Table of contents

Anthropomorphic computational phantoms are computer models of the human body for use in the evaluation of dose distributions resulting from either internal or external radiation sources. Currently, two classes of computational phantoms have been developed and widely utilized for organ dose assessment: (1) stylized phantoms and (2) voxel phantoms which describe the human anatomy via mathematical surface equations or 3D voxel matrices, respectively. Although stylized phantoms based on mathematical equations can be very flexible in regard to making changes in organ position and geometrical shape, they are limited in their ability to fully capture the anatomic complexities of human internal anatomy. In turn, voxel phantoms have been developed through image-based segmentation and correspondingly provide much better anatomical realism in comparison to simpler stylized phantoms. However, they themselves are limited in defining organs presented in low contrast within either magnetic resonance or computed tomography images—the two major sources in voxel phantom construction. By definition, voxel phantoms are typically constructed via segmentation of transaxial images, and thus while fine anatomic features are seen in this viewing plane, slice-to-slice discontinuities become apparent in viewing the anatomy of voxel phantoms in the sagittal or coronal planes. This study introduces the concept of a hybrid computational newborn phantom that takes full advantage of the best features of both its stylized and voxel counterparts: flexibility in phantom alterations and anatomic realism. Non-uniform rational B-spline (NURBS) surfaces, a mathematical modeling tool traditionally applied to graphical animation studies, was adopted to replace the limited mathematical surface equations of stylized phantoms. A previously developed whole-body voxel phantom of the newborn female was utilized as a realistic anatomical framework for hybrid phantom construction. The construction of a hybrid phantom is performed in three steps: polygonization of the voxel phantom, organ modeling via NURBS surfaces and phantom voxelization. Two 3D graphic tools, 3D-DOCTOR™ and Rhinoceros™, were utilized to polygonize the newborn voxel phantom and generate NURBS surfaces, while an in-house MATLAB™ code was used to voxelize the resulting NURBS model into a final computational phantom ready for use in Monte Carlo radiation transport calculations. A total of 126 anatomical organ and tissue models, including 38 skeletal sites and 31 cartilage sites, were described within the hybrid phantom using either NURBS or polygon surfaces. A male hybrid newborn phantom was constructed following the development of the female phantom through the replacement of female-specific organs with male-specific organs. The outer body contour and internal anatomy of the NURBS-based phantoms were adjusted to match anthropometric and reference newborn data reported by the International Commission on Radiological Protection in their Publication 89. The voxelization process was designed to accurately convert NURBS models to a voxel phantom with minimum volumetric change. A sensitivity study was additionally performed to better understand how the meshing tolerance and voxel resolution would affect volumetric changes between the hybrid-NURBS and hybrid-voxel phantoms. The male and female hybrid-NURBS phantoms were constructed in a manner so that all internal organs approached their ICRP reference masses to within 1%, with the exception of the skin (−6.5% relative error) and brain (−15.4% relative error). Both hybrid-voxel phantoms were constructed with an isotropic voxel resolution of 0.663 mm—equivalent to the ICRP 89 reference thickness of the newborn skin (dermis and epidermis). Hybrid-NURBS phantoms used to create their voxel counterpart retain the non-uniform scalability of stylized phantoms, while maintaining the anatomic realism of segmented voxel phantoms with respect to organ shape, depth and inter-organ positioning.

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This paper reports calculations of the temperature rises induced in the eye and lens by near-field exposure to radiation from communication handsets, using the finite difference time domain method and classical bioheat equation. Various models are compared, including the analytic solution for a sphere, a finite element model of an isolated eye and a modern model of the whole head. The role of the blood supply to the choroid in moderating temperature is discussed. Three different frequencies are considered, namely 380 MHz (used by TETRA), and 900 and 1800 MHz (used by GSM mobile phones). At 380 MHz, monopole and helical antennas are compared. An 'equivalent blood flow' is derived for the choroid in order to facilitate comparison of the whole head and isolated eye models. In the whole head model, the heating of the lens receives a significant contribution from energy absorbed outside the eye. The temperature rise in the lens is compared to the ICNIRP-recommended average specific energy absorption rate (SAR) and the SAR averaged over the eye alone. The temperature rise may reach 1.4 °C at the ICNIRP occupational exposure limit if an antenna is placed less than 24 mm from the eye and the exposure is sufficiently prolonged.

