Isotropic 3D Research Articles

Knee Derangements: Comparison of Isotropic 3D Fast Spin-Echo, Isotropic 3D Balanced Fast Field-Echo, and Conventional 2D Fast Spin-Echo MR Imaging

To compare diagnostic performance, subjective image quality, and artifacts of isotropic three-dimensional (3D) intermediate-weighted (IW) fast spin-echo (SE), isotropic 3D balanced fast field-echo (FFE), and conventional two-dimensional (2D) fast SE 3.0-T MR sequences in evaluation of cartilage, ligaments, menisci, and osseous knee structures in symptomatic patients. Institutional review board approval and waiver of informed consent were obtained for this HIPAA-compliant study. One hundred MR studies, each with three data sets (3D IW fast SE, 3D balanced FFE, 2D fast SE), were reviewed retrospectively. Two radiologists independently evaluated images for cartilaginous defects, anterior cruciate ligament (ACL), posterior cruciate ligament (PCL), medial meniscus (MM), lateral meniscus (LM) tears, subchondral bone marrow signal abnormalities, subjective image quality, and image artifacts. Arthroscopic results were the reference standard. Statistical analysis was performed to calculate interobserver agreement and compare diagnostic performance of sequences. Sensitivity and specificity were greater than 85% for all lesions. For cartilaginous defects, sensitivity of 3D IW fast SE was significantly greater than that of 3D balanced FFE (95.5% vs 89.7%). Sensitivity of 3D IW fast SE and 2D fast SE for MM, LM, and ACL tears tended to be greater than that of 3D balanced FFE. IW fast SE had a higher detection rate for subchondral bone marrow signal abnormality than did 3D balanced FFE (34% vs 21%); it also had the best image quality and fewest artifacts, followed by 2D fast SE and 3D balanced FFE. Interobserver agreement was excellent for evaluation of all intraarticular structures (κ = 0.85-1) and good to excellent for detection of subchondral bone marrow signal abnormality (κ = 0.76-0.91). The performance of IW fast SE is superior to that of balanced FFE in evaluation of cartilaginous defects, with no significant difference in performance between 2D fast SE, 3D IW fast SE, and 3D balanced FFE in evaluation of meniscal and ligament tears. Subchondral bone marrow signal abnormality is more easily seen on 3D IW fast SE images, with better subjective image quality and fewer artifacts, than on images obtained with other techniques.

Anisotropic parsimonious prestack depth migration

An efficient Kirchhoff-style prestack depth migration, called “parsimonious” migration, was developed a decade ago for isotropic 2D and 3D media by using measured slownesses to reduce the amount of ray tracing by orders of magnitude. It is conceptually similar to “map” migration, but its implementation has some differences. We have extended this approach to 2D tilted transversely isotropic (TTI) media and illustrated it with synthetic P-wave data. Although the framework of isotropic parsimonious may be retained, the extension to TTI media requires redevelopment of each of the numerical components, calculation of the phase and group velocity for TTI media, development of a new two-point anisotropic ray tracer, and substitution of an initial-angle isotropic shooting ray-trace algorithm for an anisotropic one. The model parameterization consists of Thomsen’s parameters ([Formula: see text], [Formula: see text], [Formula: see text]) and the tilt angle of the symmetry axis of the TI medium. The parsimonious anisotropic migration algorithm is successfully applied to synthetic data from a TTI version of the Marmousi2 model. The quality of the image improves by weighting the impulse response by the calculation of the anisotropic Fresnel radius. The accuracy and speed of this migration makes it useful for anisotropic velocity model building. The elapsed computing time for 101 shots for the Marmousi2 TTI model is 35 s per shot (each with 501 traces) in 32 Opteron cores.

Isotropic 3D Super Resolution Imaging with Self-Bending Point Spread Function

We introduce a self-bending point spread function (SB-PSF) based on Airy beams for three-dimensional (3D) super-resolution fluorescence imaging. We designed a side-lobe-free SB-PSF for the incoherent fluorescence emission and implemented a two-channel detection scheme for the SB-PSF to enable unambiguous 3D localization of fluorescent molecules. The lack of diffraction and the propagation-dependent lateral bending make the SB-PSF ideal for precise 3D localization of molecules over a large imaging depth. Using this SB-PSF, we demonstrated super-resolution imaging with isotropic localization precisions of 10-15 nm in all three dimensions over a 3 μm imaging depth without sample scanning.

