A pilot study for the development of a swelling intervertebral disc prosthesis

Transcription

1 Eindhoven University of Technology MASTER A pilot study for the development of a swelling intervertebral disc prosthesis Schaap, C.M. Award date: 1997 Disclaimer This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as presented in the repository. The required complexity or quality of research of student theses may vary by program, and the required minimum study period may vary in duration. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 09. Dec. 2017

2 A pilot study for the development of a swelling intervertebral disc prosthesis. C. M. Schaap (343279) WFW-reporinr Coaches: dr. ir. J.M. Huyghe prof. dr. ir. J.D. Janssen Eindhoven University of Technology Faculty of Mechanical Engineering Biomechanical Engineering March 1997

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4 Contents Contents Abstract... 3 Samenvatting... 5 Notation... 7 Chapter 1 9 Introduction... ~ ~ ~ = Chapter 2 13 The anatomy of the intervertebral disc The spinal column The vertebrae The intervertebral disc Collagen Proteoglycans Chapter 3 17 The swelling of cartilaginous tissues Swelling Triphasic theory Chapter 4 23 A physical model of the intervertebral disc Materials The intervertebral disc models Chapter 5 27 Axial compression and swelling experiments on the disc model The experimental set-up The experiments The 10%-compression experiment The axisymmetry experiment The swelling and compression experiment The swelling experiment Conclusions Chapter 6 41 Finite element simulation ofthe experiments in DIANA The software The simulations Simulation of the 10%-compression experiment Simulation of the swelling and compression experiment Conclusions Chapter 7 53 Conclusions and recommendations Conclusions Recommendations

5 Bibliography Appendix 1 A- 1 The preparation procedure ofthe acrylic acid-acrylamide gel... A-1 Appendix 2 A-2 The breaking of light experiment... A-2 Appendix 3 A-3 me accuracy of the experimental resdts... A-3 Appendix 4 A-6 The Young s moduli, the Poisson s ratio and the shear moduli of the disc models... A-6 Appendix 5 A-15 The fractional volumes of fibres and gel of the gel-fibre mixture. A-15 2

6 Abstract Abstract The water content of the intervertebral disc is variable. Loss of disc water due to mechanical loading is compensated through chemical attraction of water from the body fluid surrounding the disc. In designing an intervertebral disc prosthesis these swelling effects should be taken into account. The project described in this report, serves as a pilot study for the development of a swelling intervertebral disc prosthesis. The aim is to design a physical model, with acrylic acid-acrylamide hydrogei as a starting point, that illustrates the possibilities of an intervertebral disc prosthesis. Like the real disc it should be able to swell and shrink as a result of fluid exchange with its surroundings and it should be able to bear loads of the same order of magnitude as the real disc. The physical model is designed on the basis of the anatomy of the intervertebral disc and its behaviour, which are studied first. The proteoglycan gel in the nucleus is mimicked by acrylic acid-acrylamide-gel. The collagen fibres of the annulus are mimicked by polyethylene fibres. The fibres are attached using EPDM-rubber. Two different types of models are realised, the wound models and the the sleeve models. In the first type the gel is reinforced by a fibre configuration, wound by our own winding machine. The second type of models contain pre-braided sleeves as reinforcement. In order to see whether the properties of the disc model resemble those of the real intervertebral disc, experiments are performed. The relation between disc height and axial disc force is determined as well as the increase in disc radius as a result of disc loading, both chemical and mechanical for different periods of time. The important aspects of the swelling and shrinking behaviour of cartilaginous tissues, for example intervertebral disc tissue, as a response to mechanical or chemical loading is described by the triphasic theory. It is tried to explain the results from the experiments using this theory. The experiments are simulated using the triphasic finite element software in the package DIANA, assuming axisymmetry. Equilibrium results are reasonably well described by the finite element model. Simulations of the transitions following the application of the mechanical load were hampered by numerical problems, probably associated with a Peclet number above unity. The results from the experiments and simulations give an indication of how far the models resemble the real disc and in what ways they need to be improved. It is found that the models are able to resist both chemical and mechanical loads for small periods of time without being damaged. Throughout all the experiments fibres do not detach from the rubber, and do not break. The EPDM-rubber is less satisfactory, it shows tears after the swelling experiment. The different projections of the same model behave in the same order of magnitude. Leakage of gel from the models occurs during the swelling, it is found to be less in the sleeve models than in the wound models. As a result of the insecure initial state of the gel at the beginning of the swelling and compression experiments the measurement results of the displacements are not reliable. The forces in the models are lower than those in vivo. The triphasic analysis of DIANA generates output for the swelling and compression behaviour of an elastic material, with equilibrium stages, which resemble those from the experiments on the disc models. Trends in the transitions between these equilibrium stages are qualitatively described. DIANA does not generate output for certain combinations of material parameters. Using the axisymmetrical elements no fibre reinforcement can be added to the mesh that resembles the reinforcement of the models. The use of a gel-fibre mixture seems a good solution. Probably micro-fractures appear in the gel during the swelling and compression experiments, as 3

