Table of contents

Sixty years after the paper 'The Monte Carlo method' by N Metropolis and S Ulam in The Journal of the American Statistical Association (Metropolis and Ulam 1949), use of the most accurate algorithm for computer modelling of radiotherapy linear accelerators, radiation detectors and three dimensional patient dose was discussed in Wales (UK).

The Second European Workshop on Monte Carlo Treatment Planning (MCTP2009) was held at the National Museum of Wales in Cardiff. The event, organized by Velindre NHS Trust, Cardiff University and Cancer Research Wales, lasted two and a half days, during which leading experts and contributing authors presented and discussed the latest advances in the field of Monte Carlo treatment planning (MCTP).

MCTP2009 was highly successful, judging from the number of participants which was in excess of 140. Of the attendees, 24% came from the UK, 46% from the rest of Europe, 12% from North America and 18% from the rest of the World. Fifty-three oral presentations and 24 posters were delivered in a total of 12 scientific sessions. MCTP2009 follows the success of previous similar initiatives (Verhaegen and Seuntjens 2005, Reynaert 2007, Verhaegen and Seuntjens 2008), and confirms the high level of interest in Monte Carlo technology for radiotherapy treatment planning. The 13 articles selected for this special section (following Physics in Medicine and Biology's usual rigorous peer-review procedure) give a good picture of the high quality of the work presented at MCTP2009. The book of abstracts can be downloaded from http://www.mctp2009.org.

I wish to thank the IOP Medical Physics and Computational Physics Groups for their financial support, Elekta Ltd and Dosisoft for sponsoring MCTP2009, and leading manufacturers such as BrainLab, Nucletron and Varian for showcasing their latest MC-based radiotherapy solutions during a dedicated technical session. I am also very grateful to the eight invited speakers who kindly accepted to give keynote presentations which contributed significantly to raising the quality of the event and capturing the interest of the medical physics community.

I also wish to thank all those who contributed to the success of MCTP2009: the members of the local Organizing Committee and the Workshop Management Team who managed the event very efficiently, the members of the European Working Group in Monte Carlo Treatment Planning (EWG-MCTP) who acted as Guest Associate Editors for the MCTP2009 abstracts reviewing process, and all the authors who generated new, high quality work.

Finally, I hope that you find the contents of this special section enjoyable and informative.

Emiliano SpeziChairman of MCTP2009 Organizing Committee and Guest Editor

References

Metropolis N and Ulam S 1949 The Monte Carlo method J. Amer. Stat. Assoc.44 335–41

Reynaert N 2007 First European Workshop on Monte Carlo Treatment Planning J. Phys.: Conf. Ser.74 011001

Verhaegen F and Seuntjens J 2005 International Workshop on Current Topics in Monte Carlo Treatment Planning Phys. Med. Biol.50

Verhaegen F and Seuntjens J 2008 International Workshop on Monte Carlo Techniques in Radiotherapy Delivery and Verification J. Phys.: Conf. Ser.102 011001

We present two new Monte Carlo sources for the DOSXYZnrc code, which can be used to compute dose distributions due to continuously variable beam configurations. These sources support a continuously rotating gantry and collimator, dynamic multileaf collimator (MLC) motion, variable monitor unit (MU) rate, couch rotation and translation in any direction, arbitrary isocentre motion with respect to the patient and variable source-to-axis distance (SAD). These features make them applicable to Monte Carlo simulations for RapidArc™, Elekta VMAT, TomoTherapy™ and CyberKnife™. Unique to these sources is the synchronization between the motion in the DOSXYZnrc geometry and the motion within the linac head, represented by a shared library (either a BEAMnrc accelerator with dynamic component modules, or an external library). The simulations are achieved in single runs, with no intermediate phase space files.

Modern cancer treatment techniques, such as intensity-modulated radiation therapy (IMRT) and stereotactic body radiation therapy (SBRT), have greatly increased the demand for more accurate treatment planning (structure definition, dose calculation, etc) and dose delivery. The ability to use fast and accurate Monte Carlo (MC)-based dose calculations within a commercial treatment planning system (TPS) in the clinical setting is now becoming more of a reality. This study describes the dosimetric verification and initial clinical evaluation of a new commercial MC-based photon beam dose calculation algorithm, within the iPlan v.4.1 TPS (BrainLAB AG, Feldkirchen, Germany). Experimental verification of the MC photon beam model was performed with film and ionization chambers in water phantoms and in heterogeneous solid-water slabs containing bone and lung-equivalent materials for a 6 MV photon beam from a Novalis (BrainLAB) linear accelerator (linac) with a micro-multileaf collimator (m₃ MLC). The agreement between calculated and measured dose distributions in the water phantom verification tests was, on average, within 2%/1 mm (high dose/high gradient) and was within ±4%/2 mm in the heterogeneous slab geometries. Example treatment plans in the lung show significant differences between the MC and one-dimensional pencil beam (PB) algorithms within iPlan, especially for small lesions in the lung, where electronic disequilibrium effects are emphasized. Other user-specific features in the iPlan system, such as options to select dose to water or dose to medium, and the mean variance level, have been investigated. Timing results for typical lung treatment plans show the total computation time (including that for processing and I/O) to be less than 10 min for 1–2% mean variance (running on a single PC with 8 Intel Xeon X5355 CPUs, 2.66 GHz). Overall, the iPlan MC algorithm is demonstrated to be an accurate and efficient dose algorithm, incorporating robust tools for MC-based SBRT treatment planning in the routine clinical setting.

