Bio-Heat Models Revisited: Concepts, Derivations, Nondimensalization and Fractionalization Approaches

Hristov, Jordan

doi:10.3389/fphy.2019.00189

Cited by 45 publications

(34 citation statements)

References 134 publications

(382 reference statements)

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“…However, the measurement of these properties in living models can be particularly invasive, especially in organs of difficult access, such as the pancreas and the brain. Hence, the effect of blood perfusion in the whole heat transfer phenomenon can be considered by adding a term to the heat transfer equation (Equation (1)) as a heat sink during thermal ablation [ 60 ].…”

Section: Discussionmentioning

confidence: 99%

Measurement of Ex Vivo Liver, Brain and Pancreas Thermal Properties as Function of Temperature

Mohammadi

Bianchi

Asadi

et al. 2021

Sensors

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The ability to predict heat transfer during hyperthermal and ablative techniques for cancer treatment relies on understanding the thermal properties of biological tissue. In this work, the thermal properties of ex vivo liver, pancreas and brain tissues are reported as a function of temperature. The thermal diffusivity, thermal conductivity and volumetric heat capacity of these tissues were measured in the temperature range from 22 to around 97 °C. Concerning the pancreas, a phase change occurred around 45 °C; therefore, its thermal properties were investigated only until this temperature. Results indicate that the thermal properties of the liver and brain have a non-linear relationship with temperature in the investigated range. In these tissues, the thermal properties were almost constant until 60 to 70 °C and then gradually changed until 92 °C. In particular, the thermal conductivity increased by 100% for the brain and 60% for the liver up to 92 °C, while thermal diffusivity increased by 90% and 40%, respectively. However, the heat capacity did not significantly change in this temperature range. The thermal conductivity and thermal diffusivity were dramatically increased from 92 to 97 °C, which seems to be due to water vaporization and state transition in the tissues. Moreover, the measurement uncertainty, determined at each temperature, increased after 92 °C. In the temperature range of 22 to 45 °C, the thermal properties of pancreatic tissue did not change significantly, in accordance with the results for the brain and liver. For the three tissues, the best fit curves are provided with regression analysis based on measured data to predict the tissue thermal behavior. These curves describe the temperature dependency of tissue thermal properties in a temperature range relevant for hyperthermia and ablation treatments and may help in constructing more accurate models of bioheat transfer for optimization and pre-planning of thermal procedures.

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Section: Discussionmentioning

confidence: 99%

Measurement of Ex Vivo Liver, Brain and Pancreas Thermal Properties as Function of Temperature

Mohammadi

Bianchi

Asadi

et al. 2021

Sensors

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“…It is obvious, that the non-locality is not lost despite the use of exponential kernel since the last term in (77) is responsible for this. Similarly, any other relaxation functions invoked by the type of the relaxations in the observed physical problems, may form kernels of non-local terms, but this problem is more general and beyond the scope of this work (some examples are available in [30]).…”

Section: Memory Kernel Effect On the Fractional Modelmentioning

confidence: 99%

Magnetic field diffusion in ferromagnetic materials: fractional calculus approaches

Hristov

2021

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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The paper addresses diffusion approximations of magnetic field penetration of ferromagnetic materials with emphasis on fractional calculus applications and relevant approximate solutions. Examples with applications of time-fractional semi-derivatives and singular kernel models (Caputo time fractional operator) in cases of field independent and field-dependent magnetic diffusivities have been developed: Dirichlet problems and time-dependent boundary condition (power-law ramp). Approximate solutions in all theses case have been developed by applications of the integral-balance method and assumed parabolic profile with unspecified exponents. Tow version of the integral method have been successfully implemented: SDIM (single integration applicable to time-fractional semi-derivative model) and DIM (double-integration model to fractionalized singular memory models). The fading memory approach in the sense of the causality concept and memory kernel effect on the model constructions have been discussed.

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“…In the last years, researchers have proved that many phenomena in engineering, bioengineering, physics, and chemistry can be successfully described by mathematical models that use mathematical tools from fractional calculus, i.e., the theory of derivatives and integrals of noninteger order. Models of viscoelastic materials, Caputo and Mainardi [4]; the signal processing, Marks and Hall [5]; diffusion problems, Olmstead and Handelsman [6]; viscoplastic materials modeling, Diethelm and Freed [7]; mechanical systems subject to damping, Gaul et al [8]; relaxation and reaction kinetics of polymers, Glockle and Nonnenmacher [9]; and heat conduction, Hristov [10,11] are some of the important problems modeled with the help of fractional differential operators.…”

Section: Introductionmentioning

confidence: 99%

Numerical Approaches of the Generalized Time-Fractional Burgers’ Equation with Time-Variable Coefficients

Vieru¹,

Fetecău

Chung

2021

Journal of Function Spaces

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The generalized time-fractional, one-dimensional, nonlinear Burgers equation with time-variable coefficients is numerically investigated. The classical Burgers equation is generalized by considering the generalized Atangana-Baleanu time-fractional derivative. The studied model contains as particular cases the Burgers equation with Atangana-Baleanu, Caputo-Fabrizio, and Caputo time-fractional derivatives. A numerical scheme, based on the finite-difference approximations and some integral representations of the two-parameter Mittag-Leffler functions, has been developed. Numerical solutions of a particular problem with initial and boundary values are determined by employing the proposed method. The numerical results are plotted to compare solutions corresponding to the problems with time-fractional derivatives with different kernels.

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Bio-Heat Models Revisited: Concepts, Derivations, Nondimensalization and Fractionalization Approaches

Cited by 45 publications

References 134 publications

Measurement of Ex Vivo Liver, Brain and Pancreas Thermal Properties as Function of Temperature

Measurement of Ex Vivo Liver, Brain and Pancreas Thermal Properties as Function of Temperature

Magnetic field diffusion in ferromagnetic materials: fractional calculus approaches

Numerical Approaches of the Generalized Time-Fractional Burgers’ Equation with Time-Variable Coefficients

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