Modelling studies on biological tissue properties and mechanical responses under external stimuli

PhDBiological tissues maintain their homeostasis by remodelling under external mechanical stimuli. In order to understand the tissue remodelling process, it is important to characterize tissue properties before detailed mechanical responses can be investigated. This project aims to develop a computational modelling framework to characterise mechanical properties of biological tissues, and to quantify tissue responses under mechanical loading. The thesis presents, first, mechanical responses of articular cartilages under different loadings using a poroelastic model. Unique in this study, collagen fibrils are treated separately from the rest of ECM, as they only resists tension. This leads to a fibril-reinforced poroelastic model. Effects of the distribution of the collagen fibrils and their orientation on tissue mechanical responses are investigated. Most of the effort has been on the mechanical stress distribution of the human left atrium and its correlation to electrophysiology patterns in atrial fibrillation. Detailed mechanical responses of the atrial wall to a step pressure increase in the left atrium are calculated. The geometry of the left atrium is based on patient specific images using cardio CT and incorporates variations of the atrial wall thickness as well as unique fibre orientation patterns. We hypothesize that areas of high von Mises stress are correlated to foci of abnormal electrophysiology sites which sustain cardiac arrhythmia. Results from this study show a positive correlation between them. To our knowledge, this is the first study that establishes the relationship between the atrial wall stress distribution and the atrial abnormal electrophysiology sites. The project also investigates hyperelastic properties of endothelial cells and the overlying endothelial glycocalyx, based on data from AFM micro-indentation. Both endothelial cells with & without the glycocalyx layer (i.e. following enzymatic digestion) are used. This is the first time that the mechanical property of the glycocalyx is estimated using an inverse biomechanical model

Intimal and medial contributions to the hydraulic resistance of the arterial wall at different pressures: a combined computational and experimental study

The hydraulic resistances of the intima and media determine water flux and the advection of macromolecules into and across the arterial wall. Despite several experimental and computational studies, these transport processes and their dependence on transmural pressure remain incompletely understood. Here, we use a combination of experimental and computational methods to ascertain how the hydraulic permeability of the rat abdominal aorta depends on these two layers and how it is affected by structural rearrangement of the media under pressure. Ex vivo experiments determined the conductance of the whole wall, the thickness of the media and the geometry of medial smooth muscle cells (SMCs) and extracellular matrix (ECM). Numerical methods were used to compute water flux through the media. Intimal values were obtained by subtraction. A mechanism was identified that modulates pressure-induced changes in medial transport properties: compaction of the ECM leading to spatial reorganization of SMCs. This is summarized in an empirical constitutive law for permeability and volumetric strain. It led to the physiologically interesting observation that, as a consequence of the changes in medial microstructure, the relative contributions of the intima and media to the hydraulic resistance of the wall depend on the applied pressure; medial resistance dominated at pressures above approximately 93 mmHg in this vessel

Minimum design requirements for a poroelastic mimic of articular cartilage

The exceptional functional performance of articular cartilage (load-bearing and lubrication) is attributed to its poroelastic structure and resulting interstitial fluid pressure. Despite this, there remains no engineered cartilage repair material capable of achieving physiologically relevant poroelasticity. In this work we develop in silico models to guide the design approach for poroelastic mimics of articular cartilage. We implement the constitutive models in FEBio, a PDE solver for multiphasic mechanics problems in biological and soft materials. We investigate the influence of strain rate, boundary conditions at the contact interface, and fiber modulus on the reaction force and load sharing between the solid and fluid phases. The results agree with the existing literature that when fibers are incorporated the fraction of load supported by fluid pressure is greatly amplified and increases with the fiber modulus. This result demonstrates that a stiff fibrous phase is a primary design requirement for poroelastic mimics of articular cartilage. The poroelastic model is fit to experimental stress-relaxation data from bovine and porcine cartilage to determine if sufficient design constraints have been identified. In addition, we fit experimental data from FiHy™, an engineered material which is claimed to be poroelastic. The fiber-reinforced poroelastic model was able to capture the primary physics of these materials and demonstrates that FiHy™ is beginning to approach a cartilage-like poroelastic response. We also develop a fiber-reinforced poroelastic model with a bonded interface (rigid contact) to fit stress relaxation data from an osteochondral explant and FiHy™ + bone substitute. The model fit quality is similar for both the chondral and osteochondral configurations and clearly captures the first order physics. Based on this, we propose that physiological poroelastic mimics of articular cartilage should be developed under a fiber-reinforced poroelastic framework

Scaffold-Dependent Mechanical and Architectural Cues Guide Osteochondral Defect Healing in silico

