Multi-time-scale heat transfer modeling of turbid tissues exposed to short-pulsed irradiations

Development of a numerical multi-layer model of skin subjected to pulsed laser irradiation to optimise thermal stimulation in photorejuvenation procedure

BACKGROUND AND OBJECTIVE

This paper presents the development of a 3D physics-based numerical model of skin capable of representing the laser-skin photo-thermal interactions occurring in skin photorejuvenation treatment procedures. The aim of this model was to provide a rational and quantitative basis to control and predict temperature distribution within the layered structure of skin. Ultimately, this mathematical and numerical modelling platform will guide the design of an automatic robotic controller to precisely regulate skin temperature at desired depths and for specific durations.

METHODS

The Pennes bioheat equation was used to account for heat transfer in a 3D multi-layer model of skin. The effects of blood perfusion, skin pigmentation and various convection conditions are also incorporated in the proposed model. The photo-thermal effect due to pulsed laser light on skin is computed using light diffusion theory. The physics-based constitutive model was numerically implemented using a combination of finite volume and finite difference techniques. Direct sensitivity routines were also implemented to assess the influence of constitutive parameters on temperature. A stability analysis of the numerical model was conducted.

RESULTS

Finally, the numerical model was exploited to assess its ability to predict temperature distribution and thermal damage via a multi-parametric study which accounted for a wide array of biophysical parameters such as light coefficients of absorption for individual skin layers and melanin levels (correlated with ethnicity). It was shown how critical is the link between melanin content, laser light characteristics and potential thermal damage to skin.

CONCLUSIONS

The developed photo-thermal model of skin-laser interactions paves the way for the design of an automated simulation-driven photorejuvenation robot, thus alleviating the need for inconsistent and error-prone human operators.

Numerical analysis of non-Fourier thermal response of lung tissue based on experimental data with application in laser therapy

BACKGROUND AND OBJECTIVE

The thermal therapy is a minimally invasive technique used as an alternative approach to conventional cancer treatments. There is an increasing concern about the accuracy of the thermal simulation during the process of tumor ablation. This study is aimed at investigating the effect of finite speed of heat propagation in the biological lung tissue, experimentally and numerically.

METHODS

In the experimental study, a boundary heat flux is applied to the lung tissue specimens and the temperature variation is measured during a transient heat transfer procedure. In the numerical study, a code is developed based on the finite volume method to solve the classical bio-heat transfer, the Cattaneo and Vernotte, and the Dual-phase-lag (DPL) equations. The thermal response of tissue during the experiments is compared with the predictions of the three heat transfer models.

RESULTS

It is found that the trend of temperature variation by the DPL model resembles the experimental results. The experimental observation in parallel with the numerical results reveals that the accumulated thermal energy diffuses to the surrounding tissue with a slower rate in comparison with the conventional bio-heat transfer model. The DPL model is implemented to study the temperature elevation in the laser irradiation to lung tissue in the presence of gold nanoparticles (GNPs). It is concluded that the extent of the necrotic tumoral region and the area of the damaged healthy tissue are reduced, when the non-Fourier heat transfer is taken into account.

CONCLUSIONS

Results show that considering the phase lags is crucial in planning for an effective thermal treatment, in which the cancerous tissue is ablated and the surrounding tissues are preserved from irreversible thermal damage.

Incorporating an immersed boundary method to study thermal effects of vascular systems during tissue cryo-freezing

In this paper, the three-dimensional thermal effects of a clinically-extracted vascular tissue undergoing cryo-freezing are numerically investigated. Based on the measured experimental temperature field, the numerical results of the Pennes bioheat model combined with the boundary condition-enforced immersed boundary method (IBM) agreed well with experimental data with a maximum temperature discrepancy of 2.9°C. For simulating the temperature profile of a tumor sited in a dominantly vascularized tissue, our model is able to capture with ease the thermal effects at specified junctions of the blood vessels. The vascular complexity and the ice-ball shape irregularity which cannot be easily quantified via clinical experiments are also analyzed and compared for both two-dimensional and three-dimensional settings with different vessel configurations and developments. For the three-dimensional numerical simulations, a n-furcated liver vessels model from a three-dimensional segmented volume using hole-making and subdivision methods is applied. A specific study revealed that the structure and complexity of the vascular network can markedly affect the tissue's freezing configuration with increasing ice-ball irregularity for greater blood vessel complexity.

