Numerical analysis of the interactions between laser and soft tissues using generalized dual-phase lag equation

Jasiński, Marek; Majchrzak, Ewa; Turchan, Łukasz

doi:10.1016/j.apm.2015.10.025

Cited by 48 publications

(36 citation statements)

References 40 publications

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“…The irreversible thermal damage of a particular type of a tissue or a cell is described by the condition for Arrhenius damage function or integral [46,47]:

Ω (r, τ) = A \int_{0}^{τ} \exp (- \frac{E_{a}}{R_{g} T (r, t)}) d t \geq 1

…”

Section: Arrhenius Damage Integralmentioning

confidence: 99%

Towards Effective Photothermal/Photodynamic Treatment Using Plasmonic Gold Nanoparticles

Bucharskaya

Maslyakova

Terentyuk

et al. 2016

IJMS

119

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Gold nanoparticles (AuNPs) of different size and shape are widely used as photosensitizers for cancer diagnostics and plasmonic photothermal (PPT)/photodynamic (PDT) therapy, as nanocarriers for drug delivery and laser-mediated pathogen killing, even the underlying mechanisms of treatment effects remain poorly understood. There is a need in analyzing and improving the ways to increase accumulation of AuNP in tumors and other crucial steps in interaction of AuNPs with laser light and tissues. In this review, we summarize our recent theoretical, experimental, and pre-clinical results on light activated interaction of AuNPs with tissues and cells. Specifically, we discuss a combined PPT/PDT treatment of tumors and killing of pathogen bacteria with gold-based nanocomposites and atomic clusters, cell optoporation, and theoretical simulations of nanoparticle-mediated laser heating of tissues and cells.

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“…The irreversible thermal damage of a particular type of a tissue or a cell is described by the condition for Arrhenius damage function or integral [46,47]:

Ω (r, τ) = A \int_{0}^{τ} \exp (- \frac{E_{a}}{R_{g} T (r, t)}) d t \geq 1

…”

Section: Arrhenius Damage Integralmentioning

confidence: 99%

Towards Effective Photothermal/Photodynamic Treatment Using Plasmonic Gold Nanoparticles

Bucharskaya

Maslyakova

Terentyuk

et al. 2016

IJMS

119

View full text Add to dashboard Cite

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“…In 1995, taking the finite speed of thermal propagation and the micro‐structural interactions into consideration, a modified Fourier constitutive equation is proposed, namely the dual‐pulse‐lag (DPL) model. Experiments show that these modified constitutive equations can well simulate heat transfer in some special cases, such as heat transfer between the tissues, heat transfer in amorphous media, and layered‐film heating in superconductors, fins, and reactor walls . However, DPL constitutive relation can not describe abnormal diffusion or diffusion in biological tissues.…”

Section: Introductionmentioning

confidence: 99%

Efficient and accurate spectral method for the time‐fractional dual‐phase‐lag heat transfer model and its parameter estimation

Zheng

Jiang

Zhang

2019

Math Methods in App Sciences

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In the current paper, a heat transfer model is suggested based on a time‐fractional dual‐phase‐lag (DPL) model. We discuss the model in two parts, the direct problem and the inverse problem. Firstly, for solving it, the finite difference/Legendre spectral method is constructed. In the temporal direction, we employ the weighted and shifted Grünwald approximation, which can achieve second order convergence. In the spatial direction, the Legendre spectral method is used, it can obtain spectral accuracy. The stability and convergence are theoretically analyzed. For the inverse problem, the Bayesian method is used to construct an algorithm to estimate the four parameters for the model, namely, the time‐fractional order α, the time‐fractional order β, the delay time τT, and the relaxation time τq. Next, numerical experiments are provided to demonstrate the effectiveness of our scheme, with the values of τq and τT for processed meat employed. We also make a comparison with another method. The data obtained for the direct problem are used in the parameter estimation. The paper provides an accurate and efficient numerical method for the time‐fractional DPL model.

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“…Under the assumption that the metabolic heat sources Q, Q b and the blood temperature T b are constant, the generalized dual-phase lag equation for 1D problem takes the form [13,15,16] ( )…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…In this case the mathematical model consists of the basic problem (GDPLE supplemented by appropriate boundary and initial conditions) and the G. Kałuża, E. Majchrzak, Ł. Turchan 50 additional problem resulting from the differentiation of governing equations. These problems are solved using the explicit scheme of the finite difference method for hyperbolic equations [14,15]. In the final part of the paper the example of computations and conclusions are presented.…”

Section: Introductionmentioning

confidence: 99%

“…The parameter τ q is the phase lag of the heat flux and parameter τ T is the phase lag of the temperature gradient. Extension of this model is the generalized dual-phase lag equation [12][13][14][15]. In this equation the phase lag times τ q and τ T are expressed in terms of the blood and tissue properties, the interphase convective heat transfer coefficient and the blood perfusion rate.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

1D generalized dual-phase lag equation. Sensitivity analysis with respect to the porosity

Kałuża

Majchrzak

Turchan

2016

J. Appl. Math. Comput. Mech.

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Abstract. Thermal processes occurring in the heated tissue are described by the 1D generalized dual-phase lag equation supplemented by appropriate boundary and initial conditions. Using the sensitivity analysis method, the additional problem connected with the porosity is formulated. Both problems are solved by means of the explicit scheme of the finite difference method. In this way it is possible to estimate the temperature changes due to the perturbation of porosity. In the final part of the paper, the example of computation is shown and the conclusions are formulated.

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Numerical analysis of the interactions between laser and soft tissues using generalized dual-phase lag equation

Cited by 48 publications

References 40 publications

Towards Effective Photothermal/Photodynamic Treatment Using Plasmonic Gold Nanoparticles

Towards Effective Photothermal/Photodynamic Treatment Using Plasmonic Gold Nanoparticles

Efficient and accurate spectral method for the time‐fractional dual‐phase‐lag heat transfer model and its parameter estimation

1D generalized dual-phase lag equation. Sensitivity analysis with respect to the porosity

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