Confocal microscopic observation of micromechanical 3D ...mate.tue.nl/mate/pdfs/6701.pdf · Confocal microscopic observation of micromechanical 3D ﬁnite strains in intervertebral

Confocal microscopic observation of micromechanical 3D finite strains in intervertebraldisc annulus fibrosus under osmotic loading

C.J.M. JongeneelenMarch 2006BMTE 06.19

Part II of MSc-thesis

Committee:prof. dr. ir. F.P.T. Baaijensdr. ir. J.M.R. Huyghedr. C.C. van Donkelaardr. ir. C.W.J. Oomens

Eindhoven University of TechnologyDepartment of Biomedical Engineering

Abstract

The intervertebral disc is a cartilaginous tissue with a complex structure. The process of intervertebraldisc degeneration is still not fully understood. An important issue in the understanding of the discand its degeneration is the interaction between the disc cell and its surrounding matrix. Althoughswelling is proven to have a major influence, past research on disc cell-matrix interaction did notinclude the effect of swelling. To gain better knowledge of this interaction a new method is createdto visualize micromechanical swelling in the intervertebral disc annulus fibrosus. The deformationsof the collagen fibers and the cells under osmotic loading are observed by fluorescent labelling underthe confocal microscope. A digital image correlation technique calculates displacements and finitestrains. The results show the heterogeneous character of the tissue. They suggest there is an importantrole of the pericellular matrix in protecting the cell against osmotic pressure changes. The experimentsalso show some trends in cellular displacements and tissue deformation.

i

ii

Contents

Abstract i

1 Introduction 1

2 Materials and methods 3

2.1 Specimen preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 The osmotic loading chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3 Loading due to osmotic pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.4 Three-Dimensional Digital Image Correlation Technique . . . . . . . . . . . . . . . 5

2.5 Strain calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Results 11

3.1 Confocal microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1.1 Type VI collagen staining . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1.2 Deformation shown with CNA35 probe . . . . . . . . . . . . . . . . . . . . 11

3.2 3D Correlation technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.3 Strain calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3.1 Cellular level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3.2 Matrix level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4 Discussion 19

Bibliography 23

Appendix 25

iii

Contents

A Osmotic technique 27

B 3D Correlation technique 29

B.1 Rigid Displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

C Images 33

D Cell deformations 37

E Time steps 41

F Confocal laser scanning microscopy 45

F.1 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

F.2 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

iv

Chapter 1

Introduction

The human spine is build up out of vertebral bodies and intervertebral discs. The intervertebral discis a cartilaginous structure that contributes to flexibility and load support in the spine. It consists ofthe nucleus pulposus, a gelatinous core, which is surrounded by the annulus fibrosus (a fibrous ring),where the nucleus with its swelling properties mainly bears the compressive loads and the well orga-nized fibers in the annulus provide tensile stress. The disc has a complex structure, which containsvery few cells embedded in an extracellular matrix. These cells have the essential function of main-taining and repairing the matrix by synthesizing matrix macromolecules and synthesizing proteinasesfor matrix breakdown. When the balance is in place, damaged discs can be restored by cellular repairresponses. When there is an imbalance between matrix synthesis and matrix breakdown, the matrixcomposition and organization alters and the cellular repair responses are inadequate. The degradedmatrix can no longer carry load effectively. Some of the cells become necrotic. The endplate of thedisc calcifies and disc degeneration begins [6,19,27–29].Low-back pain, which is often caused by disc degeneration, is a major health problem in westernsociety. Discs degenerate far more rapidly than other tissues. The etiology of intervertebral discdegeneration is still poorly understood. Different researches have suggested that the cause of discdegeneration can be both abnormal mechanical as well as abnormal chemical factors within the in-tervertebral disc which are reflected in the disc composition, structure and properties [27, 41]. Tounderstand the mechanism of low-back pain and disc degeneration a precise knowledge of the localmechanical and chemical environment around the disc cells in both the nucleus pulposus and the an-nulus fibrosis is needed. Insight in the cell environment improves the understanding of cell death,which is linked to disc degeneration. This is also helpful in the progress of disc tissue engineering, asa tissue repair or replacement therapy.With the causes of disc degeneration one of the most important issues is imbalance between matrixsynthesis and matrix breakdown. Therefore an understanding of cell-matrix interactions is needed.The micromechanical environment of the cell is studied and in both the annulus fibrosus and thenucleus pulposus. It consists of a cell surrounded by a pericellular matrix lying in the extracellularmatrix [33]. Recent studies govern information about cell responses to mechanical stimuli in the inter-vertebral disc [2,7,8,14]. The mechanical environment of a cell in the intervertebral disc is expectedto be highly heterogeneous. This is due to spatial variations in cell morphology and phenotype andthe significant differences in material properties of the extracellular matrix among regions. Baer etal. [3,4] show that the degree of matrix anisotropy and the parameters of cell geometry have a stronginfluence on the mechanical environment of an intervertebral disc cell. They use different computa-tional models of the cell environment. Results suggest that cell geometry is an adaptation to reducecell strains.

1

Chapter 1. Introduction

Bruehlmann et al. [7–9] examined the complex structure of the disc in relation with the cellular me-chanics. They imaged the tissue and cell structure in the different regions of the annulus fibrosus.Their findings show the intercellular mechanical environment to be nonuniform and strongly depen-dent upon the structure and behaviour of the surrounding extracellular matrix. They also observedthe extracellular matrix and found it to be nonuniformly, and give the relative sliding of the collagenfibrils as a reason for this.However none of these studies included the effect of swelling of the tissue. Osmotic pressure changesare an important factor in the disc and its degeneration [21, 22, 34, 44]. As loading changes and asthe disc degenerates, the osmolarity in the disc changes. Because of the heterogenous character ofthe disc tissue, the swelling affects the strain differently in different areas. Therefore, there is need toexamine the influence of non-homogenous swelling on the cell-matrix interaction.To gain more insight of what happens in the micromechanical environment of the annulus fibrosuscells the objective of this study was to measure the state of deformation of the pericellular environ-ment as compared to the average strain of the tissue. Therefore we developed a method to obtain andcalculate the local and global matrix strains. A collagen staining method was applied to visualize thedisplacements in the disc during swelling. For the calculation of the displacements a digital imagecorrelation technique was used, which was coupled to strain calculations.

