Abstract
Objective
This project studies the effect of high-performance polyethylene (HPPE) fibers on stress distributions in a maxillary denture and the influence of fiber position on improving denture performance.
Methods
A denture was scanned with a 3D Advanced Topometric Sensor digitizing system. The measuring system converted the images into a 3D digital model. A 3D reverse engineering technology then produced a numerical model which was then refined with Rapidform software. The underlying mucosa and bone were constructed using a freeform system integrated with a PHANTOM haptic device. A fiber lamella reinforcement was incorporated into the denture at different positions (fitting side, mid-palatal plane, polished side) with SolidWorks software. Boundary conditions were constrained at the top of the basal bone while bite force of 230 N was applied to the posterior teeth on both sides. The denture models were analyzed with ABAQUS software.
Results
Stress concentrations were found at the incisal notch and at the anterior and posterior palatal surfaces of the unreinforced denture. The incorporated reinforcement effectively reduced the stress concentrations at these surfaces. Placement of the fibers at polished side was the best position in reducing stress concentrations.
Significance
3D FEM usefully provides a non-laboratory means to reveal the weak areas in the maxillary complete denture, and exhibit the effectiveness of HPPE reinforcement together with fiber positions on enhancement of denture strength.
1
Introduction
The loss of teeth impairs patients’ appearance, masticatory ability and speech, thus upsetting the quality of their social and personal life . To restore these functions, removable dentures are often used. The selection of materials for the construction of dentures is crucial because this directly relates to the performance and life span of the appliance during service in the oral cavity. Although it has been in market for seven decades, polymethylmethacrylate (PMMA) is still the most commonly and popularly used material for denture construction due to its pleasing appearance and easy manipulation . However, the low tensile and bending strengths of the material cause dentures of PMMA to fracture easily .
According to a survey reported by Darbar et al. in 1994, the Dental Practice Board in the UK spent about £7 million annually to repair about 0.8 million dentures in hospitals and community services . In 1997, the UK Dental Practice Board further reported that the expenditure was increased to £18 million annually to repair about 1.2 million dentures . Among the prevalent fracture types, 29% was mid-line fracture, in which 68% were observed in maxillary complete dentures and 28% in mandibular complete dentures . The longevity of the maxillary complete dentures for patients with occlusion against mandibular natural dentitions is about 21 months, whereas the average denture life time for those with occlusion against artificial mandibular teeth is about 10 years . Beyli and von Fraunhofer also pointed out that the ratio of maxillary to mandibular denture fractures was about 2:1 . The relative short life time of the maxillary dentures has led researchers to investigate the causes of fracture by studying the stress distribution upon mastication and to find ways to improve their mechanical performance .
Different methods such as electrical wire resistance strain gauge , brittle lacquer , photoelasticity , holography , and finite element analysis (FEA) have been used for investigating strain or stress distribution during deformation of dentures. The strain gauge and brittle lacquer methods are used to measure stress developed on the surface of dentures and to locate the area of maximum stress where failure occurs. The locations selected for placement of the strain gauges depend on the researchers’ experience and the recorded locations of denture fracture. If wrongly placed, they may not provide the most useful results . Brittle lacquer coating can only provide primitive and qualitative information about the stress distribution .
Both photoelasticity and holography are optical methods and utilize the interference characteristics of light waves. Stress distribution is derived from contours of the interference patterns. Both methods are useful in satisfying the high precision requirement of experimental stress analysis. They provide a clear visual and qualitative picture of the stress distribution. However, they are limited in giving direct information such as shear stress. Separation methods must be used to obtain all the components of the stress tensor . Moreover, they are not suitable for investigating the stress distribution of components embedded with reinforcing materials as the light beams cannot pass through the reinforcement to produce the fringe patterns for analysis.
The finite element method (FEM), originated from aerospace engineering, has been used for five decades for numerical stress analysis . 2D FEM can be applied to analyze structures with 2D plane symmetry . It complements or even eliminates the use of complicated experimental methods. The advent of 3D FEM further enables researchers to perform stress analysis on complicated geometries and provides a more detailed evaluation of the complete state of stress in the structures .
In parallel to stress analysis, many researchers have dedicated their effort to the search for alternative materials and manufacture methods to overcome the mechanical weaknesses of existing denture bases. Efforts have been made to use different polymers such as epoxy resin , polyvinyl acrylic , polystyrene , nylon and polycarbonate . However, the results were not entirely satisfactory.
Another approach, which involves reinforcing the PMMA resins, has been developed . Recently, the use of fiber reinforcement has been advocated as a means to improve the strength and durability of the denture base resin. There are reports on the use of fibrous reinforcing materials such as carbon , aramid , glass and high-performance polyethylene (HPPE) to improve the mechanical properties of denture base resins.
