Synthetic Phantom Research Articles

Artificial amniotic fluid for nuclear magnetic resonance spectroscopy studies.

Amniocentesis is the process of retrieving the nutrient-rich amniotic fluid (AF) that encompasses the growing fetus in order to diagnose fetal diseases and developmental disorders. Currently, it is only performed on pregnant persons at risk and is invasive with the potential for infection and in some cases, miscarriage. A non-invasive alternative is needed and could be developed using magnetic resonance spectroscopy (MRS). To develop such MRS sequences, ample testing and training are needed and could be most efficiently conducted on a phantom. We propose a protocol for creating such a synthetic AF phantom for MRS testing and optimization. The proposed AF is validated using nuclear magnetic resonance (NMR) proving it produces spectra comparable to those in the literature. The results from this study can aid in developing a non-invasive fetal diagnostic tool to replace amniocentesis.

Boosting transducer matrix sensitivity for 3D large field ultrasound localization microscopy using a multi-lens diffracting layer: a simulation study

Mapping blood microflows of the whole brain is crucial for early diagnosis of cerebral diseases. Ultrasound localization microscopy (ULM) was recently applied to map and quantify blood microflows in 2D in the brain of adult patients down to the micron scale. Whole brain 3D clinical ULM remains challenging due to the transcranial energy loss which significantly reduces the imaging sensitivity. Large aperture probes with a large surface can increase both resolution and sensitivity. However, a large active surface implies thousands of acoustic elements, with limited clinical translation. In this study, we investigate via simulations a new high-sensitive 3D imaging approach based on large diverging elements, combined with an adapted beamforming with corrected delay laws, to increase sensitivity. First, pressure fields from single elements with different sizes and shapes were simulated. High directivity was measured for curved element while maintaining high transmit pressure. Matrix arrays of 256 elements with a dimension of 10 × 10 cm with small (λ/2), large (4λ), and curved elements (4λ) were compared through point spread functions analysis. A large synthetic microvessel phantom filled with 100 microbubbles per frame was imaged using the matrix arrays in a transcranial configuration. 93% of the bubbles were detected with the proposed approach demonstrating that the multi-lens diffracting layer has a strong potential to enable 3D ULM over a large field of view through the bones.

Comparison of multicenter MRI protocols for visualizing the spinal cord gray matter.

Spinal cord gray-matter imaging is valuable for a number of applications, but remains challenging. The purpose of this work was to compare various MRI protocols at 1.5 T, 3T, and 7T for visualizing the gray matter. In vivo data of the cervical spinal cord were collected from nine different imaging centers. Data processing consisted of automatically segmenting the spinal cord and its gray matter and co-registering back-to-back scans. We computed the SNR using two methods (SNR_single using a single scan and SNR_diff using the difference between back-to-back scans) and the white/gray matter contrast-to-noise ratio per unit time. Synthetic phantom data were generated to evaluate the metrics performance. Experienced radiologists qualitatively scored the images. We ran the same processing on an open-access multicenter data set of the spinal cord MRI (N= 267 participants). Qualitative assessments indicated comparable image quality for 3T and 7T scans. Spatial resolution was higher at higher field strength, and image quality at 1.5T was found to be moderate to low. The proposed quantitative metrics were found to be robust to underlying changes to the SNR and contrast; however, the SNR_single method lacked accuracy when there were excessive partial-volume effects. We propose quality assessment criteria and metrics for gray-matter visualization and apply them to different protocols. The proposed criteria and metrics, the analyzed protocols, and our open-source code can serve as a benchmark for future optimization of spinal cord gray-matter imaging protocols.

