TSA and FEM Analysis Applied to CAD/CAM Titanium All-on-Four Prosthesis

Patient with fully edentulous maxillaries often suffer of several disease as an alteration of facial appearance, difficulties in eating, speech, and chews. Fixed and removable prosthesis can be a solution to rehabilitate this issue. The All-on-Four protocol is one of the possible treatment modalities for implant-supported prosthetics. It consists of placing four implants in an intermorainal position, two perpendicular to the occlusal plane and two tilted distally at a 45° angle. This paper aims to assess the stress distribution on an All-on-Four titanium prosthesis by means of a Thermoelastic Stress Analysis (TSA). This full-field non-contact measurement technique allows, through a thermal imaging camera, to observe how the surface temperature of an object changes under the effect of cyclic load. The principle on which thermoelastic analysis is based is the existence of a relationship between deformation, hence applied stress, and temperature change, called the thermoelastic effect. To perform the tests, the prosthesis was fixed to a resin jaw cast that has similar characteristics to the human bone, so that the same damping that would be present under normal working conditions could be accounted for. The distal artificial molar tooth was kept in contact to a narrow screw, which was attached to a Medium-Force (M-Series) Air-Cooled Shakers made by Santek. This shaker generates a sinusoidal load of 800N with a load cell at 10 Hz frequency, which can maintain the temperature variation of the prosthesis constant. A pre-load was applied before starting the tests. To see the change in temperature a Flir A6751SC thermal camera was used, and videos were acquired with a frame rate of 125 Hz and a resolution of 640x512 pixels. From the experimental TSA tests, the trend of the experimental stress concentration on the titanium specimen was detected. The outcomes of the experimental tests were compared to a 3D prosthesis model by Finite Element Analysis (FEM).


Introduction
Periodontitis is a chronic inflammatory disease of the periodontium, which tend to ruin adjacent tooth tissues as the gingiva and the alveolar bone [1].The loss of this bone, in fact, leads to a collapse of the underlying structure causing the loss of the tooth, which has effects in life's quality due to the masticatory dysfunction [2].
Bad habits such as alcohol, smoking or poor oral hygiene give on to increase dental plaque, which is necessary, but not solely responsible, for triggering periodontitis [3].The oral cavity harbors a unique microbial community comprising viruses, mycoplasmas, bacteria, fungi, and protozoa.These microorganisms colonize oral mucosal and tooth surfaces, forming structured three-dimensional entities known as biofilms [4].Individuals susceptible to periodontitis accumulate bacteria within the gingival pocket, which can ultimately result in the degradation of the periodontium [5] [6].The equilibrium within the microbiota can be disrupted by certain bacterial species commonly found in plaque, known as the 'red complex' (Porphyromonas gingivalis, Tannerella forsythia, and Treponema denticola) [7].These bacteria have the capacity to interfere with the human host and may gradually exert selective pressure, leading to the emergence of a dysbiotic and inflammation-prone microbiota.Indeed, studies have identified diseases such as Atrial Fibrillation (AF) [8], rheumatoid arthritis, adverse pregnancy outcomes, and Chronic Kidney Disease (CKD) [9], which can contribute to the risk factors associated with periodontitis and its potential to cause type 2 diabetes [10].Some Generalized Aggressive Periodontitis (GAP) patients procrastinate to access appropriate periodontal treatment until the disease has reached an advanced stage, which results in the loss of many teeth or the compromised preservation of the remaining teeth.These results in an insufficient number of teeth needed to retain fixed prostheses at a very young age [11].For patients with complete tooth loss, comprehensive full mouth reconstruction is crucial to restore proper chewing functions, achieve a satisfactory appearance, and enhance overall quality of life [12].The posterior maxilla's lack of teeth is commonly associated with maxillary sinus pneumatization and reduced alveolar ridge height at potential implant sites.Although maxillary sinus bone augmentation is a conventional and dependable surgical technique in implant therapy, it carries disadvantages, including patient morbidity, possible surgical complications, high costs, and an extended 6-12 month healing period [13].Alternative treatment choices encompass abbreviated dental implants, fixed partial dentures supported by implants featuring a distal overhang, inclined implants, and implants positioned within the zygoma or the tuberosity [14].Since Malò and his team introduced the all-on-four concept to address anatomical challenges in the atrophic jaw, the approach of utilizing four implants for treating patients with edentulous jaws has demonstrated consistent success and high-performing [15] [16].The rising popularity of tilted implants signifies a practical strategy in managing an edentulous maxilla through implant-supported reconstruction, negating the necessity for grafting interventions.In this approach, frontal implants are strategically placed in an axial orientation, while the posterior ones are angled to align parallelly with the anterior wall of the maxillary sinus implants.This optimization augments the interface between bone and implant, thereby elevating the overall stability of the implants.Simultaneously, it increases the spatial separation between anterior and posterior implants, fostering improved distribution of loads and the prospect of diminishing or eliminating the distal cantilever [16].The all-on-four treatment has been regarded as an option with high implant success rates in the following long-term periods.The most common mechanical complications of this type of prosthesis include prosthesis breakage, abutment fracture, or the breakage or misalignment of the fixation screw between the implant and the abutment [17].For this reason, in the literature, specific tests are often conducted to analyze what occurs in the vicinity of the implant or the stresses experienced by the screws themselves [18] [19].Differently, in this study, the aim is to analyze how stresses propagate throughout the all-on-four prosthetic bar using thermoelastic analysis (TSA), a non-contact analysis, i.e., non-invasive techniques.Applying a specific oscillatory load, orthogonal to the central fossa of the molar, it is possible to observe how small difference in temperature could be translated into strain variations.The experimental analysis will subsequently be compared with finite element analysis (FEA) to assess what occurs in the sample regions which are not exposed to the thermocamera's lens.

