Characteristics of low-angle x-ray scattering from some biological samples

Design of medical imaging devices based on the detection of low-angle coherent scattering is a subject of increasing interest. The technique is based on the differences in the distribution of photons coherently scattered from different body tissues. Coherent scattering is also useful in monitoring changes that may occur in a healthy tissue (e.g. carcinoma). In this work, low angle scattering properties of some tissues and tissue-equivalent materials are studied. Special care is given to the possibility of distinguishing between tissues of similar water content (e.g. muscle and blood). For this purpose, a Monte Carlo simulation is updated, introducing molecular form factor data, which include molecular interference effects. This program is used to simulate the angular distribution of scattered photons from two tissue-equivalent materials (lucite and water) and three biological samples (muscle, fat and blood). Simulation results agree well with previously measured angular distributions of scattered photons at 59.54 keV. Scattering from water and lucite is also measured at 8.047 keV. The effects of scattering geometry, sample thickness, incident photon energy and tissue type on the angular distribution of scattered photons are investigated. Results reveal the potential of measuring the full width at half maximum (FWHM) of the scattered photon distribution for tissue characterization. Energies up to 13 keV and sample thickness of 0.3 cm reported maximum differences between investigated samples. These conditions are expected to maximize the potential of using coherent scattering set-ups to monitor changes in biological samples even if their water contents are similar. Present results may act as a guide for the optimization of coherent scattering imaging systems.     

医用加速器8MVX射线在水模体中的一阶散射X射线能谱的蒙特卡罗计算

目的：分析医用电子直线加速器的高能X射线与水模体相互作用过程中所产生的一次散射光子的能谱角分布和光子强度角分布。方法：利用蒙特卡罗粒子输运程序Geant4,模拟粒子输运过程．计算加速器8MeV高能X射线能谱,并根据在水模体中实际测量的PDD吸收曲线为依据,修正蒙特卡洛计算的能谱;并以此能谱为虚拟源能谱,通过对X射线与水模体相互作用后的光子一电子联合输运过程进行蒙特卡罗模拟的方法获取有关散射X线能谱数据。结果：用蒙特卡洛方法得到加速器8MV初始X射线与水模体作用产生的一次散射光子的散射光子强度和散射光子能量随散射角度变化的规律。结论：根据ICRP85出版物、ICRU44报告给出的数据,可以用组织平均原子序数作为组织等效原子序数;因此,组织密度变化在物理上反映了组织的原子密度的变化,当入射光子注量改变,模体密度变化时。仅引起相互作用的总截面相对于原子微分截面的线性变化,并不影响一阶散射X射线的散射光子的相对强度角分布和散射光子能量角分布。而散射光子发射的绝对量与初始X射线强度、组织的原子密度成正比。因此,一次散射光子的注量角分布、平均能量角分布结果可形成可调用的数据库,对快速蒙特卡洛计算很有意义。     

Energy and spatial distribution of multiple order Compton scatter in SPECT: a Monte Carlo investigation

Energy and spatial projection distributions were simulated for gamma camera imaging of multiple order Compton scattered photons. SPECT imaging of a line source of radioactivity located in a water filled cylindrical phantom was modelled using Monte Carlo techniques. Photon trajectories were followed from emission to detection including the effects of all physical interactions and the resulting energy spectra and spatial projections were sorted as a function of the number of times the photon underwent Compton scattering before detection. Analysis of energy spectra demonstrates that Compton events up to second order overlap with the non-scattered events and distributions are peaked at lower energies as the scattering order increases. Analysis of spatial projections shows that, with increasing order, Compton events produce tails on the line spread function which progress from roughly exponential to nearly flat distributions. The use of Monte Carlo modelling thus allows a detailed investigation of the spatial and energy distribution of Compton scatter which could not be performed using present experimental techniques.     