DeepUCT: Complex cascaded deep learning network for improved ultrasound tomography

Ultrasound computed tomography is an inexpensive and radiation-free medical imaging technique used to quantify the tissue acoustic properties for advanced clinical diagnosis. Image reconstruction in ultrasound tomography is often modeled as an optimization scheme solved by iterative methods like full-waveform inversion. These iterative methods are computationally expensive, while the optimization problem is ill-posed and nonlinear. To address this problem, we propose to use deep learning to overcome the computational burden and ill-posedness, and achieve near real-time image reconstruction in ultrasound tomography. We aim to directly learn the mapping from the recorded time-series sensor data to a spatial image of acoustical properties. To accomplish this, we develop a deep learning model using two cascaded convolutional neural networks with an encoder–decoder architecture. We achieve a good representation by first extracting the intermediate mapping-knowledge and later utilizing this knowledge to reconstruct the image. This approach is evaluated on synthetic phantoms where simulated ultrasound data are acquired from a ring of transducers surrounding the region of interest. The measurement data is acquired by forward modeling the wave equation using the k-wave toolbox. Our simulation results demonstrate that our proposed deep-learning method is robust to noise and significantly outperforms the state-of-the-art traditional iterative method both quantitatively and qualitatively. Furthermore, our model takes substantially less computational time than the conventional full-wave inversion method.

Joint iterative reconstruction and 3D rigid alignment for X-ray tomography.

X-ray tomography is widely used for three-dimensional structure determination in many areas of science, from the millimeter to the nanometer scale. The resolution and quality of the 3D reconstruction is limited by the availability of alignment parameters that correct for the mechanical shifts of the sample or sample stage for the images that constitute a scan. In this paper we describe an algorithm for marker-free, fully automated and accurately aligned and reconstructed X-ray tomography data. Our approach solves the tomographic reconstruction jointly with projection data alignment based on a rigid-body deformation model. We demonstrate the robustness of our method on both synthetic phantom and experimental data and show that our method is highly efficient in recovering relatively large alignment errors without prior knowledge of a low resolution approximation of the 3D structure or a reasonable estimate of alignment parameters.

Validation of a robust method for quantification of three-dimensional growth of the thoracic aorta using deformable image registration.

PurposeAccurate assessment of thoracic aortic aneurysm (TAA) growth is important for appropriate clinical management. Maximal aortic diameter is the primary metric that is used to assess growth, but it suffers from substantial measurement variability. A recently proposed technique, termed vascular deformation mapping (VDM), is able to quantify three‐dimensional aortic growth using clinical computed tomography angiography (CTA) data using an approach based on deformable image registration (DIR). However, the accuracy and robustness of VDM remains undefined given the lack of ground truth from clinical CTA data, and, furthermore, the performance of VDM relative to standard manual diameter measurements is unknown.MethodsTo evaluate the performance of the VDM pipeline for quantifying aortic growth, we developed a novel and systematic evaluation process to generate 76 unique synthetic CTA growth phantoms (based on 10 unique cases) with variable degrees and locations of aortic wall deformation. Aortic deformation was quantified using two metrics: area ratio (AR), defined as the ratio of surface area in triangular mesh elements and the magnitude of deformation in the normal direction (DiN) relative to the aortic surface. Using these phantoms, we further investigated the effects on VDM's measurement accuracy resulting from factors that influence the quality of clinical CTA data such as respiratory translations, slice thickness, and image noise. Lastly, we compare the measurement error of VDM TAA growth assessments against two expert raters performing standard diameter measurements of synthetic phantom images.ResultsAcross our population of 76 synthetic growth phantoms, the median absolute error was 0.063 (IQR: 0.073–0.054) for AR and 0.181 mm (interquartile range [IQR]: 0.214–0.143 mm) for DiN. Median relative error was 1.4% for AR and 3.3% for DiN at the highest tested noise level (contrast‐to‐noise ratio [CNR] = 2.66). Error in VDM output increased with slice thickness, with the highest median relative error of 1.5% for AR and 4.1% for DiN at a slice thickness of 2.0 mm. Respiratory motion of the aorta resulted in maximal absolute error of 3% AR and 0.6 mm in DiN, but bulk translations in aortic position had a very small effect on measured AR and DiN values (relative errors <1%). VDM‐derived measurements of magnitude and location of maximal diameter change demonstrated significantly high accuracy and lower variability compared to two expert manual raters (p<0.03 across all comparisons).ConclusionsVDM yields an accurate, three‐dimensional assessment of aortic growth in TAA patients and is robust to factors such as image noise, respiration‐induced translations, and differences in patient position. Further, VDM significantly outperformed two expert manual raters in assessing the magnitude and location of aortic growth despite optimized experimental measurement conditions. These results support validation of the VDM technique for accurate quantification of aortic growth in patients and highlight several important advantages over diameter measurements.

