Effect of hydration on healthy intervertebral disc ...oconnell.berkeley.edu/wp-content/uploads/2014/09/osmopaper2015080… · Effect of hydration on healthy intervertebral disc mechanical

Effect of hydration on healthy intervertebral disc mechanical stiffness

Semih E. Bezci, BS Department of Mechanical Engineering 2166 Etcheverry Hall University of California, Berkeley Berkeley, CA 94720 [email protected]

Aditya Nandy Department of Chemical and Biomolecular Engineering 2166 Etcheverry Hall University of California, Berkeley Berkeley, CA 94720 [email protected] Grace D. O’Connell, PhD Department of Mechanical Engineering 2166 Etcheverry Hall University of California, Berkeley Berkeley, CA 94720 [email protected] ASME Membership: 000100323271

Effect of hydration on compressive stiffness

1

Abstract 1

The intervertebral disc has excellent swelling capacity to absorb water, which is thought 2

to be largely due to the high proteoglycan composition. Injury, aging, and degeneration are all 3

noted by a significant decrease in water content and tissue hydration. The objective of this study 4

was to evaluate the effect of hydration, through osmotic loading, on tissue swelling and 5

compressive stiffness of healthy intervertebral discs. The wet weight of NP and AF explants 6

following swelling was 50% or greater, demonstrating significant ability to absorb water under 7

all osmotic loading conditions (0.015 M – 3.0 M PBS). Estimated NP residual strains, calculated 8

from the swelling ratio, were approximately 1.5X greater than AF residual strains. Compressive 9

stiffness increased with hyper-osmotic loading, which is thought to be due to material 10

compaction from osmotic-loading and the nonlinear mechanical behavior. Importantly, this study 11

demonstrated that residual strains and material properties are greatly dependent on osmotic 12

loading. The findings of this study support the notion that swelling properties from osmotic 13

loading are crucial for accurately describing the effect of degeneration and injury on disc 14

mechanics. Furthermore, the tissue swelling will be an important consideration for developing 15

biological repair strategies aimed at restoring mechanical behavior towards a healthy disc. 16

17

Keywords: Intervertebral disc mechanics; residual strain; residual stress; osmotic loading; 18

compression; tissue swelling; nucleus pulposus; annulus fibrosus 19


2

Introduction 1

The intervertebral disc is a highly hydrated fibrocartilaginous tissue that functions to 2

absorb and distribute large compressive loads placed on the spine. The disc is comprised of two 3

unique substructures including, a gelatinous nucleus pulposus (NP) surrounded by the stiffer 4

annulus fibrosus (AF). Mechanical properties of these tissues are dependent on the biochemical 5

composition, consisting mostly of water, proteoglycans, and collagen (water content: 80-85% in 6

the NP and 70-80% in the AF) [1, 2]. External mechanical forces causes water to flow out of the 7

disc, while negatively charged proteoglycans act to reimbibe water during bed rest recovery [3]. 8

The disc’s water content can fluctuate by 15-20% during a diurnal cycle, resulting in altered 9

intradiscal pressure, magnetic resonance signal intensity, and load distribution from the disc 10

towards surrounding vertebral bodies [2-16]. Many in vitro studies have reported incomplete 11

fluid flow recovery within an appropriate time-scale for in vivo comparisons (e.g., 8 hours 12

recovery for 16 hours of loading). Incomplete recovery is largely due to passive diffusion being 13

3-4X slower than the rate of fluid flow out of the disc during mechanical loading [12, 17, 18]. 14

Osmotic loading has been shown to alter water absorption; however, the effect of osmotic 15

loading on the mechanical properties of healthy discs is not known [2, 19, 20]. 16

The osmolality of saline solutions applies an osmotic load, or swelling pressure, onto 17

biological tissues in vitro. Under conventional saline conditions (0.15 M), NP tissue explants are 18

capable of increasing its volume by 200% [2, 21, 22]. Urban and McMullin used osmotic loading 19

to determine the effect of osmotic loading on NP tissue hydration, and noted that an increase in 20

swelling pressure through hyper-osmotic loading decreased water absorption [2, 23]. Their 21

findings established a relationship between swelling capacity, the external osmotic environment, 22


3

and tissue fixed charge density, which is directly related to the proteoglycan content [2, 22, 24-1

27]. 2

Understanding the complex mechanical properties of the healthy disc will be important 3

for developing biomaterials or regenerative medicine strategies for injured or degenerated discs. 4

Much of the data currently available in the literature evaluates the effect of tissue hydration on 5

mechanical properties indirectly by injecting fluid into the NP, reducing the proteoglycan content 6

or evaluating degenerated discs [2, 14, 19, 20, 23]. Disc degeneration is noted by a complex 7

change in composition, including decreased proteoglycan composition and altered collagen 8

composition and architecture (e.g., crosslinking), making it difficult to separate changes in 9

mechanical properties due to hydration from material changes in the solid tissue (e.g., 10

extrafibrillar matrix) [28-31]. The effect of hydration on disc mechanics can be evaluated in vitro 11

by mechanically forcing water from the disc or allowing evaporation by performing mechanical 12

tests in air [12, 32-34]. Alternatively, osmotic loading alters the swelling pressure applied to the 13

disc, and therefore, alters the water volume imbibed by the disc. 14

Therefore, the objective of this study was to evaluate the effect of tissue hydration, 15

through osmotic loading, on the tissue swelling behavior from tissue explants from the disc 16

subcomponent (e.g., NP and AF). The second objective of this study was to evaluate the effect of 17

osmotic loading on disc joint stiffness in axial compression. We hypothesize that compressive 18

stiffness will decrease with a lower tissue swelling under hyper-osmotic loading conditions, 19

based on previous results in articular cartilage [35]. The results reported here provide 20

compressive stiffness properties of healthy discs with respect to hydration conditions (e.g. water 21

content). Importantly, these findings were performed with healthy discs, without altering the 22


4

proteoglycan composition, suggesting that disc mechanics varies significantly throughout a 1

diurnal cycle. 2

Materials and Methods 3

Caudal spines sections from skeletally mature bovines were acquired from the local 4

abattoir (n = 10 spines, 18 months). Bone-disc-bone motion segments were prepared by 5

removing the muscles and facet joints from the upper three caudal levels. An industrial bone saw 6

was used to cut parallel surfaces through the superior and inferior vertebral bodies (General 7

Slicing, Standex Co., Salem, NH). Motion segments were wrapped in saline soaked gauze and 8

stored at -20 oC until testing. 9

Experiments were performed in fresh phosphate buffered saline (PBS) that was prepared 10

at a concentration of 3.0 M, then diluted with distilled water to make 0.015, 0.15, 1.5 M PBS 11

solutions, respectively. The solution pH was adjusted to 7.2 by adding HCl and/or NaOH. Final 12

solute concentrations of 0.15 M PBS were 137 mM NaCl, 2.7 mM KCl, 5.4 mM Na2HPO4, and 13

0.6 mM KH2PO4. A freezing point osmometer was used to determine the osmolality of each 14

solution (Advanced 3D3 Osmometer, Advanced Instruments, Inc., Norwood, MA). Saline 15

osmolality was strongly linearly related to the salt concentration, as expected (range = 27 – 5554 16

mOsm/kg; Figure 1A). The osmotic pressure was calculated as 𝜋 = 𝑀𝑅𝑇, where M is the 17

molarity of the solution (mol/L), R is the gas constant (0.0083 !∗!"#!"#∗!