For EPID dosimetry, the calibration should ensure that all pixels have a similar response to a given irradiation. A calibration method (MC), using an analytical fit of a Monte Carlo simulated flood field EPID image to correct for the flood field image pixel intensity shape, was proposed. It was compared with the standard flood field calibration (FF), with the use of a water slab placed in the beam to flatten the flood field (WS) and with a multiple field calibration where the EPID was irradiated with a fixed 10 × 10 field for 16 different positions (MF). The EPID was used in its normal configuration (clinical setup) and with an additional 3 mm copper slab (modified setup). Beam asymmetry measured with a diode array was taken into account in MC and WS methods. For both setups, the MC method provided pixel sensitivity values within 3% of those obtained with the MF and WS methods (mean difference <1%, standard deviation <2%). The difference of pixel sensitivity between MC and FF methods was up to 12.2% (clinical setup) and 11.8% (modified setup). MC calibration provided images of open fields (5 × 5 to 20 × 20 cm²) and IMRT fields to within 3% of that obtained with WS and MF calibrations while differences with images calibrated with the FF method for fields larger than 10 × 10 cm² were up to 8%. MC, WS and MF methods all provided a major improvement on the FF method. Advantages and drawbacks of each method were reviewed.

Clinical investigations on post-irradiation PET/CT (positron emission tomography/computed tomography) imaging for in vivo verification of treatment delivery and, in particular, beam range in proton therapy are underway at Massachusetts General Hospital (MGH). Within this project, we have developed a Monte Carlo framework for CT-based calculation of dose and irradiation-induced positron emitter distributions. Initial proton beam information is provided by a separate Geant4 Monte Carlo simulation modelling the treatment head. Particle transport in the patient is performed in the CT voxel geometry using the FLUKA Monte Carlo code. The implementation uses a discrete number of different tissue types with composition and mean density deduced from the CT scan. Scaling factors are introduced to account for the continuous Hounsfield unit dependence of the mass density and of the relative stopping power ratio to water used by the treatment planning system (XiO (Computerized Medical Systems Inc.)). Resulting Monte Carlo dose distributions are generally found in good correspondence with calculations of the treatment planning program, except a few cases (e.g. in the presence of air/tissue interfaces). Whereas dose is computed using standard FLUKA utilities, positron emitter distributions are calculated by internally combining proton fluence with experimental and evaluated cross-sections yielding ¹¹C, ¹⁵O, ¹⁴O, ¹³N, ³⁸K and ³⁰P. Simulated positron emitter distributions yield PET images in good agreement with measurements. In this paper, we describe in detail the specific implementation of the FLUKA calculation framework, which may be easily adapted to handle arbitrary phase spaces of proton beams delivered by other facilities or include more reaction channels based on additional cross-section data. Further, we demonstrate the effects of different acquisition time regimes (e.g., PET imaging during or after irradiation) on the intensity and spatial distribution of the irradiation-induced β⁺-activity signal for the cases of head and neck and para-spinal tumour sites.

A method for registering images acquired from a prototype flat panel mobile C-arm, capable of kilovoltage (kV) cone-beam computed tomography (CT), to a linear accelerator (LINAC) isocenter is presented. A calibration procedure is performed which involves locating reflective markers placed on the C-arm and a phantom in two coordinate systems. A commercial optical tracking system locates the markers relative to the LINAC isocenter (room coordinates). The cone-beam imaging capabilities of the C-arm provide the location of the markers on the calibration phantom in image coordinates. A singular value decomposition (SVD) algorithm is used to determine the relationship between the C-arm, image coordinates and room coordinates. Once the calibration is completed, the position of the C-arm at any arbitrary location is accurately determined from the tracking system. A final transformation is calculated capable of mapping voxels in the reconstructed image set to their corresponding position in room coordinates. An evaluation to determine the accuracy of this method was performed by locating markers on a phantom. The position of the phantom markers in room coordinates was obtained directly using the optical tracking system and compared with that using the described method above. A mean absolute distance of 1.4 ± 0.5 was observed for a completely transformed image set. This is comparable to that of systems routinely used for image-guided radiation therapy (IGRT).

