Purpose: To develop computer models to mimic the impedance-controlled pulsing protocol implemented in RF generators used for clinical practice of radiofrequency ablation (RFA), and to assess the appropriateness of the models by comparing the computer results with those obtained in previous experimental studies.Methods: A 12-minute RFA was modeled using a cooled electrode (17G, 3 cm tip) inserted in hepatic tissue. The short (transverse) diameter of the coagulation zone was assessed under in vivo (with blood perfusion and considering clamping) and ex vivo (at 21ºC) conditions.The computer results obtained by programming voltage pulses were compared with current pulses.Results: The differences between voltage and current pulses protocol were noticeable: using current instead of voltage allows larger coagulation zones to be created, due to the higher energy applied by current pulses. If voltage pulses are employed, the model can accurately predict number of roll-offs, although the waveform of the applied power is clearly not realistic. If current voltages are employed, the applied power waveform matches well with those reported experimentally, but there are significantly fewer roll-offs. Our computer results were overall into the ranges of experimental ones. Conclusions:The proposed models reproduce reasonably well the electrical-thermal performance and coagulation zone size obtained during an impedance-controlled pulsing protocol.

In modern surgery, a multitude of minimally intrusive operational techniques are used which are based on the punctual heating of target zones of human tissue via laser or radio-frequency currents. Traditionally, these processes are modeled by the bioheat equation introduced by Pennes, who considers Fourier's theory of heat conduction. We present an alternative and more realistic model established by the hyperbolic equation of heat transfer. To demonstrate some features and advantages of our proposed method, we apply the obtained results to different types of tissue heating with high energy fluxes, in particular radiofrequency heating and pulsed laser treatment of the cornea to correct refractive errors. Hopefully, the results of our approach help to refine surgical interventions in this novel field of medical treatment. (M. M. Tung), matrugui@mat.upv.es (M. Trujillo), jalopez@mat.upv.es (J.A. López Molina), mjrivera@mat.upv.es (M.J. Rivera), eberjano@eln.upv.es (E.J. Berjano).

To date, all radiofrequency heating (RFH) theoretical models have employed Fourier's heat transfer equation (FHTE), which assumes infinite thermal energy propagation speed. Although this equation is probably suitable for modeling most RFH techniques, it may not be so for surgical procedures in which very short heating times are employed. In such cases, a non-Fourier model should be considered by using the hyperbolic heat transfer equation (HHTE). Our aim was to compare the temperature profiles obtained from the FHTE and HHTE for RFH modeling. We built a one-dimensional theoretical model based on a spherical electrode totally embedded and in close contact with biological tissue of infinite dimensions. We solved the electrical-thermal coupled problem analytically by including the power source in both equations. A comparison of the analytical solutions from the HHTE and FHTE showed that (1) for short times and locations close to the electrode surface, the HHTE produced temperatures higher than the FHTE, however, this trend became negligible for longer times, when both equations produced similar temperature profiles (HHTE always being higher than FHTE); (2) for points distant from the electrode surface and for very short times, the HHTE temperature was lower than the FHTE, however, after a delay time, this tendency inverted and the HHTE temperature increased to the maximum; (3) from a mathematical point of view, the HHTE solution showed cuspidal-type singularities, which were materialized as a temperature peak traveling through the medium at a finite speed. This peak rose at the electrode surface, and clearly reflected the wave nature of the thermal problem; (4) the differences between the FHTE and HHTE temperature profiles were smaller for the lower values of thermal relaxation time and locations further from the electrode surface.

Twenty-three water dams located in the Iberian Pyrite Belt were studied during March 2012 (early spring) in order to carry out an environmental assessment based on diatom communities and to define the relationships between these biological communities and the physico-chemical characteristics of the dam surface water. This is the first time that a diatom inventory has been done for dams affected by acid mine drainage (AMD) in the Spanish part of the Iberian Pyrite Belt (IPB). It was found that the pH was the main factor influencing the behaviour of the diatom communities. Then, using a dbRDA approach it was possible to organize the aggrupation of diatoms into four groups in response to the physico-chemical conditions of the ecosystem, especially pH: (1) Maris, Aac, Gos, Cmora (pH 2–3); (2) Andc, San, And, Dpin (pH 3–4.5); (3) Gran, Pleon, Oliv, Lagu, Chan, SilI, SilII, Joya, Gar, Agrio, Camp, Corum (pH 4.5–6); (4) Herr, Diq I, Diq II (pH 6–7). The obtained results confirmed the response of benthic diatom communities to changes in the physico-chemical characteristics of surface water, and helped to understand the role of diatoms as indicators of the degree of AMD contamination in those 23 dams. Special attention was given to those that have an acidophilic or acid-tolerant profile (pH 2–3 and pH 3–4.5) such as Pinnularia aljustrelica, Pinnularia acidophila, Pinnularia acoricola and Eunotia exigua, which are the two groups found in the most AMD contaminated dams.

In this paper, we solve in an analytical way the thermal-optic coupled problem associated with a 1D model of non-perfused homogeneous biological tissue irradiated by a laser beam. We consider a laser pulse duration of 200 micros and study the temperatures of areas very close to the point of laser beam application. We consider that these values of the temporal and spatial variables mean that the problem has to be solved by means of the hyperbolic heat conduction model instead of the classic or parabolic model. We therefore obtain the solution using both models and apply the temperature profiles obtained to a specific biological tissue for comparison. Finally, we theoretically study the effect of the thermal relaxation time on the temperature profiles in the tissue for both heating and cooling phases (i.e. during and after laser application).

This work presents a combination of geochemical, mineralogical, and biological data obtained in water reservoirs located in one of the most paradigmatic mining regions, suffering from acid mine drainage (AMD) problems: the Iberian Pyrite Belt (IPB). Four water reservoirs located in the Spanish sector of the IBP, storing water for different purposes, were selected to achieve an environmental classification based on the effects of AMD: two mining dams (Gossan and Águas Ácidas), a reservoir for industrial use (Sancho), and one with water used for human supply (Andévalo). The results indicated that the four reservoirs are subject to the effect of metallic loads from polluted rivers, although with different levels: Águas Ácidas > Gossan > Sancho ≥ Andévalo. In accordance, epipsammic diatom communities have differences in the respective composition and dominant taxa. The dominant diatoms in each reservoir indicated acid water: Pinnularia acidophila and Pinnularia aljustrelica were found in the most acidic dams (Gossan and Águas Ácidas, with pH <3), Pinnularia subcapitata in Sancho (pH 2.48-5.82), and Eunotia exigua in Andévalo (pH 2.34-6.15).

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ElsevierRivera Ortun, MJ.; Trujillo Guillen, M.; Romero García, V.; López Molina, JA.; Berjano Zanón, E. (2013). Numerical resolution of the hyperbolic heat equation using smoothed mathematical functions instead of Heaviside and Dirac delta distributions.