Fractional pennes' bioheat equation: theoretical and numerical studies

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.

Fractional bioheat equation

In this work we develop a new mathematical model for the Pennes’ bioheat equation assuming a fractional time derivative of single order. A numerical method for the solu- tion of such equations is proposed, and, the suitability of the new model for modelling real physical problems is studied and discussed

Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Patterns of Mycobacterium tuberculosis-complex excretion and characterization of super-shedders in naturally-infected wild boar and red deer

Wild boar (Sus scrofa) and red deer (Cervus elaphus) are the main maintenance hosts for bovine tuberculosis (bTB) in continental Europe. Understanding Mycobacterium tuberculosis complex (MTC) excretion routes is crucial to define strategies to control bTB in free-ranging populations, nevertheless available information is scarce. Aiming at filling this gap, four different MTC excretion routes (oronasal, bronchial-alveolar, fecal and urinary) were investigated by molecular methods in naturally infected hunter-harvested wild boar and red deer. In addition MTC concentrations were estimated by the Most Probable Number method. MTC DNA was amplified in all types of excretion routes. MTC DNA was amplified in at least one excretion route from 83.0% (CI95 70.8-90.8) of wild ungulates with bTB-like lesions. Oronasal or bronchial-alveolar shedding were detected with higher frequency than fecal shedding (p < 0.001). The majority of shedders yielded MTC concentrations <10(3) CFU/g or mL. However, from those ungulates from which oronasal, bronchial-alveolar and fecal samples were available, 28.2% of wild boar (CI95 16.6-43.8) and 35.7% of red deer (CI95 16.3-61.2) yielded MTC concentrations >10(3) CFU/g or mL (referred here as super-shedders). Red deer have a significantly higher risk of being super-shedders compared to wild boar (OR = 11.8, CI95 2.3-60.2). The existence of super-shedders among the naturally infected population of wild boar and red deer is thus reported here for the first time and MTC DNA concentrations greater than the minimum infective doses were estimated in excretion samples from both species.

Self-monitoring of freeze–thaw damage using triphasic electric conductive concrete

The effect of freeze–thaw cycles on concrete is of great importance for durability evaluation of concrete structures in cold regions. In this paper, damage accumulation was studied by following the fractional change of impedance (FCI) with number of freeze–thaw cycles (N). The nano-carbon black (NCB), carbon fiber (CF) and steel fiber (SF) were added to plain concrete to produce the triphasic electrical conductive (TEC) and ductile concrete. The effects of NCB, CF and SF on the compressive strength, flexural properties, electrical impedance were investigated. The concrete beams with different dosages of conductive materials were studied for FCI, N and mass loss (ML), the relationship between FCI and N of conductive concrete can be well defined by a first order exponential decay curve. It is noted that this nondestructive and sensitive real-time testing method is meaningful for evaluating of freeze–thaw damage in concrete.

Assessing the application of polypropylene multifilament yarns in brain phantoms

The currently available clinical imaging methods do not provide highly detailed information about location and severity of axonal injury or the expected recovery time of patients with traumatic brain injury [1]. High-Definition Fiber Tractography (HDFT) is a novel imaging modality that allows visualizing and quantifying, directly, the degree of axons damage, predicting functional deficits due to traumatic axonal injury and loss of cortical projections. This imaging modality is based on diffusion technology [2]. The inexistence of a phantom able to mimic properly the human brain hinders the possibility of testing, calibrating and validating these medical imaging techniques. Most research done in this area fails in key points, such as the size limit reproduced of the brain fibers and the quick and easy reproducibility of phantoms [3]. For that reason, it is necessary to develop similar structures matching the micron scale of axon tubes. Flexible textiles can play an important role since they allow producing controlled packing densities and crossing structures that match closely the human crossing patterns of the brain. To build a brain phantom, several parameters must be taken into account in what concerns to the materials selection, like hydrophobicity, density and fiber diameter, since these factors influence directly the values of fractional anisotropy. Fiber cross-section shape is other important parameter. Earlier studies showed that synthetic fibrous materials are a good choice for building a brain phantom [4]. The present work is integrated in a broader project that aims to develop a brain phantom made by fibrous materials to validate and calibrate HDFT. Due to the similarity between thousands of hollow multifilaments in a fibrous arrangement, like a yarn, and the axons, low twist polypropylene multifilament yarns were selected for this development. In this sense, extruded hollow filaments were analysed in scanning electron microscope to characterize their main dimensions and shape. In order to approximate the dimensional scale to human axons, five types of polypropylene yarns with different linear density (denier) were used, aiming to understand the effect of linear density on the filament inner and outer areas. Moreover, in order to achieve the required dimensions, the polypropylene filaments cross-section was diminished in a drawing stage of a filament extrusion line. Subsequently, tensile tests were performed to characterize the mechanical behaviour of hollow filaments and to evaluate the differences between stretched and non-stretched filaments. In general, an increase of the linear density causes the increase in the size of the filament cross section. With the increase of structure orientation of filaments, induced by stretching, breaking tenacity increases and elongation at break decreases. The production of hollow fibers, with the required characteristics, is one of the key steps to create a brain phantom that properly mimics the human brain that may be used for the validation and calibration of HDFT, an imaging approach that is expected to contribute significantly to the areas of brain related research.

