Estimation Of Electron Density Research Articles

High-order ionospheric effects on electron density estimation from Fengyun-3C GPS radio occultation

Abstract. GPS radio occultation can estimate ionospheric electron density and total electron content (TEC) with high spatial resolution, e.g., China's recent Fengyun-3C GPS radio occultation. However, high-order ionospheric delays are normally ignored. In this paper, the high-order ionospheric effects on electron density estimation from the Fengyun-3C GPS radio occultation data are estimated and investigated using the NeQuick2 ionosphere model and the IGRF12 (International Geomagnetic Reference Field, 12th generation) geomagnetic model. Results show that the high-order ionospheric delays have large effects on electron density estimation with up to 800 el cm−3, which should be corrected in high-precision ionospheric density estimation and applications. The second-order ionospheric effects are more significant, particularly at 250–300 km, while third-order ionospheric effects are much smaller. Furthermore, the high-order ionospheric effects are related to the location, the local time, the radio occultation azimuth and the solar activity. The large high-order ionospheric effects are found in the low-latitude area and in the daytime as well as during strong solar activities. The second-order ionospheric effects have a maximum positive value when the radio occultation azimuth is around 0–20°, and a maximum negative value when the radio occultation azimuth is around −180 to −160°. Moreover, the geomagnetic storm also affects the high-order ionospheric delay, which should be carefully corrected.

Multi-atlas-based CT synthesis from conventional MRI with patch-based refinement for MRI-based radiotherapy planning.

Accurate CT synthesis, sometimes called electron density estimation, from MRI is crucial for successful MRI-based radiotherapy planning and dose computation. Existing CT synthesis methods are able to synthesize normal tissues but are unable to accurately synthesize abnormal tissues (i.e., tumor), thus providing a suboptimal solution. We propose a multi-atlas-based hybrid synthesis approach that combines multi-atlas registration and patch-based synthesis to accurately synthesize both normal and abnormal tissues. Multi-parametric atlas MR images are registered to the target MR images by multi-channel deformable registration, from which the atlas CT images are deformed and fused by locally-weighted averaging using a structural similarity measure (SSIM). Synthetic MR images are also computed from the registered atlas MRIs by using the same weights used for the CT synthesis; these are compared to the target patient MRIs allowing for the assessment of the CT synthesis fidelity. Poor synthesis regions are automatically detected based on the fidelity measure and refined by a patch-based synthesis. The proposed approach was tested on brain cancer patient data, and showed a noticeable improvement for the tumor region.

Global ionospheric electron density estimation based on multisource TEC data assimilation

We developed a parameterized ionospheric electron density model based on the IRI-2012 model by spherical harmonic expansions in the horizontal and empirical orthogonal functions in the vertical. Then, after assimilating the monthly multisource total electron content (TEC) data from ground-based GPS, LEO radio occultation (RO), and the oceanic altimeter during magnetically quiet time into the model, we reanalyzed the monthly global ionospheric electron density TEC and other key parameters such as foF2 and NmF2. Both the reanalyzed and IRI-2012 model results were compared to the TEC measurements, the monthly median foF2 in a middle-latitude ionosonde station, and the global TEC map from CODE. The comparisons showed that both the reanalyzed and IRI results are consistent with those observations and the reanalyzed results perform better than the IRI model. Furthermore, the reanalyzed results are also consistent with the retrieved maps of HmF2, NmF2, and TEC from COSMIC RO observations. In summary, our method can reanalyze the global TEC and electron density using multisource TEC data assimilated into our model and improve the performance of IRI model.

Robust Estimation of Electron Density From Anatomic Magnetic Resonance Imaging of the Brain Using a Unifying Multi-Atlas Approach

