Publications

The mechanical signals sensed by the alveolar cells through the changes in the local matrix stiffness of the extracellular matrix (ECM) are determinant for regulating cellular functions. Therefore, the study of the mechanical response of lung tissue becomes a fundamental aspect in order to further understand the mechanosensing signals perceived by the cells in the alveoli. This study is focused on the development of a finite element (FE) model of a decellularized rat lung tissue strip, which reproduces accurately the mechanical behaviour observed in the experiments by means of a tensile test. For simulating the complex structure of the lung parenchyma, which consists of a heterogeneous and non-uniform network of thin-walled alveoli, a 3D model based on a Voronoi tessellation is developed. This Voronoi-based model is considered very suitable for recreating the geometry of cellular materials with randomly distributed polygons like in the lung tissue. The material model used in the mechanical simulations of the lung tissue was characterized experimentally by means of AFM tests in order to evaluate the lung tissue stiffness on the micro scale. Thus, in this study, the micro (AFM test) and the macro scale (tensile test) mechanical behaviour are linked through the mechanical simulation with the 3D FE model based on Voronoi tessellation. Finally, a micro-mechanical FE-based model is generated from the Voronoi diagram for studying the stiffness sensed by the alveolar cells in function of two independent factors: the stretch level of the lung tissue and the geometrical position of the cells on the extracellular matrix (ECM), distinguishing between pneumocyte type I and type II. We conclude that the position of the cells within the alveolus has a great influence on the local stiffness perceived by the cells. Alveolar cells located at the corners of the alveolus, mainly type II pneumocytes, perceive a much higher stiffness than those located in the flat areas of the alveoli, which correspond to type I pneumocytes. However, the high stiffness, due to the macroscopic lung tissue stretch, affects both cells in a very similar form, thus no significant differences between them have been observed. © 2021 The Authors

JTD Keywords: rat, scaffolds, stiffness, Afm, Animal cell, Animal experiment, Animal model, Animal tissue, Article, Biological organs, Cell function, Cells, Computational geometry, Cytology, Extracellular matrices, Extracellular matrix, Extracellular-matrix, Geometry, High stiffness, Human, Lung alveolus cell type 1, Lung alveolus cell type 2, Lung parenchyma, Lung tissue, Male, Mechanical behavior, Mechanical modeling, Mechanical simulations, Mechanosensing, Model-based opc, Nonhuman, Physical model, Rat, Rigidity, Stiffness, Stiffness matrix, Tensile testing, Thin walled structures, Three dimensional finite element analysis, Tissue, Type ii, Voronoi tessellations

We introduce a new method, the Local Monge Parametrizations (LMP) method, to approximate tensor fields on general surfaces given by a collection of local parametrizations, e.g. as in finite element or NURBS surface representations. Our goal is to use this method to solve numerically tensor-valued partial differential equations (PDEs) on surfaces. Previous methods use scalar potentials to numerically describe vector fields on surfaces, at the expense of requiring higher-order derivatives of the approximated fields and limited to simply connected surfaces, or represent tangential tensor fields as tensor fields in 3D subjected to constraints, thus increasing the essential number of degrees of freedom. In contrast, the LMP method uses an optimal number of degrees of freedom to represent a tensor, is general with regards to the topology of the surface, and does not increase the order of the PDEs governing the tensor fields. The main idea is to construct maps between the element parametrizations and a local Monge parametrization around each node. We test the LMP method by approximating in a least-squares sense different vector and tensor fields on simply connected and genus-1 surfaces. Furthermore, we apply the LMP method to two physical models on surfaces, involving a tension-driven flow (vector-valued PDE) and nematic ordering (tensor-valued PDE), on different topologies. The LMP method thus solves the long-standing problem of the interpolation of tensors on general surfaces with an optimal number of degrees of freedom.

