Calibration-Free Relaxation-Based Multi-Color Magnetic Particle Imaging

Magnetic particle imaging (MPI) is a novel imaging modality with important potential applications, such as angiography, stem cell tracking, and cancer imaging. Recently, there have been efforts to increase the functionality of MPI via multi-color imaging methods that can distinguish the responses of different nanoparticles, or nanoparticles in different environmental conditions. The proposed techniques typically rely on extensive calibrations that capture the differences in the harmonic responses of the nanoparticles. In this paper, we propose a method to directly estimate the relaxation time constant of the nanoparticles from the MPI signal, which is then used to generate a multi-color relaxation map. The technique is based on the underlying mirror symmetry of the adiabatic MPI signal when the same region is scanned back and forth. We validate the proposed method via simulations, and via experiments on our in-house magnetic particle spectrometer setup at 10.8 kHz and our in-house MPI scanner at 9.7 kHz. Our results show that nanoparticles can be successfully distinguished with the proposed technique, without any calibration or prior knowledge about the nanoparticles.

Related papers:

title: Human PNS and SAR study in the frequency range from 24 to 162 kHz
abstract: In order to identify suitable operating conditions for future clinical Magnetic Particle Imaging, peripheral nerve stimulation (PNS) and specific absorption rate (SAR) experiments have been performed by exposing volunteers to sinusoidally time-varying magnetic fields along and transverse to the body axis at frequencies from 24 kHz to 162 kHz. The findings show that future clinical MPI can advantageously be performed at elevated drive-field frequencies, with PNS restriction actually relaxed at higher frequencies, and with still acceptable SAR exposure.

title: Magnetostimulation Limits in Magnetic Particle Imaging
abstract: For magnetic particle imaging (MPI), specific absorption rate (SAR) and more critically magnetostimulation (i.e., dB/dt) safety limits will determine the optimal scan parameters, such as the drive field strength and frequency. These parameters will impact the scanning speed, field-of-view (FOV) and signal-to-noise ratio in MPI. Understanding the potential safety hazards of the drive field is critical for scaling MPI for human use. In this work, we demonstrate that magnetostimulation is the primary magnetic safety consideration in MPI, and we describe the first human-subject magnetostimulation threshold experiments for MPI using homogeneous coils. Our experiments, performed on the arm and leg, indicate that magnetostimulation thresholds monotonically decrease with increasing frequency. Additionally, we show for the first time that a strong inverse correlation exists between the threshold and the body part size. The chronaxie time, on the other hand, did not vary with body part size. We conclude with an estimation of the magnetostimulation thresholds for a full-body MPI scanner: a mean asymptotic threshold of 14.3 mT-pp (peak-to-peak) with a mean chronaxie time of 289 μs, which correspond to a magnetostimulation threshold of about 15 mT-pp for frequencies between 25 and 50 kHz. These findings will have a great impact on the optimization of MPI parameters, especially in determining the number of partial FOVs required to cover a region of interest.

title: MPI Safety in the View of MRI Safety Standards
abstract: In assessing the safety aspect of future clinical magnetic particle imaging (MPI), this novel imaging technique can refer to expertise that is cumulated in the IEC standard for magnetic resonance imaging (MRI) safety. Both imaging techniques employ strong dynamic magnetic fields and therefore have to take caution to refrain from physiological effects such as peripheral nerve stimulation (PNS) or excessive tissue heating. This paper starts with an outline of the differences between MPI and MRI. Then, the basics of PNS and tissue heating are reviewed and applied to the specific MPI case. Finally, sequences for MPI are presented that will allow rapid MPI imaging at 150 kHz while being safe for the patient.

title: Effects of pulse duration on magnetostimulation thresholds.
abstract: Medical imaging techniques such as magnetic resonance imaging and magnetic particle imaging (MPI) utilize time-varying magnetic fields that are subject to magnetostimulation limits, which often limit the speed of the imaging process. Various human-subject experiments have studied the amplitude and frequency dependence of these thresholds for gradient or homogeneous magnetic fields. Another contributing factor was shown to be number of cycles in a magnetic pulse, where the thresholds decreased with longer pulses. The latter result was demonstrated on two subjects only, at a single frequency of 1.27 kHz. Hence, whether the observed effect was due to the number of cycles or due to the pulse duration was not specified. In addition, a gradient-type field was utilized; hence, whether the same phenomenon applies to homogeneous magnetic fields remained unknown. Here, the authors investigate the pulse duration dependence of magnetostimulation limits for a 20-fold range of frequencies using homogeneous magnetic fields, such as the ones used for the drive field in MPI.