Three-dimensional tomographically reconstructed optical emission profiles of Hall thruster plasmas

A diagnostic system was developed for spectrally resolved, three-dimensional tomographic reconstruction of Hall thruster plasmas, and local intensity profiles of Xe I and Xe II emissions were reconstructed. In this diagnostic system, 28 virtual cameras were generated using a single, fixed charge-coupled device camera by rotating the Hall thruster to form a sufficient number of lines of sight. The Phillips–Tikhonov regularization algorithm was used to reconstruct local emission profiles from the line-integrated emission signals. The reconstruction performance was evaluated using both azimuthally symmetric and asymmetric synthetic phantom images including 5% Gaussian white noise, which resulted in a root-mean-square error of the reconstruction within an order of 10−3 even for a 1% difference in the azimuthal intensity distribution. Using the developed system, three-dimensional local profiles of Xe II emission (541.9 nm) from radiative decay of the excited state 5p4(3P2)6p2[3]°5/2 and Xe I emission (881.9 nm) from 5p5(2P°3/2)6p2[5/2]3 were obtained, and two different shapes were found depending on the wavelength and the distance from the thruster exit plane. In particular, a stretched central jet structure was distinctively observed in the Xe II emission profile beyond 10 mm from the thruster exit, while gradual broadening was found in the Xe I emission. Approximately 10% azimuthal nonuniformities were observed in the local Xe I and Xe II intensity profiles in the near-plume region (<10 mm), which could not be quantitatively distinguished by analysis of the frontal photographic image. Three-dimensional Xe I and Xe II intensity profiles were also obtained in the plume region, and the differences in the structures of both emissions were visually confirmed.

Medical B-Mode Ultrasound Imaging Reconstruction Algorithms: Evaluation and Simulation

Ultrasound is one of the most important imaging modalities in medical practice. It is the most technique development with a lot benefits and with little challenges that include low imaging quality and high variability. Medical field is the most application that exploit the ultrasonic technique widely in body imaging, especially the real time Feature which take advantage of diagnostic time. This research makes a survey on the ultrasound image reconstruction and Display. First, the Ultrasound Imaging are reviewed as overall studying include the frequency ranges, advantages, main limitations, and applications. Second, the 2D or B-mode ultrasound imaging according to generation steps and mathematic studying are reviewed. Third, the stages of the 3D ultrasound object formation which is the data acquisition, data preprocessing, reconstruction method and 3D visualization, are discussed. Fourth, MATLAB Simulation to create B-Mode Ultrasound image with Synthetic phantom of a fetus in the third month of age, by using Field II software made specially for ultrasound environment, after initializing the ultrasound environment a phantom used to yield the B-Mode image. The complete B-Mode fetus scanned image creation need 5 hours and approximately 20 mins, that each line takes around 2min and 30 sec, with a processor 1.8 GHz Dual-Core Intel Core i5, MacOS. When the parameters of transducer have been changing then the clearness of the generated image the time taken will change in response.

Application of the migration method for radiotomography of breast cancer

A new method to visualize microwave image is presented to early non-invasive detection of breast cancer tumors. A new processing method to compute microwave images of heterogeneity in a biological environment is described here, as well as a new algorithm for accelerating the calculation of three-dimensional radio images. Sounding of synthetic phantoms with dielectric properties of breast tissue was carried out in the range of 2–8 GHz using a special radar system developed by the authors. Results show that it is possible to use this microwave imaging method to form 3D accurate images using hemispherical scan Images of tumor phantoms were obtained during probing in the 2–8 GHz range with a resolution of about 5–7 mm.According to the results of the reconstruction of three-dimensional radio images, it was revealed that the calculation time can be reduced by at least 2 times with an insignificant loss of quality.

