Unravelling the mechanisms of CE-SSFP in imaging myocardium at risk: The effect of relaxation times on myocardial contrast.

PURPOSE: The aim of this study was to investigate the contrast mechanisms of Contrast-enhanced steady-state free-precession (CE-SSFP) through the utilization of Bloch simulations in an experimental porcine model and in patients with acute myocardial infarction. METHODS: Six pigs and ten patients with myocardial infarction underwent CMR and tissue characterization at 1.5 T whereas a Bloch simulation framework was utilized to simulate the CE-SSFP signal formation and compare it against the actual CE-SSFP signal acquired from the experimental porcine model and the patient population. The relaxation times of remote, salvaged, and infarcted myocardium were calculated after the injection of gadolinium, at the time of CE-SSFP acquisition. Simulations were performed using the same CE-SSFP pulse sequence as used on the scanner on a set of spins with the calculated relaxation times from the CMR scans. RESULTS: The normalized signal intensities of salvaged and infarcted myocardium obtained with simulations were lower than the corresponding normalized signal intensities obtained in vivo in pigs (p < 0.05, 134% vs 153%) and in patients (p < 0.05, 126% vs 145%). The results from simulations showed a linear relationship to the results obtained in the experimental porcine model (r2 = 0.61) and in patients (r2 = 0.69). CONCLUSION: The T1 and T2 values of remote, salvaged, and infarcted myocardium only partly explain the signal intensities in CE-SSFP images. Bloch simulations suggest that there may be more elements that contribute to the CE-SSFP contrast. Integration of other aspects of the MR experiment into the simulation model could further help to fully unravel the mechanisms of CE-SSFP.

Simulator-generated training datasets as an alternative to using patient data for machine learning: An example in myocardial segmentation with MRI.

BACKGROUND AND OBJECTIVE: Supervised Machine Learning techniques have shown significant potential in medical image analysis. However, the training data that need to be collected for these techniques in the field of MRI 1) may not be available, 2) may be available but the size is small, 3) may be available but not representative and 4) may be available but with weak labels. The aim of this study was to overcome these limitations through advanced MR simulations on a realistic computer model of human anatomy without using a real MRI scanner, without scanning patients and without having personnel and the associated expenses. METHODS: The 4D-XCAT model was used with the coreMRI simulation platform for generating artificial short-axis MR-images for training a neural-network to automatic delineate the LV endocardium and epicardium. Its performance was assessed on real MR-images acquired from eight healthy volunteers. The neural-network was also trained on real MR-images from a publicly available dataset and its performance was assessed on the same volunteers' data. RESULTS: The proposed solution demonstrated a performance of 94% (endocardium) and 90% DICE (epicardium) in real mid-ventricular slices, whereas a 10% addition of real MR-images in the artificial training dataset increased the performance to 97% DICE. The use of artificial MR-images that cover the entire LV yielded 85% (endocardium) and 88% DICE (epicardium) when combined with real MR data with an 80%-20% mix respectively. CONCLUSIONS: This study suggests a low-cost solution for constructing artificial training datasets for supervised learning techniques in the field of MR by using advanced MR simulations without the use of a real MRI scanner, without scanning patients and without having to use specialized personnel, such as technologists and radiologists.

Measuring extracellular volume fraction by MRI: First verification of values given by clinical sequences.

