Data-Driven Computational Simulation in Bone Mechanics.

The data-driven approach was formally introduced in the field of computational mechanics just a few years ago, but it has gained increasing interest and application as disruptive technology in many other fields of physics and engineering. Although the fundamental bases of the method have been already settled, there are still many challenges to solve, which are often inherently linked to the problem at hand. In this paper, the data-driven methodology is applied to a particular problem in tissue biomechanics, a context where this approach is particularly suitable due to the difficulty in establishing accurate and general constitutive models, due to the intrinsic intra and inter-individual variability of the microstructure and associated mechanical properties of biological tissues. The problem addressed here corresponds to the characterization and mechanical simulation of a piece of cortical bone tissue. Cortical horse bone tissue was mechanically tested using a biaxial machine. The displacement field was obtained by means of digital image correlation and then transformed into strains by approximating the displacement derivatives in the bone virtual geometric image. These results, together with the approximated stress state, assumed as uniform in the small pieces tested, were used as input in the flowchart of the data-driven methodology to solve several numerical examples, which were compared with the corresponding classical model-based fitted solution. From these results, we conclude that the data-driven methodology is a useful tool to directly simulate problems of biomechanical interest without the imposition (model-free) of complex spatial and individually-varying constitutive laws. The presented data-driven approach recovers the natural spatial variation of the solution, resulting from the complex structure of bone tissue, i.e. heterogeneity, microstructural hierarchy and multifactorial architecture, making it possible to add the intrinsic stochasticity of biological tissues into the data set and into the numerical approach.

Zeolites for the selective adsorption of sulfur hexafluoride.

Molecular simulations have been used to investigate at the molecular level the suitability of zeolites with different topology on the adsorption, diffusion and separation of a nitrogen-sulfur hexafluoride mixture containing the latter at low concentration. This mixture represents the best alternative for the sulfur hexafluoride in industry since it reduces the use of this powerful greenhouse gas. A variety of zeolites are tested with the aim to identify the best structure for the recycling of sulfur hexafluoride in order to avoid its emission to the atmosphere and to overcome the experimental difficulties of its handling. Even though all zeolites show preferential adsorption of sulfur hexafluoride, we identified local structural features that reduce the affinity for sulfur hexafluoride in zeolites such as MOR and EON, providing exclusive adsorption sites for nitrogen. Structures such as ASV and FER were initially considered as good candidates based on their adsorption features. However, they were further discarded based on their diffusion properties. Regarding operation conditions for separation, the range of pressure that spans from 3 × 10(2) to 3 × 10(3) kPa was identified as the optimal to obtain the highest adsorption loading and the largest SF6/N2 selectivity. Based on these findings, zeolites BEC, ITR, IWW, and SFG were selected as the most promising materials for this particular separation.

Simulation of swallowing dysfunction and mechanical ventilation after a Montgomery T-tube insertion.

The Montgomery T-tube is used as a combined tracheal stent and airway after laryngotracheoplasty, to keep the lumen open and prevent mucosal laceration from scarring. It is valuable in the management of upper and mid-tracheal lesions, while invaluable in long and multisegmental stenting lesions. Numerical simulations based on real-patient-tracheal geometry, experimental tissue characterization, and previous numerical estimation of the physiological swallowing force are performed to estimate the consequences of Montgomery T-tube implantation on swallowing and assisted ventilation: structural analysis of swallowing is performed to evaluate patient swallowing capacity, and computational fluid dynamics simulation is carried out to analyze related mechanical ventilation. With an inserted Montgomery T-tube, vertical displacement (Z-axis) reaches 8.01 mm, whereas in the Y-axis, it reaches 6.63 mm. The maximal principal stress obtained during swallowing was 1.6 MPa surrounding the hole and in the upper contact with the tracheal wall. Fluid flow simulation of the mechanical ventilation revealed positive pressure for both inhalation and exhalation, being higher for inspiration. The muscular deflections, considerable during normal breathing, are nonphysiological, and this aspect results in a constant overload of the tracheal muscle. During swallowing, the trachea ascends producing a nonhomogeneous elongation. This movement can be compromised when prosthesis is inserted, which explains the high incidence of glottis close inefficiency. Fluid simulations showed that nonphysiological pressure is established inside the trachea due to mechanical ventilation. This may lead to an overload of the tracheal muscle, explaining several related problems as muscle thinning or decrease in contractile function.

