Thermomechanical Hysteresis of Biological and Synthetic Hydrogels

The nucleus pulposus of the intervertebral disc is a gelatinous viscous hydrogel that has an essential role in the mechanics of the intervertebral disc joint. The viscoelastic properties of the nucleus pulposus significantly change in the course of time and particularly at the outset of disc degeneration. Viscoelasticity is the result of entropy production and may be characterized by hysteresis when the tissue undergoes cyclic mechanical loading. "Nature never undertakes any change unless her interests are served by an increase in entropy" once commented Max Planck. In the context of mechanobiology, we present an original concept wich is referred to the hysteresis theory and states that for a given range of frequency and biological tissue, the maximum mechanotransduction signal coincides with maximum hysteresis. If verified, this statement would introduce a relevant variable in the study of pathophysiological conditions such as degeneration of the nucleus pulposus and serve as a reliable variable to define optimized mechanical load settings for the culture of tissue engineered materials. This doctoral work deals with the proposition of this theory and defines the experimental and theoretical framework to verify this hypothesis in following studies. Hysteresis is not specific to a single process, but is the result of many internal processes that can happen simultaneously. Deformation may imply entropic and/or elastic changes in the tissue which from a phenomenolgical point of view is equivalent, and yet are fundamentally different in nature. Deformation may also be accompanied by reversible and irreversible processes that result in mechanical hysteresis. A clear knowledge on the thermomechanical processes involved during the deformation of biological tissues enables the experimenter to overcome perhaps too restrictive assumptions and may lead to new insights. In this work, we provide a prototype of a deformation calorimeter that is specifically designed for biological hydrogel tissues, thereby refocusing the theory of biological materials on solid experimental thermodynamic grounds. This prototype produced satisfactory results with a measurement precision of 3% and a characteristic time constant of 40 seconds. The thermal stability of the deformation calorimeter was, however, not suficient to experimentally investigate the thermomechanical properties of very soft tissue (kPa scale) such as the nucleus pulposus, but acceptable for stiffer materials ranging in the MPa scale. In conjunction, a theoretical framework is proposed to recover the information that is hidden in hysteresis. Based on continuum mechanics and, in particular, mixture and normal dissipation theories, the governing nonlinear heat equation for thermomechanical porous materials was derived. This equation is general and valid for finite perturbations in temperature and deformations. A particular model for hydrogels was also proposed. Finally, hysteresis and damping properties of the nucleus pulposus was measured at large physiological deformations and for frequencies ranging between 0.01 and 10 Hz. The proposed method relies on the introduction of a small testing device, called hydrogel encapsulation device, which addresses several issues when dealing with mechanical testing on soft tissues such as synthetic and biological hydrogels.

Design and Development of Injectable, Tough and Intrinsically-Adhesive Hydrogels for Biomedical Applications

Peyman Karami

Despite the development of hydrogels with a wide range of mechanical properties, insufficient adhesion between these materials and biological surfaces limits their use in the biomedical applications. Most recent advancements in highly adhesive hydrogel systems are focused on the preformed hydrogel patches and dry tapes. In the past proposed strategies for highly adhesive hydrogels, the developed materials are not intrinsically adhesive, but adhere to the targeted tissues thanks to specific developments such as chemically modifying the contacting surface. Therefore, hydrogels that exhibit both sufficient intrinsic adhesion to various biological surfaces and proper injectability, has yet to be demonstrated. The need for design, fabrication and characterization of adhesive hydrogel systems with broad physicochemical properties has remained a central challenge in the biomedical field. In the first part, by controlling toughening processes, we design a composite double-network hydrogel with high water content, which creates a dissipative interface and robustly adheres to soft tissues. No tissue surface modification was needed to obtain high adhesion properties of the developed hydrogel. Instead, mechanistic principles were used to control interfacial cracks propagation. The integration of the dissipative polymeric network on the soft tissue surfaces allowed increasing significantly the adhesion strength. Our findings highlight the significant role of controlling hydrogel structure and dissipation processes for toughening the interface. In the second part, we propose a universal framework for the design of injectable hydrogels that are intrinsically adhesive to various tissues. We fabricate a family of original polymeric backbones using a two-step functionalization process in order to make new hydrogels with available adhesive sites and the capability to form hybrid networks, as well as further enhancements through the fiber reinforcement for stronger synergetic effects. To achieve that, our approach (i) provides strong chemical bonds with nucleophiles at interface, immediately upon contact with tissues thanks to the designed available adhesive bonding sites, and (ii) forms a hybrid network by covalent and physical interactions between our engineered chains, so that the interfacial bonds and the hydrogel capability of dissipating energy produce a synergic effect for achieving high adhesion. In addition to high level of adhesion performance, the injectable hydrogel system presents a broad and tunable range of physicochemical properties. This is particularly important for biomedical applications which require superior material properties, such as for cartilage tissue engineering. Fast adhesion formation and one-pot polymerization are achieved while the biosafety concerns, which are crucial for many clinical applications, are satisfied. Finally, with various in vitro, ex vivo, and preliminary in vivo studies, the biocompatibility and potential biomedical applications of our injectable adhesive hydrogels are demonstrated for cells scaffolding, soft tissues repair and tissue sealing. This is a design strategy which has potent implication in the way hydrogels are designed to reach high tissue adhesion, as it is not only a way towards synthesis of new biomaterials, but a general design approach based on an understanding of adhesion mechanism. Our approach can even further be used to fabricate more advanced adhesive systems with novel performances.

