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Journal of Biomechanics 41 (2008) 903–906

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Short communication

Determination of the strain-dependent hydraulic permeability of thecompressed bovine nucleus pulposus

Paul Heneghan, Philip E. Riches�

Bioengineering Unit, University of Strathclyde, 106 Rottenrow, Glasgow G4 0NW, UK

Accepted 15 November 2007

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Abstract

The hydraulic permeability, k, of the nucleus pulposus (NP) is crucial, both in withstanding compressive stress and for convective

transport of nutrients within the disc. Permeability has previously been determined using biphasic mathematical models, but has not been

found by direct permeation experiments, which is the objective of this study. Bovine coccygeal nucleus samples (n ¼ 64), f10mm and

thickness 683749 mm (mean7S.D.) were compressed axially to one of l ¼ 1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4 or 0.3, where l is the stretch

ratio. Ringer’s solution was permeated through the sample, with an o-ring ensuring axial flow. During stress equilibrium, k was

determined and fitted to four permeability-strain equations. Permeability decreased exponentially with compression, and was best

described by

kðlÞ ¼ 1:59� 10�15l� 0:2

0:8

� �1:13

e½�0:02ðl2�1Þ=2�.

Values of k were comparable to those arising from mathematical models, lending confidence to permeability being determined from

such models.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Intervertebral disc; Hydraulic permeability; Compression; Soft tissue mechanics

1. Introduction

The intervertebral disc (IVD) withstands high compres-sive stress in vivo of more than 2MPa (Nachemson andMorris, 1964; Wilke et al., 1999) with a hydrostaticpressure developing in the nucleus pulposus (NP) due tothe low rate of fluid exudation from the disc (McNally andAdams, 1992; Oloyede et al., 1998). Whilst diffusiondominates the transport of small metabolites (Robertset al., 1996; Urban et al., 1978) convection may play animportant role in the transport of large essential metabo-lites such as enzymes and hormones required for main-taining its health status (Ferguson et al., 2004; Robertset al., 1996). The main route for all these nutrients intothe NP is axially through the cartilage endplate, with

e front matter r 2007 Elsevier Ltd. All rights reserved.

iomech.2007.11.014

ing author. Tel.: +44141 548 5703.

ess: philip.riches@strath.ac.uk (P.E. Riches).

convection augmenting diffusion (Ferguson et al., 2004;Ohshima et al., 1989). Nevertheless, in the healthy disc, it isthe permeability of the NP that is the limiting factor forconvective transport (Riches and McNally, 2005). Thus,the hydraulic permeability plays an important role in boththe mechanical and metabolic behaviour of the disc tissue.Despite being critical for both disc mechanics and

nutrition, the hydraulic permeability of the NP has notbeen directly determined. Direct permeation experimentshave been used to determine the hydraulic permeabilityof the healthy and degenerate human annulus fibrosus(Gu et al., 1999), and bovine articular cartilage hasdemonstrated decreasing permeability with compression(Mansour and Mow, 1976; Reynaud and Quinn, 2006).More commonly, the hydraulic permeability of the NP isestimated by fitting the linear and non-linear biphasicmodels to experimental data from confined compressionstress–relaxation experiments (Johannessen and Elliott,

ARTICLE IN PRESSP. Heneghan, P.E. Riches / Journal of Biomechanics 41 (2008) 903–906904

2005; Perie et al., 2005), results of which suggest a decreasein permeability with compressive strain (Perie et al., 2005).However, in order to test the suitability of such models toNP tissue, the permeability needs to be directly determined.Furthermore, models predict large localised compressivestrains (40.50) in vivo (Holmes and Mow, 1990; Mowet al., 1980; Riches et al., 2002), behaviour which has alsobeen found experimentally, albeit on articular cartilage(Zheng et al., 2005). Thus, it is necessary that materialproperties be characterised to high-compressive strain.

The aim of this study is to determine the strain-dependent hydraulic permeability of NP tissue by directlypermeating fluid through the compressed tissue, with thehypothesis that hydraulic permeability will decrease withincreasing compressive strain. These data are then com-pared with four different strain–permeability relations, andwith indirect measures to assess the suitability of themathematical models. The empirical data will be veryuseful for future models of the IVD to incorporate strain-dependent permeability of the NP to better modelconvective transport and mechanics under compression.

2. Methods

All procedures were approved by the University Ethics Committee.

Spinal motion segments from bovine tails (aged 14–30 months) were

excised using a scalpel. The three largest tail discs, from the tail base

adjacent to the lumbar section, were isolated and frozen at �20 1C within

12 h of slaughter. Cylindrical plugs of NP tissue, 10mm in diameter and

oriented in the axial direction, were obtained using a cork-borer. Plugs

were kept frozen while microtoming at �14 1C. Sixty-four NP samples,

thickness 683749mm (mean7S.D.), were obtained from 20 discs.