Zeolite screening for the separation of gas mixtures containing SO2, CO2 and CO.

We used a combination of experiments and molecular simulations to investigate at the molecular level the effects of zeolite structure on the adsorption and diffusion of sulfur dioxide, carbon dioxide and carbon monoxide as well as separation processes of their mixtures. Our study involved different zeolite topologies and revealed numerous structure-property trends depending on the temperature and pressure conditions. Sulfur dioxide, which has the strongest interactions with zeolites due to its size and polarity, showed the largest adsorption across investigated temperatures and pressures. Our results indicate that structures with channel-type pore topology and low pore volume are the most promising for selective adsorption of sulfur dioxide over carbon dioxide and carbon monoxide under room conditions, while structures with higher pore volume exhibit better storage capacity at higher pressure. Our results emphasize the need for considering both adsorption and diffusion processes in the selection of the optimal structure for a given separation process. Our findings help to identify the best materials for effective separation processes under realistic operating conditions.

Computational modelling and analysis of mechanical conditions on cell locomotion and cell-cell interaction.

Between other parameters, cell migration is partially guided by the mechanical properties of its substrate. Although many experimental works have been developed to understand the effect of substrate mechanical properties on cell migration, accurate 3D cell locomotion models have not been presented yet. In this paper, we present a novel 3D model for cells migration. In the presented model, we assume that a cell follows two main processes: in the first process, it senses its interface with the substrate to determine the migration direction and in the second process, it exerts subsequent forces to move. In the presented model, cell traction forces are considered to depend on cell internal deformation during the sensing step. A random protrusion force is also considered which may change cell migration direction and/or speed. The presented model was applied for many cases of migration of the cells. The obtained results show high agreement with the available experimental and numerical data.

Impedance-based outflow boundary conditions for human carotid haemodynamics.

In this study, we develop structured tree outflow boundary conditions for modelling the human carotid haemodynamics. The model geometry was reconstructed through computerised tomography scan. Unsteady-state computational fluid dynamic analyses were performed under different conditions using a commercial software package ADINA R&D, Inc., (Watertown, MA, USA) in order to assess the impact of the boundary conditions on the flow variables. In particular, the results showed that the peripheral vessels massively impact the pressure while the flow is relatively unaffected. As an example of application of these outflow conditions, an unsteady fluid-structure interaction (FSI) simulation was carried out and the dependence of the wall shear stress (WSS) on the arterial wall compliance in the carotid bifurcation was studied. In particular, a comparison between FSI and rigid-wall models was conducted. Results showed that the WSS distributions were substantially affected by the diameter variation of the arterial wall. In particular, even similar WSS distributions were found for both cases, and differences in the computed WSS values were also found.

A pre-operative planning for endoprosthetic human tracheal implantation: a decision support system based on robust design of experiments.

Swallowing depends on physiological variables that have a decisive influence on the swallowing capacity and on the tracheal stress distribution. Prosthetic implantation modifies these values and the overall performance of the trachea. The objective of this work was to develop a decision support system based on experimental, numerical and statistical approaches, with clinical verification, to help the thoracic surgeon in deciding the position and appropriate dimensions of a Dumon prosthesis for a specific patient in an optimal time and with sufficient robustness. A code for mesh adaptation to any tracheal geometry was implemented and used to develop a robust experimental design, based on the Taguchi's method and the analysis of variance. This design was able to establish the main swallowing influencing factors. The equations to fit the stress and the vertical displacement distributions were obtained. The resulting fitted values were compared to those calculated directly by the finite element method (FEM). Finally, a checking and clinical validation of the statistical study were made, by studying two cases of real patients. The vertical displacements and principal stress distribution obtained for the specific tracheal model were in agreement with those calculated by FE simulations with a maximum absolute error of 1.2 mm and 0.17 MPa, respectively. It was concluded that the resulting decision support tool provides a fast, accurate and simple tool for the thoracic surgeon to predict the stress state of the trachea and the reduction in the ability to swallow after implantation. Thus, it will help them in taking decisions during pre-operative planning of tracheal interventions.

