Magnetic resonance fingerprinting-based myelin water fraction mapping for the assessment of white matter maturation and integrity in typical development and leukodystrophies

A quantitative biomarker for myelination, such as myelin water fraction (MWF), would boost the understanding of normative and pathological neurodevelopment, improving patients' diagnosis and follow-up. We quantified the fraction of a rapidly relaxing pool identified as MW using multicomponent three-dimensional (3D) magnetic resonance fingerprinting (MRF) to evaluate white matter (WM) maturation in typically developing (TD) children and alterations in leukodystrophies (LDs). We acquired DTI and 3D MRF-based R1, R2 and MWF data of 15 TD children and 17 LD patients (9 months-12.5 years old) at 1.5 T. We computed normative maturation curves in corpus callosum and corona radiata and performed WM tract profile analysis, comparing MWF with R1, R2 and fractional anisotropy (FA). Normative maturation curves demonstrated a steep increase for all tissue parameters in the first 3 years of age, followed by slower growth for MWF while R1, R2R2 and FA reached a plateau. Unlike FA, MWF values were similar for regions of interest (ROIs) with different degrees of axonal packing, suggesting independence from fiber bundle macro-organization and higher myelin specificity. Tract profile analysis indicated a specific spatial pattern of myelination in the major fiber bundles, consistent across subjects. LD were better distinguished from TD by MWF rather than FA, showing reduced MWF with respect to age-matched controls in both ROI-based and tract analysis. In conclusion, MRF-based MWF provides myelin-specific WM maturation curves and is sensitive to alteration due to LDs, suggesting its potential as a biomarker for WM disorders. As MRF allows fast simultaneous acquisition of relaxometry and MWF, it can represent a valuable diagnostic tool to study and follow up developmental WM disorders in children.

Detection of pathological contrast enhancement with synthetic brain imaging from quantitative multiparametric MRI

BACKGROUND AND PURPOSE

We aimed to test whether synthetic T1-weighted imaging derived from a post-contrast Quantitative Transient-state Imaging (QTI) acquisition enabled revealing pathological contrast enhancement in intracranial lesions.

METHODS

The analysis included 141 patients who underwent a 3 Tesla-MRI brain exam with intravenous contrast media administration, with the post-contrast acquisition protocol comprising a three-dimensional fast spoiled gradient echo (FSPGR) sequence and a QTI acquisition. Synthetic T1-weighted images were generated from QTI-derived quantitative maps of relaxation times and proton density. Two neuroradiologists assessed synthetic and conventional post-contrast T1-weighted images for the presence and pattern of pathological contrast enhancement in intracranial lesions. Enhancement volumes were quantitatively compared.

RESULTS

Using conventional imaging as a reference, synthetic T1-weighted imaging was 93% sensitive in revealing the presence of contrast enhancing lesions. The agreement for the presence/absence of contrast enhancement was almost perfect both between readers (k = 1 for both conventional and synthetic imaging) and between sequences (k = 0.98 for both readers). In 91% of lesions, synthetic T1-weighted imaging showed the same pattern of contrast enhancement visible in conventional imaging. Differences in enhancement pattern in the remaining lesions can be due to the lower spatial resolution and the longer acquisition delay from contrast media administration of QTI compared to FSPGR. Overall, enhancement volumes appeared larger in synthetic imaging.

CONCLUSIONS

QTI-derived post-contrast synthetic T1-weighted imaging captures pathological contrast enhancement in most intracranial enhancing lesions. Further comparative studies employing quantitative imaging with higher spatial resolution is needed to support our data and explore possible future applications in clinical trials.

Fast high-resolution electric properties tomography using three-dimensional quantitative transient-state imaging-based water fraction estimation

In this study, we aimed to develop a fast and robust high-resolution technique for clinically feasible electrical properties tomography based on water content maps (wEPT) using Quantitative Transient-state Imaging (QTI), a multiparametric transient state-based method that is similar to MR fingerprinting. Compared with the original wEPT implementation based on standard spin-echo acquisition, QTI provides robust electrical properties quantification towards B1 + inhomogeneities and full quantitative relaxometry data. To validate the proposed approach, 3D QTI data of 12 healthy volunteers were acquired on a 1.5 T scanner. QTI-provided T1 maps were used to compute water content maps of the tissues using an empirical relationship based on literature ex-vivo measurements. Assuming that electrical properties are modulated mainly by tissue water content, the water content maps were used to derive electrical conductivity and relative permittivity maps. The proposed technique was compared with a conventional phase-only Helmholtz EPT (HH-EPT) acquisition both within whole white matter, gray matter, and cerebrospinal fluid masks, and within different white and gray matter subregions. In addition, QTI-based wEPT was retrospectively applied to four multiple sclerosis adolescent and adult patients, compared with conventional contrast-weighted imaging in terms of lesion delineation, and quantitatively assessed by measuring the variation of electrical properties in lesions. Results obtained with the proposed approach agreed well with theoretical predictions and previous in vivo findings in both white and gray matter. The reconstructed maps showed greater anatomical detail and lower variability compared with standard phase-only HH-EPT. The technique can potentially improve delineation of pathology when compared with conventional contrast-weighted imaging and was able to detect significant variations in lesions with respect to normal-appearing tissues. In conclusion, QTI can reliably measure conductivity and relative permittivity of brain tissues within a short scan time, opening the way to the study of electric properties in clinical settings.

