A Method for Material Parameter Determination for the Human Mandible Based on Simulation and Experiment

In cranio-maxillofacial surgery planning and implant design, it is important to know the elastic response of the mandible to load forces as they occur, e.g., in biting. The goal of the present study is to provide a method for a quantitative determination of material parameters for the human jaw bone, whose values can, e.g., be used to devise a prototype plastic model for the mandible. Non-destructive load experiments are performed on a cadaveric mandible using a specially designed test bed. The identical physiological situation is simulated in a computer program. The underlying mathematical model is based on a two component, linear elastic material law. The numerical realization of the model, difficult due to the complex geometry and morphology of the mandible, is via the finite element (FE) method. Combining the validated simulation with the results of the tests, an inverse problem for the determination of Young's modulus and the Poisson ratio of both cortical and cancellous bone can then be solved.     

Flexural and Creep Properties of Human Jaw Compact Bone for FEA Studies

The aim of this work was to improve the constitutive model of the human mandible and dentition system by taking into account the non-linear material properties of the structural boney matrix that forms the human jaw bone or mandible. Due to the specific structure of the jaw bone the time dependence of the mechanical properties also forms an important stage of the quantification process. The lack of specific experimental data of this type of material prevents the implementation of these properties into finite element simulations which results in poor quality modelling. Here an attempt was made to determine elastic and viscoelastic mechanical characteristics of the compact bone tissue forming the mandible. The elastic properties of compact bone were determined experimentally from 3 point bending tests and the viscoelastic properties were evaluated from creep tests in compression. A particular human jaw from this complex study was used to reconstruct a geometric model for further numerical experiments.     

Flexural and creep properties of human jaw compact bone for FEA studies

The aim of this work was to improve the constitutive model of the human mandible and dentition system by taking into account the non-linear material properties of the structural boney matrix that forms the human jaw bone or mandible. Due to the specific structure of the jaw bone the time dependence of the mechanical properties also forms an important stage of the quantification process. The lack of specific experimental data of this type of material prevents the implementation of these properties into finite element simulations which results in poor quality modelling. Here an attempt was made to determine elastic and viscoelastic mechanical characteristics of the compact bone tissue forming the mandible. The elastic properties of compact bone were determined experimentally from 3 point bending tests and the viscoelastic properties were evaluated from creep tests in compression. A particular human jaw from this complex study was used to reconstruct a geometric model for further numerical experiments.     

Analysis of arch‐like bones: The rodent mandible as a case study

Bone strength is determined by the mechanical properties of bone material, and the size and shape of the whole bone, i.e., its architecture. The mandible of vertebrates has been traditionally regarded as a beam oriented in relation to main masticatory loads, i.e., the longer dimension of its cross‐section being parallel to the load. Rodents follow this pattern but, in addition, their mandible possesses an intriguing arch‐like shape that is apparent when seen in the lateral view. Little attention was given to the structural capacity of this trait. The advantage of an arch is that it can withstand a greater load than a horizontal beam. The objective of this study was to model the rodent mandible like an arch to evaluate its structural strength. The bending moment in an arch‐like mandible was 15–25% lower with respect to a beam‐like mandible. Further, bending varies with mandible “slenderness” and incisor procumbency, a functionally relevant rodent trait. In the rodent Ctenomys talarum (Caviomorpha; Ctenomyidae), bone stress was substantially reduced when the mandible was modeled as an arch‐like structure as compared with a beam‐like structure, and safety factors were 15–34% higher. The shape of rodents' mandible might confer a functional advantage to high and repeatedly applied loads resulting from a unique feeding mode: gnawing. J. Morphol. 277:879–887, 2016. © 2016 Wiley Periodicals, Inc.     

