A generalized anisotropic quadric yield criterion and its application to bone tissue at multiple length scales

Nonlinear computational analysis of materials showing elasto-plasticity or damage relies on knowledge of their yield behavior and strengths under complex stress states. In this work, a generalized anisotropic quadric yield criterion is proposed that is homogeneous of degree one and takes a convex quadric shape with a smooth transition from ellipsoidal to cylindrical or conical surfaces. If in the case of material identification, the shape of the yield function is not known a priori, a minimization using the quadric criterion will result in the optimal shape among the convex quadrics. The convexity limits of the criterion and the transition points between the different shapes are identified. Several special cases of the criterion for distinct material symmetries such as isotropy, cubic symmetry, fabric-based orthotropy and general orthotropy are presented and discussed. The generality of the formulation is demonstrated by showing its degeneration to several classical yield surfaces like the von Mises, Drucker–Prager, Tsai–Wu, Liu, generalized Hill and classical Hill criteria under appropriate conditions. Applicability of the formulation for micromechanical analyses was shown by transformation of a criterion for porous cohesive-frictional materials by Maghous et al. In order to demonstrate the advantages of the generalized formulation, bone is chosen as an example material, since it features yield envelopes with different shapes depending on the considered length scale. A fabric- and density-based quadric criterion for the description of homogenized material behavior of trabecular bone is identified from uniaxial, multiaxial and torsional experimental data. Also, a fabric- and density-based Tsai–Wu yield criterion for homogenized trabecular bone from in silico data is converted to an equivalent quadric criterion by introduction of a transformation of the interaction parameters. Finally, a quadric yield criterion for lamellar bone at the microscale is identified from a nanoindentation study reported in the literature, thus demonstrating the applicability of the generalized formulation to the description of the yield envelope of bone at multiple length scales.

Ex vivo investigation of novel wound healing therapies and development of a 3-D human skin equivalent wound model

It has previously been found that complexes comprised of vitronectin and growth factors (VN:GF) enhance keratinocyte protein synthesis and migration. More specifically, these complexes have been shown to significantly enhance the migration of dermal keratinocytes derived from human skin. In view of this, it was thought that these complexes may hold potential as a novel therapy for healing chronic wounds. However, there was no evidence indicating that the VN:GF complexes would retain their effect on keratinocytes in the presence of chronic wound fluid. The studies in this thesis demonstrate for the first time that the VN:GF complexes not only stimulate proliferation and migration of keratinocytes, but also these effects are maintained in the presence of chronic wound fluid in a 2-dimensional (2-D) cell culture model. Whilst the 2-D culture system provided insights into how the cells might respond to the VN:GF complexes, this investigative approach is not ideal as skin is a 3-dimensional (3-D) tissue. In view of this, a 3-D human skin equivalent (HSE) model, which reflects more closely the in vivo environment, was used to test the VN:GF complexes on epidermopoiesis. These studies revealed that the VN:GF complexes enable keratinocytes to migrate, proliferate and differentiate on a de-epidermalised dermis (DED), ultimately forming a fully stratified epidermis. In addition, fibroblasts were seeded on DED and shown to migrate into the DED in the presence of the VN:GF complexes and hyaluronic acid, another important biological factor in the wound healing cascade. This HSE model was then further developed to enable studies examining the potential of the VN:GF complexes in epidermal wound healing. Specifically, a reproducible partial-thickness HSE wound model was created in fully-defined media and monitored as it healed. In this situation, the VN:GF complexes were shown to significantly enhance keratinocyte migration and proliferation, as well as differentiation. This model was also subsequently utilized to assess the wound healing potential of a synthetic fibrin-like gel that had previously been demonstrated to bind growth factors. Of note, keratinocyte re-epitheliasation was shown to be markedly improved in the presence of this 3-D matrix, highlighting its future potential for use as a delivery vehicle for the VN:GF complexes. Furthermore, this synthetic fibrin-like gel was injected into a 4 mm diameter full-thickness wound created in the HSE, both keratinocytes and fibroblasts were shown to migrate into this gel, as revealed by immunofluorescence. Interestingly, keratinocyte migration into this matrix was found to be dependent upon the presence of the fibroblasts. Taken together, these data indicate that reproducible wounds, as created in the HSEs, provide a relevant ex vivo tool to assess potential wound healing therapies. Moreover, the models will decrease our reliance on animals for scientific experimentation. Additionally, it is clear that these models will significantly assist in the development of novel treatments, such as the VN:GF complexes and the synthetic fibrin-like gel described herein, ultimately facilitating their clinical trial in the treatment of chronic wounds.