PURPOSE: To verify MR measurements of myocardial extracellular volume fraction (ECV) based on clinically applicable T1-mapping sequences against ECV measurements by radioisotope tracer in pigs and to relate the results to those obtained in volunteers. METHODS: Between May 2016 and March 2017, 8 volunteers (25 ± 4 years, 3 female) and 8 pigs (4 female) underwent ECV assessment with SASHA, MOLLI5(3b)3, MOLLI5(3s)3, and MOLLI5s(3s)3s. Myocardial ECV was measured independently in pigs using a radioisotope tracer method. RESULTS: In pigs, ECV in normal myocardium was not different between radioisotope (average ± standard deviation; 19 ± 2%) and SASHA (21 ± 2%; P = 0.086). ECV was higher by MOLLI5(3b)3 (26 ± 2%), MOLLI5(3s)3 (25 ± 2%), and MOLLI5s(3s)3s (25 ± 2%) compared with SASHA or radioisotope (P ≤ 0.001 for all). ECV in volunteers was higher by MOLLI5(3b)3 (26 ± 3%) and MOLLI5(3s)3 (26 ± 3%) than by SASHA (22 ± 3%; P = 0.022 and P = 0.033). No difference was found between MOLLI5s(3s)3s (25 ± 3%) and SASHA (P = 0.225). Native T1 of blood and myocardium as well as postcontrast T1 of myocardium was consistently lower using MOLLI compared with SASHA. ECV increased over time as measured by MOLLI5(3b)3 and MOLLI5(3s)3 for pigs (0.08% and 0.07%/min; P = 0.004 and P = 0.013) and by MOLLI5s(3s)3s for volunteers (0.07%/min; P = 0.032) but did not increase as measured by SASHA. CONCLUSION: Clinically available MOLLI and SASHA techniques can be used to accurately estimate ECV in normal myocardium where MOLLI-sequences show minor overestimation driven by underestimation of postcontrast T1 when compared with SASHA. The timing of imaging after contrast administration affected the measurement of ECV using some variants of the MOLLI sequence.

coreMRI: A high-performance, publicly available MR simulation platform on the cloud.

INTRODUCTION: A Cloud-ORiented Engine for advanced MRI simulations (coreMRI) is presented in this study. The aim was to develop the first advanced MR simulation platform delivered as a web service through an on-demand, scalable cloud-based and GPU-based infrastructure. We hypothesized that such an online MR simulation platform could be utilized as a virtual MRI scanner but also as a cloud-based, high-performance engine for advanced MR simulations in simulation-based quantitative MR (qMR) methods. METHODS AND RESULTS: The simulation framework of coreMRI was based on the solution of the Bloch equations and utilized a ground-up-approach design based on the principles already published in the literature. The development of a front-end environment allowed the connection of the end-users to the GPU-equipped instances on the cloud. The coreMRI simulation platform was based on a modular design where individual modules (such as the Gadgetron reconstruction framework and a newly developed Pulse Sequence Designer) could be inserted in the main simulation framework. Different types and sources of pulse sequences and anatomical models were utilized in this study revealing the flexibility that the coreMRI simulation platform offers to the users. The performance and scalability of coreMRI were also examined on multi-GPU configurations on the cloud, showing that a multi-GPU computer on the cloud equipped with a newer generation of GPU cards could significantly mitigate the prolonged execution times that accompany more realistic MRI and qMR simulations. CONCLUSIONS: coreMRI is available to the entire MR community, whereas its high performance and scalability allow its users to configure advanced MRI experiments without the constraints imposed by experimentation in a true MRI scanner (such as time constraint and limited availability of MR scanners), without upfront investment for purchasing advanced computer systems and without any user expertise on computer programming or MR physics. coreMRI is available to the users through the webpage https://www.coreMRI.org.

Comparison of short axis and long axis acquisitions of T1 and extracellular volume mapping using MOLLI and SASHA in patients with myocardial infarction and healthy volunteers.

BACKGROUND: Although previous studies have examined the impact of slice position in volumetric measurements in Cardiovascular Magnetic Resonance (CMR) imaging, very limited data are available today comparing T1 and Extra-Cellular Volume (ECV) measurements from short and long axis acquisitions. The purpose of this study was to investigate the impact of slice position and orientation on T1 and ECV measurements using the MOdified Look-Locker Inversion recovery (MOLLI) and Saturation recovery single-shot acquisition (SASHA) sequence in patients with myocardial infarction and in healthy volunteers. METHODS: Eight (8) healthy volunteers with no medical history and eight (8) patients with myocardial infarction were included in this study. MOLLI and SASHA were utilized and short-axis and long-axis images were acquired. T1 and ECV measurements were performed by drawing same size regions of interest on the myocardium as well in the blood pool at the intersections of the short axis and long axis images. RESULTS: In healthy volunteers, there were no statistically significant differences in native T1 and ECV values between short axis and long axis acquisitions using MOLLI (two-chamber, three-chamber and four-chamber) and SASHA (three-chamber). In patients, there were no statistically significant differences in native T1 and ECV values between short axis and 3-chamber long axis acquisitions in both remote and affected myocardium using MOLLI and SASHA. CONCLUSIONS: Long axis measurements of myocardial T1 and ECV using MOLLI and SASHA exhibit good agreement with the corresponding short axis measurements allowing for fast and reliable myocardial tissue characterization in cases where shortening of the overall imaging acquisition is required.