Differential pencil beam dose computation model for photons

Differential pencil beam (DPB) is defined as the dose distribution relative to the position of the first collision, per unit collision density, for a monoenergetic pencil beam of photons in an infinite homogeneous medium of unit density. We have generated DPB dose distribution tables for a number of photon energies in water using the Monte Carlo method. The three-dimensional (3D) nature of the transport of photons and electrons is automatically incorporated in DPB dose distributions. Dose is computed by evaluating 3D integrals of DPB dose. The DPB dose computation model has been applied to calculate dose distributions for 60Co and accelerator beams. Calculations for the latter are performed using energy spectra generated with the Monte Carlo program. To predict dose distributions near the beam boundaries defined by the collimation system as well as blocks, we utilize the angular distribution of incident photons. Inhomogeneities are taken into account by attenuating the primary photon fluence exponentially utilizing the average total linear attenuation coefficient of intervening tissue, by multiplying photon fluence by the linear attenuation coefficient to yield the number of collisions in the scattering volume, and by scaling the path between the scattering volume element and the computation point by an effective density.     

Correlated histogram representation of Monte Carlo derived medical accelerator photon-output phase space.

We present a method for condensing the photon energy and angular distributions obtained from Monte Carlo simulations of medical accelerators. This method represents the output as a series of correlated histograms and as such is well-suited for inclusion as the photon-source package for Monte Carlo codes used to determine the dose distributions in photon teletherapy. The method accounts for the isocenter-plane variations of the photon energy spectral distributions with increasing distance from the beam central axis for radiation produced in the bremsstrahlung target as well as for radiation scattered by the various treatment machine components within the accelerator head. Comparison of the isocenter energy fluence computed by this algorithm with that of the underlying full-physics Monte Carlo photon phase space indicates that energy fluence errors are less than 1% of the maximum energy fluence for a range of open-field sizes. Comparison of jaw-edge penumbrae shows that the angular distributions of the photons are accurately reproduced. The Monte Carlo sampling efficiency (the fraction of generated photons which clear the collimator jaws) of the algorithm is approximately 83% for an open 10x10 field, rising to approximately 96% for an open 40x40 field. Data file sizes for a typical medical accelerator, at a given energy, are approximately 150 kB, compared to the 1 GB size of the underlying full-physics phase space file.     

Simplified model of low energy x-ray backscattering

The reflection of x-rays from a half space is studied within the framework of a model that assumes multiple isotropic scattering of photons without energy loss. An exactly solvable analytical expression for the angular distribution of reflected photons is derived. The range of validity of the model was determined by the Monte Carlo simulation thereby incorporating energy loss and angular dependences. For water as a scatterer, in the energy range from 10 to 60 keV, which is often used in x-ray diagnostics, the two approaches differ by at most 5%. The analytic results, confirmed by the Monte Carlo simulation, show that the angular distribution of reflected photons for energies greater than 30 keV--where multiple scattering events dominate--may be represented by a cosine law, within a few per cent of accuracy.     

Monte Carlo simulation of primary electron production inside an a-selenium detector for x-ray mammography: physics

Selenium is among the materials under investigation that may form effective detectors and provide a major contribution to digital mammography. Till the final image formation, there is an intervention of the x-ray photons transformation to primary electrons and their subsequent ionizing drift towards the electrodes that collect them. The characteristics of the generated primary electrons inside a-Se material such as their angular, spatial and energy distribution affect the characteristics of the final image. A Monte Carlo based model has been developed that simulates the x-ray irradiation of an a-Se detector plate, including primary photon interactions (photoelectric absorption, coherent and incoherent scattering), as well as secondary ones, such as fluorescence (Kalpha, Kbeta) and emission of Auger electrons. The angular, spatial and energy distributions for the generated primary electrons inside a-Se have been produced for various mammographic x-ray spectra and their usefulness in designing and optimizing a detector made of a-Se for digital mammography is discussed.     

Calculation of the small-angle distribution of scattered photons in diagnostic radiology using a Monte Carlo collision density estimator

Calculations of various physical quantities pertaining to scattered photons in diagnostic radiology are conveniently carried out using the Monte Carlo technique. Some quantities, e.g., the small-angle distribution of scattered photons transmitted through the patient, are difficult to obtain with sufficient precision using straightforward simulation of physical experiments. By mixing the simulation of random trajectories with analytical calculations, the efficiency of deriving values for a particular field quantity may be drastically improved. This work describes a Monte Carlo collision density estimator that increases the efficiency of calculating the small-angle distribution of transmitted scattered photons by a factor of more than 50. Examples of such distributions outside laterally infinite water slabs are given for x rays generated at 40-70 kV and for various slab thicknesses (10-200 mm). Comparison with experimental results from the literature shows that cross sections for coherent scattering which take diffraction phenomena in liquid water into account must be used to get accurate results. A discrepancy between the experimental and calculated distributions of photons transmitted at very small (less than 3 degrees) angles to the normal to the slab may be interpreted in terms of experimental difficulties or insufficient accuracy in the differential scattering cross sections used in the calculations.     

