Mathematical Modeling and Numerical Simulation of Magnetic Susceptibility Artifacts in Magnetic Resonance IMAGING*

Abstract

The technique used to recognise information in Magnetic Resonance Imaging (MRI) is based on electromagnetic fields. A linearly varying field (around 10^?2 Tesla per meter) is added to a strong homogeneous magnetic field (order of magnitude of approximately one Tesla). When these fields are disturbed by the presence of a paramagnetic material, in the sample for instance, the resulting image is usually distorted, these distortions being termed artifacts. Our goal is to present a method, assuming the field disturbances are known, to construct the resulting images. A mathematical model of the MRI process is developed. The way the images are distorted in intensity and shape is explained and an algorithm to simulate magnetic susceptibility artifacts is deduced.     

Technical artifacts in magnetic resonance imaging

Various artifacts of Magnetic Resonance Imaging (MRI) typically associated with currently available imaging techniques such as projection reconstruction and two-dimensional fourier transform (2D-FT) are described and illustrated. Examples of MRI artifacts were obtained with an imaging unit with a super conducting magnet operated at .15 Tesla and .27 Tesla with corresponding proton resonance frequency of 6.4 MHz and 11.25 MHz. The .15 Tesla images were obtained using projection reconstruction and the .27 Tesla using the 2D-FT method. Instrument related artifacts include those due to direct current (DC), projection, gradient offset, active shimming, phase encoding, and pulse sequencing. Other often encountered artifacts are related to the patient. These include those due to motion, ferromagnetic effect, and tissue contents. The cause of these artifacts and how (if possible) they may be eliminated or minimized is discussed.     

Magnetic field direction differentially impacts the growth of different cell types

Magnetic resonance imaging (MRI) machines have horizontal or upright static magnetic field (SMF) of 0.1–3 T (Tesla) at sites of patients and operators, but the biological effects of these SMFs still remain elusive. We examined 12 different cell lines, including 5 human solid tumor cell lines, 2 human leukemia cell lines and 4 human non-cancer cell lines, as well as the Chinese hamster ovary cell line. Permanent magnets were used to provide 0.2–1 T SMFs with different magnetic field directions. We found that an upward magnetic field of 0.2–1 T could effectively reduce the cell numbers of all human solid tumor cell lines we tested, but a downward magnetic field mostly had no statistically significant effect. However, the leukemia cells in suspension, which do not have shape-induced anisotropy, were inhibited by both upward and downward magnetic fields. In contrast, the cell numbers of most non-cancer cells were not affected by magnetic fields of all directions. Moreover, the upward magnetic field inhibited GIST-T1 tumor growth in nude mice by 19.3% (p < 0.05) while the downward magnetic field did not produce significant effect. In conclusion, although still lack of mechanistical insights, our results show that different magnetic field directions produce divergent effects on cancer cell numbers as well as tumor growth in mice. This not only verified the safety of SMF exposure related to current MRI machines but also revealed the possible antitumor potential of magnetic field with an upward direction.     

Influence of strong static magnetic fields on primary cortical neurons

Intense uniform magnetic fields, such as those used in magnetic resonance imaging (MRI), are thought to exert little influence at the cellular level. Here we report modifications of the signaling cascades in rat cortical neurons cultured for 1 h in magnetic fields of up to 5 Tesla. The activation of c-Jun N-terminal kinase (JNK) increases monotonically with field strength, with a maximal activation of approximately 10% at 5 T, whereas the activation of extra cellular-regulated kinase (ERK) shows a maximum at 0.75 T ( approximately 10%). Since ERK is involved in cellular differentiation, these results indicate a magnetic induction of the signaling events associated with differentiation. However, the cells respond to further increases in field strength by evoking a stress response, since JNK is a stress-activated protein kinase. Three possible mechanisms are discussed and of these, the most plausible is magnetic field induced change in the membrane rest potential, a microscale magnetohydrodynamic effect. This mechanism most likely involves the activation of voltage dependent Ca(2+) channel opening; since intracellular Ca(2+) concentration was also found to be modified by the static magnetic field.     