Self-navigated free-breathing isotropic 3D whole heart MRI for the characterization of complex cardiac anatomy in patients with congenital heart malformations

Self-navigated free-breathing isotropic 3D whole heart MRI for the characterization of complex cardiac anatomy in patients with congenital heart malformations

A Partition Function Approximation Using Elementary Symmetric Functions

In statistical mechanics, the canonical partition function can be used to compute equilibrium properties of a physical system. Calculating however, is in general computationally intractable, since the computation scales exponentially with the number of particles in the system. A commonly used method for approximating equilibrium properties, is the Monte Carlo (MC) method. For some problems the MC method converges slowly, requiring a very large number of MC steps. For such problems the computational cost of the Monte Carlo method can be prohibitive. Presented here is a deterministic algorithm – the direct interaction algorithm (DIA) – for approximating the canonical partition function in operations. The DIA approximates the partition function as a combinatorial sum of products known as elementary symmetric functions (ESFs), which can be computed in operations. The DIA was used to compute equilibrium properties for the isotropic 2D Ising model, and the accuracy of the DIA was compared to that of the basic Metropolis Monte Carlo method. Our results show that the DIA may be a practical alternative for some problems where the Monte Carlo method converge slowly, and computational speed is a critical constraint, such as for very large systems or web-based applications.

Melange: A viscoelastic lattice‐particle model applicable to the lithosphere

This article introduces the software Melange, a 3D lattice‐particle hybrid model. The software was specifically designed in order to simulate ductile visco‐elasto‐plastic deformation and can be used to study tectonic processes in the lithosphere from the micro to the macro scale. Melange is under an open source license. The code takes both relevant yield mechanisms for the deformation of lithospheric material into account: dynamic brittle failure and ductile creep, where ductile creep is modeled as viscoelasticity. The software considers effects of the local geology, of the inherent disorder of geomaterials, of rheological layering of the lithosphere and applies repulsion when the material fractures. Driving forces are the externally applied strain and the gravitational load. Melange applies an elastically isotropic regular 3D lattice with HCP geometry and next‐nearest neighbor interactions. Young's modulus, viscosity, material density and system size can be freely chosen. Poisson's ratio is restricted to values <0.25. The most important innovation of the software is a physically consistent scheme to model viscoelasticity in a lattice‐particle model. The scheme couples the local lattice‐geometry to the time‐dependent volume‐conservative viscoelastic deformation of particles. The procedure achieves the typical viscoelastic stress‐strain relationship. The article incorporates a number of benchmark simulations, where the model output is being tested and evaluated. The results obtained with Melange show strong similarities with the benchmark values, e.g., stress fields in crack vicinity. Geologically relevant examples include structures associated with the brittle‐ductile transition, growth of wing cracks and brittle graben formation.

Bose-Einstein condensate in weak 3d isotropic speckle disorder

The effect of a weak three-dimensional (3d) isotropic laser speckle disorder on various thermodynamic properties of a dilute Bose gas is considered at zero temperature. First, we summarize the derivation of the autocorrelation function of laser speckles in 1d and 2d following the seminal work of Goodman. The goal of this discussion is to show that a Gaussian approximation of this function, proposed in some recent papers, is inconsistent with the general background of laser speckle theory. Then we propose a possible experimental realization for an isotropic 3d laser speckle potential and derive its corresponding autocorrelation function. Using a Fourier transform of that function, we calculate both condensate depletion and sound velocity of a Bose-Einstein condensate as disorder ensemble averages of such a weak laser speckle potential within a perturbative solution of the Gross-Pitaevskii equation. By doing so, we reproduce the expression of the normalfluid density obtained earlier within the treatment of Landau. This physically transparent derivation shows that condensate particles, which are scattered by disorder, form a gas of quasiparticles which is responsible for the normalfluid component.

