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INTRODUCTION: In this work, we aim to assess the significance of diffusion tensor imaging (DTI) and diffusion kurtosis imaging (DKI) parameters in grading gliomas. METHODS: Retrospective studies were performed on 53 subjects with gliomas belonging to WHO grade II (n = 19), grade III (n = 20) and grade IV (n = 14). Expert marked regions of interest (ROIs) covering the tumour on T2-weighted images. Statistical texture measures such as entropy and busyness calculated over ROIs on diffusion parametric maps were used to assess the tumour heterogeneity. Additionally, we propose a volume heterogeneity index derived from cross correlation (CC) analysis as a tool for grading gliomas. The texture measures were compared between grades by performing the Mann-Whitney test followed by receiver operating characteristic (ROC) analysis for evaluating diagnostic accuracy. RESULTS: Entropy, busyness and volume heterogeneity index for all diffusion parameters except fractional anisotropy and anisotropy of kurtosis showed significant differences between grades. The Mann-Whitney test on mean diffusivity (MD), among DTI parameters, resulted in the highest discriminability with values of P = 0.029 (0.0421) for grade II vs. III and P = 0.0312 (0.0415) for III vs. IV for entropy (busyness). In DKI, mean kurtosis (MK) showed the highest discriminability, P = 0.018 (0.038) for grade II vs. III and P = 0.022 (0.04) for III vs. IV for entropy (busyness). Results of CC analysis illustrate the existence of homogeneity in volume (uniformity across slices) for lower grades, as compared to higher grades. Hypothesis testing performed on volume heterogeneity index showed P values of 0.0002 (0.0001) and 0.0003 (0.0003) between grades II vs. III and III vs. IV, respectively, for MD (MK). CONCLUSION: In summary, the studies demonstrated great potential towards automating grading gliomas by employing tumour heterogeneity measures on DTI and DKI parameters.
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Neoplasias Encefálicas/diagnóstico por imagem , Neoplasias Encefálicas/patologia , Imagem de Tensor de Difusão/métodos , Glioma/diagnóstico por imagem , Glioma/patologia , Interpretação de Imagem Assistida por Computador/métodos , Adolescente , Adulto , Idoso , Criança , Pré-Escolar , Feminino , Humanos , Masculino , Pessoa de Meia-Idade , Gradação de Tumores , Reconhecimento Automatizado de Padrão/métodos , Reprodutibilidade dos Testes , Sensibilidade e Especificidade , Adulto JovemRESUMO
Performing group analysis on magnetic resonance imaging (MRI) data with linear mixed-effects (LME) models is challenging due to its large dimensionality and inherent multi-level covariance structure. In addition, as large-scale collaborative projects become commonplace in neuroimaging, data must increasingly be stored and analyzed from different locations. In such settings, substantial overhead can occur in terms of data transfer and coordination between participating research groups. In some cases, data cannot be pooled together due to privacy or regulatory concerns. In this work, we propose a decentralized LME model to perform a large-scale analysis of data from different collaborations without data pooling. This method is efficient as it overcomes the hurdles of data sharing and has lower bandwidth and memory requirements for analysis than the centralized modeling approach. We evaluate our model using features extracted from structural magnetic resonance imaging (sMRI) data. Results highlight gray matter reductions in the temporal lobe/insula and medial frontal regions in schizophrenia, consistent with prior studies. Our analysis also demonstrates that decentralized LME models achieve similar performance compared to the models trained with all the data in one location. We also implement the decentralized LME approach in COINSTAC, an open source, decentralized platform for federating neuroimaging analysis, providing an easy to use tool for dissemination to the neuroimaging community.
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Neuroimagem , Esquizofrenia , Humanos , Neuroimagem/métodos , Imageamento por Ressonância Magnética/métodos , Substância Cinzenta , Modelos LinearesRESUMO
BrainForge is a cloud-enabled, web-based analysis platform for neuroimaging research. This website allows users to archive data from a study and effortlessly process data on a high-performance computing cluster. After analyses are completed, results can be quickly shared with colleagues. BrainForge solves multiple problems for researchers who want to analyze neuroimaging data, including issues related to software, reproducibility, computational resources, and data sharing. BrainForge can currently process structural, functional, diffusion, and arterial spin labeling MRI modalities, including preprocessing and group level analyses. Additional pipelines are currently being added, and the pipelines can accept the BIDS format. Analyses are conducted completely inside of Singularity containers and utilize popular software packages including Nipype, Statistical Parametric Mapping, the Group ICA of fMRI Toolbox, and FreeSurfer. BrainForge also features several interfaces for group analysis, including a fully automated adaptive ICA approach.