Prosthesis Materials
To conduct experimental tests, Rhein83 s.r.l., in collaboration with New Ancorvis, provided a resin base model onto which four laboratory analog implants (3.5 x 10 mm; Nobel Biocare, Kloten, Switzerland) with internal connections were inserted following the "All on Four" protocol.In this protocol, implants in the incisor/lateral-canine position are orthogonal to the occlusal plane, while those in the premolar area are inclined distally by 45 degrees (figure 1).The four laboratory analogs are connected through the OT Bridge anchoring system, which incorporates an OT Equator with the Seeger System in PEEK, specifically designed to facilitate the construction of bars on implants with a passive connection, effectively preventing loosening.Even when exposed to high temperatures, reaching up to 120 °C, PEEK demonstrates exceptional corrosion resistance and maintains its mechanical properties.In environments with body fluids at 37 °C, the wear of PEEK decreases, resulting in a lowered release of potentially harmful particles and a reduced immune response.Notably, the Young's modulus of PEEK closely matches that of cortical bone, ranging from 3 to 4 GPa [20][21].The model replicating the edentulous lower jaw was made from a very hard resin to simulate the rigidity of actual bone.On this model, a precisely milled Titanium bar with extension elements was installed.Titanium, recognized for its various appealing features such as biocompatibility, excellent corrosion resistance, and high mechanical strength, is extensively employed in dentistry.With high success rates, it elicits a favorable biological response upon contact with living tissues [22] [23].Traditionally, the manufacturing of metallic dental implants occurred through techniques such as hot rolling, forging, or investment casting.However, various advanced manufacturing methods are increasingly employed due to the diverse characteristics of implant alloys, making it challenging to efficiently shape them using a uniform approach.In contrast to conventional dental casting, titanium prostheses can be more effectively fabricated using computer-aided design and computer-aided manufacturing (CAD/CAM) [24].In fact, the bar used for this study was fabricated based on an STL file and then milled from grade V Titanium using CAD/CAM technology.This bar includes an extension element or cantilever extending up to the sixth dental element, measuring approximately 7 mm (figure 2).