The recent emergence of various types of flat-panel x-ray detectors and C-arm gantries now enables the construction of novel imaging platforms for a wide variety of clinical applications. Many of these applications require interactive 3D image generation, which cannot be satisfied with inexpensive PC-based solutions using the CPU. We present a solution based on commodity graphics hardware (GPUs) to provide these capabilities. While GPUs have been employed for CT reconstruction before, our approach provides significant speedups by exploiting the various built-in hardwired graphics pipeline components for the most expensive CT reconstruction task, backprojection. We show that the timings so achieved are superior to those obtained when using the GPU merely as a multi-processor, without a drop in reconstruction quality. In addition, we also show how the data flow across the graphics pipeline can be optimized, by balancing the load among the pipeline components. The result is a novel streaming CT framework that conceptualizes the reconstruction process as a steady flow of data across a computing pipeline, updating the reconstruction result immediately after the projections have been acquired. Using a single PC equipped with a single high-end commodity graphics board (the Nvidia 8800 GTX), our system is able to process clinically-sized projection data at speeds meeting and exceeding the typical flat-panel detector data production rates, enabling throughput rates of 40–50 projections s⁻¹ for the reconstruction of 512³ volumes.

Scatter correction techniques in iterative positron emission tomography (PET) reconstruction increasingly utilize Monte Carlo (MC) simulations which are very well suited to model scatter in the inhomogeneous patient. Due to memory constraints the results of these simulations are not stored in the system matrix, but added or subtracted as a constant term or recalculated in the projector at each iteration. This implies that scatter is not considered in the back-projector. The presented scheme provides a method to store the simulated Monte Carlo scatter in a compressed scatter system matrix. The compression is based on parametrization and B-spline approximation and allows the formation of the scatter matrix based on low statistics simulations. The compression as well as the retrieval of the matrix elements are parallelizable. It is shown that the proposed compression scheme provides sufficient compression so that the storage in memory of a scatter system matrix for a 3D scanner is feasible. Scatter matrices of two different 2D scanner geometries were compressed and used for reconstruction as a proof of concept. Compression ratios of 0.1% could be achieved and scatter induced artifacts in the images were successfully reduced by using the compressed matrices in the reconstruction algorithm.

The purpose of this study was to investigate the accuracy of two-dimensional (2D) projection imaging methods in three-dimensional (3D) tumor motion monitoring. Many commercial linear accelerator types have projection imaging capabilities, and tumor motion monitoring is useful for motion inclusive, respiratory gated or tumor tracking strategies. Since 2D projection imaging is limited in its ability to resolve the motion along the imaging beam axis, there is unresolved motion when monitoring 3D tumor motion. From the 3D tumor motion data of 160 treatment fractions for 46 thoracic and abdominal cancer patients, the unresolved motion due to the geometric limitation of 2D projection imaging was calculated as displacement in the imaging beam axis for different beam angles and time intervals. The geometric uncertainty to monitor 3D motion caused by the unresolved motion of 2D imaging was quantified using the root-mean-square (rms) metric. Geometric uncertainty showed interfractional and intrafractional variation. Patient-to-patient variation was much more significant than variation for different time intervals. For the patient cohort studied, as the time intervals increase, the rms, minimum and maximum values of the rms uncertainty show decreasing tendencies for the lung patients but increasing for the liver and retroperitoneal patients, which could be attributed to patient relaxation. Geometric uncertainty was smaller for coplanar treatments than non-coplanar treatments, as superior–inferior (SI) tumor motion, the predominant motion from patient respiration, could be always resolved for coplanar treatments. Overall rms of the rms uncertainty was 0.13 cm for all treatment fractions and 0.18 cm for the treatment fractions whose average breathing peak–trough ranges were more than 0.5 cm. The geometric uncertainty for 2D imaging varies depending on the tumor site, tumor motion range, time interval and beam angle as well as between patients, between fractions and within a fraction.