Feasibility of using ultra-high field (7 T) MRI for clinical surgical targeting

The advantages of ultra-high magnetic field (7 Tesla) MRI for basic science research and neuroscience applications have proven invaluable. Structural and functional MR images of the human brain acquired at 7 T exhibit rich information content with potential utility for clinical applications. However, (1) substantial increases in susceptibility artifacts, and (2) geometrical distortions at 7 T would be detrimental for stereotactic surgeries such as deep brain stimulation (DBS), which typically use 1.5 T images for surgical planning. Here, we explore whether these issues can be addressed, making feasible the use of 7 T MRI to guide surgical planning. Twelve patients with Parkinson's disease, candidates for DBS, were scanned on a standard clinical 1.5 T MRI and a 7 T MRI scanner. Qualitative and quantitative assessments of global and regional distortion were evaluated based on anatomical landmarks and transformation matrix values. Our analyses show that distances between identical landmarks on 1.5 T vs. 7 T, in the mid-brain region, were less than one voxel, indicating a successful co-registration between the 1.5 T and 7 T images under these specific imaging parameter sets. On regional analysis, the central part of the brain showed minimal distortion, while inferior and frontal areas exhibited larger distortion due to proximity to air-filled cavities. We conclude that 7 T MR images of the central brain regions have comparable distortions to that observed on a 1.5 T MRI, and that clinical applications targeting structures such as the STN, are feasible with information-rich 7 T imaging.     

Diffusion Magnetic Resonance Imaging: What Water Tells Us about Biological Tissues

Since its introduction in the mid-1980s, diffusion magnetic resonance imaging (MRI), which measures the random motion of water molecules in tissues, revealing their microarchitecture, has become a pillar of modern neuroimaging. Its main clinical domain has been the diagnosis of acute brain stroke and neurogical disorders, but it is also used in the body for the detection and management of cancer lesions. It can also produce stunning maps of white matter tracks in the brain, with the potential to aid in the understanding of some psychiatric disorders. However, in order to exploit fully the potential of this method, a deeper understanding of the mechanisms that govern the diffusion of water in tissues is needed.In the mid-1980s, we showed that water diffusion in the human brain could be imaged by using magnetic resonance imaging (MRI) [1]. Since then, diffusion MRI has enjoyed a dramatic growth, with about 24,000 articles referenced in PubMed in 2014. MRI is a medical imaging technique consisting of magnetizing body atom nuclei, generally hydrogen nuclei of water molecules, using a very strong magnetic field (typically 30,000 to 60,000 times the earth’s natural magnetic field). The resulting very tiny magnetization can be manipulated in time by sending radiofrequency wave pulses at a resonant frequency. In turn, magnetized nuclei re-emit radiofrequency waves, creating a signal that is received through a coil (a kind of antenna), giving information on the nuclei magnetization properties. Magnetic field “gradient” pulses are used in addition to induce small variations of the magnetic field (and the associated radiowaves’ resonant frequency) in space, so as to spatially encode the magnetization information and create images. Magnetization varies a lot between tissues and various disease conditions, making MRI a very versatile imaging modality. However, the resolution of MRI images used for clinical practice often remains limited, typically around 1 mm (microscopic MRI is possible, but with dedicated preclinical MRI systems using ultra-high magnetic fields; see below). The concept of diffusion MRI emerged as a way to probe tissue structure at a microscopic (invisible) scale, although images are acquired at a millimetric scale: during their random, diffusion-driven displacements in the tissue, the water molecules probe the tissue structure at a microscopic scale, interacting with cell membranes, thus providing unique information on the functional architecture of tissues. Diffusion MRI has become a pillar of modern clinical imaging, used mainly to investigate neurological disorders such as acute brain ischemia, although it is now also a standard imaging method for other organs too, especially for the management of cancer patients. Indeed, diffusion MRI that does not require any tracer injection is rapidly becoming a modality of choice to detect and characterize malignant lesions. Moreover, in the brain, diffusion anisotropy in white matter can be exploited to produce stunning three-dimensional maps of brain connections, revealing faulty connections in some psychiatric disorders. More recently, diffusion MRI has been applied to monitor the dynamic changes occurring in the neural tissue structure during activation, a new approach to investigate functional neuroimaging and the mechanisms underlying neuronal activation.It is amazing that all these applications of diffusion MRI have emerged or developed while so little is known about water diffusion mechanisms in biological tissues. The relative importance of many factors governing water in tissues and their effects on the observed MRI signal are still not fully understood and are sometimes a subject of controversy.We will discuss the main applications and the outstanding issues remaining in the field in more detail below.     