Thermoelastic Stress Analysis (TSA)
The technique known as TSA aims to measure the trend of surface stresses within a structure or mechanical component indirectly, without direct contact between the measuring instrument and the body.[25][26].To achieve this goal, the thermoelastic effect is exploited.This effect, studied by Lord Kelvin, is a phenomenon present in all types of materials (though with different effects) and involves a connection between variations in pressure (or stress variations) and temperature variations [27].From common experience, we know that compressing or expanding a gas result in heating or cooling.
In the hypothesis of adiabatic transformation, we can express the following equations: From the previous equations, we can derive through simple steps: Recalling that, given a stress field, the pressure of a continuum is defined as one-third of the first invariant of the stress state: the connection between temperature and stress for an ideal gas assuming adiabatic conditions can be expressed as follows: This thermal variation is not confined to gaseous substances but extends to liquids and solids as well.However, the degree of temperature change in solid materials is relatively constrained.To investigate the thermoelastic effect, we consider a minuscule specimen subjected to compression and tension: compression induces a temperature rise, whereas tension prompts a temperature decrease.Under certain simplifying assumptions, such as linear and isotropic elasticity, along with adiabatic transformations, we can formulate the following relationship, establishing a connection between the state of surface stress and the temperature variation (Kelvin's relation): where ρ is density, Cp is heat capacity at constant pressure, α is coefficient of thermal expansion and T is ambient temperature, while ∆  , ∆  change in surface tension along two perpendicular directions on the surface itself.By examining the just-formulated equation, we can observe how the change in temperature resulting from the thermoelastic effect relies on the thermophysical properties of the material, its absolute temperature, and the distribution of stresses within.The absolute temperature contributes to the first stress invariant (∆σₓ + ∆σᵧ), with the z-term omitted as the body is exposed to air, and no superficial loads are applied (∆σₓ ≈ 0).The expression is crafted to establish a connection between a stress change and a temperature variation [28].

Lock-in Signal Processing
The signal acquisition involves the use of the technique known as lock-in signal processing, which can be employed only when the frequency of the input signal is known.This methodology is essential since the noise bandwidth recorded during a standard TSA measurement is about thirty times broader than the temperature fluctuations.In the experimental analysis, temperature fluctuations induced by the load are embedded in a significant background noise [29].The application of the look-in technique enables the precise isolation of these fluctuations within the background noise.
The lock-in methodology entails the correlation of the signal captured by each thermal camera pixel with another reference signal.The reference signal must share the frequency of temperature fluctuations (ΔT), matching the frequency of the signal detected by the thermal pixel [30].Typically, the reference signal is derived from the load cell or displacement and acceleration sensors.The correlation between the thermal signal and the reference signal facilitates the identification of temperature variations synchronized with the load, specifically the thermal variations caused by the thermoelastic effect [31].
Following the lock-in processing, the signal is manipulated by the processor to produce an image-based result.Notably, a digital colorization process is implemented, converting the signal from each pixel into a numerical value representing the luminous intensity on a color scale.The resulting image can either be monochromatic, utilizing a grayscale, or colored, employing a scale that ranges from blue to red, akin to thermography.In traditional thermography, red denoted the warmer zone, while blue indicated the colder zone.However, in differential thermography, the meanings of red and blue differ; vibrant red or blue signifies high temperature variations, without differentiation between positive or negative variations due to the cyclic load.The distinction between red and blue simply indicates compression in blue and tension in red, and vice versa.Softer shades of red or blue represent more moderate temperature variations.

