Phantom Maps Research Articles

Duality pairs, phantom maps, and definability in triangulated categories

We define duality triples and duality pairs in compactly generated triangulated categories and investigate their properties. This enables us to give an elementary way to determine whether a class is closed under pure subobjects, pure quotients and pure extensions, as well as providing a way to show the existence of approximations. One key ingredient is a new characterization of phantom maps. We then introduce an axiomatic form of Auslander–Gruson–Jensen duality, from which we define dual definable categories, and show that these coincide with symmetric coproduct closed duality pairs. This framework is ubiquitous, encompassing both algebraic triangulated categories and stable homotopy theories. Accordingly, we provide many applications in both settings, with a particular emphasis on silting theory and stratified tensor-triangulated categories.

A fast protocol for multicenter and multiparametric quantitative MRI studies in brain tumor patients using vendor sequences.

Multiparametric quantitative MRI (mp-qMRI) provides noninvasive, quantitative measurements sensitive to a variety of tissue properties. In brain tumors (BTs), longitudinal relaxation time (T1), effective transverse relaxation time (T2*), transverse relaxation time (T2), water content (H2O), and quantitative susceptibility (χ) give valuable insights into the microenvironment. To generate large multicenter datasets, protocols need to be short and implementable on any scanner. The goal of this work was to develop and validate an 8-min, 3T mp-qMRI protocol for BT patients solely using generalized pulse sequences (mGRE and EPI). A protocol was developed and tested on a multicompartment phantom, 5 healthy subjects (mean age: 31.64 years), and 4 BT patients (mean age:39.5 years). Phantom and healthy subject longitudinal relaxation time (T1) maps were compared to those obtained using 2 reference methods. The 5 healthy subjects were scanned on 3T MRI scanners at 2 different sites and the reproducibility between scanners was assessed by computing Coefficients of Variance (COV) maps, performing Bland-Altman analysis and t-tests. Clinical feasibility was tested on 4 BT patients. T1 values obtained using the proposed mp-qMRI protocol agree with those obtained using the reference methods in volunteers (mean error = 8.94ms). The qMRI maps (T1, T2*, H2O, and χ) of the volunteers showed good reproducibility between scanners with no significant differences for mean WM and GM qMRI values. WM and GM mean qMRI values agreed well with literature values. H2O gave the lowest COV and χ maps the highest. The proposed vendor sequence-based 3T mp-qMRI protocol gives interpolated,high resolution (1mm isotropic) T1, T2*, H2O, and maps in 8min of acquisition.

The effect of and correction for through-slice dephasing on 2D gradient-echo double angle mapping.

To show that variations through slice and slice profile effects are two major confounders affecting 2D dual angle maps using gradient-echo signals and thus need to be corrected to obtain accurate maps. The 2D gradient-echo transverse complex signal was Bloch-simulated and integrated across the slice dimension including nonlinear variations in inhomogeneities through slice. A nonlinear least squares fit was used to find the factor corresponding to the best match between the two gradient-echo signals experimental ratio and the Bloch-simulated ratio. The correction was validated in phantom and in vivo at 3T. For our RF excitation pulse, the error in the factor scales by approximately 3.8% for every 10 Hz/cm variation in along the slice direction. Higher accuracy phantom maps were obtained after applying the proposed correction; the root mean square error relative to the gold standard decreased from 6.4% to 2.6%. In vivo whole-liver maps using the corrected map registered a significant decrease in gradient through slice. inhomogeneities varying through slice were seen to have an impact on the accuracy of 2D double angle maps using gradient-echo sequences. Consideration of this confounder is crucial for research relying on accurate knowledge of the true excitation flip angles, as is the case of mapping using a spoiled gradient recalled echo sequence.