The aim of the study was to perform the Monte Carlo (MC) evaluation of RapidArc™ (Varian Medical Systems, Palo Alto, CA) dose calculations for four oropharynx midline sparing planning strategies. Six patients with squamous cell cancer of the oropharynx were each planned with four RapidArc head and neck treatment strategies consisting of single and double photon arcs. In each case, RTOG0522 protocol objectives were used during planning optimization. Dose calculations performed with the analytical anisotropic algorithm (AAA) are compared against BEAMnrc/DOSXYZnrc dose calculations for the 24-plan dataset. Mean dose and dose-to-98%-of-structure-volume (D_98%) were used as metrics in the evaluation of dose to planning target volumes (PTVs). Mean dose and dose-to-2%-of-structure-volume (D_2%) were used to evaluate dose differences within organs at risk (OAR). Differences in the conformity index (CI) and the homogeneity index (HI) as well as 3D dose distributions were also observed. AAA calculated PTV mean dose, D_98%, and HIs showed very good agreement with MC dose calculations within the 0.8% MC (statistical) calculation uncertainty. Regional node volume (PTV-80%) mean dose and D_98% were found to be overestimated (1.3%, σ = 0.8% and 2.3%, σ = 0.8%, respectively) by the AAA with respect to MC calculations. Mean dose and D_2% to OAR were also observed to be consistently overestimated by the AAA. Increasing dose calculation differences were found in planning strategies exhibiting a higher overall fluence modulation. From the plan dataset, the largest local dose differences were observed in heavily shielded regions and within the esophageal and sinus cavities. AAA dose calculations as implemented in RapidArc™ demonstrate excellent agreement with MC calculations in unshielded regions containing moderate inhomogeneities. Acceptable agreement is achieved in regions of increased MLC shielding. Differences in dose are attributed to inaccuracies in the AAA-modulated fluence modeling, modeling of material inhomogeneities and dose deposition within low-density materials. The use of MC dose calculations leads to the same general conclusion as using AAA that a two arc delivery with limited collimator opening can provide the greatest amount of midline sparing compared to the other techniques investigated.

Modern Monte Carlo codes allow for the calculation of ion chamber specific beam quality correction factors k_Q, which are needed for dosimetry in radiotherapy. While statistical (type A) uncertainties of the calculated data can be minimized sufficiently, the influence of systematic (type B) uncertainties is mostly unknown. This study presents an investigation of systematic uncertainties of Monte Carlo-based k_Q values for a NE2571 thimble ion chamber, calculated with the EGSnrc system. Starting with some general investigation on transport parameter settings, the influence of geometry and source variations is studied. Furthermore, a systematic examination of uncertainties due to cross section is introduced by determining the sensitivity of k_Q results to changes in cross section data. For this purpose, single components of the photon cross sections and the mean excitation energy I in the electron stopping powers are varied. The corresponding sensitivities are subsequently applied with information of standard uncertainties for the cross section data found in the literature. It turns out that the calculation of k_Q factors with EGSnrc is mostly insensitive to transport settings within the statistical uncertainties of ∼0.1%. Severe changes in the dimensions of the chamber lead to comparatively small, insignificant changes. Further, the inclusion of realistic beam models, delivering a complete phase space instead of simple photon spectra, does not significantly influence the result. However, the uncertainties in electron cross sections have an impact on the final uncertainty of k_Q to a comparatively large degree. For the NE2571 chamber investigated in this work, this uncertainty amounts to 0.4% at 24 MV, decreasing to 0.2% at 6 MV.

Several variance reduction techniques improving the efficiency of the Monte Carlo estimation of the scatter contribution to a cone beam computed tomography (CBCT) scan were implemented in , an EGSnrc-based application for CBCT-related calculations. The largest impact on the efficiency comes from the splitting + Russian Roulette techniques which are described in detail. The fixed splitting technique is outperformed by both the position-dependent importance splitting (PDIS) and the region-dependent importance splitting (RDIS). The superiority of PDIS over RDIS observed for a water phantom with bone inserts is not observed when applying these techniques to a more realistic human chest phantom. A maximum efficiency improvement of several orders of magnitude over an analog calculation is obtained. A scatter calculation combining the reported efficiency gain with a smoothing algorithm is already in the proximity of being of practical use if a medium size computer cluster is available.

A novel approach using nano-technology enhanced radiation modalities is investigated. The proposed methodology uses antibodies labeled with organically inert metals with a high atomic number. Irradiation using photons with energies in the kilo-electron volt (keV) range shows an increase in dose due to a combination of an increase in photo-electric interactions and a pronounced generation of Auger and/or Coster–Krönig (A–CK) electrons. The dependence of the dose deposition on various factors is investigated using Monte Carlo simulation models. The factors investigated include agent concentration, spectral dependence looking at mono-energetic sources as well as classical bremsstrahlung sources. The optimization of the energy spectrum is performed in terms of physical dose enhancement as well as the dose deposited by Auger and/or Coster–Krönig electrons and their biological effectiveness. A quasi-linear dependence on concentration and an exponential decrease within the target medium is observed. The maximal dose enhancement is dependent on the position of the target in the beam. Apart from irradiation with low-photon energies (10–20 keV) there is no added benefit from the increase in generation of Auger electrons. Interestingly, a regular 110 kVp bremsstrahlung spectrum shows a comparable enhancement in comparison with the optimized mono-energetic sources. In conclusion we find that the use of enhanced nano-particles shows promise to be implemented quite easily in regular clinics on a physical level due to the advantageous properties in classical beams.