Quantitative T1 mapping detects blood-brain barrier breakdown in apparently non-enhancing multiple sclerosis lesions

OBJECTIVES

The disruption of the blood-brain barrier (BBB) is a key and early feature in the pathogenesis of demyelinating multiple sclerosis (MS) lesions and has been neuropathologically demonstrated in both active and chronic plaques. The local overt BBB disruption in acute demyelinating lesions is captured as signal hyperintensity in post-contrast T1-weighted images because of the contrast-related shortening of the T1 relaxation time. On the contrary, the subtle BBB disruption in chronic lesions is not visible at conventional radiological evaluation but it might be of clinical relevance. Indeed, persistent, subtle BBB leakage might be linked to low-grade inflammation and plaque evolution. Here we hypothesised that 3D Quantitative Transient-state Imaging (QTI) was able to reveal and measure T1 shortening (ΔT1) reflecting small amounts of contrast media leakage in apparently non-enhancing lesions (ANELs).

MATERIALS AND METHODS

Thirty-four patients with relapsing remitting MS were included in the study. All patients underwent a 3 T MRI exam of the brain including conventional sequences and QTI acquisitions (1.1 mm isotropic voxel) performed both before and after contrast media administration. For each patient, a ΔT1 map was obtained via voxel-wise subtraction of pre- and post- contrast QTI-derived T1 maps. ΔT1 values measured in ANELs were compared with those recorded in enhancing lesions and in the normal appearing white matter. A reference distribution of ΔT1 in the white matter was obtained from datasets acquired in 10 non-MS patients with unrevealing MR imaging.

RESULTS

Mean ΔT1 in ANELs (57.45 ± 48.27 ms) was significantly lower than in enhancing lesions (297.71 ± 177.52 ms; p < 0. 0001) and higher than in the normal appearing white matter (36.57 ± 10.53 ms; p < 0.005). Fifty-two percent of ANELs exhibited ΔT1 higher than those observed in the white matter of non-MS patients.

CONCLUSIONS

QTI-derived quantitative ΔT1 mapping enabled to measure contrast-related T1 shortening in ANELs. ANELs exhibiting ΔT1 values that deviate from the reference distribution in non-MS patients may indicate persistent, subtle, BBB disruption. Access to this information may be proved useful to better characterise pathology and objectively monitor disease activity and response to therapy.

Generating Synthetic Radiological Images with PySynthMRI: An Open-Source Cross-Platform Tool

Synthetic MR Imaging allows for the reconstruction of different image contrasts from a single acquisition, reducing scan times. Commercial products that implement synthetic MRI are used in research. They rely on vendor-specific acquisitions and do not include the possibility of using custom multiparametric imaging techniques. We introduce PySynthMRI, an open-source tool with a user-friendly interface that uses a set of input images to generate synthetic images with diverse radiological contrasts by varying representative parameters of the desired target sequence, including the echo time, repetition time and inversion time(s). PySynthMRI is written in Python 3.6, and it can be executed under Linux, Windows, or MacOS as a python script or an executable. The tool is free and open source and is developed while taking into consideration the possibility of software customization by the end user. PySynthMRI generates synthetic images by calculating the pixelwise signal intensity as a function of a set of input images (e.g., T1 and T2 maps) and simulated scanner parameters chosen by the user via a graphical interface. The distribution provides a set of default synthetic contrasts, including T1w gradient echo, T2w spin echo, FLAIR and Double Inversion Recovery. The synthetic images can be exported in DICOM or NiFTI format. PySynthMRI allows for the fast synthetization of differently weighted MR images based on quantitative maps. Specialists can use the provided signal models to retrospectively generate contrasts and add custom ones. The modular architecture of the tool can be exploited to add new features without impacting the codebase.

Evaluation of iron overload in nigrosome 1 via quantitative susceptibility mapping as a progression biomarker in prodromal stages of synucleinopathies

Idiopathic rapid eye movement (REM) sleep behavior disorder (iRBD) is a prodromal stage of α-synucleinopathies, such as Parkinson's disease (PD), which are characterized by the loss of dopaminergic neurons in substantia nigra, associated with abnormal iron load. The assessment of presymptomatic biomarkers predicting the onset of neurodegenerative disorders is critical for monitoring early signs, screening patients for neuroprotective clinical trials and understanding the causal relationship between iron accumulation processes and disease development. Here, we used Quantitative Susceptibility Mapping (QSM) and 7T MRI to quantify iron deposition in Nigrosome 1 (N1) in early PD (ePD) patients, iRBD patients and healthy controls and investigated group differences and correlation with disease progression. We evaluated the radiological appearance of N1 and analyzed its iron content in 35 ePD, 30 iRBD patients and 14 healthy controls via T2*-weighted sequences and susceptibility (χ) maps. N1 regions of interest (ROIs) were manually drawn on control subjects and warped onto a study-specific template to obtain probabilistic N1 ROIs. For each subject the N1 with the highest mean χ was considered for statistical analysis. The appearance of N1 was rated pathological in 45% of iRBD patients. ePD patients showed increased N1 χ compared to iRBD patients and HC but no correlation with disease duration, indicating that iron load remains stable during the early stages of disease progression. Although no difference was reported in iron content between iRBD and HC, N1 χ in the iRBD group increases as the disease evolves. QSM can reveal temporal changes in N1 iron content and its quantification may represent a valuable presymptomatic biomarker to assess neurodegeneration in the prodromal stages of PD.

