T1-space Research Articles

Evaluation of Lesion Burden in Pediatric Patients with Multiple Sclerosis by Computer Aided Algorithm and Comparison with Standard Detection Methods

Background: The aim of this retrospective study was to assess the lesion burden in pediatric patients with multiple sclerosis (pMS) using a computer-assisted algorithm, specifically the VolBrain program. The study aimed to compare the performance of this automated tool with traditional detection methods performed by neuroimaging analysts, providing valuable insights into the potential of automated tools for lesion quantification in pMS. Materials and Methods: The study cohort consisted of 20 PMS patients, aged 10-18 years, registered at Atatürk University Research Hospital. Lesion assessment was performed using the VolBrain program (by an anatomist) and standard detection methods (by a neuroradiologist) using T2 SPACE dark matter sequences. Statistical analysis included Wilcoxon and Pearson correlation tests, and the study adhered to ethical considerations and standardised magnetic resonance imaging (MRI) protocols. Results: In this study, pMS patients aged 10-18 years, the cohort consisted of 60% females (n=12) and 40% males (n=8). The mean age for females was 15.67±1.969 and for males 14.50±2.20 years (p=0.24). Plaque count analysis showed a statistically significant difference between radiologist and VolBrain assessment in all pMS patients (p=0.021). Significant differences were also observed in female pMS patients (p=0.034) but not in males (p=0.362). Correlations between radiologist and VolBrain assessments showed significant associations in both female and male patients, with strong correlations observed for plaque number, lesion burden and Expanded Disability Status Scale (EDSS) scores (p<0.01). Conclusions: This study demonstrates the potential of the VolBrain programme in assessing lesion burden in pMS patients. The observed correlations with traditional methods and clinical parameters support the concurrent validity of VolBrain and emphasise its potential clinical relevance. Incorporating automated tools into routine clinical practice could improve the accuracy of lesion quantification and thus contribute to improved monitoring and management of pMS.

Quasi-uniform entropy vs topological entropy

In 2023 Haihambo and Olela Otafudu introduced and studied the notion of quasi-uniform entropy hQU(ψ) for a uniformly continuous self-map ψ of a quasi-metric or a quasi-uniform space X. In this paper, we discuss the connection between the topological entropy functions h,hf and the quasi-uniform entropy function hQU on a quasi-uniform space X, where h and hf are the topological entropy functions defined using compact sets and finite open covers, respectively. In particular, we have shown that for a uniformly continuous self-map ψ of a T0-quasi-uniform space (X,U) we have h(ψ)≤hQU(ψ) when X is compact and hQU(ψ)≤hf(ψ) with equality if X is a compact T2 space.

D-completion, well-filterification and sobrification

In this paper, we study the D-completion, well-filterification and sobrification of a T0 space. First, we present an example of a tapered closed set which is neither the closure of a directed set nor a closed KF-set. In 2020, Xu et al. asked whether closed RD-sets are exactly closed WD-sets for every T0 space. This example also gives a negative answer to the above problem, since each tapered closed set is a closed WD-set. Second, we provide a direct characterization for the D-completion of a poset by using the notion of pre-C-compact elements. Finally, for a given T0 space, we give some sufficient conditions which guarantee that each pair of its standard D-completion, standard well-filterification and standard sobrification agrees.

Aneurysmal Wall Enhancement of Non-Ruptured Intracranial Aneurysms after Endovascular Treatment Correlates with Higher Aneurysm Reperfusion Rates, but Only in Large Aneurysms.

Aneurysmal wall enhancement (AWE) of non-ruptured sacular intracranial aneurysms (IA) after endovascular treatment (ET) is a frequently observed imaging finding using AWE-sequences in brain magnetic resonance imaging (MRI). So far, its value remains unclear. We aimed to investigate the effect of AWE on aneurysm reperfusion rates in a longitudinal cohort. This is a retrospective MRI study over the timespan of up to 5 years, assessing the correlation of increased AWE of non-ruptured IAs and events of aneurysm reperfusion and retreatment, PHASES Score and grade of AWE. T1 SPACE fat saturation (FS) and T1 SE FS blood suppression sequences after contrast administration were used for visual interpretation of increased AWE. The IAs' sizes were assessed via the biggest diameter. The grade of enhancement was defined in a grading system from grade 1 to grade 3. 127 consecutive non ruptured IA-patients (58.9 ± 9.0 years, 94 female, 33 male) who underwent elective aneurysm occlusion were included. AWE was observed in 40.2% of patients (51/127) after ET, 6 patients already showed AWE before treatment. In large IAs (which were defined as a single maximum diameter of over 7.5 mm), AWE was significantly associated with aneurysm reperfusion in contrast to large aneurysm without AWE). All grades of AWE were significantly associated with reperfusion. Our data suggests that in patients with initially large IAs, AWE is correlated with aneurysm reperfusion.

