Transient Bioheat Equation Research Articles

Plasmonic Photothermal Heating of Gold Nanoshell Solutions

We present a theoretical approach to theoretically investigate how gold core-shellnanoparticles dispersed in water thermally respond to near-infrared-regime laser illumination. First, the absorption cross section of gold nanostructures is calculated using Mie theory. Second, we determine the absorbed power density when the solution is exposed by the laser light. Here, the solution of nanostructures is assumed to be uniform and homogenous. Third, we analytically solve the transient bioheat equation to calculate time-dependent temperature increase. Our theoretical calculations quantitatively agree with previous experiments without any adjustable parameter.This approach would provide a reliable tool to understand photothermal effects in unexplored structures.

Transient Bioheat Equation in Breast Tissue: Effect of Tumor Size and Location

Transient Bioheat Equation in Breast Tissue: Effect of Tumor Size and Location

Theoretical model for plasmonic photothermal response of gold nanostructures solutions

Photothermal effects of gold core–shell nanoparticles and nanorods dispersed in water are theoretically investigated using the transient bioheat equation and the extended Mie theory. Properly calculating the absorption cross section is an extremely crucial milestone to determine the elevation of solution temperature. The nanostructures are assumed to be randomly and uniformly distributed in the solution. Compared to previous experiments, our theoretical temperature increase during laser light illumination provides, in various systems, both reasonable qualitative and quantitative agreement. This approach can be a highly reliable tool to predict photothermal effects in experimentally unexplored structures. We also validate our approach and discuss itslimitations.

An efficient parallel numerical modeling of bioheat transfer in realistic tissue structure

A fast and accurate numerical method of solving bioheat transfer problems is critical for many biomedical applications, such as efficient implementation of thermal therapy planning in a clinical setup, and evaluation of the thermal effects induced by specific energy absorption rate (SAR) from external electromagnetic field. This paper developed a parallel finite-difference method based on alternating direction explicit (ADE) scheme to solve three dimensional transient bioheat equation for the realistic tissue structure. An optimized processing pipeline for accurate presentation of the irregular boundary condition was established to considerably reduce the staircase errors induced by cubic voxel. The voxels order aligned along diagonal direction was designed to allow fast parallel strategy for the lower and upper matrix solution involved in ADE scheme for irregular tissue. The test cases including a real head model have indicated that the developed method can support large time step and cubic voxel approximation of irregular interface and boundary, and also produce significant parallel efficiency.

Anatomical-based model for simulation of HIFU-induced lesions in atherosclerotic plaques

Purpose: The aim of this study was to simulate the effect of high intensity focused ultrasound (HIFU) in non-homogenous medium for targeting atherosclerotic plaques in vivo. Materials and methods: A finite-difference time-domain heterogeneous model for acoustic and thermal tissue response in the treatment region was derived from ultrasound images of the treatment region. A 3.5 MHz dual mode ultrasound array suitable for targeting peripheral vessels was used. The array has a lateral and elevation focus at 40 mm with fenestration in its centre through which a 7.5 MHz diagnostic transducer can be placed. Two cases were simulated where seven adjacent HIFU shots (∼5000 W/cm2, 2-s exposure time) were targeted on the plaque tissue within the femoral artery. The transient bioheat equation with a convective term to account for blood flow was used to predict the thermal dose. The results of the simulation model were then validated against the histology data. Results: The simulation model predicted the HIFU-induced damage for both cases, and correlated well with the histology data. For the first case thermal damage was detected within the targeted plaque, while for the second case thermal damage was detected in the pre-focal region. Conclusion: The results suggest that a realistic, image-based acoustic and thermal model of the treatment region is capable of predicting the extent of thermal damage to target plaque tissue. The model considered the effect of the wall thickness of large arteries and the heat-sink effect of flowing blood. The model is used for predicting the size and pattern of HIFU damage in vivo.