A new approach to the problem of modelling and predicting respiration motion has been implemented. This is a dual-component model, which describes the respiration motion as a non-periodic time series superimposed onto a periodic waveform. A periodic autoregressive moving average algorithm has been used to define a mathematical model of the periodic and non-periodic components of the respiration motion. The periodic components of the motion were found by projecting multiple inhale–exhale cycles onto a common subspace. The component of the respiration signal that is left after removing this periodicity is a partially autocorrelated time series and was modelled as an autoregressive moving average (ARMA) process. The accuracy of the periodic ARMA model with respect to fluctuation in amplitude and variation in length of cycles has been assessed. A respiration phantom was developed to simulate the inter-cycle variations seen in free-breathing and coached respiration patterns. At ±14% variability in cycle length and maximum amplitude of motion, the prediction errors were 4.8% of the total motion extent for a 0.5 s ahead prediction, and 9.4% at 1.0 s lag. The prediction errors increased to 11.6% at 0.5 s and 21.6% at 1.0 s when the respiration pattern had ±34% variations in both these parameters. Our results have shown that the accuracy of the periodic ARMA model is more strongly dependent on the variations in cycle length than the amplitude of the respiration cycles.

Accurate volume of interest (VOI) estimation in PET is crucial in different oncology applications such as response to therapy evaluation and radiotherapy treatment planning. The objective of our study was to evaluate the performance of the proposed algorithm for automatic lesion volume delineation; namely the fuzzy hidden Markov chains (FHMC), with that of current state of the art in clinical practice threshold based techniques. As the classical hidden Markov chain (HMC) algorithm, FHMC takes into account noise, voxel intensity and spatial correlation, in order to classify a voxel as background or functional VOI. However the novelty of the fuzzy model consists of the inclusion of an estimation of imprecision, which should subsequently lead to a better modelling of the 'fuzzy' nature of the object of interest boundaries in emission tomography data. The performance of the algorithms has been assessed on both simulated and acquired datasets of the IEC phantom, covering a large range of spherical lesion sizes (from 10 to 37 mm), contrast ratios (4:1 and 8:1) and image noise levels. Both lesion activity recovery and VOI determination tasks were assessed in reconstructed images using two different voxel sizes (8 mm³ and 64 mm³). In order to account for both the functional volume location and its size, the concept of % classification errors was introduced in the evaluation of volume segmentation using the simulated datasets. Results reveal that FHMC performs substantially better than the threshold based methodology for functional volume determination or activity concentration recovery considering a contrast ratio of 4:1 and lesion sizes of <28 mm. Furthermore differences between classification and volume estimation errors evaluated were smaller for the segmented volumes provided by the FHMC algorithm. Finally, the performance of the automatic algorithms was less susceptible to image noise levels in comparison to the threshold based techniques. The analysis of both simulated and acquired datasets led to similar results and conclusions as far as the performance of segmentation algorithms under evaluation is concerned.

A three-dimensional computational model is presented for studying the efficacy of high-intensity focused ultrasound (HIFU) procedures targeted near large blood vessels. The analysis applies to procedures performed at intensities below the threshold for cavitation, boiling and highly nonlinear propagation, but high enough to increase tissue temperature a few degrees per second. The model is based upon the linearized KZK equation and the bioheat equation in tissue. In the blood vessel the momentum and energy equations are satisfied. The model is first validated in a tissue phantom, to verify the absence of bubble formation and nonlinear effects. Temperature rise and lesion-volume calculations are then shown for different beam locations and orientations relative to a large vessel. Both single and multiple ablations are considered. Results show that when the vessel is located within about a beam width (few mm) of the ultrasound beam, significant reduction in lesion volume is observed due to blood flow. However, for gaps larger than a beam width, blood flow has no major effect on the lesion formation. Under the clinically representative conditions considered, the lesion volume is reduced about 40% (relative to the no-flow case) when the beam is parallel to the blood vessel, compared to about 20% for a perpendicular orientation. Procedures involving multiple ablation sites are affected less by blood flow than single ablations. The model also suggests that optimally focused transducers can generate lesions that are significantly larger (>2 times) than the ones produced by highly focused beams.