Characteristics of kilovoltage x-ray beams used for cone-beam computed tomography in radiation therapy

The purpose of this investigation is to characterize the beams produced by a kilovoltage (kV) imager integrated into a linear accelerator (Varian on-board imager integrated into the Trilogy accelerator) for acquiring high resolution volumetric cone-beam computed tomography (CBCT) images of the patient on the treatment table. The x-ray tube is capable of generating photon spectra with kVp values between 40 and 125 kV. The Monte Carlo simulations were used to study the characteristics of kV beams and the properties of imaged target scatters. The Monte Carlo results were benchmarked against measurements, and excellent agreements were obtained. We also studied the effect of including the electron impact ionization (EII), and the simulation showed that the characteristic radiation is increased significantly in the energy spectra when EII is included. Although only slight beam hardening is observed in the spectra of all photons after passing through the phantom target, there is a significant difference in the spectra and angular distributions between scattered and primary photons. The results also show that the photon fluence distributions are significantly altered by adding bow tie filters. The results indicate that a combination of large cone-beam field size and large imaged target significantly increases scatter-to-primary ratios for photons that reach the detector panel. For phantoms 10 cm, 20 cm and 30 cm thick of water placed at the isocentre, the scatter-to-primary ratios are 0.94, 3.0 and 7.6 respectively for an open 125 kVp CBCT beam. The Monte Carlo simulations show that the increase of the scatter is proportional to the increase of the imaged volume, and this also applies to scatter-to-primary ratios. This study shows both the magnitude and the characteristics of scattered x-rays. The knowledge obtained from this investigation may be useful in the future design of the image detector to improve the image quality.     

Compton scattering profile for in vivo XRF techniques

The contribution from single Compton scattered photons to the background in in vivo x-ray fluorescence analysis is evaluated by taking into account the energy broadening of the scattered photons which reflects the momentum distribution of the target electrons. A general-purpose Monte Carlo evaluation of multiple scattering components, as well as accurate experimental verifications with 59.54 keV photons impinging on various targets of interest for real-life irradiation, confirm that the single Compton scattering profiles of the elements composing the biological matrix dominate the trend and amplitude of the background in the region of interest with near-backscatter configurations. Step features are likewise explained in terms of single Compton phenomenology. Other probable sources of background, such as photoelectron Bremsstrahlung and pile-up distribution, are studied both theoretically and experimentally in order to compare their amplitude and features with those of single Compton scattered photon profiles.     

Energy imparted to water slabs by photons in the energy range 5-300 keV. Calculations using a Monte Carlo photon transport model

In diagnostic examinations of the trunk and head, the energy imparted to the patient is related to the radiation risk. In this work, the energy imparted to laterally infinite, 10-300 mm thick water slabs by 5-300 keV photons is calculated using a Monte Carlo photon transport model. The energy imparted is also derived for energy spectra of primary photons relevant to diagnostic radiology. In addition to values of energy imparted, values of backscattered and transmitted energies, quantities primarily obtained in the transport calculations, are reported. Assumptions about coherent scattering are shown to be important for values of backscattered and transmitted energies but unimportant with respect to values of energy imparted. Comparisons are made with other Monte Carlo results from the literature. Discrepancies of 10-20% in some calculated quantities can be traced back to the use of different tabulations of interaction cross-sections by various authors.     

Some properties of photon scattering in water phantoms in diagnostic radiology

Monte Carlo simulation was applied to study the histories of photon interactions in a soft-tissue-equivalent medium under diagnostic imaging conditions. We examined the dependence on incident x-ray energy and phantom thickness of the basic properties of photon scattering, including the probabilities of occurrence of the various interaction processes, and the frequency distributions of scattering events. We investigated the properties of scattered radiation for monoenergetic incident x rays, which provide a basis for deriving the physical properties of scattered radiation for any polyenergetic incident beam. We also included four incident x-ray beams with broad spectra; these represented the incident x rays typically used for diagnostic imaging.     

