Discrete Vasculature Research Articles

Hyperthermia Treatment Planning: Clinical Application and Ongoing Developments

Hyperthermia is a proven clinical anti-cancer treatment, used in combination with radiotherapy and/or chemotherapy. During hyperthermia, tumour tissue is heated to 40-43 °C using radiofrequency or microwave antennas, which strongly enhances effectiveness of radiotherapy and chemotherapy. Hyperthermia treatment quality depends on tumour temperatures achieved and treatment planning (i.e., simulation and optimization of absorbed power and temperature distributions) could be very useful to ensure and improve treatment quality. Hyperthermia treatment planning was mainly a research tool for decades, because of high computational costs and limited quantitative accuracy of treatment planning predictions due to a lack of patient-specific tissue properties. Thanks to developments over the past decade, treatment planning becomes increasingly important in the clinical workflow. Presently, main clinical applications of hyperthermia treatment planning are 1) applicator selection, 2) heating ability evaluation and 3) on-line treatment guidance. To improve the reliability and further increase applicability of treatment planning, ongoing developments focus on 1) dielectric imaging to derive patient-specific dielectric properties, 2) advanced thermal modelling including discrete vasculature and 3) biological modelling to predict the radiosensitizing effect of hyperthermia in terms of equivalent radiation dose. The increased clinical application and ongoing efforts will further improve treatment quality.

Feasibility and relevance of discrete vasculature modeling in routine hyperthermia treatment planning

Purpose: To investigate the effect of patient specific vessel cooling on head and neck hyperthermia treatment planning (HTP).Methods and materials: Twelve patients undergoing radiotherapy were scanned using computed tomography (CT), magnetic resonance imaging (MRI) and contrast enhanced MR angiography (CEMRA). 3D patient models were constructed using the CT and MRI data. The arterial vessel tree was constructed from the MRA images using the ‘graph-cut’ method, combining information from Frangi vesselness filtering and region growing, and the results were validated against manually placed markers in/outside the vessels. Patient specific HTP was performed and the change in thermal distribution prediction caused by arterial cooling was evaluated by adding discrete vasculature (DIVA) modeling to the Pennes bioheat equation (PBHE).Results: Inclusion of arterial cooling showed a relevant impact, i.e., DIVA modeling predicts a decreased treatment quality by on average 0.19 °C (T90), 0.32 °C (T50) and 0.35 °C (T20) that is robust against variations in the inflow blood rate (|ΔT| < 0.01 °C). In three cases, where the major vessels transverse target volume, notable drops (|ΔT| > 0.5 °C) were observed.Conclusion: Addition of patient-specific DIVA into the thermal modeling can significantly change predicted treatment quality. In cases where clinically detectable vessels pass the heated region, we advise to perform DIVA modeling.

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.

Application of fast isogeometric L2 projection solver for tumor growth simulations

To employ computer models of tumor proliferation for planning cancer treatment, extremely fast numerical solvers are in high demand at least for two reasons: data adaptation and multiscale character of growth dynamics. The number of complex and non-linear phenomena influencing tumor dynamics involves hundreds of variable parameters. Its matching using incoming data requires reverse optimization or learning procedures, which are very demanding computationally. We present here the fast algorithm for isogeometric L2 projection, which we propose as a numerical engine for tumor modeling. First, we introduce the continuous–discrete model of melanoma described by the system of PDEs in a simplified computational layout of a fragment of skin. Apart from the continuous density fields such as tumor cell density, flux pressure, extracellular and degraded extracellular matrices, we also introduce a discrete model of the vasculature, which is the source of oxygen and nutrients. The discrete vasculature is coupled every given time interval with the continuous model influencing the vasculature remodeling. Our tests and the results of 2-D simulations of melanoma progression clearly show that isogeometric L2 projection utilizing the alternating directions solver is superior over classical approaches in terms of computational complexity, what makes it an excellent candidate for a numerical engine for continuous–discrete models of complex biological systems.