Cell migration and cell-cell interaction in the presence of mechano-chemo-thermotaxis.

Although there are several computational models that explain the trajectory that cells take during migration, till now little attention has been paid to the integration of the cell migration in a multi-signaling system. With that aim, a generalized model of cell migration and cell-cell interaction under multisignal environments is presented herein. In this work we investigate the spatio-temporal cell-cell interaction problem induced by mechano-chemo-thermotactic cues. It is assumed that formation of a new focal adhesion generates traction forces proportional to the stresses transmitted by the cell to the extracellular matrix. The cell velocity and polarization direction are calculated based on the equilibrium of the effective forces associated to cell motility. It is also assumed that, in addition to mechanotaxis signals, chemotactic and thermotactic cues control the direction of the resultant traction force. This model enables predicting the trajectory of migrating cells as well as the spatial and temporal distributions of the net traction force and cell velocity. Results indicate that the tendency of the cells is firstly to reach each other and then migrate towards an imaginary equilibrium plane located near the source of the signal. The position of this plane is sensitive to the gradient slope and the corresponding efficient factors. The cells come into contact and separate several times during migration. Adding other cues to the substrate (such as chemotaxis and/or thermotaxis) delays that primary contact. Moreover, in all states, the average local velocity and the net traction force of the cells decrease while the cells approach the cues source. Our findings are qualitatively consistent with experimental observations reported in the related literature.

Computational methodology to determine fluid related parameters of non regular three-dimensional scaffolds.

The application of three-dimensional (3D) biomaterials to facilitate the adhesion, proliferation, and differentiation of cells has been widely studied for tissue engineering purposes. The fabrication methods used to improve the mechanical response of the scaffold produce complex and non regular structures. Apart from the mechanical aspect, the fluid behavior in the inner part of the scaffold should also be considered. Parameters such as permeability (k) or wall shear stress (WSS) are important aspects in the provision of nutrients, the removal of metabolic waste products or the mechanically-induced differentiation of cells attached in the trabecular network of the scaffolds. Experimental measurements of these parameters are not available in all labs. However, fluid parameters should be known prior to other types of experiments. The present work compares an experimental study with a computational fluid dynamics (CFD) methodology to determine the related fluid parameters (k and WSS) of complex non regular poly(L-lactic acid) scaffolds based only on the treatment of microphotographic images obtained with a microCT (µCT). The CFD analysis shows similar tendencies and results with low relative difference compared to those of the experimental study, for high flow rates. For low flow rates the accuracy of this prediction reduces. The correlation between the computational and experimental results validates the robustness of the proposed methodology.

Biomimetic hydroxyapatite coating on pore walls improves osteointegration of poly(L-lactic acid) scaffolds.

Polymer-ceramic composites obtained as the result of a mineralization process hold great promise for the future of tissue engineering. Simulated body fluids (SBFs) are widely used for the mineralization of polymer scaffolds. In this work an exhaustive study with the aim of optimizing the mineralization process on a poly(L-lactic acid) (PLLA) macroporous scaffold has been performed. We observed that when an air plasma treatment is applied to the PLLA scaffold its hydroxyapatite nucleation ability is considerably improved. However, plasma treatment only allows apatite deposition on the surface of the scaffold but not in its interior. When a 5 wt % of synthetic hydroxyapatite (HAp) nanoparticles is mixed with PLLA a more abundant biomimetic hydroxyapatite layer grows inside the scaffold in SBF. The morphology, amount, and composition of the generated biomimetic hydroxyapatite layer on the pores' surface have been analyzed. Large mineralization times are harmful to pure PLLA as it rapidly degrades and its elastic compression modulus significantly decreases. Degradation is retarded in the composite scaffolds because of the faster and extensive biomimetic apatite deposition and the role of HAp to control the pH. Mineralized scaffolds, covered by an apatite layer in SBF, were implanted in osteochondral lesions performed in the medial femoral condyle of healthy sheep. We observed that the presence of biomimetic hydroxyapatite on the pore's surface of the composite scaffold produces a better integration in the subchondral bone, in comparison to bare PLLA scaffolds.