Todevelop a reliable method to estimate electron density based on anatomic magnetic resonance imaging (MRI) of the brain. We proposed a unifying multi-atlas approach for electron density estimation based on standard T1- and T2-weighted MRI. First, a composite atlas was constructed through a voxelwise matching process using multiple atlases, with the goal of mitigating effects of inherent anatomic variations between patients. Next we computed for each voxel 2 kinds of conditional probabilities: (1) electron density given its image intensity on T1- and T2-weighted MR images; and (2) electron density given its spatial location in a reference anatomy, obtained by deformable image registration. These were combined into a unifying posterior probability density function using the Bayesian formalism, which provided the optimal estimates for electron density. We evaluated the method on 10 patients using leave-one-patient-out cross-validation. Receiver operating characteristic analysesfor detecting different tissue types were performed. The proposed method significantly reduced the errors in electron density estimation, with a mean absolute Hounsfield unit error of 119, compared with 140 and 144 (P<.0001) using conventional T1-weighted intensity and geometry-based approaches, respectively. For detection of bony anatomy, the proposed method achieved an 89% area under the curve, 86% sensitivity, 88% specificity, and 90% accuracy, which improved upon intensity and geometry-based approaches (area under the curve: 79% and 80%, respectively). The proposed multi-atlas approach provides robust electron density estimation and bone detection based on anatomic MRI. If validated on a larger population, our work could enable the use of MRI as a primary modality for radiation treatment planning.

Ionospheric tomography by gradient-enhanced kriging with STEC measurements and ionosonde characteristics

Abstract. The estimation of the ionospheric electron density by kriging is based on the optimization of a parametric measurement covariance model. First, the extension of kriging with slant total electron content (STEC) measurements based on a spatial covariance to kriging with a spatial–temporal covariance model, assimilating STEC data of a sliding window, is presented. Secondly, a novel tomography approach by gradient-enhanced kriging (GEK) is developed. Beyond the ingestion of STEC measurements, GEK assimilates ionosonde characteristics, providing peak electron density measurements as well as gradient information. Both approaches deploy the 3-D electron density model NeQuick as a priori information and estimate the covariance parameter vector within a maximum likelihood estimation for the dedicated tomography time stamp. The methods are validated in the European region for two periods covering quiet and active ionospheric conditions. The kriging with spatial and spatial–temporal covariance model is analysed regarding its capability to reproduce STEC, differential STEC and foF2. Therefore, the estimates are compared to the NeQuick model results, the 2-D TEC maps of the International GNSS Service and the DLR's Ionospheric Monitoring and Prediction Center, and in the case of foF2 to two independent ionosonde stations. Moreover, simulated STEC and ionosonde measurements are used to investigate the electron density profiles estimated by the GEK in comparison to a kriging with STEC only. The results indicate a crucial improvement in the initial guess by the developed methods and point out the potential compensation for a bias in the peak height hmF2 by means of GEK.

Microwave air plasmas in capillaries at low pressure II. Experimental investigation

This work presents an experimental study of microwave (2.45 GHz excitation frequency) micro-plasmas, generated in dry air (N2 80%: O2 20%) within a small radius silica capillary (345 µm inner radius) at low pressure (300 Pa) and low powers (80–130 W). Experimental diagnostics are performed using optical emission spectroscopy calibrated in absolute intensity. Axial-resolved measurements (50 µm spatial resolution) of atomic transitions N(3p4S) → N(3s4P); O(3p5P) → O(3s5S) and molecular transitions N2(C,v′) → N2(B,v″); (B,v′) → (X,v″) allow us to obtain, as a function of the coupled power, the absolute densities of N(3p4S), O(3p5P), N2(C), N2(B) and (B), as well as the gas (rotational) temperature (700–1000 K), the vibrational temperature of N2(C,v) (7000–10 000 K) and the excitation temperatures of N2(C) and N2(B) (11 000 K). The analysis of the Hβ line-width gives an upper limiting value of 1013 cm−3 for the electron density; its axial variation (4 × 1011–6 × 1012 cm−3) being estimated by solving the wave electrodynamics equations for the present geometry, plasma length and electron–neutral collision frequency. The experimental results were compared with the results from a 0D model, presented in companion paper I [], which couples the system of rate balance equations for the dominant neutral and charged plasma species to the homogeneous two-term electron Boltzmann equation, taking the measured gas temperature and the estimated electron density as input parameters. Good qualitative agreement is found between the measurements and calculations of the local species densities for various powers and axial positions. The dissociation degree of oxygen is found above 10%. Moreover, both the measurements and calculations show evidence of the non-equilibrium behavior of low-temperature plasmas, with vibrational and excitation temperatures at least ten times higher than the gas temperature. These observations confirm that low-pressure microwave micro-plasmas exhibit high-reactivity, and the present study shows that these features are controlled by electron kinetics, as expected.