Fast thermal simulations and temperature optimization for hyperthermia treatment planning, including realistic 3D vessel networks

Accurate thermal simulations in hyperthermia treatment planning require discrete modeling of large blood vessels. The very long computation time of the finite difference based DIscrete VAsculature model (DIVA) developed for this purpose is impractical for clinical applications. In this work, a fast steady-state thermal solver was developed for simulations with realistic 3D vessel networks. Additionally, an efficient temperature-based optimization method including the thermal effect of discrete vasculature was developed. The steady-state energy balance for vasculature and tissue was described by a linear system, which was solved with an iterative method on the graphical processing unit. Temperature calculations during optimization were performed by superposition of several precomputed temperature distributions, calculated with the developed thermal solver. The thermal solver and optimization were applied to a human anatomy, with the prostate being the target region, heated with the eight waveguide 70 MHz AMC-8 system. Realistic 3D pelvic vasculature was obtained from angiography. Both the arterial and venous vessel networks consisted of 174 segments and 93 endpoints with a diameter of 1.2 mm. Calculation of the steady-state temperature distribution lasted about 3.3 h with the original DIVA model, while the newly developed method took only ≈ 1-1.5 min. Temperature-based optimization with and without taking the vasculature into account showed differences in optimized waveguide power of more than a factor 2 and optimized tumor T90 differed up to ≈ 0.5°C. This shows the necessity to take discrete vasculature into account during optimization. A very fast method was developed for thermal simulations with realistic 3D vessel networks. The short simulation time allows online calculations and makes temperature optimization with realistic vasculature feasible, which is an important step forward in hyperthermia treatment planning.

Radiofrequency heating induced by 7T head MRI: Thermal assessment using discrete vasculature or pennes' bioheat equation

To evaluate and compare the maximum temperature (T(max) ) in the head after exposure to a 300 MHz radiofrequency (RF) field induced by a magnetic resonance imaging (MRI) coil using two thermal simulation methods: Pennes' bioheat equation (PBHE) and discrete vasculature (DIVA). The electromagnetic field induced in the head by a 7T birdcage coil was simulated using finite-difference time-domain (FDTD) and validated by MRI. The specific absorption rate (SAR) distributions normalized to the 10-gram maximum or the whole-head average were used for PBHE and DIVA simulations. For all cases, the T(max) in PBHE was slightly higher than in DIVA. The T(max) was 37.9-38.4°C, depending on the simulation method or perfusion rate. In some situations, RF exposure limited to SAR(max,10g) led to a T(max) higher than allowed by International Electrotechnical Commission (IEC) regulations. Therefore, it is advisable to use thermal simulations to evaluate RF safety of MRI. The simulation method used only slightly influenced the observed maximum temperature; the observed temperature with PBHE was higher in all situations. So PBHE is an appropriate method for RF safety assessment of MRI in the head. Using DIVA simulations, it was found unlikely that the body temperature increases significantly due to energy deposited by a head coil under normal circumstances.

Calculation of SAR and temperature rise in a high-resolution vascularized model of the human eye and orbit when exposed to a dipole antenna at 900, 1500 and 1800 MHz

The eye is considered to be a critical organ when determining safety standards for radiofrequency radiation. With a detailed anatomy of the human eye and orbit inserted in a whole-head model, the specific absorption rates (SARs) and thermal effects were determined under exposure to a dipole antenna representing a mobile phone operating at 900, 1500 and 1800 MHz with an output power of 1 W. The temperature rise was calculated by taking the blood flow into account either by the Pennes bioheat model or by including the discrete vasculature (DIVA). In addition, a simple spherical model using constant heat transfer coefficients was used. Peak SARs in the humour are 4.5, 7.7 and 8.4 W kg−1 for 900, 1500 and 1800 MHz respectively. Averaged over the whole eyeball, the SARs are 1.7, 2.5 and 2.2 W kg−1. The maximum temperature rises in the eye due to the exposure are 0.22, 0.27 and 0.25 °C for exposure of 900, 1500 and 1800 MHz, respectively, calculated with DIVA. For the Pennes bioheat model, the temperature rises are slightly lower: 0.19, 0.24, 0.22 °C respectively. For the simple spherical model, the maximum temperature rises are 0.15, 0.22 and 0.20 °C. The peak temperature is located in the anterior part of the lens for 900 MHz and deeper in the eye for higher frequencies, and in the posterior part of the lens for 1500 MHz and close to the centre of the eyeball for 1800 MHz. For these RF safety applications, both DIVA and the Pennes bioheat model could be used to relate the SAR distributions to the resulting temperature distributions. Even though, for these artificial exposure conditions, the SAR values are not in compliance with safety guidelines, the maximum temperature rises in the eye are too small to give harmful effects. The temperature in the eye also remains below body core temperature.

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 °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.

