Mechanical Engineering Department, Ecole Polytechnique de Montréal, Montréal, QC, Canada

Research Center, CHU Sainte-Justine, Université de Montréal, Montréal, QC, Canada

Philips Healthcare, Montréal, QC, Canada

CHUM Saint-Luc, Université de Montréal, Montréal, QC, Canada

Abstract

Background

The treatment planning of spine pathologies requires information on the rigidity and permeability of the intervertebral discs (IVDs). Magnetic resonance imaging (MRI) offers great potential as a sensitive and non-invasive technique for describing the mechanical properties of IVDs. However, the literature reported small correlation coefficients between mechanical properties and MRI parameters. Our hypothesis is that the compressive modulus and the permeability of the IVD can be predicted by a linear combination of MRI parameters.

Methods

Sixty IVDs were harvested from bovine tails, and randomly separated in four groups (

Results

Multilinear regressions showed that 45 to 80% of the Young’s modulus E, the aggregate modulus in absence of deformation H_{A0}, the radial permeability k_{r} and the axial permeability in absence of deformation k_{0} can be explained by the MRI parameters within both the nucleus pulposus and the annulus pulposus. The principal component analysis reduced our variables to two principal components with a cumulative variability of 52-65%, which increased to 70-82% when considering the third principal component. The dendograms showed a natural division into four clusters for the nucleus pulposus and into three or four clusters for the annulus fibrosus.

Conclusions

The compressive moduli and the permeabilities of isolated IVDs can be assessed mostly by MT and diffusion sequences. However, the relationships have to be improved with the inclusion of MRI parameters more sensitive to IVD degeneration. Before the use of this technique to quantify the mechanical properties of IVDs in vivo on patients suffering from various diseases, the relationships have to be defined for each degeneration state of the tissue that mimics the pathology. Our MRI protocol associated to principal component analysis and agglomerative hierarchical clustering are promising tools to classify the degenerated intervertebral discs and further find biomarkers and predictive factors of the evolution of the pathologies.

Background

The planning of the treatment of spine pathologies requires information on the rigidity of the tissues. The surgeons use side-bending radiographs to estimate the rigidity of the spine, but the results vary with the muscular effort made by the patient

The intervertebral disc (IVD) plays an important role in the mobility of the vertebral segments. As IVDs degenerate, the nucleus pulposus becomes more consolidated and fibrous, and is less clearly demarcated from the annulus fibrosus in which focal defects appear and there is a decrease in the number of layers ^{-15}m^{4}N^{-1}s^{-1}) to the annulus fibrosus (0.24±0.19*10^{-15}m^{4}N^{-1}s^{-1}) as computed from confined compression tests and non linear biphasic models, with no differentiation between inner and outer annulus fibrosus

Multi-parametric MRI has been investigated as an early diagnostic tool of IVD degeneration by correlating the MRI parameters to the IVD degeneration. IVD water, proteoglycan and collagen contents were found to be correlated to the longitudinal relaxation time (T1), the transverse relaxation time (T2), the time constant of the exponential decay of magnetization during a spin-lock radiofrequency pulse (T1ρ), the magnetization transfer ratio (MTR) and the diffusion

As a result of these correlations between the MRI parameters and the biochemical properties and between the biochemical properties and the mechanical properties _{A0}

Our hypothesis is that the compressive modulus and the hydraulic permeability of the IVD can be predicted by a combination of MRI parameters (T1, T2, MTR, ADC, fractional anisotropy FA). Our specific aim is to measure the mechanical properties, using confined and unconfined compression tests and direct permeability measurements, and the MRI parameters of isolated bovine IVDs and to investigate the relationships between these parameters. Bovine caudal IVDs from 6 months old animals are usually healthy. Thus, to validate the use of multi-parametric MRI to evaluate the mechanical properties of degenerated IVDs, we digested the bovine IVDs. Trypsin is known to decrease the Young’s modulus, increase the permeability and alter the structure of the disc

Methods

Samples preparation

Bovine tails were obtained from a local slaughterhouse within 4 hours of death. The skin, muscles, ligaments and vertebrae pedicles were removed from each tail. Transverse cuts were performed along the cartilaginous endplates to isolate the two proximal discs. Sixty discs with a controlled 15mm thickness were randomly separated in four groups. The discs from the

