Radial Basis Functions: Biomedical Applications and Parallelization

Radial basis function (RBF) is a real-valued function whose values depend only on the distances between an interpolation point and a set of user-specified points called centers. RBF interpolation is one of the primary methods to reconstruct functions from multi-dimensional scattered data. Its abilities to generalize arbitrary space dimensions and to provide spectral accuracy have made it particularly popular in different application areas, including but not limited to: finding numerical solutions of partial differential equations (PDEs), image processing, computer vision and graphics, deep learning and neural networks, etc. The present thesis discusses three applications of RBF interpolation in biomedical engineering areas: (1) Calcium dynamics modeling, in which we numerically solve a set of PDEs by using meshless numerical methods and RBF-based interpolation techniques; (2) Image restoration and transformation, where an image is restored from its triangular mesh representation or transformed under translation, rotation, and scaling, etc. from its original form; (3) Porous structure design, in which the RBF interpolation used to reconstruct a 3D volume containing porous structures from a set of regularly or randomly placed points inside a user-provided surface shape. All these three applications have been investigated and their effectiveness has been supported with numerous experimental results. In particular, we innovatively utilize anisotropic distance metrics to define the distance in RBF interpolation and apply them to the aforementioned second and third applications, which show significant improvement in preserving image features or capturing connected porous structures over the isotropic distance-based RBF method. Beside the algorithm designs and their applications in biomedical areas, we also explore several common parallelization techniques (including OpenMP and CUDA-based GPU programming) to accelerate the performance of the present algorithms. In particular, we analyze how parallel programming can help RBF interpolation to speed up the meshless PDE solver as well as image processing. While RBF has been widely used in various science and engineering fields, the current thesis is expected to trigger some more interest from computational scientists or students into this fast-growing area and specifically apply these techniques to biomedical problems such as the ones investigated in the present work

Structural Origin of Mechanical Prowess In Conch Shells

Conch shells are natural nanocomposites with an exquisite multiscale hierarchical architecture which exhibit coupled ultrahigh mechanical strength and toughness. What materials design strategy renders conch shells such mechanical prowess? In this study, micro/nanoscale structural and mechanical characterization of conch shells (Busycon carica) has been carried out. We demonstrate, for the first time, direct evidence that the previously claimed single-crystal third-order lamellae - the basic building blocks in conch shells are essentially assembled with aragonite nanoparticles of the size ranging from 20 to 45 nm. The third-order lamellae exhibit not only elasticity but also plasticity with the strain up to 0.7% upon mechanical loading, due to the unique nanoparticle-biopolymer architecture in which the biopolymer mediates the rotation of aragonite nanoparticles in response to external loading. Our finding - metal like deformation behavior overturns the previous assumption that aragonite lamellae are brittle in nature. The three-order crossed-lamellar architecture interlocks cracks via crack deflection along the biopolymer interfaces in a three-dimensional manner. The interlocking mechanism and the plasticity of third-order lamellae jointly contribute to the remarkable mechanical prowess. We report that conch shells display an unusual resilience against high strain rate predatory-attack vis-à-vis under quasi-static loading. Upon dynamic loading, conch shells trigger a new defense mechanism - intra-lamella fracture, involving nanoparticle rotation and formation of trapped dislocations, which differs from the inter-lamella fracture damage under quasi-static violation. Another fascinating design principle with the curve-shaped third-order lamellae is uncovered in conch spines. Such architecture enhances the fracture strength up to 30 % compared with that of conch shell bodies with straight reinforcements, unveiling the roles of spines in protection from predators. Moreover, the effects of electron beam irradiation and heat treatment on the structural and mechanical stability of conch shells were investigated. Both conditions can induce phase transformation from aragonite to calcite, to lime, altering the aforementioned properties

