Manda et al 
Statement of problem.
 Inadequate dimensioning of the connectors in a cantilever cross-arch fixed dental prosthesis (FDP) in perioprosthetic patients jeopardizes the prognosis of the restoration.
 The purpose of this study was to investigate the effect of increasing the vertical dimension (VD) on the maxi-mum stress developed within the connectors during the static loading of a cross-arch FDP extended as a 1- and 2-unit cantilever.
Material and methods.
Six digital models were developed, derived from a 3-dimensional (3-D) initial model. In the initial model, the teeth were prepared for metal ceramic restorations and splinted with a cross-arch FDP, extended as a 1- or 2-unit cantilever. The VDs of the connectors proximal to the retaining abutment were 3, 4, or 5 mm. A 3-D finite element analysis (FEA) was performed.
 The VD increase, from 3 to 4 mm and from 3 to 5 mm, of the connector distal to the retaining abutment, for each FDP, presented a maximum stress value decrease of approximately 25% and 48%, respectively. The similar VD increase of the connector mesial to the retaining abutment, for each FDP, resulted in relatively smaller stress changes. For the 2-unit cantilever restoration, the stress decreases were approximately 9% and 15%, respectively, whereas in the 1-unit cantilever restoration, the decrease was about 10% for the 4-mm connector. Further increase of the VD to 5 mm did not relieve the peak stress. The highest stress value was measured on the 3-mm connector distal to the retaining abutment in the 2-unit cantilever restoration. Despite the VD increase, the connectors proximal to the retaining abut-ment still developed the highest stress values of all the connectors for every model.
 The connector with the highest risk of failure is the 3-mm connector distal to the retaining abutment of the 2-unit cantilever restoration. Increasing the vertical dimension is beneficial for the connector distal to the retaining abutment, while the resultant stress changes are not substantial for the connectors mesial to the retaining abutment. (J Prosthet Dent 2010;103:91-100)
Effect of varying the vertical dimension of connectors of cantilever cross-arch
fixed dental prostheses in patients with severely reduced osseous support: A
 three-dimensional finite element analysis
Marianthi Manda, DDS, MSc,
 Christos Galanis, PhD,
 Vasilis Georgiopoulos, PhD,
 Christofer Provatidis, MSc, PhD,
 and Petros Koidis, DDS, MSc, PhD
School of Dentistry, Aristotle University of Thessaloniki,  Thessaloniki, Greece; School of Mechanical Engineering, National  Technical University of Athens, Athens, Greece
 The study was presented at the 13
 Annual Congress of the Balkan Stomatological Society, Limassol, Cyprus, May 2008.
PhD candidate, Department of Fixed Prosthesis and Implant Prosthodontics, School of Dentistry, Aristotle University of  Thessaloniki.
Research Associate, Section of Mechanical Design and Control Systems, School of Mechanical Engineering, National Technical University of Athens.
Research Associate, Section of Mechanical Design and Control Systems, School of Mechanical Engineering, National Technical University of Athens.
Associate Professor, Section of Mechanical Design and Control Systems, School of Mechanical Engineering, National Technical University of Athens.
Professor and Chairman, Department of Fixed Prosthesis and Implant Prosthodontics, School of Dentistry, Aristotle University of  Thessaloniki.
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 The Journal of Prosthetic Dentistry Manda et al 
Clinical Implications
Increasing the vertical dimension of the connector mesial to the retaining abutment of the cross-arch fixed dental pros-thesis has no substantial impact on its stress relief. Instead, numerical results confirm the favorable stress reduction on the distal connector of the retaining abutment induced by the increase in its vertical dimension.
Dimensioning of connectors is a critical factor in the survival of canti-lever cross-arch fixed partial dentures (FDPs) in the perioprosthetic patient, as biomechanical demands are con-siderable.
 More specifically, reduction of the osseous support moves the ful-crum of the tooth apically. This results in high stress concentrations within the connectors due to a large rotary vertical vector with long leverage for each tooth.
 The stress concentration within the connectors is further en-hanced by the addition of a cantilever segment.
 This stress increase renders connectors prone to failure, regardless of the material used, since they are the weakest points of the prosthesis due to their small cross-section.
 Proper dimensioning of the con-nectors was established by mathemat-ical calculations derived from a for-mula used by Erhardson.
