- Email: [email protected]
Restoration of non-carious cervical lesions
d e n t a l m a t e r i a l s 2 3 ( 2 0 0 7 ) 1562–1569
available at www.sciencedirect.com
journal homepage: www.intl.elsevierhealth.com/journals/dema
Restoration of non-carious cervical lesions Part II. Restorative material selection to minimise fracture I.P. Ichim a,∗ , P.R. Schmidlin b , Q. Li c , J.A. Kieser d , M.V. Swain a,e a
Department of Oral Rehabilitation, Faculty of Dentistry, University of Otago, 310 Great King Street, Dunedin 9001, New Zealand Clinic for Preventive Dentistry, Periodontology and Cariology, Centre for Dental and Oral Medicine and Maxillo-Facial Surgery, University of Zurich, Switzerland c School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, NSW 2006, Australia d Department of Oral Sciences, Faculty of Dentistry, University of Otago, Dunedin, New Zealand e Biomaterials, Faculty of Dentistry, University of Sydney, NSW 2006, Australia b
a r t i c l e
i n f o
a b s t r a c t
Article history:
Objective. It is still largely unknown as to what material parameter requirements would be
Received 11 August 2006
most suitable to minimise the fracture and maximising the retention rate of the restoration
Accepted 5 February 2007
of cervical non-carious lesions (NCCL). The present paper, as a first of its kind, proposes a radical approach to address the problems of material improvement, namely: numericalbased, fracture and damage mechanics materials optimisation engineering. It investigates
Keywords:
the influence of the elastic modulus (E) on the failure of cervical restorative materials and
Dental materials
aims to identify an E value that will minimise mechanical failure under clinically realistic
Elastic modulus
loading conditions.
Fracture mechanics
Method. The present work relies on the principle that a more flexible restorative mate-
Crack propagation
rial would partially buffer the local stress concentration. We employ a “most favourable”
Abfraction lesion
parametric analysis of the restorative’s elastic modulus using a fracture mechanics model
Restorative dentistry
embedded into finite element method. The advanced numerical modelling adopts a Rankine and rotating crack material fracture model coupled to a non-linear analysis in an explicit finite element framework. Results. The present study shows that the restorative materials currently used in non-carious cervical lesions are largely unsuitable in terms of resistance to fracture of the restoration and we suggest that the elastic modulus of such a material should be in the range of 1 GPa. We anticipate that the presented methodology would provide more informative guidelines for the development of dental restorative materials, which could be tailored to specific clinical applications cognisant of the underlying mechanical environment. © 2007 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Non-carious cervical lesions (NCCL) are commonly encountered and raise considerable restorative challenges for the dentist. A critical factor for restorative success is represented by the selection of the restorative materials [1]. These issues
∗
dictate the restoration’s integration in an area of the tooth, which involves multiple biomaterials and experiences complex stresses [2,3]. Currently, the materials of choice indicated for restoring cervical lesions include: glass-ionomer cements, resin-modified glass-ionomer cements, polyacid-modified
Corresponding author. Tel.: +64 3 21 1117437. E-mail address: [email protected] (I.P. Ichim). 0109-5641/$ – see front matter © 2007 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.dental.2007.02.002
d e n t a l m a t e r i a l s 2 3 ( 2 0 0 7 ) 1562–1569
resin-based composites (compomers) and composites resins [4,5]. However, there is no unanimous recommendation for one material or another. This may be, among other reasons, because of a fundamental lack of understanding on how the restorative elastic properties affect the retention rate of cervical restorations. There is a significant body of literature, which documents the influence of filling material type on the longevity of cervical restorations. Clinical studies have shown repeatedly that restorations of NCCL have inadequate retention rates, with higher percentages of failure at the cervical, compared with the occlusal margins [6–11]. To circumvent the existing shortcomings and improve the clinical longevity of cervical restorations, modified or unmodified preparations [6], layered restorative techniques [1,12] and improvements in the adhesion of the materials [13] have been suggested. In contrast, the influences of the elastic and fracture properties of the materials are rarely investigated, and often such information has to be inferred from comparative studies involving materials with different properties. This is surprising because the role of mechanical stress is widely accepted as a cause of failure of restorations. It is also well known that the stiffness tensor of the restorative materials considerably affects the stress distribution within the restoration and its mechanical integration with the native tooth [14,15]. There is a generally acknowledged need for different and/or improved restorative materials, which are compatible within the new biomechanical framework imposed by the current paradigm of minimally invasive dentistry concepts [16]. Such novel materials should be better tailored for some specific needs, as for instance use in cervical restoration [5]. The present paper, as a first of its kind, proposes a radical approach to address the problems of material improvement, namely: numerical-based material optimisation engineering. It investigates the influence of the elastic modulus (E) on the failure of cervical restorative materials. That is, we aim to identify the “most favourable” selection of E value for the restorative material, which will allow it to survive under the unfavourable occlusal loading conditions that may prevail. This is a continuation our previous work [17] which focused on the influence of cavity size and shape on the failure of GIC restoration in NCCL. It showed occlusal loading direction as a major factor contributing to restoration failure, and that oblique-oriented forces induce tensile stresses on the cervical margin above the strength of the material and bonding. The present work relies on the principle that a more flexible material would partially buffer the local stress concentration [1,12,15] and hence reduce the likelihood of mechanical failure of the restoration. To implement this principle, we use a parametric analysis of the restorative’s elastic modulus using a fracture mechanics model embedded into finite element method. The advanced numerical modelling adopts a Rankine and rotating crack material fracture model coupled to a non-linear analysis in an explicit finite element framework.
2.
