We analyze the necrosis growth due to thermal coagulation induced by laser light absorption and limited by heat diffusion into the surrounding live tissue. The tissue is assumed to contain a certain tumor in the undamaged tissue whereof the blood perfusion rate does not change during the action. By contrast, the normal tissue responds strongly to increase in the tissue temperature and the blood perfusion rate can grow by tenfold. We study in detail the necrosis formation under conditions typical for a real course of thermal therapy treatment, the duration of the action is taken about 5 minutes when a necrosis domain of size about or above 1 cm is formed. In particular, if the tumor size is sufficiently large, it is about 1 cm, and the tissue response is not too delayed, the delay time does not exceed 1 min, then there are conditions under which the relative volume of the damaged normal tissue is small in comparison with the tumor volume after the tumor is coagulated totally.
Previously we have developed a free boundary model for local thermal coagulation induced by laser light absorption when the tissue region affected directly by laser light is sufficiently small and heat diffusion into the surrounding tissue governs the necrosis growth. In the present paper keeping in mind the obtained results we state the point of view on the necrosis formation under these conditions as the basis of an individual laser therapy mode exhibiting specific properties. In particular, roughly speaking, the size of the resulting necrosis domain is determined by the physical characteristics of the tissue and its response to local heating, and by the applicator form rather than the treatment duration and the irradiation power.
Previously we have developed a free boundary model for local thermal coagulation induced by laser light absorption when the tissue region affected directly by laser light is sufficiently small and heat diffusion into the surrounding tissue governs the necrosis growth. In the present paper keeping in mind the obtained results we state the point of view on the necrosis formation under these conditions as the basis of an individual layer therapy mode exhibiting specific properties. In particular, roughly speaking, the size of the resulting necrosis domain is determined by the physical characteristics of the tissue and its response to local heating, and by the applicator form rather than the treatment duration and the irradiation power.
In the present paper basing ont he free boundary model proposed previously we analyze the characteristic properties of local thermal coagulation depending on the applicator form. This model assumes that direct absorption of laser light in a small region causes the temperature to attain sufficiently high values leading to the immediate tissue coagulation. Heat diffusion into the surrounding live tissue gives rise to further thermal coagulation and the subsequent growth of the necrosis domain. Keeping in mind the possible forms of applicators we study the necrosis growth considering the heat generation rate of the cylindrical and spherical symmetry. In particular, it is shown that for the 3D case the necrosis growth exhibits saturation when thermal coagulation is limited by heat diffusion. For the 2D case heat diffusion provides continuous growth of the necrosis domain during the whole time of thermotherapy treatment. It turns out that the time dependence of the temperature in the region where thermal coagulation is under way is practically insensitive to particular details of the growth conditions.
A new mathematical model is proposed for the growth of a small necrosis domain in living tissue caused by
local laser irradiation. Laser light is assumed to be delivered to a small internal region where its absorption causes the temperature to attain high values, leading to immediate tissue coagulation. The coagulation is treated in terms of irreversible phase transition, i.e., it is assumed to occur after the tissue temperature exceeds a certain threshold Tcg . The model considers tissue as involving two regions: the necrosis domain, where the blood perfusion rate is equal to zero, and the normal tissue, which responds to temperature variations by increasing the perfusion rate. The model takes into account the fact that in normal tissue changes in temperature are governed by the blood perfusion rate averaged on spatial scales over the length of the vessels directly controlling heat exchange between the tissue and blood rather than the true perfusion rate. Two alternative models, the developed one and a model allied to the classic approach to the mathematical
description of local thermal coagulation, are compared. The effects of blood flow nonuniformity and the delay in vessel response on growth of the necrosis domain are analyzed in detail.
We propose a new mathematical model for the growth of a necrosis domain due to thermal coagulation. We assume that laser light is locally delivered to a small internal region where laser energy absorption causes the temperature to attain high values leading to immediate tissue coagulation. Heat diffusion into the surrounding tissue causes its further thermal coagulation, giving rise to the growth of the necrosis domain. The coagulation is treated in terms of irreversible phase transition, i.e. the coagulation is assumed to occur after the tissue temperature exceeds a certain threshold value Tcg. Two alternative models, the developed one and the model previously used are compared. The effects of the blood flow nonuniformity, the tissue response to temperature variations, and the delay of this response are analyzed in detail.
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