Experimental Setup
To perform tests on the prosthesis, a Santek Dynamics L1025M shaker was utilized, capable of operating within a frequency range of 5 to 3000 Hz and applying a variable force ranging from 15 to 75 kN.The required excitation type for the reference specimen must be alternating or sinusoidal to attain the adiabatic condition, which is pivotal for measuring the thermoelastic effect.
To secure the specimen and provide it with the necessary oscillatory stimulus, a structure comprised of aluminum profiles was positioned above the shaker.Subsequently, the specimen was anchored beneath the horizontal block, perpendicular to the shaker's head.
To control and adjust the load transmitted to the specimen through the shaker, a load cell was employed and positioned at the center of the upper block's beam, above the plate where the prosthesis was affixed.This load cell, manufactured by CCT Transducers, has a nominal value of 2500 kg.
On the shaker's head, a screw tightened to a plate with a 3 mm wire, supported by two semi-rigid springs, was used as a plunger to apply a point load to the central fossa of the sixth element of our specimen (figure 3).By applying the load to the distal cantilever, it simulates the distal cusp of the antagonist during masticatory movements.For this study, the FLIR A6751 Thermographic Camera was employed.
It is a thermographic camera cooled by a reverse Stirling engine, which maintains the sensor at very low temperatures, imparting high sensitivity.Its key characteristics include high thermal image resolution of 640x512 pixels, achieving a thermal sensitivity of less than 20mK.The camera acquires each pixel simultaneously in less than 190 µs at room temperature, ensuring optimal acquisition even for rapidly moving objects that an uncooled thermographic camera would be unable to capture without significant blurring.Additionally, it boasts high frame rates of up to 4000 frames/s (4.1 kHz) in windowing mode.The Indium Antimonide-cooled sensor integrated into the thermographic camera operates in the wavelength range of 3-5 µm.
The specimen was previously coated with black paint to eliminate various reflections, thus avoiding excessive noise in the heat map during recordings.Subsequently, the prosthesis was excited by the load pin, causing it to oscillate at a frequency of 10 Hz using the shaker (load frequency).The signal managed by the shaker is generated by an oscilloscope at a frequency of 125 Hz (oscillation frequency).At this point, the specimen generates a force of 800 N (80 kg) on the load cell to which it is connected, resulting in a signal variation promptly acquired by the oscilloscope.Consequently, we have an input signal from the shaker and an output signal from the load cell.Finally, the acquired signal and the video recorded by the thermographic camera will be redirected to the computer, enabling the management of all load settings, frequency, frame acquisition amplitude (640 x 512), and video recording time (12 seconds in our case).The final setup is showed in figure 4.

Finite Element Analysis (FEM)
The finite element analysis was conducted using ANSYS software (student version).Three-dimensional geometries were provided by the same supplier company of the physical prosthesis.To find the right trade-off between a higher number of mesh elements in the areas of interest and computational speed to optimize the process, only half of the external titanium surface of the 3D bar was considered, including the two left analogs.The analysis performed was of a static structural nature.Constraints and forces were applied, aiming to replicate the experimental test carried out in the laboratory.Screws used to fix the prosthesis to the OT equator were not included in the ANSYS environment, but their dimensions were used as guidelines to define the support areas and the number of elements to be rigidly fixed to the prosthesis.In fact, to replicate the screw, a 5mm segment with the mechanical properties of stainless steel, divided into 3mm + 2mm, was inserted perpendicular into the holes of the 3D prosthetic bar.The end of the short segment was used as reference to identify the center of a circle with a diameter of 2.38mm (corresponding to the diameter of the screw) to determine the number of mesh elements for anchoring the prosthesis (figure 5-6).The same method was used to define the region of interest for the application of the force.Figure 7 shows the mesh elements selected, which correspond to a diameter of 5mm.That is, the diameter of the screw's plunger used to impart the force.The applied force is 800N (approximately 80 kg), orthogonal to the surface of the central molar fossa, to simulate a real chewing load, according to the Oxford Handbook of Applied Dental Sciences [32].
The number of nodes used was 110,302, while the number of elements was 63,306.Density, Young's Modulus, and Poisson's ratio of the titanium are provided in Table 1.