Despite extensive studies on the causes of denture failure, and on the properties of bar specimens reinforced with various types of fibers , little attention has been paid on the effectiveness of reinforcement and the influence of fiber position on the stress distribution in complete dentures. This is probably because conventional experimental methods cannot satisfactorily cope with the complicated geometrical shape of complete dentures. Currently, 3D FEM is most suitable for performing stress analysis on structures with complex geometry such as complete dentures. The aims of this paper were to investigate the stress distribution in a maxillary complete denture during the application of occlusal load, to evaluate the effect of fiber reinforcement on the stress distribution and to study the influence of fiber position on stress reduction.
2
Materials and methods
2.1
Denture and scanning machine
Reverse engineering technology was employed to convert a real maxillary complete denture into a virtual numerical model. In order to achieve a close correspondence between the numerical model and the real structure, an efficient coordinate measuring technique was required. A mobile 3D digitizing system, Advanced Topometric Sensor (ATOS, GOM mbH, Braunschweig Germany), with a resolution of 400,000 pixels per image was used. The measuring system consisted of a topometric sensor head on which two charge-coupled devices (CCD) were installed. Fringes were projected onto the scanning surface and the reflected fringes were recorded by the two CCD cameras. The unit was used for non-contact and material-independent 3D digitizing of various surfaces.
2.2
Scanning procedures
A thin layer of white dye (Magnavis WCP-2 Aerosol, Magnaflux, Wiltshire, UK) was sprayed onto the surface of the denture to increase its contrast for scanning. The denture was positioned on a scanning table with reference points and scanned from the top, left, right, back and front by tilting the table. The reference points were used by the system to combine the different measurements to form a complete perspective. The accuracy of the perspective was validated by measuring discrepancies between the real denture and the scanned model. Measurements were made of the molar-to-molar length, and from premolar to molar teeth on both sides of the denture, using a digital caliper (Digimatic Caliper 500-196; Mitutoyo, Kawasaki, Japan) with a resolution of 0.01 mm, and on the scanned model with modeling software (Rapidform 2002; INUS Technology, Seoul, Korea). The accuracy of the virtual model ranged from 0.03 to 0.06 mm. The polished and fitting surfaces of the denture were scanned and saved in stereolithography (STL) format.
The scanned surfaces of the denture were then imported to the software Rapidform, which combined the two surfaces and repaired any defects within to create a fully closed surface. The hollow denture was exported in initial graphics exchange specification (IGES) format and then imported into SolidWorks (SolidWorks 2005, SolidWorks, Concord, MA, USA) for conversion into a solid model.
The solid denture model in STL format was in turn imported into a freeform system with a PHANTOM force-feedback device (SensAble Technologies, Woburn, MA, USA) to fabricate the mucosa and supporting bone. The system first transformed the denture into a virtual clay model on which a maxillary cast was made by means of replication and subtraction procedures. After cutting and trimming the cast, a mucosal layer with varying thicknesses was produced. The mucosal layer was then used to create a supporting bone model by repeating the procedures.
The denture, mucosa and bone models in STL format were together imported into Rapidform for auto-surfacing and thereafter into SolidWorks in IGES format for construction of a horseshoe shape fiber lamella (FL) of 70 mm × 10 mm × 1 mm and the incisal notch (IN). The FL was constructed from PMMA resin reinforced with 40 vol.% of HPPE (Certran, Hoechst Celanese, Charlotte, NC, USA) fibers longitudinally. The properties of the HPPE fibers and the FL are listed in Tables 1 and 2 , respectively. The placement of the FL followed the concept of partial fiber reinforcement .
| Axial modulus (GPa) | 55 |
| Transverse modulus (GPa) | 1.3 |
| Shear modulus (GPa) | 1.3 |
| Poisson’s ratio | 0.4 |
| Modulus, E (MPa) | E 11 = E 22 = 1714 |
| E 33 = 22,600 | |
| Shear modulus, G (MPa) | G 31 = G 32 = 1252 |
| G 12 = 1177 | |
| Poisson’s ratio, υ | υ 13 = υ 23 = 0.03 |
| υ 12 = 0.36 | |
Three additional models of the denture, mucosa and bone were created. The original was not reinforced with fibers and served as a control for comparison, while the three replicated dentures had the FL placed at different positions. As the palatal regions of the dentures were about 2.5 mm thick, the three positions of the FL were constructed with their mid-plane lying at 0.75, 1.25 and 1.75 mm from the fitting surface ( Fig. 1 ). They were correspondingly named as the F position, which was closest to the fitting surface; the M position, which was at the mid-plane of the palate; and the P position, which was nearest to the polished surface. In order to provide optimal reinforcement to the denture, the FL was placed with its longitudinal axis crossing the mid-line of the denture at the anterior palate and close to the incisal notch (IN) because it had been identified as a crack initiator . The horseshoe FL extended from the first molar on one side of the anterior palate to the corresponding tooth on the other side of the anterior palate.
