A porous fibrous hyperelastic damage model for human periodontal ligament: Application of a microcomputerized tomography finite element model

The periodontal ligament (PDL) is a soft biological tissue that connects the tooth with the trabecular bone of the mandible. It plays a key role in load transmission and is primarily responsible for bone resorption and most common periodontal diseases. Although several numerical studies have analysed the biomechanical response of the PDL, most did not consider its porous fibrous structure, and only a few analysed damage to the PDL. This study presents an innovative numerical formulation of a porous fibrous hyperelastic damage material model for the PDL. The model considers two separate softening phenomena: fibre alignment during loading and fibre rupture. The parameters for the material model characterization were fitted using experimental data from the literature. Furthermore, the experimental tests used for characterization were computationally modelled to verify the material parameters. A finite element model of a portion of a human mandible, obtained by microcomputerized tomography, was developed, and the proposed constitutive model was implemented for the PDL. Our results confirm that damage to the PDL may occur mainly because of overpressure of the interstitial fluid, while large forces must be applied to damage the PDL fibrous network. Moreover, this study clarifies some aspects of the relationship between PDL damage and the bone remodelling process

Biomechanical time dependency of the periodontal ligament: a combined experimental and numerical approach

SUMMARY The analysis of the non-linear and time-dependent viscoelasticity of the periodontal ligament (PDL) enables a better understanding of the biomechanical features of the key regulator tissue for tooth movement. This is of great significance in the field of orthodontics as targeted tooth movement remains still one of the main goals to accomplish. The investigation of biomechanical aspects of the PDL function, a difficult area of research, helps towards this direction. After analysing the time-dependent biomechanical properties of pig PDL specimens in an in vitro experimental study, it was possible to confirm that PDL has a viscoelastic anisotropic behaviour. Three-dimensional finite element models of mini-pig mandibular premolars with surrounding tissues were developed, based on micro-computed tomography (μCT) data of the experimental specimens. Tooth mobility was numerically analysed under the same force systems as used in the experiment. A bilinear material parameter set was assumed to simulate tooth displacements. The numerical force/displacement curves were fitted to the experimental curves by repeatedly calculating tooth displacements of 0.2mm varying the loading velocities and the parameters, which describe the nonlinearity. The experimental results showed a good agreement with the numerical calculations. Mean values of Young's moduli E1, E2 and ultimate strain ε12 were derived for the elastic behaviour of the PDL for all loading velocities. E1 and E2 values increased with increasing the velocity, while ε12 remained relatively stable. A bilinear approximation of material properties of the PDL is a suitable description of measured force/displacement diagrams. The numerical results can be used to describe mechanical processes, especially stress-strain distributions in the PDL, accurately. Further development of suitable modelling assumptions for the response of PDL under load would be instrumental to orthodontists and engineers for designing more predictable orthodontic force systems and appliance

In silico study of cuspid' periodontal ligament damage under parafunctional and traumatic conditions of whole-mouth occlusions. A patient-specific evaluation

Background and objective: Although traumatic loading has been associated with periodontal ligament (PDL) damage and therefore with several oral disorders, the damage phenomena and the traumatic loads involved are still unclear. The complex composition and extremely thin size of the PDL make experimentation difficult, requiring computational studies that consider the macroscopic loading conditions, the microscopic composition and fine detailed geometry of the tissue. In this study, a new methodology to analyse the damage phenomena in the collagen network and the extracellular matrix of the PDL caused by parafunctional and traumatic occlusal forces was proposed. Methods: The entire human mandible and a portion thereof containing a full cuspid tooth were separately modelled using finite element analysis based on computed tomography and micro-computed tomography images, respectively. The first model was experimentally validated by occlusion analysis and subjected to the muscle loads produced during hard and soft chewing, traumatic cuspid occlusion, grinding, clenching, and simultaneous grinding and clenching. The occlusal forces computed by the first model were subsequently applied to the single tooth model to evaluate damage to the collagen network and the extracellular matrix of the PDL. Results: Early occlusal contact on the left cuspid tooth guided the mandible to the more occluded side (16.5% greater in the right side) and absorbed most of the lateral load. The intrusive occlusal loads on the posterior teeth were 0.77–13.3% greater than those on the cuspid. According to our findings, damage to the collagen network and the extracellular matrix of the PDL could occur in traumatic and grinding conditions, mainly due to fibre overstretching (>60%) and interstitial fluid overpressure (>4.7 kPa), respectively. Conclusions: Our findings provide important biomechanical insights into the determination of damage mechanisms which are caused by mechanical loading and the key role of the porous-fibrous behaviour of the PDL in parafunctional and traumatic loading scenarios. Besides, the 3D loading conditions computed from occlusal contacts will help future studies in the design of new orthodontics appliances and encourage the application of computing methods in medical practice