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BACKGROUND AND PURPOSE: Sleep quality is important for healthy growth and development of children. We aimed to identify associations between sleep disturbances in healthy children without clinical diagnosis of sleep disorders and brain white matter (WM) microstructure using an advanced diffusion-weighted magnetic resonance imaging (DW-MRI) based tractography analysis, and to explore whether there are sex differences in these associations. METHODS: Brain DW-MRI data were collected from sixty-two 8-year-old children (28 boys, 34 girls) whose parents also completed Children's Sleep Habits Questionnaire (CSHQ). Track-weighted imaging (TWI) measures were computed from the DW-MRI data for 37 WM tracts in each subject. Sex-specific partial correlation analyses were performed to evaluate correlations between TWI measures and a set of sleep disturbance scores derived from the CSHQ. RESULTS: Significant correlations (P < .05, FDR-corrected; r: .48-.67) were identified in 13 WM tracts between TWI and sleep disturbance scores. Sexually dimorphic differences in correlations between sleep disturbance scores and WM microstructure measurements were observed. Specifically, in boys, daytime sleepiness positively correlated with track-weighted mean or radial diffusivity in 10 WM tracts (bilateral arcuate fasciculus, left cingulum, right middle longitudinal fasciculus, and three bilateral segments of superior longitudinal fasciculus). In girls, total CSHQ score, night walking, or sleep onset delay negatively correlated with track-weighted fractional anisotropy or axial diffusivity in 4 WM tracts (bilateral inferior longitudinal fasciculus and uncinate fasciculus). CONCLUSIONS: The findings suggest that sleep disturbances without clinical diagnosis of sleep disorders are associated with lower WM microstructural integrity in children. Additionally, the associations possess unique patterns in boys and girls.
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Transtornos do Sono-Vigília , Substância Branca , Anisotropia , Encéfalo/diagnóstico por imagem , Criança , Imagem de Difusão por Ressonância Magnética , Imagem de Tensor de Difusão/métodos , Feminino , Humanos , Masculino , Qualidade do Sono , Transtornos do Sono-Vigília/diagnóstico por imagem , Transtornos do Sono-Vigília/patologia , Substância Branca/diagnóstico por imagem , Substância Branca/patologiaRESUMO
PURPOSE: Quantitative tractography using diffusion-weighted magnetic resonance imaging data is widely used in characterizing white matter microstructure throughout childhood, but more studies are still needed to investigate comprehensive brain-behavior relationships between tract-specific white matter measures and multiple cognitive functions in children. METHODS: In this study, we analyzed diffusion-weighted MRI data of 71 healthy 8-year-old children utilizing white matter tract-specific quantitative measures derived from diffusion-weighted MRI tractography based on a novel track-weighted imaging approach. Track density imaging, average path length map and 4 track-weighted diffusion tensor imaging measures including: mean diffusivity, fractional anisotropy, axial diffusivity, and radial diffusivity were computed for 63 white matter tracts. The track-weighted imaging measures were then correlated with a comprehensive set of neuropsychological test scores in different cognitive domains including intelligence, language, memory, academic skills, and executive functions to identify tract-specific brain-behavior relationships. RESULTS: Significant correlations (P < .05, false discovery rate corrected; r = 0.27-0.57) were found in multiple white matter tracts, with a total of 40 correlations identified between various track-weighted imaging measures including average path length map, track-weighted imaging-fractional anisotropy, and neuropsychological test scores and subscales. Specifically, track-weighted imaging measures indicative of better white matter connectivity and/or microstructural development significantly correlated with higher IQ and better language abilities. CONCLUSION: Our findings demonstrate the ability of track-weighted imaging measures in establishing associations between white matter and cognitive functioning in healthy children and can serve as a reference for normal brain/cognition relationships in young school-age children and further aid in identifying imaging biomarkers predictive of adverse neurodevelopmental outcomes.