) and T is temperature in 18

Kelvin (293o K). 19

The use of NaCl and KCl as osmolytes and the range of osmotic loading conditions were 20

selected based on previous work with articular cartilage and AF explants [19, 24, 26, 36-38]. 21

Moreover, previous work with NP explants suggests that hyper-osmotic loading limits tissue 22


5

swelling, which eliminates the fluid stress contribution, providing the mechanical response solely 1

due to the extrafibrillar matrix [26, 37]. 2

NP and AF Tissue Swelling 3

Swelling capacity of NP and AF explants was measured separately to determine the 4

contribution of each subcomponent to total disc joint swelling behavior. Discs were removed 5

from vertebral bodies using a scalpel (#22 blade, n = 8 discs), and a 4 mm diameter biopsy punch 6

was used to prepare core samples from the two regions (n = 4 per region; Figure 1B - inset). Due 7

to caudal disc symmetry, cores were selected from each quadrant and randomly assigned to an 8

osmotic loading group. Tissue explants were weighed immediately after being removed from the 9

disc to determine pre-swelling weight (i.e., initial weight, mi), and placed in a 1.5 mL PBS bath 10

for 60 minutes. Based on preliminary work, 60 minutes was sufficient to achieve swelling 11

equilibrium conditions. The wet-weight of hydrated samples was measured, and the tissue-12

swelling ratio was calculated as the wet weight measured after hydration, mf, divided by the wet 13

weight measured before hydration. The average swelling ratio for each osmotic loading 14

condition was normalized to values measured from the 0.15 M PBS group to compare between 15

NP and AF explants with respect to osmotic loading. Hydration, h, was calculated as the change 16

in water mass divided by the initial pre-swollen wet weight (i.e., h = mf/mi – 1). 17

To confirm that salt was not diffusing into the disc, the osmolality of the saline bath was 18

re-measured after swelling, where solute absorption by the tissue would be noted by a decrease 19

in saline osmolality. The percent change in osmolality was calculated as: (cafter – cbefore)/cbefore * 20

100, where cbefore and cafter represents the saline osmolality (mOsm/kg) before and after tissue 21

swelling, respectively. 22


6

Following tissue swelling experiments, samples were prepared for biochemical analyses. 1

Samples were lyophilized for 48 hours to measure dry weight and digested overnight at 56 oC 2

with Proteinase K enzyme (Sigma-Aldrich, St. Louis, MO). The glycosaminoglycan (GAG) 3

content was measured using the dimethyl methylene blue (DMMB) assay and normalized by the 4

tissue’s initial wet-weight (mi). Aliquots of the saline bath were preserved to measure GAGs 5

released to the bath during swelling. 6

Residual Stretch Estimation 7

Once swelling equilibrium is achieved, the pressure from the tissue is equivalent to the 8

osmotic pressure from the external bath, resulting in tissue being in a true stress-free condition. 9

The stress-free configuration was set as the reference configuration for residual stretch 10

estimations, based on the configuration used for most computational model. Therefore, the 11

residual stretch is represented as a compressive deformation. 12

The residual stretch required to deform a tissue in the stress-free reference configuration 13

to a pre-swollen condition was estimated based on the change in mass during swelling. The 14

change in mass during swelling was assumed to be solely from water absorption; therefore, the 15

change in tissue volume was calculated based on the density of water (density of water, ρH2O = 16

1000 g/m3). The volumetric change, J, is related to deformation tensor, F, through J = det F. 17

Tissue explants were assumed to be homogeneous with uniform deformation, such that F = 18

diag(𝜆!). Finally, volume-changing deformation, 𝜆!, was estimated using Equation 1, where 𝜆! 19

is equal to 1.0 in the stress-free reference condition. 20

𝜆! = 𝐽!!/!𝜆! , 𝑎 = 1,2,3 21

Elastic and Poro-elastic Response in Compression 22

(1)


7

Additional bone-disc-bone motion segments were potted in bone cement (PMMA, 1

polymetheylmethacrylate, Bosworth Co., Skokie, IL) for mechanical testing (n = 10 motion 2

segments). A bubble-level was used during potting to ensure that PMMA ends were parallel with 3

each other and the horizontal plane of the mid disc height. Samples were preserved at -20 oC 4

until testing. Prior to testing, samples were hydrated overnight in a saline bath (0.015, 0.15, 1.5 5

or 3 M) at -4 oC to allow discs to reach steady-state hydration. Samples were allowed to 6

equilibrate to room temperature prior to testing (23oC). Potted motion segments were placed in a 7

custom-built water bath attached to a mini-Bionix MTS 858 testing machine (Figure 3A; MTS, 8

Eden Prairie, MN). A nominal preload of 20 N was applied and held for 10 minutes to ensure 9

that the loading platens were engaged with the sample. 10

A slow ramp protocol or creep protocol was applied to determine the effect of osmotic 11

loading on the disc’s elastic and time-dependent response, respectively. To determine the elastic 12

response, a quasi-static compressive load was applied to 1000 N at a rate of 0.55 N/s. Samples 13

were re-hydrated in a different saline bath and retested. The testing order was randomized for 14

each sample. Force and displacement were recorded during all tests, and the total displacement 15

was normalized to the displacement measured in the 0.15 M PBS condition to compare across 16

samples and account for differences in disc height. 17

Time-dependent properties of bone-disc-bone motion segments under axial compression 18

creep were assessed in 0.15 M or 3.0 M PBS conditions. A 200 N or 1000 N load was applied at 19

a rate of 40 N/sec and held for 2.5 hours (n = 10 motion segments). The applied load was 20

selected to corresponded points along the toe- and linear-region of the force-displacement curve 21

acquired during quasi-static compression tests. Samples were re-hydrated and retested in the 22


8

second osmotic loading condition. The order of osmotic loading was randomly assigned for each 1

sample. Force and displacement were recorded during all tests. 2

The creep response was curve fit to a time-dependent rheological model using Boltzmann 3

linear superposition principle to account for displacement during ramp loading, as previously 4

described [12]. Briefly, displacement (d, mm) was described as a function of time (t, sec) and 5

applied load (L, N), which was fit to a 5-parameter rheological model consisting of two Voigt 6

solids and a spring in series (Equation 2) [12, 39, 40]. The Voigt solid consist of a spring (Si, 7

N/mm) and dashpot (ηi, N*s/mm) in parallel, which provides the material with a time-dependent 8

response (time-constant τi = ηi/Si). To reduce the number of model parameters, the elastic 9

response (SE) was set as the displacement at the end of the ramp loading period. Model 10

parameters for the fast (τ1 and S1) and slow response (τ2 and S2) were determined through curve 11

fitting the displacement-time experimental data (lsqcurvefit, Matlab, Inc., Mathworks, Natick, 12

MA) [12]. A least-squares curve fit (R2) greater than 0.96 was considered as a good fit to 13

experimental data. 14

𝑑 𝑡 = 𝐿 !!!