The apparatus used to determine the permeability is shown in

Fig. 1. It consisted of an upper cylindrical permeation chamber, a dual

INLET 1

O-RING

ATMOSPHERIC

PRESSURE

SAMPLE

PRESSURE 1

POROUS

PLATEN

FLUID INFUSED FROM

SYRINGE PUMP

Fig. 1. Apparatus. The upper chamber was lowered to compress the tissue

and fluid infused through the tissue and highly porous platens. The o-ring

ensured flow through the tissue.

syringe infusion/withdrawal pump (model 200 series, Cole–Parmer,

London, UK) using a 250ml Hamilton gastight syringe, a Honeywell

15 psi (103 kPa) compensated gauge pressure transducer (model

26PCCFA1G, RS Components, Glasgow, UK), and an o-ring. The

upper chamber was attached to the adjustable crosshead of a materials

testing system (model Z005, Zwick Roell, Ulm, Germany), and the

lower chamber attached to its fixed base. Cellulose ester 1000Da

MWCO dialysis tubing (Fisher Scientific, Loughborough, UK) was

used on each side of the sample to prevent possible proteoglycan

loss, with samples confined between two porous stainless steel

platens (average pore size, 100mm; f5mm); the permeability of the

dialysis tubing in series with the porous platens was four orders of

magnitude greater than tissue permeability, causing negligible additional

resistance to flow.

After determining the sample height with a load of 0.1N, the chamber

was filled with Ringer’s solution and vented to remove all the air. Each

sample was compressed to one of l ¼ 1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4 or 0.3

at 2mm/s and the displacement maintained for 2 h to obtain the stress

equilibrium, where l ¼ h/h0, i.e. the stretch ratio (the ratio of compressed

sample height to original height). Fluid was then injected from the syringe

pump at a high rate (�400ml/h) until a pressure difference across the

sample of 30.070.5 kPa was reached; the flow rate was manually adjusted

until the equilibrium was achieved. The pressure in the upper chamber was

continuously monitored at 1Hz. During stress equilibrium, the hydraulic

permeability, k, was calculated from

k ¼vh

DP, (1)

where v is the fluid velocity after 2 h, h is the compressed sample height and

DP is the pressure difference across the sample. The mechanical behaviour

of the dialysis tubing was found in a pilot study and was deducted from

the combined behaviour.

At each strain level, the mean and the 95% confidence interval were

calculated. The mean permeability and the 795% confidence interval

limits were fitted to l using four equations previously used for disc tissue

and cartilage permeability (Eqs. (2)–(5)), utilising non-linear OLS

regression (Holmes and Mow, 1990; Lai and Mow, 1980; Riches et al.,

2002; Argoubi and Shirazi-Adl, 1996):

kðlÞ ¼ k0l� 1þ f0

f0

� �k

e½Mðl2�1Þ=2�, (2)

kðlÞ ¼ k0eMðl�1Þ, (3)

k ¼ k0ff0

� �n

, (4)

k ¼ k0ff0

� �2

eMðl�1Þ, (5)

where k0 is the zero strain permeability, M, n and k are non-dimensional

parameters relating k to l, and f is the tissue porosity; the subscript 0

indicates zero strain values, and the zero strain porosity was assumed to be

0.8 (Roberts et al., 1989). The relationship between porosity and stretch is

given by

f ¼ 1�1� f0

l. (6)

Eqs. (3)–(5) are included even though they are not based on the finite

deformation theory, since we are interested in comparing appropriateness

of the different approaches.

3. Results

All samples achieved force equilibrium within 2 h, and avolume of fluid at least three times that of the samplewas infused by the syringe pump prior to measurement.All compressed samples (lp0.9) experienced an increase

ARTICLE IN PRESSP. Heneghan, P.E. Riches / Journal of Biomechanics 41 (2008) 903–906 905

in fluid pressure and compressive stress during thecompression phase, and all samples experienced an increasein pressure when fluid infusion began. Fig. 2 plots k againstl for lp1.0, with k found to decrease with decreasing l.Table 1 shows the equation parameters and R2 valuesfound.

0.5

k (m

4/N.s)

Argoubi and Shirazi-Adl (1996)Holmes and Mow (1990)Lai and Mow (1980)Riches et al. (2002)

1.E-14

1.E-15

1.E-16

0.3 0.4 0.6 0.7 0.8 0.9 1.0 1.1

�

Fig. 2. Plot of k against l, compared with all four permeability equations.

Data points and error bars indicate mean795% confidence intervals.

Table 1

The mean and 95% confidence interval values for the zero strain

permeability, k0, the non-dimensional parameters M, n and k, and R2

values from Eqs. (2)–(5)

Model Mean 95% C.I. range

Argoubi and Shirazi-

Adl (1996)

k0 ¼ 1.60� 10�15 k0 ¼ 1.22�1.97� 10�15

M ¼ 1.04 M ¼ 0.84�1.17

R2¼ 0.946 –

Holmes and Mow

(1990)

k0 ¼ 1.59� 10�15 k0 ¼ 1.22�1.96� 10�15

M ¼ �0.02 M ¼ �0.14�0.04

k ¼ 1U13 k ¼ 1U13

R2¼ 0.946 –

Lai and Mow (1980) k0 ¼ 1.65� 10�15 k0 ¼ 1.27�2.03� 10�15

M ¼ 2.17 M ¼ 2.00�2.29

R2¼ 0.931 –

Riches et al. (2002) k0 ¼ 1.53� 10�15 k0 ¼ 1.17�1.89� 10�15

M ¼ 3.85 M ¼ 3.41�4.17

R2¼ 0.933 –

Units for k0 are m4/N s; all other parameters are dimensionless.