Importance of standardizing timing of hematocrit measurement when using cardiovascular magnetic resonance to calculate myocardial extracellular volume (ECV) based on pre- and post-contrast T1 mapping.

BACKGROUND: Cardiovascular magnetic resonance (CMR) can be used to calculate myocardial extracellular volume fraction (ECV) by relating the longitudinal relaxation rate in blood and myocardium before and after contrast-injection to hematocrit (Hct) in blood. Hematocrit is known to vary with body posture, which could affect the calculations of ECV. The aim of this study was to test the hypothesis that there is a significant increase in calculated ECV values if the Hct is sampled after the CMR examination in supine position compared to when the patient arrives at the MR department. METHODS: Forty-three consecutive patients including various pathologies as well as normal findings were included in the study. Venous blood samples were drawn upon arrival to the MR department and directly after the examination with the patient remaining in supine position. A Modified Look-Locker Inversion recovery (MOLLI) protocol was used to acquire mid-ventricular short-axis images before and after contrast injection from which motion-corrected T1 maps were derived and ECV was calculated. RESULTS: Hematocrit decreased from 44.0 ± 3.7% before to 40.6 ± 4.0% after the CMR examination (p < 0.001). This resulted in a change in calculated ECV from 24.7 ± 3.8% before to 26.2 ± 4.2% after the CMR examination (p < 0.001). All patients decreased in Hct after the CMR examination compared to before except for two patients whose Hct remained the same. CONCLUSION: Variability in CMR-derived myocardial ECV can be reduced by standardizing the timing of Hct measurement relative to the CMR examination. Thus, a standardized acquisition of blood sample for Hct after the CMR examination, when the patient is still in supine position, would increase the precision of ECV measurements.

Simulation-based quantification of native T1 and T2 of the myocardium using a modified MOLLI scheme and the importance of Magnetization Transfer.

Quantitative cardiovascular Magnetic Resonance Imaging techniques are gaining wide acceptance within the MR community due to their potential to diagnose non-localized disease, guide therapy and improve patient outcome. During the last decade, there has been an increasing interest for developing new techniques that allow for simultaneous quantification of both T1 and T2 maps of myocardium. Newer studies demonstrated that the incorporation of MRI simulations could yield similar results to conventional mapping techniques in the myocardium. However, these simulation-based quantitative MR techniques usually compare the in-vivo T1 estimates against less accurate T1 techniques, whereas they present inconsistencies between simulation studies, phantom and in-vivo measurements. Moreover, these studies do not investigate the effect of Magnetization Transfer on the myocardial T1 and T2 estimates but are usually validated on phantoms where the MT effect is small. The main aim of this study was to perform simultaneous mapping of the native T1 and T2 of the myocardium through the utilization of a modified MOLLI pulse sequence and the incorporation of advanced MR simulations through the SQUAREMR framework. A second aim of this study was to investigate the effect of MT on simulation-based quantitative MR techniques. A conventional MOLLI pulse sequence was modified so as to present combined high T2 sensitivity and low MT effect. The new technique was applied in healthy volunteers and demonstrated an improved T1 accuracy compared to the conventional MOLLI and a T2 accuracy similar to the one provided by the T2prep-bSSFP method. The effect of MT on T1 and T2 estimates was also investigated in the current study. Phantoms with an increasing MT effect as well as phantoms without an MT effect were included in this work whereas several variants of the modified-MOLLI that introduce different amounts of T2 modulation on the MR signal and induce different MT effects were applied on the phantoms. The proposed simulation-based quantitative MR technique for simultaneous T1 and T2 mapping of the myocardium does not require the incorporation of a complicated custom designed pulse sequence and does not require a complicated reconstruction workflow. Moreover, the current study demonstrates for the first time that MT plays an important role in the simulation-based quantitative MR studies and points out the necessity of incorporating the study of MT in future techniques.

Cloud GPU-based simulations for SQUAREMR.