Integrating concrete and virtual materials in an elementary mathematics classroom : a case study of success with fractions

This paper describes an approach to introducing fraction concepts using generic software tools such as Microsoft Office's PowerPoint to create "virtual" materials for mathematics teaching and learning. This approach replicates existing concrete materials and integrates virtual materials with current non-computer methods of teaching primary students about fractions. The paper reports a case study of a 12-year-old student, Frank, who had an extremely limited understanding of fractions. Frank also lacked motivation for learning mathematics in general and interacted with his peers in a negative way during mathematics lessons. In just one classroom session involving the seamless integration of off-computer and on-computer activities, Frank acquired a basic understanding of simple common equivalent fractions. Further, he was observed as the session progressed to be an enthusiastic learner who offered to share his learning with his peers. The study's "virtual replication" approach for fractions involves the manipulation of concrete materials (folding paper regions) alongside the manipulation of their virtual equivalent (shading screen regions). As researchers have pointed out, the emergence of new technologies does not mean old technologies become redundant. Learning technologies have not replaced print and oral language or basic mathematical understanding. Instead, they are modifying, reshaping, and blending the ways in which humankind speaks, reads, writes, and works mathematically. Constructivist theories of learning and teaching argue that mathematics understanding is developed from concrete to pictorial to abstract and that, ultimately, mathematics learning and teaching is about refinement and expression of ideas and concepts. Therefore, by seamlessly integrating the use of concrete materials and virtual materials generated by computer software applications, an opportunity arises to enhance the teaching and learning value of both materials.

Bioactive inorganic materials/alginate composite microspheres with controllable drug-delivery ability

Alginate microspheres are considered a promising material as a drug carrier in bone repair due to excellent biocompatibility, but their main disadvantage is low drug entrapment efficiency and non-controllable release. The aim of this study was to investigate the effect of incorporating mesoporous bioglass (MBG), non-mesoporous bioglass (BG) or hydroxyapatite (HAp) into alginate microspheres on their drug-loading and release properties. X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and atomic emission spectroscopy (AES) were used to analyse the composition, structure and dissolution of bioactive inorganic materials and their microspheres. Dexamethasone (DEX)-loading and release ability of four microspheres were tested in phosphate buffered saline with varying pHs. Results showed that the drug-loading capacity was enhanced with the incorporation of bioactive inorganic materials into alginate microspheres. The MBG/Alginate microspheres had the highest drug loading ability. DEX release from alginate microspheres correlated to the dissolution of MBG, BG and HAp in PBS, and that the pH was an efficient factor in controlling the DEX release; a high pH resulted in greater DEX release, whereas a low pH delayed DEX release. In addition, MBG/alginate, BG/alginate and HAp/alginate microspheres had varying apatite-formation and dissolution abilities, which indicate that the composites would behave differently with respect to bioactivity. The study suggests that microspheres made of a composite of bioactive inorganic materials and alginate have a bioactivity and degradation profile which greatly improves their drug delivery capacity, thus enhancing their potential applications as bioactive filler materials for bone tissue regeneration.

Physiological investigation of periosteum structure and its application in periosteum tissue engineering

