Photoelasticity for Stress Concentration Analysis in Dentistry and Medicine

Complex stresses are created or applied as part of medical and dental treatments, which are linked to the achievement of treatment goals and favorable prognosis. Photoelasticity is an optical technique that can help observe and understand biomechanics, which is essential for planning, evaluation and treatment in health professions. The objective of this project was to review the existing information on the use of photoelasticity in medicine and dentistry and determine their purpose, the areas or treatments for which it was used, models used as well as to identify areas of opportunity for the application of the technique and the generation of new models. A literature review was carried out to identify publications in dentistry and medicine in which photoelasticity was used as an experimental method. The databases used were: Sciencedirect, PubMed, Scopus, Ovid, Springer, EBSCO, Wiley, Lilacs, Medigraphic Artemisa and SciELO. Duplicate and incomplete articles were eliminated, obtaining 84 articles published between 2000 and 2019 for analysis. In dentistry, ten subdisciplines were found in which photoelasticity was used; those related to implants for fixed prostheses were the most abundant. In medicine, orthopedic research predominates; and its application is not limited to hard tissues. No reports were found on the use of photoelastic models as a teaching aid in either medicine or dentistry. Photoelasticity has been widely used in the context of research where it has limitations due to the characteristics of the results provided by the technique, there is no evidence of use in the health area to exploit its application in learning biomechanics; on the other hand there is little development in models that faithfully represent the anatomy and characteristics of the different tissues of the human body, which opens the opportunity to take up the qualitative results offered by the technique to transpolate it to an application and clinical learning.


Introduction
The principles of physics and mechanics are applied in the daily practice of medicine and dentistry, although this is almost never done consciously, probably because few teaching methods during training reveal their relevance. The application of these concepts to biological systems is referred to as biomechanics (i.e., the distribution of forces on different parts of the body) [1]. Biomechanics, for example, can explain that the reason why most fractures after a strong blow to the chin take place in the mandibular angle, is that stress concentrates around holes, defects and geometrical irregularities [2]. Bones and teeth have a complex geometry since they have to distribute forces generated during function such as during chewing [3]. Oral diseases (e.g., caries, malocclusion, cancer) as well as treatments (e.g., restorations, prostheses, orthodontics) modify the form of dental and bony structures and even if our bodies try to adapt to these changes, muscular chains, bones or joints may be overwhelmed triggering pain, bone remodelling, or muscular or joint lesions [4].
It is therefore important to understand biomechanics to identify treatments that may initiate injuries or to be able to devise treatments that could restore equilibrium. We therefore need models that represent what happens clinically which will thus help in attaining knowledge. It is difficult to study biomechanics directly on biological systems, and it is therefore necessary to rely on simulations. Simulation techniques allow the analysis of phenomena without the need to work on the object of analysis itself. Some of the methods that have been used to analyze stress concentration include electric extensiometry [5], finite element modeling [6][7][8], interferometry [9] and Tresca stress study [10], but these methods are somewhat complex requiring specialized equipment/technology [11].
Another technique that has been applied in combination with these is photoelasticity, which allows analyzing the stress distribution in birefringent materials subjected to mechanical loads by observing the fringe pattern (isochromatic or isoclinic) produced by the optical phase differences of light passing along the material under study [12]. For isotropic optical materials, mechanical stress will lead to structure deformation, resulting in local density differences along the material axes and the change of the refractive index; then, when the light beam passes through those materials birefringence will occur. According to the plane stress-optic law [13], the stress and the refractive index can be described in a plane perpendicular to the direction of light propagation as follows: where n e and n o correspond to the refractive index along the diffraction direction of extraordinary (refracted) and ordinary (non-refracted) light, respectively; σ 1 and σ 2 are the first and second principal stresses, respectively, and K is the photoelastic coefficient of the material. When a linear polarized light is perpendicularly incident to the material sample with thickness d, the light vector can be represented into two vectors in the perpendicular plane to the direction of its propagation, which vibrates along and perpendicular to the direction of principal stress. By the birefringence effect, the optical path difference ∆ of the two linear polarized lights after passing through the sample can be expressed as: and is derived from Equations (1) and (2) and conforms the relationship between stress and the optical path difference ∆. The left side in Equation (3) helps to explain that stress must be understood as a relative measurement which needs a previous (accumulated) and a current stress status in the sample under analysis. By representing the optical path difference by its length terms where ∆ = δ.(λ/2π) stress can also be described as length quantity as: .λ (4) where δ is the phase difference in radians and λ represents the light wavelength (nm). The quotient ∆/d (nm/cm) is called the birefringence retardation and refers to the optical path delay (nm) after passing through a sample with a certain thickness (cm). From Equations (3) and (4) we can observe that the birefringence retardation is proportional to the principal stress difference. Finally, the stress can be calculated according to the optical path difference or phase difference considering the sample thickness and the photoelastic coefficient [14,15].
