were defined as linear elastic and
defined with Young’s modulus and Poisson’s ratio. A triangular waveform axial impact
load was applied to the superior face of L3 with a variable duration (∆t = 1 – 200 ms).
The maximum compressive force was set to be 3000 N. Their results showed an increase
in pore pressure, dynamic stiffness, and stress with faster impacts. Wang et al. [143]
developed a three-dimensional FE model of a complete L2-L3 motion segment –
67
including facet joints – to analyze the mechanical response of the lumbar spine to
dynamic loading. The model was considered viscoelastic, in that the material properties
of the annulus fibers were defined by a Zener model, while the annulus and nucleus
matrices were defined using the Prony series. The rest of the model components were
considered linear elastic. The motion segment was given a preload consisting of 600 N
axial and 60 N anterior shear. The dynamic loading was simulated by applying a final net
force of 2000 N axial, 200 N shear, and a 10º-flexion angle. These loads were applied at
0.3, 1, and 3 seconds. Higher intradiscal pressure, posterior longitudinal ligament, and
annulus matrix and fiber stresses were reported for the fastest loading rate. El-Rich and
colleagues also used an L2-L3 full motion segment model of the disc [109], this time to
analyze load sharing and injury risk during rapid sagittal movements as seen in frontal or
rear impacts (e.g.: car crashes). Vertebral components were defined via a visco-plastic
material law, ligaments were viscoelastic, and the disc components were governed by the
Mooney-Rivlin hyperelastic material law. Five degrees of flexion were applied on the
superior face of L2, at rates of 0.05, 0.5, and 5 º/ms. Their study found that stresses in the
ligaments and intradiscal pressure both increased with rotation rate. Yield and ultimate
stresses were also surpassed in the 5 º/ms rate case.
Through all three studies provide great insight into disc and spinal motion
segment response to impact loading conditions, they are not without limitations. Wang
notes that the loading rates presented in their work are more reflective of daily living
activities and cannot be applied to sudden loading conditions such as expected impact.
The chief limitation of all three studies is the method in which the models are validated.
Lee compares ramp load data to a vertebral body FE model study by Hakim and King
68
[110] as well as creep data to another experimental study. The Wang model was validated
by comparison with experimental data from literature of cyclic and constant compressive
strain rate loading. The El-Rich group validated their model with human cadaveric
samples subjected to quasistatic loading conditions (1.267 mm/s) to failure. None of these
studies used cadaver specimens, subjected to impact loads, to validate their FE model.
This may have limited the fidelity of these impact models.
There are two objectives in this study. The first is to develop a finite element
model of the lumbar intervertebral disc and validate it using experimental data from
cadavers subjected to sub-traumatic impact loading. The second goal is to characterize
the internal mechanical response of the disc under impacts of varying durations.
9.2. Methods
9.2.1. Model Geometry and Material Properties
An axisymmetric, poroelastic model of a vertebra-disc-vertebra motion segment
was created based on an existing model of L3-L4 for the analysis of changes in disc
mechanics due to progressive degeneration [156] using ABAQUS software (v. 6.11,
SIMULIA, Providence, RI). Several studies [94, 95, 168] have used poroelastic models to
more accurately represent disc material properties and enable the influx and efflux of
fluid in the tissue compared to simpler elastic or neo-Hookean models. The model
geometry consisted of the nucleus pulposus (NP), annulus fibrosus (AF), annular fibers,
adjacent bony and cartilaginous endplates (EB and EC, respectively), and trabecular and
cortical portions of the corresponding vertebrae (Figure 9.1). Posterior facets were not
69
included in this model. Though the facet joints play a role in spinal mechanics [133, 134],
they share only 16% of the compressive load in an upright standing posture [135]. The
functional spinal unit was made up of 2585 4-node, displacement and pore pressure
(CAX4P) elements and 3045 nodes.
All component materials were modeled as a linear elastic solid matrix with fluid
filled pores. Linear elastic properties are defined by Young’s Modulus and Poisson’s
ratio, while permeability is defined by an initial void ratio (e0) and initial hydraulic
permeability (k0). The nucleus, annulus, and cartilaginous endplate additionally
incorporated strain-dependent permeability. The endplates were given an orthotropic
permeability to reflect their preferential axial fluid flow [38, 169], while the nucleus and
annulus have isotropic permeability definitions. The annular fibers were defined as
tension-only rebar elements. Material properties were determined from selected FE
studies [109, 143, 147, 156, 167] and selected such that the model response would
provide a good fit to the experimental validation data (Table 9.1).