Physical and digital phantoms for validating tractography and assessing artifacts

Fiber tractography is widely used to non-invasively map white-matter bundles in vivo using diffusion-weighted magnetic resonance imaging (dMRI). As it is the case for all scientific methods, proper validation is a key prerequisite for the successful application of fiber tractography, be it in the area of basic neuroscience or in a clinical setting. It is well-known that the indirect estimation of the fiber tracts from the local diffusion signal is highly ambiguous and extremely challenging. Furthermore, the validation of fiber tractography methods is hampered by the lack of a real ground truth, which is caused by the extremely complex brain microstructure that is not directly observable non-invasively and that is the basis of the huge network of long-range fiber connections in the brain that are the actual target of fiber tractography methods. As a substitute for in vivo data with a real ground truth that could be used for validation, a widely and successfully employed approach is the use of synthetic phantoms. In this work, we are providing an overview of the state-of-the-art in the area of physical and digital phantoms, answering the following guiding questions: “What are dMRI phantoms and what are they good for?”, “What would the ideal phantom for validation fiber tractography look like?” and “What phantoms, phantom datasets and tools used for their creation are available to the research community?”. We will further discuss the limitations and opportunities that come with the use of dMRI phantoms, and what future direction this field of research might take.

Optimization of spin-lock times in T1ρ mapping of knee cartilage: Cramér-Rao bounds versus matched sampling-fitting.

To compare different optimization approaches for choosing the spin-lock times (TSLs), in spin-lattice relaxation time in the rotating frame (T1ρ ) mapping. Optimization criteria for TSLs based on Cramér-Rao lower bounds (CRLB) are compared with matched sampling-fitting (MSF) approaches for T1ρ mapping on synthetic data, model phantoms, and knee cartilage. The MSF approaches are optimized using robust methods for noisy cost functions. The MSF approaches assume that optimal TSLs depend on the chosen fitting method. An iterative non-linear least squares (NLS) and artificial neural networks (ANN) are tested as two possible T1ρ fitting methods for MSF approaches. All optimized criteria were better than non-optimized ones. However, we observe that a modified CRLB and an MSF based on the mean of the normalized absolute error (MNAE) were more robust optimization approaches, performing well in all tested cases. The optimized TSLs obtained the best performance with synthetic data (3.5-8.0% error), model phantoms (1.5-2.8% error), and healthy volunteers (7.7-21.1% error), showing stable and improved quality results, comparing to non-optimized approaches (4.2-13.3% error on synthetic data, 2.1-6.2% error on model phantoms, 9.8-27.8% error on healthy volunteers). A modified CRLB and the MSF based on MNAE are robust optimization approaches for choosing TSLs in T1ρ mapping. All optimized criteria allowed good results even using rapid scans with two TSLs when a complex-valued fitting is done with iterative NLS or ANN.

Feasibility study of fiducial marker localization using microwave radar.

We explore the potential use of radar technology for fiducial marker tracking for monitoring of respiratory tumor motion during radiotherapy. Historically microwave radar technology has been widely deployed in various military and civil aviation applications to provide detection, position, and tracking of single or multiples objects from far away and even through barriers. Recently, due to many advantages of the microwave technology, it has been successfully demonstrated to detect breast tumor, and to monitor vital signs in real time such as breathing signals or heart rates. We demonstrate a proof-of-concept for radar-based fiducial marker tracking through the synthetic human tissue phantom. We performed a series of experiments with the vector network analyzer (VNA) and wideband directional horn antenna. We considered the frequency range from 2.0 to 6.0GHz, with a maximum power of 3dBm. A horn antenna, transmitting and receiving radar pulses, was connected to the vector network analyzer to probe a gold fiducial marker through a customized synthetic human tissue phantom, consisting of 1-mm thickness of skin, 5-mm fat, and 25-mm muscle layers. A 1.2 × 10-mm gold fiducial marker was exploited as a motion surrogate, which was placed behind the phantom and statically positioned with an increment of 12.7mm to simulate different marker displacements. The returned signals from the marker were acquired and analyzed to evaluate the localization accuracy as a function of the marker position. The fiducial marker was successfully localized at various measurement positions through a simplified phantom study. The averaged localization accuracy across measurements was 3.5 ± 1.3mm, with a minimum error of 1.9mm at the closest measurement location and a maximum error of 4.9mm at the largest measurement location. We demonstrated that the 2-6GHz radar can penetrate through the attenuating tissues and localize a fiducial marker. This successful feasibility study establishes a foundation for further investigation of radar technology as a non-ionizing tumor localization device for radiotherapy.

