Review

Background

Finite element analysis (FEA) has been applied to investigate dental implant designs, the structure and material of the superstructure, and the stability of the surrounding bone [1, 2]. According to PubMed, only 10 FEA studies of dental implants were published in 1990, while 102 papers were published in 2014.

FEA has become an increasingly useful tool in the past few decades. In the medical field, the behavior of any structure or tissue under a particular stimulation can be evaluated using FEA, and biomechanical changes in the tissues can be analyzed. Additionally, FEA allows for measurement of the stress distribution inside of the bone and various dental implant designs during mastication; such measurements are impossible to perform in vivo [1, 2, 3].

A large number of FEA regarding dental implant and bone were published in these decades; however, the precision and accuracy of those studies in silico are still questionable. In 2009, Dumont et al. [4] indicated that FEA studies of biological structures should be validated experimentally whenever possible. Hannam [5] stated that the minimum requirements of FEA studies should include comparisons with data from other work or any data that can be gleaned from the living subjects being modeled.

According to the American Society of Mechanical Engineers Committee on verification and validation in computational solid mechanics, verification is defined as “the process of determining that a computational model accurately represents the underlying mathematical model and its solution,” while validation is defined as “the process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model.” In simple terms, verification is the process of “solving the equations right,” whereas validation is the process of “solving the right equations” [6,7,8,9]. Validation is a process by which computational predictions are compared with experimental data in an effort to assess the modeling error [6,7,8,9]. The sole purpose of these “experiments” is to produce data for comparison with model predictions rather than to address specific scientific hypotheses.

FEA studies with validation have recently become more common in the biomechanical field. FEA validations can be divided into two types: (1) direct validation, which involves experiments on the quantities of interest (from basic material characterizations to hierarchical system analysis such as model experiments and in vitro experiments), and (2) indirect validation, which involves the use of literature or the results of previous clinical studies. Indirect validation is clearly less favored than direct validation because of its uncertain experimental quality, sources of error, and high degree of variability. However, indirect validation may be unavoidable in FEA because no concrete biological outcome can be directly attributed to most FEA studies of force distribution; thus, it is difficult to generate outcome data for comparison with experimental data. Therefore, FEA studies should include a validation method to prove the close similarity of the results to the actual clinical situation. Validation is the process of “solving the right equations” [6,7,8,9] and comparing computational predictions with experimental data (the “gold standard”) in an effort to assess the modeling error.

The purpose of this literature review of FEA studies was to examine their model validation process and establish the criteria for evaluating validation methods with respect to their similarity to biological behavior.

Materials and methods

All studies included in this review (eligibility criteria) were FEA studies of the stress distribution of dental implants and surrounding bone using any type of validation method, and all were published in English. The exclusion criteria were publication in a language other than English, appearance of the word “validation” only in the references, no mention of the validation method for numerical FEA analysis, and mentioning of the requirement for validation without conduction of the actual validation.

An electronic literature search of PubMed was conducted up to January 2017 using the Medical Subject Headings “dental implants” and “finite element analysis.” After accessing the full text, the full context was searched using the words “valid” and “validation,” and all articles containing these words were read to determine whether they met the inclusion criteria. The selected articles were then read and summarized, and the validation techniques used in each article were assessed and categorized in a hierarchy (Fig. 1).

Fig. 1
figure 1

Flowchart of literature review. An electronic literature search of PubMed was conducted up to January 2017 using the Medical Subject Headings “dental implants” and “finite element analysis.” After accessing the full texts, the context of each article was searched using the words “valid” and “validation” and articles in which these words appeared were read to determine whether they met the inclusion criteria for the review

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Results

In total, 601 articles were obtained from the PubMed electronic search using the Medical Subject Headings “dental implants” and “finite element analysis.” After excluding articles for which the full text could not be accessed (n = 69) and that were not written in English (n = 10), 522 articles remained. These articles were searched using the terms “validation,” “validity,” and “valid” to determine whether the studies had performed a validation; after this process, 122 articles remained. These 122 articles were read, and 47 that met the eligibility criteria were selected and are summarized in Table 1. These articles were all FEA studies published from 1997 to 2016. The articles were categorized according to the method of validation as follows: in vivo experiments, model experiments, use of others’ clinical data or literature, and other software (Figs. 2 and 3).

