In the previous paper we have proposed a new mathematical model for local thermal coagulation due to laser light absorption and the corresponding necrosis growth. The classic bioheat equation does not hold on small spacial scales on which the fraction of undamaged tissue varies substantially. Therefore we use the free boundary approach regarding the region of partially damaged tissue as an infinitely thin layer. In order to complete the free boundary approach certain conditions should be imposed on the temperature distribution at this interface. Previously we have assumed that the coagulation occurs when the temperature at the necrosis interface exceeds a certain threshold value. This approximation, however can lead to a wrong prediction for treatment of long duration. In the present work we generalize this model which no longer considers the interface temperature fixed and is based on the relation between the interface velocity and the boundary values of temperature distribution. It is shown that this model describes adequately the necrosis growth also in the treatment course of long duration.
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