Soft tissue structural assessment using mechanical measurements

The overall aim of the work presented in this thesis is the development of quantitative relationships between the structure (histological make-up and/or tissue architecture) and the mechanical properties of soft biological tissue. The purpose of the research is to contribute towards the assessment of “tissue quality” using mechanical probing (instrumented palpation). The work focuses particularly on two case studies; the eyeball, where tissue quality relates to the corneal stiffness and the intra-ocular pressure (IOP); and the periodontal ligament (PDL), where tissue quality relates to the load displacement-time behaviour of teeth to which external forces are applied (such as in orthodontic treatment). The experimental work involves static and dynamic testing of two porcine tissues (eyeballs and periodontal ligament) and also a mechanical system (mechanical eyeball) devised to investigate separately the components expected to influence mechanical behaviour; cornea stiffness, IOP, fluid inertia and leakage rate. Special test rigs were designed, calibrated and assessed for their measurement and process capabilities and the results were compared with quasi linear visco elastic (QLV) models to identify an appropriate mechanical way of characterising the tissue for comparison with its quality. The larger part of the work concentrated on the eye with the ultimate aim of identifying symptoms of glaucoma more accurately. Dynamic testing identified a suitable indentation frequency range of 20Hz to 24Hz, the amplitude ratio in this range being capable of measuring IOP within an error of ±7mmHg which is only slightly above the ±5mmHg target for the latest tonometers. The cornea tissue was found to have 20% viscous behaviour and 80% elastic behaviour. The data were analysed using dynamic visco elastic models with an additional term for the inertia of the fluid in the eyeball. The work on the mechanical eyeball showed that it is possible to separate the effects of IOP and the stiffness of the cornea, which is of great significance in determining the true IOP, as opposed to one derived from a tonometer reading which makes assumptions about cornea stiffness. The other main contribution is on the assessment of the periodontal ligament, which plays an important shock-absorbing role during mastication and is the initiator for orthodontic tooth movement (OTM), when loads are applied to teeth using orthodontic appliances. The force-relaxation behaviour of one lower premolar in pig mandibles was measured and the resulting force relaxation curves analysed using three different visco elastic spring damper models. The analysis showed that, when longer relaxation times are allowed three or even four parameter models are not adequate to describe the behaviour. It is suggested that a more appropriate model is a multi component Maxwell model which uses more or less Maxwell components depending on the allowed relaxation time. Overall, the work shows that instrumented palpation, supported by the development of suitable models can play a significant role in measuring tissue quality. Also, using simplified models of the stress-strain behaviour, it was possible to demonstrate that the measurements made here were in general accord with those reported in the literature for eyes, corneas and periodontal ligament

Experimental and numerical investigations on the fluid contribution to the tensile-compressive mechanical behavior of the bovine periodontal ligament