Table 1 All studies in the literature that considered with an actual validation of FEA
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Fig. 2
figure 2

Hierarchy of validations based on their similarity to real biomechanical behaviors. The articles (n = 47) were categorized according to their validation method as follows: in vivo experiments in humans (n = 1) and other animals (n = 3), model experiments (n = 32), others’ clinical data and past literature (n = 9), and other software (n = 2)

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Fig. 3
figure 3

Proportion of dental implant FEA articles with a validation. (Left) Among totally 522 FEA articles of dental implants which we were able to access English full text up to January 2017, there are only 47 articles with a validation. (Right) The articles with a validation were categorized according to their validation method as follows levels: A, in vivo (human bodies); B, performed in vivo (heterogeneous animals); C, model experiment performed using part of a cadaver; D, model experiment performed using heterogeneous bone; E, model experiment performed using artificial materials; F, comparison with past literature; and G, performed with other software (n = 2)

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Based on the validation methods described in the articles, the top portion of the validation hierarchy comprised studies that used a customized clinical method in a human for validation [10]. The next level of the hierarchy comprised studies that used models for validation, including animal models [11,12,13] and mechanical experiments. Mechanical experiments were divided according to the material used for bone models and the techniques used for testing those models. The materials were divided into homogenous bone, heterogeneous bone, and artificial materials such as acrylic, polyurethane, plastic bone material, and others. Various validation methods were used in studies that employed mechanical testing of bone models using these specific artificial materials, such as digital image correction [11], photo-elastic stress analysis [15], and use of a strain gauge test attached to a model (this was the most commonly used method, described in 15 of 48 articles). These techniques also involved measurement of the implant displacement and fatigue testing of an implant body. The next level of the hierarchy comprised studies that used literature or clinical data from other articles to compare with results of FEA. The final level comprised studies that used other computer software for support but did not perform an actual experiment.

We classified all validation processes based on their similarity to real biomechanical behaviors into the following hierarchy (levels A to G) (Fig. 2):

  • Level A: performed in vivo (human bodies) (n = 1) [10]

The top level of the hierarchy, level A, includes in vivo methods of FEA validation conducted in humans. In 2006, Heckmann et al. [10] quantified the degree of stress that occurs in the bone around the implants as a result of fixation of cemented and screw-retained fixed partial dentures. They used a computer-aided design (CAD) model of an implant embedded in a bone block for FEA, and strain gauge experiments were performed under the same loading conditions with the use of a resin bone model and a human being for validation.

  • Level B: performed in vivo (heterogeneous animals) (n = 3) [11,12,13]

Three studies conducted animal experiments for FEA validation. In 2009, Hou et al. [12] conducted an FEA validation study involving rats to assess the histological change in the mechanical environment surrounding loaded and unloaded implants. In 1997, Natali et al. [11] performed a validation study in which they compared the influence of axial and nonaxial forces on the bone tissue surrounding oral implants placed in dogs. Both research groups used computed tomography data and CAD techniques to create an FEA model. Similarly, in 2015, Cha et al. [13] used murine femurs to place implants with low and high insertion torques for FEA validation.

  • Level C: model experiment performed using part of a cadaver (n = 4) [16,17,18,19]

  • Level D: model experiment performed using heterogeneous bone (n = 5) [20,21,22,23,24]

The next two levels in the hierarchy comprised in vivo model experiments on a section of a cadaver (level C) and the bone of heterogeneous animals (level D). Most of these studies involved mechanical testing, such as recording strain by a strain gauge attached to a dry skull or a section of bovine, porcine, or sheep bone. Bardyn et al. [20] compared the FEA-predicted removal torque with that measured using sheep bone and polyurethane foam as a validation technique. Olsen et al. [21] scanned a porcine mandible to create an FEA model and compared the FEA-predicted implant displacement with that measured on the same porcine mandible as a validation technique. Additionally, in 2002, Huang et al. [22] determined the vibrating behavior of a dental implant under various surrounding bone conditions using bone sections from hogs and FEA. The resonance frequency was compared between the two techniques, but in this case, FEA seemed more likely to serve as a validation technique to support the results of the model experiment.

Artificial materials such as acrylic resin, polyurethane, or plastic bone models were commonly used as embedded “bone” implants in validation experiments. Level E includes the use of special materials and specific methods to measure the force distribution and photoelastic resin as well as a technique called digital image correlation described by Tiossi et al. [14] in 2013. Comparisons of these artificial materials is difficult because it is challenging to determine how much more accurate one technique is over another technique. Even after subcategorizing the techniques from E1 to E5, we found that no one technique was superior to any other.

  • Level F: performed by comparison with past literature (n = 9) [47,48,49,50,51,52,53,54,55]

Validations in this level involve comparison of FEA with clinical data (F1) or other literature (F2). Most such studies compared FEA with “similar” conditions in patients, but either the comparisons were not customized or indirect and ill-defined clinical results (e.g., bone resorption volume in length or radiographic X-ray images) were compared with force in FEA. Level F2 includes validation using past literature with similar results or conclusions that were mostly summarized in few words in the “Discussion” section of an article.

  • Level G: performed by comparison with other software (n = 2) [56, 57]

The last level, level G, includes validation performed by another type of computer software such as two-dimensional FEA, i.e., an FEA model built in a computer is validated by another computer simulation or calculated values.

