Tests of the geometrical description of blood vessels in a thermal model using counter-current geometries

Planning, optimisation and evaluation of hyperthermia treatments

BACKGROUND

Hyperthermia treatment planning using dedicated simulations of power and temperature distributions is very useful to assist in hyperthermia applications. This paper describes an advanced treatment planning software package for a wide variety of applications.

METHODS

The in-house developed C++ software package Plan2Heat runs on a Linux operating system. Modules are available to perform electric field and temperature calculations for many heating techniques. The package also contains optimisation routines, post-treatment evaluation tools and a sophisticated thermal model enabling to account for 3D vasculature based on an angiogram or generated artificially using a vessel generation algorithm. The use of the software is illustrated by a simulation of a locoregional hyperthermia treatment for a pancreatic cancer patient and a spherical tumour model heated by interstitial hyperthermia, with detailed 3D vasculature included.

RESULTS

The module-based set-up makes the software flexible and easy to use. The first example demonstrates that treatment planning can help to focus the heating to the tumour. After optimisation, the simulated absorbed power in the tumour increased with 50%. The second example demonstrates the impact of accurately modelling discrete vasculature. Blood at body core temperature entering the heated volume causes relatively cold tracks in the heated volume, where the temperature remains below 40 °C.

CONCLUSIONS

A flexible software package for hyperthermia treatment planning has been developed, which can be very useful in many hyperthermia applications. The object-oriented structure of the source code allows relatively easy extension of the software package with additional tools when necessary for future applications.

In vivo radiofrequency heating in swine in a 3T (123.2-MHz) birdcage whole body coil

PURPOSE

To study in vivo radiofrequency (RF) heating produced due to power deposition from a 3T (Larmour frequency = 123.2 MHz), birdcage, whole body coil.

METHODS

The RF heating was simulated in a digital swine by solving the mechanistic generic bioheat transfer model (GBHTM) and the conventional, empirical Pennes bioheat transfer equation for two cases: 1) when the swine head was in the isocenter and 2) when the swine trunk was in the isocenter. The simulation results were validated by making direct fluoroptic temperature measurements in the skin, brain, simulated hot regions, and rectum of 10 swine (case 1: n = 5, mean animal weight = 84.03 ± 6.85 kg, whole body average SAR = 2.65 ± 0.22 W/kg; case 2: n = 5, mean animal weight = 81.59 ± 6.23 kg, whole body average SAR = 2.77 ± 0.26 W/kg) during 1 h of exposure to a turbo spin echo sequence.

RESULTS

The GBHTM simulated the RF heating more accurately compared with the Pennes equation. In vivo temperatures exceeded safe temperature thresholds with allowable SAR exposures. Hot regions may be produced deep inside the body, away from the skin.

CONCLUSION

SAR exposures that produce safe temperature thresholds need reinvestigation.

Discrete vessel heat transfer in perfused tissue--model comparison

The aim of this paper is to compare two methods of calculating heat transfer in perfused biological tissue using a discrete vessel description. The methods differ in two important aspects: the representation of the vascular system and the algorithm for calculating the heat flux between tissue and blood vessels. The first method was developed at the University of Utrecht between 1994 and 1998 and has been used in several clinical applications. The second method has been proposed by the first author. The methods are briefly described, their assumptions and limitations are discussed. Finally, the test simulation is introduced and the results produced by both methods are compared. The test indicates that the simpler, and less computationally intensive method proposed by the present author for calculating 2D problems containing countercurrent blood vessel systems can reproduce quite well some features of the solution obtained by the more complex 3D method. The observed discrepancies could be explained on physical grounds.

Modelling the impact of blood flow on the temperature distribution in the human eye and the orbit: fixed heat transfer coefficients versus the Pennes bioheat model versus discrete blood vessels

Prediction of the temperature distribution in the eye depends on how the impact of the blood flow is taken into account. Three methods will be compared: a simplified eye anatomy that applies a single heat transfer coefficient to describe all heat transport mechanisms between the sclera and the body core, a detailed eye anatomy in which the blood flow is accounted for either by the bioheat approach, or by including the discrete vasculature in the eye and the orbit. The comparison is done both for rabbit and human anatomies, normo-thermally and when exposed to homogeneous power densities. The first simplified model predicts much higher temperatures than the latter two. It was shown that the eye is very hard to heat when taking physiological perfusion correctly into account. It was concluded that the heat transfer coefficient describing the heat transport from the sclera to the body core reported in the literature for the first simplified model is too low. The bioheat approach is appropriate for a first-order approximation of the temperature distribution in the eye when exposed to a homogeneous power density, but the discrete vasculature down to 0.2 mm in diameter needs to be taken into account when the heterogeneity of the temperature distribution at a mm scale is of interest.