Given that photoelasticity contributes to the understanding of force distribution and concentration in simulation models, this technique has been used experimentally to study areas of stress concentration of medical and dental treatments. Reports on the use of this technique in these disciplines have been published in the scientific literature since the 1950s, contributing to important changes or innovations of treatments and materials in the area [16][17][18][19].
Academic programs of the schools of medicine and dentistry include applied biomechanics and anatomical simulation models to teach the location, shape and connections of organs and tissues, for example, the origin and insertion of a muscle. Simulation models aim to faithfully reproduce the conditions of the model they intend to simulate; however, the musculoskeletal system and human anatomy are too complex to be mimicked. How well do the models reflect this complexity? How much do these models consider the different tissues in the area that is studied?
The use of models or simulations improves the quality of learning [20]. In engineering careers, photoelastic models are used to help students identify areas where structures can fail [21]. Identifying existing models and how they have been used could provide the basis for the application of these techniques as novel didactic models that could favor a better understanding of biomechanics by students in the health area. The objective of this project was to review the existing information on the use of photoelasticity in medicine and dentistry and determine their purpose, the areas or treatments for which it was used, models used, as well as to identify areas of opportunity for the application of the technique and the generation of new models.

Sources of Information and Search Strategies
For this review we searched nine electronic databases: Sciencedirect, PubMed, Scopus, Springer, EBSCO, Wiley, Lilacs, Artemisa and SciELO; we additionally searched Google Scholar and web pages of universities and related associations. The following keywords were used: photoelasticity, photoelastic, biomechanics, "stress concentration", "stress concentration analysis", "bone model", "dental model" and "periodontal models", in different combinations using Boolean operators (AND/OR). The search focused on scientific articles, as well as theses, congress reports, and popular science articles related to the application of photoelasticity for stress concentration analysis in the dental and medical area; the documents selected were in English, Spanish and Portuguese.
We identified 192 documents (1964-2019) and found a greater increase in publications on the subject since 2000 especially in the dental field ( Figure 1) probably due to the development of the technology and materials that allowed the overcoming of previous limitations. In 2003, Orr [22] described the evolution of the technique and its application in the study of biomechanics; he mentions the importance of the development of new materials and the addition of quantitative analysis to improve the applications in medicine. We therefore decided to only include articles 2000-2019 so that the protocols did not differ dramatically in relation to the technique. Articles with full text where photoelasticity was applied as an experimental or analytical method and with direct application in dentistry or medicine were selected. Documents found were classified into dentistry or medicine, and subclassified by disciplines ( Figure 2).

Results
In the dental field, 87 documents were found (2000 to 2019): 68 scientific articles, 16 theses, two conference reports and one dissemination article. Photoelasticity was applied in 10 different areas ( Figure 3); most papers related to implants for fixed prostheses (34%), implants for removable prostheses (19%), and orthodontics (15%). Twenty documents were identified in the medical field: 16 scientific articles, one book chapter and three theses. The area of greatest impact in medicine is orthopedics (81%), where they have analyzed stress concentration in both hard and soft tissues ( Figure 3).
The articles found in both dentistry and medicine are described, ordered from the area of greatest to least coverage (Tables 1-12). It is important to mention that some articles included models with bone structures separated from dental and/or periodontal structures; these are more complete models and are marked in bold in the tables.

Results
In the dental field, 87 documents were found (2000 to 2019): 68 scientific articles, 16 theses, two conference reports and one dissemination article. Photoelasticity was applied in 10 different areas ( Figure 3); most papers related to implants for fixed prostheses (34%), implants for removable prostheses (19%), and orthodontics (15%). Twenty documents were identified in the medical field: 16 scientific articles, one book chapter and three theses. The area of greatest impact in medicine is orthopedics (81%), where they have analyzed stress concentration in both hard and soft tissues ( Figure 3).
