Multiphasic, multistructured and hierarchical strategies for cartilage regeneration

Cartilage tissue is a complex nonlinear, viscoelastic, anisotropic, and multiphasic material with a very low coefficient of friction, which allows to withstand millions of cycles of joint loading over decades of wear. Upon damage, cartilage tissue has a low self-reparative capacity due to the lack of neural connections, vascularization, and a latent pool of stem/chondroprogenitor cells. Therefore, the healing of articular cartilage defects remains a significant clinical challenge, affecting millions of people worldwide. A plethora of biomaterials have been proposed to fabricate devices for cartilage regeneration, assuming a wide range of forms and structures, such as sponges, hydrogels, capsules, fibers, and microparticles. In common, the fabricated devices were designed taking in consideration that to fully achieve the regeneration of functional cartilage it is mandatory a well-orchestrated interplay of biomechanical properties, unique hierarchical structures, extracellular matrix (ECM), and bioactive factors. In fact, the main challenge in cartilage tissue engineering is to design an engineered device able to mimic the highly organized zonal architecture of articular cartilage, specifically its spatiomechanical properties and ECM composition, while inducing chondrogenesis, either by the proliferation of chondrocytes or by stimulating the chondrogenic differentiation  of stem/chondro-progenitor cells. In this chapter we present the recent advances in the development of innovative and complex biomaterials that fulfill the required structural key elements for cartilage regeneration. In particular, multiphasic, multiscale, multilayered, and hierarchical strategies composed by single or multiple biomaterials combined in a welldefined structure will be addressed. Those strategies include biomimetic scaffolds mimicking the structure of articular cartilage or engineered scaffolds as models of research to fully understand the biological mechanisms that influence the regeneration of cartilage tissue.

Nonlinear behavior of gelatin networks reveals a hierarchical structure

We investigate the strain hardening behavior of various gelatin networks-namely physical gelatin gel, chemically cross-linked gelatin gel, and a hybrid gel made of a combination of the former two-under large shear deformations using the pre-stress, strain ramp, and large amplitude oscillations shear protocols. Further, the internal structures of physical gelatin gels and chemically cross-linked gelatin gels were characterized by small angle neutron scattering (SANS) to enable their internal structures to be correlated with their nonlinear rheology. The Kratky plots of SANS data demonstrate the presence of small cross-linked aggregates within the chemically cross-linked network whereas, in the physical gelatin gels, a relatively homogeneous structure is observed. Through model fitting to the scattering data, we were able to obtain structural parameters, such as the correlation length (ξ), the cross-sectional polymer chain radius (Rc) and the fractal dimension (df) of the gel networks. The fractal dimension df obtained from the SANS data of the physical and chemically cross-linked gels is 1.31 and 1.53, respectively. These values are in excellent agreement with the ones obtained from a generalized nonlinear elastic theory that has been used to fit the stress-strain curves. The chemical cross-linking that generates coils and aggregates hinders the free stretching of the triple helix bundles in the physical gels.

Closed hybrid hierarchical reservoirs based on the deconstruction of the cellular native microenvironment

The stem cell niche organization and dynamics provide valuable cues for the development of mimetic environments that could have potential to stimulate the regenerative process. We propose the use of biodegradable biomaterials to produce closed miniaturised structures able to encapsulate different cell types or bioactive molecules. In particular, capsules are fabricated using the so-called layer-by-layer technology, where the consecutive (nano-sized) layers are well stabilized by electrostatic interactions or other weak forces. Using alginate-based spherical templates containing cells or other elements (e.g. proteins, magnetic nanoparticles, microparticles) it is possible to produce liquefied capsules that may entrap the entire cargo under mild conditions. The inclusion of liquefied micropcapsules may be used to produce hierarchical compartmentalised systems for the delivery of bioactive agents. The presence of solid microparticles inside such capsules offers adequate surface area for adherent cell attachment increasing the biological performance of these hierarchical systems, while maintain both permeability and injectability. We demonstrated that the encapsulation of distinct cell types (including mesenchymal stem cells and endothelial cells) enhances the osteogenic capability of this system, that could be useful in bone tissue engineering applications.

Superhydrophobic surfaces as a tool for the fabrication of hierarchical spherical polymeric carriers

Hierarchical polymeric carriers with high encapsulation efficiencies are fabricated via a biocompatible strategy developed using superhydrophobic (SH) surfaces. The carries are obtained by the incorporation of cell/BSA-loaded dextran-methacrylate (DEXT-MA) microparticles into alginate (ALG) macroscopic beads. Engineered devices like these are expected to boost the development of innovative and customizable systems for biomedical and biotechnological purposes.