Crystallization of carbonate and sulfate minerals in organic matrices

Biological carbonate hard tissues, such as the shell of the bivalve Mytilus edulis, are composites of biopolymers and minerals. M. edulis has two distinct layers, the outer layer consists of fibrous calcite and the inner layer is composed of nacreous aragonite. Close to the interface between nacreous aragonite and fibrous calcite, a 1-2 micrometer wide zone exists that consists of granular aragonite. Aragonite granules and tablets as well as calcite fibrous are embedded into matrix biopolymers. In order to understand the composite nature of these hard tissues, biomimetic experiments using hydrogels were carried out. Hydrogels are able to model biogenic matrix environments due to their ability to confine space and to determine diffusion rates, local concentrations and supersaturation of the solutes. Hydrogels have local crystallization microenvironment that is distinguished from that in solution by confinement of solutes in the hydrogel pores. However, hydorgels only mimic biological extracellular matrices to some extent as the hydrogel fiber organization lacks any order, unlike it is in the case of the cholesteric liquid phase, e. g. chitin. The hydrogel strength is adjustable by changing its solid content. It further increases local hydrogel fiber co-aligments that to some extent will mimic organic matrices in biological hard tissues. Different kinds of hydrogels were used to study calcite crystallization (silica, agarose, gelatin). As each hydrogel has different characteristics, hydrogels can act differently in promoting or inhibiting crystallization. Hydrogels have an ability to mechanically impede the growth of a crystal depending on the strength of the hydrogel. Gelatin hydrogel is a poly-peptide material derived from natural collagen through hydrolytic degradation. The hyrolitic degradation breaks the triple-helix structure of collagen into single-strand molecules. Gelatin contains both acidic and basic amino acids with isoelectric point values near ∼5 and with predominance of acidic moieties. Agarose hydrogel is a linear polysaccharide extracted from marine red algae. It consists of beta-1,3 linked D-galactose and alpha-1,4 linked 3,6-anhydro-alpha-L-galactose residues. Gelatin and agarose hydrogels are composed of a fibrous structure that have varying mesh void dimensions depending on the hydrogel solid content. Hydrogel with 2.5 wt % gelatin solid content exerts less pressure against the growing calcite crystal aggregate than a hydrogel with 10 wt % gelatin solid content. Silica hydrogel does not exert strong pressure against the growing calcite crystal aggregate due to its nature as it is composed of minute (less than 20 nm) sized spherical particles that do not appear to form a network. The hydrogel strength together with the growth rate of the crystal defines the amount of incorporated hydrogel into the growing calcite crystal aggregate such that a strong hydrogel will incorporate more gel into the calcite crystal than a weak hydrogel. Calcite grown in Mg-free silica hydrogels has a rhombohedral shape and is elongated on the c-axis. It grows as dumbbell-shaped aggregates in the presence of Mg. Silica hydrogel either Mg-free or Mg-bearing does not give a major influence on the co-orientation of the obtained crystal aggregate. Calcite grown in Mg-free agarose has two morphologies: rhombohedron-shaped calcite crystals and calcite radial aggregates. Calcite grown in Mg-bearing agarose has sheaf-like and peanut like morphologies. The presence of Mg in agarose influences the co-orientation of calcite crystals within calcite Mg-bearing agarose composites. The calcite/Mg-free agarose composite has several large crystal subunits while the calcite/Mg-bearing agarose composite shows a spherulitic microstructure. In the case of gelatin hydrogel, the precipitate consists of calcite aggregates that have a variety of features i.e. the formation of mosaic crystals and mesocrystal-like subunits in one aggregate, the formation of aggregates with a fan-like distribution of the c-axis orientation and the formation of spherulitic aggregates. The formation of aggregates with different characteristic in the subunits can be explained as a result of a combination between local differences in gelatin matrix arrangement and physicochemical conditions such as the change in Mg/Ca ratio, pH, saturation, etc. The development of a fan-like distribution of the c-axes orientation in the calcite aggregate subunits can be explained as a result of Mg intrasectorial zoning. A different degree of Mg incorporation in different growth steps will accumulate misfit strain in the lattice. This misfit strain could be released through the formation of dislocations at regular intervals, such that small-angle boundaries develop. This growth further leads to the extreme split growth and the formation of fan-like and spherulitic crystal aggregates. The etching experiments of calcite/hydrogel composites reveal the structure of the incorporated hydrogel within the calcite crystals and aggregates. In the case of Mg-bearing silica hydrogel more silica hydrogel is incorporated into the calcite crystal than in the case of Mg-free silica hydrogel. Thick hydrogel membranes are observed when Mg-free gelatin and agarose hydrogels are used. These membranes do not occur when Mg is present. The formation of these membranes in Mg-free gelatin and agarose hydrogels is a result of an accumulation of the hydrogel fibers that are driven back by growing crystals or aggregates. The stiffness of the gelatin and agarose hydrogel fibers increase as Mg is added into the hydrogel. The hydrogel becomes stiffer and exerts more pressure against the growing aggregates. No hydrogel membranes are observed in aggregates grown in Mg-bearing gelatin and in agarose hydrogels. On the basis of biopolymer and mineral composites, gypsum (CaSO4)/cellulose fiber composites were prepared. The purpose of the addition of cellulose fiber to gypsum was to create a composite with a high ecological value and interesting mechanical properties such as high Young’s modulus, high bending strength and high compression strength. The cellulose fiber affects the mechanical property of the composites depending on the fiber characteristics, e.g. the nature of the cellulose (natural or synthetic), water retention value, degree of swelling, etc. Lyocell fiber, a synthetic fiber, is found to be able to increase the Young’s modulus of the final composite

