Modelling of biological tissue damage process with application of interval arithmetic
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Silesian University of Technology, Institute of Computational Mechanics and Engineering, Gliwice, Poland
Submission date: 2018-05-10
Acceptance date: 2018-10-25
Publication date: 2019-01-20
Journal of Theoretical and Applied Mechanics 2019;57(1):249-261
In the paper, the numerical analysis of thermal processes proceeding in a 2D soft biological tissue subjected to laser irradiation is presented. The transient heat transfer is described by the bioheat transfer equation in Pennes formulation. The internal heat source resulting from the laser-tissue interaction based on the solution of the diffusion equation is taken into account. Thermophysical and optical parameters of the tissue are assumed as directed intervals numbers. At the stage of numerical realization. the interval finite difference method has been applied. In the final part of the paper, the results obtained are shown.
Abraham J.P., Sparrow E.M., 2007, A thermal-ablation bioheat model including liquid-to--vapor phase change, pressure- and necrosis-dependent perfusion, and moisture-dependent properties, International Journal of Heat and Mass Transfer, 50, 13-14, 2537-2544.
Banerjee S., Sharma S.K., 2010, Use of Monte Carlo simulations for propagation of light in biomedical tissues, Applied Optics, 49, 4152-4159.
Dawood H., 2011, Theories of Interval Arithmetic: Mathematical Foundations and Applications, LAP LAMBERT Academic Publishing GmbH & Co., Germany.
Dombrovsky L.A., Baillis D., 2010, Thermal Radiation in Disperse Systems: An Engineering Approach, Begell House, New York.
Dombrovsky L.A., Randrianalisoa J.H., Lipinski W., Timchenko V., 2013, Simplified approaches to radiative transfer simulations in laser induced hyperthermia of superficial tumors, Computational Thermal Sciences, 5, 6, 521-530.
Fasano A., H¨omberg D., Naumov D., 2010, On a mathematical model for laser-induced thermotherapy, Applied Mathematical Modelling, 34, 12, 3831-3840.
Gajda K., Marciniak A., Szyszka B., 2000, Three- and four-stage implicit interval methods of Runge-Kutta type, Computational Methods in Science and Technology, 6, 41-59.
Hansen E., Walster G.W., 2004, Global Optimization Using Interval Analysis, Marcell Dekker, New York.
Henriques F.C., 1947, Studies of thermal injuries, V. The predictability and the significance of thermally induced rate process leading to irreversible epidermal injury, Journal of Pathology, 23, 489-502.
Jacques S.L., Pogue B.W., 2008, Tutorial on diffuse light transport, Journal of Biomedical Optics, 13, 4, 1-19.
Jankowska M.A., Sypniewska-Kaminska G., 2012, Interval finite difference method for bioheat transfer problem given by the Pennes equation with uncertain parameters, Mechanics and Control, 31, 2, 77-84.
Jasiński M., 2014, Modelling of tissue thermal injury formation process with application of direct sensitivity method, Journal of Theoretical and Applied Mechanics, 52, 947-957.
Jasiński M., 2015, Modelling of thermal damage in laser irradiated tissue, Journal of Applied Mathematics and Computational Mechanics, 14, 67-78.
Jasiński M., 2018, Numerical analysis of soft tissue damage process caused by laser action, AIP Conference Proceedings, 060002, 1922.
Jasiński M., Majchrzak E., Turchan L., 2016, Numerical analysis of the interactions between laser and soft tissues using generalized dual-phase lag model, Applied Mathematic Modelling, 40, 2, 750-762.
Kałuża G., Majchrzak E., Turchan L., 2017, Sensitivity analysis of temperature field in the heated soft tissue with respect to the perturbations of porosity, Applied Mathematical Modelling, 49, 498-513.
Di Lizia P., Armellin R., Bernelli-Zazzera F., Berz M., 2014, High order optimal control of space trajectories with uncertain boundary conditions, Acta Astronautica, 93, 217-229.
Majchrzak E., Mochnacki B., 2016, Dual-phase lag equation. Stability conditions of a numerical algorithm based on the explicit scheme of the finite difference method, Journal of Applied Mathematics and Computational Mechanics, 15, 89-96.
Majchrzak E., Mochnacki B., 2017, Implicit scheme of the finite difference method for 1D dual-phase lag equation, Journal of Applied Mathematics and Computational Mechanics, 16, 3, 37-46.
Majchrzak E., Turchan L., Dziatkiewicz J., 2015, Modeling of skin tissue heating using the generalized dual-phase lag equation, Archives of Mechanics, 67, 6, 417-437.
Markov S.M., 1995, On directed interval arithmetic and its applications, Journal of Universal Computer Science, 1, 514-526.
Mochnacki B., Ciesielski M., 2016, Sensitivity of transient temperature field in domain of forearm insulated by protective clothing with respect to perturbations of external boundary heat flux, Bulletin of the Polish Academy of Sciences – Technical Sciences, 64, 3.
Mochnacki B., Piasecka-Belkhayat A., 2013, Numerical modeling of skin tissue heating using the interval finite difference method, Molecular and Cellular Biomechanics, 10, 3, 233-244.
Mochnacki B., Suchy J.S., 1995, Numerical Methods in Computations of Foundry Processes, PFTA, Cracow.
Moore R.E., 1966, Interval Analysis, Prentice-Hall, Englewood Cliffs.
Nakao M., 2017, On the initial-boundary value problem for some quasilinear parabolic equations of divergence form, Journal of Differential Equations, 263, 8565-8580.
Paruch M., 2014, Hyperthermia process control induced by the electric field in order to destroy cancer, Acta of Bioengineering and Biomechanics, 16, 4, 123-130.
Piasecka-Belkhayat A., 2011, Interval Boundary Element Method for Imprecisely Defined Unsteady Heat Transfer Problems (in Polish), Silesian University of Technology, Gliwice.
Piasecka-Belkhayat A., Jasiński M., 2011, Modelling of UV laser irradiation of anterior part of human eye with interval optic, [In:] Evolutionary and Deterministic Methods for Design, Optimization and Control. Applications, Burczyński T., P´eriaux J. (Eds.), CIMNE, Barcelona, 316-321.
Piasecka-Belkhayat A., Korczak A., 2016, Numerical modelling of the transient heat transport in a thin gold film using the fuzzy lattice Boltzmann method with alpha-cuts, Journal of Applied Mathematics and Computational Mechanics, 15, 1, 123-135.
Piasecka-Belkhayat A., Korczak A., 2017, Modeling of thermal processes proceeding in a 1D domain of crystalline solids using the lattice Boltzmann method with an interval source function, Journal of Theoretical and Applied Mechanics, 55, 1, 167-175.
Popova E.D., 1994, Extended interval arithmetic in IEEE floating-point environment, Interval Computations, 4, 100-129.
Popova E.D., 2011, Multiplication distributivity of proper and improper intervals, Reliable Computing, 7, 129-140.
Welch A.J., 2011, Optical-Thermal Response of Laser Irradiated Tissue, M.J.C. van Gemert (Eds.), 2nd edit., Springer.
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