JTD Keywords: Approximation, Finite elements, Surface PDE, Tensor-valued PDE, Vector-valued PDE

Altered nutrition in the intervertebral disc affects cell viability and can generate catabolic cascades contributing to extracellular matrix (ECM) degradation. Such degradation is expected to affect couplings between disc mechanics and nutrition, contributing to accelerate degenerative processes. However, the relation of ECM changes to major biophysical events within the loaded disc remains unclear. A L4-L5 disc finite element model including the nucleus (NP), annulus (AF) and endplates was used and coupled to a transport-cell viability model. Solute concentrations and cell viability were evaluated along the mid-sagittal plane path. A design of experiment (DOE) was performed. DOE parameters corresponded to AF and NP biochemical tissue measurements in discs with different degeneration grades. Cell viability was not affected by any parameter combinations defined. Nonetheless, the initial water content was the parameter that affected the most the solute contents, especially glucose. Calculations showed that altered NP composition could negatively affect AF cell nutrition. Results suggested that AF and NP tissue degeneration are not critical to nutrition-related cell viability at early-stage of disc degeneration. However, small ECM degenerative changes may alter significantly disc nutrition under mechanical loads. Coupling disc mechano-transport simulations and enzyme expression studies could allow identifying spatiotemporal sequences related to tissue catabolism.

JTD Keywords: Cell nutrition, Finite element analysis, Intervertebral disc degeneration, Multiphysics, Tissue composition

Purpose: To assess, with finite element (FE) calculations, whether immediate weight bearing would be possible after surgical stabilization either with cannulated screws or with a locking plate in a split fracture of the lateral tibial plateau (LTP). Methods: A split fracture of the LTP was recreated in a FE model of a human tibia. A three-dimensional FE model geometry of a human femur-tibia system was obtained from the VAKHUM project database, and was built from CT images from a subject with normal bone morphologies and normal alignment. The mesh of the tibia was reconverted into a geometry of NURBS surfaces. A split fracture of the lateral tibial plateau was reproduced by using geometrical data from patient radiographs. A locking screw plate (LP) and a cannulated screw (CS) systems were modelled to virtually reduce the fracture and 80 kg static body-weight was simulated. Results: While the simulated body-weight led to clinically acceptable interfragmentary motion, possible traumatic bone shear stresses were predicted nearby the cannulated screws. With a maximum estimation of about 1.7 MPa maximum bone shear stresses, the Polyax system might ensure more reasonable safety margins. Conclusions: Split fractures of the LTP fixed either with locking screw plate or cannulated screws showed no clinically relevant IFM in a FE model. The locking screw plate showed higher mechanical stability than cannulated screw fixation. The locking screw plate might also allow full or at least partial weight bearing under static posture at time zero.

JTD Keywords: Bone fixation, Finite element, Fracture fixation, Interfragmentary motion, Tibial plateau fractures, Weight bearing

Capturing patient- or condition-specific intervertebral disk (IVD) properties in finite element models is outmost important in order to explore how biomechanical and biophysical processes may interact in spine diseases. However, disk degenerative changes are often modeled through equations similar to those employed for healthy organs, which might not be valid. As for the simulated effects of degenerative changes, they likely depend on specific disk geometries. Accordingly, we explored the ability of continuum tissue models to simulate disk degenerative changes. We further used the results in order to assess the interplay between these simulated changes and particular IVD morphologies, in relation to disk cell nutrition, a potentially important factor in disk tissue regulation. A protocol to derive patient-specific computational models from clinical images was applied to different spine specimens. In vitro, IVD creep tests were used to optimize poro-hyperelastic input material parameters in these models, in function of the IVD degeneration grade. The use of condition-specific tissue model parameters in the specimen-specific geometrical models was validated against independent kinematic measurements in vitro. Then, models were coupled to a transport-cell viability model in order to assess the respective effects of tissue degeneration and disk geometry on cell viability. While classic disk poro-mechanical models failed in representing known degenerative changes, additional simulation of tissue damage allowed model validation and gave degeneration-dependent material properties related to osmotic pressure and water loss, and to increased fibrosis. Surprisingly, nutrition-induced cell death was independent of the grade-dependent material properties, but was favored by increased diffusion distances in large IVDs. Our results suggest that in situ geometrical screening of IVD morphology might help to anticipate particular mechanisms of disk degeneration.