Noninvasive magnetic resonance imaging of the development of individual colon cancer tumors in rat liver

Monitoring tumor development is essential for the understanding of mechanisms involved in tumor progression and to determine efficacy of therapy. One of the evolving approaches is longitudinal noninvasive magnetic resonance imaging (MRI) of tumors in experimental models. We applied high-resolution MRI at 7 Tesla to study the development of colon cancer tumors in rat liver. MRI acquisition was triggered to the respiratory cycle to minimize motion artifacts. A special radio frequency (RF) coil was designed to acquire detailed T1-weighted and T2-weighted images of the liver. T2-weighted images identified hyperintense lesions representing tumors with a minimum diameter of 2 mm, enabling the determination of growth rates and morphological aspects of individual tumors. It is concluded that high-resolution MRI using a dedicated RF coil and triggering to the respiratory cycle is an excellent tool for quantitative and morphological analysis of individual diffusely distributed tumors throughout the liver. However, at present, MRI requires expensive equipment and expertise and is a time-consuming methodology. Therefore, it should preferably be used for dedicated applications rather than for high-throughput assessment of total tumor load in animals.     

Magnetic resonance imaging: bioeffects and safety concerns

Magnetic resonance imaging (MRI) is the state-of-the-art noninvasive imaging modality in clinical diagnosis. During MRI examination, the patient is exposed to three different forms of electromagnetic radiation: (i) a static magnetic field, (ii) gradient magnetic fields, and (iii) radiofrequency (RF) fields. Each of these may cause significant adverse bioeffects if applied at sufficiently high exposure levels. This article describes in some detail the areas of health concern for both the patient and the health practitioner with respect to the use of clinical MRI, in addition to describing the potential bioeffects of electromagnetic radiations used in this sophisticated imaging modality.     

Automated analysis of low-field brain MRI in cerebral malaria

A central challenge of medical imaging studies is to extract biomarkers that characterize disease pathology or outcomes. Modern automated approaches have found tremendous success in high-resolution, high-quality magnetic resonance images. These methods, however, may not translate to low-resolution images acquired on magnetic resonance imaging (MRI) scanners with lower magnetic field strength. In low-resource settings where low-field scanners are more common and there is a shortage of radiologists to manually interpret MRI scans, it is critical to develop automated methods that can augment or replace manual interpretation, while accommodating reduced image quality. We present a fully automated framework for translating radiological diagnostic criteria into image-based biomarkers, inspired by a project in which children with cerebral malaria (CM) were imaged using low-field 0.35 Tesla MRI. We integrate multiatlas label fusion, which leverages high-resolution images from another sample as prior spatial information, with parametric Gaussian hidden Markov models based on image intensities, to create a robust method for determining ventricular cerebrospinal fluid volume. We also propose normalized image intensity and texture measurements to determine the loss of gray-to-white matter tissue differentiation and sulcal effacement. These integrated biomarkers have excellent classification performance for determining severe brain swelling due to CM.     