Although many different materials, techniques and methods, including artificial or engineered bone substitutes, have been used to repair various bone defects, the restoration of critical-sized bone defects caused by trauma, surgery or congenital malformation is still a great challenge to orthopedic surgeons. One important fact that has been neglected in the pursuit of resolutions for large bone defect healing is that most physiological bone defect healing needs the periosteum and stripping off the periosteum may result in non-union or non-healed bone defects. Periosteum plays very important roles not only in bone development but also in bone defect healing. The purpose of this project was to construct a functional periosteum in vitro using a single stem cell source and then test its ability to aid the repair of critical-sized bone defect in animal models. This project was designed with three separate but closely-linked parts which in the end led to four independent papers. The first part of this study investigated the structural and cellular features in periostea from diaphyseal and metaphyseal bone surfaces in rats of different ages or with osteoporosis. Histological and immunohistological methods were used in this part of the study. Results revealed that the structure and cell populations in periosteum are both age-related and site-specific. The diaphyseal periosteum showed age-related degeneration, whereas the metaphyseal periosteum is more destructive in older aged rats. The periosteum from osteoporotic bones differs from normal bones both in terms of structure and cell populations. This is especially evident in the cambial layer of the metaphyseal area. Bone resorption appears to be more active in the periosteum from osteoporotic bones, whereas bone formation activity is comparable between the osteoporotic and normal bone. The dysregulation of bone resorption and formation in the periosteum may also be the effect of the interaction between various neural pathways and the cell populations residing within it. One of the most important aspects in periosteum engineering is how to introduce new blood vessels into the engineered periosteum to help form vascularized bone tissues in bone defect areas. The second part of this study was designed to investigate the possibility of differentiating bone marrow stromal cells (BMSCs) into the endothelial cells and using them to construct vascularized periosteum. The endothelial cell differentiation of BMSCs was induced in pro-angiogenic media under both normoxia and CoCl2 (hypoxia-mimicking agent)-induced hypoxia conditions. The VEGF/PEDF expression pattern, endothelial cell specific marker expression, in vitro and in vivo vascularization ability of BMSCs cultured in different situations were assessed. Results revealed that BMSCs most likely cannot be differentiated into endothelial cells through the application of pro-angiogenic growth factors or by culturing under CoCl2-induced hypoxic conditions. However, they may be involved in angiogenesis as regulators under both normoxia and hypoxia conditions. Two major angiogenesis-related growth factors, VEGF (pro-angiogenic) and PEDF (anti-angiogenic) were found to have altered their expressions in accordance with the extracellular environment. BMSCs treated with the hypoxia-mimicking agent CoCl2 expressed more VEGF and less PEDF and enhanced the vascularization of subcutaneous implants in vivo. Based on the findings of the second part, the CoCl2 pre-treated BMSCs were used to construct periosteum, and the in vivo vascularization and osteogenesis of the constructed periosteum were assessed in the third part of this project. The findings of the third part revealed that BMSCs pre-treated with CoCl2 could enhance both ectopic and orthotopic osteogenesis of BMSCs-derived osteoblasts and vascularization at the early osteogenic stage, and the endothelial cells (HUVECs), which were used as positive control, were only capable of promoting osteogenesis after four-weeks. The subcutaneous area of the mouse is most likely inappropriate for assessing new bone formation on collagen scaffolds. This study demonstrated the potential application of CoCl2 pre-treated BMSCs in the tissue engineering not only for periosteum but also bone or other vascularized tissues. In summary, the structure and cell populations in periosteum are age-related, site-specific and closely linked with bone health status. BMSCs as a stem cell source for periosteum engineering are not endothelial cell progenitors but regulators, and CoCl2-treated BMSCs expressed more VEGF and less PEDF. These CoCl2-treated BMSCs enhanced both vascularization and osteogenesis in constructed periosteum transplanted in vivo.

Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

Fabrication using a rapid prototyping system and in vitro characterization of PEG-PCL-PLA scaffolds for tissue engineering

n the field of tissue engineering new polymers are needed to fabricate scaffolds with specific properties depending on the targeted tissue. This work aimed at designing and developing a 3D scaffold with variable mechanical strength, fully interconnected porous network, controllable hydrophilicity and degradability. For this, a desktop-robot-based melt-extrusion rapid prototyping technique was applied to a novel tri-block co-polymer, namely poly(ethylene glycol)-block-poly(epsi-caprolactone)-block-poly(DL-lactide), PEG-PCL-P(DL)LA. This co-polymer was melted by electrical heating and directly extruded out using computer-controlled rapid prototyping by means of compressed purified air to build porous scaffolds. Various lay-down patterns (0/30/60/90/120/150°, 0/45/90/135°, 0/60/120° and 0/90°) were produced by using appropriate positioning of the robotic control system. Scanning electron microscopy and micro-computed tomography were used to show that 3D scaffold architectures were honeycomb-like with completely interconnected and controlled channel characteristics. Compression tests were performed and the data obtained agreed well with the typical behavior of a porous material undergoing deformation. Preliminary cell response to the as-fabricated scaffolds has been studied with primary human fibroblasts. The results demonstrated the suitability of the process and the cell biocompatibility of the polymer, two important properties among the many required for effective clinical use and efficient tissue-engineering scaffolding.