Nonequilibrium ensembles for the three-dimensional Navier-Stokes equations

At the molecular level fluid motions are, by first principles, described by time reversible laws. On the other hand, the coarse grained macroscopic evolution is suitably described by the Navier-Stokes equations, which are inherently irreversible, due to the dissipation term. Here, a reversible version of three-dimensional Navier-Stokes is studied, by introducing a fluctuating viscosity constructed in such a way that enstrophy is conserved, along the lines of the paradigm of microcanonical versus canonical treatment in equilibrium statistical mechanics. Through systematic simulations we attack two important questions: (a) What are the conditions that must be satisfied in order to have a statistical equivalence between the two nonequilibrium ensembles? (b) What is the empirical distribution of the fluctuating viscosity observed by changing the Reynolds number and the number of modes used in the discretization of the evolution equation? The latter point is important also to establish regularity conditions for the reversible equations. We find that the probability to observe negative values of the fluctuating viscosity becomes very quickly extremely small when increasing the effective Reynolds number of the flow in the fully resolved hydrodynamical regime, at difference from what was observed previously.

Diagnostic accuracy of quantitative susceptibility mapping in multiple system atrophy: The impact of echo time and the potential of histogram analysis

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We performed histogram analysis on χ maps at different TEs on MSA patients and HC.

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We found altered χ distribution in Pu, SN, GP, CN for MSAp and in SN, DN for MSAc.

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QSM diagnostic accuracy is TE-dependent and is enhanced at short TEs.

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Short TEs capture rapidly-decaying contributions of high χ sources.

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Histogram features detect χ spatial heterogeneities improving diagnostic accuracy.

The non-invasive quantification of iron stores via Quantitative Susceptibility Mapping (QSM) could play an important role in the diagnosis and the differential diagnosis of atypical Parkinsonisms. However, the susceptibility (χ) values measured via QSM depend on echo time (TE). This effect relates to the microstructural organization within the voxel, whose composition can be altered by the disease. Moreover, pathological iron deposition in a brain area may not be spatially uniform, and conventional Region of Interest (ROI)-based analysis may fail in detecting alterations. Therefore, in this work we evaluated the impact of echo time on the diagnostic accuracy of QSM on a population of patients with Multiple System Atrophy (MSA) of either Parkinsonian (MSAp) or cerebellar (MSAc) phenotypes. In addition, we tested the potential of histogram analysis to improve QSM classification accuracy.

We enrolled 32 patients (19 MSAp and 13 MSAc) and 16 healthy controls, who underwent a 7T MRI session including a gradient-recalled multi-echo sequence for χ mapping. Nine histogram features were extracted from the χ maps computed for each TE in atlas-based ROIs covering deep brain nuclei, and compared among groups.

Alterations of susceptibility distribution were found in the Putamen, Substantia Nigra, Globus Pallidus and Caudate Nucleus for MSAp and in the Substantia Nigra and Dentate Nucleus for MSAc. Increased iron deposition was observed in a larger number of ROIs for the two shortest TEs and the standard deviation, the 75^th and the 90^th percentile were the most informative features yielding excellent diagnostic accuracy with area under the ROC curve > 0.9.

In conclusion, short TEs may enhance QSM diagnostic performances, as they can capture variations in rapidly-decaying contributions of high χ sources. The analysis of histogram features allowed to reveal fine heterogeneities in the spatial distribution of susceptibility alteration, otherwise undetected by a simple evaluation of ROI χ mean values.

Simultaneous relaxometry and morphometry of human brain structures with 3D magnetic resonance fingerprinting: a multicenter, multiplatform, multifield-strength study

Relaxation times and morphological information are fundamental magnetic resonance imaging-derived metrics of the human brain that reflect the status of the underlying tissue. Magnetic resonance fingerprinting (MRF) enables simultaneous acquisition of T1 and T2 maps inherently aligned to the anatomy, allowing whole-brain relaxometry and morphometry in a single scan. In this study, we revealed the feasibility of 3D MRF for simultaneous brain structure-wise morphometry and relaxometry. Comprehensive test-retest scan analyses using five 1.5-T and three 3.0-T systems from a single vendor including different scanner types across 3 institutions demonstrated that 3D MRF-derived morphological information and relaxation times are highly repeatable at both 1.5 T and 3.0 T. Regional cortical thickness and subcortical volume values showed high agreement and low bias across different field strengths. The ability to acquire a set of regional T1, T2, thickness, and volume measurements of neuroanatomical structures with high repeatability and reproducibility facilitates the ability of longitudinal multicenter imaging studies to quantitatively monitor changes associated with underlying pathologies, disease progression, and treatments.