9.2.2. Model Validation
The model was validated against experimental results from impact events
imposed on individual human lumbar motion segments (n = 4, age = 30 ± 2.3 yrs., one of
each level from L1-L2 through L4-L5; Thompson grades 1 and 2). Motion segments were
dissected and potted in hard plastic (Smooth-On, Inc., Easton, PA) and tested in a
servohydraulic biaxial mechanical tester (Instron 8874, Instron, Corp., Norwood, MA).
Each specimen was placed under a 400-N pre-load to simulate body weight [63, 170,
171] and then subjected to a sequence of impact events (Δt = 80, 160, 320, 500, 1000 ms)
in random order. Each impact event was represented as a triangular waveform with a
70
displacement of 1 mm. The FE model was subjected to the same loading conditions, and
the displacement and axial stress response were plotted against the cadaver specimens
(Figure 9.2). A tolerance interval at ± 5% of the mean load-displacement curves for each
impact duration group was used to evaluate an acceptable model fit. Loading and
unloading portions of the model response curves were within the experimental corridor at
both 80 and 160 ms. At 320 ms, the loading portion provides an acceptable fit while the
unloading portion begins to fall outside of the experimental corridor. Comparisons at 500
and 1000 ms show poor fits in both loading and unloading portions of the response, due
to the dominant non-linear behavior in the experimental group present at these slower
speeds. Thus, our model was determined to accurately simulate sub-traumatic impact
events below 320 ms in duration.
9.2.3. Loading and Boundary Conditions
The bottom surface of the inferior vertebra was rigidly fixed in all displacements
and rotations. The internal nodes about the axis of symmetry had a fixed boundary
condition to restrict movement in the radial direction. The top surface of the superior
vertebra was subjected to a compressive pressure of 0.6 MPa to represent moderate daily
activity loading [170]. With the sustained functional load, the model was then subjected
to an impact event as described above, with varying durations (Δtimp = 40, 80, 120, 160,
200 ms). Time histories at each node for change in fluid volume (Vfluid), von Mises stress
(S), and pore pressure (POR) were measured in each simulation. Vfluid at a given step i is
calculated via the change in void ratio (VR):
71
,
where VR is defined as:
.
and Vsolid is assumed to be constant, so any change in VR is considered to be solely
caused by a change in Vfluid.
9.3. Results
There were no significant differences in S or POR response among the range of
impact event durations. Figure 9.3 shows the maximum von Mises stress averaged across
all nodes in the NP, AF, and EC. Highest Savg values were seen in the AF at nearly
1.5 MPa, followed closely by EC; the stress response in the NP was the lowest at
~0.25 MPa. Contour plots of the spatial distribution showed that the greatest nodal
stresses in the NP occurred at
. AF nodal stresses were higher near the AF-EC
interface, particularly with increasing radial distance from the center.
Pore pressure response is summarized in Figure 9.4. The NP, with the highest initial
fluid volume, predictably had the greatest change in average pore pressure at nearly
2.5 MPa. AF pore pressure was ~1.25 MPa – nearly half that of the NP. The highest
nodal POR values similarly occurred at
.
72
Fluid loss was negligible during all impact simulations. Figure 9.5 shows the
percent change in Vfluid for NP and AF during the 40-ms and 200-ms impact events.
There were no cases in which the change in Vfluid was more than 0.015%.
9.4. Discussion
We have successfully developed and validated a poro-elastic FE model of the
lumbar intervertebral disc for analysis of internal mechanical response during impact
loading conditions. Unlike previous FE studies in the literature, the authors utilize
experimental impact loading scenarios in order to validate the model. We allow for the
estimation of internal stresses and stress distributions throughout the functional spinal
unit which can be compared to local failure properties for the disc components. This
analysis can ultimately contribute to expanding the understanding of IVD mechanics and
injury mechanisms during transient shock loading. Limitations of this study include the
use of an axisymmetric geometry as opposed to a more robust 3-D model, which has been
employed by several investigators [63, 69, 71, 86, 101, 102, 110, 167, 172, 173], as well
as the employment of linear elastic properties for the solid portions of the disc. The IVD
has a known non-linear behavior [87, 101, 134, 143, 173, 174] and even under fast-rate
transient shocks the disc will still present non-linearities in the biomechanical response.