Magnetostimulation thresholds were measured in the arms of six healthy subjects (age: 27 ± 5 yr). Each experiment comprised testing the thresholds at eight different pulse durations between 2 and 125 ms at a single frequency, which took approximately 30-40 min/subject. A total of 34 experiments were performed at three different frequencies: 1.2, 5.7, and 25.5 kHz. A solenoid coil providing homogeneous magnetic field was used to induce stimulation, and the field amplitude was measured in real time. A pre-emphasis based pulse shaping method was employed to accurately control the pulse durations. Subjects reported stimulation via a mouse click whenever they felt a twitching/tingling sensation. A sigmoid function was fitted to the subject responses to find the threshold at a specific frequency and duration, and the whole procedure was repeated at all relevant frequencies and pulse durations.



The magnetostimulation limits decreased with increasing pulse duration (T(pulse)). For T(pulse) < 18 ms, the thresholds were significantly higher than at the longest pulse durations (p < 0.01, paired Wilcoxon signed-rank test). The normalized magnetostimulation threshold (B(Norm)) vs duration curve at all three frequencies agreed almost identically, indicating that the observed effect is independent of the operating frequency. At the shortest pulse duration (T(pulse) ≈ 2 ms), the thresholds were approximately 24% higher than at the asymptotes. The thresholds decreased to within 4% of their asymptotic values for T(pulse) > 20 ms. These trends were well characterized (R(2) = 0.78) by a stretched exponential function given by B(Norm)=1+αe(-T(pulse)/β(γ)) , where the fitted parameters were α = 0.44, β = 4.32, and γ = 0.60.



This work shows for the first time that the magnetostimulation thresholds decrease with increasing pulse duration, and that this effect is independent of the operating frequency. Normalized threshold vs duration trends are almost identical for a 20-fold range of frequencies: the thresholds are significantly higher at short pulse durations and settle to within 4% of their asymptotic values for durations longer than 20 ms. These results emphasize the importance of matching the human-subject experiments to the imaging conditions of a particular setup. Knowing the dependence of the safety limits to all contributing factors is critical for increasing the time-efficiency of imaging systems that utilize time-varying magnetic fields.

title: Effects of Duty Cycle on Magnetostimulation Thresholds in MPI
abstract: Magnetic Particle Imaging (MPI) relies on time-varying magnetic fields to generate an image of the spatial distribution of superparamagnetic iron oxide nanoparticles. However, these oscillating magnetic field form electric field patterns within the body, which in turn can cause peripheral nerve stimulations (PNS), also known as magnetostimulation. To prevent potential safety hazards and to optimize the scanning parameters such as field-of-view (FOV) and scanning speed in MPI, the factors that affect drive field magnetostimulation limits need to be determined accurately. In this work, we investigate the effects of the duty cycle on magnetostimulation thresholds in MPI. We performed human subject experiments by using a highly homogenous solenoidal coil on the upper arm of six subjects. Six different duty cycles ranging between 5\% and 100\% were applied at 25 kHz. Accordingly, magnetostimulation limits first decrease and then increase with increasing duty cycle, reaching a maximum at 100\% duty cycle. Since high duty cycles would be the preferred operating mode for rapid imaging with MPI, these results have promising implications for future human-sized MPI systems.

title: Projection X-Space Magnetic Particle Imaging
abstract: Projection magnetic particle imaging (MPI) can improve imaging speed by over 100-fold over traditional 3-D MPI. In this work, we derive the 2-D x-space signal equation, 2-D image equation, and introduce the concept of signal fading and resolution loss for a projection MPI imager. We then describe the design and construction of an x-space projection MPI scanner with a field gradient of 2.35 T/m across a 10 cm magnet free bore. The system has an expected resolution of 3.5 × 8.0 mm using Resovist tracer, and an experimental resolution of 3.8 × 8.4 mm resolution. The system images 2.5 cm × 5.0 cm partial field-of views (FOVs) at 10 frames/s, and acquires a full field-of-view of 10 cm × 5.0 cm in 4 s. We conclude by imaging a resolution phantom, a complex “Cal” phantom, mice injected with Resovist tracer, and experimentally confirm the theoretically predicted x-space spatial resolution.

title: Third Generation X-Space MPI Mouse and Rat Scanner
abstract: Here we describe the construction of our third generation x-space MPI scanner, the fifth MPI scanner built at UC Berkeley. The scanner has two goals, (1) High-resolution native MPI resolution using x-space reconstruction, and (2) extended FOV suitable for mice and rats. In this paper we describe our design criteria, and we show the initial characterizations of the 7 T/m gradient field.