The pencil beam dose calculation method is frequently used in modern radiation therapy treatment planning regardless of the fact that it is documented inaccurately for cases involving large density variations. The inaccuracies are larger for higher beam energies. As a result, low energy beams are conventionally used for lung treatments. The aim of this study was to analyze the advantages and disadvantages of dynamic IMRT treatment planning for high and low photon energy in order to assess if deviating from the conventional low energy approach could be favorable in some cases. Furthermore, the influence of motion on the dose distribution was investigated. Four non-small cell lung cancer cases were selected for this study. Inverse planning was conducted using Varian Eclipse. A total number of 31 dynamic IMRT plans, distributed amongst the four cases, were created ranging from PTV conformity weighted to normal tissue sparing weighted. All optimized treatment plans were calculated using three different calculation algorithms (PBC, AAA and MC). In order to study the influence of motion, two virtual lung phantoms were created. The idea was to mimic two different situations: one where the GTV is located centrally in the PTV and another where the GTV was close to the edge of the PTV. PBC is in poor agreement with MC and AAA for all cases and treatment plans. AAA overestimates the dose, compared to MC. This effect is more pronounced for 15 than 6 MV. AAA and MC both predict similar perturbations in dose distributions when moving the GTV to the edge of the PTV. PBC, however, predicts results contradicting those of AAA and MC. This study shows that PB-based dose calculation algorithms are clinically insufficient for patient geometries involving large density inhomogeneities. AAA is in much better agreement with MC, but even a small overestimation of the dose level by the algorithm might lead to a large part of the PTV being underdosed. It is advisable to use low energy as a default for tumor sites involving lungs. However, there might be situations where it is favorable to use high energy. In order to deviate from the recommended low energy convention, an accurate dose calculation algorithm (e.g. MC) should be consulted. The study underlines the inaccuracies introduced when calculating dose using a PB-based algorithm in geometries involving large density variations. PBC, in contrast to other algorithms (AAA and MC), predicts a decrease in dose when the density is increased.

The purpose of this study is to determine whether dose to medium, D_m, or dose to water, D_w, provides a better estimate of the dose to the radiosensitive red bone marrow (RBM) and bone surface cells (BSC) in spongiosa, or cancellous bone. This is addressed in the larger context of the ongoing debate over whether D_m or D_w should be specified in Monte Carlo calculated radiotherapy treatment plans. The study uses voxelized, virtual human phantoms, FAX06/MAX06 (female/male), incorporated into an EGSnrc Monte Carlo code to perform Monte Carlo dose calculations during simulated irradiation by a 6 MV photon beam from an Elekta SL25 accelerator. Head and neck, chest and pelvis irradiations are studied. FAX06/MAX06 include precise modelling of spongiosa based on µCT images, allowing dose to RBM and BSC to be resolved from the dose to bone. Modifications to the FAX06/MAX06 user codes are required to score D_w and D_m in spongiosa. Dose uncertainties of ∼1% (BSC, RBM) or ∼0.5% (D_m, D_w) are obtained after up to 5 days of simulations on 88 CPUs. Clinically significant differences (>5%) between D_m and D_w are found only in cranial spongiosa, where the volume fraction of trabecular bone (TBVF) is high (55%). However, for spongiosa locations where there is any significant difference between D_m and D_w, comparisons of differential dose volume histograms (DVHs) and average doses show that D_w provides a better overall estimate of dose to RBM and BSC. For example, in cranial spongiosa the average D_m underestimates the average dose to sensitive tissue by at least 5%, while average D_w is within ∼1% of the average dose to sensitive tissue. Thus, it is better to specify D_w than D_m in Monte Carlo treatment plans, since D_w provides a better estimate of dose to sensitive tissue in bone, the only location where the difference is likely to be clinically significant.

The impact of tissue heterogeneity and interseed attenuation is studied in post-implant evaluation of five clinical permanent breast ¹⁰³Pd seed implants using the Monte Carlo (MC) dose calculation method. Dose metrics for the target (PTV) as well as an organ at risk (skin) are used to visualize the differences between a TG43-like MC method and more accurate MC methods capable of considering the breast tissue heterogeneity as well as the interseed attenuation. PTV dose is reduced when using a breast tissue model instead of water in MC calculations while the dose to the skin is increased. Furthermore, we investigate the effect of varying the glandular/adipose proportion of the breast tissue on dose distributions. The dose to the PTV (skin) decreases (increases) with the increasing adipose proportion inside the breast. In a complete geometry and compared to a TG43-like situation, the average PTV D₉₀ reduction varies from 3.9% in a glandular breast to 35.5% when the breast consists entirely of adipose. The skin D₁₀ increases by 28.2% in an entirely adipose breast. The results of this work show the importance of an accurate and patient-dependent breast tissue model to be used in the dosimetry for this kind of low energy implant.