European Union Timber Regulation Impact on International Timber Markets

The trade of illegal timber, often from illegal logging, has severe environmental, social and economic consequences. The EU’s response to this problem came with the Forest Law Enforcement, Governance and Trade (FLEGT) Action Plan, with its specific goal to end illegal logging, thereby improving sustainability of forest resources. In March 2013, an additional step was taken by implementing the EU Timber Regulation (EUTR). The EUTR requires proof of timber’s origin and legality to ensure that no illegal timber is imported into the EU. To this end the EU intends to block imports of any wood or wood product which comes from unknown sources. Certification of sustainable forest management will help EU importers minimize risk, which is an essential part of their required due diligence system. Monitoring organizations are established to assist trade associations and businesses to construct comprehensive due diligence systems. National competent authorities are designated to follow the trade of the new FLEGT-licensed timber and timber products. In the first year of the EUTR there are positive impacts, of which the most important is awareness of the disastrous situation with illegal logging, driven by exports of illegal timber. Another positive development is tropical timber exporters documenting the legality of their wood exports. Yet another positive feature is establishment of due diligence systems by EU importers. However, there are considerable problems for ensuring legal trade; for example the lack of comprehensive documentation of origin and legality. Analysis of recent trends establishes changes in the European timber trade in terms of sourcing, substitution, diversion to less-demanding countries. Short-term forecasts of market trends and changes will enable further policy assessment to achieve the objectives of improved legality in international timber markets.JRC.H.3-Forest Resources and Climat

A new mixed model based on the enhanced-Refined Zigzag Theory for the analysis of thick multilayered composite plates