Spectral characteristics of high-latitude raw 40 MHz cosmic noise signals

Abstract. Cosmic noise at 40 MHz is measured at Ny-Ålesund (79° N, 12° E) using a relative ionospheric opacity meter ("riometer"). A riometer is normally used to determine the degree to which cosmic noise is absorbed by the intervening ionosphere, giving an indication of ionisation of the atmosphere at altitudes lower than generally monitored by other instruments. The usual course is to determine a "quiet-day" variation, this representing the galactic noise signal itself in the absence of absorption; the current signal is then subtracted from this to arrive at absorption expressed in decibels (dB). By a variety of means and assumptions, it is thereafter possible to estimate electron density profiles in the very lowest reaches of the ionosphere. Here however, the entire signal, i.e. including the cosmic noise itself, will be examined and spectral characteristics identified. It will be seen that distinct spectral subranges are evident which can, in turn, be identified with non-Gaussian processes characterised by generalised Hurst exponents, α. Considering all periods greater than 1 h, α ≈ 24, an indication of fractional Brownian motion, whereas for periods greater than 1 day α ≈ 0.9 – approximately pink noise and just in the domain of fractional Gaussian noise. The results are compared with other physical processes, suggesting that absorption of cosmic noise is characterised by a generalised Hurst exponent ≈ 1.24 and thus non-persistent fractional Brownian motion, whereas generation of cosmic noise is characterised by a generalised Hurst exponent ≈ 1. The technique unfortunately did not result in clear physical understanding of the ionospheric phenomena, and thus, in this respect, the application was not successful; the analysis could, however, be used as a tool for instrument validation.

On the estimation of density of collectivized electrons in plasmonic spherical metal nanoparticles: quantum static versus classical dynamic approach

The density function of a gas of collectivized electrons emerges in different theoretical models of plasmonics describing nanostructured metals. This relates to either the most simple theories based on mechanics of classic particles (e.g., the Drude theory) or more complicated continuum and quantum mechanical based ones. The knowledge of the density function parameters allows predicting new physical phenomena in plasmonic systems, making mathematical simulation and automating the design of plasmonic devices in future. In this work we propose several approaches based on the density functional theory, single particle quantum mechanics and the continuum mechanics as well for definition of the mean electron density value in spherical metal nanoparticles. By using these tools we derive the quantitative estimates of electron density, the Fermi energy and velocity for large nanoparticles and compare them against the similar data known from the theory of bulk crystals. A significant difference between them has been shown. The attention is stressed on the universality of the results obtained together with the techniques of their derivation in context of application to different theories.

SU-G-JeP2-02: A Unifying Multi-Atlas Approach to Electron Density Mapping Using Multi-Parametric MRI for Radiation Treatment Planning

Purpose: MRI has a number of advantages over CT as a primary modality for radiation treatment planning (RTP). However, one key bottleneck problem still remains, which is the lack of electron density information in MRI. In the work, a reliable method to map electron density is developed by leveraging the differential contrast of multi-parametric MRI. Methods: We propose a probabilistic Bayesian approach for electron density mapping based on T1 and T2-weighted MRI, using multiple patients as atlases. For each voxel, we compute two conditional probabilities: (1) electron density given its image intensity on T1 and T2-weighted MR images, and (2) electron density given its geometric location in a reference anatomy. The two sources of information (image intensity and spatial location) are combined into a unifying posterior probability density function using the Bayesian formalism. The mean value of the posterior probability density function provides the estimated electron density. Results: We evaluated the method on 10 head and neck patients and performed leave-one-out cross validation (9 patients as atlases and remaining 1 as test). The proposed method significantly reduced the errors in electron density estimation, with a mean absolute HU error of 138, compared with 193 for the T1-weighted intensity approach and 261 without density correction. For bone detection (HU>200), the proposed method had an accuracy of 84% and a sensitivity of 73% at specificity of 90% (AUC = 87%). In comparison, the AUC for bone detection is 73% and 50% using the intensity approach and without density correction, respectively. Conclusion: The proposed unifying method provides accurate electron density estimation and bone detection based on multi-parametric MRI of the head with highly heterogeneous anatomy. This could allow for accurate dose calculation and reference image generation for patient setup in MRI-based radiation treatment planning.