Osteochondral defects in joints require surgical intervention to relieve pain and restore function. However, no current treatment enables a complete reconstitution of the articular surface. It is known that both mechanical and biological factors play a key role on osteochondral defect healing, however the underlying principles and how they can be used in the design of treatment strategies remain largely unknown. To unravel the underlying principles of mechanobiology in osteochondral defect healing, i.e., how mechanical stimuli can guide biological tissue formation, we employed a computational approach investigating the scaffold-associated mechanical and architectural properties that would enable a guided defect healing. A previous computer model of the knee joint was further developed to simulate healing of an empty osteochondral defect. Then, scaffolds were implanted in the defect and their architectures and material properties were systematically varied to identify their relevance in osteochondral defect healing. Scaffold mechanical and architectural properties were capable of influencing osteochondral defect healing. Specifically, scaffold material elastic modulus values in the range of cancellous bone (low GPa range) and a scaffold architecture that provided stability, i.e., resistance against displacement, in both the main loading direction and perpendicular to it supported the repair process. The here presented model, despite its simplifications, is regarded as a powerful tool to screen for promising properties of novel scaffold candidates fostering osteochondral defect regeneration prior to their implementation in vivo

Multi-scale biomechanical study of transport phenomena in the intervertebral disc

Intervertebral disc (IVD) degeneration is primarily involved in back pain, a morbidity that strongly affects the quality of life of individuals nowadays. Lumbar IVDs undergo stressful mechanical loads while being the largest avascular tissues in our body: Mechanical principles alone cannot unravel the intricate phenomena that occur at the cellular scale which are fundamental for the IVD regeneration. The present work aimed at coupling biomechanical and relevant molecular transport processes for disc cells to provide a mechanobiological finite element framework for a deeper understanding of degenerative processes and the planning of regenerative strategies. Given the importance of fluid flow within the IVD, the influence of poroelastic parameters such as permeabilities and solid-phase stiffness of the IVD subtissues was explored. A continuum porohyperelastic material model was then implemented. The angles of collagen fibers embedded in the annulus fibrosus (AF) were calibrated. The osmotic pressure of the central nucleus pulposus (NP) was also taken into account. In a parallel study of the human vertebral bone, microporomechanics was used together with experimental ultrasonic tests to characterize the stiffness of the solid matrix, and to provide estimates of poroelastic coefficients. Fluid dynamics analyses and microtomographic images were combined to understand the fluid exchanges at the bone-IVD interface. The porohyperelastic model of a lumbar IVD with poroelastic vertebral layers was coupled with a IVD transport model of three solutes - oxygen, lactate and glucose - interrelated to reproduce the glycolytic IVD metabolism. With such coupling it was possible to study the effect of deformations, fluid contents, solid-phase stiffness, permeabilities, pH, cell densities of IVD subtissues and NP osmotic pressure on the solute transport. Moreover, cell death governed by glucose deprivation and lactate accumulation was included to explore the mechanical effect on cell viability. Results showed that the stiffness of the AF had the most remarkable role on the poroelastic behavior of the IVD. The permeability of the thin cartilage endplate and the NP stiffness were also relevant. The porohyperelastic model was shown to reproduce the local AF mechanics, provided the fiber angles were calibrated regionally. Such back-calculation led to absolute values of fibers angles and to a global IVD poromechanical behavior in agreement with experiments in literature. The inclusion of osmotic pressure in the NP also led to stress values under confined compression comparable to those measured in healthy and degenerated NP specimens. For the solid bone matrix, axial and transverse stiffness coefficients found experimentally in the present work agreed with universal mass density-elasticity relationships, and combined with continuum microporomechanics provided poroelastic coefficients for undrained and drained cases. The effective permeability of the vertebral bony endplate calculated with fluid dynamics was highly correlated with the porosity measured in microtomographic images. The coupling of transport and porohyperelastic models revealed a mechanical effect acting under large volume changes and high compliance, favored by healthy rather than degenerated IVD properties. Such effect was attributed to strain-dependent diffusivities and diffusion distances and was shown to be beneficial for IVD cells due to the load-dependent increases of glucose levels. Cell density, NP osmotic pressure and porosity were the most important parameters affecting the coupled mechano-transport of metabolites. This novel study highlights the restoration of both cellular and mechanical factors and has a great potential impact for novel designs of treatments focused on tissue regeneration. It also provides methodological features that could be implemented in clinical image-based tools and improve the multiscale understanding of the human spine mechanobiology

Numerical Techniques for the Noninvasive Assessment of Material Properties and Stresses in Soft Biomaterials

