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

A heat transfer model of the human upper limbs

A steady state multi-segmented heat transfer model of the human upper limbs was developed. The main purpose was to evaluate the impact of blood flow through superficial veins and subcutaneous vascular structures in the palm of the hands over the heat transfer between the limbs and the environment. The distinguishing feature of the model is the inclusion of a detailed circulatory network composed of vessels with diameter larger than 1 mm. The model was validated by comparing its results from exposures to a hot, a neutral, and a cold environment to experimental data presented in the literature. (C) 2011 Elsevier Ltd. All rights reserved.

SAR ed effetti termici su Cheratinociti sottoposti a Radiofrequenze

Negli ultimi anni, la popolazione è stata esposta a vari tipi di campi elettromagnetici generati da strumentazioni elettroniche e dispositivi di telecomunicazione. In questa tesi, si valutano SAR ed effetti termici prodotti da tre antenne patch a radiofrequenza sia su Cheratinociti (cellule dell'epidermide) in vitro che sull'epidermide umana in vivo caratterizzata in un modello multistrato contenente tessuti biologici. Le antenne progettate hanno frequenze di risonanza di 1.8 e 2.4 GHz, tipiche delle bande utilizzate rispettivamente da LTE (Long Term Evolution, la più recente evoluzione degli standard di telefonia mobile cellulare) e dalle moderne tecnologie Wi-Fi, e di 60 GHz, propria delle cosiddette onde millimetriche. Vengono valutati quindi il SAR (Specific Absorption Rate, grandezza che fornisce una misura dell'assorbimento delle onde da parte dei tessuti biologici) e le variazioni di temperatura prodotte dall'applicazione del campo elettromagnetico: ciò viene realizzato attraverso l'equazione del calore stazionaria e, nel caso dell'epidermide in vivo, con la Bioheat Equation, che contempla anche la circolazione sanguigna ed il calore generato nei processi metabolici che avvengono nell'organismo.

Modelagem dos efeitos da irradiação luminosa no cérebro de camundongos e rastreamento de neurônios durante experimentos de microscopia de fluorescência

The fluorescent proteins are an essential tool in many fields of biology, since they allow us to watch the development of structures and dynamic processes of cells in living tissue, with the aid of fluorescence microscopy. Optogenectics is another technique that is currently widely used in Neuroscience. In general, this technique allows to activate/deactivate neurons with the radiation of certain wavelengths on the cells that have ion channels sensitive to light, at the same time that can be used with fluorescent proteins. This dissertation has two main objectives. Initially, we study the interaction of light radiation and mice brain tissue to be applied in optogenetic experiments. In this step, we model absorption and scattering effects using mice brain tissue characteristics and Kubelka-Munk theory, for specific wavelengths, as a function of light penetration depth (distance) within the tissue. Furthermore, we model temperature variations using the finite element method to solve Pennes’ bioheat equation, with the aid of COMSOL Multiphysics Modeling Software 4.4, where we simulate protocols of light stimulation tipically used in optogenetics. Subsequently, we develop some computational algorithms to reduce the exposure of neuron cells to the light radiation necessary for the visualization of their emitted fluorescence. At this stage, we describe the image processing techniques developed to be used in fluorescence microscopy to reduce the exposure of the brain samples to continuous light, which is responsible for fluorochrome excitation. The developed techniques are able to track, in real time, a region of interest (ROI) and replace the fluorescence emitted by the cells by a virtual mask, as a result of the overlay of the tracked ROI and the fluorescence information previously stored, preserving cell location, independently of the time exposure to fluorescent light. In summary, this dissertation intends to investigate and describe the effects of light radiation in brain tissue, within the context of Optogenetics, in addition to providing a computational tool to be used in fluorescence microscopy experiments to reduce image bleaching and photodamage due to the intense exposure of fluorescent cells to light radiation.

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.

Shelf-life of a 2.5% sodium hypochlorite solution as determined by arrhenius equation

Accelerated stability tests are indicated to assess, within a short time, the degree of chemical degradation that may affect an active substance, either alone or in a formula, under normal storage conditions. This method is based on increased stress conditions to accelerate the rate of chemical degradation. Based on the equation of the straight line obtained as a function of the reaction order (at 50 and 70 ºC) and using Arrhenius equation, the speed of the reaction was calculated for the temperature of 20 ºC (normal storage conditions). This model of accelerated stability test makes it possible to predict the chemical stability of any active substance at any given moment, as long as the method to quantify the chemical substance is available. As an example of the applicability of Arrhenius equation in accelerated stability tests, a 2.5% sodium hypochlorite solution was analyzed due to its chemical instability. Iodometric titration was used to quantify free residual chlorine in the solutions. Based on data obtained keeping this solution at 50 and 70 ºC, using Arrhenius equation and considering 2.0% of free residual chlorine as the minimum acceptable threshold, the shelf-life was equal to 166 days at 20 ºC. This model, however, makes it possible to calculate shelf-life at any other given temperature.