2

Chapter 2

Materials and methods

2.1 Specimen preparation

For the preparation of the tissue adult bovine tail discs were obtained from a local butcher. The fouruppermost discs were dissected from the adjacent vertebral bodies by cutting as close as possibleto the endplates. They were snap frozen and stored in−80◦C until used. From the frozen disc thenucleus was removed and the annulus was sliced in± 1 mm thick samples perpendicular to the fiberdirection, by hand with a scalpel. The tissue samples where placed in phosphate buffered saline (PBS)for 1 hour to rehydrate.After this the tissue was stained. To compare the pericellular matrix (PCM) with the extracellularmatrix (ECM) in the annulus fibrosus a PCM region had to be defined. Experiments have shown [1,16,17,31,33,36] that collagen type VI is very common in the PCM. Therefor an immunohistology stainfor type VI collagen was used. For this goat antibody to bovine/human collagen type VI (Biodesign,Main, USA) was used in combination with rabbit anti-goat IgG, FITC conjugated (Sigma-Aldrich).However this immunohistology could not be used for imaging of deformations in the sample, hence arecently developed CNA35 probe was used. This probe binds to a wide range of collagen (type I to VI)with different fluorescent intensities and has little cross-reactivity with noncollagenous extracellularmatrix proteins [25]. The CNA35 probe is Oregon Green-labeled. Because of the probes affinity fora range of collagen types, it can be used to visualize both the matrix surrounding the cells and theextracellular matrix. For that reason a distinguish of possible differences in material properties inboth the extracellular and pericellular matrix could be made. The collagen fibers contribute to thestiffness of the ECM [11, 20, 35]. Therefor we have visualized only collagen. For the calculations ofthe strains, the fiber displacements were studied. Propidium Iodide was used to visualize (dead) cellsin the tissue, to locate the pericellular matrix.

2.2 The osmotic loading chamber

To visualize the material behavior under swelling condition an osmotic pressure was applied. Thetissue was placed on top of the objective glass in 0.15M NaCl (Figure 2.1). A membrane with a diam-eter of 30 mm was cut out of a dialysis tubing (MW cutoff 8000, Spectrapor, Los Angeles, USA) andplaced over the tissue (Figure 2.1). The membrane was tightened between two rings to prevent thechamber from leaking. A Zeiss LSM 510 confocal laser scanning microscope (CLSM) with a 40x LD

3

Chapter 2. Materials and methods 2.3. Loading due to osmotic pressure

ACHROPLAN/0.6 corr lens was used to visualize the tissue deformation. Every 20 minutes an imagewas made, with a total of 33 images. The images were 230.3 x 230.3 x 29.1µm with a resolutionof 512 x 512 x 21 pixels. To get a better resolution the images were made by 4 times averaging thescanning. A three-dimensional image took 15 minutes to scan.

(a) Schematic representation of thetissue chamber.

(b) A picture of the setup, a thermocouple is used tomeasure the temperature, aCO2 controle can be addedwhen working with living tissue

Figure 2.1: The osmotic loading chamber. The tissue is in the chamber under the membrane. The PEG is on topof the membrane. The membrane is semipermeable so water is able to flow through the membrane, but the PEGmolecule can not penetrate into the tissue. The circles on the side are led lights to head up the fluid temperature

Polyethylene glycol (PEG) 20,000 (Fluka BioChemika Ultra, St. Gallen, Switzerland) diluted in0.15M NaCl was used to create an osmotic pressure difference. PEG can be used to create very highosmotic pressures. It is a flexible polymeer and is unlikely to have specific interactions with biologicalchemicals. These properties make PEG one of the most useful molecules for applying osmotic pres-sure in biochemistry experiments, particularly when using the osmotic stress technique [5,22,26,39].PEG solutions with different concentration were poured on top of the membrane to look at the swellingbehaviour. The PEG calibration curve of Maroudas et al. [26] translated the PEG concentration intoa osmotic pressure. As suggested by Maroudas et al. [26] the temperature was kept constant at 25◦C,due to a temperature control device.

2.3 Loading due to osmotic pressure

The setup uses osmoses to create a pressure. Because of the differences in chemical potential in thePEG solution and the physiological salt solution in the tissue, a hydrostatic pressure difference exists.This leads to fluid flow until equilibrium is reached. Balance of forces in the disc at equilibrium:

Osmotic pressure of proteoglycans (πPG) = Collagen stress (Pc) + Externally applied pressure (swellingor osmotic pressure,πswelling).

πPG = Pc + πswelling (2.1)

The swelling pressure (πswelling) of a slice of tissue of a stated composition is defined as the pressureat which it neither loses nor gains hydration [26]. The Equilibrium of the tissue with a externalsolution requires:

4

2.4. Three-Dimensional Digital Image Correlation Technique Chapter 2. Materials and methods

πPG −RT

√(cfc)2 + 4(cs)2 = πs − 2RTcs (2.2)

in which R represents the universal gas constant (8.314J ·K−1 ·mol−1), T the absolute Temperature(K), cfc is the fixed charge density,cs is the saline concentration (0.15M) andπs is the osmoticpotential associated with the PEG and can be written as:

πs = −πPEG = −2RTcPEG (2.3)

in whichcPEG represents the concentration PEG solution andπPEG the osmotic pressure of the PEGsolution.For the displacement experiment a PEG concentration of 10 g/100g saline was used, which creates aπPEG of approximately 1 atmosphere