Theranostic Nanoparticle Uptake in Patient Brain Tumors as Quantified by MP2RAGE T1 Mapping

Modern radiation therapy techniques provide effective treatments for solid tumors, but there remain challenges with delivering high doses to elusive tumors without causing toxicity to surrounding normal tissue. Pre-clinical trials have demonstrated the theranostic properties of a recently developed gadolinium-based nanoparticle (Gd-NP). The first in-human clinical trial was conducted to assess the safety and dose tolerance of intravenous Gd-NPs in combination with whole brain radiotherapy and showed favorable results, including a significant correlation between tumor uptake and therapeutic response. The second, double-blinded, in-human clinical trial is underway in the US and aims to evaluate if brain-directed stereotactic radiation in conjunction with NPs will improve local tumor control compared to radiation alone. The current work investigates uptake patterns in brain tumors of 23 patients as quantified by magnetization prepared 2 rapid gradient echo (MP2RAGE) T1 mapping. A phantom containing eight vials of NP-saline solutions at varying concentrations was created to examine the relationship between NP concentration and longitudinal relaxation (T1, in seconds). This relationship is known as relaxivity and is dependent on the contrast agent, field strength and T1 mapping sequence. A 3T MAGNETOM Vida scanner and MP2RAGE sequence were used to image the phantom and MP2RAGE T1 maps were calculated using Bloch equations (QMRLab software). Relaxivity was determined and applied to 23 patient T1 maps (pre- and post- Gd-NP administration) to calculate uptake on an individual tumor basis. Theranostic NP uptake was calculated for every voxel in each of 129 brain metastases and examined for patterns in quantity and distribution. Average individual tumor uptake ranged from 0.02-0.12 mg/ml, where average overall uptake was equal to 0.05 mg/ml. A relationship between tumor diameter and mean NP concentration was observed and best represented by a power-based curve (R2 = 0.92). In contrast, patients with suspected placebo administration appeared to have no uptake and therefore no relationship with tumor diameter. The distribution of NP concentration within the tumor was also examined; on average, linear uptake profiles through tumor centroids (ant-post, left-right) demonstrated roughly gaussian patterns of uptake with lower concentrations at the tumor edges and higher concentrations at the tumor center. This pattern indicates robust tumor penetration and may have implications for amplifying radiation dose to hypoxic tumors. Gd-NP uptake in brain metastases can be quantified using MP2RAGE T1 mapping. Uptake was determined for each voxel in each tumor volume, where a gaussian pattern of spatial concentrations was observed. This analysis procedure will be applied to the full data set, when available, to evaluate the impact of NP uptake (in conjunction with radiation therapy) within individual patients and individual tumors.

Cavernous Malformations: What They Have Taught Us.

Cavernous Malformations: What They Have Taught Us.

Gradient-Based Pulsed Excitation and Relaxation Encoding in Magnetic Particle Imaging.

Magnetic particle imaging (MPI) is a radiation-free vessel- and target-imaging modality that can sensitively detect nanoparticles. A static magnetic gradient field, referred to as a selection field, is required in MPI to provide a field-free region (FFR) for spatial encoding. The image resolution of MPI is closely related to the size of the FFR, which is determined by the selection field gradient amplitude. Because of the limitations of existing gradient coil hardware, the image resolution of MPI cannot satisfy the clinical requirements of human in vivo imaging. Pulsed excitation has been confirmed to improve the image resolution of MPI by breaking down the 'relaxation wall.' This work proposes the use of a pulsed waveform magnetic gradient from magnetic resonance imaging to further improve the image resolution of MPI. Through alignment of the gradient direction along the field-free line (FFL), each location on the FFL is able to have a unique excitation field strength that generates a specific relaxation-induced decay signal. Through excitation of nanoparticles on the FFL with many gradient profiles, a high-resolution, one-dimensional (1D) image can be reconstructed on the FFL. For larger magnetic nanoparticles, simulation results revealed that a pulsed excitation field with a greater flat portion generates a 1D bar pattern phantom image with a higher correlation and spatial resolution. With parallel FFL and gradient coil movements, high-resolution, two-dimensional (2D) Shepp-Logan phantom and brain vessel maps were reconstructed through repetition of the spatially resolved measurement of magnetic nanoparticles on the FFL.