**Group**

**Duration**

**Concentration [mg/ml]**

6h

0.05

18h

0.1

24h

0.5

MR imaging

Immediately after digestion, samples were removed from the shaking water bath, and were gently blotted to remove absorbed water. Thickness and weight of discs from both groups (

with

Example of T1 weighted image (a), T2 weighted image (b), MT image with the off-resonance pulse (c), MT image without the off-resonance pulse (d) and Diffusion weighted image (e) for an isolated IVD

**Example of T1 weighted image (a), T2 weighted image (b), MT image with the off-resonance pulse (c), MT image without the off-resonance pulse (d) and Diffusion weighted image (e) for an isolated IVD.**

Where SI is the signal intensity, α the refocusing angle =180º, TW the time in ms between the last refocusing pulse and the next inversion pulse, and N the number of refocusing pulses.

The MTR was obtained using two gradient echo sequences (TR/TE=83/3.8 ms, single off-resonance sinc-gauss pulse, 19.25 ms duration, 620 degrees effective flip angle), one with the off-resonance pulse applied at 1100Hz down to the free water proton resonance frequency (Ms, Figure

The last sequence measured the ADC and FA using a spin-echo EPI diffusion-weighted sequence (TR/TE=2000/40 ms) with 15 non-collinear diffusion and a b value of 1000 s/mm^{2} (Figure

Where **b** is the diffusion encoding tensor, **D** the diffusion tensor and λ the eigenvalues of D.

Each MR image was semi-automatically segmented using Slice-O-Matic (Tomovision, Magog, Canada). A manual selection of 8 points on the exterior outline of the IVD and nucleus pulposus allowed the contour to be approximated by the Snake algorithm. A manual correction of each contour was then realized to improve their anterior and posterior extremities. The annulus fibrosus zone was obtained by the subtraction of the nucleus pulposus zone from the IVD zone. The repetition of the semi-automatic segmentation by a same operator and the skills of the operator did not influence the quality of the contour (p=0.8-1.0) while the instructions given prior to the segmentation influenced the quality of the contour (p<0.05).

Mechanical testing

Just after the MRI acquisitions, all discs were frozen (−80°C) until the day of mechanical testing to avoid any additional enzyme degradation or dehydration of the tissue. It is recognized that freezing does not affect the determination of the mechanical properties of IVDs and it facilitates the preparation of the tissue

Unconfined compression

The unconfined compression test was performed using the mechanical testing machine Mach-1 (Biomomentum, Montreal, QC, Canada). Before the test, tissues were bathed during 10 minutes in PBS in free condition for the annulus fibrosus or in semi-confined condition (allowing only radial displacement) for the nucleus pulposus. After the tissue sample was placed in the chamber for the unconfined compression test, the upper platen was lowered until a stable force of 8 × 10^{-5}N for the annulus fibrosus or 6 × 10^{-5}N for the nucleus pulposus was recorded, indicating that the platen was in contact with the top of the specimen with no deformation of the specimen. The thickness of the tissue sample was then deduced from the relative position of the upper platen to the bottom of the chamber. A preloading of 5% strain during 10min was applied to the annulus fibrosus. Five successive stress-relaxation ramps were applied using 5% strain increment. The relaxations were stopped when the slope of the curve reached a rate of 0.1g per min. The mechanical properties were computed (Matlab, r2007 Mathworks, Natick, MA) using a viscoelastic model _{r}), the Poisson’s ratio (ν), and the viscoelasticity (c). The Young’s modulus or modulus of elasticity can be used to predict the elongation or compression of an object as long as the stress is less than the yield strength of the material. Viscosity describes a fluid’s internal resistance to flow and may be thought of as a measure of fluid friction. The hydraulic permeability indicates the resistance to fluid flow through the intervertebral disc matrix. The Poisson’s ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force. Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation, for which the relationship between stress and strain depends on time.