Quantitative Magnetic Resonance Imaging (MRI) is a research tool, used more and more in clinical practice, as it provides objective information with respect to the tissues being imaged. Pixel-wise T1 quantification (T1 mapping) of the myocardium is one such application with diagnostic significance. A number of mapping sequences have been developed for myocardial T1 mapping with a wide range in terms of measurement accuracy and precision. Furthermore, measurement results obtained with these pulse sequences are affected by errors introduced by the particular acquisition parameters used. SQUAREMR is a new method which has the potential of improving the accuracy of these mapping sequences through the use of massively parallel simulations on Graphical Processing Units (GPUs) by taking into account different acquisition parameter sets. This method has been shown to be effective in myocardial T1 mapping; however, execution times may exceed 30min which is prohibitively long for clinical applications. The purpose of this study was to accelerate the construction of SQUAREMR's multi-parametric database to more clinically acceptable levels. The aim of this study was to develop a cloud-based cluster in order to distribute the computational load to several GPU-enabled nodes and accelerate SQUAREMR. This would accommodate high demands for computational resources without the need for major upfront equipment investment. Moreover, the parameter space explored by the simulations was optimized in order to reduce the computational load without compromising the T1 estimates compared to a non-optimized parameter space approach. A cloud-based cluster with 16 nodes resulted in a speedup of up to 13.5 times compared to a single-node execution. Finally, the optimized parameter set approach allowed for an execution time of 28s using the 16-node cluster, without compromising the T1 estimates by more than 10ms. The developed cloud-based cluster and optimization of the parameter set reduced the execution time of the simulations involved in constructing the SQUAREMR multi-parametric database thus bringing SQUAREMR's applicability within time frames that would be likely acceptable in the clinic.

Using a modified 3D-printer for mapping the magnetic field of RF coils designed for fetal and neonatal imaging.

An experimental setup for characterizing the magnetic field of MRI RF coils was proposed and tested. The setup consisted of a specially configured 3D-printer, a network analyzer and a mid-performance desktop PC. The setup was tested on a single loop RF coil, part of a phased array for fetal imaging. Then, the setup was used for determining the magnetic field characteristics of a high-pass birdcage coil used for neonatal MR imaging with a vertical static field. The scattering parameter S21, converted into power ratio, was used for mapping the B1 magnetic field. The experimental measurements from the loop coil were close to the theoretical results (R=0.924). A high degree of homogeneity was measured for the neonatal birdcage RF coil. The development of MR RF coils is time consuming and resource intensive. The proposed experimental setup provides an alternative method for magnetic field characterization of RF coils used in MRI.

Validation of a new T2* algorithm and its uncertainty value for cardiac and liver iron load determination from MRI magnitude images.

PURPOSE: To validate an automatic algorithm for offline T2* measurements, providing robust, vendor-independent T2*, and uncertainty estimates for iron load quantification in the heart and liver using clinically available imaging sequences. METHODS: A T2* region of interest (ROI)-based algorithm was developed for robustness in an offline setting. Phantom imaging was performed on a 1.5 Tesla system, with clinically available multiecho gradient-recalled-echo (GRE) sequences for cardiac and liver imaging. A T2* single-echo GRE sequence was used as reference. Simulations were performed to assess accuracy and precision from 2000 measurements. Inter- and intraobserver variability was obtained in a patient study (n = 23). RESULTS: Simulations: Accuracy, in terms of the mean differences between the proposed method and true T2* ranged from 0-0.73 ms. Precision, in terms of confidence intervals of repeated measurements, was 0.06-4.74 ms showing agreement between the proposed uncertainty estimate and simulations. Phantom study: Bias and variability were 0.26 ± 4.23 ms (cardiac sequence) and -0.23 ± 1.69 ms (liver sequence). Patient study: Intraobserver variability was similar for experienced and inexperienced observers (0.03 ± 1.44 ms versus 0.16 ± 2.33 ms). Interobserver variability was 1.0 ± 3.77 ms for the heart and -0.52 ± 2.75 ms for the liver. CONCLUSION: The proposed algorithm was shown to provide robust T2* measurements and uncertainty estimates over the range of clinically relevant T2* values. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance.

Parallel simulations for QUAntifying RElaxation magnetic resonance constants (SQUAREMR): an example towards accurate MOLLI T1 measurements.

