From an obliquely falling rod in a viscous fluid to the motion of suspended magnetic bead chains that are driven by a gradient magnetic field and that make an arbitrary angle with the magnetic force vector: A Stokes flow study.

In view of the growing role of magnetic particles under magnetic field influence in medical and other applications, and perforce the bead chaining, it is important to understand more generally the chain dynamics. As is well known, in the presence of a magnetic field, magnetic beads tend to form chains that are aligned with the magnetic field vector. In addition, if there is a magnetic field gradient, there will be a magnetic force acting on this chain. The main goal of the present research is to study the motion of a magnetic bead chain that makes an arbitrary angle with the magnetic force vector in the Stokes flow limit, that is, in the limit of zero Reynolds number. We used the public-domain computer program HYDRO++ to calculate the mobility matrix, which relates the magnetic force acting on the chain to the velocity of the chain, for a chain of N beads making an arbitrary angle with the magnetic force vector. Because of the presence of off-diagonal elements of the mobility matrix, as the chain is drawn in the direction of the magnetic force, it is also deflected to the side. We derived analytic solutions for this motion. Also, for bead chains moving in directions both parallel and perpendicular to their lengths, we fit three-parameter functions to solutions from HYDRO++. We found the fits to be excellent. Combining these results with the analytic solutions, we obtained expressions for the velocity components for the bead chains that provide excellent fits to HYDRO++ solutions for arbitrary angles. Finally, we apply the methodology used for the bead chain studies to the study of an obliquely falling rod in a viscous fluid and derive analytic solutions for the velocity components of the obliquely falling rod.

An ON-OFF Magneto-Optical Probe of Anisotropic Biofluid Crystals: A ß-Hematin Case Study.

We have designed, developed and evaluated an innovative portable magneto-optical detector (MOD) in which a light beam with variable polarization passes through a fluid sample immersed in a variable magnetic field. The light intensity is measured downstream along the forward scattering direction. The field is turned on and off through the in-and-out motion of nearby permanent magnets. As a result, for sufficiently magnetically and optically anisotropic samples, the optical absorption is sensitive to changes in the light polarization. Both detection and characterization applications are therefore available. For instance, both the degree of malaria infection can be measured and hemozoin crystalline properties can be studied. We present experimental results for synthetic hemozoin, and describe them in terms of the basic physics and chemistry underlying the correlations of the directions of the external magnetic field and the light beam polarization. We connect this work to a commercialized product for malaria detection and compare it to other magneto-optical instruments and methods. We conduct tests of absorption parameters, the electric polarizability tensor, and we discuss the connection to magnetic and electric dipole moments.

Transforming UTE-mDixon MR Abdomen-Pelvis Images Into CT by Jointly Leveraging Prior Knowledge and Partial Supervision.