1− 𝑒!! !! + !!!

1− 𝑒!! !! + !!!

15

Histomorphology 16

Samples were rehydrated in 0.15 M PBS before removing the superior and inferior 17

vertebral bodies with a scalpel. Measuring disc geometry parameters (e.g. disc height and 18

diameter) while the motion segment was intact introduced a lot of variability, partly due to the 19

vertebral body curvature at the endplates. Therefore, disc height and area were measured after 20

mechanical testing, which limited our ability to measure total disc swelling under each osmotic 21

loading condition. Once the disc was removed, the average disc height was measured using 22

digital calipers (3 measurements per disc) and a cross sectional image was acquired to calculate 23

(2)


9

disc area using a custom-written algorithm in Matlab (Mathworks, Inc.), as previously described 1

[41]. Briefly, analysis of images was performed by manually selecting the boundary of the disc 2

edge, which was used to calculate the disc area. A mm-scale within the image was used to 3

convert the area measurement from pixels2 to mm2. The Lagrangian stress was calculated as the 4

applied force divided by disc area, and strain was calculated as the displacement divided by the 5

average disc height. The toe- and linear-region moduli were calculated as the slope of the stress-6

strain response from the slow ramp protocol and from the loading portion of the creep protocol 7

(1000 N only). 8

Statistics 9

A Pearson’s rank correlation, ρ, was performed to determine the effect of osmotic 10

loading on NP and AF tissue swelling and disc joint compressive stiffness (Matlab, Mathworks 11

Inc.). A Pearson’s correlation was performed between tissue hydration and the estimated residual 12

stretch. A Student’s paired t-test was used to compare swelling properties between NP and AF 13

regions and to compare model parameters with respect to osmotic loading (0.15 M versus 3.0 M 14

PBS). Finally, an unpaired Student’s t-test was used to compare the compressive Young’s 15

modulus measured during the slow ramp test with properties measured during the loading 16

portion of the creep protocol (i.e. loading rate comparison of 0.55 N/s and 40 N/s). All values are 17

reported as average ± standard deviation. Significance was set at p ≤ 0.05 and a trend for 0.05 < 18

p ≤ 0.1. For correlation analyses, a moderate correlation was defined as |0.5| ≥ ρ > |0.7| and a 19

strong correlation was defined as ρ ≥ |0.7|. 20

Results 21

Tissue Swelling 22


10

The osmolality of the hypo-osmotic group increased from 28 mOsm/kg to 42 mOsm/kg, 1

representing an increase in saline osmolarity from 0.015 M to 0.022 M PBS (Figure 1A & B). 2

The final osmolality (mOsm/kg) of the 0.15 M and 1.5 M PBS groups was less than 10% from 3

the initial solution (Δosmolality = 18 and -93 mOsm/kg, respectively; Figure 1B). The change in 4

saline bath osmolality is a limitation of the ratio between the bath volume and tissue volume, 5

where a significantly large bath (e.g., towards infinity) would yield zero change in osmolality. 6

Swelling ratios of NP and AF tissue explants were greater than 1.5 (i.e. 50% increase in 7

tissue mass due to swelling) for all osmotic loading conditions (Figure 1C). The tissue-swelling 8

ratio decreased nonlinearly with saline osmolality (Pearson’s: ρ < -0.55, p < 0.001; Figure 1C). 9

Normalizing swelling ratio by the swelling ratio of the 0.15 M PBS group (i.e. solution typically 10

used in biomechanics research) demonstrated no significant difference in swelling capacity 11

between NP and AF explants for any osmotic loading condition (Figure 1D; t-test p-value = 0.4). 12

The total GAG content normalized by initial wet weight (ww) was 7.91 ± 5.60 %/ww in 13

the NP and 3.93 ± 1.71 % /ww in the AF, which is comparable to previously reported values for 14

bovine caudal discs [1]. GAGs measured in the saline solution comprised of less than 10% of the 15

total GAG concentration, and was not altered by saline osmolality (range for NP explants = 5.2 – 16

10.6 % and 3.1 – 5.1 % for AF explants; Pearson’s: p > 0.3). 17

The estimated NP residual stretch, 𝜆! , ranged from 0.72 ± 0.07 in hypo-osmotic 18

conditions (0.015 M PBS) to 0.82 ± 0.04 in hyper-osmotic conditions (3.0 M PBS; Figure 2A). 19

Residual stretch in the AF ranged from 0.82 ± 0.04 in hypo-osmotic loading to 0.89 ± 0.04 in 20

hyper-osmotic loading (Figure 2A – open circles). There was a strong negative correlation 21

between hydration and NP residual stretch (Pearson’s correlation: r = -0.99, p = 0.001; Figure 22


11

2B). Similarly, there was a strong negative correlation in hydration with AF residual stretch; 1

however, the relationship was not significant (r = -0.88, p = 0.11; Figure 2B). 2

Elastic compressive properties 3

Determining the effect of tissue swelling on disc mechanics is limited due to altered 4

boundary conditions in situ. Therefore, to determine the effect of osmotic loading on healthy disc 5

compressive stiffness, the entire disc joint was hydrated under osmotic loading conditions prior 6

to mechanical testing. The force-displacement curve measured under quasi-static compressive 7

loading was nonlinear and altered with saline osmolality (Figure 3B). 8

Discs were removed from the vertebral bodies to determine geometric parameters for 9

normalization. The disc height was 7.01 ± 1.23 mm and disc area was 490.9 ± 95.2 mm2. The 10

total displacement at 1000 N normalized to the displacement measured in the 0.15 M PBS 11

condition decreased nonlinearly with osmotic loading (Figure 4A; Pearson’s correlation: ρ = -12

0.68, p < 0.001), resulting in changes in toe- and linear-region apparent moduli. The toe-region 13

modulus followed a nonlinear behavior, while the linear-region modulus followed a linear 14

increase with osmotic loading (Figure 4B and 4C). Therefore, a logarithmic or linear curve was 15

used, respectively, to describe the mechanical response with osmotic loading. The apparent toe-16

region compressive Young’s modulus increased from 2.2 to 3.4 MPa, while the apparent linear-17

region modulus increased from 8.5 to 13.1 MPa (Figure 4B and 4C; Pearson’s: ρ = 0.5, p < 18