Apparent Young's modulus of human radius using inverse finite-element method

The ability to assess the elastic and failure properties of cortical bone at the radial diaphysis has a clinical importance. A new generation of quantitative ultrasound (QUS) devices and peripheral quantitative computed tomography (p-QCT) has been developed to assess non-invasively bone material and structural properties at the distal radius. This anatomical site is characterized by a thin cortical thickness that complicates traditional mechanical testing methods on specimens. Until now, mechanical properties of cortical bone at distal radius (e.g., elastic modulus, yield stress and strain) remain rarely studied probably due to experimental difficulties. The present study introduces an inverse finite-element method strategy to measure the elastic modulus and yield properties of human cortical specimens of the radial diaphysis. Twenty millimeter-thick portions of diaphysis were cut from 40 human radii (ages 45-90) for biomechanical test. Subsequently the same portion was modeled in order to obtain a specimen-specific three dimensional finite-element model (3D-FEM). Longitudinal elastic constants at the apparent level and stress characterizations were performed by coupling mechanical parameters with isotropic linear-elastic simulations. The results indicated that the mean apparent Young's modulus for radial cortical bone was 16 GPa (SD 1.8) and the yield stress was 153 MPa (SD 33). Breaking load was 12,946 N (SD 3644), cortical thickness 2.9 mm (SD 0.6), structural effective strain at the yield (epsilon(y)=0.0097) and failure (epsilon(u)=0.0154) load were also calculated. The 3D-FEM strategy described here may help to investigate bone mechanical properties when some difficulties arise from machining mechanical sample.     

On the effects of residual stress in microindentation tests of soft tissue structures

Microindentation methods are commonly used to determine material properties of soft tissues at the cell or even sub-cellular level. In determining properties from force-displacement (FD) data, it is often assumed that the tissue is initially a stress-free, homogeneous, linear elastic half-space. Residual stress, however, can strongly influence such results. In this paper, we present a new microindentation method for determining both elastic properties and residual stress in soft tissues that, to a first approximation, can be regarded as a pre-stressed layer embedded in or adhered to an underlying relatively soft, elastic foundation. The effects of residual stress are shown using two linear elastic models that approximate specific biological structures. The first model is an axially loaded beam on a relatively soft, elastic foundation (i.e., stress-fiber embedded in cytoplasm), while the second is a radially loaded plate on a foundation (e.g., cell membrane or epithelium). To illustrate our method, we use a nonlinear finite element (FE) model and experimental FD and surface contour data to find elastic properties and residual stress in the early embryonic chick heart, which, in the region near the indenter tip, is approximated as an isotropic circular plate under tension on a foundation. It is shown that the deformation of the surface in a microindentation test can be used along with FD data to estimate material properties, as well as residual stress, in soft tissue structures that can be regarded as a plate under tension on an elastic foundation. This method may not be as useful, however, for structures that behave as a beam on a foundation.     

Accuracy of elastic property measurement in mandibular cortical bone is improved by using cylindrical specimens

Ultrasonic determination of elastic properties in human craniofacial cortical bone is problematic because of a lack of information about the principal material axes, and because the cortex is often thinner than in long bones. This study investigated solutions that permit reasonable determination of elastic properties in the human mandible. We tested whether ultrasonic velocities could be reliably measured in cylindrical samples of aluminum and mandibular bone, and the effects of reduced specimen thickness. Results indicted that (1) varying shape had minimal effects on ultrasonic velocities or derived elastic properties, and (2) ultrasonic velocities have relatively increased measurement error as propagation distances decreased. The increased error in velocity measurements of mandibular cortical specimens of less than 1.2 mm in thickness should be considered when assessing the reliability of single measurements.     