Materials and method
In this study the goal was to determine the value of E of the restorative material at which failure (identified as micro-
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damage or macroscopic cracking) is avoided under a realistic clinical loading scenario. We investigate the failure of three types of NCCL restorations when the elastic and fracturing properties of the restorative material are prescribed using actual values, as reported in the literature. Subsequently, we steadily adjust the E value of the restorative until the stress profiles shows that mechanical failure is unlikely to occur.
2.1.
Tooth model
The geometry employed in this study (Fig. 1) was based on the reconstruction of a human permanent lower first premolar, extracted for orthodontic reasons and which was micro-CT scanned using a SkyScan 1072 system (SkyScan, Aartselaar, Belgium). The maximum deviation between the original CT image and reconstructed surface solids was less than 0.6%. The 3D reconstruction methodology is described in detail elsewhere [17]. The generation of the geometry for the plain strain model is described in the first part of this paper [18].
2.2.
Restoration types
A NCCL (abfractive) wedged-shaped lesion was created on the buccal cervical margin being 1.5 mm deep and 1.5 mm wide in the occluso-cervical direction. These parameters were employed to fit in vivo determined dimensions of abfraction lesions [19]. Two filling techniques were chosen for the present work (Fig. 2): (a) single bulk material, namely glass-ionomer (GIC) and (b) a layered technique. The latter consisted of a layer of GIC encompassing a composite bulk. Two thicknesses were considered for the GIC layer: 50 and 150 m.
2.3. 2D plain strain numeric model and the finite element solver The resulting 2D profile was subsequently meshed using a total of 2116 plain strain linear elements and all the interfaces of the model were considered as bonded (Fig. 1b). The region of interest (GIC filling) was meshed using element’s size of 0.025 mm in the cervical region and 0.1 mm elements in the occlusal region (Fig. 2a). The reminder of the tooth model was meshed using 0.4 mm linear triangular elements. A mesh-convergence test was then carried out using linear elastic material models under a load of 150 N applied at 40◦ obliquely on the tip of the buccal cusp to ensure that no further refinement of the mesh is necessary. Numerical analysis was carried out using ELFEN (Rockfield Software Ltd., Swansea, UK) and employing the discrete solver, which allows automatic transition from continuum to discrete, including crack initiation/propagation, modelling of self-contact in the cracking interface, material softening, and adaptive remesh with data transfer. In the non-linear finite element fracture analysis presented here, the topological update of the mesh consists in the insertion of a discrete crack when the tensile strength in a principal direction reaches zero, and the crack is orientated orthogonal to this direction. The basis of this model is
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Fig. 1 – Solid 3D geometry (a), the plain strain model extracted from it showing the loadcase and the constraints (b) and the material mapping (c) where E: enamel, D: dentine, R: restoration, P: pulp, L: periodontal ligament and B: supporting bone.
described in more detail by Klercka et al. [20] and Ichim et al. [18].
2.4.
Loading
To create a more extreme loading condition to which the restoration would be vulnerable, we considered a force of 150 N oriented at 40◦ in a buccal direction [17,21], applied on the tip of the buccal cusp of the model.
2.5.
Material failure model
To simulate cracking process in a non-linear finite element framework, the transition from continuum to discrete is governed by the coalescence of dispersed micro cracks into macroscopic fracture, where softening plasticity and damage theories are adopted. The fracture model presented in this study relies on the rotating (or reorienting) crack tip model, which assumes the initiation of
Fig. 2 – Detail of the mesh in the restoration area (a), and the filling types considered: bulk GIC (b) and the layered composite and thin GIC of 50 m thickness (c), and a layered composite with a thick GIC of 150 m thickness (d).
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Table 1 – Mechanical elastic and fracturing properties of the materials considered Material
Elastic modulus (E) (GPa)
Enamel [23] Dentine [23] Ligament [17] Bone [17] GIC [24] Composite [25]
69 16.7 12 MPa 14.7 10.8 15
Poisson ratio
Ultimate tensile strength (UTS) (MPa)
0.3 0.3 0.45 0.3 0.3 0.3
the degradation to be controlled by the maximum tensile stress. A detailed description of the fracture material model and its embedding into the discrete element solver is presented in the first part of this work [18].
2.6.
– 90 – – 12 40
Fracture toughness (Kic ) (MPa m1/2 ) – 1.79 – – 0.33 0.6
Fracture – Yes – – Yes Yes
The materials anticipated to fracture were represented by dentine, composite and glass-ionomer. The mechanical properties are given in Table 1. We need to mention that in selecting the fracturing properties of the materials from available literature data, we have chosen the conservative or lower reported values.
Material properties
The enamel, periodontal ligament, pulp and supporting bone were modelled with isotropic elasticity and the material properties were extracted from data available in literature. The periodontal ligament was taken as elastic with an E of 12 MPa and of 0.45, values which were shown previously to match the in vivo mobility of the tooth [17,22]; same material used for the pulp.
2.7. Assessment of the influence of elastic modulus on restoration failure The mechanical integration of the restoration was assessed by comparing the extent of strain softening inside the restoration as computed for different values of its elastic modulus. In the finite element context, a non-local nodal damage state indicator (ω) is computed to disperse micro-cracks coalescing
Fig. 3 – Predicted mixed adhesive/cohesive failure in bulk GIC filling (a), composite and GIC adhesive layer of 50 m (b) and the composite and GIC adhesive layer of 150 m (c). A detailed image of the failed cervical margin of the restoration (b) shows the debonding of the restoration form the underlying dentine and the limited cohesive failure.