0.01). 19

Time-dependent response in creep 20

Creep was measured at 200 N and 1000 N, based on the toe- and linear-region of the 21

force-displacement curve under quasi-static axial compression. The time-dependent response 22

with osmotic loading was similar for 200 N and 1000 N, where the overall displacement was 23


12

lower for samples hydrated in hyper-osmotic loading conditions (i.e. 3.0 M PBS; Figure 5). The 1

rheological model fit well to the displacement-time response (least-squares R2 > 0.98). Time-2

constant parameters demonstrated a fast response with a time constant on the order of minutes 3

and a slow response with a time constant on the order of hours (Table 1). Results from the 4

rheological model fit demonstrated that hyper-osmotic loading increased stiffness parameters and 5

a decrease the fast response time constant (Table 1 – asterisks; p < 0.05). 6

The effect of loading rate was evaluated for two osmotic loading conditions (0.15 M and 7

3.0 M PBS groups; Figure 6). The modulus calculated from the quasi-static compression stress-8

strain response was compared to the response during the ramp loading period for creep (1000 N 9

only). The toe-region modulus was not altered by loading rate at either osmotic loading condition 10

(0.15 M and 3.0 M PBS groups; Figure 6A). However, the apparent linear region modulus 11

increased with loading rate as expected (Figure 6B). For both osmotic-loading conditions, the 12

linear-region modulus was a 2X greater at 40 N/s than 0.55 N/s. 13

Discussion 14

Intervertebral disc mechanics and water absorption during recovery are greatly dependent 15

on biochemical composition and mechanical loading history (e.g. extended loading) [11, 42, 43]. 16

Previous work established the importance of osmotic loading on water absorption by NP tissues 17

and on tissue-level mechanical properties [2, 19, 36, 44]. The objective of this study was to 18

evaluate the effect of osmotic loading on AF and NP tissue swelling and joint-level compressive 19

stiffness from nondegenerate discs. The results of this study showed that osmotic loading-20

dependent residual stretch in the NP and AF significantly altered compressive stiffness and time-21

dependent properties in axial compression. 22


13

NP and AF explants experienced swelling ratios greater than 1.5 under all osmotic 1

loading conditions (i.e., 50% increase in mass; Figure 1), which corresponded to large residual 2

stretches (Figure 2). The swelling pressure from osmotic loading and the estimated residual 3

strain (i.e., Green Lagrangian strain: E = ½ (C-I), where C is a diagonal stretch tensor and I is 4

the identity tensor) can be used to estimate the tissue Young’s modulus. The Young’s modulus of 5

the extrafibrillar matrix in the AF was 2.30 MPa (for 0.15M PBS group), which was 6

approximately 4X greater than previously reported values (0.4-0.8 MPa) [45, 46]. However, the 7

AF pre-stretch values reported here do agree with previously reported values for the inner AF 8

(0.86 ± 0.13) [36, 47]. The NP Young’s modulus, based on residual strains in the 0.15 M PBS 9

group, was 1.44 MPa and was comparable to the compressive aggregate modulus of 10

nondegenerate NP tissues (1.01 ± 0.43 MPa for nondegenerate human NP) [48]. Importantly, AF 11

and NP residual stretches were greatly dependent on osmotic loading, as observed by the 12

nonlinear relationship between osmotic pressure and residual stretch (Figure 2). 13

Residual stretches and stresses are thought to develop from water absorption by 14

negatively charged proteoglycans [49]. In this study, residual stretch from NP explants was 15

1.55X greater than AF explants, and the NP GAG composition was approximately 2X the AF 16

GAG content. Therefore, the NP swelling response, relative to AF swelling, was expected to be 17

greater than observed, due to differences in GAG composition and resistance to swelling in the 18

AF from collagen fibers. These results suggest that GAG composition alone is not sufficient for 19

predicting residual stretch in disc subcomponents. Other matrix components, such as elastin or 20

collagen fibers, may have a significant impact on residual stresses [44, 50]. Even though elastin 21

composition in the disc is relatively low (1.7 % / dry weight), elastin fibers are well distributed 22


14

throughout the NP and AF [51]. Moreover, elastin fibers have been shown to cause large changes 1

in residual strains of cardiovascular tissues (0.014 – 10.6% elastin / dry weight) [52-54]. 2

The NP is thought to withstand much of the stresses at lower applied loads (i.e., toe-3

region response of the stress-strain curve), transferring the loads directly to the AF at higher 4

stresses (i.e. linear-region response). Water loss due to external mechanical loading occurs at 5

different rates for the NP and AF, such that the water loss is higher in the NP [11, 55]. A shift in 6

the force-displacement curve has been reported with a shift in water distribution from extended 7

loading, such that the toe-region displacement is elongated and the linear region stiffness is 8

preserved [12]. In this study, we observed an increase in toe- and linear-region compressive 9

stiffness with osmotic loading. That is, hyper-osmotic loading decreased the amount of water 10

imbibed by the disc prior to testing, resulting in a 55% increase in compressive stiffness (Figure 11

4). This finding caused us to reject our initial hypothesis. The increase in compressive stiffness 12

with hyper-osmotic loading is the opposite response observed for articular cartilage, where 13

hyper-osmotic loading decreased compressive stiffness [35, 56]. This suggests that a decrease in 14

water absorption, through hyper-osmotic loading, acts to depressurize cartilage. However, for a 15

significantly softer material, such as the intervertebral disc, hyper-osmotic loading causes larger 16

volumetric changes, decreasing material porosity (i.e. tissue compaction). The increase in solid 17

matrix porosity from tissue compaction with hyper-osmotic conditions was also observed as a 18

decrease in the fluid flow response in creep (Table 1 – τ1). 19

Previous work by Gunning and co-workers demonstrated that increased disc hydration 20

causes the disc to be more susceptible to endplate fracture [55]. Extended bed rest and space 21

flight are low mechanical loading conditions that result in an increase in disc height and 22

hydration [57]. These conditions were simulated in this study through a low-pressure 23