Modulated electron radiotherapy (MERT) has been proven to produce optimal plans for shallow tumors. This study investigates automated approaches to the field determination process in generating optimal MERT plans for few-leaf electron collimator (FLEC)-based MERT, by generating a large database of pre-calculated beamlets stored as phase-space files. Beamlets can be used in an overlapping feathered pattern to reduce the effect of abutting fields, which can contribute to dose inhomogeneities within the target. Beamlet dose calculation was performed by Monte Carlo (MC) simulations prior to direct aperture optimization (DAO). The second part of the study examines a preliminary clinical comparison between FLEC-based MERT and helical TomoTherapy. A MERT plan for spinal irradiation was not able to conform to the PTV dose constraints as closely as the TomoTherapy plan, although the TomoTherapy plan was taken as is, i.e. not Monte Carlo re-calculated. Despite the remaining gradients in the PTV, the MERT plan was superior in reducing the low-dose bath typical of TomoTherapy plans. In conclusion, the FLEC-based MERT planning techniques developed within the study produced promising MERT plans with minimal user input. The phase-space database reduces the MC calculation time and the feathered field pattern improves target homogeneity. With further investigations, FLEC-based MERT will find an important niche in clinical radiation therapy.

The electron Monte Carlo (eMC) dose calculation algorithm in Eclipse (Varian Medical Systems) is based on the macro MC method and is able to predict dose distributions for high energy electron beams with high accuracy. However, there are limitations for low energy electron beams. This work aims to improve the accuracy of the dose calculation using eMC for 4 and 6 MeV electron beams of Varian linear accelerators. Improvements implemented into the eMC include (1) improved determination of the initial electron energy spectrum by increased resolution of mono-energetic depth dose curves used during beam configuration; (2) inclusion of all the scrapers of the applicator in the beam model; (3) reduction of the maximum size of the sphere to be selected within the macro MC transport when the energy of the incident electron is below certain thresholds. The impact of these changes in eMC is investigated by comparing calculated dose distributions for 4 and 6 MeV electron beams at source to surface distance (SSD) of 100 and 110 cm with applicators ranging from 6 × 6 to 25 × 25 cm² of a Varian Clinac 2300C/D with the corresponding measurements. Dose differences between calculated and measured absolute depth dose curves are reduced from 6% to less than 1.5% for both energies and all applicators considered at SSD of 100 cm. Using the original eMC implementation, absolute dose profiles at depths of 1 cm, d_max and R50 in water lead to dose differences of up to 8% for applicators larger than 15 × 15 cm² at SSD 100 cm. Those differences are now reduced to less than 2% for all dose profiles investigated when the improved version of eMC is used. At SSD of 110 cm the dose difference for the original eMC version is even more pronounced and can be larger than 10%. Those differences are reduced to within 2% or 2 mm with the improved version of eMC. In this work several enhancements were made in the eMC algorithm leading to significant improvements in the accuracy of the dose calculation for 4 and 6 MeV electron beams of Varian linear accelerators.

This work investigated the accuracy of Monte Carlo (MC) simulations of amorphous silicon (a-Si) electronic portal imaging devices (EPIDs) for the dosimetric verification of intensity-modulated radiotherapy (IMRT). In particular, the suitability of the method for verification of head and neck IMRT with extended field segments (≈20 cm superior–inferior), covering almost the entire detector area, was studied. A solution involving schematic modelling of backscatter materials has been established to account for non-uniform backscatter to the imager from supporting structures. 96% of points within the IMRT fields evaluated passed a 'gamma' evaluation criterion of 2%, 2 mm at isocentre at a dose rate of 100 MU min⁻¹ with this solution included. Only 79% of points passed this gamma criterion without the correction for backscatter included. This work has also demonstrated the ability of the technique to detect systematic delivery errors in step and shoot IMRT. The technique identified a systematic overshoot on the first segment and an undershoot on the final segment. Results were verified by ion chamber measurements and agreed well with those reported in the literature, averaging approximately 0.1 and 0.3 MU for 100 and 300 MU min⁻¹ deliveries, respectively. MC portal verification has the potential to become a key tool in the verification of IMRT and can also facilitate selection of optimal delivery parameters, thus improving treatment accuracy. This approach can be applied to the verification of other new treatment techniques and should also enable development of methodologies to detect and correct for delivery errors, both before and during treatment.

This study presents data for verification of the iPlan RT Monte Carlo (MC) dose algorithm (BrainLAB, Feldkirchen, Germany). MC calculations were compared with pencil beam (PB) calculations and verification measurements in phantoms with lung-equivalent material, air cavities or bone-equivalent material to mimic head and neck and thorax and in an Alderson anthropomorphic phantom. Dosimetric accuracy of MC for the micro-multileaf collimator (MLC) simulation was tested in a homogeneous phantom. All measurements were performed using an ionization chamber and Kodak EDR2 films with Novalis 6 MV photon beams. Dose distributions measured with film and calculated with MC in the homogeneous phantom are in excellent agreement for oval, C and squiggle-shaped fields and for a clinical IMRT plan. For a field with completely closed MLC, MC is much closer to the experimental result than the PB calculations. For fields larger than the dimensions of the inhomogeneities the MC calculations show excellent agreement (within 3%/1 mm) with the experimental data. MC calculations in the anthropomorphic phantom show good agreement with measurements for conformal beam plans and reasonable agreement for dynamic conformal arc and IMRT plans. For 6 head and neck and 15 lung patients a comparison of the MC plan with the PB plan was performed. Our results demonstrate that MC is able to accurately predict the dose in the presence of inhomogeneities typical for head and neck and thorax regions with reasonable calculation times (5–20 min). Lateral electron transport was well reproduced in MC calculations. We are planning to implement MC calculations for head and neck and lung cancer patients.