The Refined Zigzag Theory (RZT) has been widely used in the numerical analysis of multilayered and sandwich plates in the last decay. It has been demonstrated its high accuracy in predicting global quantities, such as maximum displacement, frequencies and buckling loads, and local quantities such as through-the-thickness distribution of displacements and in-plane stresses [1,2]. Moreover, the C0 continuity conditions make this theory appealing to finite element formulations [3]. The standard RZT, due to the derivation of the zigzag functions, cannot be used to investigate the structural behaviour of angle-ply laminated plates. This drawback has been recently solved by introducing a new set of generalized zigzag functions that allow the coupling effect between the local contribution of the zigzag displacements [4]. The newly developed theory has been named enhanced Refined Zigzag Theory (en- RZT) and has been demonstrated to be very accurate in the prediction of displacements, frequencies, buckling loads and stresses. The predictive capabilities of standard RZT for transverse shear stress distributions can be improved using the Reissner’s Mixed Variational Theorem (RMVT). In the mixed RZT, named RZT(m) [5], the assumed transverse shear stresses are derived from the integration of local three-dimensional equilibrium equations. Following the variational statement described by Auricchio and Sacco [6], the purpose of this work is to implement a mixed variational formulation for the en-RZT, in order to improve the accuracy of the predicted transverse stress distributions. The assumed kinematic field is cubic for the in-plane displacements and parabolic for the transverse one. Using an appropriate procedure enforcing the transverse shear stresses null on both the top and bottom surface, a new set of enhanced piecewise cubic zigzag functions are obtained. The transverse normal stress is assumed as a smeared cubic function along the laminate thickness. The assumed transverse shear stresses profile is derived from the integration of local three-dimensional equilibrium equations. The variational functional is the sum of three contributions: (1) one related to the membrane-bending deformation with a full displacement formulation, (2) the Hellinger-Reissner functional for the transverse normal and shear terms and (3) a penalty functional adopted to enforce the compatibility between the strains coming from the displacement field and new “strain” independent variables. The entire formulation is developed and the governing equations are derived for cases with existing analytical solutions. Finally, to assess the proposed model’s predictive capabilities, results are compared with an exact three-dimensional solution, when available, or high-fidelity finite elements 3D models. References: [1] Tessler A, Di Sciuva M, Gherlone M. Refined Zigzag Theory for Laminated Composite and Sandwich Plates. NASA/TP- 2009-215561 2009:1–53. [2] Iurlaro L, Gherlone M, Di Sciuva M, Tessler A. Assessment of the Refined Zigzag Theory for bending, vibration, and buckling of sandwich plates: a comparative study of different theories. Composite Structures 2013;106:777–92. https://doi.org/10.1016/j.compstruct.2013.07.019. [3] Di Sciuva M, Gherlone M, Iurlaro L, Tessler A. A class of higher-order C0 composite and sandwich beam elements based on the Refined Zigzag Theory. Composite Structures 2015;132:784–803. https://doi.org/10.1016/j.compstruct.2015.06.071. [4] Sorrenti M, Di Sciuva M. An enhancement of the warping shear functions of Refined Zigzag Theory. Journal of Applied Mechanics 2021;88:7. https://doi.org/10.1115/1.4050908. [5] Iurlaro L, Gherlone M, Di Sciuva M, Tessler A. A Multi-scale Refined Zigzag Theory for Multilayered Composite and Sandwich Plates with Improved Transverse Shear Stresses, Ibiza, Spain: 2013. [6] Auricchio F, Sacco E. Refined First-Order Shear Deformation Theory Models for Composite Laminates. J Appl Mech 2003;70:381–90. https://doi.org/10.1115/1.1572901