Energy and angular distributions of photons from medical linear accelerators

For accurate three-dimensional treatment planning, new models of dose calculations are being developed which require the knowledge of the energy spectra and angular distributions of the photons incident on the surface of the patient. Knowledge of the spectra is also useful in other applications, including the design of filters and beam modifying devices and determination of factors to convert ionization chamber measurements to dose. We have used Monte Carlo code (EGS) to compute photon spectra for a number of different linear accelerators. Both the target and the flattening filter have been accurately modeled. We find the mean photon energy to have a value lower than the generally perceived value of one-third the maximum energy. As expected, the spectra become softer as the distance from the central axis increases. Verification of the spectra is performed by computing dose distributions and half-value layers in water using the calculated spectra and comparing the results with measured data. We also examined the angular distributions of photons incident on the surface of the phantom. In currently used models of dose computations, it is assumed that the angular distribution of photons with respect to fan lines emanating from the source is negligible. Although the angular spread of photons with respect to the incident direction has been found to be small, its contribution to the diffuseness of the beam boundaries is significant.     

Angular correction in reconstruction of electron spectra from depth dose distributions

Techniques for reconstruction of electron spectra from the depth-dose curves used to date have ignored the angular distribution of incident electrons scattered at large angles. The approximation adopted is to employ a database of monoenergetic depth-dose curves generated for normal incidence of electrons at the surface. This approximation is acceptable for direct electrons with small angular spread. However, electrons scattered from the treatment head and collimating system may have large average angles of incidence which affects the depth-dose distribution significantly at shallow depths by increasing energy deposition close to the surface. We show that ignoring the electron incident angular distribution leads to systematic errors in the low energy region of reconstructed electron spectra. We propose a simple 1-D model to correct for these systematic errors using only electron angular distribution at the central beam axis. This model provides reconstructed spectra in excellent agreement with Monte Carlo simulation in the low energy region.     

Monte Carlo simulation of diagnostic x-ray scatter

A Monte Carlo method was developed and implemented to simulate x-ray photon transport. Simulations consisted of a pencil beam of monoenergetic photons with energies from 50 to 110 keV incident on water and aluminum slabs. The dependence of scatter fraction and multiple scattering on x-ray energy, scatterer thickness, and material is reported in both number and energy fluence. The average energy of scattered photons reaching the detector plane is also reported. Comparisons are made to previous x-ray scatter computations.     

Deterministic calculations of photon spectra for clinical accelerator targets

A method is proposed to compute photon energy spectra produced in clinical electron accelerator targets, based on the deterministic solution of the Boltzmann equation for coupled electron-photon transport in one-dimensional (1-D) slab geometry. It is shown that the deterministic method gives similar results as Monte Carlo calculations over the angular range of interest for therapy applications. Relative energy spectra computed by deterministic and 3-D Monte Carlo methods, respectively, are compared for several realistic target materials and different electron beams, and are found to give similar photon energy distributions and mean energies. The deterministic calculations typically require 1-2 mins of execution time on a Sun Workstation, compared to 2-36 h for the Monte Carlo runs.     

Decomposition of a laser-Doppler spectrum for estimation of speed distribution of particles moving in an optically turbid medium: Monte Carlo validation study

A method for measurement of distribution of speed of particles moving in an optically turbid medium is presented. The technique is based on decomposition of the laser-Doppler spectrum. The theoretical background is shown together with the results of Monte Carlo simulations, which were performed to validate the proposed method. The laser-Doppler spectra were obtained by Monte Carlo simulations for assumed uniform and Gaussian speed distributions of particles moving in the turbid medium. The Doppler shift probability distributions were calculated by Monte Carlo simulations for several anisotropy factors of the medium, assuming the Hanyey-Greenstein phase function. The results of the spectra decomposition show that the calculated speed distribution of moving particles match well the distribution assumed for Monte Carlo simulations. This result was obtained for the spectra simulated in optical conditions, in which the photon is scattered with the Doppler shift not more than once during its travel between the source and detector. Influence of multiple scattering of the photon is analysed and a perspective of spectrum decomposition under such conditions is considered. Potential applications and limitations of the method are discussed.     