An in-depth exploration of intuitionistic fuzzy T_0 in the context of bitopology

Intuitionistic fuzzy topological space and bitopological space have been introduced by using the concepts of intuitionistic fuzzy sets which are the generalizations of interval valued fuzzy sets. This paper commences by presenting the notion of intuitionistic fuzzy T0 in the context of bitopological spaces (IFB-T0). Subsequently, we explore various connections and relationships between these concepts. Then, we find out the relation between intuitionistic T0 and IFB-T0 spaces. Further, we investigated continuity between two IFB spaces.

A few separation axioms on Nα*AS - closed sets in nano topological space

This work goal is to gain the relation between a number of the existing sets using inducing and investigating the capabilities of Ɲα*AS -T0 space, Nα*AS-T1space, Nα*AS -T2 space.

Multimodal neuroimaging exploration of the mechanisms of sleep quality deterioration after SARS-CoV-2 Omicron infection

BackgroundTo evaluate the neurological alterations induced by Omicron infection, to compare brain changes in chronic insomnia with those in exacerbated chronic insomnia in Omicron patients, and to examine individuals without insomnia alongside those with new-onset insomnia.MethodsIn this study, a total of 135 participants were recruited between January 11 and May 4, 2023, including 26 patients with chronic insomnia without exacerbation, 24 patients with chronic insomnia with exacerbation, 40 patients with no sleep disorder, and 30 patients with new-onset insomnia after infection with Omicron (a total of 120 participants with different sleep statuses after infection), as well as 15 healthy controls who were never infected with Omicron. Neuropsychiatric data, clinical symptoms, and multimodal magnetic resonance imaging data were collected. The gray matter thickness and T1, T2, proton density, and perivascular space values were analyzed. Associations between changes in multimodal magnetic resonance imaging findings and neuropsychiatric data were evaluated with correlation analyses.ResultsCompared with healthy controls, gray matter thickness changes were similar in the patients who have and do not have a history of chronic insomnia groups after infection, including an increase in cortical thickness near the parietal lobe and a reduction in cortical thickness in the frontal, occipital, and medial brain regions. Analyses showed a reduced gray matter thickness in patients with chronic insomnia compared with those with an aggravation of chronic insomnia post-Omicron infection, and a reduction was found in the right medial orbitofrontal region (mean [SD], 2.38 [0.17] vs. 2.67 [0.29] mm; P < 0.001). In the subgroups of Omicron patients experiencing sleep deterioration, patients with a history of chronic insomnia whose insomnia symptoms worsened after infection displayed heightened medial orbitofrontal cortical thickness and increased proton density values in various brain regions. Conversely, patients with good sleep quality who experienced a new onset of insomnia after infection exhibited reduced cortical thickness in pericalcarine regions and decreased proton density values. In new-onset insomnia patients post-Omicron infection, the thickness in the right pericalcarine was negatively correlated with the Self-rating Anxiety Scale (r = − 0.538, P = 0.002, PFDR = 0.004) and Self-rating Depression Scale (r = − 0.406, P = 0.026, PFDR = 0.026) scores.ConclusionsThese findings help us understand the pathophysiological mechanisms involved when Omicron invades the nervous system and induces various forms of insomnia after infection. In the future, we will continue to pay attention to the dynamic changes in the brain related to insomnia caused by Omicron infection.

Deep Learning-Based Reconstruction of 3D T1 SPACE Vessel Wall Imaging Provides Improved Image Quality with Reduced Scan Times: A Preliminary Study.