Computed tomography (CT) provides information for diagnosis, PET attenuation correction (AC), and radiation treatment planning (RTP). Disadvantages of CT include poor soft tissue contrast and exposure to ionizing radiation. While MRI can overcome these disadvantages, it lacks the photon absorption information needed for PET AC and RTP. Thus, an intelligent transformation from MR to CT, i.e., the MR-based synthetic CT generation, is of great interest as it would support PET/MR AC and MR-only RTP. Using an MR pulse sequence that combines ultra-short echo time (UTE) and modified Dixon (mDixon), we propose a novel method for synthetic CT generation jointly leveraging prior knowledge as well as partial supervision (SCT-PK-PS for short) on large-field-of-view images that span abdomen and pelvis. Two key machine learning techniques, i.e., the knowledge-leveraged transfer fuzzy c-means (KL-TFCM) and the Laplacian support vector machine (LapSVM), are used in SCT-PK-PS. The significance of our effort is threefold: 1) Using the prior knowledge-referenced KL-TFCM clustering, SCT-PK-PS is able to group the feature data of MR images into five initial clusters of fat, soft tissue, air, bone, and bone marrow. Via these initial partitions, clusters needing to be refined are observed and for each of them a few additionally labeled examples are given as the partial supervision for the subsequent semi-supervised classification using LapSVM; 2) Partial supervision is usually insufficient for conventional algorithms to learn the insightful classifier. Instead, exploiting not only the given supervision but also the manifold structure embedded primarily in numerous unlabeled data, LapSVM is capable of training multiple desired tissue-recognizers; 3) Benefiting from the joint use of KL-TFCM and LapSVM, and assisted by the edge detector filter based feature extraction, the proposed SCT-PK-PS method features good recognition accuracy of tissue types, which ultimately facilitates the good transformation from MR images to CT images of the abdomen-pelvis. Applying the method on twenty subjects' feature data of UTE-mDixon MR images, the average score of the mean absolute prediction deviation (MAPD) of all subjects is 140.72 ± 30.60 HU which is statistically significantly better than the 241.36 ± 21.79 HU obtained using the all-water method, the 262.77 ± 42.22 HU obtained using the four-cluster-partitioning (FCP, i.e., external-air, internal-air, fat, and soft tissue) method, and the 197.05 ± 76.53 HU obtained via the conventional SVM method. These results demonstrate the effectiveness of our method for the intelligent transformation from MR to CT on the body section of abdomen-pelvis.

mDixon-Based Synthetic CT Generation for PET Attenuation Correction on Abdomen and Pelvis Jointly Using Transfer Fuzzy Clustering and Active Learning-Based Classification.

We propose a new method for generating synthetic CT images from modified Dixon (mDixon) MR data. The synthetic CT is used for attenuation correction (AC) when reconstructing PET data on abdomen and pelvis. While MR does not intrinsically contain any information about photon attenuation, AC is needed in PET/MR systems in order to be quantitatively accurate and to meet qualification standards required for use in many multi-center trials. Existing MR-based synthetic CT generation methods either use advanced MR sequences that have long acquisition time and limited clinical availability or use matching of the MR images from a newly scanned subject to images in a library of MR-CT pairs which has difficulty in accounting for the diversity of human anatomy especially in patients that have pathologies. To address these deficiencies, we present a five-phase interlinked method that uses mDixon MR acquisition and advanced machine learning methods for synthetic CT generation. Both transfer fuzzy clustering and active learning-based classification (TFC-ALC) are used. The significance of our efforts is fourfold: 1) TFC-ALC is capable of better synthetic CT generation than methods currently in use on the challenging abdomen using only common Dixon-based scanning. 2) TFC partitions MR voxels initially into the four groups regarding fat, bone, air, and soft tissue via transfer learning; ALC can learn insightful classifiers, using as few but informative labeled examples as possible to precisely distinguish bone, air, and soft tissue. Combining them, the TFC-ALC method successfully overcomes the inherent imperfection and potential uncertainty regarding the co-registration between CT and MR images. 3) Compared with existing methods, TFC-ALC features not only preferable synthetic CT generation but also improved parameter robustness, which facilitates its clinical practicability. Applying the proposed approach on mDixon-MR data from ten subjects, the average score of the mean absolute prediction deviation (MAPD) was 89.78±8.76 which is significantly better than the 133.17±9.67 obtained using the all-water (AW) method (p=4.11E-9) and the 104.97±10.03 obtained using the four-cluster-partitioning (FCP, i.e., external-air, internal-air, fat, and soft tissue) method (p=0.002). 4) Experiments in the PET SUV errors of these approaches show that TFC-ALC achieves the highest SUV accuracy and can generally reduce the SUV errors to 5% or less. These experimental results distinctively demonstrate the effectiveness of our proposed TFCALC method for the synthetic CT generation on abdomen and pelvis using only the commonly-available Dixon pulse sequence.

UTE-mDixon-based thorax synthetic CT generation.