Alterations in the rat electrocardiogram induced by stationary magnetic fields

A field strength dependent increase in the amplitude of the T-wave signal in the rat electrocardiogram (ECG) was observed during exposure to homogeneous, stationary magnetic fields. For 24 adult Sprague-Dawley and Buffalo rats of both sexes, the T-wave amplitude was found to increase by an average of 408% in a 2.0 Tesla (1 Tesla = 10⁴ Gauss) field. No significant magnetically induced changes were observed in other components of the ECG record, including the P wave and the QRS complex. The minimum field level at which augmentation of the T wave could be detected was 0.3 Tesla. The magnetically induced increase in T-wave amplitude occurred instantaneously, and was immediately reversible after exposure to fields as high as 2.0 Tesla. No abnormalities in any component of the ECG record, including the T wave, were noted during a period of 3 weeks following cessation of a continuous 5-h exposure of rats to a 1.5-Tesla field. The heart rate and breathing rate of adult rats were not altered during, or subsequent to, application of fields up to 2.0 Tesla. The effect of animal orientation within the field was tested using juvenile rats 3–14 days old. The maximum increase in T-wave amplitude was observed when subjects were placed with the long axis of the body perpendicular to the lines of magnetic induction. These experimental observations, as well as theoretical considerations, suggest that augmentation of the signal amplitude in the T-wave segment of the ECG may result from a superimposed electrical potential generated by aortic blood flow in the presence of a stationary magnetic field.     

Effects of magnetic resonance imaging on eye development in the C57BL/6J mouse

An investigation was undertaken to ascertain the potential teratogenicity of magnetic resonance imaging (MRI) fields. The C57BL/6J mouse was chosen as the experimental model with eye malformations (microphthalmia and morphologic anomalies) designated as the biological end point. This mouse strain is genetically predisposed to this type of malformation as a 10% spontaneous incidence occurs. Dams in groups of 15 were subjected to MRI imaging conditions on gestational day (Gd) 7 for 36 minutes to a spin-echo T-2-weighted scan by using a 1.5 Tesla magnetic field and a radiofrequency (RF) field of 64 MHz. One group was exposed at the magnetic isocenter while another was exposed at the entrance to the magnet lumen. There was also a sham control group. The dams were sacrificed at Gd 14. Assessment of eye abnormality was determined by, 1) a veterinary ophthalmologist, 2) a computer-based method comparing eye areas, and 3) a methodology combining both the above subjective and quantitative methods. MRI fields were found to produce malformation rates (15-37%) higher than controls (2-19% P less than or equal to .05, Kruskal-Wallis Test) for both isocenter and lumen entrance groups. The malformation rates and degree of statistical significance varied somewhat with analytical methodology and the unit of measure (right eye, left eye, or fetus). The results suggest for the first time the potential of MRI fields to produce developmental malformations in an animal model utilizing clinically realistic exposure conditions. (However, the reader is remained that the mouse strain utilized in this investigation was genetically prone to malformations).     

Nonequilibrium Magnetic Response of Anisotropic Superparamagnetic Nanoparticles and Possible Artifacts in Magnetic Particle Imaging

Magnetic responses of superparamagnetic nanoparticles to high-frequency AC magnetic fields with sufficiently large amplitudes are numerically simulated to exactly clarify the phenomena occurring in magnetic particle imaging. When the magnetic anisotropy energy inevitable in actual nanoparticles is taken into account in considering the magnetic potential, larger nanoparticles exhibit a delayed response to alternations of the magnetic fields. This kind of delay is rather remarkable in the lower-amplitude range of the field, where the assistance by the Zeeman energy to thermally activated magnetization reversal is insufficient. In some cases, a sign inversion of the third-order harmonic response was found to occur at some specific amplitude, despite the lack in DC bias magnetic field strength. Considering the attenuation of the AC magnetic field generated in the human body, it is possible that the phases of the signals from nanoparticles deep inside the body and those near the body surface are completely different. This may lead to artifacts in the reconstructed image. Furthermore, when the magnetic/thermal torque-driven rotation of the anisotropic nanoparticles as well as the magnetic anisotropy energy are taken into account, the simulated results show that, once the easy axes are aligned toward the direction of the DC bias magnetic field, it takes time to randomize them at the field-free point. During this relaxation, the third-order harmonic response depends highly upon the history of the magnetic field. This is because non-linearity of the anhysteretic magnetization curve for the superparamagnetic nanoparticles varies with the orientations of the easy axes. This history dependence may also lead to another artifact in magnetic particle imaging, when the scanning of the field-free point is faster than the Brownian relaxations.     