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into macroscopic fractures and is interpreted as microdamage accumulation inside the material. In practice, many material and geometric parameters may, to a certain extent, contribute to the damage of the material. However, the scope of this study is restricted to the sensitivity analysis of damage with respect only to the elastic modulus of restorative material. In employing these principles, we started from an initial E of 10.8 GPa for the GIC and then we steadily reduced its value, until the calculations showed that the restorative materials have complete elastic behaviour without plastic strain-softening (micro-damage) and/or macroscopic fracture. A point to make refers to our assumption that the fracture toughness and UTS are not compromised while the Young’s modulus of the GIC is systematically reduced. Our assumption is supported by the fact that, despite many materials show a direct relationship between the values of E and those of UTS and fracture toughness, this is not universally enforced in the field of biomaterials. For example, dentine compared with enamel [26] or resin modified GIC compared with conventional ones show an increase in strength and toughness associated with a decrease in E modulus.
3.
Results
3.1.
Initial elastic modulus
Restoration failure occurred in all the cases where the GIC material was considered with its initial elastic modulus of
10.8 GPa. The failure was constantly located on the cervical interface and was mixed, mostly adhesive with some small area of cohesive failure (Fig. 3). Principal stress analysis shows the influence of the GIC thickness on the distribution of tensile stress on the cervical margin of the restoration prior to failure (Fig. 4). For the bulk GIC restoration and for the thick GIC layer failure initiates at similar force levels (90 N). In contrast, a thin layer of GIC would require a slightly larger force for the failure to occur (103 N).
3.2.
Reduced elastic modulus
Reducing the elastic modulus of the GIC to 5 GPa reveals an interesting phenomenon. While the layered restorations show a modest increase in their load-bearing capacity (7 and 9 N, respectively), the most dramatic change is recorded for the bulk filling. For the latter, the increased resilience of the bulk volume of restorative material causes the onset of failure to occur at 112 N; that is about twice the increase compared with the layered restorations. There is also a commensurate reduction of the stiffness in the loading curve. Nevertheless, all the restorations failed showing a similar mixed, adhesive/cohesive mode (Fig. 5). Fig. 6 shows the maximum tensile stress profiles, as a function of applied force, for an elastic modulus of the GIC set to 1 GPa. Only for the 50 m layered restoration was failure recorded upon loading to 150 N. In this case, the failure mode is also mixed, adhesive/cohesive and initiated at a load of 135 N.
Fig. 4 – Tensile stress contours for 10 GPa elastic modulus of the GIC before failure (a–c). The plot shows the applied force–stress relationship at the cervical margin of the GIC/dentine interface (d). Note the distinct phases of the mechanical response of the GIC: elastic (I), strain-softening (II) and fracture (III).
d e n t a l m a t e r i a l s 2 3 ( 2 0 0 7 ) 1562–1569
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Fig. 5 – Tensile stresses for GIC set to 5 GPa elastic modulus before failure (a–c). The chart shows the applied force–stress relationship at the cervical margin of the GIC/dentine interface (d). Note the significant increase in the mechanical resistance of the bulk restoration, compared with 10 GPa material as shown in Fig. 4.
By contrast, the bulk filling and the thick layer recorded maximum stress values below the critical threshold. This showed the usefulness of a thick layer of GIC material to act as stressbreaker. It should be pointed out that the cervical stresses for the 150 m layer restoration are very close to the failure point (11.3 MPa). In turn, the bulk filling showed a maximum stress well below it (7.3 MPa).
Fig. 6 – Tensile stress vs. load plot for GIC set to an elastic modulus of 1 GPa. Note that failure occurs only in the layered restoration employing a thin layer of GIC. Also, note that the cervical stresses in the 150 m thick layer are close to critical limit.
4.
Disscusion
In this paper we investigated the mechanical integration of cervical restorative materials and we aim to identify a most favourable selection of E value for the restoration, which will allow it to survive under the unfavourable loading conditions that may prevail. In the biomedical literature, there are limited studies applying reverse-engineering methods for designing or improving biomaterials and they concern mostly locomotor apparatus, e.g. components of a hip prosthesis [27,28] or the spine [29]. To the best of our knowledge such a numerical-based optimisation involving brittle materials in a non-linear FE based fracture framework was not employed for dental restorative materials. The experimental co-ordinates are derived from our previous work [17], which focused on the influence of cavity size and shape on the failure of GIC restoration in NCCL. The latter study showed that the major factor contributing to failure is the loading direction, while the lesion shape and size were non-determinant factors. Therefore, in this paper we employed only a single lesion type (wedge lesion) with the worst scenario of para-axial loading. The present study shows that the restorative materials currently used in cervical non-carious lesions are largely unsuitable in terms of resistance to fracture of the restoration. Their relative high stiffness creates stress concentration at the
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cervical margin, which in turn initiates mechanical failure due to the low fracture toughness of the material and interface. Irrespective of the filling technique, the restorative material with a Young’s modulus of 10.8 GPa failed prematurely in a mixed, adhesive/cohesive mode. Prior to fracture, the restorative material undergoes remarkable strain softening, which largely compromises its mechanical properties and initiates the path to catastrophic failure. Strain softening in quasi-brittle material is a consequence of the accumulation of micro-cracks in the area, which is overstressed. Due to the presence of these microcracks, subsequent cyclic loading results in additional new cracking damage by failure of the bridging ligaments between microcracks. Upon reloading, this offers less resistance to deformation, an aspect known as “softening”. Furthermore, a material, which accumulates strain softening induced damage is increasingly susceptible to the action of other damaging factors like chemical and mechanical degradation. In the present study, the softening of the material occurs in the interfacial cervical region of the restoration. The cervical interface was also clinically identified as locus minoris resistentiae [7,9]. Therefore, one possibility to avoid the onset of the microdamage is to employ a material, which exhibits greater flexibility and behaves more elastically for the given loadcase. This behaviour would reduce considerably the stresses on the margin and, if the UTS of the material and/or interface are not exceeded, mechanical failure is unlikely even under an oblique functional overloading. The necessity of stress-buffering was firstly acknowledged by Kemp-Scholte and Davidson [1] in the case of shrinkage stresses reduction. However, this principle can be extrapolated to other functional loadcases as shown by Ausiello et al. [30] which investigated the optimal adhesive layer thickness leading to maximum stress release while preserving the interface integrity, or by Li et al. [12] in their work regarding the improvement of the marginal adaptation by the use of existing flowable materials as an intermediate layer. The benefits of stress reduction in prevention of mechanical failure are also supported by our findings. Furthermore, we are able to point to a value of the E modulus, which should be employed to prevent failure. The best results are obtained for a bulk filling with a 1 GPa elastic modulus material case in which the tensile stresses are about 50% of the failure limit. By contrast a thin layer of the same flexible material would fail in the cervical region, mainly because its limited thickness cannot provide sufficient stress-reduction. In the case of the thick layer failure does not occur but the marginal tensile stresses are close to the failure limit, leaving a very small safety margin. However, from a clinical perspective a material, which can be applied in bulk is preferable. We suggest that the elastic modulus of such a material should be in the range of 1 GPa. Employing such a tailored material would not raise functional problems, as to a certain extent the cervical cavities are not directly load-bearing areas. Instead, the consideration of aesthetic qualities and resistance to further mechanical abrasion or biochemical corrosion should be considered when developing and testing such restorative materials.