EPFL2021

Modélisation et analyse numérique de problèmes de réaction-diffusion provenant de la solidification d'alliages binaires

In this work, we are interested in elaborating models and numerical methods in order to study some phenomena which arise in the solidification of binary alloys. We propose two distinct models based on the mass and energy conservation laws as well as on classical thermodynamics. The first model is based on the irreversible process theory and therefore requires the computation of the entropy of the system to complete the description. To obtain this quantity, we develop a formalism and a method which yields numerical results. This construction is made so that the entropy function inherits some interesting mathematical properties from physical requirements. These properties allow us to elaborate and analyze mathematically an original scheme using a time discretization depending on a real parameter to solve the solidification problem. In particular, we are able to prove that the scheme is stable for all values of the time step if the parameter is chosen correctly. Furthermore, we give some numerical results to support the theory. The second model, called phase-field model, is used to describe dendrites' formation during the solidification of binary alloys. The nature of the problem constrains us to use very fine meshes in some physical regions. To reduce the number of discrete unknowns, we develop an adaptive mesh strategy based on an ad-hoc error estimator. We make numerical tests showing that the method converges on regular meshes and that the estimator is in good agreement with the true error. We also show that the mesh refinement strategy gives good results in academic and physical cases.

EPFL1999

Experimental investigation of the mechanical behaviour and structure of the bovine periodontal ligament

Colin Sanctuary

One of the key problems in dental biomechanics is the prediction of tooth mobility under functional loads. Understanding tooth displacement due to load is becoming more important as new solutions in dental restorations, prosthodontics and orthodontic treatments become increasingly more advanced. The mechanical characterization of the alveolar bone, the tooth and the periodontal ligament surrounding the root of the tooth, is necessary to predict tooth mobility. The common assumption is that the periodontal ligament acts as the major element in the stress distribution to the supporting tissues. Obtaining parameters that describe periodontal ligament mechanical behaviour is a challenging problem. Isolating the tissue for testing, the small size of the specimen, and the necessity to maintain, as much as possible, the ligament in vitro under normal physiological conditions, are all factors that contribute to the complexity of the problem. The aim of this thesis is twofold and can be subdivided into two primary objectives. The first objective is to describe its morphology, anatomy, histology and structure of the components in order to determine its geometric parameters at different length scales. The second objective is to determine its mechanical properties by identifying key parameters through shear and uniaxial tension-compression tests. Four studies are performed to describe the morphology, anatomy and histology of the periodontal ligament. First, macroscopic and microscopic measurements of the tooth, bone, and the periodontal ligament are obtained. Second, a bovine first molar system is reconstructed in three dimensions from microcomputerized tomography scans. Third, the morphology of the ligament is observed during deformation using optical microscopy. Fourth, the histology of bovine periodontium tissue is investigated. In order to characterise the mechanical behaviour of the bovine periodontal ligament, custom- designed machines and gripping devices are constructed to subject speciallyprepared tissue specimens to shear and uniaxial tension-compression experiments. Shear experiments are performed on 2 millimetre thick transverse sections, and specimens of toothligament- bone of approximately 8x5x2 millimetres for uniaxial experiments. All specimens are obtained from first molar sites of freshly slaughtered bovines. In both shear and uniaxial testing, the specimens are subjected non-destructively to preconditioning, stress-relaxation, constant strain rate, and sinusoidal loading profiles before testing to rupture. The experiments reported in this thesis elucidate geometrical and mechanical characteristics of the periodontal ligament. Concerning its geometry, a variation in collagen fibre orientation is observed in transverse sections, moreover the symmetry of the shear tests in the apicocoronal direction suggests the periodontal ligament is vertically isotropic. Uniaxial specimens, however, may be considered to be transverse isotropic. Concerning its mechanical behaviour, the periodontal ligament is nonlinear viscoelastic in that it exhibits stiffening, nonlinear elasticity, and nonlinear pseudo-plastic viscosity. The interaction between various constituents of the periodontal ligament (collagen fibres, blood vessels, interstitial fluid etc...) during deformation contribute to the observed stress-strain response of this tissue. A nonlinear viscoelastic model presented in the literature, the Power Law, adequately simulates the nonlinear behaviour of the periodontal ligament using finite element analysis.