On the Vertigo Due to Static Magnetic Fields

Vertigo is sometimes experienced in and around MRI scanners. Mechanisms involving stimulation of the vestibular system by movement in magnetic fields or magnetic field spatial gradients have been proposed. However, it was recently shown that vestibular-dependent ocular nystagmus is evoked when stationary in homogenous static magnetic fields. The proposed mechanism involves Lorentz forces acting on endolymph to deflect semicircular canal (SCC) cupulae. To investigate whether vertigo arises from a similar mechanism we recorded qualitative and quantitative aspects of vertigo and 2D eye movements from supine healthy adults (n = 25) deprived of vision while pushed into the 7T static field of an MRI scanner. Exposures were variable and included up to 135s stationary at 7T. Nystagmus was mainly horizontal, persisted during long-exposures with partial decline, and reversed upon withdrawal. The dominant vertiginous perception with the head facing up was rotation in the horizontal plane (85% incidence) with a consistent direction across participants. With the head turned 90 degrees in yaw the perception did not transform into equivalent vertical plane rotation, indicating a context-dependency of the perception. During long exposures, illusory rotation lasted on average 50 s, including 42 s whilst stationary at 7T. Upon withdrawal, perception re-emerged and reversed, lasting on average 30 s. Onset fields for nystagmus and perception were significantly correlated (p<.05). Although perception did not persist as long as nystagmus, this is a known feature of continuous SSC stimulation. These observations, and others in the paper, are compatible with magnetic-field evoked-vertigo and nystagmus sharing a common mechanism. With this interpretation, response decay and reversal upon withdrawal from the field, are due to adaptation to continuous vestibular input. Although the study does not entirely exclude the possibility of mechanisms involving transient vestibular stimulation during movement in and out of the bore, we argue these are less likely.     

Precision and comparison of CT-, MRI- and DL-controlled interventions exemplified by lumbar facet infiltration--an experimental study]

We evaluated the accuracy of the needle tip representation by different imaging techniques for the guidance of facet infiltrations. For visualisation of the lumbar facet joints we used a high-field magnetic resonance tomograph (MRT) with a 2.0 Tesla field and 3.5 mm slice thickness, an open low-field magnetic resonance tomography (MRT) with an 0.064 Tesla field and 9 mm slice thickness, and IMATRON electron beam computed tomograph (EBCT) with a slice thickness of 6 mm, and a mobile C-arm fluoroscope. The study was performed on 4 human cadaveric lumber spine preparations, each of which had 8 facet joints. Under imaging control, special injection needles were placed as close as possible to the facet joint space. Following placement of he needle, all specimens were scanned with the electron beam tomograph using a slice thickness of 1.5 mm. The thin-slice study served as the gold standard. The distance between the tip of the needle and the facet joint was measured in all the images. Comparison of the different modalities with the gold standard revealed the following results: 1) median values of the absolute differences were 1.25 mm for high-field MRI, 1.35 mm for 6 mm EBCT, 2.05 mm for low-field MRI, and 2.30 mm for X-ray fluoroscopy. 2) While there was no statistically significant difference in the accuracy of tip localization between high-field MRI and 6" EBCT (p = 0.293), both systems were more precise than low-field MRI (p = 0.04) and X-ray fluoroscopy (p = 0.009). When choosing the best imaging technique, such additional factors as radiation, costs and time, must also be considered. Provided necessary radiological precautions are taken, and assuming careful pre-interventional planning, CT. EBCT and X-ray fluoroscopy are currently more effective than the expensive, time-consuming and costly magnetic resonance tomography.     