Hierarchical modelling of timber reference properties using probabilistic methods: Maximum Likelihood Method, Bayesian Methods and Probability Networks

In recent decades, an increased interest has been evidenced in the research on multi-scale hierarchical modelling in the field of mechanics, and also in the field of wood products and timber engineering. One of the main motivations for hierar-chical modelling is to understand how properties, composition and structure at lower scale levels may influence and be used to predict the material properties on a macroscopic and structural engineering scale. This chapter presents the applicability of statistic and probabilistic methods, such as the Maximum Likelihood method and Bayesian methods, in the representation of timber’s mechanical properties and its inference accounting to prior information obtained in different importance scales. These methods allow to analyse distinct timber’s reference properties, such as density, bending stiffness and strength, and hierarchically consider information obtained through different non, semi or destructive tests. The basis and fundaments of the methods are described and also recommendations and limitations are discussed. The methods may be used in several contexts, however require an expert’s knowledge to assess the correct statistic fitting and define the correlation arrangement between properties.

Flow and transport in electrochromatography

Analyte retention, analyte transport, axial dispersion, adsorption, charge-selectivity, concentration polarization, confocal laser scanning microscopy, donnan-exclusion, electrical double layer; electrochromatography; electrohydrodynamics, electrokinetic instability, electroosmosis; electroosmotic flow; electroosmotic mobility, electroosmotic perfusion, electrophoresis, hierarchical porous media, hydrodynamic flow, induced-charge electroosmosis, ion-permselectivity, ion-permselective transport, monolith, nonequilibrium electrical double layer, nonequilibrium electrokinetic effects, nonlinear electroosmosis, plate height, plate number, porous media, pore-scale dispersion, refractive index matching, space charge effects, sphere packing, quantitative imaging, wall effect, zeta-potential

stochastic method for automated matching of horizons across a fault in 3D seismic data

Seismic analysis, horizon matching, fault tracking, marked point process,stochastic annealing

Management of XML data by means of schema matching

Magdeburg, Univ., Fak. für Informatik, Diss., 2010

Optimal designs for the prediction in hierarchical random coefficient regression models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2015

Dynamic matching and bargaining: the role of deadlines

We consider a dynamic model where traders in each period are matched randomly into pairs who then bargain about the division of a fixed surplus. When agreement is reached the traders leave the market. Traders who do not come to an agreement return next period in which they will be matched again, as long as their deadline has not expired yet. New traders enter exogenously in each period. We assume that traders within a pair know each other's deadline. We define and characterize the stationary equilibrium configurations. Traders with longer deadlines fare better than traders with short deadlines. It is shown that the heterogeneity of deadlines may cause delay. It is then shown that a centralized mechanism that controls the matching protocol, but does not interfere with the bargaining, eliminates all delay. Even though this efficient centralized mechanism is not as good for traders with long deadlines, it is shown that in a model where all traders can choose which mechanism to

Median stable matching for college admission

We give a simple and concise proof that so-called generalized median stable matchings are well-defined stable matchings for college admissions problems. Furthermore, we discuss the fairness properties of median stable matchings and conclude with two illustrative examples of college admissions markets, the lattices of stable matchings, and the corresponding generalized median stable matchings.

Corrigendum to "On randomized matching mechanisms" [Economic Theory 8(1996)377-381]

Ma (1996) studied the random order mechanism, a matching mechanism suggested by Roth and Vande Vate (1990) for marriage markets. By means of an example he showed that the random order mechanism does not always reach all stable matchings. Although Ma's (1996) result is true, we show that the probability distribution he presented - and therefore the proof of his Claim 2 - is not correct. The mistake in the calculations by Ma (1996) is due to the fact that even though the example looks very symmetric, some of the calculations are not as ''symmetric.''

Paths to stability for matching markets with couples

We study two-sided matching markets with couples and show that for a natural preference domain for couples, the domain of weakly responsive preferences, stable outcomes can always be reached by means of decentralized decision making. Starting from an arbitrary matching, we construct a path of matchings obtained from `satisfying' blocking coalitions that yields a stable matching. Hence, we establish a generalization of Roth and Vande Vate's (1990) result on path convergence to stability for decentralized singles markets. Furthermore, we show that when stable matchings exist, but preferences are not weakly responsive, for some initial matchings there may not exist any path obtained from `satisfying' blocking coalitions that yields a stable matching.

Procedurally fair and stable matching

We motivate procedural fairness for matching mechanisms and study two procedurally fair and stable mechanisms: employment by lotto (Aldershof et al., 1999) and the random order mechanism (Roth and Vande Vate, 1990, Ma, 1996). For both mechanisms we give various examples of probability distributions on the set of stable matchings and discuss properties that differentiate employment by lotto and the random order mechanism. Finally, we consider an adjustment of the random order mechanism, the equitable random order mechanism, that combines aspects of procedural and "endstate'' fairness. Aldershof et al. (1999) and Ma (1996) that exist on the probability distribution induced by both mechanisms. Finally, we consider an adjustment of the random order mechanism, the equitable random order mechanism.

On group strategy-proof mechanisms for a many-to-one matching model

For the many-to-one matching model in which firms have substitutable and quota q-separable preferences over subsets of workers we show that the workers-optimal stable mechanism is group strategy-proof for the workers. In order to prove this result, we also show that under this domain of preferences (which contains the domain of responsive preferences of the college admissions problem) the workers-optimal stable matching is weakly Pareto optimal for the workers and the Blocking Lemma holds as well. We exhibit an example showing that none of these three results remain true if the preferences of firms are substitutable but not quota q-separable.