Intracranial vessel wall imaging is technically challenging to implement, given the simultaneous requirements of high spatial resolution, excellent blood and CSF signal suppression, and clinically acceptable gradient times. Herein, we present our preliminary findings on the evaluation of a deep learning-optimized sequence using T1-weighted imaging. Clinical and optimized deep learning-based image reconstruction T1 3D Sampling Perfection with Application optimized Contrast using different flip angle Evolution (SPACE) were evaluated, comparing noncontrast sequences in 10 healthy controls and postcontrast sequences in 5 consecutive patients. Images were reviewed on a Likert-like scale by 4 fellowship-trained neuroradiologists. Scores (range, 1-4) were separately assigned for 11 vessel segments in terms of vessel wall and lumen delineation. Additionally, images were evaluated in terms of overall background noise, image sharpness, and homogeneous CSF signal. Segment-wise scores were compared using paired samples t tests. The scan time for the clinical and deep learning-based image reconstruction sequences were 7:26 minutes and 5:23 minutes respectively. Deep learning-based image reconstruction images showed consistently higher wall signal and lumen visualization scores, with the differences being statistically significant in most vessel segments on both pre- and postcontrast images. Deep learning-based image reconstruction had lower background noise, higher image sharpness, and uniform CSF signal. Depiction of intracranial pathologies was better or similar on the deep learning-based image reconstruction. Our preliminary findings suggest that deep learning-based image reconstruction-optimized intracranial vessel wall imaging sequences may be helpful in achieving shorter gradient times with improved vessel wall visualization and overall image quality. These improvements may help with wider adoption of intracranial vessel wall imaging in clinical practice and should be further validated on a larger cohort.

The Ginsburg–Sands theorem and computability theory

The Ginsburg–Sands theorem from topology states that every infinite topological space has an infinite subspace homeomorphic to exactly one of the following five topologies on ω: indiscrete, discrete, initial segment, final segment, and cofinite. The original proof is nonconstructive, and features an interesting application of Ramsey's theorem for pairs (RT22). We analyze this principle in computability theory and reverse mathematics, using Dorais's formalization of CSC spaces. Among our results are that the Ginsburg–Sands theorem for CSC spaces is equivalent to ACA0, while for Hausdorff spaces it is provable in RCA0. Furthermore, if we enrich a CSC space by adding the closure operator on points, then the Ginsburg–Sands theorem turns out to be equivalent to the chain/antichain principle (CAC). The most surprising case is that of the Ginsburg–Sands theorem restricted to T1 spaces. Here, we show that the principle lies strictly between ACA0 and RT22, yielding arguably the first natural theorem from outside logic to occupy this interval. As part of our analysis of the T1 case we introduce a new class of purely combinatorial principles below ACA0 and not implied by RT22 which form a hierarchy generalizing the stable Ramsey's theorem for pairs (SRT22). We show that one of these, the Σ20 subset principle (Σ20-Subset), has the property that it, together with the cohesive principle (COH), is equivalent over RCA0 to the Ginsburg–Sands theorem for T1 CSC spaces.

Accuracy of Noncontrast T2 SPACE in Active MS Cord Lesion Detection.

The diagnosis of active MS lesions is often based on postgadolinium T1-weighted MR imaging. Recent studies suggest a risk of IV gadolinium to patients, predominantly based on gadolinium deposition in tissue. Noncontrast sequences have shown promise in MS diagnosis, but none differentiate acute from chronic MS lesions. We hypothesized that 3D T2 sampling perfection with application-optimized contrasts by using different flip angle evolution (SPACE) MR imaging can help detect and differentiate active-versus-chronic MS lesions without the need for IV contrast. In this single-center retrospective study, 340 spinal MR imaging cases of MS were collected in a 24-month period. Two senior neuroradiologists blindly and independently reviewed postcontrast T1-weighted sagittal and T2-SPACE sagittal images for the presence of MS lesions, associated cord expansion/atrophy on T2-SPACE, and enhancement on postcontrast T1WI. Discrepancies were resolved by consensus between the readers. Sensitivity, specificity, and accuracy of T2-SPACE compared with postcontrast T1WI were computed, and interobserver agreement was calculated. The sensitivity of lesion detection on T2-SPACE was 85.71%, 95% CI, 63.66%-96.95%; with a specificity of 93.52%, 95% CI, 90.06%-96.05%; and an accuracy of 92.99%, 95% CI, 89.58%-95.56. Additionally, 16/21 (84.2%) acute enhancing cord lesions showed cord expansion on T2-SPACE. The interobserver agreement was 92%. Our study shows that T2-SPACE facilitates noncontrast detection of acute MS lesions with high accuracy compared with postcontrast T1WI and with high interobserver agreement. The lack of gadolinium use provides an advantage, bypassing any potential adverse effects of repetitive contrast administration.