Preliminary studies on the use of magnetic resonance imaging with Gd-DTPA to monitor ovarian function in subhuman primates

These studies were initiated to explore the use of magnetic resonance imaging (MRI) to investigate follicular growth in subhuman primates. Four adult cynomolgus monkeys received an i.v. injection of a magnetic resonance (MR) contrast agent, gadolinium diethylenetriaminepentaacetic acid (Gd-DTPA), and ovaries were removed 1-20 min later. Gd-DTPA is an extracellular fluid marker that is readily detectable in MRI. Individual ovaries were imaged using a 3-in (7.62 cm) radiofrequency surface coil and a 1.5 Tesla magnet. MR images of these ovaries provided a high resolution visualization of follicles with diameters of 1 mm and greater. Results obtained with MRI were similar to hematoxylin/eosin-stained sections of the same ovaries photographed at low magnification. These results demonstrate that MRI provides excellent resolution of ovarian follicles in macaques and thus may be suitable to monitor follicular growth and atresia in this species.     

The effects of the use of piezoelectric motors in a 1.5-Tesla high-field magnetic resonance imaging system (MRI).

PURPOSE: This paper presents the results of an experimental investigation with two different rotatory piezomotors in a closed 1.5 Tesla high-field MRI. The focus of the investigation was on testing the functionality of these motors within the MRI and to determining the image interference they caused. MATERIALS AND METHODS: To obtain a differentiated estimate of the interference the motors were tested in both the passive (turned off, i.e. without current flow) and active (turned on, i.e. with current flow) state during MRI scanning. Three different types of sequences were used for the test: Spin-Echo (SE), Gradient-Echo (GE) and Echo-Planar Imaging (EPI). A plastic container filled with a gadolinium-manganese solution was used for representation of the artefacts. The motors investigated were placed parallel to the container at predetermined distances during the experiment. RESULTS AND CONCLUSIONS: The results show that the motors investigated suffered no functional limitations in the magnetic field of the MRI but, depending on the type of motor, the measurement distance and the state of the motor, the motors had different effects on the sequence images. A motor in the off-state placed immediately next to the object to be measured mainly causes artefacts because of its material properties. If, on the other hand, the piezomotor is in the on-state images with strong noise result when the motor is immediately next to the object being measured. The images regain their normal quality when the motor is approximately at a distance of 1 m from the object being investigated. Driving the motor inside the MRI, therefore, is only to be recommended during the pauses in scanning: this delivers artefact-free images if minimal, motor-specific distances are kept to. With regard to the three different types of sequences it was determined that the SE sequence was the least sensitive and the EPI sequence the most sensitive to disturbance. The GE sequence showed only minimal differences to the SE sequence with regard to signal-to-noise ratios. Since it requires considerably shorter scan-times it can be considered to be the most effective type of sequence under these conditions.     

Aligning Paramecium caudatum with static magnetic fields

As they negotiate their environs, unicellular organisms adjust their swimming in response to various physical fields such as temperature, chemical gradients, and electric fields. Because of the weak magnetic properties of most biological materials, however, they do not respond to the earth's magnetic field (5 x 10(-5) Tesla) except in rare cases. Here, we show that the trajectories of Paramecium caudatum align with intense static magnetic fields >3 Tesla. Otherwise straight trajectories curve in magnetic fields and eventually orient parallel or antiparallel to the applied field direction. Neutrally buoyant immobilized paramecia also align with their long axis in the direction of the field. We model this magneto-orientation as a strictly passive, nonphysiological response to a magnetic torque exerted on the diamagnetically anisotropic components of the paramecia. We have determined the average net anisotropy of the diamagnetic susceptibility, Deltachi(p), of a whole Paramecium: Deltachi(p) = (6.7+/- 0.7) x 10(-23) m(3). We show how the measured Deltachi(p) compares to the anisotropy of the diamagnetic susceptibilities of the components in the cell. We suggest that magnetic fields can be exploited as a novel, noninvasive, quantitative means to manipulate swimming populations of unicellular organisms.