Dual non-Kolmogorov cascades in a von Kármán flow

The experimental spatial power spectrum of the velocity fluctuations in a von Kármán flow is measured, in a wide range of Reynolds numbers, 102 < Re < 106, for the first time without using the Taylor hypothesis. At high enough Reynolds numbers, the spectra display a clear dual (direct and inverse) cascade. For any Re, the scaling of the direct cascade is steeper than the classical Kolmogorov −5/3 exponent of homogeneous and isotropic 3D turbulence. We then discuss the possibility of dual local and non-local cascades in a 3D turbulent Beltrami (a property satisfied by the von Kármán flow at large scale) flow, with inverse energy cascade and direct helicity cascade, by analogy with 2D turbulence. The corresponding energy spectra are computed in both local and non-local cases, and compared with our experimental results. The inverse cascade scaling is found to be in agreement with the non-local scenario. The direct cascade scaling is close to the non-local scenario for Re ≲ 4.104, and switches towards the local scenario at Re > 105.

Diagnostic performance of 3D SPACE for comprehensive knee joint assessment at 3 T

ObjectiveTo assess the diagnostic performance of 3D sampling perfection with application-optimised contrasts using variable flip-angle evolution (SPACE) turbo spin-echo (TSE) sequences compared to 2D TSE for comprehensive knee assessment at 3 T.MethodsFrom January to July 2011, isotropic 3D SPACE was added to a 2D knee protocol at 3 T. Forty patients underwent subsequent arthroscopy. Three readers independently assessed MR images for meniscus, anterior cruciate ligament (ACL) and cartilage lesions. Readers 1 and 2 evaluated 3D and 2D data at separate sittings; reader 3 interpreted the complete exam including 3D and 2D sequences. Accuracies were calculated using arthroscopy as reference standard. McNemar’s test (p < 0.05) was used to compare 3D and 2D techniques.ResultsThe highest diagnostic yield was obtained by reader 3 (accuracies ≥88 %). For the medial meniscus, readers performed better with the 2D technique than with 3D SPACE (accuracies 85–88 % vs. 78–80 %, respectively) (p > 0.05). For the lateral meniscus and ACL, 3D and 2D techniques had similar performance (accuracies ≥93 %). For cartilage lesions, 3D SPACE had significantly lower specificity (p = 0.0156) than the 2D protocol for one reader.ConclusionThe conventional 2D TSE acquisition is more reliable than 3D SPACE for comprehensive assessment of the knee at 3.0 T.Main Messages• 3D SPACE is a valuable component of a knee MR protocol at 3 T.• 3D SPACE cannot be used as a single sequence in the MR evaluation of the knee at 3 T.• Knee MR protocols at 3 T should include both 2D and 3D TSE sequences.

3D isotropic high‐resolution diffusion‐weighted MRI of the whole brain with a motion‐corrected steady‐state free precession sequence

The main obstacle to high-resolution (<1.5 mm isotropic) 3D diffusion-weighted MRI is the differential motion-induced phase error from shot-to-shot. In this work, the phase error is addressed with a hybrid 3D navigator approach that corrects motion-induced phase in two ways. In the first, rigid-body motion is corrected for every shot. In the second, repeatable nonrigid-body pulsation is corrected for each portion of the cardiac cycle. These phase error corrections were implemented with a 3D diffusion-weighted steady- state free precession pulse sequence and were shown to mitigate signal dropouts caused by shot-to-shot phase inconsistencies compared to a standard gridding reconstruction in healthy volunteers. The proposed approach resulted in diffusion contrast more similar to the contrast observed in the reference echo-planer imaging scans than reconstruction of the same data without correction. Fractional anisotropy and Color fractional anisotropy maps generated with phase-corrected data were also shown to be more similar to echo-planer imaging reference scans than those generated without phase correction.

2D modelling of induced polarization data with anisotropic complex conductivities

ABSTRACTInduced polarization data recorded at the field scale are usually processed using techniques based on isotropy. We study the effect of anisotropic complex conductivities in the frequency domain, with a particular emphasis on the polarization properties (i.e., phase angles). We consider anisotropy to be caused by a thin layering of isotropic media. Based on this, we derive corresponding mixing laws for the phase angles parallel and perpendicular to the layering and show that in cases of anisotropic layering, phase angles can only exist if the complex conductivity magnitudes are also anisotropic. We modified an existing isotropic finite‐element forward modelling code to support anisotropic complex conductivities. Based on an isotropic 2D inversion of a synthetic data set generated for an anisotropic model, we show that ignoring anisotropy may lead to artefacts and poor model recovery. Finally, we investigate a field data set recorded over a fault system in Germany, where anisotropic conductivities are expected. The isotropic 2D inversion of this data set yields a complex image that is difficult to interpret. We suggest an alternative interpretation based on trial‐and‐error forward modelling with anisotropic complex conductivities, using geological a priori information to constrain the model. The obtained model has a much simpler structure, consistent with the anticipated geology but yet is able to explain the measured data.