At present no such material, which would fulfil these mechanical requirements is commercially available. However, our results suggest both a methodology to follow and a goal to achieve in future design of restorative biomaterials. On theoretical grounds, a way of attaining the required restorative modulus is to combine a stiffer reinforced material in a more flexible polymeric matrix employing the following hypothetical equation for particulate systems [31] 1 1− + = E Er Em
(1)
where Er and Em are Young’s moduli for the reinforcement and matrix materials respectively, is the volume fraction of the reinforcement material. We anticipate that the presented methodology would provide more precise guidelines to be used in the development of dental restorative materials, which could be tailored to specific clinical applications with their needs based on a thorough knowledge of the underlying mechanical environment.
5.
Conclusions
Within the limitations of this numerical study, we can conclude that, from a mechanical point of view, the existing restorative materials are largely unsuited for usage in NCCL. We suggest that the “optimal” material for cervical restoration should be more flexible and have an elastic modulus in the range of 1 GPa. In future, numerical modelling should be employed as an integral part of the material design, selection and development.
Acknowledgements This paper was partially funded by a University of Otago Research Grant as well as a Deputy Vice-Chancellor’s award to the Craniofacial Biomechanics Group (Otago University). The third author is supported by James Cook University through a New Staff Grant scheme. Parts of this work were also supported by ARC grant DP 0666446.
references
[1] Kemp-Scholte CM, Davidson CL. Complete marginal seal of class V resin composite restorations effected by increased flexibility. J Dent Res 1990;69:1240–3. [2] Hood JA. Experimental studies on tooth deformation: stress distribution in class V restorations. NZ Dent J 1972;68: 116–31. [3] Rees JS. The role of cuspal flexure in the development of abfraction lesions: a finite element study. Eur J Oral Sci 1998;106:1028–32. [4] Lyttle HA, Sidhu N, Smyth B. A study of the classification and treatment of noncarious cervical lesions by general practitioners. J Prosthet Dent 1998;79:342–6. [5] Onal B, Pamir T. The 2-year clinical performance of esthetic restorative materials in noncarious cervical lesions. J Am Dent Assoc 2005;136:1547–55. [6] Brackett MG, Dib A, Brackett WW, Estrada BE, Reyes AA. One-year clinical performance of a resin-modified glass
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ionomer and a resin composite restorative material in unprepared class V restorations. Oper Dent 2002;27:112–6. Gladys S, Van Meerbeek B, Lambrechts P, Vanherle G. Marginal adaptation and retention of a glass-ionomer, resin-modified glass-ionomers and a polyacid-modified resin composite in cervical class-V lesions. Dent Mater 1998;14:294–306. Matis BA, Cochran MJ, Carlson TJ, Guba C, Eckert GJ. A 3-year clinical evaluation of two dentin bonding agents. J Am Dent Assoc 2004;135:451–7. Folwaczny M, Mehl A, Kunzelmann KH, Hickel R. Clinical performance of a resin-modified glass-ionomer and a compomer in restoring non-carious cervical lesions. Five-year results. Am J Dent 2001;14:153–6. van Dijken JW. Retention of a resin-modified glass ionomer adhesive in non-carious cervical lesions. A 6-year follow-up. J Dent 2005;33:541–7. Belluz M, Pedrocca M, Gagliani M. Restorative treatment of cervical lesions with resin composites: 4-year results. Am J Dent 2005;18:307–10. Li Q, Jepsen S, Albers HK, Eberhard J. Flowable materials as an intermediate layer could improve the marginal and internal adaptation of composite restorations in class-V-cavities. Dent Mater 2006;22:250–7. van Dijken JW. Clinical evaluation of three adhesive systems in class V non-carious lesions. Dent Mater 2000;16:285–91. Kemp-Scholte CM, Davidson CL. Marginal integrity related to bond strength and strain capacity of composite resin restorative systems. J Prosthet Dent 1990;64:658–64. Staninec M, Marshall Jr GW, Kawakami M, Lowe A. Bond strength, interfacial characterization, and fracture surface analysis for a new stress-breaking bonding agent. J Prosthet Dent 1995;74:469–75. De Munck J, Van Landuyt K, Peumans M, Poitevin A, Lambrechts P, Braem M, et al. A critical review of the durability of adhesion to tooth tissue: methods and results. J Dent Res 2005;84:118–32. Ichim I, Schmidlin PR, Kieser J, Swain M. Mechanical evaluation of cervical glass-ionomer restorations: 3D finite element study. J Dent 2007;35:28–35.