The use of a neo-Hookean or viscoplastic material law should be considered in future
work. A rate-dependent material law will allow for the comparison of impact loads seen
in this study to those that are longer in duration and allow for a wider application of the
FE model.
73
Our analysis of IVD internal mechanics shows that the average von Mises stress
in the AF and EC are much higher than the NP, while the pore pressure in the NP is
higher than that of the AF and EC. This phenomenon is due to the NP having a lower
modulus than either of the other two disc components, while simultaneously having a
higher void ratio (and, therefore, fluid volume). Values for POR in the nucleus are in
agreement with those of the FE impact study by Lee [167], and even demonstrate the
same lack of variation with impact duration at these non-physiological rates. Pore
pressure in all disc components was higher than the intradiscal pressures reported by
Schroeder [173] and Wilke [175], indicating that impact loads induce much greater
internal pressures than quasi-static loading or other daily activities such as lifting an
object or climbing stairs. This is likely due to the lack of fluid movement in the tissue
even at 10% strain, as seen in the results. The fluid, which is incompressible, takes on a
great amount of stress and results in the higher internal pressures seen in this model. This
is contrasted by typical fluid exchange in the disc during daily loading, which is
substantial [35, 37, 176], reaching nearly 16% in the highly hydrated NP [156] and
causing a large drop in hydrostatic pressure [177].
Bony elements were not included in our analysis, nor were ligaments or posterior
facets included in the model itself, since the objective was to characterize the internal
mechanical response of the IVD. However, a better understanding of the response in the
trabecular and cortical bone may provide more insight into lumbar spine impact
mechanics, since several epidemiological studies have shown that the injury mechanism
in many transient shocks involves fractures in the vertebral bodies [10, 159-161]. The FE
analysis by Lee [167] showed that, while pore pressure in the nucleus does not vary
74
significantly with impact duration, in the cancellous bone, this parameter is influenced
heavily by the loading rate.
Impact shocks have been shown to greatly affect the lumbar disc and can lead to
acute failure of the tissues, as seen in both experimental and FE studies. Our model, being
validated against impact loads instead of physiological conditions, provides a better tool
for analysis of IVD internal mechanics under transient shocks, and may aid in improved
determination of injury mechanisms.
75
Figure 9.1. Axisymmetric model of lumbar intervertebral disc consisting of nucleus, annulus, and superior
and inferior endplates and vertebrae.
76
Figure 9.2. FE model validation data, showing an acceptable fit in both loading and unloading for impact
durations below 320 ms.
77
Figure 9.3. Stress response in the disc, showing maximum Savg for the NP, AF, and EC (top) along with
stress distribution profiles of the NP and AF for both 40 and 200 ms (bottom). Both contour plots are
displaying t =
.
78
Figure 9.4. Pore pressure response in the disc. Maximum ΔPOR averaged across the nodes in each disc
component are given (top) along with POR distribution profiles of the disc for the 40 and 200 ms impact
events (bottom). Both contour plots are displaying t =
.
79
Figure 9.5. Percent change in Vfluid over time for the NP and AF at 40 and 200 ms. Fluid loss was negligible
during impact events.
80
Table 9.1. Finite element model material properties.
E (MPa) ν e0 k0 (m4/(N/s))
Nucleus Pulposus 2 0.49 4 1.20E-15
Annulus Fibrosis 8 0.45 2.33 2.00E-16
Annulus Fibers 200 0.1
Cartilaginous Endplate 5 0.17 4 1.43E-13
Bony Endplate 10000 0.3 0.05 6.43E-16
Trabecular Bone 100 0.2 1 2.00E-07
Cortical Bone 10000 0.3 0.05 6.43E-16
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10. Discussion
The body of work presented here investigates IVD mechanical characterization under
non-acute transient impact events. In a larger context, this work also begins to address the
implications of these unique loading conditions for the issue of lower back and discogenic pain.
The findings from this project have shown the changes in disc biomechanics under sub-traumatic
impact loads. Due to the abundance of interstitial fluid and the high rate at which the loads are
applied, the NP behaves as a nearly incompressible material, causing a rise in low-strain stiffness
and a decrease in energy dissipation. These factors can contribute to greater forces transmitted to
the bony elements. It is unknown, however, if the forces are actually greater and approach the
yield stress; this analysis was not attempted here and is saved for future work.