We report on terahertz (THz) time-domain spectroscopy imaging of 10 µm thick histological sections. The sections are prepared according to standard pathological procedures and deposited on a quartz window for measurements in reflection geometry. Simultaneous acquisition of visible images enables registration of THz images and thus the use of digital pathology tools to investigate the links between the underlying cellular structure and specific THz information. An analytic model taking into account the polarization of the THz beam, its incidence angle, the beam shift between the reference and sample pulses as well as multiple reflections within the sample is employed to determine the frequency-dependent complex refractive index. Spectral images are produced through segmentation of the extracted refractive index data using clustering methods. Comparisons of visible and THz images demonstrate spectral differences not only between tumor and healthy tissues but also within tumors. Further visualization using principal component analysis suggests different mechanisms as to the origin of image contrast.

Fluorescence molecular imaging/tomography may play an important future role in preclinical research and clinical diagnostics. Time- and frequency-domain fluorescence imaging can acquire more measurement information than the continuous wave (CW) counterpart, improving the image quality of fluorescence molecular tomography. Although diffusion approximation (DA) theory has been extensively applied in optical molecular imaging, high-order photon migration models need to be further investigated to match quantitation provided by nuclear imaging. In this paper, a frequency-domain parallel adaptive finite element solver is developed with simplified spherical harmonics (SP_N) approximations. To fully evaluate the performance of the SP_N approximations, a fast time-resolved tetrahedron-based Monte Carlo fluorescence simulator suitable for complex heterogeneous geometries is developed using a convolution strategy to realize the simulation of the fluorescence excitation and emission. The validation results show that high-order SP_N can effectively correct the modeling errors of the diffusion equation, especially when the tissues have high absorption characteristics or when high modulation frequency measurements are used. Furthermore, the parallel adaptive mesh evolution strategy improves the modeling precision and the simulation speed significantly on a realistic digital mouse phantom. This solver is a promising platform for fluorescence molecular tomography using high-order approximations to the radiative transfer equation.

The present study describes theoretical parametric analysis of the steady-state temperature elevation in one-dimensional three-layer (skin, fat and muscle) and one-layer (skin only) models due to millimeter-wave exposure. The motivation of this fundamental investigation is that some variability of warmth sensation in the human skin has been reported. An analytical solution for a bioheat equation was derived by using the Laplace transform for the one-dimensional human models. Approximate expressions were obtained to investigate the dependence of temperature elevation on different thermal and tissue thickness parameters. It was shown that the temperature elevation on the body surface decreases monotonically with the blood perfusion rate, heat conductivity and heat transfer from the body to air. Also revealed were the conditions where maximum and minimum surface temperature elevations were observed for different thermal and tissue thickness parameters. The surface temperature elevation in the three-layer model is 1.3–2.8 times greater than that in the one-layer model. The main reason for this difference is attributed to the adiabatic nature of the fat layer. By considering the variation range of thermal and tissue thickness parameters which causes the maximum and minimum temperature elevations, the dominant parameter influencing the surface temperature elevation was found to be the heat transfer coefficient between the body surface and air.

Two calculation methods to produce ventilation images from four-dimensional computed tomography (4DCT) acquired without added contrast have been reported. We reported a method to obtain ventilation images using deformable image registration (DIR) and the underlying CT density information. A second method performs the ventilation image calculation from the DIR result alone, using the Jacobian determinant of the deformation field to estimate the local volume changes resulting from ventilation. For each of these two approaches, there are variations on their implementation. In this study, two implementations of the Jacobian-based methodology are evaluated, as well as a single density change-based model for calculating the physiologic specific ventilation from 4DCT. In clinical practice, ^99mTc-labeled aerosol single photon emission computed tomography (SPECT) is the standard method used to obtain ventilation images in patients. In this study, the distributions of ventilation obtained from the CT-based ventilation image calculation methods are compared with those obtained from the clinical standard SPECT ventilation imaging. Seven patients with 4DCT imaging and standard ^99mTc-labeled aerosol SPECT/CT ventilation imaging obtained on the same day as part of a prospective validation study were selected. The results of this work demonstrate the equivalence of the Jacobian-based methodologies for quantifying the specific ventilation on a voxel scale. Additionally, we found that both Jacobian- and density-change-based methods correlate well with global measurements of the resting tidal volume. Finally, correlation with the clinical SPECT was assessed using the Dice similarity coefficient, which showed statistically higher (p-value < 10⁻⁴) correlation between density-change-based specific ventilation and the clinical reference than did either Jacobian-based implementation.

A model of irradiated cell survival based on rigorous accounting of microdosimetric effects is developed. The model does not assume that the distribution of lesions is Poisson and is applicable to low, intermediate and high acute doses of low or high LET radiation. For small doses, the model produces the linear-quadratic (LQ) model. However, for high doses the best-fitting LQ model grossly underestimates cell survival. The same is also true for the conventional LQ model, only more so. It is shown that for high doses, the microdosimetric distribution can be approximated by a Gaussian distribution, and the corresponding cell survival probabilities are compared.