Assimilating cell sheets and hybrid scaffolds for dermal tissue engineering

Cell sheets can be used to produce neo-tissue with mature extracellular matrix. However, extensive contraction of cell sheets remains a problem. We devised a technique to overcome this problem and applied it to tissue engineer a dermal construct. Human dermal fibroblasts were cultured with poly(lactic-co-glycolic acid)-collagen meshes and collagen-hyaluronic acid foams. Resulting cell sheets were folded over the scaffolds to form dermal constructs. Human keratinocytes were cultured on these dermal constructs to assess their ability to support bilayered skin regeneration. Dermal constructs produced with collagen-hyaluronic acid foams showed minimal contraction, while those with poly(lactic-co-glycolic acid)-collagen meshes curled up. Cell proliferation and metabolic activity profiles were characterized with PicoGreen and AlamarBlue assays, respectively. Fluorescent labeling showed high cell viability and F-actin expression within the constructs. Collagen deposition was detected by immunocytochemistry and electron microscopy. Transforming Growth Factor-alpha and beta1, Keratinocyte Growth Factor and Vascular Endothelial Growth Factor were produced at various stages of culture, measured by RT-PCR and ELISA. These results indicated that assimilating cell sheets with mechanically stable scaffolds could produce viable dermal-like constructs that do not contract. Repeated enzymatic treatment cycles for cell expansion is unnecessary, while the issue of poor cell seeding efficiency in scaffolds is eliminated.

Vitrification as a prospect for cryopreservation of tissue-engineered constructs

Cryopreservation plays a significant function in tissue banking and will presume yet larger value when more and more tissue-engineered products will routinely enter the clinical arena. The most common concept underlying tissue engineering is to combine a scaffold (cellular solids) or matrix (hydrogels) with living cells to form a tissue-engineered construct (TEC) to promote the repair and regeneration of tissues. The scaffold and matrix are expected to support cell colonization, migration, growth and differentiation, and to guide the development of the required tissue. The promises of tissue engineering, however, depend on the ability to physically distribute the products to patients in need. For this reason, the ability to cryogenically preserve not only cells, but also TECs, and one day even whole laboratory-produced organs, may be indispensable. Cryopreservation can be achieved by conventional freezing and vitrification (ice-free cryopreservation). In this publication we try to define the needs versus the desires of vitrifying TECs, with particular emphasis on the cryoprotectant properties, suitable materials and morphology. It is concluded that the formation of ice, through both direct and indirect effects, is probably fundamental to these difficulties, and this is why vitrification seems to be the most promising modality of cryopreservation

Fumaric acid monoethyl ester-functionalized poly(D,L-Lactide)/N-vinyl-2- pyrrolidone Resins for the preparation of tissue engineering scaffolds by stereolithography

Polymer networks were prepared by photocross-linking fumaric acid monoethyl ester (FAME) functionalized, three-armed poly(D,L-lactide) oligomers using Af-vinyl-2-pyrrolidone (NVP) as diluent and comonomer. The use of NVP together with FAME-functionalized oligomers resulted in copolymerization at high rates, and networks with gel contents in excess of 90 were obtained. The hydrophilicity of the poly(D,L-lactide) networks increases with increasing amounts of NVP, networks containing 50 wt of NVP absorbed 40 of water. As the amount of NVP was increased from 30 to 50 wt , the Young's modulus after equilibration in water decreased from 0.8 to 0.2 GPa, as opposed to an increase from 1.5 to 2.1 GPa in the dry state. Mouse preosteoblasts readily adhered and spread onto all prepared networks. Using stereolithography, porous structures with a well-defined gyroid architecture were prepared from these novel materials. This allows the preparation of tissue engineering scaffolds with optimized pore architecture and tunable material properties.