Ontogeny of material stiffness heterogeneity in the macaque mandibular corpus

Evidence is accumulating that bone material stiffness increases during ontogeny, and the role of elastic modulus in conditioning attributes of strength and toughness is therefore a focus of ongoing investigation. Developmental changes in structural properties of the primate mandible have been documented, but comparatively little is known about changes in material heterogeneity and their impact on biomechanical behavior. We examine a cross‐sectional sample of Macaca fascicularis (N = 14) to investigate a series of hypotheses that collectively evaluate whether the patterning of material stiffness (elastic modulus) heterogeneity in the mandible differs among juvenile, subadult and adult individuals. Because differences in age‐related activity patterns are known to influence bone stiffness and strength, these data are potentially useful for understanding the relationship between feeding behavior on the one hand and material and structural properties of the mandible on the other. Elastic modulus is shown to be spatially dependent regardless of age, with this dependence being explicable primarily by differences in alveolar versus basal cortical bone. Elastic modulus does not differ consistently between buccal and lingual cortical plates, despite likely differences in the biomechanical milieu of these regions. Since we found only weak support for the hypothesis that the spatial patterning of heterogeneity becomes more predictable with age, accumulated load history may not account for regional differences in bone material properties in mature individuals with respect to the mandibular corpus. Am J Phys Anthropol 153:297–304, 2014. © 2013 Wiley Periodicals, Inc.     

Determination of stress levels and profiles in the periodontal ligament by means of an improved three-dimensional finite element model for various types of orthodontic and natural force systems

This study was undertaken to investigate the stress-strain levels and distribution within the periodontal ligament for various types of physiological and orthodontic force systems, assuming that the bone resorption process, leading to tooth movements, is partly controlled by those conditions. Two finite element models were developed, simulating a full and partial mandibular morphology, respectively. Both models were based on morphology and physical parameters of human autopsy material. The effect of changing material parameters and structure, type of boundary conditions, calculation method and fineness of the model on the stress levels and profiles in the periodontal ligament was evaluated by a series of tests. A structure optimization technique was used to investigate the load bearing characteristics of the mandible and the influence of the anisotropic material properties of both the mandible and the segment. A ‘multiple modelling’ technique based on both the mandible and the segment was developed to test various types of boundary conditions in the analysis of the segment. Results presented as ‘stress profiles’ showing the correlation between the applied force system and the stress distribution in the periodontal ligament, based on the improved finite element models, were established.     

Consideration of anisotropic elasticity minimizes volumetric rather than shear deformation in human mandible

This article is focused on the role of anisotropic elasticity in the simulation of the load distribution in a human mandible, due to a lateral bite on the leftmost premolar. Based on experimental evidence, orthotropy of the elastic properties of the bone tissue has been adopted. The trajectories of anisotropic elasticity are reconstructed from (i) the organ's geometry and (ii) from coherent structures which can be recognized from the spatial distribution of the grey values coming from computer tomography (CT). A sensitivity analysis comprising various three-dimensional (3D) finite element (FE) simulations reveals the relevance of elastic anisotropy for the load carrying behavior of a human mandible: comparison of the load distributions in isotropic and anisotropic simulations indicates that anisotropy seems to "spare" the mandible from loading. Moreover, a maximum degree of anisotropy leads to kind of load minimization of the mandible, expressed by a minimum of different norms of local volumetric strain, evaluated throughout the organ. The observed optimization with respect to volumetric rather than shear strain seems to confirm the frequently emphazised role of volumetric-strain-induced fluid flow for the stimulation of cellular activity.     

FE study of bone quality effect on load-carrying ability of dental implants

Extreme stresses in surrounding bone are among the most important reasons for implant failure. Bone density (quality) is a variable that plays a decisive role in achieving predictable osseointegration and long-term survival of implants. The magnitudes of ultimate occlusal load, which generate ultimate von Mises stress at the critical point of peri-implant area for the spectrum of implants inserted into mandible with four different bone qualities (Lekholm and Zarb classification), were calculated. Geometric models of mandible segment were generated from computed tomography images and analysed with osseointegrated cylindrical implants of various dimensions. Occlusal loads were applied in their natural direction. All materials were assumed to be linearly elastic and isotropic. The investigation suggests that an implant's ultimate occlusal load indicates its load-carrying capacity. As a result, bone loss can be predicted, and viable implants can be selected by comparing the values of their ultimate occlusal load in different clinical conditions.     