PURPOSE: Accurate photon attenuation assessment from MR data remains an unmet challenge in the thorax due to tissue heterogeneity and the difficulty of MR lung imaging. As thoracic tissues encompass the whole physiologic range of photon absorption, large errors can occur when using, for example, a uniform, water-equivalent or a soft-tissue-only approximation. The purpose of this study was to introduce a method for voxel-wise thoracic synthetic CT (sCT) generation from MR data attenuation correction (AC) for PET/MR or for MR-only radiation treatment planning (RTP). METHODS: Acquisition: A radial stack-of-stars combining ultra-short-echo time (UTE) and modified Dixon (mDixon) sequence was optimized for thoracic imaging. The UTE-mDixon pulse sequence collects MR signals at three TE times denoted as UTE, Echo1, and Echo2. Three-point mDixon processing was used to reconstruct water and fat images. Bias field correction was applied in order to avoid artifacts caused by inhomogeneity of the MR magnetic field. ANALYSIS: Water fraction and R2* maps were estimated using the UTE-mDixon data to produce a total of seven MR features, that is UTE, Echo1, Echo2, Dixon water, Dixon fat, Water fraction, and R2*. A feature selection process was performed to determine the optimal feature combination for the proposed automatic, 6-tissue classification for sCT generation. Fuzzy c-means was used for the automatic classification which was followed by voxel-wise attenuation coefficient assignment as a weighted sum of those of the component tissues. Performance evaluation: MR data collected using the proposed pulse sequence were compared to those using a traditional two-point Dixon approach. Image quality measures, including image resolution and uniformity, were evaluated using an MR ACR phantom. Data collected from 25 normal volunteers were used to evaluate the accuracy of the proposed method compared to the template-based approach. Notably, the template approach is applicable here, that is normal volunteers, but may not be robust enough for patients with pathologies. RESULTS: The free breathing UTE-mDixon pulse sequence yielded images with quality comparable to those using the traditional breath holding mDixon sequence. Furthermore, by capturing the signal before T2* decay, the UTE-mDixon image provided lung and bone information which the mDixon image did not. The combination of Dixon water, Dixon fat, and the Water fraction was the most robust for tissue clustering and supported the classification of six tissues, that is, air, lung, fat, soft tissue, low-density bone, and dense bone, used to generate the sCT. The thoracic sCT had a mean absolute difference from the template-based (reference) CT of less than 50 HU and which was better agreement with the reference CT than the results produced using the traditional Dixon-based data. CONCLUSION: MR thoracic acquisition and analyses have been established to automatically provide six distinguishable tissue types to generate sCT for MR-based AC of PET/MR and for MR-only RTP.

Machine learning-based dual-energy CT parametric mapping.

The aim is to develop and evaluate machine learning methods for generating quantitative parametric maps of effective atomic number (Zeff), relative electron density (ρ e), mean excitation energy (I x ), and relative stopping power (RSP) from clinical dual-energy CT data. The maps could be used for material identification and radiation dose calculation. Machine learning methods of historical centroid (HC), random forest (RF), and artificial neural networks (ANN) were used to learn the relationship between dual-energy CT input data and ideal output parametric maps calculated for phantoms from the known compositions of 13 tissue substitutes. After training and model selection steps, the machine learning predictors were used to generate parametric maps from independent phantom and patient input data. Precision and accuracy were evaluated using the ideal maps. This process was repeated for a range of exposure doses, and performance was compared to that of the clinically-used dual-energy, physics-based method which served as the reference. The machine learning methods generated more accurate and precise parametric maps than those obtained using the reference method. Their performance advantage was particularly evident when using data from the lowest exposure, one-fifth of a typical clinical abdomen CT acquisition. The RF method achieved the greatest accuracy. In comparison, the ANN method was only 1% less accurate but had much better computational efficiency than RF, being able to produce parametric maps in 15 s. Machine learning methods outperformed the reference method in terms of accuracy and noise tolerance when generating parametric maps, encouraging further exploration of the techniques. Among the methods we evaluated, ANN is the most suitable for clinical use due to its combination of accuracy, excellent low-noise performance, and computational efficiency.