Visual Localisation for Knee Arthroscopy.

PURPOSE : Navigation in visually complex endoscopic environments requires an accurate and robust localisation system. This paper presents the single image deep learning based camera localisation method for orthopedic surgery. METHODS : The approach combines image information, deep learning techniques and bone-tracking data to estimate camera poses relative to the bone-markers. We have collected one arthroscopic video sequence for four knee flexion angles, per synthetic phantom knee model and a cadaveric knee-joint. RESULTS : Experimental results are shown for both a synthetic knee model and a cadaveric knee-joint with mean localisation errors of 9.66mm/0.85[Formula: see text] and 9.94mm/1.13[Formula: see text] achieved respectively. We have found no correlation between localisation errors achieved on synthetic and cadaveric images, and hence we predict that arthroscopic image artifacts play a minor role in camera pose estimation compared to constraints introduced by the presented setup. We have discovered that the images acquired for 90°and 0°knee flexion angles are respectively most and least informative for visual localisation. CONCLUSION : The performed study shows deep learning performs well in visually challenging, feature-poor, knee arthroscopy environments, which suggests such techniques can bring further improvements to localisation in Minimally Invasive Surgery.

Comprehensive Analysis of Alpha-Parametric Set for the Calculation of Intersection Lengths of Radiological Ray Path in Siddon's Algorithm Used in 3D Image Reconstruction

The Siddon algorithm is one of the radiological ray path calculation tools used in 3D image reconstruction in medical imaging. In the algorithm, a set of alpha-parametric values is computed containing the length and index values where the voxel array of the x-ray intersects the x-y-z axes. In the alpha-set creation section of the Siddon algorithm, the set elements are sorted from small to large, but some elements have been noticed to have the same value in simulations. These elements are used to calculate which voxels are hit by the ray along the radiological path and at what ratio, but it was recognized that some values of the set were zero, which means some rays did not intersect some voxels at all. This situation may lead to data loss in 3D image reconstructions in medical imaging such as digital breast tomosynthesis (DBT) and computed tomography (CT) especially for huge dimensions such as size up to 800×800×50. Considering the mentioned problems, in this study, the effect of using or eliminating the same repetitive values in the alpha parametric set of the Siddon algorithm on calculations was investigated. To prove our proposal, we performed lossy and lossless 3D image reconstruction (100×100×50) of a synthetic phantom. Using special functions that do not take into account the duplicate values and exclude them in the algorithm solved the stated problems (lossless reconstruction). In this way, data loss that may occur in 3D image reconstruction was reduced since voxel indices and intersection lengths were matched correctly.

SPECTnet: a deep learning neural network for SPECT image reconstruction

BackgroundSingle photon emission computed tomography (SPECT) is an important functional tool for clinical diagnosis and scientific research of brain disorders, but suffers from limited spatial resolution and high noise due to hardware design and imaging physics. The present study is to develop a deep learning technique for SPECT image reconstruction that directly converts raw projection data to image with high resolution and low noise, while an efficient training method specifically applicable to medical image reconstruction is presented.MethodsA custom software was developed to generate 20,000 2-D brain phantoms, of which 16,000 were used to train the neural network, 2,000 for validation, and the final 2,000 for testing. To reduce development difficulty, a two-step training strategy for network design was adopted. We first compressed full-size activity image (128×128 pixels) to a one-D vector consisting of 256×1 pixels, accomplished by an autoencoder (AE) consisting of an encoder and a decoder. The vector is a good representation of the full-size image in a lower-dimensional space and was used as a compact label to develop the second network that maps between the projection-data domain and the vector domain. Since the label had 256 pixels only, the second network was compact and easy to converge. The second network, when successfully developed, was connected to the decoder (a portion of AE) to decompress the vector to a regular 128×128 image. Therefore, a complex network was essentially divided into two compact neural networks trained separately in sequence but eventually connectable.ResultsA total of 2,000 test examples, a synthetic brain phantom, and de-identified patient data were used to validate SPECTnet. Results obtained from SPECTnet were compared with those obtained from our clinic OS-EM method. Images with lower noise and more accurate information in the uptake areas were obtained by SPECTnet.ConclusionsThe challenge of developing a complex deep neural network is reduced by training two separate compact connectable networks. The combination of the two networks forms the full version of SPECTnet. Results show that the developed neural network can produce more accurate SPECT images.