 The results obtained indicate that the technical safety of the cantilevered FDPs is en-sured by increasing the vertical dimen-sion (VD) of the connectors adjacent to the cantilever segment to 5 to 6 mm and their horizontal dimension (HD) to 4 to 5 mm.
 Clinical studies, incorporating this formula in the fab-rication of cantilever cross-arch FDPs in the perioprosthetic patient, report lower technical failure rates compared to studies in which the dimensions of the connectors were inadequate.
 The positive outcomes obtained from such therapeutic regimens have been reported primarily in clinical studies conducted in Scandinavian countries.
 In this population, the anatomic average of crown diameters could incorporate the increase of the connectors to these dimensions,
 while the posterior teeth were re-stored using complete cast crowns or pontics. However, the increased use of metal ceramic restorations in the entire restored dental arch, in com-bination with the smaller mesiodistal and buccolingual diameters recorded for the teeth of other human popula-tion groups, renders such dimensions not always attainable.
 Conse-quently, even if the elongated clinical crown resulting from advanced peri-odontal disease permits the increased height of connectors, the HD is lim-ited by the tooth size and the type of prosthetic restoration. Therefore, the question arises as to how the biome-chanical behavior of the connectors is affected when an increase in VD is not combined with a simultaneous in-crease in HD. Testing the biomechanical per-formance of the connectors related to their dimensions in clinical stud-ies is not easy because it is difficult to standardize the dimensions of the con-nectors.
 Therefore, the analysis of the biomechanics of the connectors has been studied primarily using theo-retical analyses.
 Finite element analysis (FEA) is the most suitable theoretical method of solving such complicated design problems,
using the principles of engineering and material science.
 However, few FEA studies are available,
 and the authors identified no studies pertain-ing to the optimal dimension of the connectors proximal to the retaining abutment of cross-arch FDPs, extend-ed as cantilever segments, with mini-mal osseous support. The present study used a 3-D FEA to investigate the stress concentra-tion developed within the connec-tors of 2 types of cantilever cross-arch FDPs. The restorations were applied on abutments with a minimal level of osseous support, and the VD of the connectors proximal to the retaining abutment was increased from 3 to 4 and 5 mm.
 The methodology used in this study has been described elsewhere.
 In brief, it was based on the evalua-tion of 6 digital parametric anatomic models derived from a 3-D model. All of the structures were either ob-tained from a computerized tomog-raphy (CT) image processing system (Mimics; Materialise NV, Leuven, Bel-gium) or developed in a 3-D comput-er-aided design (CAD) (Solidworks 2006; SolidWorks Corp, Concord, Mass) and reverse engineering (RE) (Geomagic Studio; Geomagic, Inc, Research Triangle Park, NC) environ-ment. The srcinal model simulated a human adult mandible, dentate bilat-erally to the second premolars, with a normal height of alveolar bone. The srcinal mandible was modified to be reduced to 50% osseous support, which is the critical point beyond which a patient is classified as perio-prosthetic.
 The teeth were restored with cross-arch FDPs, extended bi-laterally as 1- or 2-unit cantilevers (Fig. 1). The mandible and teeth were modeled in the computational envi-ronment of the image control system (Mimics; Materialise NV) through CT-scan image processing. Periodon-tal ligament models were designed
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A, One-unit cantilever restoration. B, Two-unit cantilever restoration.
Design of models: A, Model 1UC-3 (1-unit cantilever, 3-mm connectors). B, Model 1UC-4 (1-unit cantilever, 4-mm connectors). C, Model 1UC-5 (1-unit cantilever, 5-mm connectors). D, Model 2UC-3 (2-unit cantilever, 3-mm connec-tors). E, Model 2UC-4 (2-unit cantilever, 4-mm connectors). F, Model 2UC-5 (2-unit cantilever, 5-mm connectors).in the CAD module of a reverse engi-neering program (Geomagic Studio; Geomagic, Inc) as positive offsets of each root, increased by 0.25 mm.
  The prepared teeth and metal ce-ramic FDP geometries were designed in the CAD environment (SolidWorks 2006; SolidWorks Corp). Teeth were prepared incorporating a slight cham-fer finish line located 3 mm from the osseous crest.
 The FDP geometry was designed based on the fabrica-tion principles of gold metal ceramic restorations, according to which the metal thickness was 0.5 mm.