7 Abstract evidenced by the high permeability coefficient needed to fit numerical simulations with experimental data. In the design of the disc models end-plates should be included. The size and the shape of the disc models should be variable. The real intervertebral discs vary in size and shape along the spine. It should also be tried to replace the EPDM-rubber with a stronger material. The properties of the acrylic acid-acrylamide-gel should be altered to prevent the occurrence of micro-fractures in the gel. An other aspect that should be prevented is leakage of gel. A way to realise this is to design an even more dense fibre reinforcement. An other solution may be the use of a membrane, that is permeable for water and small solutes and is not permeable for polymers. The models should not contain any gas inclusions. For this purpose the models should be stored in a salt solution. More knowledge of the properties of the gel as a result of the amount of fluid uptake is needed to choose the molarity of such a salt solution. A way to determine the swelling of the gel should be developed. This way the initial condition of the gel is known before an experiment is performed. The external force applied to compress the models would increase, when the models would be more hydrated in their initial state. In future a pretension in the fibres can be achieved by letting the disc model swell in a sodium chloride solution. Doing this the fibres are stretched at the beginning of the experiments. The accuracy of the TIM-system can be improved by interpolation when determining the grey values for the pixels. The triphasic analysis of DIANA does not work for al the combinations of parameter values. The numerical scheme should be improved. A good set of parameter values for the 1:l acrylic acidacrylamide gel is needed to conclude whether or not DIANA describes the disc models satisfactory. 4

8 Samenvatting Samenvatting De water inhoud van de tussenwervelschijf is variabel. Door mechanische belasting van de schijf wordt er water uitgeperst. Dit wordt gecompenseerd door chemische aantrekking van water uit de lichaamsvloeistof, die de schijf omgeeft. Bij het ontwerpen van een tussenwervelschijf prothese moet rekening gehouden worden met dit zwellend gedrag. Het project beschreven in dit verslag, dient als verkennende studie voor de ontwikkeling van een zwellende tussenwervelschijf prothese. Het doel is het ontwerpen van een fysiek model, uitgaande van acrylzuur-acrylamide hydrogel, dat de mogelijkheden van een tussenwervelschijf prothese illustreert. Zoals de echte tussenwervelschijf moet het model in staat zijn om te zwellen en te krimpen als gevolg van vloeistof uitwisseling met de omgeving en het moet in staat zijn belastingen te dragen van dezelfde grootte orde als de echte tussenwervelschijf. Bij het ontwerp van het fysieke model is uitgegaan van de anatomie en het gedrag van de echte tussenwervelschijf. Deze zijn eerst bestudeerd. De proteoglycanen gel in de nucleus is nagebootst door acrylzuur-acrylamide hydrogel. De collageen vezels in de annulus zijn nagebootst door polyethyleen vezels. Deze vezels zijn aan elkaar bevestigd met EPDM-rubber. Twee varianten zijn gerealiseerd, de gewikkelde modellen en de kous modellen. In het eerste type is de gel versterkt met een vezel configuratie, gewikkeld op onze eigen wikkelbank. Het tweede type bevat reeds gevlochten kousen als versterking. Experimenten zijn uitgevoerd om de eigenschappen van de modellen te vergelijken met die van de echte tussenwervelschijf. De relatie tussen model hoogte en axiale kracht op het model is bepaald en de toename in model straal, als gevolg van zowel mechanische als chemische belasting op het model voor verschillende perioden van tijd. De belangrijkste aspecten van het zwel en krimp gedrag van kraakbeenachtige weefsels, bijvoorbeeld tussenwervelschijf weefsel, als gevolg van mechanische of chemische belasting wordt beschreven door de driefasen theorie. Het is getracht resultaten uit de experimenten te verklaren aan de hand van deze theorie. De experimenten zijn gesimuleerd door gebruik te maken van het driefasen eindige elementen programma in het pakket DIANA, onder veronderstelling van axisymmetrie. Evenwicht resultaten zijn redelijk beschreven door het eindige elementen model. Simulatie van de overgangen tussen de evenwicht standen volgend op het aanbrengen van een mechanische belasting, zijn belemmerd door numerieke problemen. Waarschijnlijk hebben deze problemen verband met een te hoog Peclet getal. De resultaten van de experimenten en de simulaties geven een goede indicatie in hoeverre de modellen op de echte tussenwervelschijf lijken en op welke vlakken verbeteringen nodig zijn. Het is gebleken dat de modellen zowel mechanische als chemische belasting van korte duur kunnen weerstaan zonder te beschadigen. Gedurende alle experimenten zijn de vezels niet gebroken en niet losgeraakt uit het rubber. Het rubber vertoont scheuren als gevolg van het zwel experiment. De verschillende projecties van eenzelfde model gedragen zich in dezelfde grootteorde. Gel lekt uit de modellen tijdens het zwellen, dit is meer het geval bij de wikkel modellen dan bij de kous modellen. Als gevolg van de onzekere toestand van de gel bij aanvang van de zwel en compressie experimenten zijn de meetresultaten van de toename van model straal niet betrouwbaar. De krachten in de modellen zijn lager dan die in vivo. De driefasen analyse van DIANA genereert output voor het zwel en het compressie gedrag van een elastisch materiaal met evenwicht toestanden, die lijken op die uit de experimenten op de modellen. Trends in overgangen tussen evenwicht toestanden zijn kwalitatief beschreven. DIANA genereert geen output voor bepaalde combinaties van materiaal parameters. Bij gebruik van 5