15

environment (e.g., hypo-osmotic loading). While it is difficult to directly translate tissue-level 1

findings to the entire disc joint, it is likely that the large increase in NP hydration will have a 2

significant impact on the disc residual stress prior to mechanical loading. Furthermore, the lower 3

apparent modulus in hypo-osmotic conditions (Figure 4), suggests that the disc is more 4

deformable under physiological loads (e.g., loads due to body weight). Together these results 5

suggest that an increase in disc joint swelling, followed by larger disc height loss under axial 6

compression may contribute to the 4.3X increase in disc herniations observed among astronauts 7

and more hydrated discs [15, 55]. 8

Computational models developed for the disc and its subcomponents attempt to 9

accurately describe the tissue’s nonlinear, anisotropic, poroelastic behavior using combination of 10

constitutive descriptions for the extrafibrillar matrix and collagen fibers [8, 58-63]. The NP has 11

been described as an isotropic biphasic material, consisting of a solid and fluid phase, providing 12

the tissue with its time-dependent behavior [48, 64]. These models are limited in their ability to 13

describe the effect of osmotic loading, which has been shown to alter cell behavior and tissue-14

level mechanics [36, 38, 65-68]. Recently, the effect of osmotic loading has been incorporated in 15

these model descriptions using poroelasticity or a triphasic mixture model for the extrafibrillar 16

matrix, but there is limited data to validate these models for healthy nondegenerate discs [19, 44, 17

62, 63, 69, 70]. The data reported here is useful for defining a pre-stress configuration in 18

computational models of the healthy disc joint. 19

Research in cardiovascular computational mechanics has shown that incorporating 20

residual stresses provides the tissue with uniform stress distribution in healthy tissues [49, 71-21

74]. It is likely that residual stresses play a crucial role in producing a uniform stress distribution 22

throughout the disc’s subcomponents, as observed in healthy nondegenerate discs [14]. Disc 23


16

degeneration is noted by changes in biochemical composition and structure, such as crosslinks, 1

that alters tissue-and joint-level mechanical properties and permeability [46, 48]. It is likely that 2

these changes in matrix composition alters the residual stress with respect to osmotic loading and 3

may contribute to the age-related changes in internal disc stress distributions [14]. However, 4

future work is needed to understand the effect of biochemical composition with degeneration and 5

injury on the residual stress configuration. 6

There are some limitations to the study that should be noted. To estimate residual stretch, 7

we assumed that the material was an isotropic material with uniform deformation in all 8

directions. Residual stretch in the AF is anisotropic due to the highly aligned collagen fibers 9

[36]; however, the small samples used here (4 mm diameter) likely limited the swelling 10

restriction by collagen fibers [75]. It is also interesting to note that the osmotic loading 11

conditions evaluated here were not sufficient to eliminate tissue swelling, which implies that the 12

modulus of the solid matrix is likely greater than the values reported here (Figure 4). Previous 13

studies that used uncharged osmolytes (e.g., PEG) eliminated or reversed fluid flow into the 14

tissue through osmotic loading [2, 22]. It is possible that differences in swelling behavior can be 15

attributed to differences in osmolyte type and charge (uncharged PEG versus NaCl), but 16

uncharged osmolytes have been shown to increase residual strains in the arterial wall [49]. 17

In conclusion, osmotic-loading dependent changes in NP and AF residual stretch greatly 18

alters joint-level compressive stiffness and time-dependent behaviors. Changes in disc hydration 19

and disc height loss under diurnal loads may redistribute loads to surrounding tissues or increase 20

strains experienced by cells, causing a catabolic response [7, 24, 38, 66]. To better understand 21

the effect of degeneration and herniation on disc joint mechanics, future work will focus on 22

evaluating the effect of compositional changes on osmotic-loading dependent properties. 23


17

Moreover, understanding the effect of hydration on disc mechanics and load distribution will be 1

important for developing biomimetic repair strategies or preventative methods for people that 2

experience large mechanical loads for extended periods. 3


18

Acknowledgements 1

This work was supported in part by funds from the Regents of the University of California, 2

Berkeley (Junior Faculty Research Award), and an undergraduate research fellowship by the 3

Berkeley Stem Cell Center (Aditya Nandy). The authors would like to thank Dr. Kristin Miller 4

from Tulane University for her helpful discussion regarding residual stresses. 5

6

Conflict of Interest 7

The authors certify that there is no conflict of interest related to the work presented in this 8

manuscript. 9

10


19

Figures Caption List 1

Fig. 1 (A) Osmolality for each saline group. Osmolality increased linearly with PBS 2 concentration (slope = 1851 mOsm/kg/M). (B) Percent change in saline osmolality after tissue 3 swelling experiment (C) Swelling ratio was negatively correlated with the external osmotic 4 environment (Pearson’s: ρ < -0.55, p ≤ 0.001). Inset: Representative disc showing location and 5 size of NP and AF tissue cores. * represents significant differences between the NP and AF 6 swelling ratio at each osmotic condition (t-test, p < 0.01). (C) Swelling ratio normalized by the 7 swelling ratio of the 0.15 M PBS group showed no significant differences between NP and AF 8 explants (t-test: p = 0.4). 9 10 Fig. 2 (A) Residual stress from applied osmotic loading condition with respect to the estimated 11 residual stretch (least-squares curve fit, R2 > 0.999). (B) Hydration correlated with residual 12 stretch (Pearson correlation: NP: r = -0.99, p = 0.0001, AF: r = -0.88, p = 0.1). Values for 0.15 M 13 PBS group are shown on each figure by the respective data point. 14 15 Fig. 3 (A) Representative sample in MTS device. Inset: Motion segments were potted in bone 16 cement to ensure parallel-loading surfaces, and then placed in a saline bath (osmotic 17 concentration range = 0.015 M to 3.0 M PBS) for mechanical testing. (B) Force-displacement 18 curves from a representative motion-segment. Disc joint stiffness increased with an increase in 19 saline osmolality. The dashed and solid red lines represents the toe- and linear-regions, 20 respectively. 21 22 Fig. 4 Stiffness measured from slow ramp compression to 1000N. (A) Overall displacement 23 measured during compression tests, normalized by the displacement measured in the 0.15 M 24 PBS group. (B) Toe- and (C) linear-region moduli with respect to the saline concentration. The 25 mechanical behavior with respect to saline concentration can be described using the equations 26 provided in the Figure. All parameters demonstrated a moderate significant correlation with 27 osmotic loading (Pearson’s: p < 0.01). 28 29 Fig. 5 Average creep response under (A) 200 N and (B) 1000 N load. Differences in stiffness 30 and time constant, as determined by a rheological model, are reported in Table 1. 31 32 Fig. 6 Rate-dependent change in apparent modulus measured during slow-ramp compression 33 (0.55 N/s) and during the ramp to apply 1000 N for creep (40 N/s). (A) Toe-region apparent 34 modulus was not rate dependent. (B) The linear-region apparent modulus increased by 2-fold 35 with an increase in loading rate (* represents t-test p < 0.01). Data is presented as mean ± 36 standard deviation. 37 38


20

Table Caption List 1 2

Table 1 Model parameters from creep experiments (200 N and 1000 N hold). * represents p ≤ 3 0.05 and # represents a trend (0.05 < p ≤ 0.1) for differences between osmotic loading groups 4 (i.e. 0.15 M versus 3.0 M PBS). ** represents differences in the dampening coefficient with 5 osmotic loading (η = τ*S; p ≤ 0.05). 6