Non-linear fitting with joint spatial regularization in arterial spin labeling.

Multi-Delay single-shot arterial spin labeling (ASL) imaging provides accurate cerebral blood flow (CBF) and, in addition, arterial transit time (ATT) maps but the inherent low SNR can be challenging. Especially standard fitting using non-linear least squares often fails in regions with poor SNR, resulting in noisy estimates of the quantitative maps. State-of-the-art fitting techniques improve the SNR by incorporating prior knowledge in the estimation process which typically leads to spatial blurring. To this end, we propose a new estimation method with a joint spatial total generalized variation regularization on CBF and ATT. This joint regularization approach utilizes shared spatial features across maps to enhance sharpness and simultaneously improves noise suppression in the final estimates. The proposed method is evaluated at three levels, first on synthetic phantom data including pathologies, followed by in vivo acquisitions of healthy volunteers, and finally on patient data following an ischemic stroke. The quantitative estimates are compared to two reference methods, non-linear least squares fitting and a state-of-the-art ASL quantification algorithm based on Bayesian inference. The proposed joint regularization approach outperforms the reference implementations, substantially increasing the SNR in CBF and ATT while maintaining sharpness and quantitative accuracy in the estimates.

Three-Dimensional Mapping of Shear Wave Velocity in Human Tendon: A Proof of Concept Study.

Ultrasound-based shear wave elastography (SWE) provides the means to quantify tissue mechanical properties in vivo and has proven valuable in detecting degenerative processes in tendons. Its current mode of use is for two-dimensional rendering measurements, which are highly position-dependent. We therefore propose an approach to create a volumetric reconstruction of the mechano-acoustic properties of a structure of interest based on optically tracking the ultrasound probe during free-hand measurement sweeps. In the current work, we aimed (1) to assess the technical feasibility of the three-dimensional mapping of unidirectional shear wave velocity (SWV), (2) to evaluate the possible artefacts associated with hand-held image acquisition, (3) to investigate the reproducibility of the proposed technique, and (4) to study the potential of this method in detecting local adaptations in a longitudinal study setting. Operative and technical feasibility as well as potential artefacts associated with hand-held image acquisition were studied on a synthetic phantom containing discrete targets of known mechanical properties. Measurement reproducibility was assessed based on inter-day and inter-reader scans of the patellar, Achilles, and supraspinatus tendon of ten healthy volunteers and was compared to traditional two-dimensional image acquisition. The potential of this method in detecting local adaptations was studied by testing the effect of short-term voluntary isometric loading history on SWV along the tendon long axis. The suggested approach was technically feasible and reproducible, with a moderate to very good reliability and a standard error of measurement in the range of 0.300–0.591 m/s for the three assessed tendons at the two test-retest modalities. We found a consistent variation in SWV along the longitudinal axis of each tendon, and isometric loading resulted in regional increases in SWV in the patellar and Achilles tendons. The proposed method outperforms traditional two-dimensional measurement with regards to reproducibility and may prove valuable in the objective assessment of pathological tendon changes.

Task-based assessment of binned and list-mode SPECT systems.