Inferior frontal gyrus white matter abnormalities in obsessive-compulsive disorder

The aim of the present study is to explore obsessive-compulsive disorder (OCD)-related abnormalities in white matter connectivity in OCD for a core region associated with inhibitory control [i.e. inferior frontal gyrus (IFG)]. Fifteen patients with OCD (11 men) and 15 healthy controls (nine men) underwent diffusion tensor imaging scanning to study four diffusivity indexes of white matter integrity [fractional anisotropy, mean diffusivity (MD), axial diffusivity and radial diffusivity (RD)]. The results showed that persons with OCD manifested significantly lower fractional anisotropy levels in the bilateral IFG as well as its parcellations in the pars opercularis, pars triangularis, and pars orbitalis. Significantly higher levels of MD, RD were evident for the OCD group in the IFG as a whole as well as in the bilateral subregions of the pars triangularis and pars opercularis (for MD and RD), the right side of the pars orbitalis (for RD), and the left side of the pars triangularis and right side pars opercularis (for axial diffusivity). Overall, the results suggest significant alterations in structural connectivity, probably associated with myelination and axonal abnormalities in the IFG of OCD patients.

Expressão e caracterização de uma lectina recombinante de interesse biomédico

Dissertação de mestrado integrado em Engenharia Biomédica (área de especialização em Engenharia Clínica)

Concrete with triphasic conductive materials for self-monitoring of cracking development subjected to flexure

In this study, the macro steel fiber (SF), carbon fiber (CF) and nano carbon black (NCB) as triphasic conductive materials were added into concrete, in order to improve the conductivity and ductility of concrete. The influence of NCB, SF and CF on the post crack behavior and conductivity of concrete was explored. The effect of the triphasic conductive materials on the self-diagnosing ability to the load–deflection property and crack widening of conductive concrete member subjected to bending were investigated. The relationship between the fractional change in surface impedance (FCR) and the crack opening displacement (COD) of concrete beams with conductive materials has been established. The results illustrated that there is a linear relationship between COD and FCR.

Gold nanoparticles functionalised with fast water exchanging Gd3+ chelates: Linker effects on the relaxivity

The relaxivity displayed by Gd3+ chelates immobilized onto gold nanoparticles is the result of complex interplay between nanoparticle size, water exchange rate and chelate structure. In this work we study the effect of the length of -thioalkyl linkers, anchoring fast water exchanging Gd3+ chelates onto gold nanoparticles, on the relaxivity of the immobilized chelates. Gold nanoparticles functionalized with Gd3+ chelates of mercaptoundecanoyl and lipoyl amide conjugates of the DO3A-N-(-amino)propionate chelator were prepared and studied as potential CA for MRI. High relaxivities per chelate, of the order of magnitude 28-38 mM-1s-1 (30 MHz, 25 ºC) were attained thanks to simultaneous optimization of the rotational correlation time and of the water exchange rate. Fast local rotational motions of the immobilized chelates around connecting linkers (internal flexibility) still limit the attainable relaxivity. The degree of internal flexibility of the immobilized chelates seems not to be correlated with the length of the connecting linkers. Biodistribution and MRI studies in mice suggest that the in vivo behavior of the gold nanoparticles is determined mainly by size. Small nanoparticles (HD= 3.9 nm) undergo fast renal clearance and avoidance of the RES organs while larger nanoparticles (HD= 4.8 nm) undergo predominantly hepatobiliary excretion. High relaxivities, allied to chelate and nanoparticle stability and fast renal clearance in vivo suggests that functionalized gold nanoparticles hold great potential for further investigation as MRI Contrast Agents. This study contributes to understand the effect of linker length on the relaxivity of gold nanoparticles functionalized with Gd3+ complexes. It is a relevant contribution towards “design rules” for nanostructures functionalized with Gd3+ chelates as Contrast Agents for MRI and multimodal imaging.

Determinação de psicofármacos em cabelo humano por técnicas cromatográficas hifenadas: um método alternativo não-invasivo

Dissertação de mestrado em Técnicas de Caracterização e Análise Química