Variations in cortical material properties throughout the human dentate mandible

Material properties and their variations in individual bone organs are important for understanding bone adaptation and quality at a tissue level, and are essential for accurate mechanical models. Yet material property variations have received little systematic study. Like all other material property studies in individual bone organs, studies of the human mandible are limited by a low number of both specimens and sampled regions. The aims of this study were to determine: 1) regional variability in mandibular material properties, 2) the effect of this variability on the modeling of mandibular function, and 3) the relationship of this variability to mandibular structure and function. We removed 31 samples on both facial and lingual cortices of 10 fresh adult dentate mandibles, measured cortical thickness and density, determined the directions of maximum stiffness with a pulse transmission ultrasonic technique, and calculated elastic properties from measured ultrasonic velocities. Results showed that each of these elastic properties in the dentate human mandible demonstrates unique regional variation. The direction of maximum stiffness was near parallel to the occlusal plane within the corpus. On the facial ramus, the direction of maximum stiffness was more vertically oriented. Several sites in the mandible did not show a consistent direction of maximum stiffness among specimens, although all specimens exhibited significant orthotropy. Mandibular cortical thickness varied significantly (P < 0.001) between sites, and decreased from 3.7 mm (SD = 0.9) anteriorly to 1.4 mm posteriorly (SD = 0.1). The cortical plate was also significantly thicker (P < 0.003) on the facial side than on the lingual side. Bone was 50-100% stiffer in the longitudinal direction (E(3), 20-30 GPa) than in the circumferential or tangential directions (E(2) or E(1); P < 0.001). The results suggest that material properties and directional variations have an important impact on mandibular mechanics. The accuracy of stresses calculated from strains and average material properties varies regionally, depending on variations in the direction of maximum stiffness and anisotropy. Stresses in some parts of the mandible can be more accurately calculated than in other regions. Limited evidence suggests that the orientations and anisotropies of cortical elastic properties correspond with features of cortical bone microstructure, although the relationship with functional stresses and strains is not clear.     

An efficient method of modeling material properties using a thermal diffusion analogy: an example based on craniofacial bone

The ability to incorporate detailed geometry into finite element models has allowed researchers to investigate the influence of morphology on performance aspects of skeletal components. This advance has also allowed researchers to explore the effect of different material models, ranging from simple (e.g., isotropic) to complex (e.g., orthotropic), on the response of bone. However, bone's complicated geometry makes it difficult to incorporate complex material models into finite element models of bone. This difficulty is due to variation in the spatial orientation of material properties throughout bone. Our analysis addresses this problem by taking full advantage of a finite element program's ability to solve thermal-structural problems. Using a linear relationship between temperature and modulus, we seeded specific nodes of the finite element model with temperatures. We then used thermal diffusion to propagate the modulus throughout the finite element model. Finally, we solved for the mechanical response of the finite element model to the applied loads and constraints. We found that using the thermal diffusion analogy to control the modulus of bone throughout its structure provides a simple and effective method of spatially varying modulus. Results compare favorably against both experimental data and results from an FE model that incorporated a complex (orthotropic) material model. This method presented will allow researchers the ability to easily incorporate more material property data into their finite element models in an effort to improve the model's accuracy.     

单端固定式下颌骨修复体的应力分析

目的:针对包括一侧髁状突的下颌骨缺损,通过有限元应力分析,了解单端固定式下颌骨修复体在功能运动时的受力与变形规律,以期寻求更加合理的修复体的设计和固定方式。方法:建立下颌骨断端和修复体的简易三维模型,模拟咀嚼运动,施加垂直方向载荷,进行有限元法应力分析,计算出该模型各组成部分的应力分布和受力变形。结果:在该模型加载时,延伸板基部和近断端处上部的螺钉颈部是应力集中的部位,近断端处下部的螺钉颈部和修复体的远端舌侧为形变最大的部位。结论:单端固定式下颌骨修复体在加载时,延伸板的基部和靠近断端的固定螺钉是应力集中的部位,修复体远离固定的一侧是变形最大的部位,提示我们应将延伸板形态设计为尽可能加宽,并应增加下颌骨下缘处的固定,使修复体与下颌骨断端受力更加合理,变形也尽可能缩小。     