Quantitative imaging metrics derived from magnetic resonance fingerprinting using ISMRM/NIST MRI system phantom: An international multicenter repeatability and reproducibility study

PURPOSE

To compare the bias and inherent reliability of the quantitative (T₁ and T₂ ) imaging metrics generated from the magnetic resonance fingerprinting (MRF) technique using the ISMRM/NIST system phantom in an international multicenter setting.

METHOD

ISMRM/NIST MRI system phantom provides standard reference T₁ and T₂ relaxation values (vendor-provided) for each of the 14 vials in T₁ and T₂ arrays. MRF-SSFP scans repeated over 30 days on GE 1.5 and 3.0 T scanners at three collaborative centers. MRF estimated T_1, and T₂ values averaged over 30 days were compared with the phantom vendor-provided and spin-echo (SE) based convention gold standard (GS) method. Repeatability and reproducibility were characterized by the within-case coefficient of variation (wCV) of the MRF data acquired over 30 days, along with the biases.

RESULT

For the wide ranges of MRF estimated T₁ values, vials #1-8 (T₁ relaxation time between 2033 and 184 ms) exhibited a wCV less than 3% and 4%, respectively, on 3.0 and 1.5 T scanners. T₂ values in vials #1-8 (T₂ relaxation, 1044-45 ms) have shown wCV to be <7% on both 3.0 and 1.5 T scanners. A stronger linear correlation overall for T₁ (R²  = 0.9960 and 0.9963 at center-1 and center-2 on 3.0 T scanner, and R²  = 0.9951 and 0.9988 at center-1 and center-3 on 1.5 T scanner) compared to T₂ (R²  = 0.9971 and 0.9972 at center-1 and center-2 on 3.0 T scanner, and R²  = 0.9815 and 0.9754 at center-1 and center-3 on 1.5 T scanner). Bland-Altman (BA) analysis showed MRF based T₁ and T₂ values were within the limit of agreement (LOA) except for one data point. The mean difference or bias and 95% lower bound (LB) and upper bound (UB) LOA are reported in the format; mean bias: 95% LB LOA: 95% UB LOA. The biases for T₁ values were 21.34: -50.00: 92.69, 21.32: -47.29: 89.94 ms, and for T₂ values were -19.88: -42.37: 2.61, -19.06: -43.58: 5.45 ms on 3.0 T scanner at center-1 and center-2, respectively. Similarly, on 1.5 T scanner biases for T₁ values were 26.54: -53.41: 106.50, 9.997: -51.94: 71.94 ms, and for T₂ values were -23.84: -135.40: 87.76, -37.30: 134.30: 59.73 ms at center-1 and center-3, respectively. Additionally, the correlation between the SE based GS and MRF estimated T₁ and T₂ values (R²  = 0.9969 and 0.9977) showed a similar trend as we observed between vendor-provided and MRF estimated T₁ and T₂ values (R²  = 0.9963 and 0.9972). In addition to correlation, BA analysis showed that all the vials are within the LOA between the GS and vendor-provided for the T₁ values and except one vial for T₂ . All the vials are within the LOA between GS and MRF except one vial in T₁ and T₂ array. The wCV for reproducibility was <3% for both T₁ and T₂ values in vials #1-8, for all the 14 vials, wCV calculated for reproducibility was <4% for T₁ values and <5% for T₂ .

CONCLUSION

This study shows that MRF is highly repeatable (wCV <4% for T₁ and <7% for T₂ ) and reproducible (wCV < 3% for both T₁ and T₂ ) in certain vials (vials #1-8).

Three dimensional MRF obtains highly repeatable and reproducible multi-parametric estimations in the healthy human brain at 1.5T and 3T

Magnetic resonance fingerprinting (MRF) is highly promising as a quantitative MRI technique due to its accuracy, robustness, and efficiency. Previous studies have found high repeatability and reproducibility of 2D MRF acquisitions in the brain. Here, we have extended our investigations to 3D MRF acquisitions covering the whole brain using spiral projection k-space trajectories. Our travelling head study acquired test/retest data from the brains of 12 healthy volunteers and 8 MRI systems (3 systems at 3 T and 5 at 1.5 T, all from a single vendor), using a study design not requiring all subjects to be scanned at all sites. The pulse sequence and reconstruction algorithm were the same for all acquisitions. After registration of the MRF-derived PD T1 and T2 maps to an anatomical atlas, coefficients of variation (CVs) were computed to assess test/retest repeatability and inter-site reproducibility in each voxel, while a General Linear Model (GLM) was used to determine the voxel-wise variability between all confounders, which included test/retest, subject, field strength and site. Our analysis demonstrated a high repeatability (CVs 0.7-1.3% for T1, 2.0-7.8% for T2, 1.4-2.5% for normalized PD) and reproducibility (CVs of 2.0-5.8% for T1, 7.4-10.2% for T2, 5.2-9.2% for normalized PD) in gray and white matter. Both repeatability and reproducibility improved when compared to similar experiments using 2D acquisitions. Three-dimensional MRF obtains highly repeatable and reproducible estimations of T1 and T2, supporting the translation of MRF-based fast quantitative imaging into clinical applications.