The articles found in both dentistry and medicine are described, ordered from the area of greatest to least coverage (Tables 1-12). It is important to mention that some articles included models with bone structures separated from dental and/or periodontal structures; these are more complete models and are marked in bold in the tables.

Results
In the dental field, 87 documents were found (2000 to 2019): 68 scientific articles, 16 theses, two conference reports and one dissemination article. Photoelasticity was applied in 10 different areas ( Figure 3); most papers related to implants for fixed prostheses (34%), implants for removable prostheses (19%), and orthodontics (15%). Twenty documents were identified in the medical field: 16 scientific articles, one book chapter and three theses. The area of greatest impact in medicine is orthopedics (81%), where they have analyzed stress concentration in both hard and soft tissues ( Figure 3).
The articles found in both dentistry and medicine are described, ordered from the area of greatest to least coverage (Tables 1-12). It is important to mention that some articles included models with bone structures separated from dental and/or periodontal structures; these are more complete models and are marked in bold in the tables.    To compare the stress distribution in the supporting tissues surrounding implants placed in the anterior maxilla with 5 partial fixed dental prosthetic designs.
Reproduction of an upper arch with premolars, 6 anterior implants included in a photoelastic resin and prosthetic rehabilitation. PL 2 Vishay Measurements Group Inc., Malvern, PA, USA.
Stress distribution with different partial fixed prosthetic designs. Tensions generated by marginal mismatch in implantsupported prosthesis.
References in bold indicate studies that used more complete models. Stress distribution around implants with and without palatal coverage. To evaluate the stress behavior around short implants in edentulous atrophic mandibles.
Implants included in a resin mold, reproducing the mandibular position.
Stress generated by mandibular implants according to length, width and geometry.  Stress generated around mini orthodontic implants of different brands and designs. Analysis of different orthodontic treatments to solve mesial inclination. Residual stress produced by either manually or prefabricated bending of the maxillary fixation elements. To evaluate the distribution and concentration of tension in the bone that supports the upper premolars.
Tooth cuts reproduced with photoelastic resin on a polystyrene support simulating the alveolar bone and the periodontal ligament simulated with IMPREGUM F (3M-ESPE). Non specified.
Stress distribution of the masticatory loads generated in the alveolar bone with different dental cavities and restorations. To evaluate the influence of increments in thickness on degree of conversion, Knoop microhardness, and polymerization-shrinkage stress of three dental composites.
Maxillary second premolar models with a standard class I cavity and restoration. Epoxy resin flexible GIV; Polipox, Cesário Lange, SP, Brazil.
Stress distribution and degree of conversion by polymerization of dental composites.
References in bold indicate studies that used more complete models.  Reproduction of an arch with implants included in photoelastic resin with mounted dentures. PL 2 Vishay Measurements Group Inc., Raleigh, NC, USA.
Stress distribution around implants that support maxillary obturators. Tensions generated by different removable partial dentures on different types of residual ridges.
References in bold indicate studies that used more complete models.  Next, Articles with application in the medical area are described. Stress generated in the lower lumbar area due to compression.  Mechanical properties of a gel to replace the skin.

Dentistry
The results show greater application in the field of fixed and removable prostheses associated mostly with the use of implants (Tables 1 and 2), which agrees with the findings of previous reviews [104], probably because failures due to rejection were previously associated with the load that the implants receive. Photoelasticity has provided the possibility of analysis and understanding of the phenomena of distribution of efforts to contribute to designs that generate less probability of rejection. Recent studies continue comparing different designs and variations in implantology techniques which suggests that there is still much to contribute towards better treatments [105][106][107][108] and some combine photoelasticity with other techniques such as finite element analysis providing a better description of the results [109].
The application of the photoelastic technique in orthodontics was also found, since applied loads and the phenomena related to the modification of bone and dental biological structures are due to the applied forces (Table 3). Figure 4 shows dental students how an orthodontic appliance works and how its design as well as the characteristics of the patient's teeth influence the areas where stress concentrates. These models can help students to analyze the importance of the design of appliances and the areas that could be damaged if the treatments are not adequately implemented or activated. still much to contribute towards better treatments [105][106][107][108] and some combine photoelasticity with other techniques such as finite element analysis providing a better description of the results [109].