CFD analysis of the human airways under impedance-based boundary conditions: application to healthy, diseased and stented trachea.

A computational fluid dynamics model of a healthy, a stenotic and a post-operatory stented human trachea was developed to study the respiration under physiological boundary conditions. For this, outflow pressure waveforms were computed from patient-specific spirometries by means of a method that allows to compute the peripheral impedance of the truncated bronchial generation, modelling the lungs as fractal networks. Intratracheal flow pattern was analysed under different scenarios. First, results obtained using different outflow conditions were compared for the healthy trachea in order to assess the importance of using impedance-based conditions. The resulted intratracheal pressures were affected by the different boundary conditions, while the resulted velocity field was unaffected. Impedance conditions were finally applied to the diseased and the stented trachea. The proposed impedance method represents an attractive tool to compute physiological pressure conditions that are not possible to extract in vivo. This method can be applied to healthy, pre- and post-operatory tracheas showing the possibility of predicting, through numerical simulation, the flow and the pressure field before and after surgery.

Mechanical stress redistribution in the calcaneus after autologous bone harvesting.

The calcaneus is a desirable site for harvesting autologous bone for use in foot surgery. However, fracture of the calcaneus is a serious complication associated with bone harvesting from this site. Currently it is unknown how much bone may be safely harvested from the calcaneus without inducing a fracture. The purpose of this study was to investigate the effect of progressive bone removal from the calcaneus onto the mechanical stress redistribution of the foot, and therefore on the increase in fracture risk. Different loads were applied on the talus to evaluate the calcaneus stress distribution at different situations. Because of the potential increase in mechanical stress in the calcaneus, secondary to contraction of the Achilles tendon, we also evaluated the mechanical behavior properties of the foot with increasing traction force in the Achilles tendon. A three-dimensional (3D) finite element (FE) model developed from CT images obtained from a healthy individual was used to compute displacement, tension and compression stresses in six situations, including intact foot, and five depth of the bone block removed, with a maximum depth of 7.5 mm. The results from these simulations indicated that when the maximum load was applied at the Achilles tendon, the tension stress increased from 42.16 MPa in the intact foot to 86.28 MPa with maximum bone harvesting. Furthermore, as the volume of bone extracted from the calcaneus increases, there is a redistribution of stresses that differs significantly from the intact foot. In fact, although the maximum stress was not significantly affected by increasing the volume of bone harvested-except when increasing the Achilles tendon force-, stresses did increase in areas of the calcaneus is vulnerable to injury, leading to an increase in fracture risk.

Stress transfer properties of different commercial dental implants: a finite element study.

Dental implantology has high success rates, and a suitable estimation of how stresses are transferred to the surrounding bone sheds insight into the correct design of implant features. In this study, we estimate stress transfer properties of four commercial implants (GMI, Lifecore, Intri and Avinent) that differ significantly in macroscopic geometry. Detailed three-dimensional finite element models were adopted to analyse the behaviour of the bone-implant system depending on the geometry of the implant (two different diameters) and the bone-implant interface condition. Occlusal static forces were applied and their effects on the bone, implant and bone-implant interface were evaluated. Large diameters avoided overload-induced bone resorption. Higher stresses were obtained with a debonded bone-implant interface. Relative micromotions at the bone-implant interface were within the limits required to achieve a good osseointegration. We anticipate that the methodology proposed may be a useful tool for a quantitative and qualitative comparison between different commercial dental implants.

Anisotropic microsphere-based approach to damage in soft fibered tissue.