Joint assessment of density correlations and fluctuations for analysing spatial tree patterns

Inferring the processes underlying the emergence of observed patterns is a key challenge in theoretical ecology. Much effort has been made in the past decades to collect extensive and detailed information about the spatial distribution of tropical rainforests, as demonstrated, e.g. in the 50 ha tropical forest plot on Barro Colorado Island, Panama. These kinds of plots have been crucial to shed light on diverse qualitative features, emerging both at the single-species or the community level, like the spatial aggregation or clustering at short scales. Here, we build on the progress made in the study of the density correlation functions applied to biological systems, focusing on the importance of accurately defining the borders of the set of trees, and removing the induced biases. We also pinpoint the importance of combining the study of correlations with the scale dependence of fluctuations in density, which are linked to the well-known empirical Taylor's power law. Density correlations and fluctuations, in conjunction, provide a unique opportunity to interpret the behaviours and, possibly, to allow comparisons between data and models. We also study such quantities in models of spatial patterns and, in particular, we find that a spatially explicit neutral model generates patterns with many qualitative features in common with the empirical ones.

Repeatability and reproducibility of human brain morphometry using three-dimensional magnetic resonance fingerprinting

Three-dimensional (3D) Magnetic resonance fingerprinting (MRF) permits whole-brain volumetric quantification of T1 and T2 relaxation values, potentially replacing conventional T1-weighted structural imaging for common brain imaging analysis. The aim of this study was to evaluate the repeatability and reproducibility of 3D MRF in evaluating brain cortical thickness and subcortical volumetric analysis in healthy volunteers using conventional 3D T1-weighted images as a reference standard. Scan-rescan tests of both 3D MRF and conventional 3D fast spoiled gradient recalled echo (FSPGR) were performed. For each sequence, the regional cortical thickness and volume of the subcortical structures were measured using standard automatic brain segmentation software. Repeatability and reproducibility were assessed using the within-subject coefficient of variation (wCV), intraclass correlation coefficient (ICC), and mean percent difference and ICC, respectively. The wCV and ICC of cortical thickness were similar across all regions with both 3D MRF and FSPGR. The percent relative difference in cortical thickness between 3D MRF and FSPGR across all regions was 8.0 ± 3.2%. The wCV and ICC of the volume of subcortical structures across all structures were similar between 3D MRF and FSPGR. The percent relative difference in the volume of subcortical structures between 3D MRF and FSPGR across all structures was 7.1 ± 3.6%. 3D MRF measurements of human brain cortical thickness and subcortical volumes are highly repeatable, and consistent with measurements taken on conventional 3D T1-weighted images. A slight, consistent bias was evident between the two, and thus careful attention is required when combining data from MRF and conventional acquisitions.

7-T MRI of explanted liver and ex-vivo pancreatic specimens: prospective study protocol of radiological-pathological correlation feasibility (the EXLIPSE project)

The study focuses on radiological-pathological correlation between imaging of ex vivo samples obtained by a 7-T scanner and histological examination. The specimens will be derived from native explanted cirrhotic livers, liver grafts excluded from donation because of severe steatosis, and primary pancreatic tumours. Magnetic resonance imaging (MRI) examinations will be performed within 24 h from liver or pancreatic lesion surgical removal. The MRI protocol will include morphological sequences, quantitative T1, T2, and fat-, water-fraction maps with Cartesian k-space acquisition, and multiparametric methods based on a transient-state “MRI fingerprinting”. Finally, the specimen will be fixed by formalin. Qualitative imaging analysis will be performed by two independent blinded radiologists to assess image consistency score. Quantitative analysis will be performed by drawing regions of interest on different tissue zones to measure T1 and T2 relaxation times as well as fat- and water-fraction. The same tissue areas will be analysed by the pathologists. This study will provide the possibility to improve our knowledge about qualitative and quantitative abdominal imaging assessment at 7 T, by correlating imaging characteristics and the corresponding histological composition of ex vivo specimens, in order to identify imaging biomarkers. Trial registration: ClinicalTrials.gov: 13646. Registered 9 July 2019—retrospectively registered

Rapid three-dimensional multiparametric MRI with quantitative transient-state imaging

Novel methods for quantitative, transient-state multiparametric imaging are increasingly being demonstrated for assessment of disease and treatment efficacy. Here, we build on these by assessing the most common Non-Cartesian readout trajectories (2D/3D radials and spirals), demonstrating efficient anti-aliasing with a k-space view-sharing technique, and proposing novel methods for parameter inference with neural networks that incorporate the estimation of proton density. Our results show good agreement with gold standard and phantom references for all readout trajectories at 1.5 T and 3 T. Parameters inferred with the neural network were within 6.58% difference from the parameters inferred with a high-resolution dictionary. Concordance correlation coefficients were above 0.92 and the normalized root mean squared error ranged between 4.2 and 12.7% with respect to gold-standard phantom references for T1 and T2. In vivo acquisitions demonstrate sub-millimetric isotropic resolution in under five minutes with reconstruction and inference times < 7 min. Our 3D quantitative transient-state imaging approach could enable high-resolution multiparametric tissue quantification within clinically acceptable acquisition and reconstruction times.

