Study of the one dimensional and transient bioheat transfer equation: Multi-layer solution development and applications

: In this work we derive an analytical solution given by Bessel series to the transient and one-dimensional (1D) bioheat transfer equation in a multi-layer region with spatially dependent heat sources. Each region represents an independent biological tissue characterized by temperature-invariant physiological parameters and a linearly temperature dependent metabolic heat generation. Moreover, 1D Cartesian, cylindrical or spherical coordinates are used to define the geometry and temperature boundary conditions of first, second and third kinds are assumed at the inner and outer surfaces. We present two examples of clinical applications for the developed solution. In the first one, we investigate two different heat source terms to simulate the heating in a tumor and its surrounding tissue, induced during a magnetic fluid hyperthermia technique used for cancer treatment. To obtain an accurate analytical solution, we determine the error associated with the truncated Bessel series that defines the transient solution. In the second application, we explore the potential of this model to study the effect of different environmental conditions in a multi-layered human head model (brain, bone and scalp). The convective heat transfer effect of a large blood vessel located inside the brain is also investigated. The results are further compared with a numerical solution obtained by the Finite Element Method and computed with COMSOL Multi-physics v4.1 (c). (c) 2013 Elsevier Ltd. All rights reserved.

Simulação numérica do comportamento dinâmico de uma laje

Nesta dissertação pretende-se simular o comportamento dinâmico de uma laje de betão armado aplicando o Método de Elementos Finitos através da sua implementação no programa FreeFEM++. Este programa permite-nos a análise do modelo matemático tridimensional da Teoria da Elasticidade Linear, englobando a Equação de Equilíbrio, Equação de Compatibilidade e Relações Constitutivas. Tratando-se de um problema dinâmico é necessário recorrer a métodos numéricos de Integração Directa de modo a obter a resposta em termos de deslocamento ao longo do tempo. Para este trabalho escolhemos o Método de Newmark e o Método de Euler para a discretização temporal, um pela sua popularidade e o outro pela sua simplicidade de implementação. Os resultados obtidos pelo FreeFEM++ são validados através da comparação com resultados adquiridos a partir do SAP2000 e de Soluções Teóricas, quando possível.

Mathematical modeling of pressurized system behaviour with entrapped air

The presence of entrapped air in pressurized hydraulic systems is considered a critical condition for the infrastructure security, due to the transient pressure enhancement related with its dynamic behaviour, similar to non-linear spring action. A mathematical model for the assessment of hydraulic transients resulting from rapid pressurizations, under referred condition is presented. Water movement was modeled through the elastic column theory considering a moving liquid boundary and the entrapped air pocket as lumped gas mass, where the acoustic effects are negligible. The method of characteristics was used to obtain the numerical solution of the liquid flow. The resulting model is applied to an experimental set-up having entrapped air in the top of a vertical pipe section and the numerical results are analyzed.

Contact angle of a hemispherical bubble: An analytical approach

We have calculated the equilibrium shape of the axially symmetric Plateau border along which a spherical bubble contacts a flat wall, by analytically integrating Laplace's equation in the presence of gravity, in the limit of small Plateau border sizes. This method has the advantage that it provides closed-form expressions for the positions and orientations of the Plateau border surfaces. Results are in very good overall agreement with those obtained from a numerical solution procedure, and are consistent with experimental data. In particular we find that the effect of gravity on Plateau border shape is relatively small for typical bubble sizes, leading to a widening of the Plateau border for sessile bubbles and to a narrowing for pendant bubbles. The contact angle of the bubble is found to depend even more weakly on gravity. (C) 2009 Elsevier Inc. All rights reserved.