Orthodontic treatments are all based on the experimental evidence that teeth can be forced to move in the dental arch by means of applied mechanical forces. Since it allows for prediction of dental mobility, the mechanical characterization of the tissues involved in this process is of paramount importance. In fact, as technologies and strategies in treating pathological situations become increasingly more advanced, better knowledge of dental mobility allows for the optimization of these tools and thus, minimization of the costs of the interventions. Among the tissues that made up the periodontium, the functional unit comprising the bone of the jaw, the periodontal ligament (PDL, a soft connective tissue which binds the teeth to the jaw) and the cementum of the teeth, the PDL is commonly considered to play the major role in dental movements. To obtain insights on its mechanical behavior, specimens of PDL, containing also bone and cementum parts, are extracted and tested with adequate loading profiles. However, due to morphology and size, the excision of such specimens is often delicate and represents one of the main challenge in the experimental characterization of the PDL. Furthermore, for the investigation to be pertinent, it is necessary to test the in-vitro specimens in an environment recreating at best physiological conditions. In this study, the characterization of the mechanical behavior of the periodontium was based on histo-morphological investigation, on mechanical testing of excised specimens containing the three tissues and on numerical modeling. Micro-structural aspects of the periodontium were assessed by morphometric analysis of histological sections. Since it plays a central role in the tooth supporting mechanism, the vascular system was characterized by assessing densities and sizes of blood vessels present in the PDL. Also, the roughness of the interfaces between PDL and bone and between PDL and cementum was quantified via their fractal dimensions. To approach as much as possible an in-vivo–like situation for the mechanical testing of in-vitro specimens, physiological conditions were reconstructed at best in a closed environment created in a custom-made pressure chamber filled with physiological solution. Cylindrical specimens, with diameter of approximately 6mm, were obtained from mandibular first molars of freshly slaughtered bovines. A thorough experimental determination of the contribution of the fluid phase, comprised in the periodontium, to the overall response of the tissues was carried out by imposing sinusoidal tensile-compressive loading profiles (simulating mastication) to specimens subjected to different environmental conditions. A numerical model was then developed to reproduce and analyze the observed phenomena. Eventually, the mechanical response to multiaxial loading was investigated by simultaneously applying axial displacement and lateral hydrostatic confinement to specimens which were wrapped in a thin rubbery membrane. The morphometrical investigation enhanced the high heterogeneity and porosity of the tissues involved. In fact, no general pattern could be established for the structural description of the periodontium. Moreover, the presence of large blood vessels in the PDL suggested that the vascular system should somehow be taken into consideration when describing the mechanical behavior of this ligament. The mechanical testing proved the response of the bone-PDL-cementum functional system to be characterized by the interactions between a porous solid skeleton, forming the structural matrix of the tissues, and a fluid content flowing through it during cyclic tensile-compressive loading profiles. In fact, the solid matrix alone (i.e., emptied of its fluid content) clearly showed an hyperelastic behavior (both for tensile and compressive loading), so that the highly time-dependent hysteric behavior shown during compressive loadings of fully fluid-saturated specimens was mainly attributed to the fluid phase. The numerical model, based on a multiphase mixture formulation, allowing thus for the description of the interactions between a porous compressible hyperelastic matrix (described by an Ogden's strain energy potential) and the fluid filling its pores, well reproduced the mechanical response of the periodontium subjected to cyclic tensile-compressive loadings. The model enhanced also the significant exchange of fluid taking place between the PDL and the bone part of the specimens, proving thus the importance of considering the fluid phase in the mechanical description of the periodontium. Loading rate dependences of the compressive response were also partially captured by such a model. The experimental response to a multiaxial loading showed eventually the dependence of the axial stress on the joined action of level of lateral confinement (hydrostatic pressure) and extent of fluid saturation of the solid matrix

Tissue Engineering for Periodontal Ligament Regeneration: Biomechanical Specifications

The periodontal biomechanical environment is very difficult to investigate. By the complex geometry and composition of the periodontal ligament, its mechanical behavior is very dependent on the type of loading (compressive vs. tensile loading; static vs. cyclic loading; uniaxial vs. multiaxial) and the location around the root (cervical, middle, or apical). These different aspects of the periodontal ligament make it difficult to develop a functional biomaterial to treat periodontal attachment due to periodontal diseases. This review aims to describe the structural and biomechanical properties of the periodontal ligament. Particular importance is placed in the close interrelationship that exists between structure and biomechanics: the periodontal ligament structural organization is specific to its biomechanical environment, and its biomechanical properties are specific to its structural arrangement. This balance between structure and biomechanics can be explained by a mechanosensitive periodontal cellular activity. These specifications have to be considered in the further tissue engineering strategies for the development of an efficient biomaterial for periodontal tissues regeneration

Modelling of viscoelasticity in pressure-volume curve of an intact gallbladder

Like other organs such as artery, bladder and left ventricle, human intact gallbladders (GBs) possess viscoelasticity/hysteresis in pressure-volume curves during in vitro or in vivo dynamic experiments made by using saline infusion and withdrawal cycle to simulate GB physiological emptying-filling cycle in normal and diseased conditions. However, such a viscoelastic property of GBs has not been modelled and analysed so far. A non-linear discrete viscous model and a passive elastic model were proposed to identify the elastic, active and viscous pressure responses in the experimental pressure-volume data of an intact GB under passive and active conditions found in the literature in the paper. It turns out that the elastic, viscous and active pressure responses can be separated in less than 2% error from the pressure-volume curves. The peak active state in the GB occurs at 30% dimensionless volume. The GB stimulated with cholecystokinin (CCK) or treated with indomethacin is subject to almost constant stiffness at low dimensionless volume (≤ 70%) but quick increasing stiffness at high dimensionless volume (>70%) and a larger work-to-energy ratio (0.57–0.61) compared with the normal GB in the passive state. The models are sensitive to the change in the biomechanical property of the GBs stimulated or treated with hormonal or pharmacological agents, showing a potential in clinical application. These results may contribute fresh content to the biomechanics of GBs and be helpful to GB disease diagnosis