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Substância Branca , Anisotropia , Encéfalo/diagnóstico por imagem , Criança , Cognição , Imagem de Difusão por Ressonância Magnética/métodos , Imagem de Tensor de Difusão/métodos , Humanos , Substância Branca/diagnóstico por imagemRESUMO
Structural substrates of sex differences in human function and behavior have been elucidated in previous studies. Diffusion weighted magnetic resonance imaging (DW-MRI) is a widely used non-invasive imaging technique in studying human brain white matter structural organization. While many DW-MRI studies reporting sex differences in WM structure are based on diffusion tensor imaging (DTI) measures, tract specific microstructural differences require further investigation. In this study, we aim to investigate sex differences and sex-specific hemispheric differences in white matter microstructural development in healthy 8-year-old children based on novel track weighted imaging (TWI) analysis. Average pathlength map (APM) is a TWI contrast in which the average length of fibers passing through a voxel is utilized. In this study, we employed tract specific APM measures to evaluate sex differences in WM microstructural development. A total of 37 WM tracts were analyzed including 7 commissural tracts, 9 bilateral association tracts and 6 bilateral projection tracts. APM maps were generated for each tract. Tract-wise group tests were done using the mean values of APM maps. Sex differences were tested using general linear model based group comparisons. Age and total brain volume were included as covariates in the group analysis. Sex specific hemispheric differences were performed for the 15 bilateral tracts. One sample t-tests were done independently for left>right and right>left cases and the APM measures were controlled for age and total cerebral hemispheric volume. P-values<0.05 were considered significant after correcting for multiple comparisons accounting for the total number of tracts. Significant sex differences were revealed in APM measures between boys and girls in 11 WM tracts including rostral body of corpus callosum (CC), left inferior fronto-occipital fasciculus (IFOF), right cingulum, bilateral first and second segments of superior longitudinal fasciculus (SLF), right middle longitudinal fasciculus (MLF), bilateral fronto-pontine (FPT) and right parieto-occipital pontine tracts (POPT). The sex differences showed higher APM values for these 11 tracts in boys as compared to that of girls. In hemispheric differences analysis for both boys and girls, 2 tracts, arcuate fasciculus and optic radiation showed higher APM in left tracts as compared right; 5 tracts, IFOF, MLF, third segment of SLF, FPT and superior thalamic radiation showed higher APM in right tracts as compared to left. This indicates that boys and girls possess similar lateral asymmetries in these 7 tracts. Additionally, anterior thalamic radiation (ATR) showed higher APM in left tract and 4 tracts, first segment of SLF, POPT, inferior longitudinal fasciculus and cortico-spinal tract showed higher APM in right for boys. In girls, second segment of SLF and uncinate fasciculus showed higher APM in right hemisphere. These results indicate different lateral asymmetries between boys and girls for 7 tracts. Overall, boys showed higher average fiber length in most of the tracts, even after controlling for total brain volume.
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Recent studies have demonstrated that neuroimaging data can be used to estimate biological brain age, as it captures information about the neuroanatomical and functional changes the brain undergoes during development and the aging process. However, researchers often have limited access to neuroimaging data because of its challenging and expensive acquisition process, thereby limiting the effectiveness of the predictive model. Decentralized models provide a way to build more accurate and generalizable prediction models, bypassing the traditional data-sharing methodology. In this work, we propose a decentralized method for biological brain age estimation using support vector regression models and evaluate it on three different feature sets, including both volumetric and voxelwise structural MRI data as well as resting functional MRI data. The results demonstrate that our decentralized brain age regression models can achieve similar performance compared to the models trained with all the data in one location.