The noninvasive measurement of finite displacements and strains in biomaterials by magnetic resonance imaging (MRI) may be shown to enable mathematical estimates of stress distributions and material properties within structures of the body such as articular cartilage or the intervertebral disc. Such methods will allow for non-contact and patient-specific modeling in a manner not currently possible with traditional mechanical testing or finite element techniques. Therefore, the objective of this thesis was to develop computational methods incorporating imaging-based measures of deformation, composition, and local microstructure to permit nondestructive analysis of a range of complex biomechanical systems. Finite strain-based models were developed and applied towards the analysis of several biomaterial systems of increasing material complexity. First, a model for the analysis of a homogeneous, single material system was created and applied to juvenile porcine cartilage for both linear and nonlinear material assumptions under plane stress conditions. Through this study, the viability of estimating stresses within a homogeneous material system solely from MRI-based displacement and strain measures could be established. The model was then expanded to encompass single-plane, multi-region structures and applied towards the analysis of regional stresses within a rabbit intervertebral disc degeneration model. This model incorporated imaging-based methods to estimate heterogeneous properties within the disc structure based upon local biochemical composition, and showed that the degeneration state of a tissue system could effectively be visualized through the use of finite strain-based modeling. A multi-constituent mixture-based material model was next implemented in the analysis of agarose gel constructs. Material parameter estimates from this model were found to agree with those determined by an unconfined compression validation model, establishing physical relevance of noninvasive parameter estimates produced by the models. Finally, the mixture-based material model was applied towards an in situ analysis of the human intervertebral disc

Microstructural Modeling of Collagen Network Mechanics and Interactions with the Proteoglycan Gel in Articular Cartilage

Cartilage matrix mechanical function is largely determined by interactions between the collagen fibrillar network and the proteoglycan gel. Although the molecular physics of these matrix constituents have been characterized and modern imaging methods are capable of localized measurement of molecular densities and orientation distributions, theoretical tools for using this information for prediction of cartilage mechanical behavior are lacking. We introduce a means to model collagen network contributions to cartilage mechanics based upon accessible microstructural information (fibril density and orientation distributions) and which self-consistently follows changes in microstructural geometry with matrix deformations. The interplay between the molecular physics of the collagen network and the proteoglycan gel is scaled up to determine matrix material properties, with features such as collagen fibril pre-stress in free-swelling cartilage emerging naturally and without introduction of ad hoc parameters. Methods are developed for theoretical treatment of the collagen network as a continuum-like distribution of fibrils, such that mechanical analysis of the network may be simplified by consideration of the spherical harmonic components of functions of the fibril orientation, strain, and stress distributions. Expressions for the collagen network contributions to matrix stress and stiffness tensors are derived, illustrating that only spherical harmonic components of orders 0 and 2 contribute to the stress, while orders 0, 2, and 4 contribute to the stiffness. Depth- and compression-dependent equilibrium mechanical properties of cartilage matrix are modeled, and advantages of the approach are illustrated by exploration of orientation and strain distributions of collagen fibrils in compressed cartilage. Results highlight collagen-proteoglycan interactions, especially for very small physiological strains where experimental data are relatively sparse. These methods for determining matrix mechanical properties from measurable quantities at the microscale (composition, structure, and molecular physics) may be useful for investigating cartilage structure-function relationships relevant to load-bearing, injury, and repai

Effect of Hemiarthroplasty Implant Contact Geometry and Material on Early Cartilage Wear

Hemiarthroplasty is a minimally invasive, cost-effective alternative to total arthroplasty in joints of the upper limb. Though these procedures reduce patient morbidity while restoring joint kinematics, their longevity is limited by wear of the adjacent cartilage. This work investigates the roles of contact geometry and implant stiffness on cartilage wear with the aim of elucidating the mechanics that contribute to cartilage damage. An in vitro study examined the influence of implant geometry on cartilage wear using a pin-on-plate wear simulator. A significant decrease in volumetric wear was observed as contact area increased, which suggests that maximizing contact area should be design target for hemiarthroplasty implants. A subsequent study examined the influence of stiffness using various clinically relevant biomaterials, and demonstrated no effect on cartilage wear for a range of Young\u27s moduli between 200GPa and 0.69GPa. It was concluded that the disparity between the moduli of the investigated materials and that of cartilage may be too great to demonstrate the possible effects of implant stiffness on contact mechanics. A finite element simulation was conducted to further reveal contact mechanics at the implant-cartilage interface. The stress levels determined by the study were proportional to the wear observed for both implant geometry and material, with the exception of polyether ether ketone, one of the investigated biomaterials. Further studies are required to more comprehensively characterize cartilage wear, and it is necessary to examine whether stiffness has an effect on cartilage wear when caused by implant materials with moduli approaching that of articular cartilage