In this paper, we present an anatomy-based three-dimensional dose optimization approach for HDR brachytherapy using interactive multiobjective optimization (IMOO). In brachytherapy, the goals are to irradiate a tumor without causing damage to healthy tissue. These goals are often conflicting, i.e. when one target is optimized the other will suffer, and the solution is a compromise between them. IMOO is capable of handling multiple and strongly conflicting objectives in a convenient way. With the IMOO approach, a treatment planner's knowledge is used to direct the optimization process. Thus, the weaknesses of widely used optimization techniques (e.g. defining weights, computational burden and trial-and-error planning) can be avoided, planning times can be shortened and the number of solutions to be calculated is small. Further, plan quality can be improved by finding advantageous trade-offs between the solutions. In addition, our approach offers an easy way to navigate among the obtained Pareto optimal solutions (i.e. different treatment plans). When considering a simulation model of clinical 3D HDR brachytherapy, the number of variables is significantly smaller compared to IMRT, for example. Thus, when solving the model, the CPU time is relatively short. This makes it possible to exploit IMOO to solve a 3D HDR brachytherapy optimization problem. To demonstrate the advantages of IMOO, two clinical examples of optimizing a gynecologic cervix cancer treatment plan are presented.

A small field of view, high resolution gamma camera has been integrated into a dedicated breast, single photon emission computed tomography (SPECT) device. The detector can be flexibly positioned relative to the breast and image beyond the chest wall, allowing the system to capture direct views of the heart and liver. The incomplete sampling of these organs creates artifacts in reconstructed images, complicating lesion detection. To understand the limits imposed on a 3D acquisition trajectory, sequential tilted trajectories at increasing polar tilt are utilized to collect data of anthropomorphic phantoms filled with aqueous ^99mTc in a clinically realistic concentration ratio. The counts collected per projection between different scans and the SNR, contrast and resolution (FWHM) of two hot lesions were compared. As expected, the counts per projection increased when the camera had direct views of the heart and liver, but remained relatively constant at other angles. The SNR, contrast and FWHM were more affected by the insufficient sampling of the data by the large polar angles than by the cardiac and hepatic activity. An upper bound on polar tilt for each azimuthal position reduces the artifacts in the reconstructed images. Such trajectories were implemented to show artifact-free reconstructed images.

Minimally invasive therapies such as radiofrequency ablation have been developed to treat cancers of the liver, prostate and kidney without invasive surgery. Prior work has demonstrated that ultrasound echo shifts due to temperature changes can be utilized to track the temperature distribution in real time. In this paper, a motion compensation algorithm is evaluated to reduce the impact of cardiac and respiratory motion on ultrasound-based temperature tracking methods. The algorithm dynamically selects the next suitable frame given a start frame (selected during the exhale or expiration phase where extraneous motion is reduced), enabling optimization of the computational time in addition to reducing displacement noise artifacts incurred with the estimation of smaller frame-to-frame displacements at the full frame rate. A region of interest that does not undergo ablation is selected in the first frame and the algorithm searches through subsequent frames to find a similarly located region of interest in subsequent frames, with a high value of the mean normalized cross-correlation coefficient value. In conjunction with dynamic frame selection, two different two-dimensional displacement estimation algorithms namely a block matching and multilevel cross-correlation are compared. The multi-level cross-correlation method incorporates tracking of the lateral tissue expansion in addition to the axial deformation to improve the estimation performance. Our results demonstrate the ability of the proposed motion compensation using dynamic frame selection in conjunction with the two-dimensional multilevel cross-correlation to track the temperature distribution.

Co-registration of clinical images acquired using different imaging modalities and equipment is finding increasing use in patient studies. Here we present a method for registering high-resolution positron emission tomography (PET) data of the hand acquired using high-density avalanche chambers with magnetic resonance (MR) images of the finger obtained using a 'microscopy coil'. This allows the identification of the anatomical location of the PET radiotracer and thereby locates areas of active bone metabolism/'turnover'. Image fusion involving data acquired from the hand is demanding because rigid-body transformations cannot be employed to accurately register the images. The non-rigid registration technique that has been implemented in this study uses a variational approach to maximize the mutual information between images acquired using these different imaging modalities. A piecewise model of the fingers is employed to ensure that the methodology is robust and that it generates an accurate registration. Evaluation of the accuracy of the technique is tested using both synthetic data and PET and MR images acquired from patients with osteoarthritis. The method outperforms some established non-rigid registration techniques and results in a mean registration error that is less than approximately 1.5 mm in the vicinity of the finger joints.