title: A 7 T/M 3D X-space MPI mouse and rat scanner
abstract: This prototype system has already produced high quality images with spatial resolutions very similar to the theoretically predicted resolution across mouse and rat sized FOVs. We have imaged both plastic and biological imaging phantoms, as well as ex vivo mice (not shown). Some early images are shown below in Fig. 1b-c. Imaging times are comparable to micro-MRI: full mouse and rat images (up to 12 cm × 5 cm × 5 cm) require between 2-5 minutes per image.

title: Signal encoding in magnetic particle imaging: properties of the system function
abstract: BackgroundMagnetic particle imaging (MPI) is a new tomographic imaging technique capable of imaging magnetic tracer material at high temporal and spatial resolution. Image reconstruction requires solving a system of linear equations, which is characterized by a "system function" that establishes the relation between spatial tracer position and frequency response. This paper for the first time reports on the structure and properties of the MPI system function.MethodsAn analytical derivation of the 1D MPI system function exhibits its explicit dependence on encoding field parameters and tracer properties. Simulations are used to derive properties of the 2D and 3D system function.ResultsIt is found that for ideal tracer particles in a harmonic excitation field and constant selection field gradient, the 1D system function can be represented by Chebyshev polynomials of the second kind. Exact 1D image reconstruction can thus be performed using the Chebyshev transform. More realistic particle magnetization curves can be treated as a convolution of the derivative of the magnetization curve with the Chebyshev functions. For 2D and 3D imaging, it is found that Lissajous excitation trajectories lead to system functions that are closely related to tensor products of Chebyshev functions.ConclusionSince to date, the MPI system function has to be measured in time-consuming calibration scans, the additional information derived here can be used to reduce the amount of information to be acquired experimentally and can hence speed up system function acquisition. Furthermore, redundancies found in the system function can be removed to arrive at sparser representations that reduce memory load and allow faster image reconstruction.

title: Model-Based Reconstruction for Magnetic Particle Imaging
abstract: Magnetic particle imaging (MPI) is a new imaging modality capable of imaging distributions of superparamagnetic nanoparticles with high sensitivity, high spatial resolution and, in particular, high imaging speed. The image reconstruction process requires a system function, describing the mapping between particle distribution and acquired signal. To date, the system function is acquired in a tedious calibration procedure by sequentially measuring the signal of a delta sample at the positions of a grid that covers the field of view. In this work, for the first time, the system function is calculated using a model of the signal chain. The modeled system function allows for reconstruction of the particle distribution in a 1-D MPI experiment. The approach thus enables fast generation of system functions on arbitrarily dense grids. Furthermore, reduction in memory requirements may be feasible by generating parts of the system function on the fly during reconstruction instead of keeping the complete matrix in memory.

title: Weighted iterative reconstruction for magnetic particle imaging.
abstract: Magnetic particle imaging (MPI) is a new imaging technique capable of imaging the distribution of superparamagnetic particles at high spatial and temporal resolution. For the reconstruction of the particle distribution, a system of linear equations has to be solved. The mathematical solution to this linear system can be obtained using a least-squares approach. In this paper, it is shown that the quality of the least-squares solution can be improved by incorporating a weighting matrix using the reciprocal of the matrix-row energy as weights. A further benefit of this weighting is that iterative algorithms, such as the conjugate gradient method, converge rapidly yielding the same image quality as obtained by singular value decomposition in only a few iterations. Thus, the weighting strategy in combination with the conjugate gradient method improves the image quality and substantially shortens the reconstruction time. The performance of weighting strategy and reconstruction algorithms is assessed with experimental data of a 2D MPI scanner.

title: The X-Space Formulation of the Magnetic Particle Imaging Process: 1-D Signal, Resolution, Bandwidth, SNR, SAR, and Magnetostimulation
abstract: The magnetic particle imaging (MPI) imaging process is a new method of medical imaging with great promise. In this paper we derive the 1-D MPI signal, resolution, bandwidth requirements, signal-to-noise ratio (SNR), specific absorption rate, and slew rate limitations. We conclude with experimental data measuring the point spread function for commercially available SPIO nanoparticles and a demonstration of the principles behind 1-D imaging using a static offset field. Despite arising from the nonlinear temporal response of a magnetic nanoparticle to a changing magnetic field, the imaging process is linear in the magnetization distribution and can be described as a convolution. Reconstruction in one dimension is exact and has a well-behaved quasi-Lorentzian point spread function. The spatial resolution improves cubically with increasing diameter of the SPIO domain, inverse to absolute temperature, linearly with saturation magnetization, and inversely with gradient. The bandwidth requirements approach a megahertz for reasonable imaging parameters and millimeter scale resolutions, and the SNR increases with the scanning rate. The limit to SNR as we scale MPI to human sizes will be patient heating. SAR and magnetostimulation limits give us surprising relations between optimal scanning speeds and scanning frequency for different types of scanners.

