Finite Element Method - perio-endo concept

Finite Element Method - perio-endo concept
2004
Vandana KL* and Kartik M
ABSTRACTIn the last decade the application of a well proven predictive technique theFinite Element Method, originally used in structural analysis hasrevolutionized dental biomedical research. Finite Element analysis wasintroduced originally as a method for solving structural mechanicalproblems, which was later recognized as a general procedure for numericalapproximation to all physical problems that can be modeled by a differentialequation description. Finite Element analysis has also been applied to thedescription of physical form changes in biologic structures particularly inthe area of growth and development and restorative dentistry.Finite element method which is an engineering method of calculatingstresses and strains in all materials including living tissues has made itpossible to adequately model the tooth and periodontal structure for scientificchecking and validating the clinical assumptions.Key words: Finite element method, stress-strain level, occlusal load, predictivecomputer model* Professor** Post-graduate studentDepartment of PeriodonticsCollege of Dental SciencesDavangere, Karnataka, India.IntroductionThe Finite Element Method (FEM) is acomputerized numerical iteration techniqueused to determine the stress anddisplacements through a predetermined model.The method was introduced in late sixties inthe aerospace industry and was applied indentistry in the early seventies. With age,human teeth are weakened by caries, abrasion,malocclusion and fracture. Cavity preparationprocedures and endodontic treatments, due toreduction of tooth structure and loss of nutrientsfrom dental pulp, exaggerate the fracturepotential of the remaining tooth structure.Inappropriate treatments, such as unnecessarilywide cavity preparation increase the potentialof further trauma and possible fracture ofremaining tooth structures. Fracture potentialmay be directly related to the stresses exertedupon the tooth during masticatory function. Anunderstanding of this relationship between thestresses in a tooth and its fracture potentialshould assist clinicians in eliminating orreducing the factors contributing to toothfracture, thus maintaining the remaining toothstructure without fracture1. In an attempt tobetter understand the stresses in the tooth, avariety of methods have been used to predicttissue response to load2. These includetheoretical mathematical techniques3, photo-elastic systems4and laser holographicinterferometry5. However, these techniques havethe disadvantage of only examining surfacestress, whilst having the added problem ofusually being supported by poor validationsystems as judged by the current standards6.The finite element method can be applicable tothe problem of the stress strain levels inducedin internal structures. This method also has the
potential for equivalent mathematical modelingof a real object of complicated shape anddifferent materials.Finite Element Method - generalreviewFinite analysis solves a complex problemby redefining it as the summation of the solutionby a series of interrelated simpler problems.The first step is to subdivide (i.e. discretize)the complex geometry into a suitable set ofsmaller "elements" of "finite" dimensions whencombined from the "mesh" model of theinvestigated structures. Each element canadapt a specific geometric shape (i.e. triangle,square, tetrahedron etc) with a specific internalstrain function. Using these functions and theactual geometry of the element, the equilibriumequations between the external forces actingon the element and the displacements occurringon its nodes can be determined.Information required for the software used in thecomputer is as follows.1) Coordinates the nodal points.2) Number of nodes for each element.3) Young's modulus and Poissons ratio of thematerial modeled by different elements.4) The initial and boundary conditions.5) External forces applied on the structure.The boundary condition of these models isdefined so that all the movements at the baseof the model are restrained. This manner ofrestraining prevents the model from any rigidbody motion while the load is acting. (Figure -1)The two-dimensional axisymmetric finiteelement modeling has been used in most ofthe previous research.7Although numericalresults can be easily obtained in two-dimensional modeling, it has some significantshortcomings.
The human is highly irregular inshape, such that it cannot be represented in atwo-dimensional space and the actual loadingcannot be simulated without taking the thirddimension into consideration. The distributionof various materials of the tooth structure doesnot show any symmetry. Therefore a threedimensional modeling with the actual dimensionmust be preferred for a reliable analysis.8Fig. 1. Showing the boundary conditions of the modelClinical implicationsNo quantitative guidelines exist to assistclinicians in making proper adjustment, so thatthe stresses in the supporting structures getevenly distributed. The FEM has been widelyused in Engineering, however its application tothe health sciences is relatively new andbecause of multiple variables in real life, certainapproximations and assumptions are needed.The results of this study were obtained fromsimulated model, from which biologic variabilitymight occur. The resultant value should beinterpreted only as a reference to aid in clinicaljudgment.Applications of finite elementmethodFinite element analysis has been appliedto the description of form changes inbiological structures (morphometrics),particularly in the area of growth anddevelopment.Finite element analysis as well as otherrelated morphometric techniques such asthe macro-element and the boundaryintegral equation method (BIE) is useful forVandana KL and Kartik MFinite element method...
