Freezing of Biological Tissues During Cryosurgery Using Hyperbolic Heat Conduction Model

Singh, Shubham; Kumar, Sushil

doi:10.3846/13926292.2015.1064486

Cited by 27 publications

(8 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The value of the thermal relaxation time in biological bodies has been predicted to be within 20-30 s [33]. It was found that the non-Fourier model provides a more adequate description of unsteady heat transfer processes occurring in the nonhomogeneous materials such as biological tissue [21,[34][35][36][37][38][39][40][41][42][43].…”

Section: Direct Problemmentioning

confidence: 99%

Estimation of surface heat flux in a one-dimensional hyperbolic bio-heat conduction problem with temperature-dependent properties during thermal therapy

Baghban

Ayani

2016

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

Objective function k Thermal conductivity, W/m °C L Length, m M Number of nodes at spatial coordinate N Number of temporal measurements q ′′ (t) Surface heat flux, W/m 2 q m Metabolic heat generation, W/m 3 T (x, t) Temperature, °C �T (x, t) Sensitivity problem, °C t Temporal coordinate, s W (T ) Convective heat exchange with blood flow, W/m 3 x Spatial coordinate, m Y (t) Measured temperature, °C Greek symbols β Search step size γ Conjugate coefficient δ Dirac delta function ε Convergence criterion ζ Transformed time coordinate, s (x, t) Adjoint function µ Random variable ρ Density, kg/m 3 σ Standard deviation of the measurement errors τ Thermal relaxation time, s ω Perfusion rate of blood, m 3 /s/m 3 Subscript b Blood c Conduction heat transfer es Estimated value ex Exact value f Final value initial Initial value

show abstract

Section: Direct Problemmentioning

confidence: 99%

Estimation of surface heat flux in a one-dimensional hyperbolic bio-heat conduction problem with temperature-dependent properties during thermal therapy

Baghban

Ayani

2016

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

show abstract

“…Other formulas applied to the bioheat transfer issue are the Pennes equation [ 21 ], the Cattaneo–Vernotte equation [ 22 , 23 , 24 ], and the dual phase lag (DPL) model. Bioheat transfer modelling describes phenomena that occur not only during cryopreservation by slow freezing [ 17 ] and vitrification [ 12 , 15 , 25 ], but also other examples of thermal process modelling applications, such as the characterisation of cryosurgery [ 26 , 27 , 28 , 29 , 30 ] or the destruction of biological tissue under the influence of a magnetic field [ 11 , 31 ].…”

Section: Introductionmentioning

confidence: 99%

Crystallisation Degree Analysis during Cryopreservation of Biological Tissue Applying Interval Arithmetic

Piasecka-Belkhayat

Skorupa

2023

Materials

View full text Add to dashboard Cite

This paper presents the numerical modelling of heat transfer and changes proceeding in the homogeneous sample, caused by the crystallisation phenomenon during cryopreservation by vitrification. Heat transfer was simulated in a microfluidic system in which the working fluid flowed in micro-channels. The analysed process included single-phase flow during warming, and two-phase flow during cooling. In the model under consideration, interval parameters were assumed. The base of the mathematical model is given by the Fourier equation, with a heat source including the degree of ice crystallisation. The formulated problem has been solved using the interval version of the finite difference method, with the rules of the directed interval arithmetic. The fourth order Runge–Kutta algorithm has been applied to determine the degree of crystallisation. In the final part of this paper, examples of numerical computations are presented.

show abstract

“…Examples of the modelling of phase transitions can be found in the literature [5,[9][10][11][12][13][14]. As can be seen, most of them present models related to cryosurgery.…”

Section: Introductionmentioning

confidence: 99%

Comparison of heat transfer phenomena for two different cryopreservation methods: slow freezing and vitrification

Skorupa¹,

Piasecka-Belkhayat²

2023

J. Appl. Math. Comput. Mech.

View full text Add to dashboard Cite

The purpose of the research is to prepare a mathematical and numerical model for the phenomenon of heat transfer during cryopreservation. In the paper, two popular methods, slow freezing and vitrification, are compared. Furthermore, the basic model of thermal processes is supplemented by the phenomenon of phase transitions. To determine the temperature distribution during cryopreservation processes, one uses the heat transfer equation proposed by Pennes. An integral part of the energy equation is the substitute thermal capacity (STC) performed according to the concept named one domain method (fixed domain method), The numerical model is developed using the finite difference method (FDM) connected with directed interval arithmetic. The final part of the article contains the results of numerical simulations.

show abstract

Freezing of Biological Tissues During Cryosurgery Using Hyperbolic Heat Conduction Model

Cited by 27 publications

References 37 publications

Estimation of surface heat flux in a one-dimensional hyperbolic bio-heat conduction problem with temperature-dependent properties during thermal therapy

Estimation of surface heat flux in a one-dimensional hyperbolic bio-heat conduction problem with temperature-dependent properties during thermal therapy

Crystallisation Degree Analysis during Cryopreservation of Biological Tissue Applying Interval Arithmetic

Comparison of heat transfer phenomena for two different cryopreservation methods: slow freezing and vitrification

Contact Info

Product

Resources

About