Table 2

Comparison of previous literature values on NP and AF tissue

Study Tissue

Current study Bovine tail NP

Perie et al. (2005) Bovine tail NP

Perie et al. (2005) Bovine tail NP

Johannessen et al. (2005) Human lumbar NP

Perie et al. (2005) Bovine tail AF (axial)

Perie et al. (2005) Bovine tail AF (axial)

Gu et al. (1999) Human lumbar AF (axial)

Riches et al. (2002) Human lumbar disc

4. Discussion

This is the first study to determine the hydraulicpermeability of the NP using a direct permeation experi-ment, and tissue compression clearly resulted in asubstantial decrease in hydraulic permeability: permeabil-ity was decreased by 61% when l ¼ 0.5 compared tol ¼ 0.9.Previous studies have determined the hydraulic perme-

ability of the NP using mathematical models of the tissue,and comparison of previous results is shown in Table 2.Our results compare favourably with those of Johannessenand Elliott (2005), who used a linear biphasic mathematicalmodel to predict k of the human NP in confinedcompression. Our values are also of the same order ofmagnitude as Perie et al. (2005), who used both linear andnon-linear biphasic models; the non-linear biphasic modelutilises the expression originally found by Holmes andMow (1990) for strain-dependent permeability, whichwe have found to be suitable for NP tissue. Thus, ourfindings on the NP tissue show good agreement withbiphasic models, whereas direct permeation experimentson the AF found much higher k than biphasic models(Gu et al., 1999).A pressure difference of 30 kPa across the tissue was used

to induce fluid flow through the tissue in this study.However, the external fluid pressure will exert a stress onthe solid phase of the tissue at the boundary and,internally, fluid flow will stress the tissue via viscous drag.These stresses will deform the tissue and, based on theaggregate modulus, HA, of the bovine NP (HA�300 kPa)(Perie et al., 2005), it is estimated that a pressure differenceof 30 kPa may cause compressive strain of approximately0.10, or l ¼ 0.90. This may explain why k did not differbetween l ¼ 1.0 and 0.9 (independent samples Studentt-test, p ¼ 0.92), and subsequently decreased with compres-sion. When the equation of Holmes and Mow was fit to thedata for lp0.9 only, a better fit was obtained (R2

¼ 0.983)than when fit to all data (R2

¼ 0.952), with meanparameter values of k0 ¼ 2.02� 10�15m4/N s, M ¼ 2.41and k ¼ 0.48 found. However, in the absence of clearevidence of flow induced compression, it is suggested thatthe relationship between k and l is best described by the

Method k (m4/N s)� 1015

Direct permeation 0.32�2.08

Non-linear biphasic model 0.4�0.6

Linear biphasic model 0.3�1.2

Linear biphasic model 0.90

Non-linear biphasic model 0.15�0.3

Linear biphasic model 0.1�0.9

Direct permeation 1.53

Poroelastic model 0.2�0.91

ARTICLE IN PRESSP. Heneghan, P.E. Riches / Journal of Biomechanics 41 (2008) 903–906906

equation of Holmes and Mow (1990) based on all of theavailable data, as in Table 1.

It should be noted that by definition in Eq. (1),decreasing the tissue height will decrease k, even withoutincreased resistance to flow. By calculating k from Eq. (1),but with h0 in place of h, k still decreased with decreasing l,suggesting increased resistance to flow with compression.

A potential source of error of this study is the unknownstrain state of IVDs when excised from the spine, due topossible tissue swelling. However, all samples were treatedin the same way, so comparison between the different levelsof compression remains suitable. The application of a30 kPa fluid pressure may also be considered a limitation ofthis study, and may have led to fluid-induced tissuecompression, as discussed. This was the lowest fluidpressure for which a consistent flow could be monitored,and was considered a suitable compromise.

Therefore, the hydraulic permeability of the NPdecreases with compression and the relationship is bestdescribed by the equation of Holmes and Mow (1990),which is based on finite deformation theory and is given by

kðlÞ ¼ 1:59� 10�15l� 0:2

0:8

� �1:13

e½�0:02ðl2�1Þ=2�

ðR2 ¼ 0:952Þ:

Values are comparable to those obtained from thebiphasic mathematical models, lending confidence to thesemodels at predicting the mechanical behaviour of the NPtissue.

Conflict of interest

None

Acknowledgement

The authors thank the EPSRC for its support of thiswork (Grant no. GR/S64219/01).

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