Dark Blood Contrast-Enhanced Brain MRI Using Echo-uT1RESS.

The widely used magnetization-prepared rapid gradient-echo (MPRAGE) sequence makes enhancing lesions and blood vessels appear bright after gadolinium administration. However, dark blood imaging using T1-weighted Sampling Perfection with Application optimized Contrast using different flip angle Evolution (T1 SPACE) can be advantageous since it improves the conspicuity of small metastases and leptomeningeal disease. As a potential alternative to T1 SPACE, we evaluated a new dark blood sequence called echo-uT1RESS (unbalanced T1 Relaxation-Enhanced Steady-State). We compared the performance of echo-uT1RESS with Dixon fid-uT1RESS, MPRAGE, and T1 SPACE. Retrospective, IRB approved. Phantom to assess flow properties of echo-uT1RESS. Twenty-one patients (14 female, age range 35-82 years) with primary and secondary brain tumors. 3 Tesla/MPRAGE, T1 SPACE, Dixon fid-uT1RESS, echo-uT1RESS. Flow phantom signal vs. velocity as a function of flip angle and sequence. Qualitative image assessment on 4-point scale. Quantitative evaluation of tumor-to-brain contrast, apparent contrast-to-noise ratio (aCNR), and vessel-to-brain aCNR. Friedman and Mann-Whitney U tests. A P value <0.05 was considered statistically significant. In the phantom, echo-uT1RESS showed greater flow-dependent signal loss than fid-uT1RESS. In patients, blood vessels appeared bright with MPRAGE, gray with fid-uT1RESS, and dark with T1 SPACE and echo-uT1RESS. For MPRAGE, Dixon fid-uT1RESS, echo-uT1RESS, and T1 SPACE, respective tumor-to-brain contrast values were 0.6 ± 0.3, 1.3 ± 0.5, 1.0 ± 0.4, and 0.6 ± 0.4, while normalized aCNR values were 68.9 ± 50.9, 128.4 ± 59.2, 74.2 ± 42.1, and 99.4 ± 73.9. Volumetric dark blood contrast-enhanced brain MRI is feasible using echo-uT1RESS. The dark blood effect was improved vs. fid-uT1RESS, while both uT1RESS versions provided better tumor-to-brain contrast than MPRAGE. Whereas T1 SPACE provided better tumor aSNR, echo-uT1RESS provided better Weber contrast, lesion sharpness and a more consistent dark blood effect. 3 TECHNICAL EFFICACY: Stage 1.

Open system model of choice and response time

Sequential sampling models have provided accurate accounts of people’s choice, response time, and preference strength in value-based decision-making tasks. Conventionally, these models are developed as Markov-type models (such as random walks or diffusion models) following the Kolmogorov axioms. Quantum probability theory has been proposed as an alternative framework upon which to develop models of cognition, including quantum random walk models. When modeling people’s behavior during decision-making tasks, previous work has demonstrated that both the Markov and quantum models have their respective strengths. Recently, the open system model, which is a hybrid version of the Markov and quantum models, has been shown to provide a more accurate account of preference strength compared to the Markov and quantum models in isolation. In this work, we extend the open system model to make predictions on pairwise choice and response time. We report a new experiment on preferential choice between gift cards, and we compare the fits of the open system model to the pure Markov and pure quantum random walk models using AIC, BIC, and χ2 tests. Although the pure Markov model was favored for most participants, a substantial number required the more complex open system model.

Comparison of Contrast-Enhanced 3D Imaging with 2D Imaging in the Evaluation of Perianal Fistula at 3T: A Prospective Observational Study.