BACKGROUND: T1 mapping is widely used today in CMR, however, it underestimates true T1 values and its measurement error is influenced by several acquisition parameters. The purpose of this study was the extraction of accurate T1 data through the utilization of comprehensive, parallel Simulations for QUAntifying RElaxation Magnetic Resonance constants (SQUAREMR) of the MOLLI pulse sequence on a large population of spins with physiologically relevant tissue relaxation constants. METHODS: A CMR protocol consisting of different MOLLI schemes was performed on phantoms and healthy human volunteers. For every MOLLI experiment, the identical pulse sequence was simulated for a large range of physiological combinations of relaxation constants, resulting in a database of all possible outcomes. The unknown relaxation constants were then determined by finding the simulated signals in the database that produced the least squared difference to the measured signal intensities. RESULTS: SQUAREMR demonstrated improvement of accuracy in phantom studies and consistent mean T1 values and consistent variance across the different MOLLI schemes in humans. This was true even for tissues with long T1s and MOLLI schemes with no pause between modified-Look-Locker experiments. CONCLUSIONS: SQUAREMR enables quantification of T1 data obtained by existing clinical pulse sequences. SQUAREMR allows for correction of quantitative CMR data that have already been acquired whereas it is expected that SQUAREMR may improve data consistency and advance quantitative MR across imaging centers, vendors and experimental configurations. While this study is focused on a MOLLI-based T1-mapping technique, it could however be extended in other types of quantitative MRI throughout the body.

Whole-heart four-dimensional flow can be acquired with preserved quality without respiratory gating, facilitating clinical use: a head-to-head comparison.

BACKGROUND: Respiratory gating is often used in 4D-flow acquisition to reduce motion artifacts. However, gating increases scan time. The aim of this study was to investigate if respiratory gating can be excluded from 4D flow acquisitions without affecting quantitative intracardiac parameters. METHODS: Eight volunteers underwent CMR at 1.5 T with a 5-channel coil (5ch). Imaging included 2D flow measurements and whole-heart 4D flow with and without respiratory gating (Resp(+), Resp(-)). Stroke volume (SV), particle-trace volumes, kinetic energy, and vortex-ring volume were obtained from 4D flow-data. These parameters were compared between 5ch Resp(+) and 5ch Resp(-). In addition, 20 patients with heart failure were scanned using a 32-channel coil (32ch), and particle-trace volumes were compared to planimetric SV. Paired comparisons were performed using Wilcoxon's test and correlation analysis using Pearson r. Agreement was assessed as bias±SD. RESULTS: Stroke volume from 4D flow was lower compared to 2D flow both with and without respiratory gating (5ch Resp(+) 88±18 vs 97±24.0, p=0.001; 5ch Resp(-) 86±16 vs 97.1±22.7, p<0.01). There was a good correlation between Resp(+) and Resp(-) for particle-trace derived volumes (R2=0.82, 0.2±9.4 ml), mean kinetic energy (R2=0.86, 0.07±0.21 mJ), peak kinetic energy (R2=0.88, 0.14±0.77 mJ), and vortex-ring volume (R2=0.70, -2.5±9.4 ml). Furthermore, good correlation was found between particle-trace volume and planimetric SV in patients for 32ch Resp(-) (R2=0.62, -4.2±17.6 ml) and in healthy volunteers for 5ch Resp(+) (R2=0.89, -11±7 ml), and 5ch Resp(-) (R2=0.93, -7.5±5.4 ml), Average scan duration for Resp(-) was shorter compared to Resp(+) (27±9 min vs 61±19 min, p<0.05). CONCLUSIONS: Whole-heart 4D flow can be acquired with preserved quantitative results without respiratory gating, facilitating clinical use.

High performance MRI simulations of motion on multi-GPU systems.

