Discretizing large traceable vessels and using DE-MRI perfusion maps yields numerical temperature contours that match the MR noninvasive measurements.

The success of hyperthermia treatments is dependent on thermal dose distribution. However, the three-dimensional temperature distribution remains largely unknown. Without this knowledge, the relationship between thermal dose and outcome is noisy, and therapy cannot be optimized. Accurate computations of thermal distribution can contribute to an optimized therapy. The hyperthermia modeling group in the Department of Radiotherapy, University Medical Center Utrecht devised a Discrete Vasculature [Kotte et al., Phys. Med. Biol. 41, 865-884 (1996)] model that accounts for the presence of vessel trees in the computational domain. The vessel tree geometry is tracked using magnetic resonance (MR) angiograms to a minimum diameter between 0.6 and 1 mm. However, smaller vessels (0.2-0.6 mm) are known to account for significant heat transfer. The hyperthermia group at Duke University Medical Center has proposed using perfusion maps derived from dynamic-enhanced magnetic resonance imaging to account for the tissue perfusion heterogeneity [Craciunescu et al., Int. J. Hyperthermia 17, 221-239 (2001)]. In addition, techniques for noninvasive temperature measurements have been devised to measure temperatures in vivo [Samulski et al., Int. J. Hypertherminal, 819-829 (1992)]. In this work, a patient with high-grade sarcoma has been retrospectively modeled to determine the temperature distribution achieved during a hyperthermia treatment. Available for this model were MR depicted geometry, angiograms, perfusion maps, as necessary for accurate thermal modeling, as well as MR thermometry data for validation purposes. The vasculature assembly through modifiable potential program [Van Leeuwen et al., IEEE Trans. Biomed. Eng. 45, 596-604 (1998)] was used in order to incorporate the traceable large vessels. Temperature simulations were made using different approaches to describe perfusion. The simulated cases were the bioheat equation with constant perfusion rates per tissue type, perfusion maps alone, tracked vessel tree and perfusion maps, and generated vessel tree. The results were compared with MR thermometry data for a single patient data set, concluding that a combination between large traceable vessels and perfusion map yields the best results for this particular patient. The technique has to be repeated on several patients, first with the same type of malignancy, and after that, on patients having malignancies at other different sites.

Perturbations in hyperthermia temperature distributions associated with counter-current flow: numerical simulations and empirical verification.

Two numerical techniques are used to calculate the effect of large vessel counter-current flow on hyperthermic temperature distributions. One is based on the Navier-Stokes equation for steady-state flow, and the second employs a convective-type boundary condition at the interface of the vessel walls. Steady-state temperature fields were calculated for two energy absorption rate distributions (ARD) in a cylindrical tissue model having two pairs of counter-current vessels (one pair with equal diameter vessels and another pair with unequal diameters). The first assumed a uniform ARD throughout cylinder; the second ARD was calculated for a tissue cylinder inside an existing four antenna Radiofrequency (RF) array. A tissue equivalent phantom was constructed to verify the numerical calculations. Temperatures induced with the RF array were measured using a noninvasive magnetic resonance imaging technique based on the chemical shift of water. Temperatures calculated using the two numerical techniques are in good agreement with the measured data. The results show: 1) the convective-type boundary condition technique reduces computation time by a factor of ten when compared to the fully conjugated method with little quantitative difference (approximately 0.3 degree C) in the numerical accuracy and 2) the use of noninvasive magnetic resonance imaging (thermal imaging) to quantitatively access the temperature perturbations near large vessels is feasible using the chemical shift technique.

Three-dimensional tumor perfusion reconstruction using fractal interpolation functions.