9 Samenvattin p axisymmetrische elementen kan geen vezelversterking toegevoegd worden aan het mesh, die op die van de modellen lijkt. Het gebruik van een gel-vezel mengsel lijkt een goede oplossing. Omdat de permeabiliteit coffícint, die nodig is om de experimentele resultaten numeriek te fitten, erg hoog is, lijkt het waarschijnlijk dat er micro-scheurtjes optreden in de gel tijdens de zwel en compressie experimenten. Aan het ontwerp van de modellen moet een eindplaat toegevoegd worden. Het formaat en de vorm van de modellen moet variabel zijn, want in de wervelkolom variëren deze voor de echte tussenwervelschijven. Het EPDM-rubber moet worden vervangen door een sterker materiaal. Om micro-scheuren te voorkomen moeten de eigenschappen van de gel veranderd worden. Ook moet de gel lekkage voorkomen worden. Dit kan door een dichtere vezel structuur te gebruiken of een membraan, dat doorlaatbaar is voor water en kleine ionen en niet doorlaatbaar voor polymeren. De modellen mogen geen gas bevatten. Hiertoe moeten deze in een zout oplossing bewaard worden. Er is meer kennis nodig van de eigenschappen van de gel als gevolg van de hoeveelheid vloeistof die is opgenomen, om de molariteit te kiezen van een dergelijke zout oplossing. Een methode om de mate van zwelling te bepalen moet ontwikkeld worden. Zo doende is de initiële toestand van de gel voor aanvang van een experiment bekend. De externe kracht die nodig is om de modellen in te drukken neemt toe bij toename van hydratatie. Voorspanning in de vezels kan bereikt worden door de modellen te laten zwelen in een natriumchloride oplossing. Tevens zijn dan de vezels gestrekt voor aanvang van een experiment. De nauwkeurigheid van het TIM-systeem kan verbeterd worden door te interpoleren wanneer de grijswaarden van de pixels bepaald worden. De driefase analyse van DIANA werkt niet voor alle combinaties van parameter waarden. Dit moet verbeterd worden. Correcte parameter waarden voor de 1 : 1 acrylzuur-acrylamide gel zijn nodig om te concluderen of DIANA de modellen goed beschrijft. 6

10 Notation Notation Symbols L2 A L; b c c C CfC C pg - C d d D, 0" E E - f f F F - F G h J k K, K K m m y1 y1 N O P Pswell P,t6?, Pek r R - R S S1 s2 the smallest radius of the fibre in plane 2 the Helmholtz free energy the largest ïallws of the fibïe ifi phiïe 2 (in qpendix 5) the grey-vahe of the background (in appendix 3) the internal concentration in mole per unit fluid volume the external concentration in mole per unit fluid volume the fixed charge concentration mole equivalent per unit fluid volume the proteoglycan concentration in mole per unit fluid volume the compliance matrix the density of the fibre (in appendix 5) the breadth of the element, the average for the four models (in chapter 6) the diffusion coefficient / diffusion tensor the Young modulus the Green-Lagrange strain tensor the frequency with which a value occurs (in appendix 3) the total amount of fibres in the disc model (in appendix 5) Faraday's constant (in equations (3.8) and (3.9)) the force on the disc (in chapter 7) the deformation tensor the shear modulus a mesh size parameter the relative volume change of the tissue the amount of sleeves applied in one model the permeability / permeability tensor of the swelling material the plane-strain bulk modulus (in appendix 4) the surface of the gel-fibre mixture (in appendix 5) the molar mass the volume fraction in the swelling material the unit normal vector on the boundary the amount of values the grey-value of the object the fluid pressure the swelling pressure the externally applied pressure Peclet number the radius of the polyethylene fibre the universal gas constant a defined matrix (in appendix 4) the standard deviation of the sample the surface of the polyethylene fibre in plane 1 the surface of the polyethylene fibre in plane 2 7

11 Notation sta the total surface of fibres in plane ~2x3 S the cross-section of the intervertebral disc S the second Piola-Kirchhoff stress tensor eff th the threshold value T the absolute temperature - T the transformation matrix. V the fractional volume d V the velocity vector - Y the molar volume W the weight per length of one sleeve X the value for the amount of pixels - X the sample mean for the value of the amount of pixels a the inner radius of the fibre divided by the outer radius of the fibre E the strain - P the electro chemical potential V the Poisson ratio 5 the electric potential n: the water attraction pressure Pi the mobile ion mass density per unit fluid volume PO the solid mass density per unit tissue volume in the reference state 0 the total stress 0 the stress (in appendix 4) - 0 ef~,oeff the effective Cauchy stress / stress tensor of the solid z time constant 4 the osmotic coefficient in the tissue the osmotic coefficient surrounding the tissue ( 1, the material time derivative following the solid Subscripts Superscripts b ext f g L T O at the boundary within the tissue f the fluid outside the disc S the solid the fibres a the cations or the anions thegel + the cations the longitudinal direction - the anions the transverse direction the reference state 8