SU‐F‐J‐213: Feasibility Study of Using a Dual‐Energy Cone Beam CT (DECBCT) in Proton Therapy Treatment Planning

Purpose:The aim of this study is to evaluate the feasibility of using a dual‐energy CBCT (DECBCT) in proton therapy treatment planning to allow for accurate electron density estimation.Methods:For direct comparison, two scenarios were selected: a dual‐energy fan‐beam CT (high: 140 kVp, low: 80 kVp) and a DECBCT (high: 125 kVp, low: 80 kVp). A Gammex 467 tissue characterization phantom was used, including the rods of air, water, bone (B2–30% mineral), cortical bone (SB3), lung (LN‐300), brain, liver and adipose. For the CBCT, Hounsfield Unit (HU) numbers were first obtained from the reconstructed images after a calibration was made based on water (=0) and air materials (=−1000). For each tissue surrogate, region‐of‐interest (ROI) analyses were made to derive high‐energy and low‐energy HU values (HUhigh and HUlow), which were subsequently used to estimate electron density based on the algorithm as previously described by Hunemohr N., et al. Parameters k1 and k2 are energy dependent and can be derived from calibration materials.Results:While for the dual‐energy FBCT, the electron density is found be within +/−3% error relative to the values provided by the phantom vendor: −1.8% (water), 0.03% (lung), 1.1% (brain), −2.82% (adipose), −0.49% (liver) and −1.89% (cortical bones). While for the DECBCT, the estimation of electron density exhibits a relatively larger variation: −1.76% (water), −36.7% (lung), −1.92% (brain), −3.43% (adipose), 8.1% (liver) and 9.5% (cortical bones).Conclusion:For DECBCT, the accuracy of electron density estimation is inferior to that of a FBCT, especially for materials of either low‐density (lung) or high density (cortical bone) compared to water. Such limitation arises from inaccurate HU number derivation in a CBCT. Advanced scatter‐correction and HU calibration routines, as well as the deployment of photon counting CT detectors need be investigated to minimize the difference between FBCT and CBCT.

Regional ionosphere modeling using spherical cap harmonics and empirical orthogonal functions over Iran

The ionosphere is the ionized part of the upper region of the atmosphere extending from 60 to 1500 km above the earth’s surface. In this layer, free electrons are produced during the interaction of extreme ultra violet and x-ray radiation with the upper neutral atmosphere. Knowledge of the ionospheric electron density distribution is important for scientific studies and practical applications. In this paper, a new computerized ionospheric tomography reconstruction technique is developed to estimate electron density profiles over Iran. In this method, a functional based model is used to represent the electron density in space. The functional based model uses empirical orthogonal functions and spherical cap harmonics to describe the vertical and horizontal distribution of the electron density, respectively. The degree and the number of basis functions are chosen so that, the relative error of results is minimized. For this purpose, ionosonde observations (Lat. = 35.73°, Lon. = 51.38°) at 2007.04.03 is used. To apply the method for constructing a 3D-image of the electron density, GPS measurements of the Iranian permanent GPS network (at 2012/08/11) has been used. The modeling region is between 24 to 40 N and 44 to 64 W. The result of 3D-model has been compared to that of the international reference ionosphere model 2012 (IRI-2012). The analysis conducted in this paper indicates that the choice of spherical cap harmonics to 3 (Kmax = 3) and empirical orthogonal function in 3 (Q = 3), the regional reconstructed error is less than 36 %. The results show the advantages of this method in modeling of the ionosphere electron density on local and regional scales.

A linear, separable two-parameter model for dual energy CT imaging of proton stopping power computation.