TSA Measurement
At the conclusion of the conducted tests, the various recordings made with the thermal camera were reprocessed using the lock-in technique.As a first step, an unprocessed thermographic image was acquired.Thermography is a non-contact analysis based on acquiring images in the infrared spectrum to obtain two-dimensional temperature maps for any object with a temperature above 0 K, exploiting heat exchange through radiation.Subsequently, the initial image was cropped to highlight the portion of the specimen that was subjected to greater stress (figure 8).In figure 9, it can be observed that the Region of Interest (ROI) was selected to evaluate the temporal behavior of temperature at that specific point.The orange line represents the Time History of the test, while the green line depicts the Frequency Spectrum, both temperature signal in the ROI.The Frequency Peak, at 10 Hz, represents the same frequency imposed by the Shaker on the steel abutment inside the central fossa of the sixth element.In TSA, a complex number is obtained, composed of a real and an imaginary part.The real part is the magnitude and represents the amplitude of the temperature oscillation (figure 10).The imaginary part is the phase and is used to determine whether the deformed zones are tense or compressed.In figure 11 is explained that the darker zones, circled in black, represent areas of deformation compression.In fact, even in the area below the implant, there is a compression zone, with a negative phase.This is because there is a laboratory analog and not an actual implant, and that the resin base has its own resilience.The zones circled in blue on the image are tension zones, with a positive phase, meaning the weaker structural points subjected to high stress levels.

Finite Element Analysis Result
The finite element analysis was conducted while adhering as closely as possible to the experimental test.Figure 12 reveals how the interdental zones, especially between the sixth and fifth elements, are the areas where stress is most concentrated.Despite finite element analysis being predominantly a qualitative analysis, in this type of study, it has the advantage of allowing the observation of stress distribution even in the internal arch of the prosthesis (figure 13).This was not possible with the tests conducted in the laboratory, as only the external side of the specimen was exposed to the thermal camera.It can be appreciating how the propagation of stress decreases as one approaches the incisor/lateralcanine zone, i.e., the part farthest away from the load-bearing area.

Discussion
This study illustrates how, by utilizing a shaker capable of imparting oscillating force to the test specimen and a thermal camera capable of detecting subtle temperature variations, translatable into tension variations, it was feasible to observe the stress distribution along the prosthetic bar.Through this analysis, it can be inferred that the distribution of these stresses may indeed be beneficial in preventing the stress shielding phenomena.Given that the elastic modulus of titanium is significantly greater than that of bone, this phenomenon could lead to the prosthesis's failure, as it tends to assume the entire applied load.Consequently, unloading the bone entirely from any form of load facilitates conditions conducive to diseases such as osteoporosis, a phenomenon that would promote the collapse of the bone structure [33].
As expected, FEA confirms what has been performed in laboratory tests.Even though this analysis remains mostly qualitative, the stress distribution trend is the same.Thermocamera can only detect the tension in the direction of the lens, thus only the lateral side of the sample.Thanks to the FEA it is possible to discover the stresses among the teeth from different point of views.The 3D geometry of the specimen employed for the finite element analysis can be seen as a limitation in this study, as only half of it was utilized.The choice was made to strike a balance to achieve a high number of meshes in the areas of interest.The student version of ANSYS allows only a reduced number of meshes.Therefore, the use of half of the prosthesis, in addition for optimizing and speeding up the computational calculation, is attributed to the possibility of using a denser mesh across the entire complex geometry.
To validate the Finite Element Analysis, a future study will involve the application of a strain gauge near the point of maximum stress.This will allow for the quantification of small dimensional deformations in the body subjected to mechanical stresses.

Figure 3 .
Figure 3. Plunger used to impart force to the distal cantilever.

Figure 7 .
Figure 7. Perpendicular force mesh element area on the molar fossa.

Figure 9 .
Figure 9. Orange line correspond to the time history of the test in the ROI.The green curve is the frequency spectrum in the ROI.

Figure 11 .
Figure 11.TSA Phase.Black dot-line represent the compression, while the blue areas show the tension.