It has been shown that the perfusion of blood in tumor tissue can be approximated using the relative perfusion index determined from dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool. Also, it was concluded in a previous report that the blood perfusion in a two-dimensional (2-D) tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. In this paper, the three-dimensional (3-D) tumor perfusion is reconstructed from the 2-D slices using the method of fractal interpolation functions (FIF), i.e., the piecewise self-affine fractal interpolation model (PSAFIM) and the piecewise hidden variable fractal interpolation model (PHVFIM). The fractal models are compared to classical interpolation techniques (linear, spline, polynomial) by means of determining the 2-D fractal dimension of the reconstructed slices. Using FIFs instead of classical interpolation techniques better conserves the fractal-like structure of the perfusion data. Among the two FIF methods, PHVFIM conserves the 3-D fractality better due to the cross correlation that exists between the data in the 2-D slices and the data along the reconstructed direction. The 3-D structures resulting from PHVFIM have a fractal dimension within 3%-5% of the one reported in literature for 3-D percolation. It is, thus, concluded that the reconstructed 3-D perfusion has a percolation-like scaling. As the perfusion term from bio-heat equation is possibly better described by reconstruction via fractal interpolation, a more suitable computation of the temperature field induced during hyperthermia treatments is expected.

Thermal characteristics of thermobrachytherapy surface applicators for treating chest wall recurrence.

The aim of this study was to investigate temperature and thermal dose distributions of thermobrachytherapy surface applicators (TBSAs) developed for concurrent or sequential high dose rate (HDR) brachytherapy and microwave hyperthermia treatment of chest wall recurrence and other superficial diseases. A steady-state thermodynamics model coupled with the fluid dynamics of a water bolus and electromagnetic radiation of the hyperthermia applicator is used to characterize the temperature distributions achievable with TBSAs in an elliptical phantom model of the human torso. Power deposited by 915 MHz conformal microwave array (CMA) applicators is used to assess the specific absorption rate (SAR) distributions of rectangular (500 cm(2)) and L-shaped (875 cm(2)) TBSAs. The SAR distribution in tissue and fluid flow distribution inside the dual-input dual-output (DIDO) water bolus are coupled to solve the steady-state temperature and thermal dose distributions of the rectangular TBSA (R-TBSA) for superficial tumor targets extending 10-15 mm beneath the skin surface. Thermal simulations are carried out for a range of bolus inlet temperature (T(b) = 38-43 degrees C), water flow rate (Q(b) = 2-4 L min(-1)) and tumor blood perfusion (omega(b) = 2-5 kg m(-3) s(-1)) to characterize their influence on thermal dosimetry. Steady-state SAR patterns of the R- and L-TBSA demonstrate the ability to produce conformal and localized power deposition inside the tumor target sparing surrounding normal tissues and nearby critical organs. Acceptably low variation in tissue surface cooling and surface temperature homogeneity was observed for the new DIDO bolus at a 2 L min(-1) water flow rate. Temperature depth profiles and thermal dose volume histograms indicate bolus inlet temperature (T(b)) to be the most influential factor on thermal dosimetry. A 42 degrees C water bolus was observed to be the optimal choice for superficial tumors extending 10-15 mm from the surface even under significant blood perfusion. Lower bolus temperature may be chosen to reduce the thermal enhancement ratio (TER) in the most sensitive skin where maximum radiation dose is delivered and to extend the thermal enhancement of radiation dose deeper. This computational study indicates that well-localized elevation of tumor target temperature to 40-44 degrees C can be accomplished by large surface-conforming TBSAs using appropriate selection of coupling bolus temperature.

Pulsatile blood flow effects on temperature distribution and heat transfer in rigid vessels.

The effect of blood velocity pulsations on bioheat transfer is studied. A simple model of a straight rigid blood vessel with unsteady periodic flow is considered. A numerical solution that considers the fully coupled Navier-Stokes and energy equations is used for the simulations. The influence of the pulsation rate on the temperature distribution and energy transport is studied for four typical vessel sizes: aorta, large arteries, terminal arterial branches, and arterioles. The results show that: the pulsating axial velocity produces a pulsating temperature distribution; reversal of flow occurs in the aorta and in large vessels, which produces significant time variation in the temperature profile. Change of the pulsation rate yields a change of the energy transport between the vessel wall and fluid for the large vessels. For the thermally important terminal arteries (0.04-1 mm), velocity pulsations have a small influence on temperature distribution and on the energy transport out of the vessels (8 percent for the Womersley number corresponding to a normal heart rate). Given that there is a small difference between the time-averaged unsteady heat flux due to a pulsating blood velocity and an assumed nonpulsating blood velocity, it is reasonable to assume a nonpulsating blood velocity for the purposes of estimating bioheat transfer.

Dynamic contrast-enhanced MRI and fractal characteristics of percolation clusters in two-dimensional tumor blood perfusion.

Dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool is used to study tumor tissue perfusion. The results are then analyzed using percolation models. Percolation cluster geometry is depicted using the wash-in component of MRI contrast signal intensity. Fractal characteristics are determined for each two-dimensional cluster. The invasion percolation model is used to describe the evolution of the tumor perfusion front. Although tumor perfusion can be depicted rigorously only in three dimensions, two-dimensional cases are used to validate the methodology. It is concluded that the blood perfusion in a two-dimensional tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. For all the cases studied, the front starts to grow from the periphery of the tumor (where the feeding vessel was assumed to lie) and continues to grow toward the center of the tumor, accounting for the well-documented perfused periphery and necrotic core of the tumor tissue.

Experimental evaluation of the thermal properties of two tissue equivalent phantom materials.

Tissue equivalent radio frequency (RF) phantoms provide a means for measuring the power deposition of various hyperthermia therapy applicators. Temperature measurements made in phantoms are used to verify the accuracy of various numerical approaches for computing the power and/or temperature distributions. For the numerical simulations to be accurate, the electrical and thermal properties of the materials that form the phantom should be accurately characterized. This paper reports on the experimentally measured thermal properties of two commonly used phantom materials, i.e. a rigid material with the electrical properties of human fat, and a low concentration polymer gel with the electrical properties of human muscle. Particularities of the two samples required the design of alternative measuring techniques for the specific heat and thermal conductivity. For the specific heat, a calorimeter method is used. For the thermal diffusivity, a method derived from the standard guarded comparative-longitudinal heat flow technique was used for both materials. For the 'muscle'-like material, the thermal conductivity, density and specific heat at constant pressure were measured as: k = 0.31 +/- 0.001 W(mK)(-1), p = 1026 +/- 7 kgm(-3), and c(p) = 4584 +/- 107 J(kgK)(-1). For the 'fat'-like material, the literature reports on the density and specific heat such that only the thermal conductivity was measured as k = 0.55 W(mK)(-1).

3D numerical reconstruction of the hyperthermia induced temperature distribution in human sarcomas using DE-MRI measured tissue perfusion: validation against non-invasive MR temperature measurements.

Essential to the success of optimized thermal treatment during hyperthermia is accurate modelling. Advection of energy due to blood perfusion significantly affects the temperature. Without accurate estimates of the magnitude of the local tissue blood perfusion, accurate estimates of the temperature distribution can not be made. It is shown here that the blood mass flow rate per unit volume of tissue in the Pennes' bio-heat equation can be modelled using a relative perfusion index (RPI) determined with dynamic-enhanced magnetic resonance imaging (DE-MRI). Temperature distributions in two patients treated with hyperthermia at Duke University Medical Center for high-grade leg tissue sarcomas are modelled, and the resultant temperatures are compared to measured temperatures using a non-invasive MR thermometry technique. Significant correlations are found between the DE-MRI perfusion images, the MR temperature images, and the numerical simulation of the temperature field. The correlation between DE-MRI measured values and advective heat loss in tissue is used to scale the perfusion distribution, thereby allowing the continuum model to account for the local thermal impact of vasculature in the tumour. Large vessels in tumour and neighbouring healthy tissue need to be taken into account in order to accurately describe the complete temperature distribution.