JTD Keywords: Intervertebral Disc Degeneration, Finite element modelling, Lumbar spine, Poroelasticity, Damage model, Subject-specific modelling, Disc cell nutrition

AbstractBackground Hip arthritis is a pathology linked to hip-cartilage degeneration. Although the aetiology of this disease is not well defined, it is known that age is a determinant risk factor. However, hip arthritis in young patients could be largely promoted by biomechanical factors. The objective of this paper is to analyze the impact of some normal anatomical variations on the cartilage stress distributions numerically predicted at the hip joint during walking. Methods A three-dimensional finite element model of the femur and the pelvis with the most relevant axial components of muscle forces was used to simulate normal walking activity. The hip anatomical condition was defined by: neck shaft angle, femoral anteversion angle, and acetabular anteversion angle with a range of 110-130º, 0-20º, and 0-20º, respectively. The direct boundary method was used to simulate the hip contact. Findings The hydrostatic stress found at the cartilage and labrum showed that a ± 10º variation with respect to the reference brings significant differences between the anatomic models. Acetabular anteversion angle of 0º and femoral anteversion angle of 0º were the most affected anatomical conditions with values of hydrostatic stress in the cartilage near 5 MPa under compression. Interpretation Cartilage stresses and contact areas were equivalent to the results found in literature and the most critical anatomical regions in terms of tissue loads were in a good accordance with clinical evidence. Altogether, results showed that decreasing femoral or acetabular anteversion angles isolately causes a dramatic increase in cartilage loads.

JTD Keywords: Hip arthritis, Neck shaft angle, Femoral and acetabular anteversions, Cartilage load, Hip joint contact, Finite element analysis

This chapter focuses on the use of the finite element method in the design and exploration of spinal implants. Following an introduction to biomechanical alterations of the spine in disease and to spine finite element modelling, focus is placed on different models developed for spine treatment simulations. Despite the hindrance of working thorough representations of in vivo situations, predictions of load transfer within both the implants and the tissues simulated allow improved interpretations of known clinical outcomes, and permit the educated design of new implants. The potential of probabilistic modelling is also discussed in relation to model validation and patient-specific analyses. Finally, the latest developments in the multiphysical modelling of intervertebral discs are presented, revealing a strong potential for the study of implant-based strategies that aim to restore the functional biophysics of the spine.

JTD Keywords: Spinal implant, Finite element modelling, Spine surgery, Spine biomechanics, Tissue mechanobiology

Several computational models based on experimental techniques and theories have been proposed to describe cytoskeleton (CSK) mechanics. Tensegrity is a prominent model for force generation, but it cannot predict mechanics of individual CSK components, nor explain the discrepancies from the different single cell stimulating techniques studies combined with cytoskeleton-disruptors. A new numerical concept that defines a multi-structural 3D finite element (FE) model of a single-adherent cell is proposed to investigate the biophysical and biochemical differences of the mechanical role of each cytoskeleton component under loading. The model includes prestressed actin bundles and microtubule within cytoplasm and nucleus surrounded by the actin cortex. We performed numerical simulations of atomic force microscopy (AFM) experiments by subjecting the cell model to compressive loads. The numerical role of the CSK components was corroborated with AFM force measurements on U2OS-osteosarcoma cells and NIH-3T3 fibroblasts exposed to different cytoskeleton-disrupting drugs. Computational simulation showed that actin cortex and microtubules are the major components targeted in resisting compression. This is a new numerical tool that explains the specific role of the cortex and overcomes the difficulty of isolating this component from other networks invitro. This illustrates that a combination ofcytoskeletal structures with their own properties is necessary for a complete description of cellular mechanics.

JTD Keywords: Actin bundles, Actin cortex, AFM (atomic force microscopy), Cytoskeleton, Finite element modeling, Microtubules

Osmotic phenomena influence the intervertebral disc biomechanics. Their simulation is challenging and can be undertaken at different levels of complexity. Four distinct approaches to simulate the osmotic behaviour of the intervertebral disc (a fixed boundary pore pressure model, a fixed osmotic pressure gradient model in the whole disc or only in the nucleus pulposus, and a swelling model with strain-dependent osmotic pressure) were analysed. Predictions were compared using a 3D poroelastic finite element model of a L4–L5 spinal unit under three different loading conditions: free swelling for 8 h and two daily loading cycles: (i) 200 N compression for 8 h followed by 500 N compression for 16 h; (ii) 500 N for 8 h followed by 1000 N for 16 h. Overall, all swelling models calculated comparable results, with differences decreasing under greater loads. Results predicted with the fixed boundary pore pressure and the fixed osmotic pressure in the whole disc models were nearly identical. The boundary pore pressure model, however, cannot simulate differential osmotic pressures in disc regions. The swelling model offered the best potential to provide more accurate results, conditional upon availability of reliable values for the required coefficients and material properties. Possible fields of application include mechanobiology investigations and crack opening and propagation. However, the other approaches are a good compromise between the ease of implementation and the reliability of results, especially when considering higher loads or when the focus is on global results such as spinal kinematics.

