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SUMMARY:Modeling temperature dynamics in non-uniform biological tissues un
 der cryogenic impact
DTSTART;VALUE=DATE-TIME:20240925T101000Z
DTEND;VALUE=DATE-TIME:20240925T103000Z
DTSTAMP;VALUE=DATE-TIME:20260916T082945Z
UID:indico-contribution-364@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Sergey Shevchenko (B. Verkin ILTPE of NASU)\nPhysica
 l and mathematical modeling is widely used to simulate cryoapplication pro
 cesses. Mathematical modeling of this process [1\,2] allows us to predict 
 the temperature field of the frozen region. This makes it possible to dete
 rmine the cryo-application time sufficient to destroy target cells and min
 imize damage to healthy cells under various experimental conditions. Moreo
 ver\, simulation also predicts the depth of the cryoapplication impact\, w
 hich can be difficult to measure in some situations in the living tissues.
  Then\, we use temperature-dependent thermodynamical parameters of biologi
 cal tissues to compare simulation with thermal imaging.\nThe problem with 
 moving phase boundary is known as the Stefan problem. There are several wa
 ys to numerically solve that problem. One of them is gradually changing th
 ermodynamic parameters close to the phase change boundary. This approach i
 s effectively describing the freezing dynamics of a biological tissues. Th
 e appearance of solutes in water leads to change the freezing temperature 
 in a range of temperatures around (-10C..-0.1C) due to change of solute co
 ncentration. By combining the usual thermal capacity with latent heat\, we
  can define an effective thermal capacity. That allows us to solve the hea
 t equation in 2D cylindrical geometry\, see Fig. 1.\n	Generally thermodyna
 mic properties of the biological tissues are highly dependent on temperatu
 re\, so we have a non-uniform heat equation $\\frac{\\partial T}{\\partial
  t}=\\frac{1}{\\rho C_\\text{p}}\\nabla k\\nabla T$ . To solve this equati
 on numerically\, we use the finite differences method on a rectangular mes
 h to calculate the thermal balance of each node. Then we compare our resul
 ts with thermal imaging of cryoapplication impact on rat skin [3].\n\n\n\n
 Fig. 1. (a) Principal scheme of the cryo-application problem for 2D cylind
 rical geometry with radial symmetry\, where there is the cryo-applicator w
 ith a temperature of liquid Nitrogen pressed 1-2mm inside the soft tissues
 . (b) Dynamics of the maximum radius and depth of the ice spot for several
  isotherms. Typically consists of 4 phases\, I-freezing\, II-thawing thin 
 layer of ice around the main ice spot\, III-usual thawing\, IV-finish thaw
 ing.\nAcknowledgments: This research is sponsored by the National Research
  Foundation of Ukraine (Grant No. 2022.01/0094).\n[1] M. Rossi and Y. Rabi
 n\, in: Proc. Int. Conf. "Modeling\, Simulation & Visualization Methods" (
 MSV 2007)\, CSREA Press\, 187-193.\n[2] Y. Rabin and A. Shitzer\, J. Biome
 ch. Eng.\, 1997\, 119\, 146-152. \n[3] G. Kovalev et al.\, Problems of Cry
 obiology and Cryomedicine\, 2020 30\, 359-368\n\nhttps://indico.bitp.kiev.
 ua/event/13/contributions/364/
LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst
 itute of Mathematics (Section 5) 322
URL:https://indico.bitp.kiev.ua/event/13/contributions/364/
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