Determination and validation of the actual 3D temperature distribution during interstitial hyperthermia of prostate carcinoma

To determine the thermal dose of a hyperthermia treatment, knowledge of the three-dimensional (3D) temperature distribution is mandatory. The aim of this paper is to validate an interstitial hyperthermia treatment planning system with which the full 3D temperature distribution can be obtained in individual patients. Within a phase I study, 12 patients with prostate cancer were treated with interstitial hyperthermia using our multi electrode current source interstitial hyperthermia treatment (MECS IHT) system. The temperature distribution was measured from within the heating devices and by additional thermometry. The perfusion level was estimated and the heating implant reconstructed. The steady-state temperature distribution was calculated using our interstitial hyperthermia treatment planning system. The simulated temperature distribution was validated by individually comparing the measured and simulated thermo-sensors, both for the thermometry integrated with the heating applicators and the additional thermometry. The entire procedure was also performed on a no-flow agar-agar phantom. It was shown that the calculated temperature distribution of an individual patient during MECS interstitial hyperthermia is very heterogeneous. The validation indicates that the calculated temperature elevations match the measurements within approximately 1 degrees C. Possible improvements are more precise reconstruction, incorporation of discrete vasculature and using a temperature-dependent, heterogeneous perfusion distribution. Further technical improvements of the MECS-IHT system may also result in better temperature calculations.

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.

How to apply a discrete vessel model in thermal simulations when only incomplete vessel data are available

For accurate predictions of the temperature distribution during hyperthermia treatment a thermal model should incorporate the individual impact of discrete vessels. In clinical practice not all vessels can be reconstructed individually. This paper investigates five possible strategies to model the thermal impact of these missing vessels. A tissue volume with a detailed, realistic, counter-current discrete vasculature is heated and the steady-state temperature distribution is calculated using our Discrete Vasculature (DIVA) thermal model. To mimic incomplete discrete vasculatures the full tree is gradually stripped, that is, the number of discretely described vessels is reduced in four steps until no discrete vessels are left. At each strip level the steady state temperature distribution is calculated for five different strategies to model the missing vessels. The strategies all use a local or global heat sink model in addition to the discrete vasculature. The resulting temperature distributions are compared with the full tree simulation. With increasing strip level the correspondence with the full tree simulation deteriorated for all strategies. An optimal strategy was found to model the missing vessels depending on the available angiographic data. It was also found that simulations with a decreased number of discrete vessels, or no vessels at all, yield temperatures which are too high. Theoretically this can be compensated by increasing the thermal conductivity; finding the optimal value is done empirically.

Numerical modeling of temperature distributions within the neonatal head

Introduction of hypothermia therapy as a neuroprotection therapy after hypoxia-ischemia in newborn infants requires appraisal of cooling methods. In this numerical study thermal simulations were performed to test the hypothesis that cooling of the surface of the cranium by the application of a cooling bonnet significantly reduces deep brain temperature and produces a temperature differential between the deep brain and the body core. A realistic three-dimensional (3-D) computer model of infant head anatomy was used, derived from magnetic resonance data from a newborn infant. Temperature distributions were calculated using the Pennes heatsink model. The cooling bonnet was at a constant temperature of 10 degrees C. When modeling head cooling only, a constant body core temperature of 37 degrees C was imposed. The computed result showed no significant cooling of the deep brain regions, only the very superficial regions of the brain are cooled to temperatures of 33-34 degrees C. Poor efficacy of head cooling was still found after a considerable increase in the modeled thermal conductivities of the skin and skull, or after a decrease in perfusion. The results for the heatsink thermal model of the infant head were confirmed by comparison of results computed for a scaled down adult head, using both the heatsink description and a discrete vessel thermal model with both anatomy and vasculature obtained from MR data. The results indicate that significant reduction in brain temperature will only be achieved if the infant's core temperature is lowered.

Hyperthermia treatment planning

The development of hyperthermia, the treatment of tumours with elevated temperatures in the range of 40-44 degrees C with treatment times over 30 min, greatly benefits from the development of hyperthermia treatment planning. This review briefly describes the state of the art in hyperthermia technology, followed by an overview of the developments in hyperthermia treatment planning. It particularly highlights the significant problems encountered with heating realistic tissue volumes and shows how treatment planning can help in designing better heating technology. Hyperthermia treatment planning will ultimately provide information about the actual temperature distributions obtained and thus the tumour control probabilities to be expected. This will improve our understanding of the present clinical results of thermoradiotherapy and thermochemotherapy, and will greatly help both in optimizing clinical heating technology and in designing optimal clinical trials.

Temperature simulations in tissue with a realistic computer generated vessel network

The practical use of a discrete vessel thermal model for hyperthermia treatment planning requires a number of choices with respect to the unknown part of the patient's vasculature. This work presents a study of the thermal effects of blood flow in a simple tissue geometry with a detailed artificial vessel network. The simulations presented here demonstrate that an incomplete discrete description of the detailed network results in a better prediction of the temperature distribution than is obtained using the conventional bio-heatsink equation. Therefore, efforts to obtain information on the positions of the large vessels in an individual hyperthermia patient will be rewarded with a more accurate prediction of the temperature distribution.