title: Multidimensional X-Space Magnetic Particle Imaging
abstract: Magnetic particle imaging (MPI) is a promising new medical imaging tracer modality with potential applications in human angiography, cancer imaging, in vivo cell tracking, and inflammation imaging. Here we demonstrate both theoretically and experimentally that multidimensional MPI is a linear shift-invariant imaging system with an analytic point spread function. We also introduce a fast image reconstruction method that obtains the intrinsic MPI image with high signal-to-noise ratio via a simple gridding operation in x-space. We also demonstrate a method to reconstruct large field-of-view (FOV) images using partial FOV scanning, despite the loss of first harmonic image information due to direct feedthrough contamination. We conclude with the first experimental test of multidimensional x-space MPI.

title: First experimental evidence of the feasibility of multi-color magnetic particle imaging.
abstract: Magnetic particle imaging is a new approach to visualizing magnetic nanoparticles. It is capable of 3D real-time in vivo imaging of particles injected into the blood stream and is a candidate for medical imaging applications. To date, only one particle type has been imaged at a time, however, the ability to separate signals acquired simultaneously from different particle types or from particles in different environments would substantially increase the scope of the method. Different colors could be assigned to different signal sources to allow for visualization in a single image. Successful signal separation has been reported in spectroscopic experiments, but it was unclear how well separation would work in conjunction with spatial encoding in an imaging experiment. This work presents experimental evidence of the separability of signals from different particle types and aggregation states (fluid versus powder) using a 'multi-color' reconstruction approach. Several mechanisms are discussed that may form the basis for successful signal separation.

title: Magnetic Particle Imaging: A Resovist based Marking Technology for Guide Wires and Catheters for Vascular Interventions.
abstract: Magnetic Particle Imaging (MPI) is able to provide high temporal and good spatial resolution, high signal to noise ratio and sensitivity. Furthermore, it is a truly quantitative method as its signal strength is proportional to the concentration of its tracer, superparamagnetic iron oxide nanoparticles (SPIOs), over a wide range practically relevant concentrations. Thus, MPI is proposed as a promising future method for guidance of vascular interventions. To implement this, devices such as guide wires and catheters have to be discernible in MPI, which can be achieved by coating already commercially available devices with SPIOs. In this proof of principle study the feasibility of that approach is demonstrated. First, a Ferucarbotran-based SPIO-varnish was developed by embedding Ferucarbotran into an organic based solvent. Subsequently, the biocompatible varnish was applied to a commercially available guidewire and diagnostic catheter for vascular interventional purposes. In an interventional setting using a vessel phantom, the coating proved to be mechanically and chemically stable and thin enough to ensure normal handling as with uncoated devices. The devices were visualized in 3D on a preclinical MPI demonstrator using a system function based image reconstruction process. The system function was acquired with a probe of the dried varnish prior to the measurements. The devices were visualized with a very hightemporal resolution and a simple catheter/guide wire maneuver was demonstrated.

title: Steering of magnetic devices with a magnetic particle imaging system
abstract: The time-domain device localization scheme can be combined with focus-field based shifting of the imaging volume in order to stabilize and manipulate the device position. In the 1D steering experiment, localization and force exertion are interleaved. The device is initially localized on the right side (1) and steered to the center (2). Once arrived and localized at the desired position, the steering algorithm centers the imaging volume on the device position (3) in order to average out the forces. After the user defines a new target position, the device is steered to this point (4) and stabilized there (5). This experiment has been done in a viscous medium to reduce the device velocity explaining the long steering times. In another experiment not shown here, a steering sequence levitates the object in a viscous medium demonstrating that the method can create forces greater than gravitational force.

title: Interactive Magnetic Catheter Steering With 3-D Real-Time Feedback Using Multi-Color Magnetic Particle Imaging
abstract: Magnetic particle imaging (MPI) is an emerging tomographic method that enables sensitive and fast imaging. It does not require ionizing radiation and thus may be a safe alternative for tracking of devices in the catheterization laboratory. The 3-D real-time imaging capabilities of MPI have been demonstrated in vivo and recent improvements in fast online image reconstruction enable almost real-time data reconstruction and visualization. Moreover, based on the use of different magnetic particle types for catheter visualization and blood pool imaging, multi-color MPI enables reconstruction of separate images for the catheter and the vessels from simultaneously measured data. While these are important assets for interventional imaging, MPI field generators can furthermore apply strong forces on a magnetic catheter tip. It is the aim of this paper to give a first demonstration of the combination of real-time multi-color MPI with online reconstruction and interactive field control for the application of forces on a magnetic catheter model in a phantom experiment.