Accuracy, repeatability, and reproducibility of T1 and T2 relaxation times measurement by 3D magnetic resonance fingerprinting with different dictionary resolutions

ObjectivesTo assess the accuracy, repeatability, and reproducibility of T1 and T2 relaxation time measurements by three-dimensional magnetic resonance fingerprinting (3D MRF) using various dictionary resolutions.MethodsThe ISMRM/NIST phantom was scanned daily for 10 days in two 3 T MR scanners using a 3D MRF sequence reconstructed using four dictionaries with varying step sizes and one dictionary with wider ranges. Thirty-nine healthy volunteers were enrolled: 20 subjects underwent whole-brain MRF scans in both scanners and the rest in one scanner. ROI/VOI analyses were performed on phantom and brain MRF maps. Accuracy, repeatability, and reproducibility metrics were calculated.ResultsIn the phantom study, all dictionaries showed high T1 linearity to the reference values (R2 > 0.99), repeatability (CV < 3%), and reproducibility (CV < 3%) with lower linearity (R2 > 0.98), repeatability (CV < 6%), and reproducibility (CV ≤ 4%) for T2 measurement. The volunteer study demonstrated high T1 reproducibility of within-subject CV (wCV) < 4% by all dictionaries with the same ranges, both in the brain parenchyma and CSF. Yet, reproducibility was moderate for T2 measurement (wCV < 8%). In CSF measurement, dictionaries with a smaller range showed a seemingly better reproducibility (T1, wCV 3%; T2, wCV 8%) than the much wider range dictionary (T1, wCV 5%; T2, wCV 13%). Truncated CSF relaxometry values were evident in smaller range dictionaries.ConclusionsThe accuracy, repeatability, and reproducibility of 3D MRF across various dictionary resolutions were high for T1 and moderate for T2 measurements. A lower-resolution dictionary with a well-defined range may be adequate, thus significantly reducing the computational load.Key Points• A lower-resolution dictionary with a well-defined range may be sufficient for 3D MRF reconstruction.• CSF relaxation times might be underestimated due to truncation by the upper dictionary range.• Dictionary with a higher upper range might be advisable, especially for CSF evaluation and elderly subjects whose perivascular spaces are more prominent.

A uniformity correction method to reduce scan time for 7T sodium imaging of brain tumors.

Sodium imaging shows great potential for the characterization of brain tumors. Intensity correction is required but the additional scan time is costly. Recent developments can halve the time but were optimized in normal brains and may not be applicable in brain tumor imaging. We aim to develop an individualized uniformity correction for sodium imaging optimized for brain tumor patients that reduces scan time but provides high-resolution images for clinical practice. Two-, 4-, and 6-mm iso-cubic voxel resolution birdcage coil images were used to calculate the 2-mm iso-cubic voxel individual sensitivity maps in healthy subjects (n=3). Cut profiles were compared to determine the optimal approach. In addition, a 3-dimensional phantom was developed to test a generalized uniformity correction approach in both healthy subjects (n=3) and tumor patients (n=3). The cut profiles showed that the average correlation coefficient between 2- and 4-mm birdcage image correction results was r=.9937, and r=.9876 for 2- and 6-mm birdcage images. The correlation result between individual map correction and phantom map correction was r=.9817. The 4mm birdcage coil image provided the optimal approach for both as a compromise between the time-savings effect and image quality. This method allows for a 2-mm iso-cubic voxel resolution clinical sodium scan within 12minutes. We also presented prescanned phantom sensitivity map results, which were designed to cover all patient head sizes. This approach provides an alternative solution in more time-sensitive cases.

Virtual Reality combined with Robotic facilitated movements for pain management and sensory stimulation of the upper limb following a Brachial Plexus injury: A case study.