Current and Evolving Concepts in Musculoskeletal Imaging

AJR:199, September 2012 overuse injuries of the elbow in both the athlete and nonathlete. The current treatments of tendon disease, including corticosteroid injections, prolotherapy, percutaneous tenotomy, autologous blood injections, and platelet rich plasma, are reviewed. These musculoskeletal interventional procedures could be added to your armamentarium for treatment in the painful elbow. Finally, Drs. Ali Naraghi and Lawrence White [8] from Mount Sinai Hospital in Toronto, ON, Canada, review 3D MRI techniques of the musculoskeletal system. The article addresses the common question: Are isotropic 3D sequences sufficiently accurate to replace 2D FSE sequences? The article reviews the latest commonly available 3D MR techniques and usefulness of implementing these techniques into daily practice in the assessment and interpretation of internal joint derangement. Donna G. Blankenbaker AJR Section Editor, Musculoskeletal Imaging; University of Wisconsin School of Medicine and Public Health, Madison, WI dblankenbaker@uwhealth.org

Fluorescence imaging beyond the ballistic regime by ultrasound pulse guided digital phase conjugation.

Fluorescence imaging has revolutionized biomedical research over the past three decades. Its high molecular specificity and unrivaled single molecule level sensitivity have enabled breakthroughs in a variety of research fields. For in vivo applications, its major limitation is the superficial imaging depth as random scattering in biological tissues causes exponential attenuation of the ballistic component of a light wave. Here we present fluorescence imaging beyond the ballistic regime by combining single cycle pulsed ultrasound modulation and digital optical phase conjugation. We demonstrate a near isotropic 3D localized sound-light interaction zone. With the exceptionally high optical gain provided by the digital optical phase conjugation system, we can deliver sufficient optical power to a focus inside highly scattering media for not only fluorescence imaging but also a variety of linear and nonlinear spectroscopy measurements. This technology paves the way for many important applications in both fundamental biology research and clinical studies.

Characteristic equation solution strategy for deriving fundamental analytical solutions of 3D isotropic elasticity

A simple characteristic equation solution strategy for deriving the fundamental analytical solutions of 3D isotropic elasticity is proposed. By calculating the determinant of the differential operator matrix obtained from the governing equations of 3D elasticity, the characteristic equation which the characteristic general solution vectors must satisfy is established. Then, by substitution of the characteristic general solution vectors, which satisfy various reduced characteristic equations, into various reduced adjoint matrices of the differential operator matrix, the corresponding fundamental analytical solutions for isotropic 3D elasticity, including Boussinesq-Galerkin (B-G) solutions, modified Papkovich-Neuber solutions proposed by Min-zhongWANG (P-N-W), and quasi HU Hai-chang solutions, can be obtained. Furthermore, the independence characters of various fundamental solutions in polynomial form are also discussed in detail. These works provide a basis for constructing complete and independent analytical trial functions used in numerical methods.

TU-C-BRB-02: Identification of a Targeting Error in a Small Field Biological Irradiator Using 3D Dosimetry Techniques