Surgical correction of scoliosis: Numerical analysis and optimization of the procedure

A previously developed model is used to numerically simulate real clinical cases of the surgical correction of scoliosis. This model consists of one-dimensional finite elements with spatial deformation in which (i) the column is represented by its axis; (ii) the vertebrae are assumed to be rigid; and (iii) the deformability of the column is concentrated in springs that connect the successive rigid elements. The metallic rods used for the surgical correction are modeled by beam elements with linear elastic behavior. To obtain the forces at the connections between the metallic rods and the vertebrae geometrically, non-linear finite element analyses are performed. The tightening sequence determines the magnitude of the forces applied to the patient column, and it is desirable to keep those forces as small as possible. In this study, a Genetic Algorithm optimization is applied to this model in order to determine the sequence that minimizes the corrective forces applied during the surgery. This amounts to find the optimal permutation of integers 1, ... , n, n being the number of vertebrae involved. As such, we are faced with a combinatorial optimization problem isomorph to the Traveling Salesman Problem. The fitness evaluation requires one computing intensive Finite Element Analysis per candidate solution and, thus, a parallel implementation of the Genetic Algorithm is developed.

Explicit series solution for a glucose-induced electrical activity model of pancreatic beta-cells

In this work, we present the explicit series solution of a specific mathematical model from the literature, the Deng bursting model, that mimics the glucose-induced electrical activity of pancreatic beta-cells (Deng, 1993). To serve to this purpose, we use a technique developed to find analytic approximate solutions for strongly nonlinear problems. This analytical algorithm involves an auxiliary parameter which provides us with an efficient way to ensure the rapid and accurate convergence to the exact solution of the bursting model. By using the homotopy solution, we investigate the dynamical effect of a biologically meaningful bifurcation parameter rho, which increases with the glucose concentration. Our analytical results are found to be in excellent agreement with the numerical ones. This work provides an illustration of how our understanding of biophysically motivated models can be directly enhanced by the application of a newly analytic method.

Identification of tsunami-induced deposits using numerical modeling and rock magnetism techniques: A study case of the 1755 Lisbon tsunami in Algarve, Portugal

Storm- and tsunami-deposits are generated by similar depositional mechanisms making their discrimination hard to establish using classic sedimentologic methods. Here we propose an original approach to identify tsunami-induced deposits by combining numerical simulation and rock magnetism. To test our method, we investigate the tsunami deposit of the Boca do Rio estuary generated by the 1755 earthquake in Lisbon which is well described in the literature. We first test the 1755 tsunami scenario using a numerical inundation model to provide physical parameters for the tsunami wave. Then we use concentration (MS. SIRM) and grain size (chi(ARM), ARM, B1/2, ARM/SIRM) sensitive magnetic proxies coupled with SEM microscopy to unravel the magnetic mineralogy of the tsunami-induced deposit and its associated depositional mechanisms. In order to study the connection between the tsunami deposit and the different sedimentologic units present in the estuary, magnetic data were processed by multivariate statistical analyses. Our numerical simulation show a large inundation of the estuary with flow depths varying from 0.5 to 6 m and run up of similar to 7 m. Magnetic data show a dominance of paramagnetic minerals (quartz) mixed with lesser amount of ferromagnetic minerals, namely titanomagnetite and titanohematite both of a detrital origin and reworked from the underlying units. Multivariate statistical analyses indicate a better connection between the tsunami-induced deposit and a mixture of Units C and D. All these results point to a scenario where the energy released by the tsunami wave was strong enough to overtop and erode important amount of sand from the littoral dune and mixed it with reworked materials from underlying layers at least 1 m in depth. The method tested here represents an original and promising tool to identify tsunami-induced deposits in similar embayed beach environments.

Tsunami vulnerability assessment of Casablanca-Morocco using numerical modelling and GIS tools

Earthquakes and tsunamis along Morocco's coasts have been reported since historical times. The threat posed by tsunamis must be included in coastal risk studies. This study focuses on the tsunami impact and vulnerability assessment of the Casablanca harbour and surrounding area using a combination of tsunami inundation numerical modelling, field survey data and geographic information system. The tsunami scenario used here is compatible with the 1755 Lisbon event that we considered to be the worst case tsunami scenario. Hydrodynamic modelling was performed with an adapted version of the Cornell Multigrid Coupled Tsunami Model from Cornell University. The simulation covers the eastern domain of the Azores-Gibraltar fracture zone corresponding to the largest tsunamigenic area in the North Atlantic. The proposed vulnerability model attempts to provide an insight into the tsunami vulnerability of building stock. Results in the form of a vulnerability map will be useful for decision makers and local authorities in preventing the community resiliency for tsunami hazards.