Brachial Plexus injuries are complex in nature caused in large by high impact traffic accidents which can lead to additional complications such as Complex Regional Pain Syndrome and even lead to amputation or the need for further surgical intervention. Treatment options to help repair the brachial plexus initially involve surgical intervention and post-surgery rehabilitation with medication to help with ongoing pain. Pain treatments used for these types of injuries are limited and differ in effectiveness. Paradigms utilising multimodal systems such as the one described in this paper based on virtual reality and robotics could yield results that are non-invasive and provide better rehabilitation outcomes for the sufferers. In this paper we present a single case study exploring whether Virtual Reality plus Haptic feedback have any practical potential for reducing upper limb pain and improving function in patients with brachial plexus injuries. The case study is presented with long standing complex combination of phantom limb and neuropathic pain. A decrease in perceived levels of pain was reported which amounts to a 50% reduction in pain from baseline and an improved range of motion. An examination of the sensory phantom map on the stump seems to indicate an early establishment of the thumb representation on the stump close to the area being stimulated with potential implications for prosthesis use.

Creation of sensory phantom map of hand using VR robotic system: initial case series

Creation of sensory phantom map of hand using VR robotic system: initial case series

Telerobotic interventions from a distance: an initial experience in 3D phantom mapping

IntroductionThe current COVID-19 pandemic has fostered several accelerations in “remote” patient care such as video and telephone clinics, as well as multidisciplinary collaborations using online platforms with experts consulting the local teams from a distance. The next logical step would be to also offer remote-controlled interventions which the expert operator not on site, but in support of the local team. This is especially valuable for complex interventions when either patient or expert operator can not be present at the same place.PurposeWe aimed to demonstrate that an expert operator located at far distance (Austria) could directly interact with the remote magnetic navigation system in London (UK) whilst mapping a 3D phantom using an electroanatomical mapping system.MethodTwo experienced operators of the magnetic navigation system were tasked with creating fast anatomic maps (FAM) of the atrial and ventricular chambers of a 3D phantom using remote magnetic navigation in combination with 3D electroanatomical mapping. One was located in the control room of the magnetic catheter lab (UK) and the second one was in Tirol, Austria and connected through a secure remote desktop connection (via high speed fibre optic cable). Using a solid tip magnetic catheter connected to a mechanical drive, all interactions with the system were carried out via the Odyssey platform. Acquisitions for right and left atrium, as well as right and left ventricles plus aorta was compared with regards to mapping duration, map completeness (as judged by the average distance of surface points from 3D CT scan reconstruction), total 3D map volume and need for additional radiation exposure during the mapping process.ResultsMapping time and map completeness when performed by the distant operator was not inferior to the local operator and both did not require any additional radiation exposure during the mapping process. Table 1 demonstrates the mean parameters for each chamber, respectively. Figure 1 depicts the matched data for chamber completeness as compared for the LA (green= local operator, pink= distant operator) using a contrast CT scan as the gold standard.ConclusionTelerobotic 3D mapping of a 3D phantom from a distance was equally fast delivered from the control room as compared to an operator located 1200 km away without compromising on map completeness. This demonstrates the feasibility of telerobotic interventions and stress the need for remote collaboration which is especially valuable when travel of patients and/or physician experts is restricted.Funding AcknowledgementType of funding sources: None. Matched data for aorta

Telerobotic interventions from a distance: an initial experience in 3D phantom mapping