Proton therapy can be particularly sensitive to changes or errors in range. Thus, methods for the in vivo measurement of range could be of great use to improve the quality and accuracy of proton-based radiotherapy. In this paper, we introduce the concept of the 'range probe'. This is a low-dose, high-energy proton pencil beam that would pass through a patient, and whose integral Bragg peak would be measured on the exit side using a multi-layer detector. We propose that by comparing the measured integral Bragg peak with that calculated based on the patient's planning CT, such a range probe could provide useful information about the accuracy of range calculations in vivo. To study the feasibility of this approach, a Monte Carlo-based study has been performed. Using a patient's planning CT, MC simulations (VMCpro) have been made for single pencil beams laterally traversing the head and stopping in a simulated range telescope behind the patient. Range probes have been calculated for different locations, and the residual range from the Bragg peak 'signal' in the range telescope has been assessed for different assumed detector thicknesses. The sensitivity of this approach to changes in CT values, calibration curve and positional shifts of the CT have been investigated. From our analysis, range resolutions of 1 mm may be possible with a detector thickness of 4 mm for homogeneous regions. Additionally, for heterogeneous regions, changes of the Bragg peak shape due to spatial shifts of the CT could be a sensitive measure for detecting patient set-up errors directly in the treatment position. The concept of the proton 'range probe' appears to be feasible for high-resolution range verification. We now want to test this concept experimentally using different possible range telescope detectors.

Widespread adoption of quantitative pharmacokinetic modeling methods in conjunction with dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) has led to increased recognition of the importance of obtaining accurate patient-specific arterial input function (AIF) measurements. Ideally, DCE-MRI studies use an AIF directly measured in an artery local to the tissue of interest, along with measured tissue concentration curves, to quantitatively determine pharmacokinetic parameters. However, the numerous technical and practical difficulties associated with AIF measurement have made the use of population-averaged AIF data a popular, if sub-optimal, alternative to AIF measurement. In this work, we present and characterize a new algorithm for determining the AIF solely from the measured tissue concentration curves. This Monte Carlo blind estimation (MCBE) algorithm estimates the AIF from the subsets of D concentration–time curves drawn from a larger pool of M candidate curves via nonlinear optimization, doing so for multiple (Q) subsets and statistically averaging these repeated estimates. The MCBE algorithm can be viewed as a generalization of previously published methods that employ clustering of concentration–time curves and only estimate the AIF once. Extensive computer simulations were performed over physiologically and experimentally realistic ranges of imaging and tissue parameters, and the impact of choosing different values of D and Q was investigated. We found the algorithm to be robust, computationally efficient and capable of accurately estimating the AIF even for relatively high noise levels, long sampling intervals and low diversity of tissue curves. With the incorporation of bootstrapping initialization, we further demonstrated the ability to blindly estimate AIFs that deviate substantially in shape from the population-averaged initial guess. Pharmacokinetic parameter estimates for K^trans, k_ep, v_p and v_e all showed relative biases and uncertainties of less than 10% for measurements having a temporal sampling rate of 4 s and a concentration measurement noise level of σ = 0.04 mM. A companion paper discusses the application of the MCBE algorithm to DCE-MRI data acquired in eight patients with malignant brain tumors.

Accurate quantification of pharmacokinetic model parameters in tracer kinetic imaging experiments requires correspondingly accurate determination of the arterial input function (AIF). Despite significant effort expended on methods of directly measuring patient-specific AIFs in modalities as diverse as dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), dynamic positron emission tomography (PET), and perfusion computed tomography (CT), fundamental and technical difficulties have made consistent and reliable achievement of that goal elusive. Here, we validate a new algorithm for AIF determination, the Monte Carlo blind estimation (MCBE) method (which is described in detail and characterized by extensive simulations in a companion paper), by comparing AIFs measured in DCE-MRI studies of eight brain tumor patients with results of blind estimation. Blind AIFs calculated with the MCBE method using a pool of concentration–time curves from a region of normal brain tissue were found to be quite similar to the measured AIFs, with statistically significant decreases in fit residuals observed in six of eight patients. Biases between the blind and measured pharmacokinetic parameters were the dominant source of error. Averaged over all eight patients, the mean biases were +7% in K ^trans, 0% in k_ep, −11% in v_p and +10% in v_e. Corresponding uncertainties (median absolute deviation from the best fit line) were 0.0043 min⁻¹ in K ^trans, 0.0491 min⁻¹ in k_ep, 0.29% in v_p and 0.45% in v_e. The use of a published population-averaged AIF resulted in larger mean biases in three of the four parameters (−23% in K ^trans, −22% in k_ep, −63% in v_p), with the bias in v_e unchanged, and led to larger uncertainties in all four parameters (0.0083 min⁻¹ in K ^trans, 0.1038 min⁻¹ in k_ep, 0.31% in v_p and 0.95% in v_e). When blind AIFs were calculated from a region of tumor tissue, statistically significant decreases in fit residuals were observed in all eight patients despite larger deviations of these blind AIFs from the measured AIFs. The observed decrease in root-mean-square fit residuals between the normal brain and tumor tissue blind AIFs suggests that the local blood supply in tumors is measurably different from that in normal brain tissue and that the proposed method is able to discriminate between the two. We have shown the feasibility of applying the MCBE algorithm to DCE-MRI data acquired in brain, finding generally good agreement with measured AIFs and decreased biases and uncertainties relative to the use of a population-averaged AIF. These results demonstrate that the MCBE algorithm is a useful alternative to direct AIF measurement in cases where acquisition of high-quality arterial input function data is difficult or impossible.