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Encéfalo , Imageamento por Ressonância Magnética , Imageamento por Ressonância Magnética/métodos , Encéfalo/diagnóstico por imagem , Neuroimagem/métodosRESUMO
Background: Physical activity is known to improve mental health, and is regarded as safe and desirable for uncomplicated pregnancy. In this novel study, we aim to evaluate whether there are associations between maternal physical activity during pregnancy and neonatal brain cortical development. Methods: Forty-four mother/newborn dyads were included in this longitudinal study. Healthy pregnant women were recruited and their physical activity throughout pregnancy were documented using accelerometers worn for 3-7 days for each of the 6 time points at 4-10, â¼12, â¼18, â¼24, â¼30, and â¼36 weeks of pregnancy. Average daily total steps and daily total activity count as well as daily minutes spent in sedentary/light/moderate/vigorous activity modes were extracted from the accelerometers for each time point. At â¼2 weeks of postnatal age, their newborns underwent an MRI examination of the brain without sedation, and 3D T1-weighted brain structural images were post-processed by the iBEAT2.0 software utilizing advanced deep learning approaches. Cortical surface maps were reconstructed from the segmented brain images and parcellated to 34 regions in each brain hemisphere, and mean cortical thickness for each region was computed for partial correlation analyses with physical activity measures, with appropriate multiple comparison corrections and potential confounders controlled. Results: At 4-10 weeks of pregnancy, mother's daily total activity count positively correlated (FDR corrected P ≤ 0.05) with newborn's cortical thickness in the left caudal middle frontal gyrus (rho = 0.48, P = 0.04), right medial orbital frontal gyrus (rho = 0.48, P = 0.04), and right transverse temporal gyrus (rho = 0.48, P = 0.04); mother's daily time in moderate activity mode positively correlated with newborn's cortical thickness in the right transverse temporal gyrus (rho = 0.53, P = 0.03). At â¼24 weeks of pregnancy, mother's daily total activity count positively correlated (FDR corrected P ≤ 0.05) with newborn's cortical thickness in the left (rho = 0.56, P = 0.02) and right isthmus cingulate gyrus (rho = 0.50, P = 0.05). Conclusion: We identified significant relationships between physical activity in healthy pregnant women during the 1st and 2nd trimester and brain cortical development in newborns. Higher maternal physical activity level is associated with greater neonatal brain cortical thickness, presumably indicating better cortical development.
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Brain age estimation is a widely used approach to evaluate the impact of various neurological or psychiatric brain disorders on the brain developmental or aging process. Current studies show that neuroimaging data can be used to predict brain age, as it captures structural and functional changes that the brain undergoes during development and the aging process. A robust brain age prediction model not only has the potential in assisting early diagnosis of brain disorders but also helps in monitoring and evaluating effects of a treatment. Although access to large amounts of data helps build better models and validate their effectiveness, researchers often have limited access to brain data because of its challenging and expensive acquisition process. This data is not always sharable due to privacy restrictions. Decentralized models provide a way which does not require data exchange between the multiple involved groups. In this work, we propose a decentralized approach for brain age prediction and evaluate our models using features extracted from structural MRI data. Results demonstrate that our decentralized brain age model achieves similar performance compared to the models trained with all the data in one location.
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Encefalopatias , Neuroimagem , Encéfalo/diagnóstico por imagem , Humanos , Imageamento por Ressonância MagnéticaRESUMO
Cortical asymmetry and functional lateralization form intriguing and fundamental features of human brain organization, and is complicated by individual differences and evolvement with age. While many studies have investigated neuroanatomical differences between hemispheres as well as functional lateralization of the brain for different age groups, few have looked into the associations between cortical asymmetry and development of cognitive functions in children. In this study, we aimed to identify relationships between hemispheric asymmetry in brain cortex measured by MRI and cognitive development in healthy young children evaluated by a comprehensive battery of neuropsychological tests. Structural MRI data were obtained from 71 children in the age range of 7.5 to 8.5 years. Structural lateralization index (SLI), a reflection of the brain asymmetry, was computed for each of the 3 cortical morphometry measurements: cortical thickness, surface area and gray matter volume. A total of 34 bilateral regions were studied for the whole brain cortex as defined by the Desikan atlas. Region-wise SLI was correlated with domain specific cognitive scores using partial correlation analysis controlled for the potential confounding effects of age and sex. Significant correlations were identified between test scores of multiple cognitive domains and SLI of several cortical regions. Specifically, SLI of total surface area of precuneus and insula significantly correlated with measures of executive function behavior; significant relationships were also found between SLI of mean cortical thickness of superior parietal cortex and memory and language tests scores; in addition, SLI of parahippocampal gyrus also showed significant correlations with language test scores for all 3 morphometry features. These findings revealed regional hemispheric asymmetries that may be linked to specific cognitive abilities in children.Clinical relevance- This study shows associations between structural lateralization in different brain cortical regions and variations in specific cognitive functions in healthy children.