Purpose: To characterize the targeting accuracy of a small animal irradiator, (XRad225Cx, Precision X-Ray Inc.), producing 225kVp circular or square fields ranging from 1mm–40mm dimensions. Targeting accuracy is critical for accurate interpretation of pre-clinical dose-volume response, but is extremely challenging, due to the extremely small field sizes. Characterization was performed with a uniquely suited novel high-resolution 3D dosimetry system. Methods: Targeting accuracy was evaluated on cylindrical 3D PRESAGE™dosimeters (5cm diameter, 7cm long) containing a range of physical targets. Each target corresponded to the tip-point of a 1.3mm channel drilled into the dosimeter at various locations and depths. Conebeam-CT image guided targeting was applied for treatment positioning, according to normal preclinical procedures. Each target was treated with 7 beam, varying angle, co-planar plan using the 2.5mm circular cone, including a delivery to an undrilled position, for undisturbed optical-CT data. Post-treatment, the dosimeter was imaged with the Duke Midsized Optical-CT Scanner (DMOS), producing 0.5mm isotropic 3D dose measurements. Targeting accuracy was evaluated by comparing the central position of the dose distribution to the targeted position (visible on optical-CT). Results: High-quality optical-CT scans were obtained, revealing both the physical target and the delivered dose distribution. High-resolution 3D analysis revealed a consistent targeting error of ∼1.5mm in all targets (along the long axis of the channel). The full-width half maximum of the beam intersection region was 2.2mm. Intersection of the beam central axes showed an error of 1.1mm in the direction perpendicular to the long axis. Conclusions: The value of high-resolution 3D dosimetry data was critical for this challenging problem of precisely evaluating the targeting accuracy of a very small field irradiator. The study enabled precise quantification of 3D targeting accuracy. The reason for the observed targeting errors is under investigation, and the accuracy of other cones will be explored. This work was supported by NIH R01CA100835, S103034539, NCI S10RR027610, NIAID K02AI093866 and NASA NSCOR NNX11AC60G. One potential conflict of interest is the dosimeter used in this work, PRESAGE™ is manufactured by Heuris Pharma, LLC, a company owned by John Adamovics.

Abstract 249: Stationary Signal and Flow Velocity Assessment by MRI of a New Nitinol Nanocomposite Polymer Stent-Graft

Objective: To assess MRI compatibility and suitability of a new sutureless stent-graft made from Nitinol bonded to nanocomposite polymer (NP). Methods: 1. Using MRI and Magnevist contrast, isotropic 3D T1-weighted FFE images of NP stent-graft were acquired to observe artefacts and stationary signal attenuation. Average signal magnitude was calculated. Medtronic ValiantTM was used as control. 2. In second stage, steady flow phantom was setup for flow-encoded MRI signal assessment of both stent-grafts. Baseline values were obtained by velocity measurements without stent-graft using identical settings. 2D through-plane phase contrast images were acquired and average velocity and amount of flow (flux) were calculated. Results: On static assessment of NP and ValiantTM stent-grafts no significant image artefacts were seen. The signal inside and outside the ValiantTM stent-graft was 644.2(SD 36.2) and 659.6(SD 85.8) respectively. The signal attenuation for this device was 2.39%. The signal inside and outside the NP stent graft was 1561.7(SD 31.2) and 1595.5(SD 40.8) respectively with comparable signal attenuation of 2.16%. In MRI velocity attenuation study, steady flow phantom was set at mean volume of 105.3 ml and mean velocity of 79.5 cm/sec. Flux measured in ValiantTM stent-graft was 102±2.27 ml/sec with no significant difference to baseline (104±1.98 ml/sec; P=0.892). Similarly flux for NP stent-graft at mean stroke volume 104.4 ml and mean velocity of 92.3 cm/sec showed no difference to baseline (99.8±2.4 vs. 104±0.96 ml/sec; P=0.176). There was no significant difference in flux between Medtronic and NP stent-grafts (102±2.27 vs. 99.8±2.4 ml/sec; P=0.328). Conclusion: NP stent-graft does not display any material-induced artefacts on MRI. On flow assessment, signal attenuation is comparable with the commercial device. These properties are important in developing this stent-graft, compliant, durable, visco-elastic, biocompatible and anti-thrombogenic, for future clinical use.

Graphene Network Organisation in Conductive Polymer Composites

AbstractA latex technique is used to prepare graphene/polystyrene and graphene/poly(propylene) composites with varying GR loadings. Their electrical properties and the corresponding volume organisation of GR networks are studied. Percolation thresholds for conduction are found to be about 0.9 and 0.4 wt% for GR/PS and GR/PP with maximum obtained conductivities of 12 and 0.4 S m−1 for GR loadings of 2 wt%, respectively. Investigations using SEM and electrical conductivity measurements show that for the preparation conditions used GR forms an isotropic 3D network in the PS matrix, but GR forms a 2D network in the PP matrix. The different GR network organisations are possibly forced by the different melt flow behaviour of the matrix polymers during processing and the subsequent crystallisation of PP.