12 Chapter 1 Low back pain Low back pain is a complaint which many people have experienced. In an epidemiological study of a Dutch population between 1975 and 1978 is found that 51 % of the men and 57 % of the women have experienced low back pain [42]. At the time of examination 22 % of the men and 30 % of the women were suffering from low back pain. For a British survey these figures are 11 % and 19 %, respectively [20]. Of the Dutch survey nearly half of the men and one third of the women ever suffering from low back pain, reported they have been unfit to work because of the low back pain, and 8 % of the men and 4 % of the women had to change jobs as a result of it. In the United states back and spine conditions ranked third in limitation of activity after heart disease, and arthritis and rheumatism in persons 45 to 64 years of age [7]. As can be understood the economical impact on the industry is large. The costs related to low back pain in the Netherlands in 1983 are estimated to be 1 billion US dollars [44]. There are two categories of low back pain: acute (pain period less than 3 months) and chronic pain. Although the aetiology of low back pain is often found to be unclear, Nachemson [23] states that of the acute pain 90 % is caused by mechanical damage. An example of this is disc herniation [15], [24] and [29]. In herniation of the intervertebral disc the fibres of the annulus are ruptured, allowing the nucleus to be pushed outwards through the fissure. In the case of a posterior hernia, expression of nucleus material may cause compression of the nerve root, causing low back pain radiating to the lower limb. When chronic pain continues over 1 year it is found that the nature is for 80 % psychosocial [6]. An other cause is suggested by [37] which states that in the Netherlands 25 % of people receiving a social security allowance for being unfit to work on medical grounds are incapacitated because of pain in the lower back as a result of intervertebral disc degeneration. Degeneration of the disc is a progressive process, which is caused by a change in the biosynthesis of proteoglycans, a mayor constituent of the intervertebral disc. Treatment A possible treatment of patients suffering from low back pain caused by for example herniated or degenerated intervertebral discs may be to replace the disc by a disc prosthesis. Even today no well-functioning disc prosthesis is available, that could help to solve these problems. On this topic Fairbank, a Consultant Orthopaedic Surgeon [lo] says: The concept of the artificial disc is something which has interested spine surgeons for a long time. In theory it seems a good idea to maintain a useful range of movement in the back in this group of patients. However if you arthrodese a joint in the spine, there is very little cost to range of movement and there are adjacent joints that are capable of taking it up. It would be quite easy to put an artificial disc in when using an anterior approach, this is the approach that was developed in Berlin for the Charite total disc replacement. In practice this disc only allows a small amount of movement and the success in terms of pain relief is very limited. It is extremely important that research is continued into the development of an effective disc prosthesis. 9

13 Chapter 1 Introduction When studying the functioning of the intervertebral disc the requirements are found which the disc prosthesis has to meet. Disc replacements that have been developed already are based on the mechanical function of the disc. In literature is found that also chemical effects play a role in the functioning of the intervertebral disc. The following literature review points this out. Literature review Some studies have been performed to measure or calculate the forces working on the intervertebral disc. Nachemson [22] found by intravital pressure measurements approximate values for the loads on the L3 disc of a person in various postures. He states that the disc pressure is a direct reflection of the load to which the motion segment of the spine is subjected. The values vary from 250 N for supine, awake to 2100 N for forward flexed at 20 and rotated 20, carrying a load of 10 kg. The maximum permissible limit for lumbar disc compression suggested by the National Institute of Occupational Safety and Health is 6400 N [25]. Combining data collected from in vivo experiments and a numerical linked-segment and -lumbar model Potvin [36] found the compression forces on the L4-L5 disc vary between 2700 N and 3500 N for both squat and stoop lifts, when lifting statically loads ranging between kg. In short the intervertebral disc consists of the fibrous annulus fibrosus, surrounding a gelatinous centre, the nucleus pulposus. The cranial and the caudal sides of the disc are called the end plates [17]. In the past it has been studied through what ways fluid flows to and from the intervertebral disc. Broberg [4] found that the ratio between the flow to and from the nucleus and the flow to and from the whole disc varies somewhat with the current disc height, but can be calculated as the ratio between the volume changes. The ratio is approximately 1:2. For his calculations he used a fluid flow model. Ohshima [27] investigated intervertebral discs of a pig tail in vitro. The diffusion of tritiated water in the intervertebral disc was traced using two pathway models: the peranular route and the end-plate route. The diffusion of water in the unloaded disc for both uptake and washout is about 2 to 3 times larger in the peranular route than in the endplate route. Under load, the water diffusion is inhibited in both pathways. Urban [40] studied the diffusion of small solutes into the intervertebral discs of dogs in vivo. About 40 percent of the endplate area was found to be permeable to small solutes, the central portion of the endplate was found to be more permeable than the rest. The total surface of the annulus is permeable to small solutes. On the basis of this in vivo study and from his in vitro work on other solutes Urban makes the following general statement. For a small anion, such as (35s) sulphate, the amount supplied through the periphery of the annulus is almost twice as much, as that diffusing through the endplates. For a small uncharged solute, such as (3H) methyl glucose, the two routes are of equal importance. For cations it is the endplate route that is the most effective. The water content of the intervertebral disc is variable and represents an equilibrium between two opposing pressures: mechanical pressure, which dehydrates the gel, and the swelling pressure of the hydrophilic proteoglycans (a mayor constituent of the intervertebral disc), which causes the disc to absorb fluid. Any change in the loading of the disc disturbs this equilibrium, and fluid flows until a new balance is achieved. As a result the height of the disc is altered. The fluid flow can aid the nutrition of the discs [i]. Adams [i] studied the effect of posture on the fluid content of lumbar intervertebral discs. Cadaveric lumbar motion segments were creep loaded for 4 hours, and the fluid content of the discs was measured and compared with that of unloaded discs. The results showed that flexed discs loose more fluid. especially from the nucleus pulposus, than the erect discs. The overall fluid loss is about 11 %, this reduces the volume and height by 9 %, or about mm for a typical disc. This is only two-thirds of the average height loss, so the remaining one-third must be due to creep deformation of the vertebrae and the annulus fibrosus. The mean change in disc height is 1.5 mm. 10