Significantly greater stresses and pore pressures during impact loading are also
experienced in the AF and endplates. The latter can be particularly troubling, since the endplates
provide the primary nutritional pathway for the disc. These non-physiologic stress states could
potentially lead to tissue damage or occlusion in the endplate, which can cause cell death and
eventual disc degeneration [64, 80, 146, 178]. It would be beneficial to also understand what
effect the increased stress and pore pressure have on the extracellular matrix of the disc tissues,
particularly proteoglycans.
Changes in IVD impact mechanics with increased interstitial fluid loss due to creep
appear to counter the adverse effects noted above. HYS was shown to increase and toe stiffness
decrease with additional creep, while there was only a negligible change in linear stiffness. This
would indicate a recommendation for working populations who experience repeated, transient
shocks to avoid this type of activity until later in the workday, allowing for more time for fluid to
be driven out of their discs. There is caution in using this approach, however, as interstitial fluid
efflux also causes an increase in neutral zone, or disc laxity. More laxity in the disc can lead to
82
different mechanical problems such as increased clinical instability during axial loading [77, 87,
179].
The primary focus of this work has been the response to impact loading conditions from
intervertebral disc. However, the spinal column is also comprised of vertebral bodies, posterior
elements, and ligaments, all which are important for overall mechanical function. The posterior
facets do play a role in spinal mechanics [140, 180], as they share up to 16% of the compressive
load in a standing posture [36]. The vertebral bodies themselves are often the first sites of failure
in the spinal motion segment during high-rate or high-magnitude loading [10, 65, 66, 109, 162,
165, 181]. Because the intervertebral disc during impact conditions has been shown to have less
energy dissipative properties [144], it is likely that more load is being transferred to the
surrounding tissues, such as the vertebrae. A better understanding of the effects of the impact
loading environment on the vertebral bodies would aid in improved determination of injury
mechanisms in the lumbar spine. Integrity of the spinal ligaments is also important for overall
spinal function and disc stability. Though there is less of a focus on spinal ligaments in the
literature, work by Bass [182, 183] and El-Rich [109] has shown that the stiffness and failure
stress of these ligaments increases under fast-rate loading, and is particularly more common under
flexion-extension movements.
Ultimately, this work will be used to inform updates to ISO 2631-5, currently widely
used for seat design for HSBs and other similar craft. As explain earlier, the standard is limited in
that it does not account for the duration of transient shocks when estimating an individual’s
exposure threshold. The work has shown that, in addition to acceleration or force magnitude,
impact shock duration (acceleration rate, or jerk) is an important factor determining in lumbar
IVD mechanical response, and therefore affects injury tolerance as well. It is recommended that
these findings be incorporated into the next ISO standard that addresses exposure to transient
shocks.
83
10.1. Limitations
The ages of the cadaver specimen use in Aims 1 and 2 were fairly higher than the typical
HSB occupational population. Because the test samples were comparatively older than the target
population, they are likely in a more degenerative state. This would indicate slightly altered disc
mechanics, including less hydration and a stiffer annulus [19, 53, 85, 126, 156, 158, 181, 184].
Therefore, it is possible that our results are not completely indicative of what occurs to HSB
personnel. Our results in effect present a worst case scenario, demonstrating IVD mechanics for
an individual with discs in worse condition that the average HSB occupant. It should be noted,
though, that the cadaver specimen used to validate the FE model in Aim 3 were younger and
closer to the target population age range. Furthermore, the overall goal was to characterize
general IVD mechanics during impact loads, without regard for age or degenerative state.
The sub-traumatic impact shocks imposed on IVDs in this work were intended to mimic
those seen on Naval HSBs. However, there was no direct method of measuring these shocks on
the lumbar disc during trial boat runs. Thus, impact loads on the lumbar disc had to be
approximated. There was no known method to estimate forces from the given accelerations;
therefore, it was decided to use displacements for testing. In our initial approach, data was taken
from the accelerometer rigged to the boat deck. A transfer function from the ISO 2631-5 standard
[58] and based on a recurring neural network [59] was used to approximate accelerations at the
lumbar disc. Then, to obtain displacements, a numerical double integration was performed on the
transformed data using a technique to minimize the propagation of noise [185]. Unfortunately, the
resultant data yielded some displacements as high as 12mm at the disc level, which is not
physiologically relevant. It is unclear whether the transfer function step or the numerical
integration step was the cause of the error. The method to simulate impact loads in the laboratory
ultimately involved an iterative process. Using a triangular pulse in displacement control with
durations within the range of those measured on HSBs, the pulse amplitude was modulated until
we obtained a reasonable stress response. The final criteria for a HSB impact load was one that
84
(1) had a haver-triangle waveform; (2) was within the pre-determined duration range; and (3)
imparted loads which were deemed to be non-injurious, that is, did not cause acute spinal
segment injury. The third criteria was particularly important, as the goal was to characterize sub-
traumatic impact loads and investigate potential implications for low back pain over time due to
repeated occurrences.