Calculation of change in brain temperatures due to exposure to a mobile phone

In this study we evaluated for a realistic head model the 3D temperature rise induced by a mobile phone. This was done numerically with the consecutive use of an FDTD model to predict the absorbed electromagnetic power distribution, and a thermal model describing bioheat transfer both by conduction and by blood flow. We calculated a maximum rise in brain temperature of 0.11 degrees C for an antenna with an average emitted power of 0.25 W, the maximum value in common mobile phones, and indefinite exposure. Maximum temperature rise is at the skin. The power distributions were characterized by a maximum averaged SAR over an arbitrarily shaped 10 g volume of approximately 1.6 W kg(-1). Although these power distributions are not in compliance with all proposed safety standards, temperature rises are far too small to have lasting effects. We verified our simulations by measuring the skin temperature rise experimentally. Our simulation method can be instrumental in further development of safety standards.

An investigation of the flow dependence of temperature gradients near large vessels during steady state and transient tissue heating

Temperature distributions measured during thermal therapy are a major prognostic factor of the efficacy and success of the procedure. Thermal models are used to predict the temperature elevation of tissues during heating. Theoretical work has shown that blood flow through large blood vessels plays an important role in determining temperature profiles of heated tissues. In this paper, an experimental investigation of the effects of large vessels on the temperature distribution of heated tissue is performed. The blood flow dependence of steady state and transient temperature profiles created by a cylindrical conductive heat source and an ultrasound transducer were examined using a fixed porcine kidney as a flow model. In the transient experiments, a 20 s pulse of hot water, 30 degrees C above ambient, heated the tissues. Temperatures were measured at selected locations in steps of 0.1 mm. It was observed that vessels could either heat or cool tissues depending on the orientation of the vascular geometry with respect to the heat source and that these effects are a function of flow rate through the vessels. Temperature gradients of 6 degrees C mm(-1) close to large vessels were routinely measured. Furthermore, it was observed that the temperature gradients caused by large vessels depended on whether the heating source was highly localized (i.e. a hot needle) or more distributed (i.e. external ultrasound). The gradients measured near large vessels during localized heating were between two and three times greater than the gradients measured during ultrasound heating at the same location, for comparable flows. Moreover, these gradients were more sensitive to flow variations for the localized needle heating. X-ray computed tomography data of the kidney vasculature were in good spatial agreement with the locations of all of the temperature variations measured. The three dimensional vessel path observed could account for the complex features of the temperature profiles. The flow dependences of the transient temperature profiles near large vessels during the pulsed experiments were consistent with the temperature distributions measured in the steady state experiments and provided unique insights into the process of convective heat transfer in tissues. Finally, it was shown that even for very short treatment times (3-20 s), large vessels had significant effects on the tissue temperature distributions.

Modelling the thermal impact of a discrete vessel tree

Based on a modelling technique to calculate the thermal influence of a single vessel segment, a combination of segments representing a vessel tree is presented. At segment junctions the blood temperature is passed with a correction for a single vessel artefact. Blood leaving the modelled arterial vessel network at a junction or at the end of a terminal branch need not be equilibrated with the local surrounding tissue temperature. The thermal effect of this equilibration process can be taken into account using the 'sink set'. Blood entering a venous vessel tree is given an inflow temperature based on the tissue temperatures in the 'sample set'. With these sets we model the thermal impact of the vasculature too small to be taken into account discretely. The formation of the sink/sample sets is subject of current research; to show the capabilities of the presented method we present a minimal simulation collection with cube-shaped sets in combination with limited vasculature. The results of using the entire simulation volume as sink and sample sets for all the terminal branches matches the reference temperature profile best.

Dose uniformity of ferromagnetic seed implants in tissue with discrete vasculature: a numerical study on the impact of seed characteristics and implantation techniques

The results from simulations with a new three-dimensional treatment planning system for interstitial hyperthermia with ferromagnetic seeds are presented in this study. The thermal model incorporates discrete vessel structures as well as a heat sink and enhanced thermal conductivity. Both the discrete vessels and the ferroseeds are described parametrically in separate calculation spaces. This parametric description has the advantage of an arbitrary orientation of the structures within the tissue grid, easy manipulation of the structures and independence from the resolution of the tissue voxels (tissue calculation space). The power absorption of the self-regulating seeds is according to empirical data. The thermal effects of an unlimited number of thin layers surrounding the seed (coatings, catheters) can be modelled. The initial calculations have been performed for an array of 12 identical ferromagnetic seeds in a tissue volume with a computer generated artificial vessel network spanning four vessel generations in both the arterial and venous tree. The heterogeneously distributed large isolated vessels impair the temperature distribution significantly, indicating the limited accuracy of continuum models. Simulations with different types of ferromagnetic seeds have confirmed that the efforts of previous studies to optimize the self-regulating temperature control and the implantation techniques of the ferroseeds will improve the homogeneity of the temperature distribution in the target volume. Multifilament seeds implanted in brachytherapy needles and tubular seeds appear to be the most favourable configurations. The division of long seeds into shorter segments with the appropriate Curie temperature will further improve the homogeneity of the temperature distribution without increasing the average temperature in the volume of interest. Given the proper thermal tissue data, the model presented in this study will prove to be a useful tool in making choices for the implant geometry, seed spacing and Curie temperature.