Introduction Perianal fistula and its recurrence is a challenging entity for surgeons. It is a well-establi1shed fact that magnetic resonance imaging (MRI) findings influence surgical procedures and reduce the rate of recurrence. In this study, we assessed the contrast-enhanced (CE) three dimensional T1 sequences [sampling perfection with application optimized contrast using different flip angle evolution (SPACE) and volumetric interpolated breath-hold examination (VIBE)] in a 3T MRI system to evaluate perianal fistulas and compared them with two-dimensional (2D) sequences. Materials and Methods Forty-four patients (mean age, 38.8 ± 15.3 [standard deviation]; 32 males, 12 females) with perianal fistula were included in this prospective study. The patients underwent conventional noncontrast, 2D sequences, diffusion-weighted imaging, followed by postcontrast, 2D T1 images in both axial and coronal planes, and 3D sequences at 3T. Acquisition times were recorded for each sequence. Each postcontrast sequence was evaluated in terms of image quality, presence of artifacts, fistula type, presence of an abscess, visibility, and number of internal orifices. The surgical findings were considered the gold standard. The imaging findings were compared with the surgical findings. Results In all three sequences, the fistula type and abscess were identified correctly in all patients. The sensitivity value for identification of ramifications utilizing CE 3D T1 VIBE sequence, CE 3D T1 SPACE, and CE 2D T1 images was 100, 86, and 36%, respectively. The number of internal orifices was identified by the CE 3D T1 VIBE and CE 3D T1 SPACE sequences in 100 and 92% of patients, respectively. CE 2D T1 images correctly identified internal orifices in 80% of patients. The overall scan time for each 3D sequence was shorter than for the combined postcontrast 2D sequences. Conclusion CE 3D T1 SPACE and CE 3D T1 VIBE sequences outperformed conventional CE 2D sequences in the evaluation of perianal fistulas in terms of visibility and the number of internal orifices with a shorter scanning time. Among the 3D sequences, CE 3D T1 VIBE is slightly superior to CE 3D T1 SPACE sequence.

The value of 3D T2-weighted SPACE sequence in the differential diagnosis of spinal arteriovenous fistula and acute transverse myelitis.

Spinal arteriovenous fistulas (SAVF) was often neglected and misdiagnosed as acute transverse myelitis (ATM) due to its insidious onset and non-specific clinical symptoms. This study aims to investigate the differential diagnostic value of high-resolution T2-weighted volumetric sequence (3D sampling perfection with application-optimized contrasts using different flip-angle evolutions [SPACE]) in patients with SAVF and ATM. Retrospectively analyzed the clinical and radiological findings of 32 SDAVF patients and 32 ATM patients treated at our institutions from May 2018 to January 2023. They all underwent conventional spinal MRI and T2-SPACE examination, compared their performance in identifying lesions, to estimate the value of T2 SPACE sequence in the diagnosis of SAVF and ATM patients. The clue of cauda equina area change (CEAC) in conventional MRI and T2-SPACE sequences is specific for the diagnosis of SAVF. The diagnostic model composed of perimedullary flow voids (PFV) and CEAC has good diagnostic performance (AUCMRI = 0.95; AUCSPACE = 0.935). Compared with conventional MRI, the T2-SPACE sequence has a higher detection rate, sensitivity, and negative predictive value for PFV and CEAC in SAVF patients, but lower specificity and positive predictive value. In T2-SPACE images, there are significant differences in the distribution range, quadrant, and maximum diameter of PFV vessels between SAVF and ATM patients. Moreover, T2-SPACE sequence can determine the site of fistula in most SAVF patients preferably, and the inter-rater agreement was good in the assessment of the fistula. The CEAC is a new and useful clue for the diagnosis of thoracolumbar SAVF. And T2-SPACE sequence can more intuitively observe the lesions of SAVF, has good differential diagnostic value for SAVF and ATM patients.

