Optimizing Bone Scaffold Porosity Distributions

We consider a simple one-dimensional time-dependent model for bone regeneration in the presence of a bio-resorbable polymer scaffold. Within the framework of the model, we optimize the effective mechanical stiffness of the polymer scaffold together with the regenerated bone matrix. The result of the optimization procedure is a scaffold porosity distribution which maximizes the stiffness of the scaffold-bone system over the regeneration time, such that the propensity for mechanical failure is reduced

Integrated additive design and manufacturing approach for the bioengineering of bone scaffolds for favorable mechanical and biological properties

Additive manufacturing (AM) presents the possibility of personalized bone scaffolds with unprecedented structural and functional designs. In contrast to earlier conventional design concepts, e.g. raster-angle, a workflow was established to produce scaffolds with triply periodic minimal surface (TPMS) architecture. A core challenge is the realization of such structures using melt-extrusion based 3D printing. This study presents methods for generation of scaffold design files, finite element (FE) analysis of scaffold Young's moduli, AM of scaffolds with polycaprolactone (PCL), and a customized in vitro assay to evaluate cell migration. The reliability of FE analysis when using computer-aided designed models as input may be impeded by anomalies introduced during 3D printing. Using micro-computed tomography reconstructions of printed scaffolds as an input for numerical simulation in comparison to experimentally obtained scaffold Young's moduli showed a moderate trend (R 2 = 0.62). Interestingly, in a preliminary cell migration assay, adipose-derived mesenchymal stromal cells (AdMSC) migrated furthest on PCL scaffolds with Diamond, followed by Gyroid and Schwarz P architectures. A similar trend, but with an accelerated AdMSC migration rate, was observed for PCL scaffolds surface coated with calcium-phosphate-based apatite. We elaborate on the importance of start-to-finish integration of all steps of AM, i.e. design, engineering and manufacturing. Using such a workflow, specific biological and mechanical functionality, e.g. improved regeneration via enhanced cell migration and higher structural integrity, may be realized for scaffolds intended as temporary guiding structures for endogenous tissue regeneration

Saturation in Liquid/Gas Coalescence

The problem was to construct a mathematical model for a liquid/gas coalescer, in order that the model could be analyzed to find combinations of parameters that would minimize the effects of saturation. The team has developed three complementary models, each with different strengths and weaknesses so that, depending on the information desired, one model may be more useful than another. The three models are: 1. A continuum model giving a macroscopic description of the filter. The governing equations are derived from first-principle consider- ations of conservation of mass and momentum. Constitutive relations for this model are derived by considering the processes going on in the filter at a microscopic level. 2. A stochastic model based on a Markov Decision Process. Each droplet is modelled as a single entity that can merge or move stochastically. This leads to a Markov simulation of the filter and the computation of average quantities. 3. A Lattice-Boltzmann model. The droplets are modelled to interact with each other and with the filter, using a Boltzmann distribution for their speed. This simulates the hydrodynamic behaviour of the droplet inside the filter

Lipschitz percolation

We prove the existence of a (random) Lipschitz function F : Z(d-1) -> Z(+) such that, for every x is an element of Z(d-1), the site (x, F(x)) is open in a site percolation process on Z(d). The Lipschitz constant may be taken to be 1 when the parameter p of the percolation model is sufficiently close to 1

Optimization of Bone Scaffold Porosity Distributions

Additive manufacturing (AM) is a rapidly emerging technology that has the potential to produce personalized scaffolds for tissue engineering applications with unprecedented control of structural and functional design. Particularly for bone defect regeneration, the complex coupling of biological mechanisms to the scaffolds’ properties has led to a predominantly trial-and-error approach. To mitigate this, shape or topology optimization can be a useful tool to design a scaffold architecture that matches the desired design targets, albeit at high computational cost. Here, we consider an efficient macroscopic optimization routine based on a simple one-dimensional time-dependent model for bone regeneration in the presence of a bioresorbable polymer scaffold. The result of the optimization procedure is a scaffold porosity distribution which maximizes the stiffness of the scaffold and regenerated bone system over the entire regeneration time, so that the propensity for mechanical failure is minimized

Contributions to the revision of the genus Entoloma (Basidiomycota, Agaricales) in Europe : six new species from subgenus Cyanula and typification of E. incarnatofuscescens

In anticipation of a phylogenetically revised monograph of Entoloma in Europe, six new species of subgenus Cyanula are described here. Entoloma cistocruentatum is associated with Cistus in Spain, E. dislocatum occurs in montane regions in Catalonia (Spain) and Tuscany (Italy), E. indikon is known from Denmark and three species are mainly distributed in the Nordic countries in Europe: E. calceus , E. perchalybeum and E. praecipuum. Entoloma incarnatofuscescens, from the /Rusticoides clade is neotypified. A fully amended description is given based on molecular evidence, which includes the recently described E. violaceoparkensis and E. klofacianum which became later synonyms.publishedVersio

A Bound on the Pseudospectrum for a Class of Non-normal Schrödinger Operators

We are concerned with the non-normal Schrödinger operator H=−Δ+VH=−Δ+V on L2(Rn)L2(Rn) , where V∈W1,∞loc(Rn)V∈Wloc1,∞(Rn) and ReV(x)≥c∣x∣2−dReV(x)≥c∣x∣2−d for some c,d>0c,d>0 . The spectrum of this operator is discrete and its real part is bounded below by −d−d . In general, the ε-pseudospectrum of H will have an unbounded component for any ε>0ε>0 and thus will not approximate the spectrum in a global sense. By exploiting the fact that the semigroup e−tHe−tH is immediately compact, we show a complementary result, namely that for every δ>0δ>0 , R>0R>0 there exists an ε>0ε>0 such that the ε-pseudospectrum σε(H)⊂{z:Rez≥R}∪⋃λ∈σ(H){z:∣∣z−λ∣∣<δ}.σε(H)⊂{z:Rez≥R}∪⋃λ∈σ(H){z:∣z−λ∣<δ}. In particular, the unbounded part of the pseudospectrum escapes towards +∞+∞ as ε decreases. In addition, we give two examples of non-selfadjoint Schrödinger operators outside of our class and study their pseudospectra in more detail