Retrospective rigid motion correction of three-dimensional magnetic resonance fingerprinting of the human brain

PURPOSE

To obtain three-dimensional (3D), quantitative and motion-robust imaging with magnetic resonance fingerprinting (MRF).

METHODS

Our acquisition is based on a 3D spiral projection k-space scheme. We compared different orderings of trajectory interleaves in terms of rigid motion-correction robustness. In all tested orderings, we considered the whole dataset as a sum of 56 segments of 7-s duration, acquired sequentially with the same flip angle schedule. We performed a separate image reconstruction for each segment, producing whole-brain navigators that were aligned to the first segment using normalized correlation. The estimated rigid motion was used to correct the k-space data, and the aligned data were matched with the dictionary to obtain motion-corrected maps.

RESULTS

A significant improvement on the motion-affected maps after motion correction is evident with the suppression of motion artifacts. Correlation with the motionless baseline improved by 20% on average for both T₁ and T₂ estimations after motion correction. In addition, the average motion-induced quantification bias of 70 ms for T₁ and 18 ms for T₂ values was reduced to 12 ms and 6 ms, respectively, improving the reliability of quantitative estimations.

CONCLUSION

We established a method that allows correcting 3D rigid motion on a 7-s timescale during the reconstruction of MRF data using self-navigators, improving the image quality and the quantification robustness.

Alignment of Nonspherical Active Particles in Chaotic Flows

We study the orientation statistics of spheroidal, axisymmetric microswimmers, with shapes ranging from disks to rods, swimming in chaotic, moderately turbulent flows. Numerical simulations show that rodlike active particles preferentially align with the flow velocity. To explain the underlying mechanism, we solve a statistical model via the perturbation theory. We show that such an alignment is caused by correlations of fluid velocity and its gradients along particle paths combined with fore-aft symmetry breaking due to both swimming and particle nonsphericity. Remarkably, the discovered alignment is found to be a robust kinematical effect, independent of the underlying flow evolution. We discuss its possible relevance for aquatic ecology.

Magnetic resonance fingerprinting with dictionary-based fat and water separation (DBFW MRF): A multi-component approach

Purpose

To obtain a fast and robust fat‐water separation with simultaneous estimation of water T₁, fat T₁, and fat fraction maps.

Methods

We modified an MR fingerprinting (MRF) framework to use a single dictionary combination of a water and fat dictionary. A variable TE acquisition pattern with maximum TE = 4.8 ms was used to increase the fat–water separability. Radiofrequency (RF) spoiling was used to reduce the size of the dictionary by reducing T₂ sensitivity. The technique was compared both in vitro and in vivo to an MRF method that incorporated 3‐point Dixon (DIXON MRF), as well as Cartesian IDEAL with different acquisition parameters.

Results

The proposed dictionary‐based fat–water separation technique (DBFW MRF) successfully provided fat fraction, water, and fat T₁, B₀, and B₁₊ maps both in vitro and in vivo. The fat fraction and water T₁ values obtained with DBFW MRF show excellent agreement with DIXON MRF as well as with the reference values obtained using a Cartesian IDEAL with a long TR (concordance correlation coefficient: 0.97/0.99 for fat fraction–water T₁). Whereas fat fraction values with Cartesian IDEAL were degraded in the presence of T₁ saturation, MRF methods successfully estimated and accounted for T₁ in the fat fraction estimates.

Conclusion

The DBFW MRF technique can successfully provide T₁ and fat fraction quantification in under 20 s per slice, intrinsically correcting T₁ biases typical of fast Dixon techniques. These features could improve the diagnostic quality and use of images in presence of fat.

Point-particle method to compute diffusion-limited cellular uptake

We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used to calibrate the method, linking the numerical parameters to the physical particle radius and uptake rate. We study the configurations of multiple absorbers of increasing complexity to examine the performance of the method by comparing our simulations with available exact analytical or numerical results. We demonstrate the potential of the method to resolve the complex diffusive interactions, here quantified by the Sherwood number, measuring the uptake rate in terms of that of isolated absorbers. We implement the method in a pseudospectral solver that can be generalized to include fluid motion and fluid-particle interactions. As a test case of the presence of a flow, we consider the uptake rate by a particle in a linear shear flow. Overall, our method represents a powerful and flexible computational tool that can be employed to investigate many complex situations in biology, chemistry, and related sciences.