To evaluate the accuracy and robustness of a simple, linear, separable, two-parameter model (basis vector model, BVM) in mapping proton stopping powers via dual energy computed tomography (DECT) imaging. The BVM assumes that photon cross sections (attenuation coefficients) of unknown materials are linear combinations of the corresponding radiological quantities of dissimilar basis substances (i.e., polystyrene, CaCl2 aqueous solution, and water). The authors have extended this approach to the estimation of electron density and mean excitation energy, which are required parameters for computing proton stopping powers via the Bethe-Bloch equation. The authors compared the stopping power estimation accuracy of the BVM with that of a nonlinear, nonseparable photon cross section Torikoshi parametric fit model (VCU tPFM) as implemented by the authors and by Yang et al. ["Theoretical variance analysis of single- and dual-energy computed tomography methods for calculating proton stopping power ratios of biological tissues," Phys. Med. Biol. 55, 1343-1362 (2010)]. Using an idealized monoenergetic DECT imaging model, proton ranges estimated by the BVM, VCU tPFM, and Yang tPFM were compared to International Commission on Radiation Units and Measurements (ICRU) published reference values. The robustness of the stopping power prediction accuracy of tissue composition variations was assessed for both of the BVM and VCU tPFM. The sensitivity of accuracy to CT image uncertainty was also evaluated. Based on the authors' idealized, error-free DECT imaging model, the root-mean-square error of BVM proton stopping power estimation for 175 MeV protons relative to ICRU reference values for 34 ICRU standard tissues is 0.20%, compared to 0.23% and 0.68% for the Yang and VCU tPFM models, respectively. The range estimation errors were less than 1 mm for the BVM and Yang tPFM models, respectively. The BVM estimation accuracy is not dependent on tissue type and proton energy range. The BVM is slightly more vulnerable to CT image intensity uncertainties than the tPFM models. Both the BVM and tPFM prediction accuracies were robust to uncertainties of tissue composition and independent of the choice of reference values. This reported accuracy does not include the impacts of I-value uncertainties and imaging artifacts and may not be achievable on current clinical CT scanners. The proton stopping power estimation accuracy of the proposed linear, separable BVM model is comparable to or better than that of the nonseparable tPFM models proposed by other groups. In contrast to the tPFM, the BVM does not require an iterative solving for effective atomic number and electron density at every voxel; this improves the computational efficiency of DECT imaging when iterative, model-based image reconstruction algorithms are used to minimize noise and systematic imaging artifacts of CT images.

Radiative transfer modeling of the OI 135.6 nm emission in the nighttime ionosphere

AbstractRemote sensing of the nighttime OI 135.6 nm emissions has been a widely used method for measuring theFregion ionospheric plasma densities. In this work, we first develop a comprehensive radiative transfer model from first principles to investigate the effects of different physical processes on the production and transport of the 135.6 nm photons in the ionosphere and then propose a new approach for estimating electron densities from the nightglow. The forward modeling investigation indicates that under certain conditions mutual neutralization can contribute up to ∼38% of the total production of the nighttime 135.6 nm emissions. Moreover, depending on the ionospheric conditions, resonant scattering by atomic oxygen and pure absorption by oxygen molecules can reduce the limb brightness observed by satellite‐borne instruments by up to ∼40% while enhancing the brightness viewing in the nadir direction by typically ∼25%. Further analysis shows that without properly addressing these effects in the inversion process, the peak electron density in theF region (NmF2) obtained using limb observations can be overestimated by up to ∼24%. For accurate estimation of the ionospheric electron density, we develop a new type of inverse model that accounts for the effects of mutual neutralization, resonant scattering, and pure absorption. This inversion method requires the knowledge of O and O2densities in order to solve the radiative transfer equations. Application of the inverse model to the nighttime ionosphere in the noiseless cases demonstrates that the electron density can be accurately quantified with only ∼1% error in NmF2 and hmF2.

Data assimilation of plasmasphere and upper ionosphere using COSMIC/GPS slant TEC measurements

AbstractIncreasing total electron content (TEC) measurements from the low Earth orbiting satellites to Global Positioning System satellites flourish the exploration of the ionosphere and plasmasphere for decades. This paper indicates a method that 3‐D Var is applied to assimilate precise orbit determination antenna TEC measurements of Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) satellites into the background global core plasma model (GCPM). The slant TEC data archived in the COSMIC Data Analysis and Archive Center from 500 km to 20,200 km are used to reconstruct a new electron density model. This model has a temporal resolution of 2 h and spatial resolutions of 2.5° in geomagnetic latitude, 5° in longitude, 50 km in the upper ionosphere, and several hundred kilometers in the plasmasphere. Preliminary results show that the data assimilation modifies the initial GCPM forecast to be better coincident with actual COSMIC measurements in internal quality check. Furthermore, independent validation with upper ionosphere‐retrieved electron density and TEC of global ionosphere maps implies a reasonable improvement in the estimation of plasmaspheric electron density after the assimilation.

Dust storm and electron density in the equatorial D region ionosphere of Mars: Comparison with Earth's ionosphere from rocket measurements in Brazil

AbstractWe report the first model result for the dust densities and electron densities in the D region ionosphere of Mars for aerosol particles of different sizes during a major dust storm that occurred in Martian Year (MY) 25 at low latitude. These calculations are made at latitude 10°S and solar longitudes (Ls) = 200°, 220°, 250°, and 280° for high, medium, low, and absence of dust storms, respectively. Four corresponding dust layers were found at 50 km, 50 km, 38 km, and 25 km during these events. During high dust storm period, the optical depth and dust density increased by a factor of ~20 from its normal condition. The electron densities estimated for the D region ionosphere of Mars for submicron sized dust particles are largest as compared to that estimated for larger particles. The electron density reduced by ~2 orders of magnitude during high dust storm. The estimated electron density in the clear atmosphere of Mars is compared with measurements of Earth's ionosphere at nearly the same geophysical condition.

