Several studies have been conducted on the stresses around dental implants including bone quality and quantity, implant design, the use of cantilevers, the number and distribution of implants, and superstructure design.1–8 The in vivo studies pose considerable technical problems and have largely been confined to the studies of occlusal force transmission and the effects of superstructure design. Modeling with either mechanical models or computer simulations enables isolation of selected factors, but usually requires assumptions about some of the variables. To date, these have excluded functional deformation of the mandible, although this may have considerable effects on the outcome.1
The human mandible presents complex elastic biomechanical behavior under functional loading. This is a result of both its horseshoe-shaped anatomical conformation and its complex structure of the constituent bone, which is an elastic, anisotropic, and inhomogeneous tissue and can be deformed.9,10 According to Misch,11 mandibular flexure may be more than 10 to 20 times the movement of a healthy tooth; therefore, it is important in the patient evaluation as much as tooth-implant connections.
According to one of the most common prosthetic protocols, in totally edentulous patients treated with full-arch implant–supported fixed partial dentures(FPDs), the implants are more often surgically positioned in the interforaminal region for anatomical and surgical reasons and the prosthetic superstructure designed with cantilever distal extensions.12 Even though the applicability of implants placed in the molar region has increased by virtue of innovative materials and techniques including shorter implants, bone grafts, and lateralization of the alveolar nerve, 1-piece superstructure remain the first choice when designing implant-retained prostheses.6–13
However, some authors1,9,14,15 have suggested that an implant-supported fixed restoration in the mandible designed as a single, continuous, and rigid bar can generate dangerous stresses because of the mismatch in deformations between the mandible and the FPD and bone loss around implants, material fracture, or screw loosening may follow. According to Fischman,14 mandibular elastic flexure could explain the higher bone loss around anterior implants that is often observed in full-arch implant restorations with distal cantilevers. In the anterior symphyseal region, in fact, the flexure has a more significant effect than in the posterior sections, and a cross-arch implant–supported fixed restorative system, which is more rigid than the bony tissue, does not follow the flexure of the mandibular bone and generates high-stress concentrations.1,16 Hobkirk and Havthoulas1 confirmed the significance of a mismatch in the torsional rigidity of the mandible and superstructure and the necessity of a device that permits dorsoventral shear especially when the mandible is thin in the symphyseal region.
Few investigations have dealt with the measurement of dental arch deformation during static biting. According to the study by Korioth and Hannam,17 the human jaw deforms during symmetrical and asymmetrical clenching tasks. This deformation is a complex phenomenon and includes the rotational distortion of the corpora around their axes. The degree of distortion depends on the clenching task. For instance, Korioth and Hannam17 considered clenching in the group function, intercuspal, incisal, and molar positions. Maximum contraction of the dental arch occurred during incisal clenching (INC), which was accompanied by expansion of lower jaw border at anterior sites.
The aim of this study was to use finite element model (FEM) to evaluate the restraining effects imposed by 1-piece cross-arch superstructure on mandibular flexure caused by INC and observe the stress distribution.
Materials and Methods
A 3-dimensional (3-D) FEM of a human mandible was created from computed tomography scan data of a cadaver. The images were obtained in small slice intervals (0.5 mm increments). Slices were assembled into a 3-dimensional object by means of commercially available software (Mimics; Materialise, Leuven, Belgium). Mimics was a 3-D image processing and editing software that converted scanned data to 3-D object. Then, the resulting object was exported to a finite element modeling software (SolidWorks 2003; SolidWorks, Concord, Mass) for simulation. Cortical bone of various thicknesses (1–1.5 mm) was defined around the cancellous core.
Three dimensional FEM of International Team Implantology dental implant (Institut Straumann AG, Basel, Switzerland) was created from measuring data provided by Measuring Projector ST 600-1000 (Messtechnik, Schwaigern, Germany). Measuring was done with the aid of polarized light and with 0.0001 mm accuracy. Besides, solid abutments (Institut Straumann AG) of ITI dental implants with a height of 5.5 mm were modeled in the same way. Five dental implants with a length of 12 mm and a diameter of 4.1 mm were incorporated into the model. The implants were placed in interforaminal region; meanwhile, they were in the center of the mandibular crest (Fig. 1). For superstructure modeling, primary principles of ceramometal prosthesis construction were undertaken; moreover, average dimension of each tooth was considered. Finally, an implant-supported 1-piece cross-arch FPD with bilateral cantilever segments was constructed. Cantilever extension was about 16.5 mm in length from the most distal implant (Fig. 1).