We compare the consistency and accuracy of two image binning approaches used in 4D-CT imaging. One approach, phase binning (PB), assigns each breathing cycle 2π rad, within which the images are grouped. In amplitude binning (AB), the images are assigned bins according to the breathing signal's full amplitude. To quantitate both approaches we used a NEMA NU2-2001 IEC phantom oscillating in the axial direction and at random frequencies and amplitudes, approximately simulating a patient's breathing. 4D-CT images were obtained using a four-slice GE Lightspeed CT scanner operating in cine mode. We define consistency error as a measure of ability to correctly bin over repeated cycles in the same field of view. Average consistency error μ_e ± σ_e in PB ranged from 18% ± 20% to 30% ± 35%, while in AB the error ranged from 11% ± 14% to 20% ± 24%. In PB nearly all bins contained sphere slices. AB was more accurate, revealing empty bins where no sphere slices existed. As a proof of principle, we present examples of two non-small cell lung carcinoma patients' 4D-CT lung images binned by both approaches. While AB can lead to gaps in the coronal images, depending on the patient's breathing pattern, PB exhibits no gaps but suffers visible artifacts due to misbinning, yielding images that cover a relatively large amplitude range. AB was more consistent, though often resulted in gaps when no data existed due to patients' breathing pattern. We conclude AB is more accurate than PB. This has important consequences to treatment planning and diagnosis.

The use of bioactive nanostructured TiO₂ has recently been proposed for improving orthopaedic implant adhesion due to its improved biocompatibility with bone, since it induces: (i) osteoblast function, (ii) apatite nucleation and (iii) protein adsorption. The present work focuses on a non-ionizing radiation emitting technique for quantifying in real time the improvement in terms of mechanical properties of the surrounding bone due to the presence of the nanostructured TiO₂ prepared by controlled precipitation and acid ageing. The mechanical strength is the ultimate goal of a bone implant and is directly related to the elastic moduli. Ultrasonics are high frequency mechanical waves and are therefore suited for characterizing elastic moduli. As opposed to echographic techniques, which are not correlated to elastic properties and are not able to penetrate bone, a low frequency ultrasonic transmission test is proposed, in which a P-wave is transmitted through the specimen and recorded. The problem is posed as an inverse problem, in which the unknown is a set of parameters that describe the mechanical constants of the sequence of layers. A finite element numerical model that depends on these parameters is used to predict the transformation of the waveform and compare to the measurement. The parameters that best describe the real tissue are obtained by minimizing the discrepancy between the real and numerically predicted waveforms. A sensitivity study to the uncertainties of the model is performed for establishing the feasibility of using this technique to investigate the macroscopic effect on bone growth of nanostructured TiO₂ and its beneficial effect on implant adhesion.

This work investigated the selection of beam margins in lung-cancer stereotactic body radiotherapy (SBRT) with 6 MV photon beams. Monte Carlo dose calculations were used to systematically and quantitatively study the dosimetric effects of beam margins for different lung densities (0.1, 0.15, 0.25, 0.35 and 0.5 g cm⁻³), planning target volumes (PTVs) (14.4, 22.1 and 55.3 cm³) and numbers of beam angles (three, six and seven) in lung-cancer SBRT in order to search for optimal beam margins for various clinical situations. First, a large number of treatment plans were generated in a commercial treatment planning system, and then recalculated using Monte Carlo simulations. All the plans were normalized to ensure that 95% of the PTV at least receives the prescription dose and compared quantitatively. Based on these plans, the relationships between the beam margin and quantities such as the lung toxicity (quantified by V₂₀, the percentage volume of the two lungs receiving at least 20 Gy) and the maximum target (PTV) dose were established for different PTVs and lung densities. The impact of the number of beam angles on the relationship between V₂₀ and the beam margin was assessed. Quantitative information about optimal beam margins for lung-cancer SBRT was obtained for clinical applications.