The puzzling spectrum of HD 94509

The spectral features of HD 94509 are highly unusual, adding an extreme to the zoo of Be and shell stars. The shell dominates the spectrum, showing lines typical for spectral types mid-A to early-F, while the presence of a late/mid B-type central star is indicated by photospheric hydrogen line wings and helium lines. Numerous metallic absorption lines have broad wings but taper to narrow cores. They cannot be fit by Voigt profiles. We aim to describe and illustrate unusual spectral features of this star, and make rough calculations to estimate physical conditions and abundances in the shell. Furthermore, the central star is characterized. We assume mean conditions for the shell. An electron density estimate is made from the Inglis-Teller formula. Excitation temperatures and column densities for Fe I and Fe II are derived from curves of growth. The neutral H column density is estimated from high Paschen members. The column densities are compared with calculations made with the photoionization code Cloudy. Atmospheric parameters of the central star are constrained employing non-LTE spectrum synthesis. Overall chemical abundances are close to solar. Column densities of the dominant ions of several elements, as well as excitation temperatures and the mean electron density are well accounted for by a simple model. Several features, including the degree of ionization, are less well described. HD 94509 is a Be star with a stable shell, close to the terminal-age main sequence. The dynamical state of the shell and the unusually shaped, but symmetric line profiles, require a separate study.

Robust inverse-consistent affine CT-MR registration in MRI-assisted and MRI-alone prostate radiation therapy.

CT-MR registration is a critical component of many radiation oncology protocols. In prostate external beam radiation therapy, it allows the propagation of MR-derived contours to reference CT images at the planning stage, and it enables dose mapping during dosimetry studies. The use of carefully registered CT-MR atlases allows the estimation of patient specific electron density maps from MRI scans, enabling MRI-alone radiation therapy planning and treatment adaptation. In all cases, the precision and accuracy achieved by registration influences the quality of the entire process. Most current registration algorithms do not robustly generalize and lack inverse-consistency, increasing the risk of human error and acting as a source of bias in studies where information is propagated in a particular direction, e.g. CT to MR or vice versa. In MRI-based treatment planning where both CT and MR scans serve as spatial references, inverse-consistency is critical, if under-acknowledged. A robust, inverse-consistent, rigid/affine registration algorithm that is well suited to CT-MR alignment in prostate radiation therapy is presented. The presented method is based on a robust block-matching optimization process that utilises a half-way space definition to maintain inverse-consistency. Inverse-consistency substantially reduces the influence of the order of input images, simplifying analysis, and increasing robustness. An open source implementation is available online at http://aehrc.github.io/Mirorr/. Experimental results on a challenging 35 CT-MR pelvis dataset demonstrate that the proposed method is more accurate than other popular registration packages and is at least as accurate as the state of the art, while being more robust and having an order of magnitude higher inverse-consistency than competing approaches. The presented results demonstrate that the proposed registration algorithm is readily applicable to prostate radiation therapy planning.

A unifying probabilistic Bayesian approach to derive electron density from MRI for radiation therapy treatment planning