Abstract Introduction The current COVID-19 pandemic has fostered several accelerations in “remote” patient care such as video and telephone clinics, as well as multidisciplinary collaborations using online platforms with experts consulting the local teams from a distance. The next logical step would be to also offer remote-controlled interventions which the expert operator not on site, but in support of the local team. This is especially valuable for complex interventions when either patient or expert operator can not be present at the same place. Purpose We aimed to demonstrate that an expert operator located at far distance (Austria) could directly interact with the remote magnetic navigation system in London (UK) whilst mapping a 3D phantom using an electroanatomical mapping system. Method Two experienced operators of the magnetic navigation system were tasked with creating fast anatomic maps (FAM) of the atrial and ventricular chambers of a 3D phantom using remote magnetic navigation in combination with 3D electroanatomical mapping. One was located in the control room of the magnetic catheter lab (UK) and the second one was in Tirol, Austria and connected through a secure remote desktop connection (via high speed fibre optic cable). Using a solid tip magnetic catheter connected to a mechanical drive, all interactions with the system were carried out via the Odyssey platform. Acquisitions for right and left atrium, as well as right and left ventricles plus aorta was compared with regards to mapping duration, map completeness (as judged by the average distance of surface points from 3D CT scan reconstruction), total 3D map volume and need for additional radiation exposure during the mapping process. Results Mapping time and map completeness when performed by the distant operator was not inferior to the local operator and both did not require any additional radiation exposure during the mapping process. Table 1 demonstrates the mean parameters for each chamber, respectively. Figure 1 depicts the matched data for chamber completeness as compared for the LA (green= local operator, pink= distant operator) using a contrast CT scan as the gold standard. Conclusion Telerobotic 3D mapping of a 3D phantom from a distance was equally fast delivered from the control room as compared to an operator located 1200 km away without compromising on map completeness. This demonstrates the feasibility of telerobotic interventions and stress the need for remote collaboration which is especially valuable when travel of patients and/or physician experts is restricted. Funding Acknowledgement Type of funding sources: None. Matched data for aorta

$$\xi $$-Phantom Maps in $$(n+2)$$-Angulated Categories

$$\xi $$-Phantom Maps in $$(n+2)$$-Angulated Categories

Relative phantom maps and rational homotopy

We generalize some results of Gray and McGibbon-Roitberg on relations between phantom maps and rational homotopy to relative phantom maps. Since the l i m ⟵ 1 \underset {\longleftarrow }{\mathrm {lim}}^{1} and the profinite completion techniques do not apply to relative phantom maps, we develop new techniques.

Relative phantom maps

The de Bruijn-Erd\H{o}s theorem states that the chromatic number of an infinite graph equals the maximum of the chromatic numbers of finite subgraphs. Such a determinativeness by finite subobjects appears in the definition of a phantom map which is classical in algebraic topology. The topological method in combinatorics connects these two, which leads us to define the relative version of a phantom map: a map $f\colon X\to Y$ is called a relative phantom map to a map $\varphi\colon B\to Y$ if the restriction of $f$ to any finite subcomplex of $X$ lifts to $B$ through $\varphi$, up to homotopy. There are two kinds of maps which are obviously relative phantom maps: (1) the composite of a map $X\to B$ with $\varphi$; (2) a usual phantom map $X\to Y$. A relative phantom map of type (1) is called trivial, and a relative phantom map out of a suspension which is a sum of (1) and (2) is called relatively trivial. We study the (relative) triviality of relative phantom maps and in particular, we give rational homology conditions for the (relative) triviality.

Dry tDCS: Tolerability of a novel multilayer hydrogel composite non-adhesive electrode for transcranial direct current stimulation