High‐resolution regional hyperthermia treatment planning

The major difficulties in electromagnetic regional hyperthermia are the occurrence of systematic stress and local high temperatures (hot spots). This thesis describes the development of a planning system to get more insight in hyperthermia treatments. The system is based on a finite‐difference time‐domain computer model to calculate the specific absorption rate (SAR) distribution within a patient. Segmenting a CT data set into fat, muscle, and bone and using literature‐based values of the dielectric properties results in the required dielectric patient model. Because the SAR computation on CT‐resolution (1×1×5 would require 310 days, this high‐resolution is down‐scaled to a lower resolution of 1 (computation time 2.8 hours). The use of the HTP system reveals the close relation between SAR distribution and patient anatomy, stressing the need for high‐resolution computations. For this purpose a method called quasistatic zooming has been developed: from the low‐resolution E‐field distribution the high‐resolution potential distribution at the surface of a small subvolume is calculated. With this potential distribution and the high‐resolution patient geometry, the high‐resolution SAR distribution is computed using a quasistatic SAR model. Repeating this procedure yields the high‐resolution SAR distribution for an arbitrary volume of interest. With this method it takes 4.3 days to compute CT‐resolution SAR distributions. SAR maxima that are predicted by both quasistatic zooming and high‐resolution SAR modeling are not predicted by low‐resolution computations and vice versa. Hence, zooming is required for reliable treatment planning. Whether SAR maxima lead to hot spots depends on local blood flow (discrete vasculature, local perfusion) and will be investigated in a succeeding project.

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

For accurate predictions of the temperature distribution during hyperthermiatreatment a thermal model should incorporate the individual impact of discretevessels. In clinical practice not all vessels can be reconstructedindividually. This paper investigates five possible strategies to model thethermal impact of these missing vessels.A tissue volume with a detailed, realistic, counter-current discretevasculature is heated and the steady-state temperature distribution iscalculated using our DIscrete VAsculature (DIVA) thermal model. To mimicincomplete discrete vasculatures the full tree is gradually stripped, that is,the number of discretely described vessels is reduced in four steps until nodiscrete vessels are left.At each strip level the steady state temperature distribution is calculatedfor five different strategies to model the missing vessels. The strategies alluse a local or global heat sink model in addition to the discrete vasculature.The resulting temperature distributions are compared with the full treesimulation.With increasing strip level the correspondence with the full tree simulationdeteriorated for all strategies. An optimal strategy was found to model themissing vessels depending on the available angiographic data. It was alsofound that simulations with a decreased number of discrete vessels, or novessels at all, yield temperatures which are too high. Theoretically this can becompensated by increasing the thermal conductivity; finding the optimal valueis done empirically.

Modelling individual temperature profiles from an isolated perfused bovine tongue

To predict the temperature distribution during hyperthermia treatments a thermal model that accounts for the thermal effect of blood flow is mandatory. The DIscrete VAsculature (DIVA) thermal model developed at our department is able to do so; geometrically described vessels are handled individually and the remaining vasculature is modelled collectively. The goal of this paper is to experimentally validate the DIVA model by comparing measured with modelled temperature profiles on an individual basis. Temperature profiles in an isolated bovine tongue heated with three hot water tubes were measured at three controlled perfusion levels, 0, 6 and 24 ml (100 g)-1 min-1. The geometries of the tongue, the hot water tubes, thermocouples and discrete vasculature down to 0.5 mm diameter were reconstructed by using cryo-microtome slices at 0.1 mm cubic resolution. This reconstruction of the experimental set-up is used for the modelling of individual profiles. In a no-flow agar-agar phantom, DIVA showed nearly perfect correspondence between measurements and simulations. In the isolated bovine tongue the correspondence at no flow was slightly disturbed due to geometrical distortion in the reconstruction of the experimental set-up. Measurements showed decreasing temperature profiles with increasing perfusion. DIVA correctly predicted this decrease in temperature as well as the thermal impact of a large vessel close to a thermocouple. Blood flow was modelled using discrete vasculature and using a heat sink model. Although at 24 ml (100 g)-1 min-1 correspondence between heat sink simulations and measurements was reasonable, modelling discrete vasculature yielded the best correspondence at both 6 and 24 ml (100 g)-1 min-1. The results strongly suggest that with accurate data acquisition DIVA can predict temperature profiles on an individual basis. For this kind of patient-specific treatment planning in the clinic, geometrical reconstruction of the anatomy, vasculature and the heating implant is necessary. MRI is capable of providing these data. Further research will be done on thermal simulations of actual clinical hyperthermia treatments.