14 Chapter 1 Introduction Broberg [4] used a mechanical model of lumbar disc functions to calculate both the extent of fluid flow and its implications for disc height, as well as the role played by viscoelastic deformation of annulus fibres. The normal diurnal fluid flow is found to be about k 40 % of the disc fluid content late in the evening. Viscoelastic deformation of annulus fibres contributes approximately one quarter of the height change obtained after several hours normal activity, but dominates during the first hour. No long-time laboratory measurement results on compression of single discs are available in literature to compare these calculated results with. However the only results that might serve as comparison are those of Adams [i]. He found a 2.4 mm height decrease and 19 % fluid loss. The initial state of the disc in this experiment is not known, this may account for the difference between these two results. Swelling properties of the intervertebral disc As is understood from the literature review the water content of the intervertebral disc is variable. Loss of disc water due to mechanical loading is compensated through chemical attraction of water from the body fluid surrounding the disc. This swelling and shrinking behaviour of the disc as a response to mechanical or chemical loading is described by the triphasic theory [39]. Taking the view that the more a prosthesis resembles the real structure it is to replace, the more satisfactory the prosthesis is, it should be tried to introduce these swelling effects in an intervertebral disc prosthesis. Aim of the project At the Eindhoven University of Technology in combination with AZG Groningen, BMTC Groningen, Fokker Space & Systems and Ortomed a project has been started which aims at designing an adequate material for an intervertebral disc prosthesis, that is able to swell and shrink like the real intervertebral disc. The project described in this report serves as a kind of pilot study for the former project. The aim of this study is to design a physical model, with acrylic acid-acrylamide hydrogel [14] as a starting point, that illustrates the possibilities of an intervertebral disc prosthesis. For this purpose some experiments are performed on the disc model. The experiments are simulated in the finite element software of DIANA with its triphasic component. The simulations serve as a tool in the process of developing a disc prosthesis. Contents of the report In chapter 2 the anatomy of the intervertebral disc is described. In order to make a model of the intervertebral disc, the structure of the disc is studied. From that point on simplifications and assumptions are made. The triphasic theory describes the important aspects of the behaviour of cartilaginous tissues, for example intervertebral disc tissue. The intervertebral disc model is to behave in a similar way as the real intervertebral disc. This implies that the triphasic theory should be able to describe the behaviour of the intervertebral disc model as well. A summary of this theory is given in chapter 3. In chapter 4 two designs of disc models are presented: the wound models and the sleeve models. Like the real disc they are able to swell and shrink as a result of fluid exchange with its surroundings. The designs are based on a fibre reinforced hydrogel. In chapter 5 some experiments are described, in order to see whether the properties of the disc model resemble those of the real intervertebral disc. The relation between disc height and disc load are determined as well as the increase in disc radius as a result of disc loading, both chemical and mechanical. It is tried to explain the results from experiments on the disc models using this theory. In chapter 6 the results are simulated where possible with the finite element software packet DIANA containing a component based on the triphasic theory. Differences between the experiments and the simulations are discussed. 11

15 Chavter 1 Introduction Finally in chapter 7 the project is discussed and recommendations are given for the continuing of the project. 12

16 Chapter 2 The anatomy of the intervertebral disc In order to make a model of the intervertebral disc, the structure of the disc has to be studied. From that point on simplifications and assumptions are made (chapter 4). Hence a rather lengthy description of the anatomy of the intervertebral disc is included in this report. 2.1 The spinal column The spinal column is composed of 33 vertebrae, that strongly look alike. It can be divided in five parts: the cervical part consisting of 7 vertebrae, the thoracic part consisting of 12 vertebrae, the lumbar part consisting of 5 vertebrae, the sacral part consisting of 5 fused vertebrae and the coccyx consisting of 4 fused vertebrae.[l7], [30] With the exception of the first and the second cervical vertebrae the vertebral bodies are separated one from the other by intervertebral discs. One-fourth of the total length of the spinal column above the sacrum may be accounted for by the discs. During the course of a typical day the length of the spine may shorten because of shrinkage of the disc through dehydration as a result of mechanical loading of the spinal column. During the night, when the mechanical loading is much less [24], the disc swells again. [17], [30] This will briefly be explained in paragraph 2.5 and The vertebrae The vertebrae consist The neural arch consists of two paired pedicles and two paired laminae and two transverse, four articular and one spinous process. The arches are connected by ligaments and small synovial joints, the facet joints. From cranial to caudal the massiveness of each subsequent vertebrae increases progressively.[ 171, [30], [47] Two successive vertebrae and the intervertebral disc in between together with the ligaments and muscles crossing the level of the intervertebral disc are called a motor segment unit. This can be considered to be the functional unit of the spinal column.[

17 Chauter 2 The anatomv of the intervertebral disc Figure 2.2.1: A part of the spinal column, consisting of two and a half vertebrae and an intervertebral disc [45]. 2.3 The intervertebral disc The intervertebral discs form the chief structural units between adjacent vertebral bodies. They serve to allow greater motion between the vertebral bodies than if they were in direct apposition. More importantly, they distribute weight over a large surface of the vertebral body during bending motions, weight that would otherwise be concentrated on the edge toward which the spine is bent. They also serve a shock-absorbing function during direct vertical loading.[30] The intervertebral disc consists of the fibrous annulus fibrosus, surrounding a gelatinous centre, the nucleus pulposus. The cranial and the caudal sides of the intervertebral disc are called the end-plates. [ 171 end-plat annulus Figure 2.3.1: A schematic view of a sagittal cross-section of a part of the motion segment: two vertebral bodies and an intervertebral disc [45]. The annulus fibrosus forms the outer boundary of the disc and is composed of fibrocartilaginous tissue in which fibrous tissue predominates [30]. The annulus also contains approximately 70 % water by wet weight [9], in which small ions are dissolved [39]. The collagen fibres are embedded in proteoglycans (PG) and are arranged in concentric lamellae from which the fibres run obliquely from one vertebra to the next. In successive layers the fibres slant in alternate directions at an angle of 30" to 60" to the longitudinal axis of the disc [ 171, or is stated elsewhere at 30" [47]. According to Pooni [35] the fibres are tilted by 65", with respect to the axis of the spine, in the cervical region but by about 70" in the thoracic and lumbar regions. 14