Informasi Anatomi Mri Knee Joint Sekuen T2 Space FS dan PD Space FS pada Potongan Sagital Dengan Klinis Ruptur Anterior Cruciate Ligament (ACL)

Background: The T2 and PD sequences are the most sensitive sequences in evaluating injury to the ACL and surrounding soft tissue. Based on observations at the Radiology Installation of Dr. Sardjito Hospital Yogyakarta, the anatomical information generated in the MRI knee joint examination of the PD SPACE FS sequence is almost the same as the T2 SPACE FS sequence. The purpose of this study is to determine the differences in anatomical information and optimal sequences on MRI examination of the knee joint sagittal section sequences of PD SPACE FS and T2 SPACE FS in clinical ACL rupture.Method: This research was a quantitative study with an experimental approach, carried out at the Radiology Installation of Dr. Sardjito Hospital Yogyakarta on 10 samples with the application of different sequences for each sample, with the anatomy assessed by the informant namely ACL, meniscus, articular cartilage, and bone marrow. Further data analysis was carried out using the Wilcoxon test. Result: There was a difference in anatomical information between PD SPACE FS sequences and T2 SPACE FS sequences on MRI examination of the sagittal knee joint with clinical ACL rupture, with the ρ-value of the Wilcoxon test 0.001 or ρ-value0.05. This was due to differences in the use of TR and TE parameters in each sequence. The PD SPACE FS sequence was more optimal in visualizing anatomical information than the T2 SPACE FS sequence with an anatomical mean rank of meniscus 3.50, articular cartilage 3.50, and bone marrow 5.50, whereas in ACL anatomy the mean rank value was the same between the two sequences, which is 2.00. Conclusion: It was because the PD SPACE FS sequence had a more heterogeneous contrast difference than the T2 SPACE FS sequence so each anatomy could be well evaluated in the PD SPACE FS sequence.

To explore the pathogenesis of Bell's palsy using diffusion tensor image

To explore the pathogenesis of Bell's palsy using the diffusion tensor image on 3.0 T MR. The healthy people and the patients with Bell's palsy underwent intraparotid facial nerve scanning by using the DTI and T1 structural sequence at 3.0 T MR. The raw DTI data were performed affine transformation and nonlinear registration in the common MNI152_T1 space and resampled to the 0.4 mm3 voxel size. A group of 4 spherical seed regions were placed on the intratemporal facial nerves in the common space, bilaterally and symmetrically. The DTI data in the common space were used to track the intratemporal facial nerve fibers by using TrackVis and its Diffusion Toolkit. Each tractography was used to construct the maximum probability map (MPM) according to the majority rule. The fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD) and radial diffusivity (RD) were calculated and extracted on the basis of MPM. For healthy people, there was no significant difference in FA, MD, RD and AD of bilateral facial nerves. For patients with Bell's palsy, there was no significant difference in AD, there was significant difference in FA, MD and RD between the affected nerve and the healthy nerve (P < 0.02). This study showed that the myelin sheath injury of the intratemporal facial nerve is the main cause of Bell's palsy. Most neural axons are not damaged. The results may explain the pathogenesis of the Bell's palsy, which is self-limited for most cases.

Reliability of High-resolution Gadolinium-enhanced MR Cisternography and Gasket-seal Technique for Management of Anterior Skull Base Defects

PurposePrecise preoperative localization of anterior skull base defects is important to plan surgical access, increase the success rate and reduce complications. A stable closure of the defect is vital to prevent recurrence of cerebrospinal fluid (CSF) rhinorrhea. The purpose of this retrospective case series was to evaluate the reliability of a new high-resolution gadolinium-enhanced compressed-sensing SPACE technique (CS T1 SPACE) for magnetic resonance (MR) cisternography to detect cerebrospinal fluid leaks of the anterior skull base and to assess the long-term success rate of the gasket-seal technique for closure of skull base defects.MethodAll patients with spontaneous or postoperative cerebrospinal fluid rhinorrhea and defects of the anterior skull base presenting to the Departments of Otorhinolaryngology and Neurosurgery between 2019 and 2020, receiving a computed tomography (CT) cisternography and MR cisternography (on a 3T whole-body MR scanner using a 64-channel head and neck coil) with CS T1 SPACE sequence and closure of the defect with the gasket-seal technique, were enrolled in the study. For the cisternography, iodinated contrast agent (15 ml Solutrast 250 M®), saline (4 mL) mixed with a 0.5 mL of gadoteridol was injected into the lumbar subarachnoid space.ResultsA total of four patients were included in the study and MR cisternography with CS T1 SPACE sequence was able to precisely localize CSF leaks in all patients. The imaging results correlated with intraoperative findings. All defects could be successfully closed with the gasket-seal technique. The mean follow-up was 35.25 months (range 33–37 months).ConclusionMR cisternography with CS T1 SPACE sequence could be a promising technique for precise localization of CSF leaks and the gasket-seal technique resulted in good closure of the CSF fistula in this case series.