Tripling the maximum imaging depth with third-harmonic generation microscopy

The growing interest in performing high-resolution, deep-tissue imaging has galvanized the use of longer excitation wavelengths and three-photon-based techniques in nonlinear imaging modalities. This study presents a threefold improvement in maximum imaging depth of ex vivo porcine vocal folds using third-harmonic generation (THG) microscopy at 1552-nm excitation wavelength compared to two-photon microscopy (TPM) at 776-nm excitation wavelength. The experimental, analytical, and Monte Carlo simulation results reveal that THG improves the maximum imaging depth observed in TPM significantly from 140 to 420 μm in a highly scattered medium, reaching the expected theoretical imaging depth of seven extinction lengths. This value almost doubles the previously reported normalized imaging depths of 3.5 to 4.5 extinction lengths using three-photon-based imaging modalities. Since tissue absorption is substantial at the excitation wavelength of 1552 nm, this study assesses the tissue thermal damage during imaging by obtaining the depth-resolved temperature distribution through a numerical simulation incorporating an experimentally obtained thermal relaxation time (τ). By shuttering the laser for a period of 2τ, the numerical algorithm estimates a maximum temperature increase of ∼2°C at the maximum imaging depth of 420 μm. The paper demonstrates that THG imaging using 1552 nm as an illumination wavelength with effective thermal management proves to be a powerful deep imaging modality for highly scattering and absorbing tissues, such as scarred vocal folds.

Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study

Parabolic heat equation based on Fourier's theory (FHE), and hyperbolic heat equation (HHE), has been used to mathematically model the temperature distributions of biological tissue during thermal ablation. However, both equations have certain theoretical limitations. The FHE assumes an infinite thermal energy propagation speed, whereas the HHE might possibly be in breach of the second law of thermodynamics. The relativistic heat equation (RHE) is a hyperbolic-like equation, whose theoretical model is based on the theory of relativity and which was designed to overcome these theoretical impediments. In this study, the three heat equations for modelling of thermal ablation of biological tissues (FHE, HHE and RHE) were solved analytically and the temperature distributions compared. We found that RHE temperature values were always lower than those of the FHE, while the HHE values were higher than the FHE, except for the early stages of heating and at points away from the electrode. Although both HHE and RHE are mathematically hyperbolic, peaks were only found in the HHE temperature profiles. The three solutions converged for infinite time or infinite distance from the electrode. The percentage differences between the FHE and the other equations were larger for higher values of thermal relaxation time in HHE.

Phase-function normalization for accurate analysis of ultrafast collimated radiative transfer

The scattering of radiation from collimated irradiation is accurately treated via normalization of phase function. This approach is applicable to any numerical method with directional discretization. In this study it is applied to the transient discrete-ordinates method for ultrafast collimated radiative transfer analysis in turbid media. A technique recently developed by the authors, which conserves a phase-function asymmetry factor as well as scattered energy for the Henyey-Greenstein phase function in steady-state diffuse radiative transfer analysis, is applied to the general Legendre scattering phase function in ultrafast collimated radiative transfer. Heat flux profiles in a model tissue cylinder are generated for various phase functions and compared to those generated when normalization of the collimated phase function is neglected. Energy deposition in the medium is also investigated. Lack of conservation of scattered energy and the asymmetry factor for the collimated scattering phase function causes overpredictions in both heat flux and energy deposition for highly anisotropic scattering media. In addition, a discussion is presented to clarify the time-dependent formulation of divergence of radiative heat flux.

Thermal interaction of short-pulsed laser focused beams with skin tissues

Time-dependent thermal interaction is developed in a skin tissue cylinder subjected to the irradiation of a train of short laser pulses. The skin embedded with a small tumor is stratified as three layers: epidermis, dermis and subcutaneous fat with different optical, thermal and physiological properties. The laser beam is focused to the tumor site by an objective lens for thermal therapy. The ultrafast radiation heat transfer of the focused beam is simulated by the transient discrete ordinates method. The transient Pennes bio-heat equation is solved numerically by the finite volume method with alternating direction implicit scheme. Emphasis is placed on the characterization of the focused beam propagation and absorption and the temperature rise in the focal spot. The effects of the focal spot size and location, the laser power, and the bio-heat equation are investigated. Comparisons with collimated irradiation are conducted. The focused beam can penetrate a greater depth and produce higher temperature rise at the target area, and thus reduce the possibility of thermal damage to the surrounding healthy tissue. It is ideal for killing cancerous cells and small tumors.