2.4 Three-Dimensional Digital Image Correlation Technique

A three-dimensional digital image correlation was used to calculate the displacements. The DigitalImage Correlation (DIC) is a numerical technique that compares several points of two digitized im-ages, to determine the displacement of these points. The method used is based on the two-dimensionaltechnique developed by Sutton et al. [37]. Verhulp et al. [15, 42] has extended this two-dimensionaltechnique to three dimensions for strain measurements. When an images is digitized the intensitypattern of the reflected light is stored as grey values. The method compares the images by using thesegrey values. Each small subset of grey values in the reference situation is related to a small subset inthe deformed situation. To link the position of these subsets linear deformation is assumed:

x′ − x = u + ∂u∂xdx + ∂u

∂y dy + ∂u∂z dz (2.4)

y′ − y = v + ∂v∂xdx + ∂v

∂ydy + ∂v∂z dz (2.5)

z′ − z = u + ∂w∂x dx + ∂w

∂y dy + ∂w∂z dz (2.6)

where(x, y, z) represent the position of a point in a reference situation,(x′, y′, z′) represent the po-sition of that point in the deformed situation,(u, v, w) represent the displacement components of thecenter of a subset and(dx, dy, dz) represent the distance form(x, y, z) to the center of the subset.When a reference subsetA (x, y, z) is compared to a deformed subsetB (x′, y′, z′) the optimizedimage correlation technique maximizes the correlation coefficient R by minimizing the function:

S = 1−R = 1−∑N

i,j,k=1 A(xi, yj , zk)∑N

i,j,k=1 B(x′i, y′j , z

′k)(∑N

i,j,k=1 A(xi, yj , zk)2∑N

i,j,k=1 B(x′i, y′j , z

′k)

2) 1

2

(2.7)

which corresponds to a search for the best position and deformation of the subsetA (x, y, z) in subsetB (x′, y′, z′). The subset is called a window, both subset A and B are shown in figure 2.2The functionS that must be minimized is a function of 12 independent variables denoted by the vector:

W3D =(

u, v, w,∂u

∂x,∂u

∂y,∂u

∂z,∂v

∂x,∂v

∂y,∂v

∂z,∂w

∂x,∂w

∂y,∂w

∂z

)(2.8)

5

Chapter 2. Materials and methods 2.5. Strain calculations

To improve the convergence the correlation will take two steps. 1) The window is assumed to trans-late without deformation or rotation. The displacement gradients are therefore set to zero and a FastFourier Transformation (FFT) calculation is used to determine the correlation functions for all possi-ble window positions in the search area (u,v and w are determined). 2) An iterative search algorithmis used to determine the location of maximum correlation more accurately. The FFT-calculated dis-placements u, v and w are used as initial estimates in the Broyden-Fletcher-Goldfarb-Shanno (BFGS)method. This is a quasi-Newton method that minimizes the correlation function S at a sub-pixel level.The calculation allows the window to deform linearly and a four-point cubic interpolation is used toevaluate image values between adjacent pixels. This gives the calculations a sub-pixel accuracy. Thesize of the window and the search area used in the DIC program had to be optimized for each regionand time step, but they were all approximately 13 x 13 x 13 and 40 x 40 x 40 pixels for the matrixcalculations and 7 x 7 x 7 and 25 x 25 x 25 pixels for the cell calculations. Different points wereselected close to the cell and further into the matrix.

(a) A 2D example of the window andsearch area in the reference situation

(b) A 2D example of the window andsearch area in the deformed situation

Figure 2.2: Subset A and subset B with their search areas

Hendriks et al. [15, 23] have shown that this technique is applicable for confocal images. Althoughthey have used it on human epidermis, the image types were similar.Sets of points in the extracellular matrix around three different cells were selected to measure the cellstrains and the strains locally around the cells. Based on the collagen type VI immunolocation studyand previous research by Roberts et al. [33] pericellular matrix is defined as a spherical regions ofradius 15µm around the cell. Three different locations within the extracellular matrix were defined tocalculate the local strains in the matrix and there were points defined more spread through the matrixover the intra- and inter fibrillar space to measure the global strains in the extracellular matrix.

The correlation technique was tested for our images and described in Appendix B. A total of 22images were used for the calculations.

2.5 Strain calculations

A three-dimensional strain field can be calculated from the displacement field. Peters [30] presenteda method in which the local differences in the displacements have been expanded in a Taylor series,which was truncated after the first, linear term. This method is shown to be insufficient in the presenceof steep strain gradients. Therefor the method is improved by Geers et al. [13]. A deformation tensor

6

2.5. Strain calculations Chapter 2. Materials and methods

Cell 1

Cell 2

Cell 3

(a) Location of the cells used for calculations, Cell 1 (Red),Cell 2 (Yellow), Cell 3 (Green)

Matrix 1

Matrix 2Matrix 3

(b) Location of the matrix regions used for calculations, Ma-trix 1 (Red), Matrix 2 (Yellow), Matrix 3 (Green)

(c) Location of the global grid used for calculations

Figure 2.3: A two-dimensional representation of the different regions with marker points used for the imagecorrelations

7


must be calculated from the discrete displacement field. A particle P0 at time t=0 is observed and thedistance to its neighbouring particle Q0 is calculated. P0 has position vector x0, the position vector ofQ0 is defined as x0+dx0. The same is done in the deformed state at time t as shown in figure 2.4.

Figure 2.4: Infinitesimal deformation in the 2D-plane, adapted from Geers(1996)

The deformation vector in Pt at time t is defined as:

dxt = F · dx0 (2.9)

resulting in

F = (∇0xt)c =

∂xt

∂x0(2.10)

The position of the neighbouring pointxt+∆xt can be written as a Taylor-series expansion:

∆xt =∂xt

∂x0·∆x0 +

∂2xt

∂x20

: ∆x0∆x0 + a (2.11)

where a is the truncation error. A particle Pt is surrounded byk neighbouring particles as shown infigure 2.5. For each of these neighbouring particles∆xt can be calculated which will eventually resultin a estimation for the deformation tensor F.