Confined compression

The confined compression test was performed with the same apparatus used for the unconfined compression test. A custom non porous acrylic chamber (5 millimeters diameter) was designed and manufactured. The protocol described in previous studies _{A0} and the axial hydraulic permeability k_{0} for zero-strain and their respective nonlinear coefficients β and M were computed from a non linear biphasic model

Permeability measurement

The apparatus used to measure the axial permeability consisted of a cylindrical acrylic chamber (Figure _{a}) was calculated from the Darcy law: for a laminar fluid flow with a low Reynolds number, the intrinsic permeability k (m^{4}/Ns) of a saturated porous sample is derived from Equation 7 where Q (m^{3}/s) is the flow rate, ΔP (Pa) is the pressure difference, μ (Ns/m^{2}) is the fluid dynamic viscosity, l (m) is the length of the sample and S (m^{2}) is the cross-section of the sample

Experimental setup to measure the axial permeability

**Experimental setup to measure the axial permeability.**

Statistical analyses

Only the compressive modulus and the permeabilities were chosen for the statistical tests as they presented the smallest standard deviation per group and represent the most important mechanical properties of a biphasic material. For each mechanical property or MRI parameter, a one way ANOVA was performed on the 4 groups followed by a post-hoc multiple comparison with the Dunn-Sidak method. Multi linear regressions were performed between dependent (E, k_{r}, H_{A0}, k_{0} and k_{a}) and independent (T1, T2, MT, FA and ADC) variables to verify our hypothesis.

However, the MR parameters might be found dependant. Thus, a principal component analysis was used to convert the set of possibly correlated variables into a set of linearly uncorrelated variables. The data were first centered and reduced, and organized as a matrix where each row represents a different observation of the experiment and each column gives a different mechanical or MR parameter. The covariance matrix and its eigenvectors and eigenvalues were computed. The cumulative energy content for each eigenvector was used to select a subset of eigenvectors as basis vectors. The source data were then converted into the new basis. The first principal component (F1) has the largest possible variance, and each succeeding component (F2, F3, …Fn) in turn has the highest variance possible under the constraint that it is orthogonal to the preceding components.

Agglomerative Hierarchical Clustering was performed on the 3 first principal components (F1, F2 and F3) computed from the mechanical properties or the MRI parameters. Each observation was a cluster and the process successively merged clusters into larger clusters until it reached one big cluster containing all the samples. We used the Euclidian distance to determine a pairwise distance metric between each observation. The merging of clusters, or linkage, was based on the calculation of the Ward’s distance between clusters. Ward’s linkage uses the incremental sum of squares; that is, the increase in the total within-cluster sum of squares as a result of joining two clusters. The within-cluster sum of squares is defined as the sum of the squares of the distances between all objects in the cluster and the centroid of the cluster. These successive clustering operations produced a binary clustering tree (dendrogram), whose roots contained all the observations.

All statistical tests were performed using XLSTATS (Addinsoft, New York, United States). All results were expressed as Mean±SD and the significance of all tests was set to p≤0.05.

Results

The enzyme treatment induced mechanical changes in both the annulus fibrosus and nucleus pulposus, with a decrease of the compressive moduli and an increase of the permeabilities (Table