18 Chapter 2 The anatomy of the intervertebral disc Figure 2.3.2: A schematic representation of the intervertebral disc showing the collagen fibre orientations [ 191 The peripheral fibres pass over the edge of the cartilaginous end plates to unite with the bone of the vertebral body (as Sharpey s fibres) [30]. These fibres are mainly collagen of type I [17]. The deeper fibres insert into the hyaline cartilage at each end of the disc Hyaline cartilage mainly consists of collagen fibres of type I1 [17]. The most superficial anterior fibres blend with the anterior longitudinal ligament as the posterior fibres blend with the posterior longitudinal ligament. The annulus fibrosus is basophilic, a property which increases towards the nucleus. Superficially the layers stain acidophilic as do the longitudinal ligaments. [30] The nucleus pulposus is centrally situated and consists of collagen fibres enmeshed in a mucoprotein gel [30]. The nucleus contains relatively less fibres and mainly proteoglycans. Due to their strong hydrophilic properties the proteoglycans generate a high hydrostatic pressure in the disc. As a result the annulus is pre-stressed. Water, containing small ions [39], accounts for over 80 % of the wet weight of the nucleus [12]. When ageing the disc dehydrates, so its relative amount of collagen increases [ 171. The line of delineation between the nucleus pulposus and the annulus fibrosus is rather clear in young specimens and becomes less so in adults.[30] The nucleus occupies approximately 40 per cent of the disc s cross-sectional area [30], or 25 to 50 per cent as is stated in [47]. Kapandji [19] states that the nucleus in the lumbar spine is located at 4/10 of the total diameter of the intervertebral disc from the anterior and that the diameter of the nucleus is 3/10 of the total diameter. For the thoracic spine these figures are in respective order 4/10 and 3/10 and for the lumbar spine 4/10 and 4/10. The cartilaginous plates limit the upper and lower borders of the disc and are composed of hyaline cartilage. They are at the zone of junction between the bone of the vertebra and the fibrous portion of the disc. This cartilage covers the perforated bony end-plate but does not cover the compact peripheral epiphysis. Much of the collagen fibres which lead to the annulus fibrosus take origin from these cartilaginous plates. Whether this cartilaginous plate is a portion of the disc or of the vertebral body is merely a question of terminology.[30] The end-plates contain approximately 55 % of water by wet weight [38], in which small ions are dissolved [39]. The discs in the cervical region are thicker anteriorly than posteriorly. They do not conform completely to the surface of the vertebral bodies with which they are connected, being slightly smaller in width than the vertebral bodies. The discs bulge anteriorly beyond the adjacent vertebrae. The nucleus pulposus in the cervical spine is located more anteriorly than in other portions of the spine [30]. According to [19] the average height of these discs is 3 mm. These discs tend to have an elliptical cross-sectional shape [35]. 15

19 Chapter 2 The anatomy of the intervertebral disc The discs in the thoracic region are of equal height anteriorly and posteriorly. The thoracic discs are thinner than those in the cervical or lumbar area. One might then expect the mobility of the thoracic vertebral column to be some what restricted as compared to that of the cervical and lumbar spine [30]. According to [i91 the average height of these discs is 5 mm. The thoracic discs have a more circular cross-sectional shape then the cervical ones [35]. The lumbar intervertebral discs tend to be of greater height anteriorly than posteriorly and this tendency is most marked in the fifth lumbar disc [30]. According to [I91 the average height of these discs is 9 mm. These discs tend to have an elliptical cross-section which is flattened or reentrant posteriorly [30]. According to [47] the height of the discs varies between 9 and 12 mm and the cross sectional area varies between 1400 and 2100 mm2. The degenerated disc has a shorter height caused by dehydration, but no significant difference in cross-sectional area. Values of disc height differ between authors, this may be caused by the fact that, as is mentioned before, the disc height decreases during the day as a result of dehydration caused by mechanical loading. 2.4 Collagen Collagen is built of long polypeptide chains. A peptide is a combination of two or more amino acids. A monomer of collagen is called tropo collagen and consists of 3 polypeptide sub units, in a triple helical configuration, linked by hydrogen bonds. There is a variety of sub units, each forming in different combinations different types of collagen. At least ten types are biochemical identified. The polymer is a fibril formed of a large amount of linked tropo collagen molecules, partly overlapping each other. There are no head-tail links between the tropo collagen molecules, but cross-links. The polymerisation is influenced by the proteoglycans.[ Proteoglycans Proteoglycans are large molecules consisting of many glycosaminoglycans (GAG) covalently linked to core proteins. GAG are linear polysaccharides built from disaccharide, each consisting from a hexamine and a hexuron acid. GAG has negatively electrically charged hydroxyl-, carboxyl- and sulphate groups. These fixed charges enable the proteoglycans to bind large amounts of water (50 times its own mass), allowing the tissue to build up an internal pressure and swell.[l7], [28] 16