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Cognição , Imageamento por Ressonância Magnética , Encéfalo , Mapeamento Encefálico , Criança , Pré-Escolar , Humanos , IdiomaRESUMO
INTRODUCTION: Subcortical ischemic vascular disease (SIVD) and Alzheimer's disease (AD) related dementia can coexist in older subjects, leading to mixed dementia (MX). Identification of dementia sub-groups is important for designing proper treatment plans and clinical trials. METHOD: An Alzheimer's disease severity (ADS) score and a vascular disease severity (VDS) score are calculated from CSF and MRI biomarkers, respectively. These scores, being sensitive to different Alzheimer's and vascular disease processes are combined orthogonally in a double-dichotomy plot. This formed an objective basis for clustering the subjects into four groups, consisting of AD, SIVD, MX and leukoaraiosis (LA). The relationship of these four groups is examined with respect to cognitive assessments and clinical diagnosis. RESULTS: Cluster analysis had at least 83% agreement with the clinical diagnosis for groups based either on Alzheimer's or on vascular sensitive biomarkers, and a combined agreement of 68.8% for clustering the four groups. The VDS score was correlated to executive function (r = -0.28, p < 0.01) and the ADS score to memory function (r = -0.35, p < 0.002) after adjusting for age, sex, and education. In the subset of patients for which the cluster scores and clinical diagnoses agreed, the correlations were stronger (VDS score-executive function: r = -0.37, p < 0.006 and ADS score-memory function: r = -0.58, p < 0.0001). CONCLUSIONS: The double-dichotomy clustering based on imaging and fluid biomarkers offers an unbiased method for identifying mixed dementia patients and selecting better defined sub-groups. Differential correlations with neuropsychological tests support the hypothesis that the categories of dementia represent different etiologies.
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BACKGROUND: Vascular cognitive impairment and dementia (VCID) and Alzheimer's disease are predominant diseases among the aging population resulting in decline of various cognitive domains. Diffusion weighted MRI (DW-MRI) has been shown to be a promising aid in the diagnosis of such diseases. However, there are various models of DW-MRI and the interpretation of diffusion metrics depends on the model used in fitting data. Most previous studies are entirely based on parameters calculated from a single diffusion model. NEW METHOD: We employ a data fusion framework wherein diffusion metrics from different models such as diffusion tensor imaging, diffusion kurtosis imaging and constrained spherical deconvolution model are fused using well known blind source separation approach to investigate white matter microstructural changes in population comprising of controls and VCID subgroups. Multiple comparisons between subject groups and prediction analysis using features from individual models and proposed fusion model are carried out to evaluate performance of proposed method. RESULTS: Diffusion features from individual models successfully distinguished between controls and disease groups, but failed to differentiate between disease groups, whereas fusion approach showed group differences between disease groups too. WM tracts showing significant differences are superior longitudinal fasciculus, anterior thalamic radiation, arcuate fasciculus, optic radiation and corticospinal tract. COMPARISON WITH EXISTING METHOD: ROC analysis showed increased AUC for fusion (AUC = 0.913, averaged across groups and tracts) compared to that of uni-model features (AUC = 0.77) demonstrating increased sensitivity of proposed method. CONCLUSION: Overall our results highlight the benefits of multi-model fusion approach, providing improved sensitivity in discriminating VCID subgroups.
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Disfunção Cognitiva , Substância Branca , Idoso , Imagem de Difusão por Ressonância Magnética , Imagem de Tensor de Difusão , Humanos , Tratos Piramidais , Substância Branca/diagnóstico por imagemRESUMO
Diffusion MRI studies characterizing the changes in white matter (WM) due to vascular cognitive impairment, which includes all forms of small vessel disease are reviewed. We reviewed the usefulness of diffusion methods in discriminating the affected WM regions and its relation to cognitive impairment. These studies were categorized based on the diffusion MRI techniques used. The most common method was the diffusion tensor imaging, whereas other methods included diffusion weighted imaging, diffusion kurtosis imaging, intravoxel incoherent motion, and studies based on diffusion tractography. The diffusion measures showed correlation with cognitive scores and disease progression, with mean diffusivity being the most robust parameter. Future studies should focus on incorporating multi-compartment and higher order diffusion models, which can handle the presence of multiple and crossing fibers inside a voxel.