A poly(D,L-lactide) resin for the preparation of tissue engineering scaffolds by stereolithography

Porous polylactide constructs were prepared by stereolithography, for the first time without the use of reactive diluents. Star-shaped poly(D,L-lactide) oligomers with 2, 3 and 6 arms were synthesised, end-functionalised with methacryloyl chloride and photocrosslinked in the presence of ethyl lactate as a non-reactive diluent. The molecular weights of the arms of the macromers were 0.2, 0.6, 1.1 and 5 kg/mol, allowing variation of the crosslink density of the resulting networks. Networks prepared from macromers of which the molecular weight per arm was 0.6 kg/mol or higher had good mechanical properties, similar to linear high molecular weight poly(D,L-lactide). A resin based on a 2-armed poly(D,L-lactide) macromer with a molecular weight of 0.6 kg/mol per arm (75 wt%), ethyl lactate (19 wt%), photo-initiator (6 wt%), inhibitor and dye was prepared. Using this resin, films and computer-designed porous constructs were accurately fabricated by stereolithography. Pre-osteoblasts showed good adherence to these photocrosslinked networks. The proliferation rate on these materials was comparable to that on high molecular weight poly(D,L-lactide) and tissue culture polystyrene.

Mathematically defined tissue engineering scaffold architectures prepared by stereolithography

The technologies employed for the preparation of conventional tissue engineering scaffolds restrict the materials choice and the extent to which the architecture can be designed. Here we show the versatility of stereolithography with respect to materials and freedom of design. Porous scaffolds are designed with computer software and built with either a poly(d,l-lactide)-based resin or a poly(d,l-lactide-co-ε-caprolactone)-based resin. Characterisation of the scaffolds by micro-computed tomography shows excellent reproduction of the designs. The mechanical properties are evaluated in compression, and show good agreement with finite element predictions. The mechanical properties of scaffolds can be controlled by the combination of material and scaffold pore architecture. The presented technology and materials enable an accurate preparation of tissue engineering scaffolds with a large freedom of design, and properties ranging from rigid and strong to highly flexible and elastic.

A two-compartment mechanochemical model of the roles of transforming growth factor-beta and tissue tension in dermal wound healing

The repair of dermal tissue is a complex process of interconnected phenomena, where cellular, chemical and mechanical aspects all play a role, both in an autocrine and in a paracrine fashion. Recent experimental results have shown that transforming growth factor-beta (TGF-beta) and tissue mechanics play roles in regulating cell proliferation, differentiation and the production of extracellular materials. We have developed a 1D mathematical model that considers the interaction between the cellular, chemical and mechanical phenomena, allowing the combination of TGF-beta and tissue stress to inform the activation of fibroblasts to myofibroblasts. Additionally, our model incorporates the observed feature of residual stress by considering the changing zero-stress state in the formulation for effective strain. Using this model, we predict that the continued presence of TGF-beta in dermal wounds will produce contractures due to the persistence of myofibroblasts; in contrast, early elimination of TGF-beta significantly reduces the myofibroblast numbers resulting in an increase in wound size. Similar results were obtained by varying the rate at which fibroblasts differentiate to myofibroblasts and by changing the myofibroblast apoptotic rate. Taken together, the implication is that elevated levels of myofibroblasts is the key factor behind wounds healing with excessive contraction, suggesting that clinical strategies which aim to reduce the myofibroblast density may reduce the appearance of contractures.

Development of a 3-dimensional human skin equivalent wound model for investigating novel wound healing therapies

Numerous difficulties are associated with the conduct of preclinical studies related to skin and wound repair. Use of small animal models such as rodents is not optimal because of their physiological differences to human skin and mode of wound healing. Although pigs have previously been used because of their human-like mode of healing, the expense and logistics related to their use also renders them suboptimal. In view of this, alternatives are urgently required to advance the field. The experiments reported herein were aimed at developing and validating a simple, reproducible, three-dimensional ex vivo de-epidermised dermis human skin equivalent wound model for the preclinical evaluation of novel wound therapies. Having established that the human skin equivalent wound model does in fact “heal," we tested the effect of two novel wound healing therapies. We also examined the utility of the model for studies exploring the mechanisms underpinning these therapies. Taken together the data demonstrate that these new models will have wide-spread application for the generation of fundamental new information on wound healing processes and also hold potential in facilitating preclinical optimization of dosage, duration of therapies, and treatment strategies prior to clinical trials.