单端固定式下颌骨修复体的应力分析

目的：针对包括一侧髁状突的下颌骨缺损,通过有限元应力分析,了解单端固定式下颌骨修复体在功能运动时的受力与变形规律,以期寻求更加合理的修复体的设计和固定方式。方法：建立下颌骨断端和修复体的简易三维模型,模拟咀嚼运动,施加垂直方向载荷,进行有限元法应力分析,计算出该模型各组成部分的应力分布和受力变形。结果：在该模型加载时,延伸板基部和近断端处上部的螺钉颈部是应力集中的部位,近断端处下部的螺钉颈部和修复体的远端舌侧为形变最大的部位。结论：单端固定式下颌骨修复体在加载时,延伸板的基部和靠近断端的固定螺钉是应力集中的部位,修复体远离固定的一侧是变形最大的部位,提示我们应将延伸板形态设计为尽可能加宽,并应增加下颌骨下缘处的固定,使修复体与下颌骨断端受力更加合理,变形也尽可能缩小。     

Mechanics of the right whale mandible: Full scale testing and finite element analysis

In an effort to better understand the mechanics of ship-whale collision and to reduce the associated mortality of the critically endangered North Atlantic right whale, a comprehensive biomechanical study has been conducted by the Woods Hole Oceanographic Institution and the University of New Hampshire. The goal of the study is to develop a numerical modeling tool to predict the forces and stresses during impact and thereby the resulting mortality risk to whales from ship strikes.Based on post-mortem examinations, jaw fracture was chosen as a fatal endpoint for the whales hit by a vessel. In this paper we investigate the overall mechanical behavior of a right whale mandible under transverse loading and develop a finite element analysis model of the bone. The equivalent elastic modulus of the cortical component of right whale mandible is found by comparing full-scale bending tests with the results of numerical modeling. The finite element model of the mandible can be used in conjunction with a vessel-whale collision event model to predict bone fracture for various ship strike scenarios.     

Numerical estimation of bone density and elastic constants distribution in a human mandible

In this paper, we try to predict the distribution of bone density and elastic constants in a human mandible, based on the stress level produced by mastication loads using a mathematical model of bone remodelling. These magnitudes are needed to build finite element models for the simulation of the mandible mechanical behavior. Such a model is intended for use in future studies of the stability of implant-supported dental prostheses. Various models of internal bone remodelling, both phenomenological and more recently mechanobiological, have been developed to determine the relation between bone density and the stress level that bone supports. Among the phenomenological models, there are only a few that are also able to reproduce the level of anisotropy. These latter have been successfully applied to long bones, primarily the femur. One of these models is here applied to the human mandible, whose corpus behaves as a long bone. The results of bone density distribution and level of anisotropy in different parts of the mandible have been compared with various clinical studies, with a reasonable level of agreement.     

Transversely isotropic elasticity imaging of cancellous bone

To measure spatial variations in mechanical properties of biological materials, prior studies have typically performed mechanical tests on excised specimens of tissue. Less invasive measurements, however, are preferable in many applications, such as patient-specific modeling, disease diagnosis, and tracking of age- or damage-related degradation of mechanical properties. Elasticity imaging (elastography) is a nondestructive imaging method in which the distribution of elastic properties throughout a specimen can be reconstructed from measured strain or displacement fields. To date, most work in elasticity imaging has concerned incompressible, isotropic materials. This study presents an extension of elasticity imaging to three-dimensional, compressible, transversely isotropic materials. The formulation and solution of an inverse problem for an anisotropic tissue subjected to a combination of quasi-static loads is described, and an optimization and regularization strategy that indirectly obtains the solution to the inverse problem is presented. Several applications of transversely isotropic elasticity imaging to cancellous bone from the human vertebra are then considered. The feasibility of using isotropic elasticity imaging to obtain meaningful reconstructions of the distribution of material properties for vertebral cancellous bone from experiment is established. However, using simulation, it is shown that an isotropic reconstruction is not appropriate for anisotropic materials. It is further shown that the transversely isotropic method identifies a solution that predicts the measured displacements, reveals regions of low stiffness, and recovers all five elastic parameters with approximately 10% error. The recovery of a given elastic parameter is found to require the presence of its corresponding strain (e.g., a deformation that generates ??? is necessary to reconstruct C????), and the application of regularization is shown to improve accuracy. Finally, the effects of noise on reconstruction quality is demonstrated and a signal-to-noise ratio (SNR) of 40 dB is identified as a reasonable threshold for obtaining accurate reconstructions from experimental data. This study demonstrates that given an appropriate set of displacement fields, level of regularization, and signal strength, the transversely isotropic method can recover the relative magnitudes of all five elastic parameters without an independent measurement of stress. The quality of the reconstructions improves with increasing contrast, magnitude of deformation, and asymmetry in the distributions of material properties, indicating that elasticity imaging of cancellous bone could be a useful tool in laboratory studies to monitor the progression of damage and disease in this tissue.     

