Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.

PHB-PEO electrospun fiber membranes containing chlorhexidine for drug delivery applications

Fiber meshes of poly(hydroxybutyrate) (PHB) and poly(hydroxybutyrate)/ poly(ethylene oxide) (PHB/PEO) with different concentrations of chlorhexidine (CHX) were prepared by electrospinning, for assessment as a polymer based drug delivery system. The electrospun fibers were characterized at morphological, molecular and mechanical levels. The bactericidal potential of PHB and PHB/PEO electrospun fibers with and without CHX was investigated against Escherichia coli (E. coli) and Staphylococcus aureus (S. aureus) by disk diffusion susceptibility tests. Electrospun fibers containing CHX exhibited bactericidal activity. PHB/PEO-1%CHX displayed higher CHX release levels and equivalent antibacterial activity when compared to PHB/PEO with 5 and 10 wt% CHX. Bactericidal performance of samples with 1 wt% CHX was assessed by Colony Forming Units (CFU), where a reduction of 100 % and 99.69 % against E. coli and S. aureus were achieved, respectively.

Real-time 3D interactive segmentation of echocardiographic data through user-based deformation of B-spline explicit active surfaces

Image segmentation is an ubiquitous task in medical image analysis, which is required to estimate morphological or functional properties of given anatomical targets. While automatic processing is highly desirable, image segmentation remains to date a supervised process in daily clinical practice. Indeed, challenging data often requires user interaction to capture the required level of anatomical detail. To optimize the analysis of 3D images, the user should be able to efficiently interact with the result of any segmentation algorithm to correct any possible disagreement. Building on a previously developed real-time 3D segmentation algorithm, we propose in the present work an extension towards an interactive application where user information can be used online to steer the segmentation result. This enables a synergistic collaboration between the operator and the underlying segmentation algorithm, thus contributing to higher segmentation accuracy, while keeping total analysis time competitive. To this end, we formalize the user interaction paradigm using a geometrical approach, where the user input is mapped to a non-cartesian space while this information is used to drive the boundary towards the position provided by the user. Additionally, we propose a shape regularization term which improves the interaction with the segmented surface, thereby making the interactive segmentation process less cumbersome. The resulting algorithm offers competitive performance both in terms of segmentation accuracy, as well as in terms of total analysis time. This contributes to a more efficient use of the existing segmentation tools in daily clinical practice. Furthermore, it compares favorably to state-of-the-art interactive segmentation software based on a 3D livewire-based algorithm.

Effect of filler content on morphology and physical-chemical characteristics of poly(vinylidene fluoride)/NaY-zeolite filled membranes

Poly(vinylidene fluoride) electrospun membranes have been prepared with different NaY zeolite contents up to 32%wt. Inclusion of zeolites induces an increase of average fiber size from ~200 nm in the pure polymer up to ~500 nm in the composite with 16%wt zeolite content. For higher filler contents, a wider distribution of fibers occurs leading to a broader size distributions between the previous fiber size values. Hydrophobicity of the membranes increases from ~115º water contact angle to ~128º with the addition of the filler and is independent on filler content, indicating a wrapping of the zeolite by the polymer. The water contact angle further increases with fiber alignment up to ~137º. Electrospun membranes are formed with ~80 % of the polymer crystalline phase in the electroactive  phase, independently on the electrospinning processing conditions or filler content. Viability of MC3T3-E1 cells on the composite membranes after 72 h of cell culture indicates the suitability of the membranes for tissue engineering applications.

Effect of fiber orientation in gelled poly (vinylience fluoride) electrospun membranes for Li-ion battery applications

Battery separators based on electrospun membranes of poly(vinylidene fluoride) (PVDF) have been prepared in order to study the effect of fiber alignment on the performance and characteristics of the membrane. The prepared membranes show an average fiber diameter of ~272 nm and a degree of porosity of ~87 %. The gel polymer electrolytes are prepared by soaking the membranes in the electrolyte solution. The alignment of the fibers improves the mechanical properties for the electrospun membranes. Further, the microstructure of the membrane also plays an important role in the ionic conductivity, being higher for the random electrospun membrane due to the lower tortuosity value. Independently of the microstructure, both membranes show good electrochemical stability up to 5.0 V versus Li/Li+. These results show that electrospun membranes based on PVDF are appropriate for battery separators in lithium-ion battery applications, the random membranes showing a better overall performance.

Modifying fish gelatin electrospun membranes for biomedical applications: cross- linking and swelling behavior

Development of suitable membranes is a fundamental requisite for tissue and biomedical engineering applications. This work presents fish gelatin random and aligned electrospun membranes cross-linked with glutaraldehyde (GA). It was observed that the fiber average diameter and the morphology is not influenced by the GA exposure time and presents fibers with an average diameter around 250 nm. Moreover, when the gelatin mats are immersed in a phosphate buffered saline solution (PBS), they can retain as much as 12 times its initial weight of solution almost instantaneously, but the material microstructure of the fiber mats changes from the characteristic fibrous to an almost spherical porous structure. Cross-linked gelatin electrospun fiber mats and films showed a water vapor permeability of 1.37 ± 0.02 and 0.13 ± 0.10 (g.mm)/(m2.h.kPa), respectively. Finally, the processing technique and cross-linking process does not inhibit MC-3T3-E1 cell adhesion. Preliminary cell culture results showed good cell adhesion and proliferation in the cross-linked random and aligned gelatin fiber mats.

Effect of neutralization and cross-linking on the thermal degradation of chitosan electrospun membranes

Thermal degradation of as electrospun chitosan membranes and samples subsequently treated with ethanol and cross-linked with glutaraldehyde (GA) have been studied by thermogravimetry (TG) coupled with an infrared spectrometer (FTIR). The influence of the electrospinning process and cross-linking in the electrospun chitosan thermal stability was evaluated. Up to three degradation steps were observed in the TG data, corresponding to water dehydration reaction at temperatures below 100 ºC, loss of side groups formed between the amine groups of chitosan and trifluoroacetic acid between 150 – 270 ºC and chitosan thermal degradation that starts around 250 ºC and goes up to 400 ºC. The Kissinger model was employed to evaluate the activation energies of the electrospun membranes during isothermal experiments and revealed that thermal degradation activation energy increases for the samples processed by electrospinning and subsequent neutralization and cross-linking treatments with respect to the neat chitosan powder.