JTD Keywords: Intervertebral disc, Boundary pore pressure, Osmotic pressure, Swelling, Finite element, Poroelasticity

Mechanical stimuli are one of the factors that influence tissue differentiation. In the development of biomaterials for bone tissue engineering, mechanical stimuli and formation of a vascular network that transport oxygen to cells within the pores of the scaffolds are essential. Angiogenesis and cell differentiation have been simulated in scaffolds of regular porosity; however, the dynamics of differentiation can be different when the porosity is not uniform. The objective of this study was to investigate the effect of the mechanical stimuli and the capillary network formation on cell differentiation within a scaffold of irregular morphology. A porous scaffold of calcium phosphate based glass was used. The pores and the solid phase were discretized using micro computed tomography images. Cell activity was simulated within the interconnected pore domain of the scaffold using a lattice modeling approach. Compressive strains of 0.5 and 1% of total deformation were applied and two cases of mesenchymal stem cells initialization (in vitro seeding and in vivo) were simulated. Similar capillary networks were formed independently of the cell initialization mode and the magnitude of the mechanical strain applied. Most of vessels grew in the pores at the periphery of the scaffolds and were blocked by the walls of the scaffold. When 0.5% of strain was applied, 70% of the pore volume was affected by mechano-regulatory stimuli corresponding to bone formation; however, because of the lack of oxygen, only 40% of the volume was filled with osteoblasts. 40% of volume was filled with chondrocytes and 3% with fibroblasts. When the mechanical strain was increased to 1%, 11% of the pore volume was filled with osteoblasts, 59% with chondrocytes, and 8% with fibroblasts. This study has shown the dynamics of the correlation between mechanical load, angiogenesis and tissue differentiation within a scaffold with irregular morphology.

JTD Keywords: Tissue engineering, Calcium phosphates, Mechanoregulation, Micro computer tomography, Finite element modeling

Quantitative measurement of the low-frequency dielectric constants of thick insulators at the nanoscale is demonstrated utilizing ac electrostatic force microscopy combined with finite-element calculations based on a truncated cone with hemispherical apex probe geometry. The method is validated on muscovite mica, borosilicate glass, poly(ethylene naphthalate), and poly(methyl methacrylate). The dielectric constants obtained are essentially given by a nanometric volume located at the dielectric-air interface below the tip, independently of the substrate thickness, provided this is on the hundred micrometer-length scale, or larger.

JTD Keywords: Borosilicate glasses, Finite element analysis, Insulating thin films, Mica, Nanostructured materials, Permittivity, Polymers, Scanning probe microscopy

A computational model of mechanoregulation is proposed to predict bone tissue formation stimulated mechanically by overall dynamical compression within a porous polymeric scaffold rendered by micro-CT. Dynamic compressions of 0.5-5% at 0.0025-0.025 s(-1) were simulated. A force-controlled dynamic compression was also performed by imposing a ramp of force from 1 to 70 N. The model predicts homogeneous mature bone tissue formation under strain levels of 0.5-1% at strain rates of 0.0025-0.005 s(-1). Under higher levels of strain and strain rates, the scaffold shows heterogeneous mechanical behaviour which leads to the formation of a heterogeneous tissue with a mixture of mature bone and fibrous tissue. A fibrous tissue layer was also predicted under the force-controlled dynamic compression, although the same force magnitude was found promoting only mature bone during a strain-controlled compression. The model shows that the mechanical stimulation of bone tissue formation within a porous scaffold closely depends on the loading history and on the mechanical behaviour of the scaffold at local and global scales.