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[18] Ichim I, Li Q, Loughran J, Swain M, Kieser J. Restoration of non-carious cervical lesions. Part I. Modelling of restorative fracture. Dent Mater, 2006. [19] Aw TC, Lepe X, Johnson GH, Mancl L. Characteristics of noncarious cervical lesions: a clinical investigation. J Am Dent Assoc 2002;133:725–33. [20] Klercka PA, Sellersb EJ, Owen DRJ. Discrete fracture in quasi-brittle materials under compressive and tensile stress states. Comp Meth Appl Mech Eng 2004;139:3035–56. [21] Borcic J, Anic I, Smojver I, Catic A, Miletic I, Ribaric SP. 3D finite element model and cervical lesion formation in normal occlusion and in malocclusion. J Oral Rehabil 2005;32:504–10. [22] Muhlemann HR. Tooth mobility: a review of clinical aspects and research findings. J Periodontol 1967;38:686–713. Suppl. [23] Imbeni V, Kruzic JJ, Marshall GW, Marshall SJ, Ritchie RO. The dentin–enamel junction and the fracture of human teeth. Nat Mater 2005;4:229–32. [24] Tam LE, Dev S, Pilliar RM. Fracture toughness of conventional or photopolymerized glass ionomer/dentin interfaces. Oper Dent 1995;20:144–50. [25] Knobloch LA, Kerby RE, Seghi R, Berlin JS, Clelland N. Fracture toughness of packable and conventional composite materials. J Prosthet Dent 2002;88:307–13. [26] Imbeni V, Nalla RK, Bosi C, Kinney JH, Ritchie RO. In vitro fracture toughness of human dentin. J Biomed Mater Res A 2003;66:1–9. [27] Hedia HS. Parameteric optimisation of materials for acetabular cup. Biomed Mater Eng 2001;11:79–88. [28] Hedia HS, Barton DC, Fisher J. Material optimisation of the femoral component of a hip prosthesis based on the fatigue notch fatigue approach. Biomed Mater Eng 1997;7:83–98. [29] Hallab N, Link HD, McAfee PC. Biomaterial optimization in total disc arthroplasty. Spine 2003;28:S139–52. [30] Ausiello P, Apicella A, Davidson CL. Effect of adhesive layer properties on stress distribution in composite restorations—a 3D finite element analysis. Dent Mater 2002;18:295–303. [31] Darwell BW. Materials science for dentistry. Hong Kong: B W Darwell; 2000. p. 120–1.
available at www.sciencedirect.com
journal homepage: www.intl.elsevierhealth.com/journals/dema
Restoration of non-carious cervical lesions Part II. Restorative material selection to minimise fracture I.P. Ichim a,∗ , P.R. Schmidlin b , Q. Li c , J.A. Kieser d , M.V. Swain a,e a
Department of Oral Rehabilitation, Faculty of Dentistry, University of Otago, 310 Great King Street, Dunedin 9001, New Zealand Clinic for Preventive Dentistry, Periodontology and Cariology, Centre for Dental and Oral Medicine and Maxillo-Facial Surgery, University of Zurich, Switzerland c School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, NSW 2006, Australia d Department of Oral Sciences, Faculty of Dentistry, University of Otago, Dunedin, New Zealand e Biomaterials, Faculty of Dentistry, University of Sydney, NSW 2006, Australia b
a r t i c l e
i n f o
a b s t r a c t
Article history:
Objective. It is still largely unknown as to what material parameter requirements would be
Received 11 August 2006
most suitable to minimise the fracture and maximising the retention rate of the restoration
Accepted 5 February 2007
of cervical non-carious lesions (NCCL). The present paper, as a first of its kind, proposes a radical approach to address the problems of material improvement, namely: numericalbased, fracture and damage mechanics materials optimisation engineering. It investigates
Keywords:
the influence of the elastic modulus (E) on the failure of cervical restorative materials and
Dental materials
aims to identify an E value that will minimise mechanical failure under clinically realistic
Elastic modulus
loading conditions.