Existing studies have suggested some debate on whether the quality of radiation that delivers dose outside of the primary field of a radiotherapy photon beam can be considered the same as that inside the primary field. We used a Monte Carlo approach to simulate the electron fluence differential in energy inside a water phantom in response to irradiation by a 6 MV photon beam. The goal was to quantify how significantly the electron fluence changes when moving from a volume exposed to the primary field to one outside of the primary field, and understand any potential biological implications. We scored the electron fluence outwards in annular volumes in response to a 5 cm radius 6 MV beam and at the central axis in response to a rectangular 6 MV beam partially blocked by an MLC. The resulting fluence spectra were compared to different low-LET sources for which biological response in the form of chromosomal aberrations has been published. Our results show a significant increase in the low energy component of the fluence spectra outside of the primary field, which increases the mean LET to values similar to that seen in response to a ¹³⁷Cs photon source. In turn, it is shown that this has the potential to increase the RBE.

In emission tomography imaging, respiratory motion causes artifacts in lungs and cardiac reconstructed images, which lead to misinterpretations, imprecise diagnosis, impairing of fusion with other modalities, etc. Solutions like respiratory gating, correlated dynamic PET techniques, list-mode data based techniques and others have been tested, which lead to improvements over the spatial activity distribution in lungs lesions, but which have the disadvantages of requiring additional instrumentation or the need of discarding part of the projection data used for reconstruction. The objective of this study is to incorporate respiratory motion compensation directly into the image reconstruction process, without any additional acquisition protocol consideration. To this end, we propose an extension to the maximum likelihood expectation maximization (MLEM) algorithm that includes a respiratory motion model, which takes into account the displacements and volume deformations produced by the respiratory motion during the data acquisition process. We present results from synthetic simulations incorporating real respiratory motion as well as from phantom and patient data.

In emission tomography, anatomical side information, in the form of organ and lesion boundaries, derived from intra-patient coregistered CT or MR scans can be incorporated into the reconstruction. Our interest is in exploring the efficacy of such side information for lesion detectability. To assess detectability we used the SNR of a channelized Hotelling observer and a signal-known exactly/background-known exactly detection task. In simulation studies, we incorporated anatomical side information into a SPECT MAP (maximum a posteriori) reconstruction by smoothing within but not across organ or lesion boundaries. A non-anatomical prior was applied by uniform smoothing across the entire image. We investigated whether the use of anatomical priors with organ boundaries alone or with perfect lesion boundaries alone would change lesion detectability relative to the case of a prior with no anatomical information. Furthermore, we investigated whether any such detectability changes for the organ-boundary case would be a function of the distance of the lesion to the organ boundary. We also investigated whether any detectability changes for the lesion-boundary case would be a function of the degree of proximity, i.e. a difference in the radius of the true functional lesion and the radius of the anatomical lesion boundary. Our results showed almost no detectability difference with versus without organ boundaries at any lesion-to-organ boundary distance. Our results also showed no difference in lesion detectability with and without lesion boundaries, and no variation of lesion detectability with degree of proximity.

We develop algorithms for imaging the time-varying optical absorption within the breast given diffuse optical tomographic data collected over a time span that is long compared to the dynamics of the medium. Multispectral measurements allow for the determination of the time-varying total hemoglobin concentration and of oxygen saturation. To facilitate the image reconstruction, we decompose the hemodynamics in time into a linear combination of spatio-temporal basis functions, the coefficients of which are estimated using all of the data simultaneously, making use of a Newton-based nonlinear optimization algorithm. The solution of the extremely large least-squares problem which arises in computing the Newton update is obtained iteratively using the LSQR algorithm. A Laplacian spatial regularization operator is applied, and, in addition, we make use of temporal regularization which tends to encourage similarity between the images of the spatio-temporal coefficients. Results are shown for an extensive simulation, in which we are able to image and quantify localized changes in both total hemoglobin concentration and oxygen saturation. Finally, a breast compression study has been performed for a normal breast cancer screening subject, using an instrument which allows for highly accurate co-registration of multispectral diffuse optical measurements with an x-ray tomosynthesis image of the breast. We are able to quantify the global return of blood to the breast following compression, and, in addition, localized changes are observed which correspond to the glandular region of the breast.