The application of the photoelastic technique in orthodontics was also found, since applied loads and the phenomena related to the modification of bone and dental biological structures are due to the applied forces (Table 3). Figure 4 shows dental students how an orthodontic appliance works and how its design as well as the characteristics of the patient's teeth influence the areas where stress concentrates. These models can help students to analyze the importance of the design of appliances and the areas that could be damaged if the treatments are not adequately implemented or activated. Sitting of the appliance without activation of the screw; the isochromes indicate that the appliance is not passive and that stresses are already present due to (1) a poor hook design (2) an irregular vestibular archwire and (3) the presence of cavities due to caries. (B) After activation of the screw (observe the opening of the midline), the isochromes intensify in the areas where they were seen before and also spread towards the palate [110].
Other areas such as operative dentistry and occlusion in which biomechanics is central have just begun to take advantage of this technique; the number of papers found is increasing (Tables 4-10). The use of photoelastic models has generated important contributions in different areas of dentistry, defining the attachments and techniques that are most favorable considering the generation of efforts. However, they use different models, limiting photoelastic models according to their specific interest. It is noteworthy that only some take the general anatomy into account, and few consider the different properties of the resins. Some have made efforts to reproduce the characteristics of tissues that have very different strength and hardness; only six of the articles marked in bold considered these differences. It is necessary to develop models that come closer to clinical reality, considering the complexity of the anatomy and the importance of masticatory loads. Some papers mention photoelasticity as an accessible technique for analysis for a specific purpose, such as Al-Omiri et al. [111] where they review the biomechanical behavior of teeth restored with endoposts with the possibility of making recommendations on techniques and materials that provide better clinical results. They mention how methods such as photoelasticity and finite element analysis back recommendations by providing important information, which supports our proposal for the use of photoelasticity as a didactic tool to demonstrate the importance of biomechanics to dentists.
Although there are other techniques beside photoelasticity that may facilitate learning biomechanics, most are complex and specialized (e.g., finite element analysis, interferometry), that may explain why we did not find any study using these techniques to explain biomechanics to dental students. It would probably make the understanding of Sitting of the appliance without activation of the screw; the isochromes indicate that the appliance is not passive and that stresses are already present due to (1) a poor hook design (2) an irregular vestibular archwire and (3) the presence of cavities due to caries. (B) After activation of the screw (observe the opening of the midline), the isochromes intensify in the areas where they were seen before and also spread towards the palate [110].
Other areas such as operative dentistry and occlusion in which biomechanics is central have just begun to take advantage of this technique; the number of papers found is increasing (Tables 4-10). The use of photoelastic models has generated important contributions in different areas of dentistry, defining the attachments and techniques that are most favorable considering the generation of efforts. However, they use different models, limiting photoelastic models according to their specific interest. It is noteworthy that only some take the general anatomy into account, and few consider the different properties of the resins. Some have made efforts to reproduce the characteristics of tissues that have very different strength and hardness; only six of the articles marked in bold considered these differences. It is necessary to develop models that come closer to clinical reality, considering the complexity of the anatomy and the importance of masticatory loads. Some papers mention photoelasticity as an accessible technique for analysis for a specific purpose, such as Al-Omiri et al. [111] where they review the biomechanical behavior of teeth restored with endoposts with the possibility of making recommendations on techniques and materials that provide better clinical results. They mention how methods such as photoelasticity and finite element analysis back recommendations by providing important information, which supports our proposal for the use of photoelasticity as a didactic tool to demonstrate the importance of biomechanics to dentists.
Although there are other techniques beside photoelasticity that may facilitate learning biomechanics, most are complex and specialized (e.g., finite element analysis, interferometry), that may explain why we did not find any study using these techniques to explain biomechanics to dental students. It would probably make the understanding of biomechanics even more difficult because they would also have to understand the operational basis behind these other techniques. Even if it is easier to visualize stress with photoelasticity, we did not find any mention of its use either as a teaching aid in dentistry.