An anisotropic damage model for soft fibered tissue is presented in this paper, using a multi-scale scheme and focusing on the directionally dependent behavior of these materials. For this purpose, a micro-structural or, more precisely, a microsphere-based approach is used to model the contribution of the fibers. The link between micro-structural contribution and macroscopic response is achieved by means of computational homogenization, involving numerical integration over the surface of the unit sphere. In order to deal with the distribution of the fibrils within the fiber, a von Mises probability function is incorporated, and the mechanical (phenomenological) behavior of the fibrils is defined by an exponential-type model. We will restrict ourselves to affine deformations of the network, neglecting any cross-link between fibrils and sliding between fibers and the surrounding ground matrix. Damage in the fiber bundles is introduced through a thermodynamic formulation, which is directly included in the hyperelastic model. When the fibers are stretched far from their natural state, they become damaged. The damage increases gradually due to the progressive failure of the fibrils that make up such a structure. This model has been implemented in a finite element code, and different boundary value problems are solved and discussed herein in order to test the model features. Finally, a clinical application with the material behavior obtained from actual experimental data is also presented.

Numerical simulation of bone remodelling around dental implants.

Crestal bone loss can result in the failure of dental implants and can be caused, by among other factors, the development of non-physiological mechanical conditions. Bone remodelling (BR) is the physiological process through which bone adapts itself to the mechanical environment. A previously published mathematical model of BR is used in this work to study the homogenized structural evolution of peri-implant bone. This model is used to study the influence of the diameter and length of a dental implant of pure titanium on its long-term stability. The temporal evolution of porosity and microstructural damage of the peri-implant bone are the variables analysed in this study. The results show that damage and porosity increase as the implant length decreases and, more pronouncedly, as its diameter decreases. The increase in damage and porosity levels is localized, as many other studies confirm, at the implant neck due to the stress concentration that is created in that area. The main conclusion of this study is that in implants with a diameter equal to or greater than 3 mm the damage is under control and there is no mechanical failure of the peri-implant bone in the long term.

Mechanical characterization and numerical simulation of polyether-ether-ketone (PEEK) cranial implants.

Cranial implants have experienced a significant evolution in the last decade in different aspects such as materials, method of fixation, and the structure. In addition, patient-specific cranial implants have recently been started to be developed. To achieve this objective, efficient mechanical characterization and numerical modeling of the implant are required to guarantee its functionality on each patient as well as to facilitate further developments. In this work, mechanical characterization and numerical models have been performed for patient-specific Polyaryletherketone (PEEK) scaffold cranial implants. Mechanical characterization has been performed at the scaffold and the whole implant levels under displacement control tests. Two different implant designs for the same patient but with different scaffold structure were experimentally characterized, and finite element models of the implants were developed within the framework of linear elasticity. Two types of finite element models were developed: a detailed finite element model with the actual scaffold geometry, and a solid shell-like model with effective material properties. These effective material properties were obtained by means of the Asymptotic Expansion Homogenization (AEH) theory which accounts for the periodicity of the underlying structure of the material. Experimental results showed a linear response of the material and the implant up to failure, therefore supporting the use of linear elastic models for simulation. Numerical models showed excellent agreement with experiments regarding load-displacement response. Models also showed a very consistent behavior with regard to the location and the value of the maximum principal stress in the implant when subjected to the maximum load of the experiments. The two numerical models were compared. The homogenized model gave results that were very close to those obtained with the detailed model, while reducing the number of degrees of freedom by 90%, and therefore the overall computational burden. The results showed that the models are able to reproduce experimental results conducted on actual implants, offering a valid alternative to be used in the design of customized cranial implants with a scaffold structure.

FSI analysis of a human trachea before and after prosthesis implantation.

In this work we analyzed the response of a stenotic trachea after a stent implantation. An endotracheal stent is the common treatment for tracheal diseases such as stenosis, chronic cough, or dispnoea episodes. Medical treatment and surgical techniques are still challenging due to the difficulties in overcoming potential complications after prosthesis implantation. A finite element model of a diseased and stented trachea was developed starting from a patient specific computerized tomography (CT) scan. The tracheal wall was modeled as a fiber reinforced hyperelastic material in which we modeled the anisotropy due to the orientation of the collagen fibers. Deformations of the tracheal cartilage rings and of the muscular membrane, as well as the maximum principal stresses, are analyzed using a fluid solid interaction (FSI) approach. For this reason, as boundary conditions, impedance-based pressure waveforms were computed modeling the nonreconstructed vessels as a binary fractal network. The results showed that the presence of the stent prevents tracheal muscle deflections and indicated a local recirculatory flow on the stent top surface which may play a role in the process of mucous accumulation. The present work gives new insight into clinical procedures, predicting their mechanical consequences. This tool could be used in the future as preoperative planning software to help the thoracic surgeons in deciding the optimal prosthesis type as well as its size and positioning.