20 Chapter 3 The swelling of cartilaginous tissues In this chapter the triphasic theory is explained briefly. This theory describes the most important aspects of the behaviour of cartilaginous tissues, for example intervertebral disc tissue. The intervertebral disc model is to behave in a similar way as the real intervertebral disc. This implies that the triphasic theory should be able to describe the behaviour of the intervertebral disc model as well. It is tried to explain the results from experiments on the disc models using this theory (chapter 5), and the results are simulated where possible with the software packet DIANA containing a component based on this theory. For more information about the triphasic theory the reader is referred to [39], [161, [141, E281 and [ Swelling When describing the behaviour of cartilaginous tissues, for instance the intervertebral disc, one has to look at both mechanical and chemical behaviour. As is mentioned in paragraph 2.5 proteoglycans have strong hydrophilic properties, as a result the intervertebral disc can be seen as a highly hydrated barrel. It is sealed off by the annular rings and the cartilaginous end-plates. As the iron rings prestress the wooden staves in a barrel, so is the proteoglycan gel of the annulus prestressed by the tensile stiffness of the collagen fibres. An increase in the axial compressive force on the intervertebral disc causes the nucleus pressure to rise. As a result the annular fibres are circumferentially stretched as they are pushed outwards. During this compression, tissue water is expressed out of the disc under the influence of the compressive force. Viscous forces (fluid-fluid and fluid-solid interaction) control the rate of fluid loss. [16] Loss of disc water due to mechanical loading is compensated through chemical attraction of water from the body fluid surrounding the disc. This is caused by the following components [16]: 1. the Donnan osmosis component, 2. the chemical expansion component, 3. the excluded volume osmosis component. The origin of the chemical attraction pressure for water in the intervertebral disc is mainly found in the presence of the fixed charges of the macromolecular proteoglycans in the disc, as has been mentioned before in paragraph 2.5. The fixed negative charges on the proteoglycans cause positive ions to be attracted to ensure bulk electroneutrality. This causes the total ion concentration inside the disc to be larger than that outside the disc. The imbalance of ions between the disc and the external solution gives rise to an osmotic effect, called Donnan osmosis. In cartilage aggregates of proteoglycans may be restrained to 1110th of their volume in free solution. At this concentration their fixed negative charges are so close to each other that they repel each other, resulting in swelling of the tissue. The internal cations concentration determines the amount of charge shielding, the fixed charges of the proteoglycans experience between 17

21 Chapter 3 The swelling of cartilaginous tissues themselves. This charge to charge repelling force is called the chemical expansion stress. This component is not taken into account by Snijders [39] in his triphasic model. In the situation where the large molecules do not carry electrical charges, water would be attracted into the disc as a result of an osmotic pressure difference due to the presence of the large molecules. This type of osmosis is called excluded volume osmosis. The mechanical behaviour of the tissue as a whole is determined primarily by the interaction between the swelling, water absorbing proteoglycans and the restraining collagen fibre network. The balance between these two mechanisms and the external loading determines the mechanical state of the material. [28] Urban and Maroudas E411 defined the tissue swelling pressure as the external pressure that needs to be applied on the tissue to keep the tissue volume constant. With: pwen the swelling pressure 71: the water attraction pressure oefl the effective stress (= the total stress in the material plus the fluid pressure) pextern the externally applied pressure Using expressions for electro neutrality both inside the disc as outside the disc as well as expressions for equal chemical potential of the ions and equal chemical potential of the fluid Snijders [39] derives the following expression for the osmotic pressure (the water attraction pressure): 71: =RT{$ (c'+c-+cpg)-~(c++c-)} (3.2) with for equilibrium of the disc: 2c+ = cfc + JpjG-F 2c- = -cfc + J(cfc)2 +4c2 With: R the universal gas constant T the absolute temperature 0 the osmotic coefficient in the tissue - 4) the osmotic coefficient surrounding the tissue C the internal concentration in mole per unit fluid volume - C the external concentration in mole per unit fluid volume suffixes + and - represent the cations and the anions respectively cpg the proteoglycan concentration in mole per unit fluid volume cfc the fixed charge concentration in mole equivalent per unit fluid volume 18

22 Chapter 3 The swelling of cartilaginous tissues 3.2 Triphasic theory A basic assumption of the triphasic theory is that any mixture may be viewed as a superposition of a number of single continua, each following its own motion, and that at any time each position in the mixture is occupied with particles of each component. This implies that all properties have to be regarded as averaged properties over some volume. The three phases used in this theory are the solid phase, the fluid phase and the ion phase. For the intervertebral disc the collagen network and the proteoglycan ground matrix are modelled as a charged, porous, permeable, intrinsically incompressible solid phase. The interstitial fluid is modelled as an intrinsically incompressible fluid phase. Small nutrients and ions dissolved within the fluid are modelled as the ion phase, represented by a monovalent salt (NaCl). All phases are considered as interacting continua. [39] The triphasic theory is a simplification of the quadriphasic theory. The four phases in the quadriphasic theory are the solid phase, the fluid phase and two ion phases: a cation phase and an anion phase [ 181. As the cations and the anions do not behave in the same way the quadriphasic theory is more correct than the triphasic theory. In this study the triphasic theory is used as it is implemented in software. However it is useful to understand the simplifications made when deriving the triphasic theory from the quadriphasic theory. For this purpose some of the equations from the quadriphasic theory are given besides the ones from the triphasic theory in the following description of the triphasic theory. The uni-axial response of these cartilaginous materials to a mechanical or chemical load is described by three coupled differential equations, governing [39] the following: I) The momentum balance of the mixture: With: 0, the effective Cauchy stress tensor of the solid p the fluid pressure II) The flow of liquid relative to the solid phase, which is driven by a pressure gradient and a concentration gradient of the mobile ions and the fixed charge groups. The flow of liquid is governed by: with from the quadriphasic theory: 19