JTD Keywords: Bone tissue engineering, Scaffold, Tissue differentiation, Mechanoregulation, Finite element analysis

An analysis of accuracy of time-constant spectrum extraction from thermal transients has been performed. Numerical calculations based on analytical models and finite element method simulations have been used in order to obtain the thermal transients. Simple geometries have been used such that analytical expressions for their time-constant spectrums are known. Results show that a large error in the time-constant spectrum is obtained for very small rms error ( 1 mK) in the thermal transient. The estimation problem is ill-conditioned. Moreover, the differential structure function shows a low accuracy identifying stacked structures. The initial part of the differential structure function shows numerical oscillations and the final part has an asymptotic behavior to infinity that has been identified as an artifact related to errors in the time-constant spectrum estimation. Peak identification from the differential structure function heavily depends on an accurate determination of the time-constant spectrum. The limited spectral resolution and dynamic range of the differential structure function are a direct consequence of the time-constant spectrum imprecision.

JTD Keywords: Finite element analysis, Spectral analysis

Readers of this chapter will learn about our approach to computer simulation of tissue differentiation in response to mechanical forces. It involves defining algorithms for mechanoregulation of each of following cell activities: proliferation, apoptosis, migration, and differentiation using a stimulus based on a combination of strain and fluid flow (Prendergast et al., J. Biomech., 1997) - algorithms are based on a lattice-modelling which also facilitates building algorithms for complex processes such as angiogenesis. The algorithms are designed to be collaboratable individually. They can be combined to create a computational simulation method for tissue differentiation, using finite element analysis to compute the mechanical stimuli in even quite complex biomechanical environments. Examples are presented of the simulation method in use.

JTD Keywords: Mechanobiology, Lattice modeling, Differentiation, Tissue engineering, Finite element modeling, Scaffolds

A computational model based on finite element method (FEM) and computational fluid dynamics (CFD) is developed to analyse the mechanical stimuli in a composite scaffold made of polylactic acid (PLA) matrix with calcium phosphate glass (Glass) particles. Different bioreactor loading conditions were simulated within the scaffold. In vitro perfusion conditions were reproduced in the model. Dynamic compression was also reproduced in an uncoupled fluid-structure scheme: deformation level was studied analyzing the mechanical response of scaffold alone under static compression while strain rate was studied considering the fluid flow induced by compression through fixed scaffold. Results of the model show that during perfusion test an inlet velocity of 25mum/s generates on scaffold surface a fluid flow shear stress which may stimulate osteogenesis. Dynamic compression of 5% applied on the PLA-Glass scaffold with a strain rate of 0.005s(-1) has the benefit to generate mechanical stimuli based on both solid shear strain and fluid flow shear stress on large scaffold surface area. Values of perfusion inlet velocity or compression strain rate one order of magnitude lower may promote cell proliferation while values one order of magnitude higher may be detrimental for cells. FEM-CFD scaffold models may help to determine loading conditions promoting bone formation and to interpret experimental results from a mechanical point of view.

JTD Keywords: Bone tissue engineering, Scaffold, Finite element analysis, Computational fluid dynamics, Mechanical stimuli

Tissue engineering scaffolds provide temporary mechanical support for tissue regeneration and transfer global mechanical load to mechanical stimuli to cells through its architecture. In this study the interactions between scaffold pore morphology, mechanical stimuli developed at the cell microscopic level, and culture conditions applied at the macroscopic scale are studied on two regular scaffold structures. Gyroid and hexagonal scaffolds of 55% and 70% porosity were modeled in a finite element analysis and were submitted to an inlet fluid flow or compressive strain. A mechanoregulation theory based on scaffold shear strain and fluid shear stress was applied for determining the influence of each structures on the mechanical stimuli on initial conditions. Results indicate that the distribution of shear stress induced by fluid perfusion is very dependent on pore distribution within the scaffold. Gyroid architectures provide a better accessibility of the fluid than hexagonal structures. Based on the mechanoregulation theory, the differentiation process in these structures was more sensitive to inlet fluid flow than axial strain of the scaffold. This study provides a computational approach to determine the mechanical stimuli at the cellular level when cells are cultured in a bioreactor and to relate mechanical stimuli with cell differentiation.