 The  VD of the connectors proximal to the retaining abutment was investigated for the values 3 mm (conventional), 4 mm, and 5 mm, while the HD re-mained stable at 2.5 mm.
 The re-sulting models and their symbols are shown in Fig. 2. All 6 parametric models were subsequently imported into the FEA
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program (Algor; Algor, Inc, Pittsburg, Pa) where they were transformed into solids and meshed with brick/tetrahe-dral elements through an automated mesh generator. Mesh generation was followed by the adjustment of analysis parameters, including the assignment of boundary conditions, the applica-tion of forces, and the attribution of material properties. More specifically, fixed displacements and rotations in all directions (rigid) were applied at the outer surface of the ramus and angle area. In the cross-sectional area of the symphysis and half of the cen-tral connector, only the displacement at the x-axis and rotation at the y-axis and z-axis were fixed.
 The loading situation simulated the maximal mas-ticatory force in habitual occlusion, according to the suggested occlusal pattern for Angle Class I subjects (Fig. 3).
 The vectors of the forces were parallel to the longitudinal tooth axis and were distributed on the 4 nodes of an element. The magnitude of force applied to each tooth was selected from reported values.
 Due to the effect of the elastic deflection of the cantilever beam during loading (api-cal yielding), as recorded by Laurell and Lundgren,
 the force applied to the second cantilever was determined as one sixth of the force applied to the first cantilever. Linear elastic, homo-geneous, isotropic material proper-ties of dental tissue, the periodontal ligament (PDL), and the prosthesis were assumed in simulations and adopted from the literature (Table I).
 Stress values and distribution within the connectors were obtained by calculating von Mises equivalent stresses.
 The stress distribution pattern within the connectors for all exam-ined models is presented in Figures 4 and 5, based on a color measurement bar in which each color corresponds to a range of stress values (Fig. 4, G).  The red color at the top of the bar represents the highest stress values, while the violet color at the bottom of the bar represents the lowest stress values. Stress concentration was ob-served within the connectors and in the region of splinted crowns around the connectors of all the examined models.  The stress distribution within the connectors proximal to the anterior teeth was similar for each type of can-tilever FDP, independent of the VD of connectors proximal to the retaining abutment. The connectors proximal to the retaining abutment presented different distribution patterns as the  VD was increased. The range of the stress field was proportional to the obtained stress values, except for the connector mesial to the retaining abutment of the 1-unit cantilever res-toration.  The peak stress values calculated for the connectors of the metal frame-work for all investigated models are shown in Table II. Figure 6
represents the comparative evaluation of stress fields within the connectors of the bilateral 1- and 2-unit cantilevered cross-arch FDPs, in relation to the in-creased VD of the connectors, at the 50% osseous support level. The stress values obtained for the connectors proximal to the anterior teeth, for all of the investigated models, were rela-tively small.  The highest stress values were ob-tained for the connectors proximal to the retaining abutment, despite the VD increase, in every investigated situation. The connectors distal to the retaining abutments of the 1-unit cantilever restoration presented a progressive decrease in stress concen-tration as the VD increased. A vertical increase from 3 to 4 mm and, finally, to 5 mm, resulted in progressive stress reductions of approximately 26% and 48%, respectively. The connectors mesial to the retaining abutment pre-sented a smaller stress decrease (10%)
 Table I.
Mechanical properties
Force distribution along splinted teeth and cantilever seg-ment. Red dots represent region in which occlusal forces were applied on splinted teeth and cantilever segment.
Periodontal ligament
Alveolar bone
Gold alloy 
Poisson’s RatioMaterials
 Young’s Modulus (MPa)
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Stress distribution of connectors proximal to anterior teeth of models: A, 1-unit-cantilever restoration, 3-mm connector (1UC-3). B, 1-unit cantilever restoration, 4-mm connectors (1UC-4). C, 1-unit cantilever restoration, 5-mm connectors (1UC-5). D, 2-unit cantilever restoration, 3-mm connectors (2UC-3). E, 2-unit cantilever res-toration, 4-mm connectors (2UC-4). F, 2-unit cantilever restoration, 5-mm connectors (2UC-5) (lingual aspect), based on G, colored measurement bar. Each color corresponds to different range of increasing stress values (MPa). Red and violet colors represent upper and lower stress limits of measurement bar, respectively.
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