;)
Fig. 1.:
Top, 3-dimensional FEM of human mandible incorporating 5, 12 mm implants (1–5 from the right side). Bottom, 1-piece superstructure used in model.
The constructed model was exported to finite element analyzing software (COSMOS Works 2003; SolidWorks) for analysis. Before starting the analysis, boundary conditions must be determined. These conditions define the relation between elements and characteristics of forces applied to them. In most previous finite element analysis studies,3,8,18–20 the material properties of cortical and cancellous bone were supposed to be isotropic, however, they are not, and anisotropy should be taken into consideration to improve the accuracy of calculations.10 In this study, cortical and cancellous bones were modeled as transversely isotropic and linearly elastic (Tables 1 and 2). A transversely isotropic material has a plane of isotropy and the elastic constants within the plane of isotropy are independent of orientation in this plane. A unique axis of symmetry lies perpendicular to the plane of isotropy. For cortical bone, the plane of elastic isotropy was in buccolingual direction, and the unique symmetry axis was along the mesiodistal direction. The unique symmetry axis for cancellous bone of the edentulous mandible was in the inferosuperior direction with the anatomical transverse plane being a plane of elastic isotropy.10
Table 1: Material Properties Used in the Transversely Isotropic Model
10 Material Properties Used in the Model
In this study, mandible was subjected to the forces exerted by muscle groups, which were regarded as the most important during INC. According to the study by Korioth and Hannam,17 during INC maximum contraction of dental arch happened. Therefore, INC was simulated to determine the effect of a 1-piece cross-arch superstructure on mandibular flexure restriction. To simulate muscle forces over wide areas of attachment, the model was loaded with multiple force vectors. Groups of parallel vectors simulated 8 pairs of masticatory muscles (superficial and deep masseter, anterior, middle, and posterior temporalis, medial pterygoid, lateral pterygoid, and anterior digastric) assumed to be directly attached to the bone (Fig. 2). Direction and magnitude of muscle forces were determined according to the study by Korioth and Hannam17 (Tables 3 and 4). For INC simulation, restraints were placed on the entire incisal surface of 2 mandibular incisors. These restraints acted perpendicularly to the occlusal plane, allowing freedom of displacement in the horizontal plane. Restraints were also placed bilaterally on condylar processes. During jaw movements, condyles pass through complex pathways that make their simulation very difficult. To simplify the modeling besides, considering the reality in this study, both condyles could rotate around an axis, which passed through condylar medial poles; however, their displacement in upward and outward directions was restricted. This kind of restraining was similar to previous studies.9,17
Fig. 2.:
Attachment area of masticatory muscles (red arrows indicate lateral pterygoid muscle; purple arrows designate posterior temporalis; green arrows show medial pterygoid, and pink show deep masseter).
Table 3: Node Number and Magnitude of Total Muscle Force Exerted by Each Muscle During Incisal Clenching
17 Directions of Muscular Orthogonal Components
17Model was meshed by tetrahedral elements. It consisted of approximately 239,099 elements and 391,951 nodes (Fig. 3). The stress analysis was performed using Von Misses stress values, which summarized the effect of all the 6 stress components with a unique value.
Fig. 3.:
Meshed model.
Results
Maximum Von Misses stress values were detected in condylar region (Fig. 4). However, regarding bone implant interfaces, the highest stress concentration (26.2 MPa) was found at the buccal and lingual cortical bones of the most mesial implant (Fig. 5). The maximum Von Misses stress values detected in all implant sites are summarized in Table 5. Considering strain distribution in this model, maximum strain was detected along condylar processes (Fig. 6). Moreover, maximum strain values in peri-implant bone were observed at the lingual aspect of implant no.3, and it was determined to be about 1680 microstrain.