**E**

**k**
_{
r
}

**H**
_{
A0
}

**k**
_{
0
}

**k**
_{
a
}

**
Nucleus pulposus
**

**In-situ**

0.019±0.017

32±27

0.12±0.08

15±17

10±2

**Dig 6h**

0.008±0.007

74±40

0.04±0.04

31±15

13±3

**Dig 18h**

0.012±0.015

111±154

0.03±0.03

26±19

14±2

**Dig 24h**

0.007±0.008

218±210

0.02±0.01

40±22

16±3

**
Annulus fibrosus
**

**In-situ**

0.035±0.030

11±8

0.22±0.17

20±27

8±4

**Dig 6h**

0.029±0.019

12±17

0.09±0.06

11±16

7±2

**Dig 18h**

0.023±0.018

21±16

0.04±0.03

37±28

7±2

**Dig 24h**

0.012±0.013

59±58

0.07±0.06

9±8

9±2

**T1**

**T2**

**MTR**

**FA.10**
^{
-2
}

**ADC.10**
^{
-4
}

**
Nucleus pulposus
**

**In-situ**

1140±76

124±16

34±20

8.03±4.59

15.04±0.62

**Dig 6h**

1056±130

87±26

28±15

18.59±6.67

15.25±1.58

**Dig 18h**

1115±130

123±5

33±24

8.15±4.52

14.79±1.13

**Dig 24h**

1144±78

118±7

32±22

13.03±7.08

14.17±0.84

**
Annulus fibrosus
**

**In-situ**

706±44

70±11

44±15

15.83±3.05

15.89±1.06

**Dig 6h**

659±71

62±11

38±13

23.87±5.24

16.87±0.95

**Dig 18h**

663±73

65±5

42±18

17.10±4.60

15.34±1.27

**Dig 24h**

710±85

68±5

42±16

20.89±4.93

15.42±1.13

**E**

**k**
_{
r
}

**H**
_{
A0
}

**K**
_{
0
}

**k**
_{
a
}

**T1**

**T2**

**MTR**

**ADC**

**FA**

**
Nuclus Pulposus
**

**Global**

0.09

0.002

0.0001

0.03

0.0001

0.19

0.0003

0.88

0.10

0.0002

**In situ / Dig. 6h**

0.07

0.53

0.0002

0.07

0.006

0.06

0.0001

0.45

0.65

0.0001

**In situ / Dig. 18h**

0.73

0.66

0.0001

0.2

0.0001

0.58

0.94

0.89

0.58

0.96

**In situ / Dig. 24h**

0.03

0.001

0.0001

0.004

0.0001

0.92

0.53

0.75

0.06

0.04

**Dig. 6h / Dig. 18h**

0.15

0.85

0.67

0.58

0.14

0.20

0.0002

0.54

0.32

0.0001

**Dig. 6h / Dig. 24h**

0.77

0.0006

0.36

0.26

0.01

0.05

0.001

0.66

0,02

0.03

**Dig. 18h / Dig. 24h**

0.08

0.003

0.64

0.09

0.30

0.52

0.58

0.86

0.18

0.05

**
Annulus Fibrosus
**

**Global**

0.04

0.002

0.001

0.05

0.38

0.18

0.33

0.86

0.008

0.0004

**In situ / Dig. 6h**

0.52

0.84

0.005

0.40

0.43

0.12

0.009

0.40

0.04

0.0001

**In situ / Dig. 18h**

0.06

0.44

0.0001

0.14

0.23

0.16

0.26

0.82

0.24

0.5

**In situ / Dig. 24h**

0.01

0.001

0.001

0.24

0.71

0.88

0.67

0.78

0.31

0.009

**Dig. 6h / Dig. 18h**

0.22

0.57

0.21

0.02

0.67

0.88

0.55

0.55

0.002

0.001

**Dig. 6h / Dig. 24h**

0.05

0.001

0.5

0.75

0.25

0.09

0.19

0.57

0.003

0.12

**Dig. 18h / Dig. 24h**

0.47

0.007

0.53

0.01

0.12

0.12

0.49

0.96

0.87

0.05

Multi linear regressions showed that 52 to 70% of E and H_{A0} can be explained by the MRI parameters within the annulus fibrosus, except for E within the _{A0} within the _{A0} can be explained by the MRI parameters, except for H_{A0} within the _{r} can be explained by the MRI parameters for both annulus fibrosus and nucleus pulposus, except for the annulus fibrosus within the _{0} and 41 to 70% of the axial permeability k_{a} can be explained by the MRI parameters.