Centripetal focusing of gyrotactic phytoplankton

A suspension of gyrotactic microalgae Chlamydomonas augustae swimming in a cylindrical water vessel in solid-body rotation is studied. Our experiments show that swimming algae form an aggregate around the axis of rotation, whose intensity increases with the rotation speed. We explain this phenomenon by the centripetal orientation of the swimming direction towards the axis of rotation. This centripetal focusing is contrasted by diffusive fluxes due to stochastic reorientation of the cells. The competition of the two effects lead to a stationary distribution, which we analytically derive from a refined mathematical model of gyrotactic swimmers. The temporal evolution of the cell distribution, obtained via numerical simulations of the stochastic model, is in quantitative agreement with the experimental measurements in the range of parameters explored.

Chaotic synchronizations of spatially extended systems as nonequilibrium phase transitions

Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength. As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via power-law coupling is considered. Furthermore, each unit in the one-dimensional chain is linked to the corresponding one in the replica via a local coupling. The synchronization transition is studied as a nonequilibrium phase transition, and its critical properties are analyzed at varying the spatial interaction range as well as the nonlinearity of the dynamical units composing each system. In particular, continuous and discontinuous local maps are considered. In both cases the transitions are of the second order with critical indices varying with the exponent characterizing the interaction range. For discontinuous maps it is numerically shown that the transition belongs to the anomalous directed percolation (ADP) family of universality classes, previously identified for Levy-flight spreading of epidemic processes. For continuous maps, the critical exponents are different from those characterizing ADP, but apart from the nearest-neighbor case, the identification of the corresponding universality classes remains an open problem. Finally, to test the influence of deterministic correlations for the studied synchronization transitions, the chaotic dynamical evolutions are substituted by suitable stochastic models. In this framework and for the discontinuous case, it is possible to derive an effective Langevin description that corresponds to that proposed for ADP.

Universal intermittent properties of particle trajectories in highly turbulent flows

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R{lambda}in[120:740]. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. Parisi-Frisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.

Heavy particle concentration in turbulence at dissipative and inertial scales

Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles form fractal clusters with properties independent of the Reynolds number. Clustering is there optimal when the particle response time is of the order of the Kolmogorov time scale tau(eta). In the inertial range, the particle distribution is no longer scale invariant. It is, however, shown that deviations from uniformity depend on a rescaled contraction rate, which is different from the local Stokes number given by dimensional analysis. Particle distribution is characterized by voids spanning all scales of the turbulent flow; their signature in the coarse-grained mass probability distribution is an algebraic behavior at small densities.

Clustering of heavy particles in random self-similar flow

A statistical description of heavy particles suspended in incompressible rough self-similar flows is developed. It is shown that, differently from smooth flows, particles do not form fractal clusters. They rather distribute inhomogeneously with a statistics that only depends on a local Stokes number, given by the ratio between the particles' response time and the turnover time associated with the observation scale. Particle clustering is reduced by the fluid roughness. Heuristic arguments supported by numerics explain this effect in terms of the algebraic tails of the probability density function of the velocity difference between two particles.

Thin front propagation in random shear flows

Front propagation in time-dependent laminar flows is investigated in the limit of very fast reaction and very thin fronts--i.e., the so-called geometrical optics limit. In particular, we consider fronts stirred by random shear flows, whose time evolution is modeled in terms of Ornstein-Uhlembeck processes. We show that the ratio between the time correlation of the flow and an intrinsic time scale of the reaction dynamics (the wrinkling time tw) is crucial in determining both the front propagation speed and the front spatial patterns. The relevance of time correlation in realistic flows is briefly discussed in light of the bending phenomenon--i.e., the decrease of propagation speed observed at high flow intensities.

Turbulence and coarsening in active and passive binary mixtures

Phase separation between two fluids in two dimensions is investigated by means of direct numerical simulations of coupled Navier-Stokes and Cahn-Hilliard equations. We study the phase ordering process in the presence of an external stirring acting on the velocity field. For both active and passive mixtures we find that, for a sufficiently strong stirring, coarsening is arrested in a stationary dynamical state characterized by a continuous rupture and formation of finite domains. Coarsening arrest is shown to be independent of the chaotic or regular nature of the flow.

Brownian motion and diffusion: from stochastic processes to chaos and beyond

One century after Einstein's work, Brownian motion still remains both a fundamental open issue and a continuous source of inspiration for many areas of natural sciences. We first present a discussion about stochastic and deterministic approaches proposed in the literature to model the Brownian motion and more general diffusive behaviors. Then, we focus on the problems concerning the determination of the microscopic nature of diffusion by means of data analysis. Finally, we discuss the general conditions required for the onset of large scale diffusive motion.

Closure of two-dimensional turbulence: the role of pressure gradients

Inverse energy cascade regime of two-dimensional turbulence is investigated by means of high resolution numerical simulations. Numerical computations of conditional averages of transverse pressure gradient increments are found to be compatible with a recently proposed self-consistent Gaussian model. An analogous low-order closure model for the longitudinal pressure gradient is proposed and its validity is numerically examined. In this case numerical evidence for the presence of higher-order terms in the closure is found. The fundamental role of conditional statistics between longitudinal and transverse components is highlighted.