21

1

2

Figure 1. (A) Osmolality for each saline group. Osmolality increased linearly with PBS 3

concentration (slope = 1851 mOsm/kg/M). (B) Percent change in saline osmolality after tissue 4

swelling experiment (C) Swelling ratio was negatively correlated with the external osmotic 5

environment (Pearson’s: ρ < -0.55, p ≤ 0.001). Inset: Representative disc showing location and 6

size of NP and AF tissue cores. * represents significant differences between the NP and AF 7

swelling ratio at each osmotic condition (t-test, p < 0.01). (C) Swelling ratio normalized by the 8

swelling ratio of the 0.15 M PBS group showed no significant differences between NP and AF 9

explants (t-test: p = 0.4). 10

11


22

1

Figure 2. (A) Residual stress from applied osmotic loading condition with respect to the 2

estimated residual stretch (least-squares curve fit, R2 > 0.999). (B) Hydration correlated with 3

residual stretch (Pearson correlation: NP: r = -0.99, p = 0.0001, AF: r = -0.88, p = 0.1). Values 4

for 0.15 M PBS group are shown on each figure by the respective data point. 5

6


23

1

Figure 3. (A) Representative sample in MTS device. Inset: Motion segments were potted in 2

bone cement to ensure parallel-loading surfaces, and then placed in a saline bath (osmotic 3

concentration range = 0.015 M to 3.0 M PBS) for mechanical testing. (B) Force-displacement 4

curves from a representative motion-segment. Disc joint stiffness increased with an increase in 5

saline osmolality. The dashed and solid red lines represents the toe- and linear-regions, 6

respectively. 7

8


24

1

Figure 4. Stiffness measured from slow ramp compression to 1000N. (A) Overall displacement 2

measured during compression tests, normalized by the displacement measured in the 0.15 M 3

PBS group. (B) Toe- and (C) linear-region moduli with respect to the saline concentration. The 4

mechanical behavior with respect to saline concentration can be described using the equations 5

provided in the Figure. All parameters demonstrated a moderate significant correlation with 6

osmotic loading (Pearson’s: p < 0.01). 7

8


25

1

Figure 5. Average creep response under (A) 200 N and (B) 1000 N load. Differences in stiffness 2

and time constant, as determined by a rheological model, are reported in Table 1. 3

4


26

1

Figure 6. Rate-dependent change in apparent modulus measured during slow-ramp compression 2

(0.55 N/s) and during the ramp to apply 1000 N for creep (40 N/s). (A) Toe-region apparent 3

modulus was not rate dependent. (B) The linear-region apparent modulus increased by 2-fold 4

with an increase in loading rate (* represents t-test p < 0.01). Data is presented as mean ± 5

standard deviation. 6

7


27

1

Table 1. Model parameters from creep experiments (200 N and 1000 N hold). * represents p ≤ 2

0.05 and # represents a trend (0.05 < p ≤ 0.1) for differences between osmotic loading groups 3

(i.e. 0.15 M versus 3.0 M PBS). ** represents differences in the dampening coefficient with 4

osmotic loading (η = τ*S; p ≤ 0.05). 5

6


28

References 1

1. Beckstein, J.C., et al., Comparison of animal discs used in disc research to human 2 lumbar disc: axial compression mechanics and glycosaminoglycan content. Spine 3 (Phila Pa 1976), 2008. 33(6): p. E166-‐73. 4

2. Urban, J.P. and J.F. McMullin, Swelling pressure of the lumbar intervertebral discs: 5 influence of age, spinal level, composition, and degeneration. Spine (Phila Pa 1976), 6 1988. 13(2): p. 179-‐87. 7

3. Adams, M.A., P. Dolan, and W.C. Hutton, Diurnal variations in the stresses on the 8 lumbar spine. Spine (Phila Pa 1976), 1987. 12(2): p. 130-‐7. 9

4. Ludescher, B., et al., T2-‐ and diffusion-‐maps reveal diurnal changes of intervertebral 10 disc composition: an in vivo MRI study at 1.5 Tesla. J Magn Reson Imaging, 2008. 11 28(1): p. 252-‐7. 12

5. Botsford, D.J., S.I. Esses, and D.J. Ogilvie-‐Harris, In vivo diurnal variation in 13 intervertebral disc volume and morphology. Spine (Phila Pa 1976), 1994. 19(8): p. 14 935-‐40. 15

6. Hutton, W.C., J.A. Malko, and W.A. Fajman, Lumbar disc volume measured by MRI: 16 effects of bed rest, horizontal exercise, and vertical loading. Aviat Space Environ Med, 17 2003. 74(1): p. 73-‐8. 18

7. O'Connell, G.D., E.J. Vresilovic, and D.M. Elliott, Human intervertebral disc internal 19 strain in compression: the effect of disc region, loading position, and degeneration. 20 Journal of orthopaedic research : official publication of the Orthopaedic Research 21 Society, 2011. 29(4): p. 547-‐55. 22

8. Kelly, T.A., et al., Tissue-‐engineered articular cartilage exhibits tension-‐compression 23 nonlinearity reminiscent of the native cartilage. J Biomech, 2013. 46(11): p. 1784-‐91. 24

9. Reiter, D.A., et al., In vitro measurements of porcine anterior column units under free 25 swelling. J Biomech Eng, 2003. 125(6): p. 875-‐80. 26

10. Adams, M.A., et al., Diurnal changes in spinal mechanics and their clinical significance. 27 J Bone Joint Surg Br, 1990. 72(2): p. 266-‐70. 28

11. Masuoka, K., et al., Different effects of static versus cyclic compressive loading on rat 29 intervertebral disc height and water loss in vitro. Spine (Phila Pa 1976), 2007. 30 32(18): p. 1974-‐9. 31

12. O’Connell, G.D., et al., Axial Creep Loading and Unloaded Recovery of the Human 32 Intervertebral Disc and the Effect of Degeneration. Journal of Mechanical Behavior 33 and Biomedical Materials, 2011. 34

13. Arun, R., et al., 2009 ISSLS Prize Winner: What influence does sustained mechanical 35 load have on diffusion in the human intervertebral disc?: an in vivo study using serial 36 postcontrast magnetic resonance imaging. Spine (Phila Pa 1976), 2009. 34(21): p. 37 2324-‐37. 38

14. Adams, M.A., D.S. McNally, and P. Dolan, 'Stress' distributions inside intervertebral 39 discs. The effects of age and degeneration. J Bone Joint Surg Br, 1996. 78(6): p. 965-‐40 72. 41

15. Johnston, S.L., et al., Risk of herniated nucleus pulposus among U.S. astronauts. Aviat 42 Space Environ Med, 2010. 81(6): p. 566-‐74. 43