Crystallization of carbonate and sulfate minerals in organic matrices

Biological carbonate hard tissues, such as the shell of the bivalve Mytilus edulis, are composites of biopolymers and minerals. M. edulis has two distinct layers, the outer layer consists of fibrous calcite and the inner layer is composed of nacreous aragonite. Close to the interface between nacreous aragonite and fibrous calcite, a 1-2 micrometer wide zone exists that consists of granular aragonite. Aragonite granules and tablets as well as calcite fibrous are embedded into matrix biopolymers. In order to understand the composite nature of these hard tissues, biomimetic experiments using hydrogels were carried out. Hydrogels are able to model biogenic matrix environments due to their ability to confine space and to determine diffusion rates, local concentrations and supersaturation of the solutes. Hydrogels have local crystallization microenvironment that is distinguished from that in solution by confinement of solutes in the hydrogel pores. However, hydorgels only mimic biological extracellular matrices to some extent as the hydrogel fiber organization lacks any order, unlike it is in the case of the cholesteric liquid phase, e. g. chitin. The hydrogel strength is adjustable by changing its solid content. It further increases local hydrogel fiber co-aligments that to some extent will mimic organic matrices in biological hard tissues. Different kinds of hydrogels were used to study calcite crystallization (silica, agarose, gelatin). As each hydrogel has different characteristics, hydrogels can act differently in promoting or inhibiting crystallization. Hydrogels have an ability to mechanically impede the growth of a crystal depending on the strength of the hydrogel. Gelatin hydrogel is a poly-peptide material derived from natural collagen through hydrolytic degradation. The hyrolitic degradation breaks the triple-helix structure of collagen into single-strand molecules. Gelatin contains both acidic and basic amino acids with isoelectric point values near ∼5 and with predominance of acidic moieties. Agarose hydrogel is a linear polysaccharide extracted from marine red algae. It consists of beta-1,3 linked D-galactose and alpha-1,4 linked 3,6-anhydro-alpha-L-galactose residues. Gelatin and agarose hydrogels are composed of a fibrous structure that have varying mesh void dimensions depending on the hydrogel solid content. Hydrogel with 2.5 wt % gelatin solid content exerts less pressure against the growing calcite crystal aggregate than a hydrogel with 10 wt % gelatin solid content. Silica hydrogel does not exert strong pressure against the growing calcite crystal aggregate due to its nature as it is composed of minute (less than 20 nm) sized spherical particles that do not appear to form a network. The hydrogel strength together with the growth rate of the crystal defines the amount of incorporated hydrogel into the growing calcite crystal aggregate such that a strong hydrogel will incorporate more gel into the calcite crystal than a weak hydrogel. Calcite grown in Mg-free silica hydrogels has a rhombohedral shape and is elongated on the c-axis. It grows as dumbbell-shaped aggregates in the presence of Mg. Silica hydrogel either Mg-free or Mg-bearing does not give a major influence on the co-orientation of the obtained crystal aggregate. Calcite grown in Mg-free agarose has two morphologies: rhombohedron-shaped calcite crystals and calcite radial aggregates. Calcite grown in Mg-bearing agarose has sheaf-like and peanut like morphologies. The presence of Mg in agarose influences the co-orientation of calcite crystals within calcite Mg-bearing agarose composites. The calcite/Mg-free agarose composite has several large crystal subunits while the calcite/Mg-bearing agarose composite shows a spherulitic microstructure. In the case of gelatin hydrogel, the precipitate consists of calcite aggregates that have a variety of features i.e. the formation of mosaic crystals and mesocrystal-like subunits in one aggregate, the formation of aggregates with a fan-like distribution of the c-axis orientation and the formation of spherulitic aggregates. The formation of aggregates with different characteristic in the subunits can be explained as a result of a combination between local differences in gelatin matrix arrangement and physicochemical conditions such as the change in Mg/Ca ratio, pH, saturation, etc. The development of a fan-like distribution of the c-axes orientation in the calcite aggregate subunits can be explained as a result of Mg intrasectorial zoning. A different degree of Mg incorporation in different growth steps will accumulate misfit strain in the lattice. This misfit strain could be released through the formation of dislocations at regular intervals, such that small-angle boundaries develop. This growth further leads to the extreme split growth and the formation of fan-like and spherulitic crystal aggregates. The etching experiments of calcite/hydrogel composites reveal the structure of the incorporated hydrogel within the calcite crystals and aggregates. In the case of Mg-bearing silica hydrogel more silica hydrogel is incorporated into the calcite crystal than in the case of Mg-free silica hydrogel. Thick hydrogel membranes are observed when Mg-free gelatin and agarose hydrogels are used. These membranes do not occur when Mg is present. The formation of these membranes in Mg-free gelatin and agarose hydrogels is a result of an accumulation of the hydrogel fibers that are driven back by growing crystals or aggregates. The stiffness of the gelatin and agarose hydrogel fibers increase as Mg is added into the hydrogel. The hydrogel becomes stiffer and exerts more pressure against the growing aggregates. No hydrogel membranes are observed in aggregates grown in Mg-bearing gelatin and in agarose hydrogels. On the basis of biopolymer and mineral composites, gypsum (CaSO4)/cellulose fiber composites were prepared. The purpose of the addition of cellulose fiber to gypsum was to create a composite with a high ecological value and interesting mechanical properties such as high Young’s modulus, high bending strength and high compression strength. The cellulose fiber affects the mechanical property of the composites depending on the fiber characteristics, e.g. the nature of the cellulose (natural or synthetic), water retention value, degree of swelling, etc. Lyocell fiber, a synthetic fiber, is found to be able to increase the Young’s modulus of the final composite

A study of change in human trabecular bone structure with age and during osteoporosis