Endodontology, Vol. 16, 2004the assessment of complex shapechanges.The knowledge of physiological values ofalveolar stresses is important for theunderstanding of stress related boneremodeling and also provides a guidelinereference for the design of dental implants.Finite element method is also useful forstructures with inherent materialhomogeneity and potentially complicatedshapes such as dental implants.Analysis of stresses produced in theperiodontal ligament when subjected toorthodontic forces.To study stress distribution in tooth inrelation to different designs.To optimize the design of dentalrestorations.To investigate stress distribution in toothwith cavity preparation.The type of predictive computer modeldescribed may be used to study thebiomechanics of tooth movement, whilstaccurately assessing the effect of newappliance systems and materials withoutthe need to go to animal or other lessrepresentative models.Disadvantages of FEMThe tooth is treated as pinned to thesupporting bone, which is considered to be rigid,and the nodes connecting the tooth to the boneare considered fixed. This assumption willintroduce some error however maximumstresses are generally located in the cusp areaof the tooth. The progress in the finite elementanalysis will be limited until better definedphysical properties for enamel, dentin andperiodontal ligament and cancellous and corticalbone are available.FEM: Perio-endo conceptThe finite element method offers an idealmethod for accurate modeling of the tooth -periodontium system with its complicated three-dimensional geometry.Abnormal stress levelsmay allow the clinician to estimate the tissuedamage and implement therapeutic modalitiessooner.Using the finite element program NISA IIDISPLAY III a study was conducted in theDepartment of Periodontics, College of DentalSciences, Davangere, using a three dimensionalfinite element model of maxillary central incisorto find out the stresses induced within the tooth,periodontal ligament and alveolar bone due tonormal occlusal force directed in a palato-labialdirection. The results showed maximum stressin the tooth at the labial and palatal aspect ofthe cervical region, which may be a cause fornon-carious cervical lesions, i.e. abfractions.9(Figure-2). There was no stress seen in the pulp.In the periodontal ligament, maximum stresswas seen at the cervical region and apex andthere was insignificant stress distribution in thealveolar bone. Lertchirakarn et al10validatedfinite element studies, which showed goodPALATAL VIEWLABIO-PALATAL VIEWFig.2. Showing the stress distribution in the model inlabial-palatal and palatal view. The color-coding bar onthe right is for calculation of stresses.qualitative and quantitative correspondence withstrain-gauge data in experimental studies.ConclusionIn future with this proviso, computer models ofvarious types can be used increasingly for
41fundamental biomechanics research indentistry. They also provide an ideal "test-bed"for research and development of new materialsfor use in mouth. However the effects oftraumatic occlusal load in inducing damagingstresses in the tooth and pulp have to beconsidered in further studies.References1. Khera SC, Goel VK, Chen RCS and Gurusami SA. Athree-dimensional finite element mode. Oper Dent 1988;13,128-37.2. Darendeliler S, Darendelilier H and Kinoglu T.Analysisof a maxillary central incisor by using a three-dimensionalfinite element method. J Oral Rehab 1992; 19:371-83.3. Hillam DG. Stress in the periodontal ligament. JPeriodont 1973;8:51:56.4. Mehta NR, Roeber FW, Gaddad AW, Glickman I andGoodman JB. Stresses created by occlusal prematuritiesin a new photoelastic model system. J Amer Dent Assoc.1996; 93:334-341.5. Burstome CJ and Pryputniewicz RJ. Holographicdetermination of centers of rotation produced byorthodontic forces". Am J Orthod. 1980; 396-409.6. Geramy A and Sharafoddin F. Abfraction: 3D analysisby means of the finite element methods. Quint Int 2003;34:526-533.7. Farah W, Craig RG and Merouch RG. Finite elementanalysis of mandibular model. J Oral Rehab 1988; 15:615-624.8. Rubin C, Krishnamurthy N, Capilouto E and Yi H. Stressanaly