29

16. Iatridis, J.C., J.P. Laible, and M.H. Krag, Influence of fixed charge density magnitude 1 and distribution on the intervertebral disc: applications of a poroelastic and chemical 2 electric (PEACE) model. J Biomech Eng, 2003. 125(1): p. 12-‐24. 3

17. Ayotte, D.C., K. Ito, and S. Tepic, Direction-‐dependent resistance to flow in the endplate 4 of the intervertebral disc: an ex vivo study. J Orthop Res, 2001. 19(6): p. 1073-‐7. 5

18. Gu, W.Y., et al., The anisotropic hydraulic permeability of human lumbar anulus 6 fibrosus. Influence of age, degeneration, direction, and water content. Spine (Phila Pa 7 1976), 1999. 24(23): p. 2449-‐55. 8

19. Stokes, I.A., et al., Refinement of elastic, poroelastic, and osmotic tissue properties of 9 intervertebral disks to analyze behavior in compression. Ann Biomed Eng, 2011. 10 39(1): p. 122-‐31. 11

20. Andersson, G.B. and A.B. Schultz, Effects of fluid injection on mechanical properties of 12 intervertebral discs. J Biomech, 1979. 12(6): p. 453-‐8. 13

21. Urban, J.P., S. Roberts, and J.R. Ralphs, The nucleus of the intervertebral disc from 14 development to degeneration. Amer Zool, 2000. 40: p. 53-‐61. 15

22. van Dijk, B., E. Potier, and K. Ito, Culturing Bovine Nucleus Pulposus Explants by 16 Balancing Medium Osmolarity. Tissue engineering. Part C, Methods, 2011. 17

23. Urban, J.P. and J.F. McMullin, Swelling pressure of the inervertebral disc: influence of 18 proteoglycan and collagen contents. Biorheology, 1985. 22(2): p. 145-‐57. 19

24. Urban, J.P., et al., Swelling pressures of proteoglycans at the concentrations found in 20 cartilaginous tissues. Biorheology, 1979. 16(6): p. 447-‐64. 21

25. Hendry, N.G., The hydration of the nucleus pulposus and its relation to intervertebral 22 disc derangement. J Bone Joint Surg Br, 1958. 40-‐B(1): p. 132-‐44. 23

26. Ateshian, G.A., et al., The correspondence between equilibrium biphasic and triphasic 24 material properties in mixture models of articular cartilage. J Biomech, 2004. 37(3): 25 p. 391-‐400. 26

27. Chahine, N.O., et al., Effect of dynamic loading on the transport of solutes into agarose 27 hydrogels. Biophys J, 2009. 97(4): p. 968-‐75. 28

28. Adam, M. and Z. Deyl, Degenerated annulus fibrosus of the intervertebral disc contains 29 collagen type II. Ann Rheum Dis, 1984. 43(2): p. 258-‐63. 30

29. Antoniou, J., et al., The human lumbar intervertebral disc: evidence for changes in the 31 biosynthesis and denaturation of the extracellular matrix with growth, maturation, 32 ageing, and degeneration. J Clin Invest, 1996. 98(4): p. 996-‐1003. 33

30. Urban, J.P. and S. Roberts, Degeneration of the intervertebral disc. Arthritis Res Ther, 34 2003. 5(3): p. 120-‐30. 35

31. Yu, J., et al., A Detailed Examination of the Elastic Network Leads to a New 36 Understanding of Annulus Fibrosus Organisation. Spine (Phila Pa 1976), 2015. 37

32. Ferguson, S.J., K. Ito, and L.P. Nolte, Fluid flow and convective transport of solutes 38 within the intervertebral disc. J Biomech, 2004. 37(2): p. 213-‐21. 39

33. Costi, J.J., T.C. Hearn, and N.L. Fazzalari, The effect of hydration on the stiffness of 40 intervertebral discs in an ovine model. Clin Biomech (Bristol, Avon), 2002. 17(6): p. 41 446-‐55. 42

34. Race, A., N.D. Broom, and P. Robertson, Effect of loading rate and hydration on the 43 mechanical properties of the disc. Spine (Phila Pa 1976), 2000. 25(6): p. 662-‐9. 44


30

35. Chahine, N.O., et al., Anisotropic strain-‐dependent material properties of bovine 1 articular cartilage in the transitional range from tension to compression. J Biomech, 2 2004. 37(8): p. 1251-‐61. 3

36. Cortes, D.H. and D.M. Elliott, Extra-‐fibrillar matrix mechanics of annulus fibrosus in 4 tension and compression. Biomech Model Mechanobiol, 2012. 11(6): p. 781-‐90. 5

37. Lai, W.M., J.S. Hou, and V.C. Mow, A triphasic theory for the swelling and deformation 6 behaviors of articular cartilage. J Biomech Eng, 1991. 113(3): p. 245-‐58. 7

38. Wuertz, K., et al., Influence of extracellular osmolarity and mechanical stimulation on 8 gene expression of intervertebral disc cells. J Orthop Res, 2007. 25(11): p. 1513-‐22. 9

39. Johannessen, W., et al., Trans-‐endplate nucleotomy increases deformation and creep 10 response in axial loading. Ann Biomed Eng, 2006. 34(4): p. 687-‐96. 11

40. Keller, T.S., D.M. Spengler, and T.H. Hansson, Mechanical behavior of the human 12 lumbar spine. I. Creep analysis during static compressive loading. J Orthop Res, 1987. 13 5(4): p. 467-‐78. 14

41. O'Connell, G.D., E.J. Vresilovic, and D.M. Elliott, Comparison of animals used in disc 15 research to human lumbar disc geometry. Spine (Phila Pa 1976), 2007. 32(3): p. 328-‐16 33. 17

42. Johannaber, K. and F.A. Fathallah, Spinal disc hydration status during simulated 18 stooped posture. Work, 2012. 41 Suppl 1: p. 2384-‐6. 19

43. Waters, T.R. and R.B. Dick, Evidence of Health Risks Associated with Prolonged 20 Standing at Work and Intervention Effectiveness. Rehabil Nurs, 2014. 21

44. Cortes, D.H., et al., Mechanical properties of the extra-‐fibrillar matrix of human 22 annulus fibrosus are location and age dependent. J Orthop Res, 2013. 31(11): p. 23 1725-‐32. 24

45. Best, B.A., et al., Compressive mechanical properties of the human anulus fibrosus and 25 their relationship to biochemical composition. Spine (Phila Pa 1976), 1994. 19(2): p. 26 212-‐21. 27

46. Perie, D.S., et al., Correlating material properties with tissue composition in 28 enzymatically digested bovine annulus fibrosus and nucleus pulposus tissue. Ann 29 Biomed Eng, 2006. 34(5): p. 769-‐77. 30

