Papers by María José Rivera
Mathematical Biosciences and Engineering, 2015
It has been suggested that during RF thermal ablation of biological tissue the thermal lesion cou... more It has been suggested that during RF thermal ablation of biological tissue the thermal lesion could reach an equilibrium size after 1-2 minutes. Our objective was to determine under which circumstances of electrode geometry (needle-like vs. ball-tip), electrode type (dry vs. cooled) and blood perfusion the temperature will reach a steady state at any point in the tissue. We solved the bioheat equation analytically both in cylindrical and spherical coordinates and the resultant limit temperatures were compared. Our results demonstrate mathematically that tissue temperature reaches a steady value in all cases except for cylindrical coordinates without the blood perfusion term, both for dry and cooled electrodes, where temperature increases infinitely. This result is only true when the boundary condition far from the active electrode is considered to be at infinitum. In contrast, when a finite and sufficiently large domain is considered, temperature reaches always a steady state.
GERARDO ARANGO OSPINA (*) JUAN ANTONIO L ÓPEZ MOLINA MAR ÍA JOS É RIVERA ORTIZ (**) Resumen. En u... more GERARDO ARANGO OSPINA (*) JUAN ANTONIO L ÓPEZ MOLINA MAR ÍA JOS É RIVERA ORTIZ (**) Resumen. En un trabajo anterior [2], los autores obtuvieron algunos resultados sobre espacios Lp ponderados para usarlos en la construcción de medidas conmensurables en algunos espacios medibles, resultados que son conocidos para los espacios Lp, pero no en espacios Lp ponderados. El propósito del artículo es dar a conocer esos resultados.
Zeitschrift für Analysis und ihre Anwendungen, 2001
Given an Orlicz function H satisfying the ∆ 2 property at zero, one can use the Orlicz sequence s... more Given an Orlicz function H satisfying the ∆ 2 property at zero, one can use the Orlicz sequence space H to define a tensor norm g c H and the minimal (H c -nuclear) and maximal (H c -integral) operator ideals associated to g c H in the sense of Defant and Floret. The aim of this paper is to characterize H c -integral operators by a factorization theorem.
Proyecciones (Antofagasta), 2006
Classical theory of tensornorms and operator ideals studies mainly those defined by means of sequ... more Classical theory of tensornorms and operator ideals studies mainly those defined by means of sequence spaces p . Considering Orlicz sequence spaces as natural generalization of p spaces, in a previous paper an Orlicz sequence space was used to define a tensornorm, and characterize minimal and maximal operator ideals associated, by using local techniques. Now, in this paper we give a new characterization of the maximal operator ideal to continue our analysis of some coincidences among such operator ideals. Finally we prove some new metric properties of tensornorm mentioned above.
Bulletin of the Australian Mathematical Society, 2004
We study the tensor norm defined by a sequence space λ and its minimal and maximal operator ideal... more We study the tensor norm defined by a sequence space λ and its minimal and maximal operator ideals associated in the sense of Defant and Floret. Our results extend the classical theory related to the tensor norms of Saphar [16]. They show the key role played by the finite dimensional structure of the ultrapowers of λ in this kind of problems.
Czechoslovak Mathematical Journal, 2001
Given a Young function Φ, we study the existence of copies of c 0 and ∞ in cabv Φ (µ, X) and in c... more Given a Young function Φ, we study the existence of copies of c 0 and ∞ in cabv Φ (µ, X) and in cabsv Φ (µ, X), the countably additive, µ-continuous, and X-valued measure spaces of bounded Φ-variation and bounded Φ-semivariation, respectively.
Rocky Mountain Journal of Mathematics, 2000
The purpose of this paper is to extend the de la Vallée Poussin theorem to cabv(µ, X), the space ... more The purpose of this paper is to extend the de la Vallée Poussin theorem to cabv(µ, X), the space of measures defined in Σ with values in the Banach space X which are countably additive, of bounded variation and µ-continuous, endowed with the variation norm.
Proceedings of the American Mathematical Society, 2005
The two better-known ways of understanding the notion of local unconditional structure allow us t... more The two better-known ways of understanding the notion of local unconditional structure allow us to define successive extensions of the wellknown class of the L p spaces of Lindenstrauss and Pelczyǹski. This paper also studies stability properties of these classes under ultrapowers, biduals and complemented subspaces.
International Journal of Hyperthermia, 2016
To develop computer models to mimic the impedance-controlled pulsing protocol implemented in RF g... more 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.
The Open Biomedical Engineering Journal, 2008
Theoretical modeling is a technique widely used to study the electrical-thermal performance of di... more Theoretical modeling is a technique widely used to study the electrical-thermal performance of different surgical procedures based on tissue heating by use of radiofrequency (RF) currents. Most models employ a parabolic heat transfer equation (PHTE) based on Fourier’s theory, which assumes an infinite propagation speed of thermal energy. We recently proposed a one-dimensional model in which the electrical-thermal coupled problem was analytically solved by using a hyperbolic heat transfer equation (HHTE), i.e. by considering a non zero thermal relaxation time. In this study, we particularized this solution to three typical examples of RF heating of biological tissues: heating of the cornea for refractive surgery, cardiac ablation for eliminating arrhythmias, and hepatic ablation for destroying tumors. A comparison was made of the PHTE and HHTE solutions. The differences between their temperature profiles were found to be higher for lower times and shorter distances from the electrode...
Mathematical and Computer Modelling, 2009
In modern surgery, a multitude of minimally intrusive operational techniques are used which are b... more 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.
Journal of Mathematical Analysis and Applications, 2004
We characterize the minimal and maximal operator ideals associated, in the sense of Defant and Fl... more We characterize the minimal and maximal operator ideals associated, in the sense of Defant and Floret, to a wide class of tensor norms derived from a Banach sequence space. Our results are extensions of classical ones about tensor norms of Saphar [Studia Math. 38 (1972) 71-100] and show the key role played by the structure of finite-dimensional subspaces in this kind of problems.
Medical Physics, 2009
The objectives of this study were to model the temperature progress of a pulsed radiofrequency (R... more The objectives of this study were to model the temperature progress of a pulsed radiofrequency (RF) power during RF heating of biological tissue, and to employ the hyperbolic heat transfer equation (HHTE), which takes the thermal wave behavior into account, and compare the results to those obtained using the heat transfer equation based on Fourier theory (FHTE). A theoretical model was built based on an active spherical electrode completely embedded in the biological tissue, after which HHTE and FHTE were analytically solved. We found three typical waveforms for the temperature progress depending on the relations between the dimensionless duration of the RF pulse and the expression , with as the dimensionless thermal relaxation time of the tissue and as the dimensionless position. In the case of a unique RF pulse, the temperature at any location was the result of the overlapping of two different heat sources delayed for a duration (each heat source being produced by a RF pulse of li...
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Papers by María José Rivera