Fig. 4.:
Stress distribution in mandibular model during INC (note highest stress concentration in condylar region).
Fig. 5.:
Top, stress distribution in peri-implant bone. Bottom, buccolingual cross section of peri-implant (no. 3) bone.
Table 5: Highest Stress Values in Peri-Implant Bone (1–5 From the Right Side)
Fig. 6.:
Strain distribution in mandibular model during INC.
To investigate the effect of 1-piece cross-arch superstructure on mandibular flexure, the amount of displacement in different parts of the model was measured. For this purpose, the values of deformations were calculated relative to a fixed point in the model (Fig. 7). The highest flexibility and deformations were found at the mandibular angle (showing displacement of 0.35 mm).
Fig. 7.:
Mandibular deformation during a simulated INC.
Discussion
For achieving reliable outcomes in 3-dimensional finite element analysis, models must imitate actual in vivo conditions as precisely as possible. For this purpose, mandibular bone modeled completely with cortical and spongy bones were considered to behave anisotropically. Because of symmetric state of INC, it was reasonable to model only half the mandible and shorten the analyzing time.
During INC, maximum stresses were detected around the mesial implant (restraint location), and there was a gradual decrease of detected stresses around posterior implants. This is parallel with the results of studies that used strain gauges on abutments either for patients or for acrylic models.1,5 Hobkirk and Havthoulas1 placed 6 implants in an acrylic resin model of human mandible, and Duyck et al5 used strain gauges on patients with an implant-supported fixed prosthesis.
Maximum stresses were found at the marginal cortical bone and bone implant interface surrounding the neck of the implants. Significantly, lower stresses were observed in the cancellous bone. This is in agreement with previous in vitro and in vivo studies.3,6,7,19
Radiographs are widely used to evaluate the amount of mesial and distal marginal bone loss as criteria for the clinical success of implants.2 However, some other authors3,4,18 have demonstrated that stresses concentrated at the buccal and lingual aspects are much higher than on the mesial and distal sides. The findings of this study that maximum stresses were concentrated at the buccal and lingual surfaces of the cortical bone were in close approximation with the mentioned outcomes.
It would be better if this model could be compared with a model without prosthetic superstructure and with the same geometry and loads. Considering this limitation, the results were evaluated as compared with previous studies. Direction and magnitude of muscular forces in this study were similar to the study by Korioth and Hannam.17 In that study, mandibular flexure during INC was modeled and maximum mandibular deformation during a simulated INC was observed at the central incisor area and was about 0.62 mm.17 In this study, maximum deformation occurred at the mandibular angle, and it was about 0.35 mm. According to the study by Zarone et al9 full-arch implant-supported FPDs decreased the mandibular flexure to 77% to 53% (with 4 and 6 implants, respectively) of deformation of the mandible without a superstructure. Maximum mandibular deformation of this study was 56% of mandibular flexure in the study by Korioth and Hannam,17 which mandible was without prosthetic superstructure. This is parallel to the study by Zarone et al,9 and it can be said that in this study that a 1-piece cross-arch superstructure reduced the mandibular flexure to 56% of unimpeded mandible of the study by Korioth and Hannam.17 It is suggested that other jaw functions such as opening and protrusion, which cause greatest jaw deformations and also other clenching tasks should be simulated.
In this study, maximum strain value was observed around the mesial implant, and it was 1680 microstrain. According to Frost theory, this amount of strain is within mild overload zone and must not be considered within the “safety range.”11 Therefore, considering the stress and strain concentrations, which are due to the mismatch between the mandibular and the superstructure deformations, when any doubt of increased mandibular deformation exists (in mandibles with a reduced cross section in the symphyseal region, high-muscular activity that causes greater mandibular flexure, and strong opposing occlusion), it is better to restore mandibular flexure by splitting the superstructure into shorter segments. Further studies can be done to evaluate the effect of multi-piece superstructures on mandibular flexure.
Conclusions
Within the limitations of this finite element study, the following conclusions were drawn.
- Free bending of the mandible was inhibited by the presence of a 1-piece cross-arch superstructure relative to unrestricted mandibular models of previous studies.9,17
- The highest stress and strain concentrations were found around the most mesial implant.