An optimized 1.5 Tesla MRI protocol of the brachial plexus.

Creating an effective MRI protocol for examining the brachial plexus poses significant challenges, and despite the abundance of protocols in the literature, there is a lack of reference standards for basic sequences and essential parameters needed for replication. The aim of this study is to establish a reproducible 1.5 T brachial plexus imaging protocol, including patient positioning, coil selection, imaging planes, and essential sequence parameters. We systematically investigated MRI sequences, testing each parameter through in vivo experiments, examining their effects on signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), visual quality scores, and acquisition time. Sequences were refined based on optimal quality and timing scores. The final protocol was tested on scanners from two other vendors for reliability. The final protocol included a combination of 2D turbo-spin-echo and 3D SPACE T1, SPACE STIR, and VIBE DIXON sequences. Recommendations for imaging planes, phase encoding, field of view, TR, TE, resolution, number of slices, slice thickness, fat and blood suppression, and acceleration strategies are provided. The protocol was successfully translated to other vendor's scanners with comparable quality. We present an optimized protocol detailing the essential parameters for reproducibility. Our comprehensive list of experiments describes the impact of each parameter on image quality and scan time, addressing common artifacts and potential solutions. This protocol can benefit both young radiologists new to the field and experienced professionals seeking to refine their existing protocols.

Characterizations of Some Topological Spaces

This paper is concerned with the concepts of some topological spaces. Firstly, we introduce the notions of δs(Λ, p)-open sets. Some properties concerning δs(Λ, p)-open sets are discussed. Secondly, the concept of s(Λ, p)-connected spaces is introduced. Moreover, we give several characterizations of s(Λ, p)-connected spaces by utilizing δs(Λ, p)-open sets. Thirdly, we apply the notion of s(Λ, p)-open sets to present and study new classes of spaces called s(Λ, p)-regular spaces and s(Λ, p)-normal spaces. Especially, some characterizations of s(Λ, p)-regular spaces and s(Λ, p)-normal spaces are established. Fourthly, we introduce and investigate the concepts of s(Λ, p)-T2 spaces and s(Λ, p)-Urysohn spaces. Finally, the notion of S(Λ, p)-closed spaces is studied. Basic properties and characterizations of S(Λ, p)-closed spaces are considered.

On Hausdorff operators in ZF$\mathsf {ZF}$

AbstractA Hausdorff space is called effectively Hausdorff if there exists a function F—called a Hausdorff operator—such that, for every with , , where U and V are disjoint open neighborhoods of x and y, respectively. Among other results, we establish the following in , i.e., in Zermelo–Fraenkel set theory without the Axiom of Choice (): is equivalent to “For every set X, the Cantor cube is effectively Hausdorff”. This enhances the result of Howard, Keremedis, Rubin and Rubin [13] that is equivalent to “Hausdorff spaces are effectively Hausdorff” in . The Boolean Prime Ideal Theorem and the statement “For every infinite set X, the Stone space of the Boolean algebra is effectively Hausdorff” are mutually independent. In particular, the latter statement is not provable in . The Axiom of Choice for non‐empty subsets of () is equivalent to each of “Separable Hausdorff spaces are effectively Hausdorff” and “The Cantor cube is effectively Hausdorff”. The Principle of Dependent Choices in conjunction with the Axiom of Choice for continuum sized families of non‐empty subsets of does not imply the axiom of choice for partitions of . The latter independence result fills the gap in information in Howard and Rubin's book “Consequences of the Axiom of Choice”. The axiom of countable choice for non‐empty subsets of is equivalent to each of “Denumerable Hausdorff spaces are effectively Hausdorff”, “Denumerable T3 spaces are completely normal” and “Denumerable Tychonoff spaces are Urysohn”.