J. A. López Molina

Modeling the heating of biological tissue based on the hyperbolic heat transfer equation

In modern surgery, a multitude of minimally intrusive operational techniques are used which are based on the point heating of target zones of human tissue via laser or radiofrequency currents. Traditionally, these processes are modeled by the bioheat equation introduced by Pennes, who considers Fouriers theory of heat conduction. We present an alternative and more realistic model established using the hyperbolic equation of heat transfer. To demonstrate some features and advantages of our proposed method, we apply the results obtained 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. We hope that the results from our approach will help with refining surgical interventions in this novel field of medical treatment.

The associated tensor norm to (q,p)-absolutely summing operators on C(K)-Spaces

AbstractWe give an explicit description of a tensor norm equivalent on

Operator ideals and tensor norms defined by a sequence space

C(K){\text{ }} \otimes {\text{ }}F

On operator ideals related to (p,σ)-absolutely continuous operators

to the associated tensor norm νqp to the ideal of (g,p)-absolutely summing operators. As a consequence, we describe a tensor norm on the class of Banach spaces which is equivalent to the left projective tensor norm associated to νqp.

Numerical resolution of the hyperbolic heat equation using smoothed mathematical functions instead of Heaviside and Dirac delta distributions

In this paper we show the advantages of using Mathematica software in engineering mathematics classes through the study of an example problem concerning heat conduction in a slab. Firstly the problem is solved from the point of view of a parabolic model of heat conduction, and secondly from the viewpoint of a hyperbolic model.

Characterization of g∞,σ-integral operators

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.

Ultraproducts of real interpolation spaces between Lp-spaces

In this paper we outline our main findings about the differences between the use of the Bioheat Equation and the Hyperbolic Bioheat Equation in theoretical models for RF ablation. At the moment, we have been working on the analytical approach to solve both equations, but more recently, we have considered numerical models based on the Finite Element Method (FEM). As a first step to use FEM, we conducted a comparative study between the temperature profiles obtained from the analytical solutions and those obtained from FEM.