The use of THz radiation as a potential tool for medical imaging is of increasing interest. In this paper three methods of analysis of THz spectroscopic information for diagnosis of tissue pathologies at THz frequencies are presented. The frequency-dependent absorption coefficients, refractive indices and Debye relaxation times of pure water and pure lipids were measured and used as prior knowledge in the different theoretical methods for the determination of concentration. Three concentration analysis methods were investigated: (a) linear spectral decomposition, (b) spectrally averaged dielectric coefficient method and (c) the Debye relaxation coefficient method. These methods were validated on water and lipid emulsions by determining the concentrations of phantom chromophores and comparing to the known composition. The accuracy and resolution of each method were determined to assess the potential of each method as a tool for medical diagnosis at THz frequencies.

Ultrasound is emerging as an attractive alternative modality to standard x-ray and CT methods for bone assessment applications. As of today, however, there is a lack of systematic studies that investigate the performance of diagnostic ultrasound techniques in bone imaging applications. This study aims at understanding the performance limitations of new ultrasound techniques for imaging bones in controlled experiments in vitro. Experiments are performed on samples of mammalian and non-mammalian bones with controlled defects with size ranging from 400 µm to 5 mm. Ultrasound findings are statistically compared with those obtained from the same samples using standard x-ray imaging modalities and optical microscopy. The results of this study demonstrate that it is feasible to use diagnostic ultrasound imaging techniques to assess sub-millimeter bone defects in real time and with high accuracy and precision. These results also demonstrate that ultrasound imaging techniques perform comparably better than x-ray imaging and optical imaging methods, in the assessment of a wide range of controlled defects both in mammalian and non-mammalian bones. In the future, ultrasound imaging techniques might provide a cost-effective, real-time, safe and portable diagnostic tool for bone imaging applications.

The effects of a transverse magnetic field on an in-line side-coupled 6 MV linear accelerator are given. The results are directly applicable to a linac–MR system used for real-time image guided adaptive radiotherapy. Our previously designed end-to-end linac simulation incorporated the results from the axisymmetric 2D electron gun program EGN2w. However, since the magnetic fields being investigated are non-axisymmetric in nature for the work presented here, the electron gun simulation was performed using OPERA-3d/SCALA. The simulation results from OPERA-3d/SCALA showed excellent agreement with previous results. Upon the addition of external magnetic fields to our fully 3D linac simulation, it was found that a transverse magnetic field of 6 G resulted in a 45 ± 1% beam loss, and by 14 G, no electrons were incident on the target. Transverse magnetic fields on the linac simulation produced a highly asymmetric focal spot at the target, which translated into a 13% profile asymmetry at 6 G. Upon translating the focal spot with respect to the target coordinates, profile symmetry was regained at the expense of a lateral shift in the dose profiles. It was found that all points in the penumbra failed a 1%/1 mm acceptance criterion for fields between 4 and 6 G. However, it was also found that the lateral profile shifts were corrected by adjusting the jaw positions asymmetrically.

Pharmacokinetic modeling is a promising quantitative analysis technique for cancer diagnosis. However, diagnostic dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) of the breast is commonly performed with low temporal resolution. This limits its clinical utility. We investigated for a range of temporal resolutions whether pharmacokinetic parameter estimation is impacted by the use of data-derived arterial input functions (AIFs), obtained via analysis of dynamic data from a reference tissue, as opposed to the use of a standard AIF, often obtained from the literature. We hypothesized that the first method allows the use of data at lower temporal resolutions than the second method. Test data were obtained by downsampling high-temporal-resolution rodent data via a k-space-based strategy. To fit the basic Tofts model, either the data-derived or the standard AIF was used. The resulting estimates of K^trans and v_e were compared with the standard estimates obtained by using the original data. The deviations in K^trans and v_e, introduced when lowering temporal resolution, were more modest using data-derived AIFs compared with using a standard AIF. Specifically, lowering the resolution from 5 to 60 s, the respective changes in K^trans were 2% (non-significant) and 18% (significant). Extracting the AIF from a reference tissue enables accurate pharmacokinetic parameter estimation for low-temporal-resolution data.

An integrated MRI-accelerator system provides MRI images before and during irradiation. Our purpose is to investigate the feasibility of treatment plan adaptation using solely MRI data, which lack density information. In this study we used CT data to quantify the tissue density effect. Treatment planning was performed for five prostate cancer patients. We simulated correction of a 3, 5, 7 and 10 mm prostate shift relative to the body contour in the anterior, posterior, superior and inferior directions. We applied the original treatment plan to each corrected prostate shift and recalculated the dose distribution using the same monitor units (MU). We calculated the dose differences with and without density information. The latter mimics geometrically correct MRI data. Physical path lengths, available in MRI data, are used to perform MU rescaling per beam and are shown to be of more importance than tissue densities for treatment plan adaptation in prostate cancer. As the change in the physical path length of the central beam axis is representative of the entire beam, MU rescaling based on central beam axis information works fine. In conclusion, MRI data could be used for treatment plan adaptation in prostate cancer provided that the images are geometrically correct.

In this note, we address the estimation of the noise level in magnitude magnetic resonance (MR) images in the absence of background data. Most of the methods proposed earlier exploit the Rayleigh distributed background region in MR images to estimate the noise level. These methods, however, cannot be used for images where no background information is available. In this note, we propose two different approaches for noise level estimation in the absence of the image background. The first method is based on the local estimation of the noise variance using maximum likelihood estimation and the second method is based on the local estimation of the skewness of the magnitude data distribution. Experimental results on synthetic and real MR image datasets show that the proposed estimators accurately estimate the noise level in a magnitude MR image, even without background data.