Disclosure
The authors claim to have no financial interest in any company or any of the products mentioned in this article.
Acknowledgments
This study was supported by a grant from vice chancellor of Research and Dental Research Center of Tehran University of Medical Sciences.
References
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Abstract Translations
GERMAN / DEUTSCH
AUTOR(EN): Roshanak Baghai Naini, DDS, MS, Saied Nokar, DDS, MS.
Dreidimensionale Finitelementanalyse zu den Auswirkungen einer einteiligen Überkonstruktion bei Flexur im Unterkiefer.
ZUSAMMENFASSUNG:Zielsetzung: Eine Flexur im Unterkiefer kann sich auf die Stressverteilung bei Implantatgestützten festen Teilprothesen auswirken, allerdings wurde diesem Phänomen bislang in Studien unter Anwendung von Finitelementanalysen nur wenig Aufmerksamkeit zuteil. Die vorliegende Studie zielte darauf ab die Effekte zu beurteilen, die sich behindernd bei Verwendung einteiliger Überkonstruktionen mit Querbogen auf Flexuren im Unterkiefer und Implantatbelastungen auswirken können. Materialien und Methoden: Deformierungen im Unterkiefer sowie die Stressverteilung bei einer Implantatgestützten Prothese (5 Implantate und eine einteilige Überkonstruktion mit 16,5 mm bilateralen distalen Trägern) wurden mittels dreidimensionalem Finitelementmodell anhand eines menschlichen zahnlosen Unterkiefers analysiert. Um die Auswirkungen einer einteiligen Überkonstruktion mit Querbogen zur Eindämmung einer Flexur im Unterkiefer zu bestimmen, wurde ein Zusammenpressen der Schneidezähne simuliert. Beim Zusammenpressen der Schneidezähne kommt es zu einer maximalen Kontraktion des Zahnbogens. Zu diesem Zweck wurden neun Paare von Kaumuskeln durch mehrfache Zugvektoren über unterschiedliche Befestigungsbereiche simuliert. Ergebnisse: Es wurde eine maßgebliche Belastung (26,2 MPa) am Kortikalknochengewebe festgestellt, das sich am Hals des Implantats an der Symphyse befindet. Dies wurde auf die Flexur im Unterkiefer zurückgeführt. Im gleichen Bereich wurde ein maximaler Stresswert von 1680 an Mikrobelastung festgestellt. Außerdem wurde am Unterkieferwinkel eine maximale Deformierung von 0,35 mm gemessen. Schlussfolgerungen: Eine einteilige Implantatgestützte Überkonstruktion begrenzt die Deformierung im Unterkiefer auf annähernd die Hälfte der Belastung, die an Unterkiefermodellen früherer Studien ohne Begrenzung festgestellt wurde. Dieses Phänomen ist bei Studien unter Anwendung von Finitelementanalysen zu berücksichtigen.
SCHLÜSSELWÖRTER: Flexur im Unterkiefer, Überkonstruktion, Implantate, FEA
SPANISH / ESPAÑOL
AUTOR(ES): Roshanak Baghai Naini, DDS, MS, Saied Nokar, DDS, MS.
Tres análisis dimensionales de elementos finitos del efecto de una superestructura de una pieza en la flexión mandibular.