title: Simultaneous magnetic particle imaging (MPI) and temperature mapping using multi-color MPI
abstract: Magnetic Particle Imaging (MPI) is a novel imaging technique based on the non-linear magnetization response of super-paramagnetic iron oxide nanoparticles (SPIOs). It has previously been shown that beside the spatial particle distribution, information about the particle type, its environment, and the particle temperature can be obtained from the magnetic particle signal. Successful separation of particle types and temperature measurements have been reported in spectroscopic experiments, but a simultaneous mapping of the particle distribution and temperature in a spatially encoded imaging experiment has not been performed. This work presents simultaneous imaging and temperature mapping using a ‘multi-color’ reconstruction approach.

title: Measurement of molecular binding using the Brownian motion of magnetic nanoparticle probes
abstract: Molecular binding is important in many venues including antibody binding for diagnostic and therapeutic agents and pharmaceutical function. We demonstrate that a method of measuring nanoparticle Brownian motion, termed magnetic spectroscopy of nanoparticle Brownian motion (MSB), can be used to monitor molecular binding and the bound fraction. It is plausible that MSB can be used to measure binding in vivo because the same signal has been used to image nanoparticles in nanogram quantities in vivo.

title: Multifunctional Nanocarriers for diagnostics, drug delivery and targeted treatment across blood-brain barrier: perspectives on tracking and neuroimaging
abstract: Nanotechnology has brought a variety of new possibilities into biological discovery and clinical practice. In particular, nano-scaled carriers have revolutionalized drug delivery, allowing for therapeutic agents to be selectively targeted on an organ, tissue and cell specific level, also minimizing exposure of healthy tissue to drugs. In this review we discuss and analyze three issues, which are considered to be at the core of nano-scaled drug delivery systems, namely functionalization of nanocarriers, delivery to target organs and in vivo imaging. The latest developments on highly specific conjugation strategies that are used to attach biomolecules to the surface of nanoparticles (NP) are first reviewed. Besides drug carrying capabilities, the functionalization of nanocarriers also facilitate their transport to primary target organs. We highlight the leading advantage of nanocarriers, i.e. their ability to cross the blood-brain barrier (BBB), a tightly packed layer of endothelial cells surrounding the brain that prevents high-molecular weight molecules from entering the brain. The BBB has several transport molecules such as growth factors, insulin and transferrin that can potentially increase the efficiency and kinetics of brain-targeting nanocarriers. Potential treatments for common neurological disorders, such as stroke, tumours and Alzheimer's, are therefore a much sought-after application of nanomedicine. Likewise any other drug delivery system, a number of parameters need to be registered once functionalized NPs are administered, for instance their efficiency in organ-selective targeting, bioaccumulation and excretion. Finally, direct in vivo imaging of nanomaterials is an exciting recent field that can provide real-time tracking of those nanocarriers. We review a range of systems suitable for in vivo imaging and monitoring of drug delivery, with an emphasis on most recently introduced molecular imaging modalities based on optical and hybrid contrast, such as fluorescent protein tomography and multispectral optoacoustic tomography. Overall, great potential is foreseen for nanocarriers in medical diagnostics, therapeutics and molecular targeting. A proposed roadmap for ongoing and future research directions is therefore discussed in detail with emphasis on the development of novel approaches for functionalization, targeting and imaging of nano-based drug delivery systems, a cutting-edge technology poised to change the ways medicine is administered.

title: Viscous effects on nanoparticle magnetization harmonics
abstract: Dynamic magnetization of nanoparticles is a promising means of functional biosensing. We demonstrate a method for rapid monitoring of relative changes in the viscous environment of superparamagnetic nanoparticles using a ratio of magnetization harmonics. Initial results are capable of detecting changes in viscosity on the order of 0.05 cP. This technique should allow for real-time monitoring of many of the dynamic magnetization applications which have been proposed using AC susceptibility. Further, incorporation of this technique into a harmonic-based imaging system like magnetic particle imaging would allow for in vivo functional imaging capabilities.

title: Magnetic nanoparticle temperature estimation.
abstract: The authors present a method of measuring the temperature of magnetic nanoparticles that can be adapted to provide in vivo temperature maps. Many of the minimally invasive therapies that promise to reduce health care costs and improve patient outcomes heat tissue to very specific temperatures to be effective. Measurements are required because physiological cooling, primarily blood flow, makes the temperature difficult to predict a priori. The ratio of the fifth and third harmonics of the magnetization generated by magnetic nanoparticles in a sinusoidal field is used to generate a calibration curve and to subsequently estimate the temperature. The calibration curve is obtained by varying the amplitude of the sinusoidal field. The temperature can then be estimated from any subsequent measurement of the ratio. The accuracy was 0.3 degree K between 20 and 50 degrees C using the current apparatus and half-second measurements. The method is independent of nanoparticle concentration and nanoparticle size distribution.