23 Chapter 3 The swelling of cartilaginous tissues RT In c- - F$ p- = p; + -- V (3-9) With: -.. v the velocity vector the suffixesfand s represent the fluid and the solid respectively n the volume fraction - K the permeability tensor p the electro chemical potential the suffix O denoting the reference state F Faraday's constant $ the electric potential - V the molar volume - n+ - n - In the triphasic theory is assumed that (- V. p+ + TV. p- ) is negligible as the nf n volume fractions of the anions and of the cations are much smaller than the volume fraction of the fluid. Now the following equation is derived instead of equation (3.7): In) The convection diffusion of Naf and Cl- ions is described in the quadriphasic theory by the equations: (3.11) with: the suffix a represents the cations or the anions the mobile ion mass density per unit fluid volume p i - D" the diffusion tensor Using equations (3.11), (3.8) and (3.9) and assuming the following: (3.12) (3.13) the convection diffusion of Na+ and C1- ions in the triphasic theory is simplified to: (3.14) With: ( ), the material time derivative following the solid The terms on the left-side represent the movement of ions with respect to the solid. This movement is partly influenced by convection (second term on the left) and partly by diffusion (first term on the right hand side). [39] The fixed charge concentration and the volume fraction of the fluid are deformation 20

24 Chapter 3 The swelling of cartilaginous tissues dependent and thus influence the movement of ions. (3.15) (3.16) With: J the rehtive volume change of the tissue The initial conditions and the boundary conditions are given by the equilibrium results: 2Cb = -cfc + Il(.'.>" (3.17) Pb = 0 RT{2(c, - C) + Cf"} (3.18) With: the subscript denoting at the boundary within the tissue The boundary condition for the momentum of the mixture is: - With: y1 the unit normal vector on the boundary the subscript ext denoting outside the disc (3.19) The other boundary conditions are: P f --Pes f (3.20) (3.21) The boundary conditions depend on the local proteoglycan and ion concentrations. These concentrations change during deformation. Hence, the boundary conditions are deformation dependent. [39] The equations (3.5), (3.6) and (3.14) form the set of equations describing the triphasic swelling behaviour of intervertebral disc tissue. In order to complete this set, additional constitutive relations are needed to describe the stress-strain behaviour of the solid phase and the permeability and diffusion behaviour. The effective Cauchy stress, the hydraulic permeability, and the diffusion coefficient are in principle dependent on the deformation of the material and the local salt concentration. In soft tissue mechanics, the contribution of the salt concentration is generally assumed to be negligible compared to the deformation contribution. [ 161 In the stress-strain relation chosen by Snijders [39] the effective Piola-Kirchhoff stress is introduced. It is related to the effective Cauchy stress by: 21

25 Chapter 3 The swelling of cartilaginous tissues (3.23) With:,Yeff the second Piola-Kirchhoff stress tensor - F A - E p ; the deformation tensor the Helmholtz free energy the Green-Lagrange strain tensor the solid mass density per unit tissue volume in the reference state Finally, the following deformation-dependent expressions for the permeability tensor K and the diffusion tensor Q E391 are used: (3.24) (3.25) 22

26 Chapter 4 A pkysicd model of the intervertebral disc The physical model is designed on the basis of the anatomy of the intervertebral disc (chapter 2) and its behaviour (chapter 3). Like the real disc it should be able to swell and shrink as a result of fluid exchange with its surroundings and it should be able to bear loads of the same order of magnitude as the real disc (chapter 1). In paragraph 4.1 the materials out of which the physical models consist are presented. In paragraph 4.2 the design and the way to realise it are described. 4.1 Materials Acrylic acid- acrylamide-gel De Heus [14] developed a hydrogel, that consists of acrylic acid-acrylamide copolymer, and which has strong swelling and shrinking properties. It was developed for the verification of mathematical models describing the behaviour of soft charged hydrated tissues. As a case study the intervertebral disc tissue was chosen. When the gel is copolymerised in the pores of open cell microporous PUR-foams, this yields soft charged hydrated materials exhibiting hydraulic permeability, ion diffusivity and swelling characteristics quantitatively similar to intervertebral disc tissue [14]. The mathematical triphasic model developed by Snijders 1391 is able to describe the finite equilibrium of the materials during one-dimensional confined swelling and compression for axial strains of more than 50 % [14]. This gel, without the PUR-foam, is taken as startingpoint for the design of the physical model of the intervertebral disc. In appendix 1 is described how the gel is prepared. For further information the reader is referred to [14]. Polyethybne8bres In the real intervertebral disc the tensile stiffness of the collagen fibres prestress the proteoglycan gel. An increase in the axial compressive force on the intervertebral disc causes the nucleus pressure to rise. As a result the collagen fibres of the annulus are circumferentially stretched as they are pushed outwards. In the physical model of the disc a similar structure is needed to fulfil the function of the collagen fibres for the hydrogel. As the gel becomes rather weak when swollen, a reinforcement of some kind is needed to give a model, made from this gel, enough strength to bear loads in the same order of magnitude, as those working on the real intervertebral disc. Looking at the anatomy of the latter, the design of the fibre reinforcement should resemble the way the collagen fibres are arranged in the real disc. Polyethylene fibres ( ho, Emmen, The Netherlands) are used as reinforcement. The diameter of the fibres is 0.06 mm. 23