Field effect and light-assisted a-Si:H sensors for detection of ions in solution

In this paper we present an amorphous silicon device that can be used in two operation modes to measure the concentration of ions in solution. While crystalline devices present a higher sensitivity, their amorphous counterpart present a much lower fabrication cost, thus enabling the production of cheap disposable sensors for use, for example, in the food industry. The devices were fabricated on glass substrates by the PECVD technique in the top gate configuration, where the metallic gate is replaced by an electrolytic solution with an immersed Ag/AgCl reference electrode. Silicon nitride is used as gate dielectric enhancing the sensitivity and passivation layer used to avoid leakage and electrochemical reactions. In this article we report on the semiconductor unit, showing that the device can be operated in a light-assisted mode, where changes in the pH produce changes on the measured ac photocurrent. In alternative the device can be operated as a conventional ion selective field effect device where changes in the pH induce changes in the transistor's threshold voltage.

Response of a multi-domain continental margin to compression: Study from seismic reflection-refraction and numerical modelling in the Tagus Abyssal Plain

The effects of the Miocene through Present compression in the Tagus Abyssal Plain are mapped using the most up to date available to scientific community multi-channel seismic reflection and refraction data. Correlation of the rift basin fault pattern with the deep crustal structure is presented along seismic line IAM-5. Four structural domains were recognized. In the oceanic realm mild deformation concentrates in Domain I adjacent to the Tore-Madeira Rise. Domain 2 is characterized by the absence of shortening structures, except near the ocean-continent transition (OCT), implying that Miocene deformation did not propagate into the Abyssal Plain, In Domain 3 we distinguish three sub-domains: Sub-domain 3A which coincides with the OCT, Sub-domain 3B which is a highly deformed adjacent continental segment, and Sub-domain 3C. The Miocene tectonic inversion is mainly accommodated in Domain 3 by oceanwards directed thrusting at the ocean-continent transition and continentwards on the continental slope. Domain 4 corresponds to the non-rifted continental margin where only minor extensional and shortening deformation structures are observed. Finite element numerical models address the response of the various domains to the Miocene compression, emphasizing the long-wavelength differential vertical movements and the role of possible rheologic contrasts. The concentration of the Miocene deformation in the transitional zone (TC), which is the addition of Sub-domain 3A and part of 3B, is a result of two main factors: (1) focusing of compression in an already stressed region due to plate curvature and sediment loading; and (2) theological weakening. We estimate that the frictional strength in the TC is reduced in 30% relative to the surrounding regions. A model of compressive deformation propagation by means of horizontal impingement of the middle continental crust rift wedge and horizontal shearing on serpentinized mantle in the oceanic realm is presented. This model is consistent with both the geological interpretation of seismic data and the results of numerical modelling.

Enthalpies of Solution of 1-Butyl-3-methylimidazolium Tetrafluoroborate in 15 Solvents at 298.15 K

Enthalpies of solution of 1-butyl-3-methylimidazolium tetra fluoroborate, [BMIm]BF4, are reported at 298.15 K in a set of 15 hydrogen bond donor and hydrogen bond acceptor solvents, chosen by their diversity, namely, water, methanol, ethanol, 1,2-ethanediol, 2-choroethanol, 2-methoxyethanol, formamide, propylene carbonate, nitromethane, acetonitrile, dimethyl sulfoxide, acetone, N,N-dimethylformamide, N,N-dimethylacetamide, and aniline. These values are shown to be largely independent of [BMIm]BF4 concentration. The obtained enthalpies of solution vary from very endothermic to quite exothermic, thus showing a very high sensitivity of the enthalpies of solution of [BMIm]BF4 to solvent properties. Solvent effects on the solution process of this IL are analyzed by a quantitative structure-property relationship methodology, using the TAKA equation and a modified equation, which significantly improves the model's predictive ability. The observed differences in the enthalpies of solution are rationalized in terms of the solvent properties found to be relevant, that is, pi* and E-T(N).

