Adapting source grid parameters to improve the condition of the magnetostatic linear inverse problem of estimating nanoparticle distributions

Data-driven model optimization for optically pumped magnetometer sensor arrays

Optically pumped magnetometers (OPMs) have reached sensitivity levels that make them viable portable alternatives to traditional superconducting technology for magnetoencephalography (MEG). OPMs do not require cryogenic cooling and can therefore be placed directly on the scalp surface. Unlike cryogenic systems, based on a well-characterised fixed arrays essentially linear in applied flux, OPM devices, based on different physical principles, present new modelling challenges. Here, we outline an empirical Bayesian framework that can be used to compare between and optimise sensor arrays. We perturb the sensor geometry (via simulation) and with analytic model comparison methods estimate the true sensor geometry. The width of these perturbation curves allows us to compare different MEG systems. We test this technique using simulated and real data from SQUID and OPM recordings using head-casts and scanner-casts. Finally, we show that given knowledge of underlying brain anatomy, it is possible to estimate the true sensor geometry from the OPM data themselves using a model comparison framework. This implies that the requirement for accurate knowledge of the sensor positions and orientations a priori may be relaxed. As this procedure uses the cortical manifold as spatial support there is no co-registration procedure or reliance on scalp landmarks.

Multi-color magnetic nanoparticle imaging using magnetorelaxometry

Magnetorelaxometry (MRX) is a well-known measurement technique which allows the retrieval of magnetic nanoparticle (MNP) characteristics such as size distribution and clustering behavior. This technique also enables the non-invasive reconstruction of the spatial MNP distribution by solving an inverse problem, referred to as MRX imaging. Although MRX allows the imaging of a broad range of MNP types, little research has been done on imaging different MNP types simultaneously. Biomedical applications can benefit significantly from a measurement technique that allows the separation of the resulting measurement signal into its components originating from different MNP types. In this paper, we present a theoretical procedure and experimental validation to show the feasibility of MRX imaging in reconstructing multiple MNP types simultaneously. Because each particle type has its own characteristic MRX signal, it is possible to take this a priori information into account while solving the inverse problem. This way each particle type's signal can be separated and its spatial distribution reconstructed. By assigning a unique color code and intensity to each particle type's signal, an image can be obtained in which each spatial distribution is depicted in the resulting color and with the intensity measuring the amount of particles of that type, hence the name multi-color MNP imaging. The theoretical procedure is validated by reconstructing six phantoms, with different spatial arrangements of multiple MNP types, using MRX imaging. It is observed that MRX imaging easily allows up to four particle types to be separated simultaneously, meaning their quantitative spatial distributions can be obtained.

Magnetorelaxometry procedures for quantitative imaging and characterization of magnetic nanoparticles in biomedical applications

BACKGROUND

Quantitative knowledge about the spatial distribution and local environment of magnetic nanoparticles (MNPs) inside an organism is essential for guidance and improvement of biomedical applications such as magnetic hyperthermia and magnetic drug targeting. Magnetorelaxometry (MRX) provides such quantitative information by detecting the magnetic response of MNPs following a fast change in the applied magnetic field.

METHODS

In this article, we review our MRX based procedures that enable both the characterization and the quantitative imaging of MNPs in a biomedical environment.

RESULTS

MRX characterization supported the selection of an MNP system with colloidal stability and suitable cellular MNP uptake. Spatially resolved MRX, a procedure employing multi-channel MRX measurements allowed for in-vivo monitoring of the MNP distribution in a pre-clinical carcinoma animal model. Extending spatially resolved MRX by consecutive magnetization of distinct parts of the sample led to a demonstration of MRX tomography. With this tomography, we reconstructed the three dimensional MNP distribution inside animal sized phantoms with a sensitivity of milligrams of MNPs per cm3. In addition, the targeting efficiency of MNPs in whole blood was assessed using a flow phantom and MRX quantification.