While there is a previous review on photoelasticity in dentistry [104], the review concentrated on the experimental use, focusing on the numerical validation of the method, probably due to the importance of comparing materials and techniques. Although they do mention that this technique is very useful because of the geometry of the models, they do not specifically mention their use as a teaching aid.

Medicine
There are few papers related to the application of photoelasticity in medicine although there are many bibliographic reference books concerning applied biomechanics in medical education. For this reason, in the medical area biomechanics is used to teach how fractures, dislocations and other traumas are induced and how different parts of the body work; mostly, with anatomical models, figures and diagrams with applied forces [112], but we did not find any documents mentioning photoelasticity for teaching.
Although we found fewer papers on photoelasticity in the medical area, the importance of biomechanical principles is better emphasized. Photoelasticity facilitates its understanding and, as in dentistry, its main objective is to improve devices and techniques, as well as an in-depth analysis of the causes that generate pathologies, fractures or affect the prognosis of treatments. The area that has exploited this technique either on its own or in combination with others, such as finite element, is orthopedics (Table 11). Prosthetic treatments and the knowledge of how different pathologies or traumatic injuries are produced has been extended thanks to the study of human biomechanics. In orthopedic surgery the photoelastic technique has contributed analyzing procedures with spinal and hip implants among others, as well as other surgical procedures (Table 12). It is important to point out that some studies do not only include bone elements but also joint and muscle elements, broadening the perspectives in the application of the technique. In other words, in medicine this technique has not been limited to the study of hard tissues of the human body.
In more recent papers in medicine the application goes beyond the analysis of forces on the body. For example, Maxwell et al. (2020) studied a dynamic image of photoelasticity to analyze ultrasound waves used to rupture urinary tract stones [113]. In medicine, improvements of different techniques that could be used together with photoleasticity are being developed [114].
A point to highlight in the medical area is that the type of models that could be developed may be more complex and diverse, due to the number of components, the different types of joints and the type of movements the joints perform, while in dentistry there are only two types of joints: the temporomandibular and the alveolo-dental, with the same models replicated in different publications.

Compiled Considerations
The results of this review indicate that photoelasticity has been used in different fields of medicine and dentistry. In dentistry most studies relate to implants for fixed and removable prostheses, and some have applied this technique to better understand materials or techniques for direct or indirect restorations, orthopedic and orthodontic appliances, as well as surgical or therapeutic techniques. Finding only 68 papers in dentistry and 16 in medicine during the period between 2000-2019 indicates that this technique has been underused.
The distribution of the reports shown in Figure 1 may be due to the development and advances in methods to obtain and process the data, and the improvement in the techniques as well as improvements in the production of the models. As an example of the improvements, we found the use of mineral oil to smoothen the change in the refraction indexes allowing a better signal from the isochromes [106,115], as well as the standardization in the thickness of the samples and stress-freezing [18].
Photoelasticity, similar to other techniques, offers advantages and disadvantages in relation to the precision of the results depending on the type of models used. Photoelasticity is an experimental technique that, despite not being a numerical technique by itself, is nevertheless valuable since it can back other techniques to obtain better results of the application to biological systems with complex geometries. Although photoelasticity is better adjusted to flat 2D models for the observation of the isochromes, it has been adapted to be used in 3D models or thicker ones. Of course, based on the required result there is always the possibility of complementing some techniques with others. Photoelasticity, however, has merits that grant its validity with the possibility of obtaining visual results to observe stress and strain in complex geometries that are more difficult to observe with other techniques [18,68,104] and that if needed can provide numerical values.
An important finding was that most studies used simple models and that complex anatomy is not considered, reproducing only the small area of interest for the device under study (e.g., a dental implant in a cube of resin [28] or a reproduction of the alveolar process with dental implants [55]). A slightly more complex model includes individual teeth in one type of resin enclosed in a maxillary section made out of another type of resin [43].
Of all the papers in the dental field, only three models include the reproduction of the entire skull combining photoelastic materials with other non-photoelastic resins or with natural bony structures. The periodontal ligament was taken into account as a separate structure in only a few of the reviewed articles. This tissue has an important biomechanical role absorbing loads during chewing; it would therefore be important to study the possibility of including it in the models with some material that resembles its properties. In contrast, in the medical field, anatomical considerations were better replicated in the models; from the simplest ones that consider the bone shape in only two dimensions [93] to the reproduction of complete joints such as the knee [91]. Very complete models were developed for some theses [116][117][118]. Chrcanovic [119] in his review mentions that to be able to better suggest reality with photoelasticity the complete anatomical shape should be taken into account and reproduced. A wide variety of models have been used, but there is room for improvement. Even if difficult, models need to be developed according to the needs of each area and should include all the structures involved so that they are closer to reality.