Mapping anisotropy of the proximal femur for enhanced image based finite element analysis

Finite element (FE) models of bone derived from quantitative computed tomography (QCT) rely on realistic material properties to accurately predict bone strength. QCT cannot resolve bone microarchitecture, therefore QCT-based FE models lack the anisotropy apparent within the underlying bone tissue. This study proposes a method for mapping femoral anisotropy using high-resolution peripheral quantitative computed tomography (HR-pQCT) scans of human cadaver specimens. Femur HR-pQCT images were sub-divided into numerous overlapping cubic sub-volumes and the local anisotropy was quantified using a ‘direct-mechanics’ method. The resulting directionality reflected all the major stress lines visible within the trabecular lattice, and provided a realistic estimate of the alignment of Harvesian systems within the cortical compartment. QCT-based FE models of the proximal femur were constructed with isotropic and anisotropic material properties, with directionality interpolated from the map of anisotropy. Models were loaded in a sideways fall configuration and the resulting whole bone stiffness was compared to experimental stiffness and ultimate strength. Anisotropic models were consistently less stiff, but no statistically significant differences in correlation were observed between material models against experimental data. The mean difference in whole bone stiffness between model types was approximately 26%, suggesting that anisotropy can still effect considerable change in the mechanics of proximal femur models. The under prediction of whole bone stiffness in anisotropic models suggests that the orthotropic elastic constants require further investigation. The ability to map mechanical anisotropy from high-resolution images and interpolate information into clinical-resolution models will allow testing of new anisotropic material mapping strategies.     

The impact of the parameters of the constitutive model on the distribution of strain in the femoral head

The rapid spread of the finite element method has caused that it has become, among other methods, the standard tool for pre-clinical estimates of bone properties. This paper presents an application of this method for the calculation and prediction of strain and stress fields in the femoral head. The aim of the work is to study the influence of the considered anisotropy and heterogeneity of the modeled bone on the mechanical fields during a typical gait cycle. Three material models were tested with different properties of porous bone carried out in literature: a homogeneous isotropic model, a heterogeneous isotropic model, and a heterogeneous anisotropic model. In three cases studied, the elastic properties of the bone were determined basing on the Zysset-Curnier approach. The tensor of elastic constants defining the local properties of porous bone is correlated with a local porosity and a second order fabric tensor describing the bone microstructure. In the calculations, a model of the femoral head generated from high-resolution tomographic scans was used. Experimental data were drawn from publicly available database “Osteoporotic Virtual Physiological Human Project.” To realistically reflect the load on the femoral head, main muscles were considered, and their contraction forces were determined based on inverse kinematics. For this purpose, the results from OpenSim packet were used. The simulations demonstrated that differences between the results predicted by these material models are significant. Only the anisotropic model allowed for the plausible distribution of stresses along the main trabecular groups. The outcomes also showed that the precise evaluation of the mechanical fields is critical in the context of bone tissue remodeling under mechanical stimulations.