Front speed enhancement in cellular flows

The problem of front propagation in a stirred medium is addressed in the case of cellular flows in three different regimes: slow reaction, fast reaction and geometrical optics limit. It is well known that a consequence of stirring is the enhancement of front speed with respect to the nonstirred case. By means of numerical simulations and theoretical arguments we describe the behavior of front speed as a function of the stirring intensity, U. For slow reaction, the front propagates with a speed proportional to U(1/4), conversely for fast reaction the front speed is proportional to U(3/4). In the geometrical optics limit, the front speed asymptotically behaves as U/ln U. (c) 2002 American Institute of Physics.

Inverse statistics of smooth signals: the case of two dimensional turbulence

The problem of inverse statistics (statistics of distances for which the signal fluctuations are larger than a certain threshold) in differentiable signals with power law spectrum, E(k) approximately k(-alpha), 3< or =alpha<5, is discussed. We show that for these signals, with random phases, exit-distance moments follow a bifractal distribution. We also investigate two dimensional turbulent flows in the direct cascade regime, which display a more complex behavior. We give numerical evidences that the inverse statistics of 2D turbulent flows is described by a multifractal probability distribution; i.e., the statistics of laminar events is not simply captured by the exponent alpha characterizing the spectrum.

Linear and nonlinear information flow in spatially extended systems

Infinitesimal and finite amplitude error propagation in spatially extended systems are numerically and theoretically investigated. The information transport in these systems can be characterized in terms of the propagation velocity of perturbations Vp. A linear stability analysis is sufficient to capture all the relevant aspects associated to propagation of infinitesimal disturbances. In particular, this analysis gives the propagation velocity VL of infinitesimal errors. If linear mechanisms prevail on the nonlinear ones Vp=VL. On the contrary, if nonlinear effects are predominant finite amplitude disturbances can eventually propagate faster than infinitesimal ones (i.e., Vp>VL). The finite size Lyapunov exponent can be successfully employed to discriminate the linear or nonlinear origin of information flow. A generalization of the finite size Lyapunov exponent to a comoving reference frame allows us to state a marginal stability criterion able to provide Vp both in the linear and in the nonlinear case. Strong analogies are found between information spreading and propagation of fronts connecting steady states in reaction-diffusion systems. The analysis of the common characteristics of these two phenomena leads to a better understanding of the role played by linear and nonlinear mechanisms for the flow of information in spatially extended systems.

Chaos or noise: difficulties of a distinction

In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set, it is not possible to reconstruct the invariant measure up to an arbitrarily fine resolution and an arbitrarily high embedding dimension. These restrictions limit our ability to distinguish between signals generated by different systems, such as regular, chaotic, or stochastic ones, when analyzed from a time series point of view. We propose to classify the signal behavior, without referring to any specific model, as stochastic or deterministic on a certain scale of the resolution epsilon, according to the dependence of the (epsilon,tau) entropy, h(epsilon, tau), and the finite size Lyapunov exponent lambda(epsilon) on epsilon.

Exit-time approach to epsilon-entropy

An efficient approach to the calculation of the epsilon-entropy is proposed. The method is based on the idea of looking at the information content of a string of data, by analyzing the signal only at the instants when the fluctuations are larger than a certain threshold epsilon, i.e., by looking at the exit-time statistics. The practical and theoretical advantages of our method with respect to the usual one are shown by the examples of a deterministic map and a self-affine stochastic process.

Nonasymptotic properties of transport and mixing

We study relative dispersion of passive scalar in nonideal cases, i.e., in situations in which asymptotic techniques cannot be applied; typically when the characteristic length scale of the Eulerian velocity field is not much smaller than the domain size. Of course, in such a situation usual asymptotic quantities (the diffusion coefficients) do not give any relevant information about the transport mechanisms. On the other hand, we shall show that the Finite Size Lyapunov Exponent, originally introduced for the predictability problem, appears to be rather powerful in approaching the nonasymptotic transport properties. This technique is applied in a series of numerical experiments in simple flows with chaotic behaviors, in experimental data analysis of drifter and to study relative dispersion in fully developed turbulence. (c) 2000 American Institute of Physics.

Exit time of turbulent signals: a way to detect the intermediate dissipative range

The exit-time statistics of experimental turbulent data is analyzed. By looking at the exit-time moments (inverse structure functions) it is possible to have a direct measurement of scaling properties of the laminar statistics. It turns out that the inverse structure functions show a much more extended intermediate dissipative range than the structure functions, leading to the first clear evidence of the existence of such a range of scales.

Transport in finite size systems: An exit time approach

In the framework of chaotic scattering we analyze passive tracer transport in finite systems. In particular, we study models with open streamlines and a finite number of recirculation zones. In the nontrivial case with a small number of recirculation zones a description by means of asymptotic quantities (such as the eddy diffusivity) is not appropriate. The nonasymptotic properties of dispersion are characterized by means of the exit time statistics, which shows strong sensitivity on initial conditions. This yields a probability distribution function with long tails, making impossible a characterization in terms of a unique typical exit time. (c) 1999 American Institute of Physics.