JTD Keywords: Tissue engineering, Scaffold, Rapid prototyping, Computational fluid dynamics, Finite element

A statistical factorial analysis approach was conducted on a poroelastic finite element model of a lumbar intervertebral disc to analyse the influence of six material parameters (permeabilities of annulus, nucleus, trabecular vertebral bone, cartilage endplate and Young's moduli of annulus and nucleus) on the displacement, fluid pore pressure and velocity fields. Three different loading modes were investigated: compression, flexion and axial rotation. Parameters were varied considering low and high levels in agreement with values found in the literature for both healthy and degenerated lumbar discs. Results indicated that annulus stiffness and cartilage endplate permeability have a strong effect on the overall fluid- and solid-phase responses in all loading conditions studied. Nucleus stiffness showed its main relevance in compression while annulus permeability influenced mainly the annular pressure field. This study confirms the permeability's central role in biphasic modelling and highlights for the lumbar disc which experiments of material property characterization should be performed. Moreover, such sensitivity study gives important guidelines in poroelastic material modelling and finite element disc validation.

JTD Keywords: Intervertebral disc, Permeability, Fractional factorial design, Design of experiments, Finite element analysis

Mechanical stimuli are one of the factors that affect cell proliferation and differentiation in the process of bone tissue regeneration. Knowledge on the specific deformation sensed by cells at a microscopic level when mechanical loads are applied is still missing in the development of biomaterials for bone tissue engineering. The objective of this study was to analyze the behavior of the mechanical stimuli within some calcium phosphate-based scaffolds in terms of stress and strain distributions in the solid material phase and fluid velocity, fluid pressure and fluid shear stress distributions in the pores filled of fluid, by means of micro computed tomographed (CT)-based finite element (FE) models. Two samples of porous materials, one of calcium phosphate-based cement and another of biodegradable glass, were used. Compressive loads equivalent to 0.5% of compression applied to the solid material phase and interstitial fluid flows with inlet velocities of 1, 10 and 100 mu m/s applied to the interconnected pores were simulated, changing also the inlet side and the viscosity of the medium. Similar strain distributions for both materials were found, with compressive and tensile strain maximal values of 1.6% and 0.6%, respectively. Mean values were consistent with the applied deformation. When 10 mu m/s of inlet fluid velocity and 1.45 Pa s viscosity, maximal values of fluid velocity were 12.76 mm/s for CaP cement and 14.87 mm/s for glass. Mean values were consistent with the inlet ones applied, and mean values of shear stress were around 5 x 10(-5) Pa. Variations on inlet fluid velocity and fluid viscosity produce proportional and independent changes in fluid velocity, fluid shear stress and fluid pressure. This study has shown how mechanical loads and fluid flow applied on the scaffolds cause different levels of mechanical stimuli within the samples according to the morphology of the materials.

JTD Keywords: Bone tissue engineering, Finite element analysis, Scaffolds, Mechanical stimuli

This study involves the mechanical and structural characterisation of completely degradable scaffolds for tissue engineering applications. The scaffolds are a composite of polylactic acid (PLA) and a soluble calcium phosphate glass, and are thus completely degradable. A factorial experimental design was applied to optimise scaffold composition prior to simultaneous microtomography and micromechanical testing. Synchrotron X-ray microtomography combined with in situ micromechanical testing was performed to obtain three-dimensional 3D images of the scaffolds under compression. The 3D reconstruction was converted into a finite element mesh which was validated by simulating a compression test and comparing it with experimental results. The experimental design reveals that larger glass particle and pore sizes reduce the stiffness of the scaffolds, and that the porosity is largely unaffected by changes in pore sizes or glass weight content. The porosity ranges between 93% and 96.5%, and the stiffness ranges between 50 and 200 kPa. X-ray projections show a homogeneous distribution of the glass particles within the PLA matrix, and illustrate pore-wall breakage under strain. The 3D reconstructions are used qualitatively to visualise the distribution of the phases of the composite material, and to follow pore deformation under compression. Quantitatively, scaffold porosity, pore interconnectivity and surface/volume ratios have been calculated. Finite element analysis revealed the stress and strain distribution in the scaffold under compression, and could be used in the future to characterise the mechanical properties of the scaffolds.

JTD Keywords: Synchrotron x-ray microtomography, Mechanical test, Biodegradable, Glass, Scaffold, Finite element analysis