When the deformation tensor F is known, the Green-Lagrange strain tensor E can be derived by

E =12

(F c · F − I) (2.12)

where I is the unit tensor.

8

2.5. Strain calculations Chapter 2. Materials and methods

Figure 2.5: Particle distribution around the central point, adapted from Geers(1996)

9


10

Chapter 3

Results

3.1 Confocal microscopy

3.1.1 Type VI collagen staining

Figure 3.1 shows the pericellular matrix of the annulus cells with the collagen VI immunostaining.These images determine the pericellular region in the annulus fibrosus which lies within 10 to 15µmfrom the cell nuclei.

(a) bar = 20µm (b) bar = 50µm

Figure 3.1: Confocal images, red: nuclei (PI), green: Collagen Type VI, showing Pericellular Matrix (FITC)

3.1.2 Deformation shown with CNA35 probe

Figure 3.2 shows the swelling observed with the 40x objective of the confocal microscope, with thecollagen fibers stained with the CNA35 probe (in green). The cells were stained with PI (in red). Onglobal scale it looks like the swelling has a major influence. Large changes in distance between thecells point at great deformation. But on a local scale (Figure 3.3) the displacements seem to be much

11

Chapter 3. Results 3.1. Confocal microscopy

(a) t=0, 10% PEG in 0.15M NaCl (b) t=8h, 0.15M NaCl

Figure 3.2: Images from confocal microscopy

(a) ECM before deformation (b) ECM after deformation

Figure 3.3: 2D point distribution in the Extracellular matrix, local scale

12

3.2. 3D Correlation technique Chapter 3. Results

smaller. The swelling occurs mostly between the lamellae (Figure 3.2). Around these intralamellarspaces the strains are suspected to be high, but on a local scale in the interlammelar spaces the strainsare expected to be much lower.

3.2 3D Correlation technique

As shown in Appendix B the image correlation technique gave good results for the rigid displace-ments. Different regions of interest were chosen for the image correlation. Figure 2.3(a) shows thethree cells used for the calculations. Cell 1 and 2 are both surrounded by normal extracellular matrix.Cell 3 is in a region were the collagen packing is less dense and the fluid is able to flow in duringswelling. Figure 2.3(b) shows three different extracellular matrix regions. Matrix 1 and 3 are in acollagen rich lamella region. Matrix 3 includes the pericellular environment of cell 1. Matrix 2 ischosen in a ’bridge’ region between two lamellae. And in figure 2.3(c) the global grid is shown. Thedisplacement field of the global grid (Figure 3.4) shows that the displacements can be properly calcu-lated. The image correlation technique was not able to find all the points in the deformed state, some

(a) Displacement vectors starting in the given grid points forthe undeformed situation

(b) Displacement vectors pointing at the new coordinates ofthe calculated grid points in the deformed situation

Figure 3.4: 2D displacement field of the global grid, calculated by the image correlation

points got lost due to the change in contrast in the deformed state (figure 3.3). Tabel 3.1 shows thepercentage of calculated points. Because the PI is less influenced by bleaching, the contrast for thecell images does not change much. Hence the percentage of convergence of the image correlation ofthe cells is higher than the CNA stained matrix image. All the deformed states were only comparedwith the undeformed state at t=0.

13

Chapter 3. Results 3.3. Strain calculations

Table 3.1: Number of points found with the image correlation

Region number of defined points number of calculated pointspercentage

Cell 1 (PI) 819 634 77%Cell 2 (PI) 800 684 86%Cell 3 (PI) 880 467 53%

Cell 1 in Matrix 3 (PI + CNA) 2805 918 33%Matrix 1 (CNA) 1859 1065 57%Matrix 2 (CNA) 1331 494 37%Matrix 3 (CNA) 2805 1497 53%

Global 200 49 25%

3.3 Strain calculations

3.3.1 Cellular level

To find the cellular strains in vitro, the PI nuclear stain was used to look at the deformations. Thethree different cells can be compared to each other. The mean volume ratio (det(F)) and maximumshear strain are plotted in figure 3.5. Cell 3 seems to experience higher strains than cell 1 and 2.To visualize how the cells deform figure 3.6 shows the grid around cell 1 and the undeformed anddeformed situation. The first and third principal strains for the deformation of this cell are plotted forthree views (Figure 3.7). The third principal strain is 5 times as high as the absolute first principalstrain and the first principal strain is mainly negative. These figures show that the cell stretchesperpendicular to the fiber direction. Besides this stretching there also is a rotation. The same figuresare shown for cell 2 and 3 in appendix D.

Cell 1 Cell 2 Cell 30

0.5

1

1.5

2

2.5

det(

F)

(a) Volume rationdVdV0

for cell 1 to 3

Cell 1 Cell 2 Cell 30

0.5

1

1.5

2

2.5

3

max

she

ar

(b) Maximum shear strainE3−E12

Figure 3.5: Differences in deformations for the different cells

3.3.2 Matrix level

The deformation of the pericellular matrix is examined with the region matrix 3. Figure 3.8 showsthe point distribution of the grid and the coordinates to compare them to the contour plots of figure

14

3.3. Strain calculations Chapter 3. Results

(a) cell 1 before deformation (b) cell 1 after deformation

Figure 3.6: 2D point distribution for cell 1, used for the image correlation

0.128 0.13 0.132 0.134 0.136 0.138

0.077

0.078

0.079

0.08

0.081

0.082

x [mm]

y [m

m]

(a) the projection of the vector field in the x-y plane ,perpendicular to the fiber direction

0.078 0.08 0.082

0.009

0.01

0.011

0.012

0.013

0.014

0.015

0.016

0.017

0.018

0.019

y [mm]

z [m

m]

(b) the projection of the vector field in the y-z plane

0.1280.130.1320.1340.1360.138

0.009

0.01

0.011

0.012

0.013

0.014

0.015

0.016

0.017

0.018

0.019

x [mm]

z [m

m]