**Coefficient of determination R**
^{
2
}**Standard error of estimate Power with α=0.05**

**E**

**k**
_{
r
}

**H**
_{
A0
}

**k**
_{
0
}

**k**
_{
a
}

**
Nucleus Pulposus
**

0.48

0.53

0.48

0.49

**0.70**

0.04

55.6

0.08

73.4

1.2

0.73

0.79

0.72

0.74

0.95

0.48

**0.62**

0.34

0.45

**0.67**

0.007

34.6

0.06

15.6

2.2

0.67

0.85

0.47

0.63

0.90

**0.68**

**0.62**

0.45

0.34

0.55

0.01

151.9

0.05

21.9

2.1

0.91

0.85

0.63

0.48

0.76

**0.65**

**0.63**

0.27

0.38

0.41

0.006

173.7

0.03

24.5

3.2

0.91

0.90

0.41

0.58

0.63

**
Annulus Fibrosus
**

0.52

0.17

**0.65**

**0.65**

0.48

0.03

9.8

0.14

40.4

3.6

0.78

0.26

0.91

0.88

0.73

0.15

0.52

0.49

0.39

0.45

0.02

41.7

0.06

62.5

2.1

0.21

0.73

0.72

0.49

0.63

**0.70**

**0.66**

**0.63**

0.32

0.48

0.01

13.1

0.03

266.2

2.2

0.92

0.89

0.86

0.44

0.68

0.01

**0.80**

0.21

0.32

**0.71**

0.93

35.1

0.07

34.1

1.6

**0.67**

0.99

0.32

0.48

0.95

The linear regressions found for each mechanical property included all the MRI parameters measured in this study (Equation 8). The variance inflation factor (VIF) of T1 and T2 was always higher than the VIF of MT, ADC and FA, suggesting that these parameters were likely candidates for elimination in the equation. However, after removing T2 that presented the highest VIF, all parameters had equivalent VIF and the coefficient of determination did not change significantly.

Where MP is one of the mechanical properties E, k_{r}, H_{A0}, k_{0} and k_{a}, and a_{i} (i=0-5) are constants.

The principal component analysis reduced our six variables (one mechanical property E, k_{r}, H_{A0}, k_{0} or k_{a}, and five MR parameters T1, T2, MTR, ADC and FA) to two principal components F1 and F2 with a cumulative variability of 52-65%, which increased to 70-82% when considering the third principal component F3. The representation of the six variables in the (F1, F2) plane for the nucleus pulposus (Figure _{a} and k_{r} were far away from the circle, which suggested that these parameters were not expressed only by F1 or F2. The eigenvectors of the covariance matrix showed that these parameters were expressed more by F3 than F1 or F2. The representation of the six variables in the (F1, F2) plane for the annulus fibrosus (Figure _{A0}, k_{0} and k_{r} were expressed more by F3 than F1 or F2.

Principal component analysis, representation of the mechanical property (a- E, b- H_{A0}, c- k_{0}, d- k_{a}, e- k_{r}) and MRI parameters (T1, T2, MTR, ADC and FA) in the (F1, F2) plane for the nucleus pulposus

**Principal component analysis, representation of the mechanical property (a- E, b- H**
_{
A0
}
**, c- k**
_{
0
}
**, d- k**
_{
a
}
**, e- k**
_{
r
}
**) and MRI parameters (T1, T2, MTR, ADC and FA) in the (F1, F2) plane for the nucleus pulposus.**

Principal component analysis, representation of the mechanical property (a- E, b- H_{A0}, c- k_{0}, d- k_{a}, e- k_{r}) and MRI parameters (T1, T2, MTR, ADC and FA) in the (F1, F2) plane for the annulus fibrosus

**Principal component analysis, representation of the mechanical property (a- E, b- H**
_{
A0
}
**, c- k**
_{
0
}
**, d- k**
_{
a
}
**, e- k**
_{
r
}
**) and MRI parameters (T1, T2, MTR, ADC and FA) in the (F1, F2) plane for the annulus fibrosus.**

One way to determine the natural cluster division in a dataset is to compare the height of each link in the dendogram. A link, whose height differs noticeably from the height of the links below, indicates that the objects joined at this level are much farther apart from each other than their components were when they were joined. The dendograms obtained from the MRI parameters showed a natural division into four clusters for the nucleus pulposus but only three clusters for the annulus fibrosus (Figure

Dendograms generated from the principal components of the MRI parameters for the nucleus pulposus (a) and the annulus fibrosus (b). The Y axis is the distance between the two objects being connected and the X axis is the node number

**Dendograms generated from the principal components of the MRI parameters for the nucleus pulposus (a) and the annulus fibrosus (b).** The Y axis is the distance between the two objects being connected and the X axis is the node number.

Dendograms generated from the principal components of the mechanical properties for the nucleus pulposus (a) and the annulus fibrosus (b). The Y axis is the distance between the two objects being connected and the X axis is the node number

**Dendograms generated from the principal components of the mechanical properties for the nucleus pulposus (a) and the annulus fibrosus (b).** The Y axis is the distance between the two objects being connected and the X axis is the node number.