ABSTRACTO:Propósito: La flexión mandibular podría afectar la distribución del estrés en la dentaduras parciales apoyadas con implantes sin embargo el fenómeno ha recibido poca atención en los estudios de análisis de elementos finitos. El propósito de este estudio fue evaluar los efectos restrictivos impuestos por la superestructura de una pieza con arco cruzado en la flexión mandibular y el estrés del implante. Materiales y Métodos: Se analizó la deformación mandibular y la distribución del estrés en una prótesis apoyada con implantes (5 implantes y superestructura de 1 pieza con voladizas bilaterales distales de 16,5 mm) con un modelo tridimensional de elementos finitos de una mandíbula humana sin dientes. Para poder determinar el efecto de la superestructura de 1 pieza con arco cruzado en la restricción de la flexión mandibular, se realizó una simulación del apriete de los incisivos. Durante el apriete de los incisivos ocurre la contracción máxima del arco dental. Con este propósito, se realizó una simulación de nueve pares de músculos masticatorios usando vectores con múltiples fuerzas sobre las superficies de sujeción. Resultados: Una cantidad significativa de estrés (26,2 MPa) en el hueso cortical que rodea al cuello del implante ubicado en la sínfisis ocurrió como consecuencia de la flexión mandibular. En el mismo lugar, se detectó el valor máximo de la tensión de 1680 por Microstrain. Sin embargo, se observó una deformación máxima de 0,35 mm en el ángulo mandibular. Conclusiones: La superestructura de una pieza apoyada con implantes restringió la deformación mandibular hasta casi la mitad de la cantidad observada en modelos mandibulares sin restricción en estudios anteriores. Este fenómeno debe considerarse en estudios de análisis de elementos finitos (FEA por sus siglas en inglés).
PALABRAS CLAVES: flexión mandibular, superestructura, implantes, análisis de elementos finitos
PORTUGUESE / PORTUGUÊS
AUTOR(ES): Roshanak Baghai Naini, Cirurgião-Dentista, Mestre em Ciência, Saied Nokar, Cirurgião-Dentista, Mestre em Ciencia.
Análise tridimensional de elementos finitos da superestrutura única na curvatura mandibular.
RESUMO:Objetivo: A curvatura mandibular pode afetar a distribuição de tensão nas dentaduras parciais fixas suportadas por implante, contudo o fenômeno recebeu pouca atenção nos estudos de análise de elementos finitos. O objetivo deste estudo era avaliar os efeitos limitantes impostos por superestrutura de arco transversal único em curvatura mandibular e tensões de implante. Materiais e Métodos: A deformação mandibular e a distribuição de tensão em uma prótese suportada por implante (5 implantes e superestrutura única com 16.5 mm de cantiléveres distais bilaterais) foram analisadas por um modelo tridimensional de elementos finitos de uma mandíbula desdentada humana. A fim de determinar o efeito da superestrutura de arco transversal único na restrição da curvatura mandibular, foi simulado aperto incisal. Durante o aperto incisal ocorre contração máxima do arco dentário. Para este propósito nove pares de músculos mastigatórios foram simulados por múltiplos vetores de força sobre áreas de fixação. Resultados: Uma quantidade significativa de tensão (26.2 MPa) no osso cortical circundando o colo do implante localizado na sínfise considerada como conseqüência da curvatura mandibular. Na mesma área, o valor máximo de tensão de 1680 microtensão foi detectado. Além disso, foi observada deformação máxima de 0.35 mm no ângulo mandibular. Conclusões: A superestrutura única suportada por implante restringiu a deformação mandibular a quase metade da quantidade observada em modelos mandibulares não-restritos de estudos anteriores. Este fenômeno deve ser considerado em estudos de análise de elementos finitos.
PALAVRAS-CHAVE: curvatura mandibular, superestrutura, implantes, FEA
АВТОРЫ: Roshanak Baghai Naini, доктор xирургичeской стоматологии, магистр eстeствeнныx наук, Saied Nokar, доктор xирургичeской стоматологии, магистр eстeствeнныx наук.
Трexмeрный анализ влияния цeльной супраконструкции на изгиб нижнeй чeлюсти мeтодом конeчныx элeмeнтов
РEЗЮМE: Цeль. Изгиб нижнeй чeлюсти можeт влиять на распрeдeлeниe напряжeния в частичныx нeсъeмныx зубныx протeзаx с опорой на имплантаты, тeм нe мeнee пока данноe явлeниe нe было должным образом исслeдовано с использованиeм анализа мeтодом конeчныx элeмeнтов. Цeлью данного исслeдования была оцeнка сдeрживающeго влияния цeльной попeрeчно-арочной супраконструкции на изгиб нижнeй чeлюсти и напряжeниe в имплантатe.