CONCLUSION

These MRX based measurement and analysis procedures have substantially supported the development of MNP based biomedical applications.

Toward 2D and 3D imaging of magnetic nanoparticles using EPR measurements

PURPOSE

Magnetic nanoparticles (MNPs) are an important asset in many biomedical applications. An effective working of these applications requires an accurate knowledge of the spatial MNP distribution. A promising, noninvasive, and sensitive technique to visualize MNP distributions in vivo is electron paramagnetic resonance (EPR). Currently only 1D MNP distributions can be reconstructed. In this paper, the authors propose extending 1D EPR toward 2D and 3D using computer simulations to allow accurate imaging of MNP distributions.

METHODS

To find the MNP distribution belonging to EPR measurements, an inverse problem needs to be solved. The solution of this inverse problem highly depends on the stability of the inverse problem. The authors adapt 1D EPR imaging to realize the imaging of multidimensional MNP distributions. Furthermore, the authors introduce partial volume excitation in which only parts of the volume are imaged to increase stability of the inverse solution and to speed up the measurements. The authors simulate EPR measurements of different 2D and 3D MNP distributions and solve the inverse problem. The stability is evaluated by calculating the condition measure and by comparing the actual MNP distribution to the reconstructed MNP distribution. Based on these simulations, the authors define requirements for the EPR system to cope with the added dimensions. Moreover, the authors investigate how EPR measurements should be conducted to improve the stability of the associated inverse problem and to increase reconstruction quality.

RESULTS

The approach used in 1D EPR can only be employed for the reconstruction of small volumes in 2D and 3D EPRs due to numerical instability of the inverse solution. The authors performed EPR measurements of increasing cylindrical volumes and evaluated the condition measure. This showed that a reduction of the inherent symmetry in the EPR methodology is necessary. By reducing the symmetry of the EPR setup, quantitative images of larger volumes can be obtained. The authors found that, by selectively exciting parts of the volume, the authors could increase the reconstruction quality even further while reducing the amount of measurements. Additionally, the inverse solution of this activation method degrades slower for increasing volumes. Finally, the methodology was applied to noisy EPR measurements: using the reduced EPR setup's symmetry and the partial activation method, an increase in reconstruction quality of ≈ 80% can be seen with a speedup of the measurements with 10%.

CONCLUSIONS

Applying the aforementioned requirements to the EPR setup and stabilizing the EPR measurements showed a tremendous increase in noise robustness, thereby making EPR a valuable method for quantitative imaging of multidimensional MNP distributions.

Optimal Magnetic Sensor Vests for Cardiac Source Imaging

Magnetocardiography (MCG) non-invasively provides functional information about the heart. New room-temperature magnetic field sensors, specifically magnetoresistive and optically pumped magnetometers, have reached sensitivities in the ultra-low range of cardiac fields while allowing for free placement around the human torso. Our aim is to optimize positions and orientations of such magnetic sensors in a vest-like arrangement for robust reconstruction of the electric current distributions in the heart. We optimized a set of 32 sensors on the surface of a torso model with respect to a 13-dipole cardiac source model under noise-free conditions. The reconstruction robustness was estimated by the condition of the lead field matrix. Optimization improved the condition of the lead field matrix by approximately two orders of magnitude compared to a regular array at the front of the torso. Optimized setups exhibited distributions of sensors over the whole torso with denser sampling above the heart at the front and back of the torso. Sensors close to the heart were arranged predominantly tangential to the body surface. The optimized sensor setup could facilitate the definition of a standard for sensor placement in MCG and the development of a wearable MCG vest for clinical diagnostics.