Discussion

Multi-parametric MRI acquisitions, unconfined and confined stress-relaxation tests in compression and direct permeability measurements were performed on isolated bovine IVDs, as opposed to previous studies done on bovine tail segments

The mechanical properties were sensitive to our enzyme digestion: the compressive modulus decreased while the permeability increased, in agreement with the literature _{A0} decrease is associated to both structural matrix integrity and biochemical content. The permeability, highly anisotropic for healthy IVDs, becomes slightly more isotropic with degeneration. The degeneration process is associated with a change in water content and induces an increase in the pore size in the radial direction only, but no change in the porosity between collagen lamella

Trypsin digestion did not affect T1, T2 and MTR, as previously reported on bovine tails

The MRI parameters chosen in this study (T1, T2, MT, FA, ADC) can assess the compressive moduli and the radial or axial permeability, in agreement with the literature _{0}. However, the direct measurement of the permeability reduces the standard deviations and the differences between the linear regressions. The quantification of the MR parameters is more accurate than the determination of the mechanical properties because the MRI protocol was rigorously the same for all acquisitions and the annulus fibrosus or nucleus pulposus segmentations were fully automatic using a Canny edge detection algorithm. The differences between the

The reduction of the variables to two or three principal components confirmed that the relationships between the mechanical properties and MRI parameters may be non linear. Principal component analysis is very useful to reduce the dimensionality of a data set by projecting high dimensional data into a lower dimensional space. The natural division into three or four clusters on the dendrograms from the MRI parameters did not reflect our 4 experimental groups, due to the lack of differences between groups for T1, MTR and ADC. The natural division into four clusters on the dendograms from the mechanical properties reflected our 4 experimental groups. However, the differentiation between the

Only 15 samples were considered per group. The power of all the significant statistical tests was over 0.8, justifying this number of samples. The quantification of the mechanical properties was limited to compression tests. The compression loading on the intervertebral disc in vivo is expected to result in large hydrostatic pressures within the nucleus pulposus. Thus the relationships established between the mechanical properties and MRI parameters are appropriated for the nucleus pulposus. However, the highly oriented annulus fibrosus is submitted to more complicated deformation patterns. Shear is an important loading mode in the annulus fibrosus, particularly relevant under bending and torsion loading of the IVD. Future studies of the relationships between mechanical properties and MRI parameters within the annulus fibrosus should include shear tests as well as traction tests. Diffusion tensor imaging might be the most relevant MRI technique to reflect the shear behavior of the tissue.

Conclusions

Multi-parametric MRI is a sensitive and non-invasive technique for describing the alterations in mechanical properties of IVDs. This study showed that the compressive modulus and the permeability of isolated IVDs can be assessed mostly by magnetization transfer sequences and diffusion tensor imaging. However, the relationships have to be improved with the inclusion of MRI parameters more sensitive to IVD degeneration such as T1ρ or CEST (Chemical Exchange Saturation Transfer). Before the use of this technique to quantify the mechanical properties of IVDs in vivo on patients suffering from various diseases, the relationships have to be defined for each degeneration type of the tissue that mimics the pathology. Our MRI protocol associated to principal component analysis and agglomerative hierarchical clustering are promising tools to classify the degenerated intervertebral discs and further find biomarkers and predictive factors of the evolution of the pathologies.

Competing interests

The authors declare that they have no competing interests, except GG who receives financial support (salary) from Philips Healthcare.

Authors’ contributions

MR carried out the experiments, all the data analysis, discussed the results and drafted the manuscript. DP proposed the design of the study, participated in the results discussion and helped to draft the manuscript. GG carried out the MRI experiments, participated to the data analysis and to the results discussion, and corrected the manuscript. GB participated in the results discussion and corrected the manuscript. All authors read and approved the final manuscript.

Acknowledgment

The Natural Sciences and Engineering Research Council of Canada (NSERC, Discovery Grant), the Mechanical Engineering Department and the Research and Innovation Directorate, Ecole Polytechnique de Montréal (Canada), for the financial support.

Pre-publication history

The pre-publication history for this paper can be accessed here: