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.

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.

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).

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.

Electromagnetic thermal therapy power optimization for multiple source applicators.

The optimization of power deposition for electromagnetic (EM) thermal therapy is investigated. Several goal or objective functions are examined using a generalized mathematical formulation. These include maximization of: (1) target power absorption, (2) the ratio of target to non-target power absorption, (3) target power absorption weighted by the ratio of target to non-target power absorption, and (4) target power absorption subject to the constraint that the non-target high power volume ('hot spot' volume) is below a chosen level. The merit of these functions was retrospectively tested using an anatomic data base containing 38 cancer patients that were clinically heated with EM phased arrays. CT and/or MRI image data were used to define relevant anatomic geometries and tissue properties for finite element numerical models. Power optimization is achieved by variation of seven available control parameters (four amplitudes and three phases) for these clinical array devices. The results indicate that site dependent improvements in target power absorption can be achieved using these goal functions relative to a configuration that utilizes equal phase and amplitude for the sources. The relative merit among these various functions favours an optimization strategy that maximizes the target power absorption weighted by the ratio of target power to non-target power absorption.

Computational techniques for fast hyperthermia temperature optimization.

Hyperthermia temperature optimization involves arriving at a temperature distribution which minimizes a stated goal function, the goal function having a biological basis in maximizing tumor cell kill while not exceeding normal tissue toxicity. This involves the computationally intensive process of multiple evaluations of the temperature goal function, requiring repeated evaluations of the power deposition and its corresponding temperature distribution. Two computational schemes are proposed to expedite the temperature optimization process: (1) temperature distribution evaluation by superpositioning precomputed distributions, and (2) using representative tissue groups (rather than every point in the domain) to evaluate the goal function. The application of these schemes is illustrated with a typical optimization problem, as applied to symmetric and asymmetric, heterogeneous models. Application of these schemes reduced the optimization time on a DEC Alpha 1000 4/266 (Alpha is a registered trademark of Digital Equipment Corporation.) from several h to min, with little difference in results. The computational schemes, though demonstrated in the context of electromagnetic hyperthermia, are generally applicable to other forms of nonionizing radiation employed in hyperthermia therapy.

Magnetic resonance thermometry during hyperthermia for human high-grade sarcoma.

PURPOSE: To determine the feasibility of measuring temperature noninvasively with magnetic resonance imaging during hyperthermia treatment of human tumors. METHODS: The proton chemical shift detected using phase-difference magnetic resonance imaging (MRI) was used to measure temperature in phantoms and human tumors during treatment with hyperthermia. Four adult patients having high-grade primary sarcoma tumors of the lower leg received 5 hyperthermia treatments in the MR scanner using an MRI-compatible radiofrequency heating applicator. Prior to each treatment, an average of 3 fiberoptic temperature probes were invasively placed into the tumor (or phantom). Hyperthermia was applied concurrent with MR thermometry. Following completion of the treatment, regions of interest (ROI) were defined on MR phase images at each temperature probe location, in bone marrow, and in gel standards placed outside the heated region. The median phase difference (compared to pretreatment baseline images) was calculated for each ROI. This phase difference was corrected for phase drift observed in standards and bone marrow. The observed phase difference, with and without corrections, was correlated with the fiberoptic temperature measurements. RESULTS: The phase difference observed with MRI was found to correlate with temperature. Phantom measurements demonstrated a linear regression coefficient of 4.70 degrees phase difference per degree Celsius, with an R2 = 0.998. After human images with artifact were excluded, the linear regression demonstrated a correlation coefficient of 5.5 degrees phase difference per degree Celsius, with an R2 = 0.84. In both phantom and human treatments, temperature measured via corrected phase difference closely tracked measurements obtained with fiberoptic probes during the hyperthermia treatments. CONCLUSIONS: Proton chemical shift imaging with current MRI and hyperthermia technology can be used to monitor and control temperature during treatment of large tumors in the distal lower extremity.

Estimation of cell survival in tumours heated to nonuniform temperature distributions.

UNLABELLED: A stochastic model describing the probability of cell survival as a function of thermal exposure was developed and fit to data arising from studies of CHO cell survival under hyperthermic conditions. This model characterizes the separate risks of temperature-induced cell death and induction of thermotolerance during heating. Tumour cells are assumed to be affected independently of each other by hyperthermia. Tumour geometry, perfusion and power deposition affect hyperthermia-induced temperature distributions in tumours, producing nonuniform temperatures. Two tumours may respond to hyperthermia slightly differently because of differences in tumour geometry, perfusion, power deposition, or by chance alone and the approach presented here incorporates chance and these other factors explicitly. THE RESULTS: (1) the time-temperature history is important for estimating tumour cell survival; (2) tumour temperature heterogeneity leaves more surviving cells at a given T90 temperature than would be expected if the entire tumour were uniformly heated to that same temperature; and (3) changes in the shape of the temperature distribution because of tumour geometry and perfusion distribution greatly influence cell survival between tumours, even when the standard temperature descriptors, such as T90, are fixed. The simulations also showed a modest effect on cell kill attributable to varying the lengths of the warm-up and the cool-down periods. These simulations indicate that these types of sensitivity studies can be used to investigate relationships between various modifiers of temperature distributions achieved when treating tumours with hyperthermia and to assess their potential therapeutic impact in clinical trials.

Hyperthermia treatment planning and temperature distribution reconstruction: a case study.

While a great deal of effort has been applied toward solving the technical problems associated with modelling clinical hyperthermia treatments, much of that effort has focused on only estimating the power deposition. Little effort has been applied toward using the modelled power depositions (either electromagnetic (EM) or ultrasonic) as inputs to estimate the hyperthermia induced three-dimensional temperature distributions. This paper presents a case report of a patient treated with hyperthermia at the Duke University Medical Center where numerical modelling of the EM power deposition was used to prospectively plan the treatment. Additionally, the modelled power was used as input to retrospectively reconstruct the transient three-dimensional temperature distribution. The modelled power deposition indicated the existence of an undesirable region of high power in the normal tissue. Based upon this result, amplitudes and phases for driving the hyperthermia applicator were determined that eliminated the region of high power and subsequent measurements confirmed this. The steady-state and transient three-dimensional temperature distributions were reconstructed for four out of the seven treatments. The reconstructed steady-state temperatures agreed with the measured temperatures; root-mean-square error ranged from 0.45 to 1.21 degrees C. The transient three-dimensional tumour temperature was estimated assuming that the perfusion was constant throughout the treatment. Using the computed three-dimensional transient temperature distribution, the hyperthermia thermal dose was computed. The equivalent minutes at 43 degrees C achieved by 50% (T50Eq43) of the tumour volume was computed from the measured data and the three-dimensional reconstructed distribution yielding T50Eq43 = 40.6 and 19.8 min respectively.

Simulation of electromagnetically induced hyperthermia: a finite element gridding method.

A finite element gridding method for simulating electromagnetically (EM) induced hyperthermia is presented. The method uses patient CT data as its primary input, with critical structures manually outlined (on a graphics workstation) for explicit demarcation. The paper outlines the various stages involved in mesh creation, including procedures for conforming the finite element representation of critical structures to their smooth boundaries, modelling of heating equipment, and modelling of the outer boundaries. The procedure for generating the finite element model is illustrated for an example treatment. Additionally, the results of computing the SAR in six patients are compared to measured values. The comparison reveals agreement between the model prediction and actual treatment within the limits of measurement error.

Verification of a hyperthermia model method using MR thermometry.

Simulation of hyperthermia induced power and temperature distributions is becoming generally accepted and finding its way into clinical hyperthermia treatments. Such simulations provide a means for understanding the complete three-dimensional temperature distribution. However, the results of the simulation studies should be regarded with caution since modelling errors will result in differences between the actual and simulated temperature distribution. This study uses a diffusion weighted magnetic resonance (MR) based technique to measure hyperthermia induced temperature distributions in a three-dimensional space in a non-perfused phantom. The measured data are used to verify the accuracy of numerical simulations of the same three-dimensional temperature distributions. The simulation algorithm is a finite element based method that first computes the electromagnetic induced power deposition then the temperature distribution. Two non-perfused phantom studies were performed and qualitatively the MR and simulated distributions agreed for steady-state. However, due to the long MR sampling time (approximately 4 min), poor agreement between the simulations and MR measurements were obtained for thermal transients. Good agreement between the simulations and fibreoptic thermometry measurements were obtained. The fiberoptic measurements differed from the simulations by 0.11 +/- 0.59 degrees C and -0.17 +/- 0.29 degrees C (mean +/- standard deviation for the two studies).

Application of new technology in clinical hyperthermia.

Two areas of technical progress related to hyperthermic oncology are presented: (1) numerical modelling of absorbed power and temperature distributions; and (2) non-invasive thermometry using magnetic resonance imaging. The results represent achievements made during the past 5 years at Duke University Medical Center's Departments of Radiation Oncology and Radiology. They represent examples of progress in the technology of hyperthermia that have potential for greatly improving the delivery, monitoring and assessment of clinical hyperthermia.

Inverse techniques in hyperthermia: a sensitivity study.

Numerical modeling methods and hyperthermia treatment temperature measurements have been used together to reconstruct steady-state tumor temperature distributions. However, model errors will exist which may in turn produce errors in the reconstructed temperature distributions. A series of computer experiments was conducted to study the sensitivity of reconstructed two-dimensional temperature distributions to perfusion distribution modeling errors. Temperature distributions were simulated using a finite element approximation of Pennes' bioheat transfer equation. Relevant variables such as tumor shape, perfusion distribution, and power deposition were modeled. An optimization method and the temperatures "measured" from the simulated temperature distributions were used to reconstruct the tumor temperature distribution. Using this procedure, the sensitivity of the reconstructed tumor temperature distribution to model-related errors, such as the perfusion function, was studied. It was found that: 1) if the problem is conduction dominated, large errors in the perfusion distribution produce only small errors in the reconstructed temperature distribution (maximum error < 1.0 degrees C), and 2) when the actual perfusion distribution contains a small random variation (+/- 15%) which is neglected by the model, the reconstructed temperature distribution will be in good agreement with the actual temperature distribution (maximum error < or = 0.3 degrees.

Reconstruction of experimental hyperthermia temperature distributions: application of state and parameter estimation.

Subsets of data from spatially sampled temperatures measured in each of nine experimental heatings of normal canine thighs were used to test the feasibility of using a state and parameter estimation (SPE) technique to predict the complete measured data set in each heating. Temperature measurements were made at between seventy-two and ninety-six stationary thermocouple locations within the thigh, and measurements from as few as thirteen of these locations were used as inputs to the estimation algorithm. The remaining (non "input") measurements were compared to the predicted temperatures for the corresponding "unmeasured" locations to judge the ability of the estimation algorithm to accurately reconstruct the complete experimental data set. The results show that the predictions of the "unmeasured" steady-state temperatures are quite accurate in general (average errors usually < 0.5 degrees C; and small variances about those averages) and that this reconstruction procedure can yield improved descriptors of the steady-state temperature distribution. The accuracy of the reconstructed temperature distribution was not strongly affected by either the number of perfusion zones or by the number of input sensors used by the algorithm. One situation extensively considered in this study modeled the thigh with twenty-seven independent regions of perfusion. For this situation, measurements from ninety-six to thirteen sensors were used as input to the estimation algorithm. The average error for all of these cases ranged from -0.55 degrees C to +0.75 degrees C, respectively, and was not strongly related to the number of sensors used as input to the estimation algorithm.(ABSTRACT TRUNCATED AT 250 WORDS)

Sensitivity of hyperthermia trial outcomes to temperature and time: implications for thermal goals of treatment.

PURPOSE: In previous work we have found that the cumulative minutes of treatment for which 90% of measured intratumoral temperatures (T90) exceeded 39.5 degrees C was highly associated with complete response of superficial tumors. Similarly, the cumulative time for which 50% of intratumoral temperatures (T50) exceeded 41.5 degrees C was highly associated with the presence of > 80% necrosis in soft tissue sarcomas resected after radiotherapy and hyperthermia. In the present work we have calculated the time for isoeffective treatments with T90 = 43 degrees C and T50 = 43 degrees C, respectively, using published thermal isoeffective dose formulae. The purpose of these calculations was to determine the sensitivity of treatment outcome to variations in thermal isoeffective dose. METHODS AND MATERIALS: The basis for the calculations were the thermal parameters and treatment outcomes in three patient populations: 44 patients with moderate or high grade soft tissue sarcoma treated preoperatively with hyperthermia and radiation; 105 patients with superficial tumors treated with hyperthermia and radiation, and 59 patients with deep tumors treated with hyperthermia and radiation. RESULTS: The thermal dose values calculated are strongly associated with outcome in multivariate logistic regression analysis. Simple dose-response equations result from the analysis, and we use these equations to assess the sensitivity of outcome upon variations in thermal dose. This information, in turn, allows us to estimate the number of patients required in Phase II and III trials of hyperthermia and radiation therapy. CONCLUSIONS: For regimens of 5 to 10 hyperthermia treatments, improvements in median T90 (superficial tumors) and T50 (deep tumors) parameters by 1.2-1.5 degrees C could result in response rates high enough (compared to radiotherapy alone) to justify Phase III trials. A similar improvement in response rates would require an increase in overall duration of treatment by a factor of 3 to 5. This would be difficult to achieve while also avoiding thermal tolerance induction. Achieving these temperature goals may be possible with improvements in hyperthermia technology. Alternatively, there may be ways to increase the sensitivity of cells to temperatures that can be achieved currently, such as pH reduction or chemosensitization.

Feasibility of estimating the temperature distribution in a tumor heated by a waveguide applicator.

The feasibility of using a 2-dimensional (2D) modeling approach for retrospectively describing complete temperature distributions in the midplane of a tumor during a clinical hyperthermia treatment was tested. An experimental treatment, using a 915-MHz waveguide applicator to heat a large melanoma in a dog, was modeled. Detailed measurements of temperatures were made during the treatment. The steady-state blood flow distribution at the midplane was imaged by positron emission tomography (PET), and these data were used to prescribe the modeled perfusion pattern. A 2D finite element method (FEM) was used to approximate the solution to Maxwell's Equations to obtain the specific absorption rate (SAR) distribution. The blood-flow estimates, assumed material properties, SAR distribution, and temperature boundary conditions were then used with the same mesh in a second FEM program to obtain a solution to the bioheat transfer equation. This latter routine was embedded in a state-and-parameter-estimation program that systematically varied selected parameters until the differences between computed and measured temperatures were minimized. Optimizations were performed independently for three subsets of the measured temperature data to assess the sensitivity of the predicted temperature field to the number of measurements. The calculated temperature distributions that resulted were similar to each other, and the predicted temperatures at the sensor points excluded from these optimizations were in reasonable agreement with the measurements. However, lack of unique blood flow values following optimization indicates that the methods of estimating blood flow will need to be improved or that there are problems with model mismatch. This work is a clinical case study of an evolving 2D system of thermal dosimetry which relies on both empirical and theoretical concepts. The methodology is being evaluated for its ability to generate prognostically significant descriptors of the treatment temperature field.

Estimating three-dimensional temperature fields during hyperthermia: studies of the optimal regularization parameter and time sampling period.

During hyperthermia therapy it is desirable to know the entire temperature field in the treatment region. However, accurately inferring this field from the limited number of temperature measurements available is very difficult, and thus state and parameter estimation methods have been used to attempt to solve this inherently ill-posed problem. To compensate for this ill-posedness and to improve the accuracy of this method, Tikhonov regularization of order zero has been used to significantly improve the results of the estimation procedure. It is also shown that the accuracies of the temperature estimates depend upon the value of the regularization parameter, which has an optimal value that is dependent on the perfusion pattern and magnitude. In addition, the transient power-off time sampling period (i.e., the length of time over which transient data is collected and used) influences the accuracy of the estimates, and an optimal sampling period is shown to exist. The effects of additive measurement noise are also investigated, as are the effects of the initial guess of the perfusion values, and the effects of both symmetric and asymmetric blood perfusion patterns. Random perfusion patterns with noisy data are the most difficult cases to evaluate. The cases studied are not a comprehensive set, but continue to show the feasibility of using state and parameter estimation methods to reconstruct the entire temperature field.

Preliminary studies of interstitial hyperthermia using hot water.

A hot water interstitial hyperthermia unit was used to heat normal tissue in the thighs of rabbits and pigs. A 4 x 4 array of metal needles or plastic tubes spaced at 10 or 14 mm was implanted. Temperature measurements were made using five-sensor thermocouple probes inserted parallel to the implanted needles or tubes. With a water temperature of 48 degrees C, tissue temperature within the implant exceeded 42.5 degrees C when tube spacing was 14 mm and reached 47 degrees C when the spacing was 10 mm. However, at the lower water temperature of 45.5 degrees C inter-tube spacing was more critical, since the tissue temperature was above 43.5 degrees C for a spacing of 10 mm but below 42.5 degrees C for a spacing of 14 mm. Temperatures observed in vivo tended to be higher than those predicted by computer simulations, in which blood flow was assumed to be greater than that of resting muscle i.e. approximately greater than 0.45 kg m-3 s-1. The results show that an interstitial system using hot water can be a simple and efficient method of inducing hyperthermia.