BACKGROUND: MRI physics simulators have been developed in the past for optimizing imaging protocols and for training purposes. However, these simulators have only addressed motion within a limited scope. The purpose of this study was the incorporation of realistic motion, such as cardiac motion, respiratory motion and flow, within MRI simulations in a high performance multi-GPU environment. METHODS: Three different motion models were introduced in the Magnetic Resonance Imaging SIMULator (MRISIMUL) of this study: cardiac motion, respiratory motion and flow. Simulation of a simple Gradient Echo pulse sequence and a CINE pulse sequence on the corresponding anatomical model was performed. Myocardial tagging was also investigated. In pulse sequence design, software crushers were introduced to accommodate the long execution times in order to avoid spurious echoes formation. The displacement of the anatomical model isochromats was calculated within the Graphics Processing Unit (GPU) kernel for every timestep of the pulse sequence. Experiments that would allow simulation of custom anatomical and motion models were also performed. Last, simulations of motion with MRISIMUL on single-node and multi-node multi-GPU systems were examined. RESULTS: Gradient Echo and CINE images of the three motion models were produced and motion-related artifacts were demonstrated. The temporal evolution of the contractility of the heart was presented through the application of myocardial tagging. Better simulation performance and image quality were presented through the introduction of software crushers without the need to further increase the computational load and GPU resources. Last, MRISIMUL demonstrated an almost linear scalable performance with the increasing number of available GPU cards, in both single-node and multi-node multi-GPU computer systems. CONCLUSIONS: MRISIMUL is the first MR physics simulator to have implemented motion with a 3D large computational load on a single computer multi-GPU configuration. The incorporation of realistic motion models, such as cardiac motion, respiratory motion and flow may benefit the design and optimization of existing or new MR pulse sequences, protocols and algorithms, which examine motion related MR applications.

MRISIMUL: a GPU-based parallel approach to MRI simulations.

A new step-by-step comprehensive MR physics simulator (MRISIMUL) of the Bloch equations is presented. The aim was to develop a magnetic resonance imaging (MRI) simulator that makes no assumptions with respect to the underlying pulse sequence and also allows for complex large-scale analysis on a single computer without requiring simplifications of the MRI model. We hypothesized that such a simulation platform could be developed with parallel acceleration of the executable core within the graphic processing unit (GPU) environment. MRISIMUL integrates realistic aspects of the MRI experiment from signal generation to image formation and solves the entire complex problem for densely spaced isochromats and for a densely spaced time axis. The simulation platform was developed in MATLAB whereas the computationally demanding core services were developed in CUDA-C. The MRISIMUL simulator imaged three different computer models: a user-defined phantom, a human brain model and a human heart model. The high computational power of GPU-based simulations was compared against other computer configurations. A speedup of about 228 times was achieved when compared to serially executed C-code on the CPU whereas a speedup between 31 to 115 times was achieved when compared to the OpenMP parallel executed C-code on the CPU, depending on the number of threads used in multithreading (2-8 threads). The high performance of MRISIMUL allows its application in large-scale analysis and can bring the computational power of a supercomputer or a large computer cluster to a single GPU personal computer.

Potential of the predatory mite Phytoseius finitimus (Acari: Phytoseiidae) to feed and reproduce on greenhouse pests.

Phytoseiid mites of the genus Phytoseius are natural enemies of tetranychid and eriophyid herbivorous mites mostly found on hairy plants where they feed on prey, as well as on pollen. Nevertheless, the nutritional ecology and the role of these predators in biological pest control are only rarely addressed. In the present study, we evaluated the potential of Phytoseius finitimus to feed and reproduce on three major greenhouse pests, the two-spotted spider mite, the greenhouse whitefly and the western flower thrips. Additionally, we estimated the effect of cattail pollen when provided to the predator alone or in mixed diets with prey. Contrary to thrips larvae, both spider mite larvae and whitefly crawlers sustained the development of P. finitimus. In addition, females consumed more spider mite eggs and larvae, as well as whitefly crawlers than thrips larvae, but laid eggs when feeding on all prey. When provided alone, cattail pollen sustained the development and reproduction of the predator. The addition of pollen in mixed diets with prey reduced prey consumption, though it increased the predator's egg production. We discuss the implications of our findings for biological pest control.

Assessment of the limiting spatial resolution of an MRI scanner by direct analysis of the edge spread function.

Limiting spatial resolution is a key metric of the quality of magnetic resonance (MR) images, which can provide an indication of the smallest region that can effectively be imaged. In this paper a novel methodology for measuring the limiting spatial resolution of MR images is mathematically analyzed and successfully implemented on phantom images. The methodology presented in this paper is based on a direct fit of a mathematical expression of the edge spread function (ESF) profile to the ESF data acquired at the interface between different materials. The mathematical expression of ESF was determined by approximating the line spread function (LSF) of the system with a sinc function. The proposed methodology can be applied using signal data from magnitude MRI spin echo images and is not sensitive to noise amplification introduced by differentiating the ESF to produce the LSF, as performed in previous studies. In addition, the proposed methodology provides a quantitative, representative measurement of the limiting spatial resolution of MR images.