title: Relaxation-based viscosity mapping for magnetic particle imaging.
abstract: Magnetic particle imaging (MPI) has been shown to provide remarkable contrast for imaging applications such as angiography, stem cell tracking, and cancer imaging. Recently, there is growing interest in the functional imaging capabilities of MPI, where 'color MPI' techniques have explored separating different nanoparticles, which could potentially be used to distinguish nanoparticles in different states or environments. Viscosity mapping is a promising functional imaging application for MPI, as increased viscosity levels in vivo have been associated with numerous diseases such as hypertension, atherosclerosis, and cancer. In this work, we propose a viscosity mapping technique for MPI through the estimation of the relaxation time constant of the nanoparticles. Importantly, the proposed time constant estimation scheme does not require any prior information regarding the nanoparticles. We validate this method with extensive experiments in an in-house magnetic particle spectroscopy (MPS) setup at four different frequencies (between 250 Hz and 10.8 kHz) and at three different field strengths (between 5 mT and 15 mT) for viscosities ranging between 0.89 mPa · s-15.33 mPa · s. Our results demonstrate the viscosity mapping ability of MPI in the biologically relevant viscosity range.

title: Dual-frequency magnetic particle imaging of the Brownian particle contribution
abstract: Magnetic particle imaging (MPI) is an emerging medical imaging modality based on the non-linear response of magnetic nanoparticles to an exciting magnetic field. MPI has been recognized as a fast imaging technique with high spatial resolution in the mm range. For some applications of MPI, especially in the field of functional imaging, the determination of the particle mobility (Brownian rotation) is of great interest, as it enables binding detection in MPI. It also enables quantitative imaging in the presence of Brownian-dominated particles, which is otherwise implausible. Discrimination of different particle responses in MPI is possible via the joint reconstruction approach. In this contribution, we propose a dual-frequency acquisition scheme to enhance sensitivity and contrast in the detection of different particle mobilities compared to a standard single-frequency MPI protocol. The method takes advantage of the fact, that the magnetization response of the tracer is strongly frequency-dependent, i.e. for low excitation frequencies a stronger Brownian contribution is observed.

title: Preliminary experimental X-space color MPI
abstract: Previous work has explored the effects of nanoparticle relaxation from the system matrix and x-space reconstruction points of view [1-8]. Here we demonstrate how relaxation can be used to “colorize” an image based on relaxation mechanisms using x-space reconstruction [9] and a pixel-wise linear model.

title: Relaxation in X-Space Magnetic Particle Imaging
abstract: Magnetic particle imaging (MPI) is a new imaging modality that noninvasively images the spatial distribution of superparamagnetic iron oxide nanoparticles (SPIOs). MPI has demonstrated high contrast and zero attenuation with depth, and MPI promises superior safety compared to current angiography methods, X-ray, computed tomography, and magnetic resonance imaging angiography. Nanoparticle relaxation can delay the SPIO magnetization, and in this work we investigate the open problem of the role relaxation plays in MPI scanning and its effect on the image. We begin by amending the X-space theory of MPI to include nanoparticle relaxation effects. We then validate the amended theory with experiments from a Berkeley x-space relaxometer and a Berkeley x-space projection MPI scanner. Our theory and experimental data indicate that relaxation reduces SNR and asymmetrically blurs the image in the scanning direction. While relaxation effects can have deleterious effects on the MPI scan, we show theoretically and experimentally that x-space reconstruction remains robust in the presence of relaxation. Furthermore, the role of relaxation in x-space theory provides guidance as we develop methods to minimize relaxation-induced blurring. This will be an important future area of research for the MPI community.

title: Low drive field amplitude for improved image resolution in magnetic particle imaging.
abstract: Magnetic particle imaging (MPI) is a new imaging technology that directly detects superparamagnetic iron oxide nanoparticles. The technique has potential medical applications in angiography, cell tracking, and cancer detection. In this paper, the authors explore how nanoparticle relaxation affects image resolution. Historically, researchers have analyzed nanoparticle behavior by studying the time constant of the nanoparticle physical rotation. In contrast, in this paper, the authors focus instead on how the time constant of nanoparticle rotation affects the final image resolution, and this reveals nonobvious conclusions for tailoring MPI imaging parameters for optimal spatial resolution.



The authors first extend x-space systems theory to include nanoparticle relaxation. The authors then measure the spatial resolution and relative signal levels in an MPI relaxometer and a 3D MPI imager at multiple drive field amplitudes and frequencies. Finally, these image measurements are used to estimate relaxation times and nanoparticle phase lags.