In SPECT, list-mode (LM) format allows storing data at higher precision compared to binned data. There is significant interest in investigating whether this higher precision translates to improved performance on clinical tasks. Towards this goal, in this study, we quantitatively investigated whether processing data in LM format, and in particular, the energy attribute of the detected photon, provides improved performance on the task of absolute quantification of region-of-interest (ROI) uptake in comparison to processing the data in binned format. We conducted this evaluation study using a DaTscan brain SPECT acquisition protocol, conducted in the context of imaging patients with Parkinson's disease. This study was conducted with a synthetic phantom. A signal-known exactly/background-known-statistically (SKE/BKS) setup was considered. An ordered-subset expectation-maximization algorithm was used to reconstruct images from data acquired in LM format, including the scatter-window data, and including the energy attribute of each LM event. Using a realistic 2-D SPECT system simulation, quantification tasks were performed on the reconstructed images. The results demonstrated improved quantification performance when LM data was used compared to binning the attributes in all the conducted evaluation studies. Overall, we observed that LM data, including the energy attribute, yielded improved performance on absolute quantification tasks compared to binned data.

Technical Note: CT calibration for proton treatment planning by cross-calibration with proton CT data.

This study explores the possibility of a new method for x-ray computed tomography (CT) calibration by means of cross-calibration with proton CT (pCT) data. The proposed method aims at a more accurate conversion of CT Hounsfield Units (HU) into proton stopping power ratio (SPR) relative to water to be used in proton-therapy treatment planning. X-ray CT scan was acquired on a synthetic anthropomorphic phantom, composed of different tissue equivalent materials (TEMs). A pCT apparatus was instead adopted to obtain a reference three-dimensional distribution of the phantom's SPR values. After rigid registration, the x-ray CT was artificially blurred to the same resolution of pCT. Then a scatter plot showing voxel-by-voxel SPR values as a function of HU was employed to link the two measurements and thus obtaining a cross-calibrated x-ray CT calibration curve. The cross-calibration was tested at treatment planning system and then compared with a conventional calibration based on exactly the same TEMs constituting the anthropomorphic phantom. Cross-calibration provided an accurate SPR mapping, better than by conventional TEMs calibration. The dose distribution of single beams optimized on the reference SPR map was recomputed on cross-calibrated CT, showing, with respect to conventional calibration, minor deviation at the dose fall-off (lower than 1%). The presented data demonstrated that, by means of reference pCT data, a heterogeneous phantom can be used for CT calibration, paving the way to the use of biological samples, with their accurate description of patients' tissues. This overcomes the limitations of conventional CT calibration requiring homogenous samples, only available by synthetic TEMs, which fail in accurately mimicking the properties of biological tissues. Once a heterogeneous biological sample is provided with its corresponding reference SPR maps, a cross-calibration procedure could be adopted by other PT centers, even when not equipped with a pCT system.

Solution of 2D MIT Forward Problem by Considering Skin and Proximity Effects in Coils

Previous studies on the forward problem of magnetic induction tomography (MIT) have used simplified Maxwell's equations which assume a constant and position-independent total current density (TCD) inside the coils (ignoring skin effect). Moreover, they assume that TCD is independent of relative position of the coils (ignoring proximity effect). This article presents an improved finite element (FE) modeling for the two-dimensional (2D) forward problem of MIT by incorporating skin and proximity effects in the exciter and sensor coils. Consideration of skin and proximity effects requires the use of a position-dependent TCD in Maxwell's equations inside the coil domain. The FE method implementation of the improved forward method is validated with a simple analytical test problem. To evaluate the performance of the improved method in possible medical and industrial applications with low conductivity regions, a 16 coils 2D MIT system is modeled and the FE method is employed to solve the forward problem using a synthetic phantom. Results show the difference between the real parts of induced voltages obtained from the early and improved method falls into the range which is meaningful in terms of achievable conductivity contrast from the improved one. This discrepancy can generate considerable errors in image reconstruction. By considering skin and proximity effects, the improved method generates lower voltages in the coils suggesting the use of more precise hardware to detect inclusion. Findings show the importance and necessity of using improved method for modeling 2D MIT coils especially at low conductivity applications where measured signals are inherently weak.