(c) the projection of the vector field in the x-z plane

Figure 3.7: vector field of the first and third principal strain for cell 2. Red is the first principal strain E11, blueis the third principal strain E33. E33=5*E11

15


3.8. These figures show strains and changes as a function of the distance to the cell. The further awayfrom the cell the higher the strains seem to get.Figure 3.9 shows the mean values of the volume change and shear factor for the different regions ofthe matrix defined by figure 2.4(b). These values show that the collagen packing seems to get tighterin the lamellae. When the three regions are compared to each other the shear strain in matrix 2 ishigher than in matrix 1 and 3. This was the region in between the lamellae.The deformations of region matrix 1 is calculated over time. Figure 3.3(a) and (b) show the pointdistribution in the reference state and the deformed state of matrix 1. The results of the strain fields(Figure 3.11) of the local region matrix 1 (Figure 3.3) over time show the heterogeneous characterof the material. The first and third principal strain, the volume ratio(det(F)) (Figure 3.10) and firstprincipal strain fields (Figure 3.11), show shift in size of the principal strain as well as in principalstrain direction. All the time steps are plotted in Appendix E. There is a difference in the numberof calculated points for the time steps, this was due to the difference in resolution of the images.To compute the total deformation in the sample calculations were done on the global matrix grid asshown in figure 2.3(c) and figure 3.4. The calculations of the strains at the global matrix level show aincrease of the volume.

16

3.3. Strain calculations Chapter 3. Results

(a) point distribution in image

0.11 0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15 0.1550.06

0.065

0.07

0.075

0.08

0.085

0.09

0.095

(b) coordinates of the point distribution

x [mm]

y [m

m]

0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15

0.065

0.07

0.075

0.08

0.085

0.09

−0.46

−0.44

−0.42

−0.4

−0.38

−0.36

−0.34

(c) First principal strain

x [mm]

y [m

m]

0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15

0.065

0.07

0.075

0.08

0.085

0.09

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

(d) Third principal strain

x [mm]

y [m

m]

0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15

0.065

0.07

0.075

0.08

0.085

0.09

0.25

0.3

0.35

0.4

0.45

0.5

0.55

(e) Maximum shear strainE3−E12

x [mm]

y [m

m]

0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15

0.065

0.07

0.075

0.08

0.085

0.09

−0.4

−0.2

0

0.2

(f) Volume ratiodVdV0

for cell 1 in Matrix 3

Figure 3.8: 2D point distribution for cell 1 in matrix 3, used for the image correlation (a,b). Strain distributionfor cell 1 in matrix 3 (c-f). These images show that the strain increases as a function of the distance from thecell.

17


Matrix 1 Matrix 2 Matrix 3 Global0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2de

t(F

)

(a) Volume ratiodVdV0

for matrix 1 to 3 and the global matrix

Matrix 1 Matrix 2 Matrix 3 Global 0

0.5

1

1.5

2

2.5

3

max

she

ar


Figure 3.9: Differences in deformations for the different defined matrix regions

0 100 200 300 400 500 600 7000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.5

t [min]

det(

F)

(a) Volume ratiodVdV0

0 100 200 300 400 500 600 7000.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

t [min]

max

she

ar


Figure 3.10: Strain variation for matrix 1 over time

0.160.18

0.20.22

0.24

0.08

0.1

0.12

0.14

0.160.005

0.01

0.015

0.02

(a) At t=120 min

0.16

0.18

0.2

0.22

0.06

0.08

0.1

0.12−0.01

0

0.01

0.02

0.03

(b) At t=260 min

Figure 3.11: First principal strain field in the extracellular matrix (region matrix 1) at different time points

18

Chapter 4

Discussion

A new method is developed to observe swelling in the matrix of the intervertebral disc with the useof a confocal microscope. Three-dimensional strain distributions of cellular environment and extra-cellular matrix are measured successfully in bovine annulus fibrosus samples under osmotic loading.The boundary conditions of the annulus sample ensure physiological osmolarity and a physiologicalprestress. Both osmolarity and prestress are well defined. The pericellular matrix was located in theinner annulus fibrosus, which is consistent with earlier immunolocalization studies from Roberts andHorikawa [17, 33]. Measurements of the strain distribution around the cell show an increase of thestrains as a function of the distance from the cell (Figure 3.8). This may suggest that there is a dif-ference in pericellular and extracellular strains. This pericellular region plays an important role inprotecting the cells from excessive strain following changes in pressure or osmolarity. More researchis needed to show that the difference is significant in a series of measurement on different samples.Although the collagen probe which we applied has shown more affinity with the extracellular colla-gen type I, it also binds to the pericellular type III and VI collagen [25]. Hence both pericellular andextracellular displacements were measured. With a more specific probe for the pericellular collagentypes, there might be a better contrast for the image correlation, so that pericellular regions can bebetter defined in the experiment. It was not possible to use the immunohistology stain to measurethe pericellular strains with swelling. Because this staining method only worked properly when weadded a fixation step in the staining protocol, which influences the strains tremendously. A highermagnification may also help in the quantification of the pericellular material properties.The three-dimensional images suggest that with swelling the fluid flows into the spaces between thelamellae. Large global changes are seen but locally the deformations seem small. The calculationsfor the local regions even show a reduction of volume. This suggests that with swelling the osmoticpressure makes the collagenous lamellae contract. This finding is consistent with the observation ofMaroudas et al. and Basser et al. [5, 26] in articular cartilage. Maroudas et al suggested this to bebecause of a difference in proteoglycan concentration in the intrafibrillar and extrafibrillar space. Another explanation for the increase of the packing density may be that the fibrils are pressed togetherdue to the hydrostatic pressure, which reduces the permeability of the lamellae.Different studies show a increase in permeability with an increase of hydration [18, 38], the resultsof the current study suggest that this increase in permeability is only because of the dilatation of thedistance between the lamellae.Basser et al. [5] already showed the importance of the stiffness of the collagen network in limiting hy-dration. Cells normally want to attract fluid because of the relative high proteoglycan content aroundthe cells [40]. This contraction of the collagen network seems to protect the cell from swelling. Thisdependence of collagen density can also been seen when comparing the three different cells. The