The authors demonstrate that spatial resolution, as measured by full-width at half-maximum, improves at lower drive field amplitudes. The authors further determine that relaxation in MPI can be approximated as a frequency-independent phase lag. These results enable the authors to accurately predict MPI resolution and sensitivity across a wide range of drive field amplitudes and frequencies.



To balance resolution, signal-to-noise ratio, specific absorption rate, and magnetostimulation requirements, the drive field can be a low amplitude and high frequency. Continued research into how the MPI drive field affects relaxation and its adverse effects will be crucial for developing new nanoparticles tailored to the unique physics of MPI. Moreover, this theory informs researchers how to design scanning sequences to minimize relaxation-induced blurring for better spatial resolution or to exploit relaxation-induced blurring for MPI with molecular contrast.

title: Simultaneous relaxation estimation and image reconstruction in MPI
abstract: Blurring of the images due to the relaxation effects of the magnetic nanoparticles is one of the important issues in Magnetic Particle Imaging (MPI)[1-4]. In x-space reconstructed images, relaxation blurs the image along the scanning direction, and deteriorates both the resolution and the signal-to-noise ratio (SNR) of the image[5]. Hence, removing the effects of relaxation without distorting the underlying image is crucial for increasing the efficiency of the MPI technique. Theoretically, relaxation is modelled as an exponential function r(t) = (1/τ)exp(-t/τ)u(t) using the first-order Debye process, where r(t) is then convolved with the adiabatic MPI signal[5]. Previous studies have looked into estimating the relaxation time constant, τ, using a calibration scan on a point source or using an MPI relaxometer setup[5]. In theory, if one can estimate the relaxation time constant, a deconvolution technique could be employed to obtain the underlying adiabatic MPI signal, which would yield an image unaffected by the relaxation blur. In this work, we propose a solution for blind estimation of τ directly from the MPI signal, without using a calibration scan and without the knowledge of the Langevin response of the nanoparticles.

title: Linearity and Shift Invariance for Quantitative Magnetic Particle Imaging
abstract: Magnetic Particle Imaging (MPI) is a promising tracer imaging modality that employs a kidney-safe contrast agent and does not use ionizing radiation. MPI already shows high contrast and sensitivity in small animal imaging, with great potential for many clinical applications, including angiography, cancer detection, inflammation imaging, and treatment monitoring. Currently, almost all clinically relevant imaging techniques can be modeled as systems with linearity and shift invariance (LSI), characteristics crucial for quantification and diagnostic utility. In theory, MPI has been proven to be LSI. However, in practice, high-pass filters designed to remove unavoidable direct feedthrough interference also remove information crucial to ensuring LSI in MPI scans. In this work, we present a complete theoretical and experimental description of the image artifacts from filtering. We then propose and validate a robust algorithm to completely restore the lost information for the x-space MPI method. We provide the theoretical, simulated, and experimental proof that our algorithm indeed restores the LSI properties of MPI.

title: Some methods for classification and analysis of multivariate observations
abstract: The main purpose of this paper is to describe a process for partitioning an N-dimensional population into k sets on the basis of a sample. The process, which is called 'k-means,' appears to give partitions which are reasonably efficient in the sense of within-class variance. That is, if p is the probability mass function for the population, S = {S1, S2, * *, Sk} is a partition of EN, and ui, i = 1, 2, * , k, is the conditional mean of p over the set Si, then W2(S) = ff=ISi f z u42 dp(z) tends to be low for the partitions S generated by the method. We say 'tends to be low,' primarily because of intuitive considerations, corroborated to some extent by mathematical analysis and practical computational experience. Also, the k-means procedure is easily programmed and is computationally economical, so that it is feasible to process very large samples on a digital computer. Possible applications include methods for similarity grouping, nonlinear prediction, approximating multivariate distributions, and nonparametric tests for independence among several variables. In addition to suggesting practical classification methods, the study of k-means has proved to be theoretically interesting. The k-means concept represents a generalization of the ordinary sample mean, and one is naturally led to study the pertinent asymptotic behavior, the object being to establish some sort of law of large numbers for the k-means. This problem is sufficiently interesting, in fact, for us to devote a good portion of this paper to it. The k-means are defined in section 2.1, and the main results which have been obtained on the asymptotic behavior are given there. The rest of section 2 is devoted to the proofs of these results. Section 3 describes several specific possible applications, and reports some preliminary results from computer experiments conducted to explore the possibilities inherent in the k-means idea. The extension to general metric spaces is indicated briefly in section 4. The original point of departure for the work described here was a series of problems in optimal classification (MacQueen ) which represented special

