6 resultados para Riemann–Liouville Fractional Differentiation and Integration Operators

em Universidade do Minho


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Tese de Doutoramento em Engenharia de Tecidos, Medicina Regenerativa e Células Estaminais.

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Published online first in 10 July 2013

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In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.

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The use of stem cells is a promising therapeutic approach for the substantial challenge to regenerate cartilage. Considering the two prerequisites, namely the use of a 3D system to enable the chondrogenic differentiation and growth factors to avoid dedifferentiation, the diffusion efficiency of essential biomolecules is an intrinsic issue. We already proposed a liquified bioencapsulation system containing solid microparticles as cell adhesion sites1. Here, we intend to use the optimized system towards chondrogenic differentiation by encapsulating stem cells and collagenII-TGF-β3 PLLA microparticles. As a proof-of-concept, magnetite-nanoparticles were incorporated into the multilayered membrane. This can be a great advantage after implantation procedures to fixate the capsules in situ with the held of an external magnetic patch and for the follow-up through imaging. Results showed that the production of glycosaminoglycans and the expression of cartilage-relevant markers (collagen II, Sox9, aggrecan, and COMP) increased up to 28 days, while hypertrophic (collagen X) and fibrotic (collagen I) markers were downregulated. The presence of nanofibers in the newly deposited ECM was visualized by SEM, which resembles the collagen fibrils of native cartilage. The presence of the major constituent of cartilage, collagen II, was detected by immunocytochemistry and afranin-O and alcian blue stainings revealed a basophilic ECM deposition, which is characteristic of neocartilage. These findings suggest that the proposed system may provide a suitable environment for chondrogenic differentiation.

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The MAP-i Doctoral Programme in Informatics, of the Universities of Minho, Aveiro and Porto

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Tissue engineering often rely on scaffolds for supporting cell differentiation and growth. Novel paradigms for tissue engineering include the need of active or smart scaffolds in order to properly regenerate specific tissues. In particular, as electrical and electromechanical clues are among the most relevant ones in determining tissue functionality in tissues such as muscle and bone, among others, electroactive materials and, in particular, piezoelectric ones, show strong potential for novel tissue engineering strategies, in particular taking also into account the existence of these phenomena within some specific tissues, indicating their requirement also during tissue regeneration. This referee reports on piezoelectric materials used for tissue engineering applications. The most used materials for tissue engineering strategies are reported together with the main achievements, challenges and future needs for research and actual therapies. This review provides thus a compilation of the most relevant results and strategies and a start point for novel research pathways in the most relevant and challenging open questions.