19

Chapter 4. Discussion

number of cells observed in the experiments is too small to draw clear conclusions. Besides that inthe present experiment the cells were dead. Therefore any observation regarding the cells, cannot beextrapolated to the in vivo tissue. However, from the data some trends are detected. When the threedifferent cell regions are compared to each other it can be seen that the strain levels for cell 3 arehigher than these for cell 1 and 2. Cell 1 and 2 lie in a collagen dense region, and thus they are moreprotected. Where cell 3 shows a volume increase the volumes of cell 1 and 2 decrease. Because of thedifferences in staining method, the cellular calculations were done on the PI staining and the matrixcalculations on the CNA staining, the cellular strains can not be compared to the matrix strains.The strain fields (Figure 3.7 and Appendix D) of the cells suggest that the cells in the collagen richmatrix enlarge perpendicular to the fiber direction and shrink in the fiber direction. Unfortunately nocomparison can be made with other studies. Cell studies have been done with isolated cells underosmotic loading. We advise to examine the cellular deformation under osmotic loading in the matrixsurrounding cells more closely. To cut the tissue in the fiber direction would be very useful to gainmore insight in this.The setup is suitable to mimick in vivo osmolarity and pressure in an in vitro set-up of cartilaginoustissues. In life cell studies, this should result in physiological hydration of the tissue and the cells. Wedo not exclude that indentation of the samples is possible across the dialysis membrane.The experiments have shown that our osmotic pressure chamber is applicable to study 3D strain inintervertebral disc tissue. However the following limitations still need improvements.The correlation technique was originally made for and tested on micro-Computed Tomography (µCT)[42] which has the same resolution in all directions. However because our images have been madewith a confocal microscope the resolution in the z-direction (2,1µm) is lower than that in the x- and ydirection (0.4µm). This affects the accuracy of the strain values in z-direction. The experiments withthe ridged displacements show that the images have enough contrast to use the image correlation inthe x- and y-directions (Appendix B). Rotational changes and ridged displacements in the z-directioncould not be tested because of the limitations of the set up. Indeed, the correlation technique had sometroubles calculating the displacements in the z-direction. An optimization was needed for the windowor subset size in combination with the size of the search area, to get the program to calculate smoothz-displacement fields. The lower z-resolution and the limited number of z-stacks (21 against 512 x512 pixels in x and y) are probably the cause of the difficulty.Because of the difficulty of finding the correct displacements in z-direction less points could be usedfor the strain calculation. For the local calculations this was no problem. The grid that was used in-cluded so many points that enough points were left after the displacement calculations. Besides that,they were equally spread so the strain calculations gave reliable values. However for the global gridthis was more of a problem. Because the major differences of displacements of the points in the grideach of the 200 points had to be calculated on its own, where with the local grid all the points could becalculated in one calculation. About 25 % of the points could be correctly calculated and in the globalgrid these calculated points were not equally spread over the grid. Therefore values of the strains inthis region were probably underestimated.During the staining of the samples there may have been a proteoglycan leakage when they were ex-posed to a salt solution [38]. Once the tissue is exposed to a PEG concentration the leaking is lessbecause the PEG-loading reduces the hydration. It may be favorable to stain while having a PEGprestressing.The imaging depth we have reached was at most 80µm. At the surface collagen fibers roll up andthe material there is of no use for measuring the material properties. For good microscopic measure-ments the tissue samples need to have a flat edge. The flatness of the edge is adversely affected bythe swelling during the staining. If the tissue sample is too thin (100-500µm)it can not be used formicroscopy anymore because the surface becomes irregular. With thicker samples the influence of theswelling is less because the collagen network is stiffer.The contrast of the images decreased over time. This is due to the bleaching of the CNA probe. Be-

20


cause reaching a pressure equilibrium takes a couple of hours and this process is followed over time,there is a decrease of fluorescence. Although we have tried to correct a little for the loss of resolutionin time by turning up the laser power in steps, there was still a loss of resolution in time.The confocal laser scanning microscope had a shift in x- and y- direction due to a possible error inthe moving device. We have corrected this shift by moving the sample in a similar focus position byhand. This could not been done automatically because this shift was not the same over time. Becauseof an error in the correction, some of the images were not useful because they did not image the totalarea of interest.In conclusion the current study shows a new method to study swelling in intervertebral disc tissue.A way is created to include the osmotic pressure in in vitro experiments. This is the first time thecell-matrix deformation is studied in the annulus fibrosus under physiological osmolarity and pres-sure. Images and strain calculations show the heterogeneous character of the tissue. Furthermore, theobservations suggest the presence of a pericellular matrix which protects the cells against excessivestrains. This study provides a base to further investigate the effect of swelling on the micromechanicalenvironment of the cell.Future studies are needed to improve the correlation in the z-direction of the images. It is possible toimprove the z-resolution with the confocal microscope but it might be useful to continue working witha two-photon microscope to improve the imaging depth and z-resolution. Besides this, the bleachingis much less with a two-photon microscope because it does not have the hourglass-shaped light pathlike the confocal microscope but it is limited to a spot at the focus [24,32].

21


22

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25

BIBLIOGRAPHY BIBLIOGRAPHY

26

Appendix A

Osmotic technique

To show that the setup can be used for applying a osmotic pressure a picture was taken before andafter the placement of a PEG solution on top of the membrane. The tissue sample is stretched but atthe same time it gets thinner (Figure A.1). The stretching is due to the osmotic pressure differencebetween the two fluids which is higher than the osmotic pressure difference between the PEG solutionand the tissue.