BackgroundThe adoption of transcranial Direct Current Stimulation (tDCS) is encouraged by portability and ease-of-use. However, the preparation of tDCS electrodes remains the most cumbersome and error-prone step. Here, we validate the performance of the first “dry” electrodes for tDCS. A “dry electrode” excludes 1) any saline or other electrolytes, that are prone to spread and leaving a residue; 2) any adhesive at the skin interface; or 3) any electrode preparation steps except the connection to the stimulator. The Multilayer Hydrogel Composite (MHC) dry-electrode design satisfied these criteria. Objective/HypothesisOver an exposed scalp (supraorbital (SO) regions of forehead), we validated the performance of the first “dry” electrode for tDCS against the state-of-the-art conventional wet sponge-electrode to test the hypothesis that whether tDCS can be applied with a dry electrode with comparable tolerability as conventional “wet” techniques? MethodsMHC dry-electrode performance was verified using a skin-phantom, including mapping voltage at the phantom surface and mapping current inside the electrode using a novel biocompatible flexible printed circuit board current sensor matrix (fPCB-CSM). MHC dry-electrode performance was validated in a human trial including tolerability (VAS and adverse events), skin redness (erythema), and electrode current mapping with the fPCB-CSM. Experimental data from skin-phantom stimulation were compared against a finite element method (FEM) model. ResultsUnder the tested conditions (1.5 mA and 2 mA tDCS for 20 min using MHC-dry and sponge-electrode), the tolerability was improved, and the erythema and adverse-events were comparable between the MHC dry-electrode and the state-of-the-art sponge electrodes. ConclusionDry (residue-free, non-spreading, non-adhesive, and no-preparation-needed) electrodes can be tolerated under the tested tDCS conditions, and possibly more broadly used in non-invasive electrical stimulation.

Automatic hand phantom map generation and detection using decomposition support vector machines

BackgroundThere is a need for providing sensory feedback for myoelectric prosthesis users. Providing tactile feedback can improve object manipulation abilities, enhance the perceptual embodiment of myoelectric prostheses and help reduce phantom limb pain. Many amputees have referred sensation from their missing hand on their residual limbs (phantom maps). This skin area can serve as a target for providing amputees with non-invasive tactile sensory feedback. One of the challenges of providing sensory feedback on the phantom map is to define the accurate boundary of each phantom digit because the phantom map distribution varies from person to person.MethodsIn this paper, automatic phantom map detection methods based on four decomposition support vector machine algorithms and three sampling methods are proposed, complemented by fuzzy logic and active learning strategies. The algorithms and methods are tested on two databases: the first one includes 400 generated phantom maps, whereby the phantom map generation algorithm was based on our observation of the phantom maps to ensure smooth phantom digit edges, variety, and representativeness. The second database includes five reported phantom map images and transformations thereof. The accuracy and training/ classification time of each algorithm using a dense stimulation array (with 100 times 100 actuators) and two coarse stimulation arrays (with 3 times 5 and 4 times 6 actuators) are presented and compared.ResultsBoth generated and reported phantom map images share the same trends. Majority-pooling sampling effectively increases the training size, albeit introducing some noise, and thus produces the smallest error rates among the three proposed sampling methods. For different decomposition architectures, one-vs-one reduces unclassified regions and in general has higher classification accuracy than the other architectures. By introducing fuzzy logic to bias the penalty parameter, the influence of pooling-induced noise is reduced. Moreover, active learning with different strategies was also tested and shown to improve the accuracy by introducing more representative training samples. Overall, dense arrays employing one-vs-one fuzzy support vector machines with majority-pooling sampling have the smallest average absolute error rate (8.78% for generated phantom maps and 11.5% for reported and transformed phantom map images). The detection accuracy of coarse arrays was found to be significantly lower than for dense array.ConclusionsThe results demonstrate the effectiveness of support vector machines using a dense array in detecting refined phantom map shapes, whereas coarse arrays are unsuitable for this task. We therefore propose a two-step approach, using first a non-wearable dense array to detect an accurate phantom map shape, then to apply a wearable coarse stimulation array customized according to the detection results. The proposed methodology can be used as a tool for helping haptic feedback designers and for tracking the evolvement of phantom maps.

Task-based design of a synthetic-collimator SPECT system used for small animal imaging.