MRI significantly improves the accuracy and reliability of target delineation in radiation therapy for certain tumors due to its superior soft tissue contrast compared to CT. A treatment planning process with MRI as the sole imaging modality will eliminate systematic CT/MRI co-registration errors, reduce cost and radiation exposure, and simplify clinical workflow. However, MRI lacks the key electron density information necessary for accurate dose calculation and generating reference images for patient setup. The purpose of this work is to develop a unifying method to derive electron density from standard T1-weighted MRI. We propose to combine both intensity and geometry information into a unifying probabilistic Bayesian framework for electron density mapping. For each voxel, we compute two conditional probability density functions (PDFs) of electron density given its: (1) T1-weighted MRI intensity, and (2) geometry in a reference anatomy, obtained by deformable image registration between the MRI of the atlas and test patient. The two conditional PDFs containing intensity and geometry information are combined into a unifying posterior PDF, whose mean value corresponds to the optimal electron density value under the mean-square error criterion. We evaluated the algorithm’s accuracy of electron density mapping and its ability to detect bone in the head for eight patients, using an additional patient as the atlas or template. Mean absolute HU error between the estimated and true CT, as well as receiver operating characteristics for bone detection (HU > 200) were calculated. The performance was compared with a global intensity approach based on T1 and no density correction (set whole head to water). The proposed technique significantly reduced the errors in electron density estimation, with a mean absolute HU error of 126, compared with 139 for deformable registration (p = 2 × 10−4), 283 for the intensity approach (p = 2 × 10−6) and 282 without density correction (p = 5 × 10−6). For 90% sensitivity in bone detection, the proposed method achieved a specificity of 86%, compared with 80, 11 and 10% using deformable registration, intensity and without density correction, respectively. Notably, the Bayesian approach was more robust against anatomical differences between patients, with a specificity of 62% in the worst case (patient), compared to 30% specificity in registration-based approach. In conclusion, the proposed unifying Bayesian method provides accurate electron density estimation and bone detection from MRI of the head with highly heterogeneous anatomy.

A Unifying Method to Derive Electron Density From MRI for Radiation Therapy Treatment Planning

MRI has a number of advantages over CT as a primary modality for patient simulation and treatment planning in radiation therapy. Due to its superior soft tissue contrast, MRI significantly improves the accuracy and reliability of target delineation. An MRI based simulation will eliminate systematic image co-registration errors, reduce cost and simplify clinical workflow, with the additional benefit of zero ionizing radiation. However, one key bottleneck problem still remains, which is the lack of electron density information in MRI. The purpose of this work is to develop a reliable method to derive electron density from MRI. We adopt a probabilistic Bayesian approach for electron density mapping based on T1-weighted MRI. The probabilistic approach allows us to explicitly recognize the various sources of uncertainties (such as deformable registration and density mapping) and incorporate them into the analysis. We utilize a head and neck patient with co-registered CT/MRI as the atlas. For each voxel, we compute two conditional probabilities or likelihood functions: (1) electron density given its MR image intensity (T1 value), and (2) electron density given its geometry or position in a reference anatomy, obtained by deformable image registration between the MRI of the test patient and atlas. The two sources of information (image intensity and spatial location) are combined into a unifying posterior probability density function, using the Bayesian formalism. The mean value of the posterior or its mode (value that corresponds to the maximum probability) gives the electron density. To evaluate the proposed method, we calculated the mean absolute HU error between the estimated and true CT, as well as area under the ROC curve for bone detection (HU > 200). The performance was compared with a global intensity approach based on T1 value and no density correction (set whole head to water). The proposed technique significantly reduced the errors in electron density estimation, with a mean absolute HU error of 117, compared with 232 for the intensity approach and 273 without density correction. For bone detection, the proposed method had an accuracy of 87%, with a sensitivity of 90% and specificity of 90% (AUC = 94%). In comparison, the AUC for bone detection is only 70% and 50% using the intensity approach and without density correction, respectively. The proposed unifying method provides accurate electron density estimation and bone detection from MRI of the head with highly heterogeneous regions. This paves the way for accurate dose calculation and generating reference images for patient setup in MRI-based treatment planning.

Estimates of relativistic electron and proton energy densities in starburst galactic nuclei from radio measurements

The energy density of energetic protons, U_p, in several nearby starburst nuclei (SBNs) has been directly deduced from gamma-ray measurements of the radiative decay of neutral pions produced in interactions with ambient protons. Lack of sufficient sensitivity and spatial resolution makes this direct deduction unrealistic in the foreseeable future for even moderately distant SBNs. A more viable indirect method for determining U_p in star-forming galaxies is to use its theoretically based scaling to the energy density of energetic electrons, U_e, which can be directly deduced from radio synchrotron and possibly also nonthermal hard X-ray emission. In order to improve the quantitative basis and diagnostic power of this leptonic method we reformulate and clarify its main aspects. Doing so we obtain a basic expression for the ratio U_p/U_e in terms of the proton and electron masses and the power-law indices that characterize the particle spectral distributions in regions where the total particle energy density is at equipartition with that of the mean magnetic field. We also express the field strength and the particle energy density in the equipartition region in terms of the region's size, mean gas density, IR and radio fluxes, and distance from the observer, and determine values of U_p in a sample of nine nearby and local SBNs.