(a) Before adding the PEG solution on top ofthe membrane

(b) After 6 hours of 10% PEG on top of themembrane

Figure A.1: The shrinkage of the tissue observed over time in the setup

27

Appendix A. Osmotic technique

28

Appendix B

3D Correlation technique

B.1 Rigid Displacement

To check if the resolution of our images is good enough for the image correlation a test with a rigiddisplacement is done. The microscopic position was moved in steps of 3µm in x- and y- direction.The images were made with a 40x objective and an image dimensions were 325.8 x 325.8 x 30.4µmrespectively 512 x 512 x 23 pixels. Hence a displacement of 3µm x 3µm corresponds with a shift of4.71 x 4.71 pixels. Looking at the images a shift in pixels of over 4.71 pixels in x and y was observed.The shift was approximately 10 pixels. This means there is an uncertainty in the confocal movementsystem, that causes a difference in in- and output of the displacement. However this was not relevantsince we used a different approach for the final study. Because of this uncertainty an estimation of thepixel displacements is made to compare with the correlation calculations.The results of the calculations of the rigid displacements are shown in table B.1 and B.2. They arevery close to the estimated values hence we can say that the program is capable of calculating the rigiddisplacements. Figure B.1 shows the calculated displacement vectors of one of the calculations.

29

Appendix B. 3D Correlation technique B.1. Rigid Displacement

260265

270275

280

210

215

220

225

23012

14

16

18

20

22

x (pixels)y (pixels)

z (p

ixel

s)

Figure B.1: The displacement field as it was calculated with the image correlation programm

Table B.1: Rigid displacement, the x-displacement for different displacement steps, column 2 gives the pre-scribed displacement, column 3 gives the estimated displacement and column 4 gives the calculated displace-ment

Image number [number of steps]Displacement (µm) Estimated (pixels) Calculated (pixels [µm])

1 and 2 [1] 3 11 11.481± 0.56167 [7.21]2 and 3 [1] 3 11 11.596± 0.68013 [7.39]3 and 4 [1] 4 13 12.755± 0.56861 [8.12]4 and 5 [1] -10 -10 -10.448± 0.44303 [6.65]1 and 3 [2] 6 23 23.202± 0.5987 [14.78]1 and 4 [3] 10 36 36.383± 0.96376 [23.17]

21 and 22 [1] 5 10 10.152± 0.15095 [6.47]21 and 23 [2] -5 -3 -2.3021± 0.30988 [-1.47]22 and 23 [1] -10 -13 -12.525± 0.15216 [7.98]22 and 24 [2] -5 -5 -3.4944± 0.64013 [2.23]23 and 24 [1] 5 8 7.7118± 0.32507 [5.65]

30

B.1. Rigid Displacement Appendix B. 3D Correlation technique

Table B.2: Rigid displacement, the y-displacement for different displacement steps, column 2 gives the pre-scribed displacement, column 3 gives the estimated displacement and column 4 gives the calculated displace-ment

Image number [number of steps]Displacement (µm) Estimated (pixels) Calculated (pixels [µm])

1 and 2 [1] 3 10 9.7718± 0.68156 [6.22]2 and 3 [1] 3 11 11.32± 0.68693 [7.21]3 and 4 [1] 4 13 12.687± 0.59762 [8.08]4 and 5 [1] -10 -10 -10.118± 0.29588 [-6.44]1 and 3 [2] 6 21 21.098± 0.45037 [13.44]1 and 4 [3] 10 34 33.609± 0.97999 [21.41]

21 and 22 [1] 5 10 9.6965± 0.36037 [6.18]21 and 23 [2] -5 -3 -2.5345± 0.14278 [-1.61]22 and 23 [1] -10 -13 -12.383± 0.38012 [7.89]22 and 24 [2] -5 -4 -4.409± 0.97644 [2.81]23 and 24 [1] 5 9 7.7118± 0.32507 [4.91]

31

Appendix B. 3D Correlation technique B.1. Rigid Displacement

32

Appendix C

Images

Figure C.1 and C.2 show the different z-stacks for the undeformed (PEG solution is 10g/100g saline)and the deformed (PEG solution is 0g/100g saline) situation of the sample. A small shift in x- and y-direction can be observed from the beginning until the end of the z-stack. This shift is not constantin time so this may cause a deviation in the calculations. These depths are relative depths, so theydo not start at the surface of the tissue. The cells are a good markers as a reference while comparingthese three-dimensional images. There is a shift in both the x- and y- direction. A correction for thisis made in the first step of the image correlation.

33

Appendix C. Images

Figure C.1: Z-stack images with 10% PEG

34

Appendix C. Images

Figure C.2: Z-stack images without PEG in 0.15M NaCl

35

Appendix C. Images

36

Appendix D

Cell deformations


Figure D.1: 2D point distribution for cell 2, used for the image correlation

0.118 0.119 0.12 0.121 0.122 0.123 0.124 0.125 0.126

0.151

0.152

0.153

0.154

0.155

0.156

0.157

x [mm]

y [m

m]

(a) the projection of the vector field in the x-y plane ,perpendicular to the fiber direction

37

Appendix D. Cell deformations

0.152 0.154 0.156

0.008

0.01

0.012

0.014

0.016

0.018

y [mm]

z [m

m]


0.1180.120.1220.1240.126

0.008

0.01

0.012

0.014

0.016

0.018

x [mm]

z [m

m]


Figure D.2: vector field of the first and third principal strain for cell 2. Red is the first principal strain E11,blue is the third principal strain E33. E33=5*E11


Figure D.3: 2D point distribution for cell 3, used for the image correlation

0.179 0.18 0.181 0.182 0.183 0.184

0.177

0.178

0.179

0.18

0.181

0.182

0.183

0.184

0.185

x [mm]

y [m

m]

(a) the projection of the vector field in the x-y plane,perpendicular to the fiber direction.