In traditional multipinhole SPECT systems, image multiplexing - the overlapping of pinhole projection images - may occur on the detector, which can inhibit quality image reconstructions due to photon-origin uncertainty. One proposed system to mitigate the effects of multiplexing is the synthetic-collimator SPECT system. In this system, two detectors, a silicon detector and a germanium detector, are placed at different distances behind the multipinhole aperture, allowing for image detection to occur at different magnifications and photon energies, resulting in higher overall sensitivity while maintaining high resolution. The unwanted effects of multiplexing are reduced by utilizing the additional data collected from the front silicon detector. However, determining optimal system configurations for a given imaging task requires efficient parsing of the complex parameter space, to understand how pinhole spacings and the two detector distances influence system performance. In our simulation studies, we use the ensemble mean-squared error of the Wiener estimator (EMSEW ) as the figure of merit to determine optimum system parameters for the task of estimating the uptake of an 123 I-labeled radiotracer in three different regions of a computer-generated mouse brain phantom. The segmented phantom map is constructed by using data from the MRM NeAt database and allows for the reduction in dimensionality of the system matrix which improves the computational efficiency of scanning the system's parameter space. To contextualize our results, the Wiener estimator is also compared against a region of interest estimator using maximum-likelihood reconstructed data. Our results show that the synthetic-collimator SPECT system outperforms traditional multipinhole SPECT systems in this estimation task. We also find that image multiplexing plays an important role in the system design of the synthetic-collimator SPECT system, with optimal germanium detector distances occurring at maxima in the derivative of the percent multiplexing function. Furthermore, we report that improved task performance can be achieved by using an adaptive system design in which the germanium detector distance may vary with projection angle. Finally, in our comparative study, we find that the Wiener estimator outperforms the conventional region of interest estimator. Our work demonstrates how this optimization method has the potential to quickly andefficiently explore vast parameter spaces, providing insight into the behavior of competing factors, which are otherwise very difficult to calculate and study using other existing means.

The Usefulness of Readout-Segmented Echo-Planar Imaging (RESOLVE) for Bio-phantom Imaging Using 3-Tesla Clinical MRI.

Readout-segmented echo-planar imaging (RESOLVE) is a multi-shot echo-planar imaging (EPI) modality with k-space segmented in the readout direction. We investigated whether RESOLVE decreases the distortion and artifact in the phase direction and increases the signal-to-noise ratio (SNR) in phantoms image taken with 3-tesla (3T) MRI versus conventional EPI. We used a physiological saline phantom and subtraction mapping and observed that RESOLVE's SNR was higher than EPI's. Using RESOLVE, the combination of a special-purpose coil and a large-loop coil had a higher SNR compared to using only a head/neck coil. RESOLVE's image distortioas less than EPI's. We used a 120 mM polyethylene glycol phantom to examine the phase direction artifact.vThe range where the artifact appeared in the apparent diffusion coefficient (ADC) image was shorter with RESOLVE compared to EPI. We used RESOLVE to take images of a Jurkat cell bio-phantom: the cell-region ADC was 856×10-6mm2/sec and the surrounding physiological saline-region ADC was 2,951×10-6mm2/sec. The combination of RESOLVE and the 3T clinical MRI device reduced image distortion and improved SNR and the identification of accurate ADC values due to the phase direction artifact reduction. This combination is useful for obtaining accurate ADC values of bio-phantoms.

Groups of homotopy classes of phantom maps

We introduce a new approach to phantom maps which largely extends the rational-ization-completion approach developed by Meier and Zabrodsky. Our approach enables us to deal with the set Ph(X,Y) of homotopy classes of phantom maps and the subset SPh(X,Y) of homotopy classes of special phantom maps simultaneously. We give a sufficient condition for Ph(X,Y) and SPh(X,Y) to have natural group structures, which is much weaker than the conditions obtained by Meier and McGibbon. Previous calculations of Ph(X,Y) have generally assumed that [X,ΩŶ] is trivial, in which case generalizations of Miller’s theorem are directly applicable, and calculations of SPh(X,Y) have rarely been reported. Here, we calculate not only Ph(X,Y) but also SPh(X,Y) in many important cases of nontrivial [X,ΩŶ].