This work, however, did not attempt to impose repeated impacts on the disc, but merely
tried to predict how repeated loads of this type would affect the long-term health and injury
tolerance of the disc based on single impact events. One factor that made testing of repeated
impacts difficult is that there are no comprehensive data on the frequency of occurrence of impact
loads to HSB personnel during boat travel. Recovery between impacts is likely key to assessing
individual injury thresholds, but the extent of recovery is unknown in vivo and would be difficult
to achieve in an ex vivo laboratory setup. The work in Aim 2 was carried out to begin to shed
some light on this phenomenon – we wanted to better understand how the typical creep response
of the disc affected its mechanical behavior under impact loading. The FE model developed in
Aim 3 could be used to overcome some of the intrinsic limitations in testing long term repeated
impacts on cadaver specimen and help gain more insight on this problem.
Through quantitative and qualitative methods, we have successfully characterized lumbar
IVD impact mechanics. Mechanical response of the whole motion segment were determined in
Aims 1 and 2, while the impact FE model allowed for the analysis of individual tissue internal
mechanics. A constitutive model formed from experimental observations of the disc under these
loading conditions would have provided the ability to make predictions on the stress-strain
response of the disc, and potentially allow for a better representative FE model. Such a predictive
model was not attempted in this work; however, it is worth noting possible models to consider. A
hyperelastic model is appropriate for compressible, non-linear elastic, fluid-filled tissues such as
the IVD. The phenomenological Mooney-Rivlin model can potentially provide a good description
of the observed impact behavior, and has been used in several FE analyses. Hyperelastic models
85
are limited, however, in that they do not account for strain-rate dependency. A viscoplastic model
could also provide a good quantitative description of impact phenomena, since it includes rate-
dependent behavior and is useful in systems subjected to high strain rates. The Johnson-Cook
model is worthy of consideration for this system; however, only the inelastic behavior is modeled
as strain-rate dependent.
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11. Conclusions
The goal of this work was to characterize human lumbar intervertebral disc mechanics
when subjected to sub-traumatic axial impact loading conditions. This was achieved via
experimental and finite element techniques. We simulated transient shocks from Naval high
speed boats on cadaveric spines in the laboratory. The transition from quasi-static to impact
behavior was found in impacts at or below 160 ms in duration and caused higher stiffness and
lower energy dissipation. Fluid loss due to creep was found to be responsible for lower toe-region
stiffness and increased hysteresis in the disc. Despite this seemingly beneficial result, greater
clinical instability (as shown through neutral zone measurements) and moderately higher linear-
region stiffness with increasing fluid loss signify that creep deformation may be increase the risk
of injury during exposure to impact shocks. Lastly, a novel, poroelastic finite element model of
the lumbar motion segment was developed and subsequently validated against axial impact
exposure in cadavers. The model allows for an observation of stress distributions in the individual
components during impact loading and showed higher total stresses and pore pressure compared
to physiologic loading on the spine.
This work has been published in several conference proceedings and is “in press” and “in
revision” in a peer-reviewed journal. Most notably, this work appears in the following:
International Conference on Human Performance at Sea – conference proceedings. This
work also won the award for Best Student Paper at this meeting.
Orthopaedic Research Society Annual Meeting (2010, 2011) and ASME Bioengineering
Division Conference (2011-2013) – conference proceedings.
87
At the time of writing, Aim 1 is currently in press in the Journal of Biomechanical
Engineering as a Research Paper.
At the time of writing, Aim 2 is currently in revision in the Journal of Biomechanical
Engineering as a Research Paper.
11.1. Novel Contributions
This work presents several novel contributions to the field. They are:
Development of an experimental model to test impact loading events in the laboratory.
Specifically, the simulation of HSB impact events using the Instron on cadaveric
specimen.
Showed a transition from quasi-static to impact mechanics in the disc between 160 and
320 ms, signaled by changes in dynamic stiffness and hysteresis.