Quantitative model selection for enhanced magnetic nanoparticle imaging in magnetorelaxometry

PURPOSE

The performance of an increasing number of biomedical applications is dependent on the accurate knowledge of the spatial magnetic nanoparticle (MNP) distribution in the body. Magnetorelaxometry (MRX) imaging is a promising and noninvasive technique for the reconstruction of this distribution. To date, no accurate and quantitative measure is available to compare and optimize different MRX imaging models and setups independent of the MNP distribution. In this paper, the authors employ statistical parameters to develop quantitative MRX imaging models. Using these models, a straightforward optimization of setups and models is possible resulting in improved MNP reconstructions.

METHODS

A MRX imaging setup is considered with different coil configurations, each corresponding to a MRX imaging model. The models can be represented by a sensitivity matrix. These are compared by employing the matrices as inputs to statistical parameters such as conditional entropy and mutual information (MI). These parameters determine the best model to reconstruct the MNP amount for each volume-element (voxel) in the sample. The matrix is transformed by multiplying the columns with different weightings depending on the performance of the MRX imaging model with respect to the other models. This transformed matrix is compared to the original sensitivity matrix without weightings.

RESULTS

Compared to the original sensitivity matrix, an increased numerical stability and improved noise robustness for the transformed sensitivity matrix are observed. The reconstruction of the MNP shows improvements: a correlation to the actual MNP distribution of 99.2%, whereas the original matrix only had 82.5%. By selecting the MRX models with the smallest MI, the authors are able to reduce the measurement time by 65% and still obtain an improved imaging accuracy and noise robustness. The statistical parameters allow a direct measure of the relative information content within the setup such that the optimal voxel size for the MRX setup is determined to be between 5 and 15 mm, while other sizes show a significant change in the statistical parameters.

CONCLUSIONS

The use of statistical parameters in MRX imaging models results in quantitative models which can optimize MRX setups in a very fast and elegant way such that improved MNP imaging can be realized. Finally, the presented measure allows to quantitatively and accurately compare different MRX models and setups independent of the MNP distribution.

Real-Time MEG Source Localization Using Regional Clustering

With its millisecond temporal resolution, Magnetoencephalography (MEG) is well suited for real-time monitoring of brain activity. Real-time feedback allows the adaption of the experiment to the subject's reaction and increases time efficiency by shortening acquisition and off-line analysis. Two formidable challenges exist in real-time analysis: the low signal-to-noise ratio (SNR) and the limited time available for computations. Since the low SNR reduces the number of distinguishable sources, we propose an approach which downsizes the source space based on a cortical atlas and allows to discern the sources in the presence of noise. Each cortical region is represented by a small set of dipoles, which is obtained by a clustering algorithm. Using this approach, we adapted dynamic statistical parametric mapping for real-time source localization. In terms of point spread and crosstalk between regions the proposed clustering technique performs better than selecting spatially evenly distributed dipoles. We conducted real-time source localization on MEG data from an auditory experiment. The results demonstrate that the proposed real-time method localizes sources reliably in the superior temporal gyrus. We conclude that real-time source estimation based on MEG is a feasible, useful addition to the standard on-line processing methods, and enables feedback based on neural activity during the measurements.

Magnetic nanoparticle imaging by random and maximum length sequences of inhomogeneous activation fields

Biomedical applications of magnetic nanoparticles require a precise knowledge of their biodistribution. From multi-channel magnetorelaxometry measurements, this distribution can be determined by means of inverse methods. It was recently shown that the combination of sequential inhomogeneous excitation fields in these measurements is favorable regarding the reconstruction accuracy when compared to homogeneous activation . In this paper, approaches for the determination of activation sequences for these measurements are investigated. Therefor, consecutive activation of single coils, random activation patterns and families of m-sequences are examined in computer simulations involving a sample measurement setup and compared with respect to the relative condition number of the system matrix. We obtain that the values of this condition number decrease with larger number of measurement samples for all approaches. Random sequences and m-sequences reveal similar results with a significant reduction of the required number of samples. We conclude that the application of pseudo-random sequences for sequential activation in the magnetorelaxometry imaging of magnetic nanoparticles considerably reduces the number of required sequences while preserving the relevant measurement information.