Magnetic resonance imaging of the knee at 3 and 7 Tesla: a comparison using dedicated multi-channel coils and optimised 2D and 3D protocols

To show the feasibility and possible superiority of two 7 Tesla knee protocols ("7 T high resolution" and "7 T quick") using a new 28-channel knee coil compared to an optimised 3 T knee protocol using an 8-channel knee coil. The study was approved by the ethics committee. Both 3 T and 7 T MRI of the knee were performed in 10 healthy volunteers (29.6 ± 7.9 years), with two 2D sequences (PD-TSE and T1-SE) and three isotropic 3D sequences (TRUFI, FLASH and PD-TSE SPACE). Quantitative contrast-to-noise ratio (CNR) and qualitative evaluations were performed by different readers, and intra- and inter-rater agreement was assessed. The signal-to-noise ratio (SNR) as well as the CNR values for cartilage-bone, cartilage-fluid, cartilage-menisci and menisci-fluid were, in most cases, higher at 7 T compared to 3 T, and the 7 T quick measurement was slightly superior compared to the 7 T high-resolution measurement. The results of the subjective qualitative analysis were higher for the 7 T measurements compared to the 3 T measurements. Inter- and intra-observer reliability was high (0.884-0.999). Through higher field strength and an optimal coil, resolution at 7 T can be increased and acquisition time can be reduced, with superior quantitative and comparable qualitative results compared to 3 T.

Constraints on the ICM velocity power spectrum from the X-ray lines width and shift

Future X-ray observations of galaxy clusters by high spectral resolution missions will provide spatially resolved measurements of the energy and width for the brightest emission lines in the intracluster medium (ICM) spectrum. In this paper we discuss various ways of using these high resolution data to constrain velocity power spectrum in galaxy clusters. We argue that variations of these quantities with the projected distance R in cool core clusters contain important information on the velocity field length scales in the ICM. The effective length $l_{\rm eff}$ along the line of sight, which provides dominant contribution to the line flux, increases with R, allowing one to probe the amplitude of the velocity variations at different spatial scales. In particular, we show that the width of the line as a function of R is closely linked to the structure function of the 3D velocity field. Yet another easily obtainable proxy of the velocity field length scales is the ratio of the amplitude of the projected velocity field (line energy) variations to the dispersion of the velocity along the line of sight (line width). Finally the projected velocity field can be easily converted into 3D velocity field, especially for clusters like Coma with an extended flat core in the surface brightness. Under assumption of a homogeneous isotropic Gaussian 3D velocity field we derived simple expressions relating the power spectrum of the 3D velocity field (or structure function) and the observables. The uncertainties in the observables, caused by stochastic nature of the velocity field, are estimated by making multiple realizations of the random Gaussian velocity field and evaluating the scatter in observables. If large scale motions are present in the ICM these uncertainties may dominate the statistical errors of line width and shift measurements.

The effect of the 2D internal strain state on the critical current in GdBCO coated conductors

A reversible effect of strain on the critical current (Ic) has been reported for REBa2Cu3O7−δ (REBCO) coated conductors. In this study, the strain sensitivity of Ic was compared for GdBCO coated conductors with different crystal orientations. Extremely small strain sensitivity was confirmed from tensile and bending tests at 77 K for a GdBCO film with the [110] direction parallel to the tape length (Gd-F), while a GdBCO film with the [100] or [010] direction parallel to the tape length (Gd-I) has much stronger strain dependence of Ic. To compare the strain sensitivity of Ic based on internal strain, the lattice strain was evaluated for a GdBCO film in a composite conductor by employing a diffraction technique using synchrotron radiation. The lattice strain was determined along both the a- and b-axes for the orthogonal domains that are generated by the twin structure of GdBCO film. A distinct difference in the 2D strain state that depended on the crystal orientation was revealed for the GdBCO coated conductors. In Gd-I, the lattice strains along the axial and lateral directions are tensile and compressive under tensile loading, respectively, that is, the 2D internal strain state is anisotropic. On the other hand, an almost isotropic 2D strain state was confirmed in Gd-F. In addition, the strain components along the crystal axes in Gd-F are much smaller than the axial strain components in Gd-I. This difference in the internal strain state is attributed to the difference in strain sensitivity between the GdBCO coated conductors with different crystal orientations. The contributions of the strain components along the a- and b-axes to Ic are discussed on the basis of the measured strain sensitivities and internal strains for two conductors.