Solvent effects on solution enthalpies of adamantyl derivatives

Solution enthalpies of 1-bromoadamantane, 1-adamantanol, and 2-adamantanone in a large set of protic and aprotic solvents are reported at 298.15 K. Solvent effects on the solution processes of these solutes are analyzed in terms of a modified TAKA equation, involving delta(cav) h (s) as the cavity term. The nature and magnitude of the major interactions which influence these processes are assessed and discussed in terms of the solutes' characteristics. New insights on the solution processes under scrutiny are presented.

Identification of tsunami-induced deposits using numerical modeling and rock magnetism techniques: A study case of the 1755 Lisbon tsunami in Algarve, Portugal

Storm- and tsunami-deposits are generated by similar depositional mechanisms making their discrimination hard to establish using classic sedimentologic methods. Here we propose an original approach to identify tsunami-induced deposits by combining numerical simulation and rock magnetism. To test our method, we investigate the tsunami deposit of the Boca do Rio estuary generated by the 1755 earthquake in Lisbon which is well described in the literature. We first test the 1755 tsunami scenario using a numerical inundation model to provide physical parameters for the tsunami wave. Then we use concentration (MS. SIRM) and grain size (chi(ARM), ARM, B1/2, ARM/SIRM) sensitive magnetic proxies coupled with SEM microscopy to unravel the magnetic mineralogy of the tsunami-induced deposit and its associated depositional mechanisms. In order to study the connection between the tsunami deposit and the different sedimentologic units present in the estuary, magnetic data were processed by multivariate statistical analyses. Our numerical simulation show a large inundation of the estuary with flow depths varying from 0.5 to 6 m and run up of similar to 7 m. Magnetic data show a dominance of paramagnetic minerals (quartz) mixed with lesser amount of ferromagnetic minerals, namely titanomagnetite and titanohematite both of a detrital origin and reworked from the underlying units. Multivariate statistical analyses indicate a better connection between the tsunami-induced deposit and a mixture of Units C and D. All these results point to a scenario where the energy released by the tsunami wave was strong enough to overtop and erode important amount of sand from the littoral dune and mixed it with reworked materials from underlying layers at least 1 m in depth. The method tested here represents an original and promising tool to identify tsunami-induced deposits in similar embayed beach environments.

Transport properties in microcrystalline silicon solar cells under AM1.5 illumination analysed by two-dimensional numerical simulation

Microcrystalline silicon is a two-phase material. Its composition can be interpreted as a series of grains of crystalline silicon imbedded in an amorphous silicon tissue, with a high concentration of dangling bonds in the transition regions. In this paper, results for the transport properties of a mu c-Si:H p-i-n junction obtained by means of two-dimensional numerical simulation are reported. The role played by the boundary regions between the crystalline grains and the amorphous matrix is taken into account and these regions are treated similar to a heterojunction interface. The device is analysed under AM1.5 illumination and the paper outlines the influence of the local electric field at the grain boundary transition regions on the internal electric configuration of the device and on the transport mechanism within the mu c-Si:H intrinsic layer.

Solution enthalpies of hydroxylic compounds

Solution enthalpies of adamantan-1-ol, 2-methyl- butan-2-ol, and 3-methylbutan-1-ol have been measured at 298.15 K, in a set of 16 protogenic and non-protogenic solvents. The identification and quantification of solvent effects on the solution processes under study were performed using quantitative-structure property relationships. The results are discussed in terms of solute-solvent-solvent interactions and also in terms of the influence of compound's size and position of its hydroxyl group.