Discussion

The use of FEA for dental implants and surrounding bone has increased during the past few decades. Our PubMed search using the terms “dental implants” and “finite element analysis” revealed about 450 papers published in the past 10 years. However, FEA studies of implants using validation experiments are comparatively rare. While prior studies had effectively outlined the importance of validation in biomechanical FEA, no reviews of studies that applied validation to computational biomechanics of dental implants have been performed.

Table 1 shows all studies in the literature that considered the need for validation of FEAs. According to these studies, we established a hierarchy based on the evidence level of the validations (A to G, i.e., high to low) (Fig. 2).

Level A: validation using living humans

Level B: validation using living heterogeneous animals

Levels C and D: validation using homogenous and heterogeneous bone

Level E: validation using artificial bone materials

Level F: validation using past literature

Level G: validation using other software

FEA using model verification cannot be considered to be a validation method for entire study. Model verification should be performed to ensure accurate FEA; however, finite element models verified with clinical data such as a patient’s computed tomography findings are categorized in a low level of validation or without validation. For this reason, studies that used only model verification (some studies may called it by "model validation") were not included in our review [58,59,60,61,62].

Many recent papers [10,11,12, 14, 15, 25,26,27,28,29,30,31, 33, 35, 36, 39, 41,42,43,44,45, 47, 48, 50,51,52, 54, 55, 58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74] have described the use of FEA to evaluate the stress distribution of implant fixtures and surrounding bone, with a particular focus on different fixture lengths, shapes, connection designs, and prostheses. However, most such studies [15, 58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74] were performed without validation executed under the same conditions with the FEA. The following questions are worthy of consideration by oral scientists and clinicians: Can a finite element model really create a virtual condition simulating the biomechanical behavior of the craniomandibular system? To what extent can we predict biological activities with finite element models [9]?

The complexity of living organisms and internal biological phenomena is impossible to fully and precisely duplicate with individual-level specificity using a computer. However, we can evaluate the limitations of current technology and build a model with the highest level of evidence possible.

Because of the limitations of computer technology, most FEA models [75,76,77,78,79] simplify the skeletal muscle architecture in terms of a uniform fiber length, pennation angle, and line of action and represent the architecture using a Hill-based muscle model. However, how well the modeling of skeletal muscles as one-dimensional strings represents the behavior of the full three-dimensional muscles remains unknown. Reducing the complexity of the muscles to strings entirely neglects the variations in muscle density (deformation) and structure during the complex movement of real muscle specimens, which is difficult to acquire.

This review focused on validation of FEA and established a hierarchy of validation techniques from high to low as a reference for further FEA studies. However, due to the limitations of this study, the boundary conditions and finite element method (FEM) settings were not considered. For example, some research may have involved high-level validation performed in vivo, but the original FEM model was built by CAD using only a simple flat two-layer bone and without any model verification. Some other studies used a simulated bone (computed tomography data from homogeneous, heterogeneous, or artificial materials) as an FEM geometry reference and performed the validation on that material only, without seeking to perform validation using a more realistic material. Both the use of a detailed, accurate model that closely resembles the real condition and the performance of validation to prove its accuracy are important. As computer technology has progressed, model verification has become more sophisticated and complicated; however, validation still should not be ignored.

While conducting this review, we also considered future efforts. There are two types of FEA studies: time-dependent studies, which have a validity period within which the process must take place, and time-independent studies, which have no validity period but only analyze the stress distribution at a single point in time. To date, several biomechanical studies have been published with time-independent analysis [10,11,12, 14, 15, 25,26,27,28,29,30,31, 33, 35, 36, 39, 41,42,43,44,45, 47, 48, 50,51,52, 54, 55, 58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74, 80] (e.g., examination of bone resorption underneath the denture base, analysis of the instant stress distribution of a dental implant, and the bones or components of an artificial knee joint). Maeda and Wood [80] simulated a bone-dependent bone resorption process using an FEM model and shape-optimization algorithm.

To explain or analyze the mechanical properties involved in biological phenomena such as motor tasks (mastication, walking, or heart contraction), a time-dependent finite element model may provide a more realistic view. However, if time-dependent performance criteria are considered (the most common is to clarify the influence of musculoskeletal structure on function or the performance of a motor task), dynamic optimization and boundary conditions are required. This means that a much more complex model including many parameters and properties must be built, despite some of these real-world physiological data being unknown. This difficulty may explain why time-dependent models of mastication for FEA are rare.

Conclusions

  1. 1.

    High-level validation of FEA using in vivo experiments is still rare in the dental implant field.

  2. 2.

    It is necessary to clearly indicate the validation process of the model when a study using FEA is presented.

  3. 3.

    The hierarchy proposed in this study based on the evidence level of the validations can be applied to evaluate the clinical significance of studies using FEA.