Fracture mechanics
Method. The present work relies on the principle that a more flexible restorative mate-
Crack propagation
rial would partially buffer the local stress concentration. We employ a “most favourable”
Abfraction lesion
parametric analysis of the restorative’s elastic modulus using a fracture mechanics model
Restorative dentistry
embedded into finite element method. The advanced numerical modelling adopts a Rankine and rotating crack material fracture model coupled to a non-linear analysis in an explicit finite element framework. Results. The present study shows that the restorative materials currently used in non-carious cervical lesions are largely unsuitable in terms of resistance to fracture of the restoration and we suggest that the elastic modulus of such a material should be in the range of 1 GPa. We anticipate that the presented methodology would provide more informative guidelines for the development of dental restorative materials, which could be tailored to specific clinical applications cognisant of the underlying mechanical environment. © 2007 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Non-carious cervical lesions (NCCL) are commonly encountered and raise considerable restorative challenges for the dentist. A critical factor for restorative success is represented by the selection of the restorative materials [1]. These issues
∗
dictate the restoration’s integration in an area of the tooth, which involves multiple biomaterials and experiences complex stresses [2,3]. Currently, the materials of choice indicated for restoring cervical lesions include: glass-ionomer cements, resin-modified glass-ionomer cements, polyacid-modified
Corresponding author. Tel.: +64 3 21 1117437. E-mail address: [email protected] (I.P. Ichim). 0109-5641/$ – see front matter © 2007 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.dental.2007.02.002
d e n t a l m a t e r i a l s 2 3 ( 2 0 0 7 ) 1562–1569
resin-based composites (compomers) and composites resins [4,5]. However, there is no unanimous recommendation for one material or another. This may be, among other reasons, because of a fundamental lack of understanding on how the restorative elastic properties affect the retention rate of cervical restorations. There is a significant body of literature, which documents the influence of filling material type on the longevity of cervical restorations. Clinical studies have shown repeatedly that restorations of NCCL have inadequate retention rates, with higher percentages of failure at the cervical, compared with the occlusal margins [6–11]. To circumvent the existing shortcomings and improve the clinical longevity of cervical restorations, modified or unmodified preparations [6], layered restorative techniques [1,12] and improvements in the adhesion of the materials [13] have been suggested. In contrast, the influences of the elastic and fracture properties of the materials are rarely investigated, and often such information has to be inferred from comparative studies involving materials with different properties. This is surprising because the role of mechanical stress is widely accepted as a cause of failure of restorations. It is also well known that the stiffness tensor of the restorative materials considerably affects the stress distribution within the restoration and its mechanical integration with the native tooth [14,15]. There is a generally acknowledged need for different and/or improved restorative materials, which are compatible within the new biomechanical framework imposed by the current paradigm of minimally invasive dentistry concepts [16]. Such novel materials should be better tailored for some specific needs, as for instance use in cervical restoration [5]. The present paper, as a first of its kind, proposes a radical approach to address the problems of material improvement, namely: numerical-based material optimisation engineering. It investigates the influence of the elastic modulus (E) on the failure of cervical restorative materials. That is, we aim to identify the “most favourable” selection of E value for the restorative material, which will allow it to survive under the unfavourable occlusal loading conditions that may prevail. This is a continuation our previous work [17] which focused on the influence of cavity size and shape on the failure of GIC restoration in NCCL. It showed occlusal loading direction as a major factor contributing to restoration failure, and that oblique-oriented forces induce tensile stresses on the cervical margin above the strength of the material and bonding. The present work relies on the principle that a more flexible material would partially buffer the local stress concentration [1,12,15] and hence reduce the likelihood of mechanical failure of the restoration. To implement this principle, we use a parametric analysis of the restorative’s elastic modulus using a fracture mechanics model embedded into finite element method. The advanced numerical modelling adopts a Rankine and rotating crack material fracture model coupled to a non-linear analysis in an explicit finite element framework.
2.
Materials and method
In this study the goal was to determine the value of E of the restorative material at which failure (identified as micro-
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damage or macroscopic cracking) is avoided under a realistic clinical loading scenario. We investigate the failure of three types of NCCL restorations when the elastic and fracturing properties of the restorative material are prescribed using actual values, as reported in the literature. Subsequently, we steadily adjust the E value of the restorative until the stress profiles shows that mechanical failure is unlikely to occur.
2.1.
Tooth model
The geometry employed in this study (Fig. 1) was based on the reconstruction of a human permanent lower first premolar, extracted for orthodontic reasons and which was micro-CT scanned using a SkyScan 1072 system (SkyScan, Aartselaar, Belgium). The maximum deviation between the original CT image and reconstructed surface solids was less than 0.6%. The 3D reconstruction methodology is described in detail elsewhere [17]. The generation of the geometry for the plain strain model is described in the first part of this paper [18].
2.2.
Restoration types
A NCCL (abfractive) wedged-shaped lesion was created on the buccal cervical margin being 1.5 mm deep and 1.5 mm wide in the occluso-cervical direction. These parameters were employed to fit in vivo determined dimensions of abfraction lesions [19]. Two filling techniques were chosen for the present work (Fig. 2): (a) single bulk material, namely glass-ionomer (GIC) and (b) a layered technique. The latter consisted of a layer of GIC encompassing a composite bulk. Two thicknesses were considered for the GIC layer: 50 and 150 m.
2.3. 2D plain strain numeric model and the finite element solver The resulting 2D profile was subsequently meshed using a total of 2116 plain strain linear elements and all the interfaces of the model were considered as bonded (Fig. 1b). The region of interest (GIC filling) was meshed using element’s size of 0.025 mm in the cervical region and 0.1 mm elements in the occlusal region (Fig. 2a). The reminder of the tooth model was meshed using 0.4 mm linear triangular elements. A mesh-convergence test was then carried out using linear elastic material models under a load of 150 N applied at 40◦ obliquely on the tip of the buccal cusp to ensure that no further refinement of the mesh is necessary. Numerical analysis was carried out using ELFEN (Rockfield Software Ltd., Swansea, UK) and employing the discrete solver, which allows automatic transition from continuum to discrete, including crack initiation/propagation, modelling of self-contact in the cracking interface, material softening, and adaptive remesh with data transfer. In the non-linear finite element fracture analysis presented here, the topological update of the mesh consists in the insertion of a discrete crack when the tensile strength in a principal direction reaches zero, and the crack is orientated orthogonal to this direction. The basis of this model is
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Fig. 1 – Solid 3D geometry (a), the plain strain model extracted from it showing the loadcase and the constraints (b) and the material mapping (c) where E: enamel, D: dentine, R: restoration, P: pulp, L: periodontal ligament and B: supporting bone.
described in more detail by Klercka et al. [20] and Ichim et al. [18].
2.4.