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Imagem de Difusão por Ressonância Magnética , Leucoencefalopatias/diagnóstico por imagem , Leucoencefalopatias/patologia , Anisotropia , Doenças de Pequenos Vasos Cerebrais/complicações , Doença Crônica , Disfunção Cognitiva/complicações , Demência Vascular , Imagem de Tensor de Difusão , Humanos , Leucoencefalopatias/complicaçõesRESUMO
Alzheimer's disease (AD) and vascular cognitive impairment and dementia (VCID) are major causes of dementia, and when combined lead to accelerated cognitive loss. We hypothesized that biomarkers of neurodegeneration and neuroinflammation could be used to stratify patients into diagnostic groups. Diagnosis of AD can be made biologically with detection of amyloid and tau proteins in the cerebrospinal fluid (CSF) and vascular disease can be identified with diffusion tensor imaging (DTI). We recruited patients with cognitive complaints and made an initial clinical diagnosis. After one year of follow-up we made a biological diagnosis based on the use of biomarkers obtained from DTI, CSF AD, and inflammatory proteins, and neuropsychological testing. Patients with AD had primarily findings of neurodegeneration (CSF showing increased tau and reduced amyloid), while patients with neuroinflammation had abnormal DTI mean diffusion (MD) in the white matter. Using the biological biomarkers resulted in many of the clinically diagnosed AD patients moving into mixed dementia (MX). Biomarkers of inflammation tended to be higher in the MX than in either the AD or VCID, suggesting dual pathology leads to increased inflammation, which could explain accelerated cognitive decline in that group.
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Blood-brain barrier (BBB) separates the systemic circulation and the brain, regulating transport of most molecules to protect the brain microenvironment. Multiple structural and functional components preserve the integrity of the BBB. Several imaging modalities are available to study disruption of the BBB. However, the subtle changes in BBB leakage that occurs in vascular cognitive impairment and Alzheimer's disease have been less well studied. Dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) is the most widely adopted non-invasive imaging technique for evaluating BBB breakdown. It is used as a significant marker for a wide variety of diseases with large permeability leaks, such as brain tumors and multiple sclerosis, to more subtle disruption in chronic vascular disease and dementia. DCE-MRI analysis of BBB includes both model-free parameters and quantitative parameters using pharmacokinetic modelling. We review MRI studies of BBB breakdown in dementia. The challenges in measuring subtle BBB changes and the state of the art techniques are initially examined. Subsequently, a systematic review comparing methodologies from recent in-vivo MRI studies is presented. Various factors related to subtle BBB permeability measurement such as DCE-MRI acquisition parameters, arterial input assessment, T1 mapping and data analysis methods are reviewed with the focus on finding the optimal technique. Finally, the reported BBB permeability values in dementia are compared across different studies and across various brain regions. We conclude that reliable measurement of low-level BBB permeability across sites remains a difficult problem and a standardization of the methodology for both data acquisition and quantitative analysis is required. This article is part of the Special Issue entitled 'Cerebral Ischemia'.
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Barreira Hematoencefálica/diagnóstico por imagem , Barreira Hematoencefálica/fisiopatologia , Demência/diagnóstico por imagem , Imageamento por Ressonância Magnética , Animais , HumanosRESUMO
The critical challenge in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is the trade-off between spatial and temporal resolution due to the limited availability of acquisition time. To address this, it is imperative to under-sample k-space and to develop specific reconstruction techniques. Our proposed method reconstructs high-quality images from under-sampled dynamic k-space data by proposing two main improvements; i) design of an adaptive k-space sampling lattice and ii) edge-enhanced reconstruction technique. A high-resolution data set obtained before the start of the dynamic phase is utilized. The sampling pattern is designed to adapt to the nature of k-space energy distribution obtained from the static high-resolution data. For image reconstruction, the well-known compressed sensing-based total variation (TV) minimization constrained reconstruction scheme is utilized by incorporating the gradient information obtained from the static high-resolution data. The proposed method is tested on seven real dynamic time series consisting of 2 breast data sets and 5 abdomen data sets spanning 1196 images in all. For data availability of only 10%, performance improvement is seen across various quality metrics. Average improvements in Universal Image Quality Index and Structural Similarity Index Metric of up to 28% and 24% on breast data and about 17% and 9% on abdomen data, respectively, are obtained for the proposed method as against the baseline TV reconstruction with variable density random sampling pattern.