Analysis of the change in IVD impact mechanics with progressive creep and fluid loss.
To our knowledge, this relationship had never been investigated prior to this work.
Found correlations between measured parameters (stiffness, neutral zone, hysteresis) and
time of creep as well as impact duration.
Validation of a FE impact model against the same impact events which would be
simulated in the model itself. Previous impact models in literature all used creep or ramp
loading on cadaveric specimen to verify their model, which is insufficient.
Showed greater stress and pore pressure in the nucleus pulposus and annulus compared to
static/quasi-static loading literature. Showed high pore pressure in the endplate as well,
indicated potential mechanism for disc injury.
88
11.2. Future Work and Direction
Ultimately, the purpose of this work is to advance the field of disc biomechanics,
particularly increasing our understanding of mechanical response to impact loading conditions
and its relation to low back pain. Our findings will be used to begin to develop more advanced
standards for the development of shock mitigation equipment in vehicles for working populations
that are exposed to transient shock loads. We will be able to better understand the injury
mechanisms of the spine under these loading conditions, which will enable improvements injury
threshold determination and predictive injury prevention.
The concepts and methodology within this work can be extended to applications in other
soft tissue injury investigations where a similar void in the collective knowledge exists, such as
cartilage and brain tissue. Cartilage wear and degeneration and cumulative brain injury are
persistent health problems. This work could potentially lend itself to addressing these problems as
well.
There are several big-picture questions which remain and should be considered. As noted
previously, disc mechanics during impact events were characterized without regard to the level of
degeneration in the specimen. It is well known, however, that advanced degeneration causes
changes in disc mechanics under creep and cyclic loading. The effect of disc degeneration on
impact mechanics – and vice versa – is unknown, and should be investigated in future work.
Degenerative grade in the disc can be assessed using several methods, including a visual
assessment of gross morphology [44], radiographs [119], or MRI imaging techniques [186].
Degeneration can also be induced in live or cadaver tissue [57, 118, 187] or simulated
numerically in a computational model [85, 156, 184, 188].
Though the impact loads used in this work were not intended to cause acute damage, it is
certainly possible that microfractures could have been induced in the bony of soft tissues. Future
work should assure the lack of acute tissue damage from these types of shocks with a visual
89
assessment. This could be done by bisecting the disc after testing and visually inspecting it, or
using a non-destructive imaging modality such as CT scanning.
The work in Aim 2 focused on analyzing the changes in disc impact mechanics due to
progressive creep and interstitial fluid loss. However, fluid content in the disc was not directly
measured. Future work could certainly address this, by measuring the change in wet weight at
varying levels of creep or using MRI [37].
The finite element model could also be enhanced in several ways in future work, yielding
a better numerical representative of the lumbar disc when subjected to impact loading conditions.
Improvements include the following:
Use of non-linear material laws to represent the different components, as discussed
previously – particularly the soft tissues
Incorporating regional variations in porosity in the annulus and endplates, along with
radial variations in annular fiber concentration
Incorporating osmotic swelling to enable accurate recovery of fluid content during
relaxation
Incorporating fixed charge density into the model to simulate different degenerative
grades
Additional loading modes during impact loading, including shear, flexion/extension, and
lateral bending
Use of a 3-D model, with mesh geometry taken from CT scan composites of human
tissue
Loading conditions which include repeated impacts and recovery.
90
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Vita
David Jamison, IV was born September 9, 1985 in Philadelphia, Pennsylvania. He was
raised for most of his childhood in nearby Yeadon, PA. David earned numerous achievements
prior to his graduation from Archmere Academy in 2003, including the National Honors Society,
the Union League Good Citizenship Award, the Union League Youth Works Scholarship, and
achieving the rank of Eagle Scout.
David attended Johns Hopkins University where he earned a Bachelor of Science in
Engineering Mechanics in 2008. Following this venture, David worked briefly as a Fire
Protection Engineer at Hughes Associates in Baltimore, Maryland.
David earned his Doctorate of Philosophy in Biomedical Engineering in 2013. During
this time he published one paper in a peer-reviewed journal, as well as a book chapter in
Orthopaedic Biomechanics (ed.: Beth Winkelstein). There are two more peer-reviewed journal
articles planned from his thesis work, one of which is currently in revision with the Journal of
Biomechanical Engineering.
Upon conferral of his Ph.D., David will be joining the Mechanical Engineering
department at Villanova University as a Visiting Assistant Professor.
