Soft tissue freezing process. Identification of the dual-phase lag model parameters using the evolutionary algorithm (original) (raw)
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International Journal of Heat and Mass Transfer, 2017
In the paper, the problem of biological tissue freezing is discussed. In contrast to the previously presented models based on the Pennes equation, the thermal interactions between the cryoprobe tip and soft tissue are described using the dual-phase lag model (DPLM). This model contains two delay times (the relaxation and thermalization times) and in this way, the finite velocity of the thermal wave is considered. The model of the freezing process is based on the introduction of a parameter called 'substitute thermal capacity' to the dual-phase lag equation. At the stage of numerical computations, the explicit scheme of the finite difference method is used. In the final part of the paper the examples of the computation are shown. A comparison with the solution resulting from the adoption of the Pennes equation and also the model verification with the experimental data are presented in the final part of the paper.
Numerical study on triple layer skin tissue freezing using dual phase lag bio-heat model
International Journal of Thermal Sciences, 2014
The present article proposes dual-phase lag (DPL) bio-heat model in triple layer skin tissue for freezing procedure during cryosurgery with non-ideal property of tissue, metabolism and blood perfusion. The enthalpy formulation and the finite difference schemes are used to evaluate temperature distribution, solidus and liquidus interfaces in soft skin tissue during the freezing process. The effect of phase lags of heat flux and temperature gradient are also discussed in this study. It is mentioned that the different values of phase lags of heat flux and temperature gradient have important effect on temperature distribution, liquidus and solidus interfaces within the skin tissue.
On One Mathematical Model of Cooling Living Biological Tissue
Mathematics and Statistics, 2021
When cooling living biological tissue (active, non-inert medium), cryomedicine uses cryo-instruments with various forms of cooling surface. Cryoinstruments are located on the surface of biological tissue or completely penetrate into it. With a decrease in the temperature of the cooling surface, an unsteady temperature field appears in the tissue, which in the general case depends on three spatial coordinates and time. To date, there are a large number of scientific publications that consider mathematical models of cryodestruction of biological tissue. However, in the overwhelming majority of them, the Pennes equation (or some of its modifications) is taken as the basis of the mathematical model, from which the linear nature of the dependence of heat sources of biological tissue on the desired temperature field is visible. This character of the dependence does not allow one to describe the actually observed spatial localization of heat. In addition, Pennes' model does not take into account the fact that the freezing of the intercellular fluid occurs much earlier than the freezing of the intracellular fluid and the heat corresponding to these two processes is released at different times. In the proposed work, a new mathematical model of cooling and freezing of living biological tissue are built with a flat rectangular applicator located on its surface. The model takes into account the above features and is a three-dimensional boundary-value problem of the Stefan type with nonlinear heat sources of a special type and has applications in cryosurgery. A method is proposed for the numerical study of the problem posed, based on the use of locally one-dimensional difference schemes without explicitly separating the boundary of the influence of cold and the boundaries of the phase transition. The method was previously successfully tested by the author in solving other two-dimensional problems arising in cryomedicine.
Two boundary model for freezing front propagation in biological tissue
1998
The response of the living tissue to the effects of strong heating or cooling can cause the blood flow rate to vary by an order of magnitude. A mathematical model for the freezing of living tissue is formulated which takes into account the nonlocal temperature dependence of the blood flow rate when the temperature distribution in the tissue is substantially
Optimization of Organ Freezing Protocols With Specified Allowable Thermal Stress Levels
Advances in Heat and Mass Transfer in Biotechnology, 2000
A novel concept of determining optimized cooling protocols for freezing three-dimensional organs has been developed and its feasibility examined computationally. The concept is based on determining correct spatial variation of temperature distribution on the walls of a freezing container at every instant of time during the cooling process so that local thermal stresses in the heterogeneous organ are always kept below a specified level while maximizing the local cooling rates. The cryo-preservation medium must be gelatin which prevents thermal convection. The optimized cooling protocol was simulated by developing a time-accurate finite element computer program to predict unsteady heat conduction with phase change and thermal stresses within a realistically shaped and sized organ made of tissues with temperature-dependent physical properties. A micro-genetic optimization algorithm was then used to achieve nonlinear constrained optimization of parameterized time-varying container wall ...
Mathematical modeling of freezing and thawing process in tissues: A porous media approach
Imperial College Press, 2010
Biological tissues can be treated as porous media as it is composed of dispersed cell separated by connective voids which allow flow of nutrients, minerals, etc., to reach all cells within the tissue. In this present study, a mathematical model has been developed to study the phase change phenomena during the freezing and thawing process in biological tissues using porous media approach. Effective heat capacity formulation is used for the phase change problem. Numerical simulation is used to study the effect of porosity, on the motion of freezing and thawing front and transient temperature distribution in tissue. It is observed that porosity has significant effect on transient temp profile and phase change interfaces; further decrease in freezing and heating rate has been found with increased value of porosity.
Identification of latent heat of biological tissue subjected to the freezing
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej, 2006
In the paper the inverse problem consisting in the identification of volumetric latent heat of tissue subjected to the freezing is presented. Three different hypotheses concerning the substitute thermal capacity associated with the latent heat evolution are discussed. The 1D problem is considered and on the basis of the cooling curve on the skin surface the volumetric latent heat is estimated. In order to solve the inverse problem the least squares method containing the sensitivity coefficients is applied. In the final part of the paper the results of computations are shown.