Photon scatter in portal images: physical characteristics of pencil beam kernels generated using the EGS Monte Carlo code

Pencil beam kernels describing scattered photon fluence behind homogeneous water slabs at various air gap distances were generated using the EGS Monte Carlo code. Photon scatter fluence was scored in separate bins based on the particle's history: singly scattered, multiply scattered, and bremsstrahlung and positron annihilation photons. Simultaneously, the mean energy and mean angle with respect to the incident photon pencil beam were tallied. Kernels were generated for incident photon pencil beams exhibiting monoenergetic spectra of 2.0 and 10.0 MeV, and polyenergetic spectra representative of 6 and 24 MV beams. Reciprocity was used to generate scatter fractions on the central axis for various field sizes, phantom thicknesses, and air gaps. The scatter kernels were further characterized by full width at half-maximum estimates. Modulation transfer functions were calculated, providing theoretical estimates of the limit of performance of portal imaging systems due to the intrinsic scattering of photon radiation through the patient.     

Photon scatter kernels for intensity modulating radiation therapy filters.

The most important beam property while optimizing photon therapy is the ability to modulate the intensity of the beam. The use of photon absorbers for intensity modulation of beam profiles requires special attention to be paid to the alteration of beam properties due to scatter and spectral changes, in addition to the desired intensity modulation. In this study the influence of photon scatter in high-density filters irradiated with very narrow photon pencil beams was investigated. A simple analytical relation is developed to quantify the contribution by scattered photons. A scatter kernel was derived by convolving the first Compton scatter distribution with an approximate expression for the second-order scattered photons. The calculations were validated experimentally with film dosimetry and also by using Monte Carlo simulations. Results show that the difference in photon scatter estimation by different methods is relatively small when higher order scattering is accounted for. At 6 MV x-rays the agreement is slightly better than that for 18 MV x-rays results. The simple relation presented in this paper can be used to account for the scattered photon contribution in filter optimization codes to deliver biologically or physically optimized intensity modulated treatments.     

Commissioning stereotactic radiosurgery beams using both experimental and theoretical methods

The purpose of this investigation is to study the feasibility of using an alternative method to commission stereotactic radiosurgery beams shaped by micro multi-leaf collimators by using Monte Carlo simulations to obtain beam characteristics of small photon beams, such as incident beam particle fluence and energy distributions, scatter ratios, depth-dose curves and dose profiles where measurements are impossible or difficult. Ionization chambers and diode detectors with different sensitive volumes were used in the measurements in a water phantom and the Monte Carlo codes BEAMnrc/DOSXYZnrc were used in the simulation. The Monte Carlo calculated data were benchmarked against measured data for photon beams with energies of 6 MV and 10 MV produced from a Varian Trilogy accelerator. The measured scatter ratios and cross-beam dose profiles for very small fields are shown to be not only dependent on the size of the sensitive volume of the detector used but also on the type of detectors. It is known that the response of some detectors changes at small field sizes. Excellent agreement was seen between scatter ratios measured with a small ion chamber and those calculated from Monte Carlo simulations. The values of scatter ratios, for field sizes from 6 x 6 mm2 to 98 x 98 mm2, range from 0.67 to 1.0 and from 0.59 to 1.0 for 6 and 10 MV, respectively. The Monte Carlo calculations predicted that the incident beam particle fluence is strongly affected by the X-Y-jaw openings, especially for small fields due to the finite size of the radiation source. Our measurement confirmed this prediction. This study demonstrates that Monte Carlo calculations not only provide accurate dose distributions for small fields where measurements are difficult but also provide additional beam characteristics that cannot be obtained from experimental methods. Detailed beam characteristics such as incident photon fluence distribution, energy spectra, including composition of primary and scattered photons, can be independently used in dose calculation models and to improve the accuracy of measurements with detectors with an energy-dependent response. Furthermore, when there are discrepancies between results measured with different detectors, the Monte Carlo calculated values can indicate the most correct result. The data set presented in this study can be used as a reference in commissioning stereotactic radiosurgery beams shaped by a BrainLAB m3 on a Varian 2100EX or 600C accelerator.