Multi–Frequency Analysis For Interstitial Microwave Hyperthermia Using Multi–Slot Coaxial Antenna

Abstract The presented paper shows a new concept of multi-slot coaxial antenna working at different frequencies to predict the best solution for interstitial microwave hyperthermia treatment. The described method concerns a microwave heating of unhealthy cells using a thin microwave antenna located in the human tissue. Therefore, the coupled wave equation in a sinusoidal steady-state and the transient bioheat equation under an axial symmetrical model are considered. The 4-Cole-Cole approximation has been used to compute the complex relative permittivity of the human tissues at different antenna operating frequencies. At the stage of numerical simulation the finite element method (FEM) is used. Special attention has been paid to estimate the optimal antenna parameters for thermal therapy for three microwave frequencies mainly used in medical practice and make comparison of the obtained results in the case of single-, double- and triple-slot antennas.

A meshless point collocation treatment of transient bioheat problems

A meshless numerical method is proposed for the solution of the transient bioheat equation in two and three dimensions. The Pennes bioheat equation is extended in order to incorporate water evaporation, tissue damage, and temperature-dependent tissue properties during tumor ablation. The conductivity of the tissue is not assumed constant but is treated as a local function to simulate local variability due to the existence of usually unclear interfacing of healthy and pathological segments. In this way, one avoids the need for accurate identification of the boundaries between pathological and healthy regions, which is a typical problem in medical practice, and sidesteps, evidently, the corresponding mathematical treatment of such boundaries, which is usually a tedious procedure with some inevitable degree of approximation. The numerical results of the new method for test applications of the bioheat transfer equation are validated against analytical predictions and predictions of other numerical methods. 3D simulations are presented that involve the modeling of tumor ablation and account for metabolic heat generation, blood perfusion, and heat ablation using realistic values for the various parameters. An evaluation of the effective medium approximation to homogenize conductivity fields for use with the bioheat equation is also provided.

Space-dependent perfusion coefficient identification in the transient bio-heat equation

The identification of the space-dependent perfusion coefficient in the one-dimensional transient bio-heat conduction equation is investigated. While Dirichlet boundary conditions are assumed, the additional measurement necessary to render a unique solution is either a heat-flux measurement or a time-average temperature measurement inside the space region of interest. A numerical approach based on the Crank–Nicolson finite-difference scheme combined with the first-order Tikhonov’s regularization method is developed. Numerical results are presented and discussed.

Estimation for the heating effect of magnetic nanoparticles in perfused tissues

This work uses the transient bio-heat equation to predict the temperature rise behavior occurring in biological tissues during magnetic nanoparticles hyperthermia. A numerical scheme is proposed to solve the bio-heat transfer problem in a bi-layered spherical tissue with blood perfusion and metabolism. The analytical solution evidences the accuracy of the numerical scheme and examines the results in the literature.

An analytical study on the thermal effects of cryosurgery on selective cell destruction

The aim of cryosurgery is to kill cells within a closely defined region maintained at a predetermined low temperature. To effectively kill cells, it is important to be able to predict and control the cooling rate over some critical range of temperatures and freezing states in order to regulate the spatial extent of injury during any freeze–thaw protocol. The objective of manipulating the freezing parameters is to maximize the destruction of cancer cells within a defined spatial domain while minimizing cryoinjury to the surrounding healthy tissue. An analytical model has been developed to study the rate of cell destruction within a liver tumor undergoing a freeze–thaw cryosurgical process. Temperature transients in the tumor undergoing cryosurgery have been quantitatively investigated. The simulation is based on solving the transient bioheat equation using the finite volume scheme for a single or multiple-probe geometry. Simulated results show good agreement with experimental data obtained from in vivo clinical study. The calibrated model has been employed to study the effects of different freezing rates, freeze–thaw cycle(s), and multi-probe freezing on cell damage in a liver tumor. The effectiveness of each treatment protocol is estimated by generating the cell survival–volume signature and comparing the percentage of cell damaged within the ice-ball. Results from the model show that employing freeze–thaw cycles has the potential to enhance cell destruction within the cancerous tissue. Results from this study provide the basis for designing an optimized cryosurgical protocol which incorporates thermal effects and the extent of cell destruction within tumors.