title: Magnetic Particle Imaging With Tailored Iron Oxide Nanoparticle Tracers
abstract: Magnetic particle imaging (MPI) shows promise for medical imaging, particularly in angiography of patients with chronic kidney disease. As the first biomedical imaging technique that truly depends on nanoscale materials properties, MPI requires highly optimized magnetic nanoparticle tracers to generate quality images. Until now, researchers have relied on tracers optimized for MRI T2*-weighted imaging that are sub-optimal for MPI. Here, we describe new tracers tailored to MPI's unique physics, synthesized using an organic-phase process and functionalized to ensure biocompatibility and adequate in vivo circulation time. Tailored tracers showed up to 3 × greater signal-to-noise ratio and better spatial resolution than existing commercial tracers in MPI images of phantoms.

title: Twenty-fold acceleration of 3D projection reconstruction MPI
abstract: We experimentally demonstrate a 20-fold improvement in acquisition time in projection reconstruction (PR) magnetic particle imaging (MPI) relative to the state-of-the-art PR MPI imaging results. We achieve this acceleration in our imaging system by introducing an additional Helmholtz electromagnet pair, which creates a slow shift (focus) field. Because of magnetostimulation limits in humans, we show that scan time with three-dimensional (3D) PR MPI is theoretically within the same order of magnitude as 3D MPI with a field free point; however, PR MPI has an order of magnitude signal-to-noise ratio gain.

title: Image reconstruction for echo planar imaging with nonequidistant k‐space sampling
abstract: Echo planar imaging is characterized by scanning the 2D k‐space after a single excitation. Different sampling patterns have been proposed. A technically feasible method uses a sinusoidal readout gradient resulting in measured data that does not sample k‐space in an equidistant manner. In order to employ a conventional 2D‐FFT image reconstruction, the data have to be converted to a Cartesian grid. This can be done either by interpolation or alternatively by a generalized transformation. Filtering methods are described to minimize ghosting artifact that is typical in echo planar imaging. Results both from computer simulation and from experiments will be presented. Experimental images were obtained using a 2‐T whole‐body research system.

title: Non-Equispaced System Matrix Acquisition for Magnetic Particle Imaging Based on Lissajous Node Points
abstract: Magnetic Particle Imaging (MPI) is an emerging technology in the field of (pre)clinical imaging. The acquisition of a particle signal is realized along specific sampling trajectories covering a defined field of view (FOV). In a system matrix (SM) based reconstruction procedure, the commonly used acquisition path in MPI is a Lissajous trajectory. Such a trajectory features an inhomogeneous coverage of the FOV, i.e. the center region is sampled less dense than the regions towards the edges of the FOV. Conventionally, the respective SM acquisition and the subsequent reconstruction do not reflect this inhomogeneous coverage. Instead, they are performed on an equispaced grid. The objective of this work is to introduce a sampling grid that inherently features the aforementioned inhomogeneity by using node points of Lissajous trajectories. Paired with a tailored polynomial interpolation of the reconstructed MPI signal, the entire image can be recovered. It is the first time that such a trajectory related non-equispaced grid is used for image reconstruction on simulated and measured MPI data and it is shown that the number of sampling positions can be reduced, while the spatial resolution remains constant.

title: Electronic Field Free Line Rotation and Relaxation Deconvolution in Magnetic Particle Imaging
abstract: It has been shown that magnetic particle imaging (MPI), an imaging method suggested in 2005, is capable of measuring the spatial distribution of magnetic nanoparticles. Since the particles can be administered as biocompatible suspensions, this method promises to perform well as a tracer-based medical imaging technique. It is capable of generating real-time images, which will be useful in interventional procedures, without utilizing any harmful radiation. To obtain a signal from the administered superparamagnetic iron oxide (SPIO) particles, a sinusoidal changing external homogeneous magnetic field is applied. To achieve spatial encoding, a gradient field is superimposed. Conventional MPI works with a spatial encoding field that features a field free point (FFP). To increase sensitivity, an improved spatial encoding field, featuring a field free line (FFL) can be used. Previous FFL scanners, featuring a 1-D excitation, could demonstrate the feasibility of the FFL-based MPI imaging process. In this work, an FFL-based MPI scanner is presented that features a 2-D excitation field and, for the first time, an electronic rotation of the spatial encoding field. Furthermore, the role of relaxation effects in MPI is starting to move to the center of interest. Nevertheless, no reconstruction schemes presented thus far include a dynamical particle model for image reconstruction. A first application of a model that accounts for relaxation effects in the reconstruction of MPI images is presented here in the form of a simplified, but well performing strategy for signal deconvolution. The results demonstrate the high impact of relaxation deconvolution on the MPI imaging process.