Comparison of temperature distributions in interstitial hyperthermia: experiments in bovine tongues versus generic simulations

Temperature distributions resulting from hyperthermia treatments on isolated perfused bovine tongues were compared with simulations by a treatment planning system. The aim was to test whether the discrete vessel model used for the treatment planning is able to predict correct generic temperature distributions. Tongues were heated with the multielectrode current source interstitial hyperthermia treatment (MECS IHT) system, while the steady-state temperature distribution was mapped by scanning 10 thermocouples along paths perpendicular to the interstitial implant. For simulations a tongue was defined with generic discrete vasculature and an electrode implant analogue to the experiments. To model vascular generations not described discretely, a local heatsink was implemented at the end of each terminating branch. The discretely modelled vasculature showed itself on the temperature distributions in two ways. Individual vessels caused very local, sharp wells in the tracked temperature profiles. In the presence of large vessels a collective behaviour was also seen, i.e. a regional lowering of temperature. Both phenomena can be recognized in the experimentally obtained temperature distributions too. Predicting correct generic temperature distributions is feasible with the discrete vessel model used.

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.

Modelling tissue heating with ferromagnetic seeds

Interstitial hyperthermia using ferromagnetic seeds demands accurate treatment planning: the seed characteristics and implant geometry must be determined prior to the treatment. A new, finite difference based, seed modelling method is presented. The seed, together with all its surrounding (non-tissue) layers is described as one unit, independent of the tissue grid. The calculation of the seed-tissue interaction is based on the local seed temperature and several tissue temperature samples in the direct vicinity. All the layers between the seed and the surrounding tissue are taken into account in this interaction calculation. The presented implementation describes the analytical solution of the modelled steady-state configurations very accurately. The separation between tissue and seed allows easy assessment of the resulting seed temperature profile which is essential to the optimization of the seed characteristics in treatment planning. The thermal effect due to blood flow in the modelled tissue volume surrounding the seed can be accounted for by inclusion of a heat sink term as well as by inclusion of realistic discrete vasculature.

The multielectrode current‐source interstitial hyperthermia system

The multielectrode current‐source interstitial hyperthermia (MECS‐IHT) system uses metallic electrodes inserted into plastic catheters and connected to 27 MHz sources. The heat deposition (SAR) along the catheter track is controlled by using several independent electrodes in a single catheter. The MECS probes incorporate multi‐sensor thermocouple thermometry. The planning system contains modules for the calculation of the power deposition in tissue, heat transport calculation, incorporating discrete vasculature, electrode power control, analysis of temperature distributions, implant planning and the visualisation of temperature distributions and of the implant setup. The ideal current source approximation used in the treatment planning/SAR model is validated and it is shown that tissue inhomogeneities do not pose major electrical problems. The temperatures measured in the catheter can be used for power control during treatment. The temperature distributions during treatment were investigated using models of idealized anatomies with and without discrete vasculature. Even with high contrasts in electrical and thermal conductivity in the implant it remains possible to obtain satisfactory temperature distributions with the MECS system. Inhomogeneities in the implant volume lead to inferior temperature distributions if no longitudinal SAR control is available. The spatial SAR control of the MECS‐IHT system, combined with the temperature feedback, is essential for optimizing the temperature control. Treatments using the system are technically successful.

The influence of vasculature on temperature distributions in MECS interstitial hyperthermia: Importance of longitudinal control

The quality of temperature distributions that can be generated with the Multi Electrode Current Source (MECS) interstitial hyperthermia (IHT) system, which allows 3D control of the temperature distribution, has been investigated. For the investigations, computer models of idealised anatomies containing discrete vessels, were used. A 7-catheter hexagonal implant geometry with a nearest neighbour distance of 15 mm was used. In each interstitial catheter with a diameter of 21 mm a number of 1 up to 4 electrodes were placed along an ‘active section’ with a length of 50 mm. The electrode segments had lengths of 50, 20, 12 and 9 mm respectively. Both single vessel and vessel network situations were analysed. This study shows that even in situations with discrete vasculature and perfusion heterogeneity it remains possible to obtain satisfactory temperature distributions with the MECS IHT system. Due to its 3D spatial control the temperature homogeneity in the implant can be made quite satisfactory.