Search results for: A. Zamfirescu

Authors: Hudson Akewe

Abstract:

We prove that the convergence of explicit Mann, explicit Ishikawa, explicit Noor, explicit SP, explicit multistep and explicit multistep-SP fixed point iterative procedures are equivalent for the classes of multi-valued phi-contraction, phi-Zamfirescu and phi-quasi-contractive mappings in the framework of modular function spaces. Our results complement equivalence results on normed and metric spaces in the literature as they elegantly cut out the triangle inequality.

Keywords: multistep iterative procedures, multivalued mappings, equivalence results, fixed point

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Authors: Hudson Akewe

Abstract:

This research presents complementary results with wider applications on convergence and rate of convergence of classical fixed point theory in Banach spaces to the world of the theory of fixed points of mappings defined in classes of spaces of measurable functions, known in the literature as modular function spaces. The study gives a comprehensive survey of various iterative fixed point results for the classes of multivalued ρ-contractive-like, ρ-quasi-contractive-like, ρ-quasi-contractive, ρ-Zamfirescu and ρ-contraction mappings in the framework of modular function spaces. An example is presented to demonstrate the applicability of the implicit-type iterative schemes to the system of ordinary differential equations. Furthermore, numerical examples are given to show the rate of convergence of the various explicit Kirk-type and implicit Kirk-type iterative schemes under consideration. Our results complement the results obtained on normed and metric spaces in the literature. Also, our methods of proof serve as a guide to obtain several similar improved results for nonexpansive, pseudo-contractive, and accretive type mappings.

Keywords: implicit Kirk-type iterative schemes, multivalued mappings, convergence results, fixed point

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Authors: C. Busuioc, I. Stancu, A. Nicoara, A. Zamfirescu, A. Evanghelidis

Abstract:

The field of tissue engineering has expanded its potential due to the use of composite biomaterials belonging to increasingly complex systems, leading to bone substitutes with properties that are continuously improving to meet the patient's specific needs. Furthermore, the development of biomaterials based on ceramic and polymeric phases is an unlimited resource for future scientific research, with the final aim of restoring the original tissue functionality. Thus, in the first stage, composite scaffolds based on polycaprolactone (PCL) or polylactic acid (PLA) and inorganic powders were prepared by employing the electrospinning technique. The targeted powders were: commercial and laboratory synthesized hydroxyapatite (HAp), as well as barium titanate (BT). By controlling the concentration of the powder within the precursor solution, together with the processing parameters, different types of three-dimensional architectures were achieved. In the second stage, both the mineral powders and hybrid composites were investigated in terms of composition, crystalline structure, and microstructure so that to demonstrate their suitability for tissue engineering applications. Regarding the scaffolds, these were proven to be homogeneous on large areas and loaded with mineral particles in different proportions. The biological assays demonstrated that the addition of inorganic powders leads to modified responses in the presence of simulated body fluid (SBF) or cell cultures. Through SBF immersion, the biodegradability coupled with bioactivity were highlighted, with fiber fragmentation and surface degradation, as well as apatite layer formation within the testing period. Moreover, the final composites represent supports accepted by the cells, favoring implant integration. Concluding, the purposed fibrous materials based on bioresorbable polymers and mineral powders, produced by the electrospinning technique, represent candidates with considerable potential in the field of tissue engineering. Future improvements can be attained by optimizing the synthesis process or by simultaneous incorporation of multiple inorganic phases with well-defined biological action in order to fabricate multifunctional composites.

Keywords: barium titanate, electrospinning, fibre networks, hydroxyapatite, smart scaffolds

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Authors: Irina Alexandra Paun, Mona Mihailescu, Marian Zamfirescu, Catalin Romeo Luculescu, Adriana Maria Acasandrei, Cosmin Catalin Mustaciosu, Roxana Cristina Popescu, Maria Dinescu

Abstract:

A major concern in bone tissue engineering is to develop complex 3D architectures that mimic the natural cells environment, facilitate the cells growth in a defined manner and allow the flow transport of nutrients and metabolic waste. In particular, porous structures of controlled pore size and positioning are indispensable for growing human-like bone structures. Another concern is to monitor both the structures and the seeded cells with high spatial resolution and without interfering with the cells natural environment. The present approach relies on laser-based technologies employed for fabricating porous biomimetic structures that support the growth of osteoblast-like cells and for their non-invasive 3D imaging. Specifically, the porous structures were built by two photon polymerization –direct writing (2PP_DW) of the commercially available photoresists IL-L780, using the Photonic Professional 3D lithography system. The structures consist of vertical tubes with micrometer-sized heights and diameters, in a honeycomb-like spatial arrangement. These were fabricated by irradiating the IP-L780 photoresist with focused laser pulses with wavelength centered at 780 nm, 120 fs pulse duration and 80 MHz repetition rate. The samples were precisely scanned in 3D by piezo stages. The coarse positioning was done by XY motorized stages. The scanning path was programmed through a writing language (GWL) script developed by Nanoscribe. Following laser irradiation, the unexposed regions of the photoresist were washed out by immersing the samples in the Propylene Glycol Monomethyl Ether Acetate (PGMEA). The porous structures were seeded with osteoblast like MG-63 cells and their osteogenic potential was tested in vitro. The cell-seeded structures were analyzed in 3D using the digital holographic microscopy technique (DHM). DHM is a marker free and high spatial resolution imaging tool, where the hologram acquisition is performed non-invasively i.e. without interfering with the cells natural environment. Following hologram recording, a digital algorithm provided a 3D image of the sample, as well as information about its refractive index, which is correlated with the intracellular content. The axial resolution of the images went down to the nanoscale, while the temporal scales ranged from milliseconds up to hours. The hologram did not involve sample scanning and the whole image was available in one frame recorded going over 200μm field of view. The digital holograms processing provided 3D quantitative information on the porous structures and allowed a quantitative analysis of the cellular response in respect to the porous architectures. The cellular shape and dimensions were found to be influenced by the underlying micro relief. Furthermore, the intracellular content gave evidence on the beneficial role of the porous structures in promoting osteoblast differentiation. In all, the proposed laser-based protocol emerges as a promising tool for the fabrication and non-invasive imaging of porous constructs for bone tissue engineering. Acknowledgments: This work was supported by a grant of the Romanian Authority for Scientific Research and Innovation, CNCS-UEFISCDI, project PN-II-RU-TE-2014-4-2534 (contract 97 from 01/10/2015) and by UEFISCDI PN-II-PT-PCCA no. 6/2012. A part of this work was performed in the CETAL laser facility, supported by the National Program PN 16 47 - LAPLAS IV.

Keywords: biomimetic, holography, laser, osteoblast, two photon polymerization

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