Rigid or flexible epoxy resins are generally used. Few authors consider the properties of bones, teeth and ligaments; when they do so they combine materials [84]. Some resins have properties similar to bone or teeth; when choosing the resin with which to make a model it is necessary to find a balance between those that allow a correct visualization of the optical phenomenon and consistency. Resins that are more flexible are more sensitive to light but do not reflect the characteristics of all the tissues intended to replicate. It is necessary to consider alternatives of the resins to use since the most frequently mentioned resins are not always available or commercialized in all countries.
While photoelasticity has been used in research it has not been fully taken advantage of for teaching. In other areas such as engineering, the use of this technique as a teaching tool has already been validated by demonstrating a better understanding by the students of the physical phenomena of stress distribution. Pérez et al. [120] described "solid mechanics" to students using photoelasticity. They questioned them on how useful the technique was for understanding this complex subject; 91% mentioned the technique as useful and 88% indicated that they would consider using this technique again for other issues in solid mechanics. There were no reports of its use as a didactic tool at either the undergraduate or graduate level in the health areas. It is easy to imagine that if the use of photoelasticity improves the understanding of the concepts and facilitates their application in engineering students for whom the theory of stress distribution is a familiar concept, dental and medical students would greatly benefit from the introduction of biomechanical concepts in a much more user-friendly way and making the most of these concepts in the clinical field. Dental and medical schools should, therefore, include photoelastic models to illustrate the biomechanical functioning of biological systems. Improving students' awareness of the impact of treatments on bone, joint, dental and periodontal structures with these models could reduce the number of unfavorable circumstances that may arise from the unawareness of stress distribution on the tissues.
Limitations of this study were not reporting the complete methodology in the tables to compare variations in the way the models were obtained, or if photoelasticity was complemented by some other method, to try to determine which ones work better; however, in that case, we would have had to communicate with several authors to obtain missing data. Since we did not include the studies prior to 2000 we may have missed studies that could have mentioned the use of photoelasticity for teaching. Although this project was limited to inquiring into the applications of photoelasticity in the medical and dental area and only takes into account other techniques for comparative purposes, the possibility of combining photoelasticity with other techniques and in other areas of health could later be analyzed. Therefore, an in-depth analysis of the models and materials used to apply this method could be carried out and information could be obtained on which materials provide better observation results and image quality and thus obtain useful quantitative data for teaching.
More research is needed to better support the information that photoelasticity can provide to research in the health areas, but there is great potential in its use in didactics. While it is true that the technique has several limitations, these limitations are not truly problematical for its use in teaching, as long as models that are closer to clinical reality can be developed. Other available techniques to describe the same phenomena in biomechanics, are more complex and their cost make them unfeasible to be used in classrooms.

Conclusions
In both medicine and dentistry, the use of the photoelastic method has been underused and limited to a few specialties; however, in the medical field, the models used are more complex and not limited to hard tissues. In dentistry, only specialties related to implantology have clearly taken advantage of its possibilities.
Photoelastic models are an alternative towards the understanding of biomechanics in the area of the health sciences; they visually provide qualitative information on the extension, origin and direction of stress. The objectives reported in the documents found were mainly for research and some simplify the geometry in order to have fewer errors in the calculations and because of this they do not faithfully copy the complex anatomy of the stomatognathic or human systems. Few models have taken the different anatomical characteristics and types of tissues involved into account which are essential to better emulate human biomechanics; further improvements are therefore required.
It is important to highlight that, despite the fact that photoelastic models have been used since the 1970s, especially in the engineering area, we did not find any evidence on their use as a material to assist education related to biomechanics in medicine or dentistry. Therefore, there are many areas of opportunity for the use of this technique in research to better explain biomechanical behavior, but even more so to simplify and support teaching biomechanics in an affordable and straightforward way to both dentists and doctors in training.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.