The numerical models of the denture, the mucosa, the bone and the FL were meshed with a total of 56,085 nodes and 256,431 tetrahedral elements. Different mesh sizes had been used in order to obtain converged results. The mucosa was attached to the bone with shared nodes, while ‘tied contact’ was used between the mucosa and denture to tie the two sets of adjoining nodes together at all times, simulating the retention forces . The mechanical properties of the denture, the mucosa layer and the bone are listed in Table 3 .
| Material | Young’s modulus (MPa) | Poisson’s ratio |
|---|---|---|
| Denture (PMMA) | 3200 | 0.36 |
| Mucosa | 2.8 | 0.4 |
| Bone | 13,700 | 0.3 |
2.3
Boundary constraints and occlusal load
Boundary constraints were applied to the top surface of the bone model according to the union of the maxilla to the base of the skull, i.e. the curved edges of the bone was confined by the skull and the central thin strip was constrained by the vomer of the nose . The movements of the associated nodes were fully restrained. Occlusal forces of 230 N each were applied onto the posterior teeth bilaterally so that the denture was subjected to a 3-point loading with the less compressible mid-palate as a fulcrum point .
All the models were analyzed using the FE software ABAQUS (Version 6.4.1, ABAQUS, Pawtucket, RI, USA).
2
Materials and methods
2.1
Denture and scanning machine
Reverse engineering technology was employed to convert a real maxillary complete denture into a virtual numerical model. In order to achieve a close correspondence between the numerical model and the real structure, an efficient coordinate measuring technique was required. A mobile 3D digitizing system, Advanced Topometric Sensor (ATOS, GOM mbH, Braunschweig Germany), with a resolution of 400,000 pixels per image was used. The measuring system consisted of a topometric sensor head on which two charge-coupled devices (CCD) were installed. Fringes were projected onto the scanning surface and the reflected fringes were recorded by the two CCD cameras. The unit was used for non-contact and material-independent 3D digitizing of various surfaces.
2.2
Scanning procedures
A thin layer of white dye (Magnavis WCP-2 Aerosol, Magnaflux, Wiltshire, UK) was sprayed onto the surface of the denture to increase its contrast for scanning. The denture was positioned on a scanning table with reference points and scanned from the top, left, right, back and front by tilting the table. The reference points were used by the system to combine the different measurements to form a complete perspective. The accuracy of the perspective was validated by measuring discrepancies between the real denture and the scanned model. Measurements were made of the molar-to-molar length, and from premolar to molar teeth on both sides of the denture, using a digital caliper (Digimatic Caliper 500-196; Mitutoyo, Kawasaki, Japan) with a resolution of 0.01 mm, and on the scanned model with modeling software (Rapidform 2002; INUS Technology, Seoul, Korea). The accuracy of the virtual model ranged from 0.03 to 0.06 mm. The polished and fitting surfaces of the denture were scanned and saved in stereolithography (STL) format.
The scanned surfaces of the denture were then imported to the software Rapidform, which combined the two surfaces and repaired any defects within to create a fully closed surface. The hollow denture was exported in initial graphics exchange specification (IGES) format and then imported into SolidWorks (SolidWorks 2005, SolidWorks, Concord, MA, USA) for conversion into a solid model.
The solid denture model in STL format was in turn imported into a freeform system with a PHANTOM force-feedback device (SensAble Technologies, Woburn, MA, USA) to fabricate the mucosa and supporting bone. The system first transformed the denture into a virtual clay model on which a maxillary cast was made by means of replication and subtraction procedures. After cutting and trimming the cast, a mucosal layer with varying thicknesses was produced. The mucosal layer was then used to create a supporting bone model by repeating the procedures.
The denture, mucosa and bone models in STL format were together imported into Rapidform for auto-surfacing and thereafter into SolidWorks in IGES format for construction of a horseshoe shape fiber lamella (FL) of 70 mm × 10 mm × 1 mm and the incisal notch (IN). The FL was constructed from PMMA resin reinforced with 40 vol.% of HPPE (Certran, Hoechst Celanese, Charlotte, NC, USA) fibers longitudinally. The properties of the HPPE fibers and the FL are listed in Tables 1 and 2 , respectively. The placement of the FL followed the concept of partial fiber reinforcement .
| Axial modulus (GPa) | 55 |
| Transverse modulus (GPa) | 1.3 |
| Shear modulus (GPa) | 1.3 |
| Poisson’s ratio | 0.4 |
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