Loading
To create a more extreme loading condition to which the restoration would be vulnerable, we considered a force of 150 N oriented at 40◦ in a buccal direction [17,21], applied on the tip of the buccal cusp of the model.
2.5.
Material failure model
To simulate cracking process in a non-linear finite element framework, the transition from continuum to discrete is governed by the coalescence of dispersed micro cracks into macroscopic fracture, where softening plasticity and damage theories are adopted. The fracture model presented in this study relies on the rotating (or reorienting) crack tip model, which assumes the initiation of
Fig. 2 – Detail of the mesh in the restoration area (a), and the filling types considered: bulk GIC (b) and the layered composite and thin GIC of 50 m thickness (c), and a layered composite with a thick GIC of 150 m thickness (d).
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Table 1 – Mechanical elastic and fracturing properties of the materials considered Material
Elastic modulus (E) (GPa)
Enamel [23] Dentine [23] Ligament [17] Bone [17] GIC [24] Composite [25]
69 16.7 12 MPa 14.7 10.8 15
Poisson ratio
Ultimate tensile strength (UTS) (MPa)
0.3 0.3 0.45 0.3 0.3 0.3
the degradation to be controlled by the maximum tensile stress. A detailed description of the fracture material model and its embedding into the discrete element solver is presented in the first part of this work [18].
2.6.
– 90 – – 12 40
Fracture toughness (Kic ) (MPa m1/2 ) – 1.79 – – 0.33 0.6
Fracture – Yes – – Yes Yes
The materials anticipated to fracture were represented by dentine, composite and glass-ionomer. The mechanical properties are given in Table 1. We need to mention that in selecting the fracturing properties of the materials from available literature data, we have chosen the conservative or lower reported values.
Material properties
The enamel, periodontal ligament, pulp and supporting bone were modelled with isotropic elasticity and the material properties were extracted from data available in literature. The periodontal ligament was taken as elastic with an E of 12 MPa and of 0.45, values which were shown previously to match the in vivo mobility of the tooth [17,22]; same material used for the pulp.
2.7. Assessment of the influence of elastic modulus on restoration failure The mechanical integration of the restoration was assessed by comparing the extent of strain softening inside the restoration as computed for different values of its elastic modulus. In the finite element context, a non-local nodal damage state indicator (ω) is computed to disperse micro-cracks coalescing
Fig. 3 – Predicted mixed adhesive/cohesive failure in bulk GIC filling (a), composite and GIC adhesive layer of 50 m (b) and the composite and GIC adhesive layer of 150 m (c). A detailed image of the failed cervical margin of the restoration (b) shows the debonding of the restoration form the underlying dentine and the limited cohesive failure.
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into macroscopic fractures and is interpreted as microdamage accumulation inside the material. In practice, many material and geometric parameters may, to a certain extent, contribute to the damage of the material. However, the scope of this study is restricted to the sensitivity analysis of damage with respect only to the elastic modulus of restorative material. In employing these principles, we started from an initial E of 10.8 GPa for the GIC and then we steadily reduced its value, until the calculations showed that the restorative materials have complete elastic behaviour without plastic strain-softening (micro-damage) and/or macroscopic fracture. A point to make refers to our assumption that the fracture toughness and UTS are not compromised while the Young’s modulus of the GIC is systematically reduced. Our assumption is supported by the fact that, despite many materials show a direct relationship between the values of E and those of UTS and fracture toughness, this is not universally enforced in the field of biomaterials. For example, dentine compared with enamel [26] or resin modified GIC compared with conventional ones show an increase in strength and toughness associated with a decrease in E modulus.
3.
Results
3.1.
Initial elastic modulus
Restoration failure occurred in all the cases where the GIC material was considered with its initial elastic modulus of
10.8 GPa. The failure was constantly located on the cervical interface and was mixed, mostly adhesive with some small area of cohesive failure (Fig. 3). Principal stress analysis shows the influence of the GIC thickness on the distribution of tensile stress on the cervical margin of the restoration prior to failure (Fig. 4). For the bulk GIC restoration and for the thick GIC layer failure initiates at similar force levels (90 N). In contrast, a thin layer of GIC would require a slightly larger force for the failure to occur (103 N).
3.2.
Reduced elastic modulus
Reducing the elastic modulus of the GIC to 5 GPa reveals an interesting phenomenon. While the layered restorations show a modest increase in their load-bearing capacity (7 and 9 N, respectively), the most dramatic change is recorded for the bulk filling. For the latter, the increased resilience of the bulk volume of restorative material causes the onset of failure to occur at 112 N; that is about twice the increase compared with the layered restorations. There is also a commensurate reduction of the stiffness in the loading curve. Nevertheless, all the restorations failed showing a similar mixed, adhesive/cohesive mode (Fig. 5). Fig. 6 shows the maximum tensile stress profiles, as a function of applied force, for an elastic modulus of the GIC set to 1 GPa. Only for the 50 m layered restoration was failure recorded upon loading to 150 N. In this case, the failure mode is also mixed, adhesive/cohesive and initiated at a load of 135 N.
Fig. 4 – Tensile stress contours for 10 GPa elastic modulus of the GIC before failure (a–c). The plot shows the applied force–stress relationship at the cervical margin of the GIC/dentine interface (d). Note the distinct phases of the mechanical response of the GIC: elastic (I), strain-softening (II) and fracture (III).
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Fig. 5 – Tensile stresses for GIC set to 5 GPa elastic modulus before failure (a–c). The chart shows the applied force–stress relationship at the cervical margin of the GIC/dentine interface (d). Note the significant increase in the mechanical resistance of the bulk restoration, compared with 10 GPa material as shown in Fig. 4.