A multi-resolution hybrid strain estimator is presented. The estimator is locally initialized by the B-mode tracking stage. Nonlinear and linear stretching regimes are applied in successive RF tracking stages for refining the estimated axial and lateral displacements. A staggering operator is used to derive the strain images from the reconstructed axial displacements. Simulations and experiments, conducted at a center frequency of 12 MHz, 40% fractional bandwidth, on a 128 element transducer with 0.2 mm pitch, with elastographic window length of 2 mm and overlap of 90%, demonstrate a 3–6 dB improvement in the elastographic contrast-to-noise ratio over the results obtained using conventional multi-stage stretching based strain estimators. The average image cross-correlation coefficient obtained using the proposed algorithm was improved by 6–8%. 3D elastographic simulations conducted to study the performance of a 3D elastographic imaging framework predict achievable axial and lateral resolutions of approximately five and ten wavelengths, respectively. A close correspondence between inclusions reconstructed from experimental elastograms and the known physical shape of actual 3D inclusions demonstrates the potential application of 3D elastography for identifying and classifying the detected lesions (invisible in sonograms) on the basis of their shape.

For tumors with highly complex shapes, a 'patching' strategy is often used in passively scattered proton therapy to match the sharp distal edge of the spread-out Bragg peak (SOBP) of the patch field to the lateral penumbra of the through field at 50% dose level. The differences in the dose gradients at the distal edge and at the lateral penumbra could cause hot and cold doses at the junction. In this note, we describe an algorithm developed to optimize the range compensator design to yield a more uniform dose distribution at the junction. The algorithm is based on the fact that the distal fall-off of the SOBP can be tailored using a grid filter that is placed perpendicular to the beam's path. The filter is optimized so that the distal fall-off of the patch field complements the lateral penumbra fall-off of the through field. In addition to optimizing the fall-off, the optimization process implicitly accounts for the limitations of conventional compensator design algorithms. This algorithm uses simple ray tracing to determine the compensator shape and ignore scatter. The compensated dose distribution may therefore differ substantially from the intended dose distribution, especially when complex heterogeneities are encountered, such as those in the head and neck. In such a case, an adaptive optimization strategy can be used to optimize the 'grid' filter locally considering the tissue heterogeneities. The grid filter thus obtained is superimposed on the original range compensator so that the composite compensator leads to a more uniform dose distribution at the patch junction. An L-shaped head and neck tumor was used to demonstrate the validity of the proposed algorithm. A robustness analysis with focus on range uncertainty effect is carried out.

The latest developments in x-ray imaging are associated with techniques based on the phase contrast. However, the image reconstruction procedures demand significant improvements of the traditional methods, and/or new algorithms have to be introduced to take advantage of the high contrast and sensitivity of the new experimental techniques. In this letter, an improved iterative reconstruction algorithm based on the maximum likelihood expectation maximization technique is presented and discussed in order to reconstruct the distribution of the refractive index from data collected by an analyzer-based imaging setup. The technique considered probes the partial derivative of the refractive index with respect to an axis lying in the meridional plane and perpendicular to the propagation direction. Computer simulations confirm the reliability of the proposed algorithm. In addition, the comparison between an analytical reconstruction algorithm and the iterative method has been also discussed together with the convergent characteristic of this latter algorithm. Finally, we will show how the proposed algorithm may be applied to reconstruct the distribution of the refractive index of an epoxy cylinder containing small air bubbles of about 300 μ of diameter.