Mechanical behaviour of synthetic surgical meshes: finite element simulation of the herniated abdominal wall.

The material properties of meshes used in hernia surgery contribute to the overall mechanical behaviour of the repaired abdominal wall. The mechanical response of a surgical mesh has to be defined since the haphazard orientation of an anisotropic mesh can lead to inconsistent surgical outcomes. This study was designed to characterize the mechanical behaviour of three surgical meshes (Surgipro®, Optilene® and Infinit®) and to describe a mechanical constitutive law that accurately reproduces the experimental results. Finally, through finite element simulation, the behaviour of the abdominal wall was modelled before and after surgical mesh implant. Uniaxial loading of mesh samples in two perpendicular directions revealed the isotropic response of Surgipro® and the anisotropic behaviour of Optilene® and Infinit®. A phenomenological constitutive law was used to reproduce the measured experimental curves. To analyze the mechanical effect of the meshes once implanted in the abdomen, finite element simulation of the healthy and partially herniated repaired rabbit abdominal wall served to reproduce wall behaviour before and after mesh implant. In all cases, maximal displacements were lower and maximal principal stresses higher in the implanted abdomen than the intact wall model. Despite the fact that no mesh showed a behaviour that perfectly matched that of abdominal muscle, the Infinit® mesh was able to best comply with the biomechanics of the abdominal wall.

Experimental study and constitutive modelling of the passive mechanical properties of the porcine carotid artery and its relation to histological analysis: Implications in animal cardiovascular device trials.

The present study focusses on the determination, comparison and constitutive modelling of the passive mechanical properties of the swine carotid artery over very long stretches in both proximal and distal regions. Special attention is paid to the histological and mechanical variations of these properties depending on the proximity to the heart. The results can have clinical relevance, especially in the research field of intravascular device design. Before the final clinical trials on humans, research in the vascular area is conducted on animal models, swine being the most common due to the similarities between the human and swine cardiovascular systems as well as the fact that the swine size is suitable for testing devices, in this case endovascular carotid systems. The design of devices usually involves numerical techniques, and an important feature is the appropriate modelling of the mechanical properties of the vessel. Fourteen carotid swine arteries were harvested just after sacrifice and cyclic uniaxial tension tests in longitudinal and circumferential directions were performed for distal and proximal samples. The stress-stretch curves obtained were fitted with a hyperelastic anisotropic model. Stress-free configuration states were also analyzed. Finally, human and swine samples were processed in a histological laboratory and images were used to quantify their microconstituents. The statistical analysis revealed significant differences between the mechanical behavior of proximal and distal locations in the circumferential but not in the longitudinal direction. Circumferential direction samples show clear differences both in residual stretches and tensile curves between the two locations, while the features of longitudinal specimens are independent of the axial position. The statistical analysis provides significant evidence of changes depending on the position of the sample, mainly in elastin and SMC quantification.

Mechanical characterization of the softening behavior of human vaginal tissue.

The mechanical properties of vaginal tissue need to be characterized to perform accurate simulations of prolapse and other pelvic disorders that commonly affect women. This is also a fundamental step towards the improvement of therapeutic techniques such as surgery. In this paper, the softening behavior or Mullins effect of vaginal tissue is studied by proposing an appropriate constitutive model. This effect is an important factor after the birth, since vaginal tissue has been supporting a high load distribution and therefore does not recover its original behavior. Due to the anisotropy of the tissue, the mechanical testing of vaginal tissue, consists in loading-unloading uniaxial tension tests performed along the longitudinal and transverse axes of the vagina. A directional pseudo-elastic model was used to reproduce the inelastic behavior of the tissue. The obtained results may be helpful in the design of surgical procedures with autologous tissue or smart prostheses. A good qualitative agreement has been found between the numerical and experimental results for the vaginal tissue examples, indicating that the constitutive softening model can capture the typical stress-strain behavior observed in this kind of fibrous soft tissue.