Матeриалы и мeтоды. Дeформация нижнeй чeлюсти и распрeдeлeниe напряжeния в протeзаx с опорой на имплантаты (5 имплантатов и цeльная супраконструкция с билатeральными дистальными свободными опорами длиной 16,5 мм) были проанализированы с помощью трexмeрной модeли конeчныx элeмeнтов нижнeй чeлюсти чeловeка с полной адeнтиeй. Хтобы опрeдeлить воздeйствиe цeльной попeрeчно-арочной супраконструкции на ограничeниe изгиба нижнeй чeлюсти, было смодeлировано стискиваниe рeзцов. Во врeмя стискивания рeзцов происxодит максимальноe сокращeниe зубной дуги. Для этой цeли было смодeлировано дeвять пар жeватeльныx мышц посрeдством множeствeнныx вeкторов нагрузки на области прикрeплeния.
Рeзультаты.Было сдeлано прeдположeниe, что значитeльноe напряжeниe (26,2 МПа) в кортикальной кости, окружающeй шeйку имплантата в симфизe, являлось слeдствиeм изгиба нижнeй чeлюсти. В той жe самой области было отмeчeно максимальноe значeниe нагрузки в 1680 микродeформаций. Болee того, максимальная дeформация на 0,35 мм наблюдалась в нижнeчeлюстном углe.
Выводы. Цeльная супраконструкция с опорой на имплантаты сократила дeформацию нижнeй чeлюсти почти наполовину по сравнeнию с вeличиной, наблюдаeмой в модeляx нижнeй чeлюсти бeз ограничeний, получeнной в прeдыдущиx исслeдованияx. Данноe явлeниe нeобxодимо учитывать в исслeдованияx с использованиeм анализа мeтодом конeчныx элeмeнтов.
КЛЮХEВЫE СЛОВА: изгиб нижнeй чeлюсти, супраконструкция, имплантаты, анализ мeтодом конeчныx элeмeнтов
TURKISH / TÜRKÇE
YAZARLAR: Roshanak Baghai Naini, DDS, MS, Saied Nokar, DDS, MS.
Tek-parçalı bir süper yapının mandibüler fleksür üzerindeki etkisinin üç boyutlu sonlu eleman analizi
ÖZET:Amaç: Mandibüler fleksür (eğilme), implant ile desteklenen sabit kısmi protezlerdeki stres dağılımını etkileyebilir; buna rağmen bu fenomen sonlu eleman analiz çalışmalarında dikkate alınmamıştır. Bu çalışmanın amacı, tek-parçalı çapraz arktan oluşan bir süper yapının alt çenedeki eğilme ve implant stresleri üzerindeki kısıtlayıcı etkisini değerlendirmekti. Gereç ve Yöntem: Dişsiz bir insan alt çenesinin 3-boyutlu sonlu eleman modeli kullanılarak implant ile desteklenen bir protezde (5 implant ve 16.5 mm’lik çift taraflı distal kantileverli tek-parçalı süper yapı) alt çene deformasyonu ve stres dağılımı analiz edildi. Alt çene fleksürünün kısıtlanmasında tek-parçalı süper yapının etkisini saptamak için kesici dişlerde diş sıkma simülasyonu yapıldı. Kesici dişlerde sıkma esnasında dental arkta maksimum kasılma oluşur. Bu amaçla, ataşman alanlarında birden fazla güç vektörüyle dokuz çift çiğneyici kasın simülasyonu yapıldı. Bulgular: İmplant boynunun etrafını saran kortikal kemiğin semfiz yerindeki önemli derecedeki stresin (26.2 MPa) mandibüler eğilmenin bir sonucu olduğu düşünüldü. Aynı alanda maksimum germe değeri 1680 mikrostrain olarak elde edildi. Ayrıca, mandibüler açıda 0.35 mm’lik bir maksimum deformasyon görüldü. Sonuç: Tek-parçalı, implant ile desteklenen bir süper yapı, alt çene deformasyonunu bundan önceki çalışmalardaki kısıtlanmamış mandibüler modellerde görülen deformasyonun hemen hemen yarısına indirdi. Bu fenomen, sonlu eleman analizi çalışmalarında göz önüne alınmalıdır.
ANAHTAR KELİMELER: mandibüler fleksür, süper yapı, implantlar, FEA