The objective of this work was to develop new techniques to view trabecular bone three-dimensionally, and to study its structure and the changes that occur with age and in osteoporosis; the methods used included 3D methods in the SEM, laser confocal microscopy, pseudo-holograms and a "continuous motion parallax method". A detailed analysis of trabecular bone from fourth lumbar vertebral bodies used macro-stereophotographs produced by tilting a sample 10°. Models are proposed for both normal and osteoporotic architecture. A quantitative analysis of the lengths of horizontally oriented trabeculae was carried out. A significant decrease in the number of both vertically and horizontally oriented trabeculae was found. The importance of the influence of different developmental patterns on the formation of the normal structure and of the changing vascularisation on osteoporotic structure are emphasised. Two-dimensional fast Fourier transform methods were employed to study changes in the spatial frequency of trabeculae as a function of orientation. A decrease in spatial frequency was observed in both sexes, but in males this was evident only after the mid-sixth decade in the limited sample studied. Contoured power spectra discriminated different trabecular patterns and the intensity mapping of optical density provided volume density information. Templated reverse transformation was used to study individual orientations of trabeculae. Changes in the quality of trabecular bone with age were also investigated using techniques that analyse bone before and after removal of unmineralised matrix. All specimens were less stiff after removal of osteoid; this was more marked in older specimens. Locally defective mineralisation would explain the changed behaviour observed in some old and osteoporotic specimens. Trabecular fracture patterns had a strong relationship to architecture and microstructure. Scanning electron microscopy was used to study trabecular surfaces. An uncoupling between resorption and formation was evident in older specimens. Two resorption patterns responsible for thinning and perforation and removal trabecular elements were identified. Trabecular microfractures were also investigated

A Combinatorial Method for Discovery of BaTiO3-based Positive Temperature Coefficient Resistors

PhDThe conventional materials discovery is a kind of empirical (“trial and error”) science that of handling one sample at a time in the processes of synthesis and characterization. However, combinatorial methodologies present the possibility of a vastly increased rate of discovery of novel materials which will require a great deal of conventional laboratory work. The work presented in this thesis, involved the practice of a conceptual framework of combinatorial research on BaTiO3-based positive temperature coefficient resistor (PTCR) materials. Those including (i) fabrication of green BaTiO3 base discs via high-throughput dip-pen printing method. Preparation and formulation of BaTiO3 inks (selection of dispersant and binder/volume fraction) were studied. The shape of drying residues and the morphogenesis control of droplet drying were discussed. (ii) investigation of a fast droplet-doping method, which induced the dopant precursor solution infiltrating into the porous BT base disc. Various characterization methods were used to examine the dopant distribution in the body of disc. (iii) devising a high-throughput electrical measurement system including an integrated unit of temperature control and automatic measurement operation, and an arrayed multichannel jig. (iv) synthesis of donor-doped BaTiO3 libraries, which involved lanthanum, erbium, yttrium as donor elements and manganese as an acceptor dopant element respectively. Their temperature dependant resistivities were also explored. The work successfully developed an integrated tool including high-throughput synthesis of a large batch of libraries and high-throughput electrical property measurement for combinatorial research on BaTiO3-based PTCR ceramics. The Abstract ii combinatorial method, thus validated, has the potential to deliver dopant-doped BTbased PTCR libraries rapidly with a very wide range of dopant mixtures and concentrations for electrical property measurement and deserves to be applied to other low level dopant ceramic systems. These approaches are novel and paving the way for other new materials selection and materials research

KINE[SIS]TEM'17 From Nature to Architectural Matter

Kine[SiS]tem – From Kinesis + System. Kinesis is a non-linear movement or activity of an organism in response to a stimulus. A system is a set of interacting and interdependent agents forming a complex whole, delineated by its spatial and temporal boundaries, influenced by its environment. How can architectural systems moderate the external environment to enhance comfort conditions in a simple, sustainable and smart way? This is the starting question for the Kine[SiS]tem’17 – From Nature to Architectural Matter International Conference. For decades, architectural design was developed despite (and not with) the climate, based on mechanical heating and cooling. Today, the argument for net zero energy buildings needs very effective strategies to reduce energy requirements. The challenge ahead requires design processes that are built upon consolidated knowledge, make use of advanced technologies and are inspired by nature. These design processes should lead to responsive smart systems that deliver the best performance in each specific design scenario. To control solar radiation is one key factor in low-energy thermal comfort. Computational-controlled sensor-based kinetic surfaces are one of the possible answers to control solar energy in an effective way, within the scope of contradictory objectives throughout the year.FC