38


0.178 0.18 0.182 0.184

0.006

0.008

0.01

0.012

0.014

0.016

0.018

y [mm]

z [m

m]


0.180.1820.184

0.006

0.008

0.01

0.012

0.014

0.016

0.018

x [mm]

z [m

m]


Figure D.4: vector field of the first and third principal strain for cell 3. Red is the first principal strain E11,blue is the third principal strain E33. E33=10*E11

39


40

Appendix E

Time steps

Figure E.1: Principal strain vectors 1st principal strain

0.16

0.18

0.2

0.22

0.1

0.12

0.14

0.160

0.005

0.01

0.015

0.02

0.025

(a) t=60 min

0.16

0.18

0.2

0.22

0.08

0.1

0.12

0.14

0.160

0.005

0.01

0.015

0.02

(b) t=80 min

0.160.18

0.20.22

0.24

0.08

0.1

0.12

0.14

0.160.005

0.01

0.015

0.02

(c) t=120 min

0.150.16

0.170.18

0.190.2

0.08

0.1

0.12

0.14

0.160.005

0.01

0.015

0.02

0.025

(d) t=140 min

41

Appendix E. Time steps

0.160.18

0.20.22

0.24

0.08

0.1

0.12

0.14

0.160

0.005

0.01

0.015

0.02

0.025

(e) t=160 min

0.180.19

0.20.21

0.220.23

0.06

0.08

0.1

0.120.005

0.01

0.015

0.02

0.025

(f) t=180 min

0.16

0.18

0.2

0.22

0.06

0.08

0.1

0.120

0.005

0.01

0.015

0.02

0.025

0.03

(g) t=200 min

0.16

0.18

0.2

0.22

0.06

0.08

0.1

0.120

0.005

0.01

0.015

0.02

0.025

0.03

(h) t=220 min

0.16

0.18

0.2

0.22

0.06

0.08

0.1

0.12−0.01

0

0.01

0.02

0.03

(i) t=260 min

0.160.18

0.20.22

0.24

0.04

0.06

0.08

0.1−0.01

0

0.01

0.02

0.03

(j) t=280 min

42


0.16

0.18

0.2

0.22

0.04

0.06

0.08

0.10

0.005

0.01

0.015

0.02

(k) t=300 min

0.180.19

0.20.21

0.220.23

0.04

0.06

0.08

0.10

0.005

0.01

0.015

0.02

(l) t=320 min

0.16

0.18

0.2

0.22

0.04

0.06

0.08

0.10

0.01

0.02

0.03

0.04

(m) t=340 min

0.16

0.18

0.2

0.22

0.04

0.06

0.08

0.10

0.005

0.01

0.015

0.02

0.025

0.03

(n) t=380 min

0.16

0.18

0.2

0.22

0.04

0.06

0.08

0.10

0.005

0.01

0.015

0.02

0.025

(o) t=400 min

0.16

0.18

0.2

0.22

0.02

0.04

0.06

0.080

0.005

0.01

0.015

0.02

0.025

(p) t=440 min

43


0.16

0.18

0.2

0.22

0.04

0.06

0.08

0.10

0.005

0.01

0.015

0.02

(q) t=460 min

0.16

0.18

0.2

0.22

0.06

0.08

0.1

0.120.005

0.01

0.015

0.02

0.025

(r) t=500 min

0.16

0.18

0.2

0.22

0.04

0.06

0.08

0.10

0.01

0.02

0.03

0.04

(s) t=560 min

0.16

0.18

0.2

0.22

0.02

0.04

0.06

0.08

0.10

0.005

0.01

0.015

0.02

0.025

(t) t=580 min

0.16

0.18

0.2

0.22

0.04

0.06

0.08

0.10

0.005

0.01

0.015

0.02

0.025

(u) t=620 min

44

Appendix F

Confocal laser scanning microscopy

F.1 Principle

Confocal laser scanning microscopy (CLSM) provides optical serial sections through thick biologicalsamples. It makes it possible to perform both three-dimensional visualization and three-dimensionalquantitative analysis [10]. The specimen in a CLSM is irradiated in a pointwise way. To obtain in-formation about the entire specimen, it is necessary to guide the laser beam across the specimen. In aCLSM a confocal aperture (pinhole) is arranged in a plane conjugate to the intermediate image planeand, thus to the object plane of the microscope (Figure F.1). Excitatory light from a laser is reflectedby a dichroic mirror and focused by the microscope objective lens to illuminate a point on the focalplane inside the 3D specimen. The illuminated spot is then imaged onto a detector through the pin-hole. Only in-focus light is imaged through the pinhole, whereas out-of-focus light is rejected by theedge.

Figure F.1: Schematic diagram of a confocal microscope [12]

The quality of the image generated in a CLSM is not only influenced by the optics (as in a conven-tional microscope) but also, by the confocal aperture (pinhole) and by the digitization of the objectinformation (pixel size). Another important factor is light noise (laser noise, or the shot noise of thefluorescent light) [43].

45

Appendix F. Confocal laser scanning microscopy F.2. Resolution

F.2 Resolution

The resolution is meant to express the separate visibility, both laterally and axially, of points during thescanning process. The resolution is based on the Rayleigh-criterion. This defines the distance betweentwo sources that can be imaged independently, as the distance at which a maximum of the one Airypattern (interference pattern) coincides with the first minimum of a second one. The resolution is notthe same for all three dimensions. For a numerical aperture> 0.5 the axial resolution is given by thefollowing equation:

raxial =0.88 · λexc(

n−√n2 −NA2)

Whereraxial is the axial resolution,λexc is the excitation wavelength, n is the refractive index of theimmersion liquid and NA is the numerical aperture [43]. The lateral resolution is given by:

rlateral = 0.51λexc

NA

Whererlateral is the lateral resolution [43].The lateral resolution has a linear relationship with the numerical aperture (NA) of the lens, whereasthe axial resolution varies as the square of the NA. So the axial resolution is in general poorer than thelateral resolution.

Table F.1: Resolution of the images

Stain λexc[nm] raxial[µm] rlateral[µm]

CNA 488 2.15 0.41PI 543 2.39 0.46

46

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