47. Michalek, A.J., M.G. Gardner-‐Morse, and J.C. Iatridis, Large residual strains are present 31 in the intervertebral disc annulus fibrosus in the unloaded state. J Biomech, 2012. 32 45(7): p. 1227-‐31. 33

48. Johannessen, W. and D.M. Elliott, Effects of degeneration on the biphasic material 34 properties of human nucleus pulposus in confined compression. Spine (Phila Pa 1976), 35 2005. 30(24): p. E724-‐9. 36

49. Han, E.H., et al., Contribution of proteoglycan osmotic swelling pressure to the 37 compressive properties of articular cartilage. Biophys J, 2011. 101(4): p. 916-‐24. 38

50. Cortes, D.H., et al., Elastic, permeability and swelling properties of human 39 intervertebral disc tissues: A benchmark for tissue engineering. J Biomech, 2014. 40 47(9): p. 2088-‐94. 41

51. Mikawa, Y., et al., Elastin in the human intervertebral disk. A histological and 42 biochemical study comparing it with elastin in the human yellow ligament. Arch 43 Orthop Trauma Surg, 1986. 105(6): p. 343-‐9. 44

52. Carmo, M., et al., Alteration of elastin, collagen and their cross-‐links in abdominal 45 aortic aneurysms. Eur J Vasc Endovasc Surg, 2002. 23(6): p. 543-‐9. 46


31

53. Zeller, P.J. and T.C. Skalak, Contribution of individual structural components in 1 determining the zero-‐stress state in small arteries. J Vasc Res, 1998. 35(1): p. 8-‐17. 2

54. Venturi, M., et al., Biochemical assay of collagen and elastin in the normal and varicose 3 vein wall. J Surg Res, 1996. 60(1): p. 245-‐8. 4

55. Gunning, J.L., J.P. Callaghan, and S.M. McGill, Spinal posture and prior loading history 5 modulate compressive strength and type of failure in the spine: a biomechanical study 6 using a porcine cervical spine model. Clin Biomech (Bristol, Avon), 2001. 16(6): p. 7 471-‐80. 8

56. Eisenberg, S.R. and A.J. Grodzinsky, Swelling of articular cartilage and other 9 connective tissues: electromechanochemical forces. J Orthop Res, 1985. 3(2): p. 148-‐10 59. 11

57. Holguin, N., et al., Short applications of very low-‐magnitude vibrations attenuate 12 expansion of the intervertebral disc during extended bed rest. Spine J, 2009. 9(6): p. 13 470-‐7. 14

58. Lu, Y.M., W.C. Hutton, and V.M. Gharpuray, Do bending, twisting, and diurnal fluid 15 changes in the disc affect the propensity to prolapse? A viscoelastic finite element 16 model. Spine (Phila Pa 1976), 1996. 21(22): p. 2570-‐9. 17

59. Elliott, D.M. and L.A. Setton, Anisotropic and inhomogeneous tensile behavior of the 18 human anulus fibrosus: experimental measurement and material model predictions. J 19 Biomech Eng, 2001. 123(3): p. 256-‐63. 20

60. Chahine, N.O., et al., Anisotropic strain-‐dependent material properties of bovine 21 articular cartilage in the transitional range from tension to compression. Journal of 22 biomechanics, 2004. 37(8): p. 1251-‐61. 23

61. Gu, W.Y., W.M. Lai, and V.C. Mow, A triphasic analysis of negative osmotic flows 24 through charged hydrated soft tissues. J Biomech, 1997. 30(1): p. 71-‐8. 25

62. Yao, H. and W.Y. Gu, Three-‐dimensional inhomogeneous triphasic finite-‐element 26 analysis of physical signals and solute transport in human intervertebral disc under 27 axial compression. J Biomech, 2007. 40(9): p. 2071-‐7. 28

63. Huyghe, J.M., et al., An ionised/non-‐ionised dual porosity model of intervertebral disc 29 tissue. Biomech Model Mechanobiol, 2003. 2(1): p. 3-‐19. 30

64. Eyre, D.R., Biochemistry of the intervertebral disc. International review of connective 31 tissue research, 1979. 8: p. 227-‐91. 32

65. Yao, H., et al., Effects of swelling pressure and hydraulic permeability on dynamic 33 compressive behavior of lumbar annulus fibrosus. Ann Biomed Eng, 2002. 30(10): p. 34 1234-‐41. 35

66. O'Connell, G.D., I.B. Newman, and M.A. Carapezza, Effect of long-‐term osmotic loading 36 culture on matrix synthesis from intervertebral disc cells. Biores Open Access, 2014. 37 3(5): p. 242-‐9. 38

67. Johnson, Z.I., I.M. Shapiro, and M.V. Risbud, Extracellular osmolarity regulates matrix 39 homeostasis in the intervertebral disc and articular cartilage: evolving role of TonEBP. 40 Matrix Biol, 2014. 40: p. 10-‐6. 41

68. Boyd, L.M., et al., Osmolarity regulates gene expression in intervertebral disc cells 42 determined by gene array and real-‐time quantitative RT-‐PCR. Ann Biomed Eng, 2005. 43 33(8): p. 1071-‐7. 44


32

69. Galbusera, F., et al., Comparison of four methods to simulate swelling in poroelastic 1 finite element models of intervertebral discs. J Mech Behav Biomed Mater, 2011. 4(7): 2 p. 1234-‐41. 3

70. Schroeder, Y., et al., Osmoviscoelastic finite element model of the intervertebral disc. 4 Eur Spine J, 2006. 15 Suppl 3: p. S361-‐71. 5

71. Chuong, C.J. and Y.C. Fung, On residual stresses in arteries. J Biomech Eng, 1986. 6 108(2): p. 189-‐92. 7

72. Lanir, Y., Osmotic swelling and residual stress in cardiovascular tissues. J Biomech, 8 2012. 45(5): p. 780-‐9. 9

73. Sorrentino, T.A., et al., Local versus global mechanical effects of intramural swelling in 10 carotid arteries. J Biomech Eng, 2015. 137(4): p. 041008. 11

74. Azeloglu, E.U., et al., Heterogeneous transmural proteoglycan distribution provides a 12 mechanism for regulating residual stresses in the aorta. Am J Physiol Heart Circ 13 Physiol, 2008. 294(3): p. H1197-‐205. 14

75. Adams, M.A. and T.P. Green, Tensile properties of the annulus fibrosus. I. The 15 contribution of fibre-‐matrix interactions to tensile stiffness and strength. Eur Spine J, 16 1993. 2(4): p. 203-‐8. 17

18

Documents

Effect of hydration on healthy intervertebral disc ...oconnell.berkeley.edu/wp-content/uploads/2014/09/osmopaper2015080… · Effect of hydration on healthy intervertebral disc mechanical