By contrast, the bulk filling and the thick layer recorded maximum stress values below the critical threshold. This showed the usefulness of a thick layer of GIC material to act as stressbreaker. It should be pointed out that the cervical stresses for the 150 m layer restoration are very close to the failure point (11.3 MPa). In turn, the bulk filling showed a maximum stress well below it (7.3 MPa).
Fig. 6 – Tensile stress vs. load plot for GIC set to an elastic modulus of 1 GPa. Note that failure occurs only in the layered restoration employing a thin layer of GIC. Also, note that the cervical stresses in the 150 m thick layer are close to critical limit.
4.
Disscusion
In this paper we investigated the mechanical integration of cervical restorative materials and we aim to identify a most favourable selection of E value for the restoration, which will allow it to survive under the unfavourable loading conditions that may prevail. In the biomedical literature, there are limited studies applying reverse-engineering methods for designing or improving biomaterials and they concern mostly locomotor apparatus, e.g. components of a hip prosthesis [27,28] or the spine [29]. To the best of our knowledge such a numerical-based optimisation involving brittle materials in a non-linear FE based fracture framework was not employed for dental restorative materials. The experimental co-ordinates are derived from our previous work [17], which focused on the influence of cavity size and shape on the failure of GIC restoration in NCCL. The latter study showed that the major factor contributing to failure is the loading direction, while the lesion shape and size were non-determinant factors. Therefore, in this paper we employed only a single lesion type (wedge lesion) with the worst scenario of para-axial loading. The present study shows that the restorative materials currently used in cervical non-carious lesions are largely unsuitable in terms of resistance to fracture of the restoration. Their relative high stiffness creates stress concentration at the
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cervical margin, which in turn initiates mechanical failure due to the low fracture toughness of the material and interface. Irrespective of the filling technique, the restorative material with a Young’s modulus of 10.8 GPa failed prematurely in a mixed, adhesive/cohesive mode. Prior to fracture, the restorative material undergoes remarkable strain softening, which largely compromises its mechanical properties and initiates the path to catastrophic failure. Strain softening in quasi-brittle material is a consequence of the accumulation of micro-cracks in the area, which is overstressed. Due to the presence of these microcracks, subsequent cyclic loading results in additional new cracking damage by failure of the bridging ligaments between microcracks. Upon reloading, this offers less resistance to deformation, an aspect known as “softening”. Furthermore, a material, which accumulates strain softening induced damage is increasingly susceptible to the action of other damaging factors like chemical and mechanical degradation. In the present study, the softening of the material occurs in the interfacial cervical region of the restoration. The cervical interface was also clinically identified as locus minoris resistentiae [7,9]. Therefore, one possibility to avoid the onset of the microdamage is to employ a material, which exhibits greater flexibility and behaves more elastically for the given loadcase. This behaviour would reduce considerably the stresses on the margin and, if the UTS of the material and/or interface are not exceeded, mechanical failure is unlikely even under an oblique functional overloading. The necessity of stress-buffering was firstly acknowledged by Kemp-Scholte and Davidson [1] in the case of shrinkage stresses reduction. However, this principle can be extrapolated to other functional loadcases as shown by Ausiello et al. [30] which investigated the optimal adhesive layer thickness leading to maximum stress release while preserving the interface integrity, or by Li et al. [12] in their work regarding the improvement of the marginal adaptation by the use of existing flowable materials as an intermediate layer. The benefits of stress reduction in prevention of mechanical failure are also supported by our findings. Furthermore, we are able to point to a value of the E modulus, which should be employed to prevent failure. The best results are obtained for a bulk filling with a 1 GPa elastic modulus material case in which the tensile stresses are about 50% of the failure limit. By contrast a thin layer of the same flexible material would fail in the cervical region, mainly because its limited thickness cannot provide sufficient stress-reduction. In the case of the thick layer failure does not occur but the marginal tensile stresses are close to the failure limit, leaving a very small safety margin. However, from a clinical perspective a material, which can be applied in bulk is preferable. We suggest that the elastic modulus of such a material should be in the range of 1 GPa. Employing such a tailored material would not raise functional problems, as to a certain extent the cervical cavities are not directly load-bearing areas. Instead, the consideration of aesthetic qualities and resistance to further mechanical abrasion or biochemical corrosion should be considered when developing and testing such restorative materials.
At present no such material, which would fulfil these mechanical requirements is commercially available. However, our results suggest both a methodology to follow and a goal to achieve in future design of restorative biomaterials. On theoretical grounds, a way of attaining the required restorative modulus is to combine a stiffer reinforced material in a more flexible polymeric matrix employing the following hypothetical equation for particulate systems [31] 1 1− + = E Er Em
(1)
where Er and Em are Young’s moduli for the reinforcement and matrix materials respectively, is the volume fraction of the reinforcement material. We anticipate that the presented methodology would provide more precise guidelines to be used in the development of dental restorative materials, which could be tailored to specific clinical applications with their needs based on a thorough knowledge of the underlying mechanical environment.
5.
Conclusions
Within the limitations of this numerical study, we can conclude that, from a mechanical point of view, the existing restorative materials are largely unsuited for usage in NCCL. We suggest that the “optimal” material for cervical restoration should be more flexible and have an elastic modulus in the range of 1 GPa. In future, numerical modelling should be employed as an integral part of the material design, selection and development.
Acknowledgements This paper was partially funded by a University of Otago Research Grant as well as a Deputy Vice-Chancellor’s award to the Craniofacial Biomechanics Group (Otago University). The third author is supported by James Cook University through a New Staff Grant scheme. Parts of this work were also supported by ARC grant DP 0666446.
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