Exact solutions to the multiregion time-dependent bioheat equation. II: Numerical evaluation of the solutions

Solution to the bioheat equation for hyperthermia with La(1-x)Ag(y)MnO(3-delta) nanoparticles: the effect of temperature autostabilization

This work aimed to analyze the possibility and performance of the temperature controlled hyperthermia based on AC heating of magnetic nanoparticles with low Curie temperature. Temperature dependence of dynamic magnetic susceptibility has been studied experimentally on fine powders of La(0.8)Ag(0.15)MnO(2.95) in the frequency range of 0.5-2.0 MHz. Critical drop of the AC magnetic losses was found in the vicinity of the Curie point, T(C) = 42 degrees C. The obtained data was used in the numerical analysis of the bioheat equations under typical conditions of the hyperthermia treatment. The mathematical model includes a spherical tumor containing magnetic particles and surrounded by concentric healthy tissue, with account made for the blood perfusion. The calculations performed for various AC power, tumor sizes and doping geometries predict effective autostabilization of the temperature at T congruent with T(C) inside the tumor and steep temperature profile at the interface with the healthy tissue.

A fully coupled binary biochemical reactive-diffusion model with analytic solution

Coupled multicomponent biochemical reactive diffusion underlies a variety of biological signalling processes and pharmacokinetic applications, such as paracrine signalling involving "cocktails" comprised of growth promoter/inhibitor factors and proteases associated with tumor angiogenesis, invasion and metastasis, extravascular drug delivery, and polymeric controlled-release drug codelivery design. Here, we present a model and develop a new analytic solution to illustrate the spatiotemporal behavior associated with fully coupled binary biochemical reactive diffusion. The complete coupling renders the solution appreciably more complex in structure and behavior than solutions for unicomponent or partially coupled models. Concentration behavior is illustrated by the computational simulation of binary-species tumor angiogenesis factor reactive-diffusion in the extravascular tissue matrix. The computational results indicate that (a) steady-state concentration profiles are achieved within 1 h of a change in factor production; (b) in the steady state, the spatial profiles of the two components tend to be similar; (c) exceedingly steep concentration gradients, involving several orders-of-magnitude differences in concentration over a few tenths of a millimeter, can occur in the vicinity of boundary sources due to inter-species reaction; (d) the concentration profiles of the two species differ from unicomponent predictions due to the simultaneous mass interchange between the two species. The analytic solution predictions are also used to provide a first-ever validation of a time-dependent, binary-component Crank-Nicholson numerical solution. The ability to quantitatively model interacting and often strongly varying concentration levels as a function of time and position can serve as a powerful complementary tool to experimental analyses for assessing disease state and interventional pharmacological efficacy, especially when the spatial scales on which in vivo behavior occurs taxes the limits of imaging capabilities.

Analytical study on bioheat transfer problems with spatial or transient heating on skin surface or inside biological bodies

Several closed form analytical solutions to the bioheat transfer problems with space or transient heating on skin surface or inside biological bodies were obtained using Green's function method. The solutions were applied to study several selected typical bioheat transfer processes, which are often encountered in cancer hyperthermia, laser surgery, thermal comfort analysis, and tissue thermal parameter estimation. Thus a straightforward way to quantitatively interpret the temperature behavior of living tissues subject to constant, sinusoidal, step, point or stochastic heatings etc. both in volume and on boundary were established. Further solution to the three-dimensional bioheat transfer problems was also given to illustrate the versatility of the present method. Implementations of this study to the practical problems were addressed.

SPECT electronic collimation resolution enhancement using chi-square minimization

An electronic collimation technique is developed which utilizes the chi-square goodness-of-fit measure to filter scattered gammas incident upon a medical imaging detector. In this data mining technique, Compton kinematic expressions are used as the chi-square fitting templates for measured energy-deposition data involving multiple-interaction scatter sequences. Fit optimization is conducted using the Davidon variable metric minimization algorithm to simultaneously determine the best-fit gamma scatter angles and their associated uncertainties, with the uncertainty associated with the first scatter angle corresponding to the angular resolution precision for the source. The methodology requires no knowledge of materials and geometry. This pattern recognition application enhances the ability to select those gammas that will provide the best resolution for input to reconstruction software. Illustrative computational results are presented for a conceptual truncated-ellipsoid polystyrene position-sensitive fibre head-detector Monte Carlo model using a triple Compton scatter gamma sequence assessment for a 99mTc point source. A filtration rate of 94.3% is obtained, resulting in an estimated sensitivity approximately three orders of magnitude greater than a high-resolution mechanically collimated device. The technique improves the nominal single-scatter angular resolution by up to approximately 24 per cent as compared with the conventional analytic electronic collimation measure.

Exact solutions to the multiregion time-dependent bioheat equation. I: Solution development

Exact solutions are obtained to the classical time-dependent linear bioheat equation in one-dimensional multiregion cartesian and spherical geometries with temperature-invariant physiological parameters. These solutions enable the study of transient temperature behaviour in an arbitrary number of coupled physiologically distinct regions.