Existence Results for Abstract Partial Neutral Integro-differential Equation with Unbounded Delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.

Equation of state for the magnetic-color-flavor-locked phase and its implications for compact star models

Using the solutions of the gap equations of the magnetic-color-flavor-locked (MCFL) phase of paired quark matter in a magnetic field, and taking into consideration the separation between the longitudinal and transverse pressures due to the field-induced breaking of the spatial rotational symmetry, the equation of state of the MCFL phase is self-consistently determined. This result is then used to investigate the possibility of absolute stability, which turns out to require a field-dependent ""bag constant"" to hold. That is, only if the bag constant varies with the magnetic field, there exists a window in the magnetic field vs bag constant plane for absolute stability of strange matter. Implications for stellar models of magnetized (self-bound) strange stars and hybrid (MCFL core) stars are calculated and discussed.

Entropy production in irreversible systems described by a Fokker-Planck equation

We analyze the irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation. The irreversible character is provided either by nonconservative forces or by the contact with heat baths at distinct temperatures. The expression for the entropy production is deduced from a general definition, which is related to the probability of a trajectory in phase space and its time reversal, that makes no reference a priori to the dissipated power. Our formalism is applied to calculate the heat conductance in a simple system consisting of two Brownian particles each one in contact to a heat reservoir. We show also the connection between the definition of entropy production rate and the Jarzynski equality.

Equivalence between Redfield- and master-equation approaches for a time-dependent quantum system and coherence control

We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-1/2 system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times T(1) and T(2) (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operator-sum representation and the equivalent phenomenological-operator approach. Finally, we present a protocol to circumvent the decoherence processes due to the loss of energy (and thus, associated with T(1)). To this end, we simply associate the time dependence of the quantum system to an easily achieved modulated frequency. A possible implementation of the protocol is also proposed in the context of nuclear magnetic resonance.

A coupled boundary element/differential equation method formulation for plate-beam interaction analysis

In this work, a new boundary element formulation for the analysis of plate-beam interaction is presented. This formulation uses a three nodal value boundary elements and each beam element is replaced by its actions on the plate, i.e., a distributed load and end of element forces. From the solution of the differential equation of a beam with linearly distributed load the plate-beam interaction tractions can be written as a function of the nodal values of the beam. With this transformation a final system of equation in the nodal values of displacements of plate boundary and beam nodes is obtained and from it, all unknowns of the plate-beam system are obtained. Many examples are analyzed and the results show an excellent agreement with those from the analytical solution and other numerical methods. (C) 2009 Elsevier Ltd. All rights reserved.

Darcy`s law and the differential equation of motion

This note addresses the relation between the differential equation of motion and Darcy`s law. It is shown that, in different flow conditions, three versions of Darcy`s law can be rigorously derived from the equation of motion.

Scaling of structures subject to impact loads when using a power law constitutive equation

It is well known that structures subjected to dynamic loads do not follow the usual similarity laws when the material is strain rate sensitive. As a consequence, it is not possible to use a scaled model to predict the prototype behaviour. In the present study, this problem is overcome by changing the impact velocity so that the model behaves exactly as the prototype. This exact solution is generated thanks to the use of an exponential constitutive law to infer the dynamic flow stress. Furthermore, it is shown that the adopted procedure does not rely on any previous knowledge of the structure response. Three analytical models are used to analyze the performance of the technique. It is shown that perfect similarity is achieved, regardless of the magnitude of the scaling factor. For the class of material used, the solution outlined has long been sought, inasmuch as it allows perfect similarity for strain rate sensitive structures subject to impact loads. (C) 2009 Elsevier Ltd. All rights reserved.

AN ASSESSMENT ON THE USE OF THE DEBYE-HUCKEL EQUATION FOR THE THERMODYNAMIC MODELING OF AQUEOUS SYSTEMS CONTAINING POLYMERS AND SALTS

In this work, a study on the role of the long-range term of excess Gibbs energy models in the modeling of aqueous systems containing polymers and salts is presented. Four different approaches on how to account for the presence of polymer in the long-range term were considered, and simulations were conducted considering aqueous solutions of three different salts. The analysis of water activity curves showed that, in all cases, a liquid-phase separation may be introduced by the sole presence of the polymer in the long-range term, regardless of how it is taken into account. The results lead to the conclusion that there is no single exact solution for this problem, and that any kind of approach may introduce inconsistencies.