Improved magnetic drug targeting with maximized magnetic forces and limited particle spreading.

BACKGROUND: In magnetic drug targeting (MDT), micro- or nanoparticles are injected into the human body to locally deliver therapeutics. These magnetic particles can be guided from a distance by external magnetic fields and gradients from electromagnets. PURPOSE: During the particles' movement through the vascular network, they are affected by magnetic forces, fluid (drag) forces, particle interactions, diffusion, etc. Adequate targeting is hindered when drag forces overcome the magnetic forces and particles present in vessels are carried away from the targeted region. Moreover, the magnetic force directions and diffusion mechanisms can cause particles to scatter, while they should remain together for an effective targeting performance. In this work, these adverse effects are tackled using optimization methods. METHODS: We formulate an optimization problem with respect to the currents in surrounding electromagnets that aims to maximize the magnetic force on a particle along a predefined direction. A boundary on the magnetic force divergence is introduced as a constraint to limit particle spreading. We also consider particles to be moved from an initial to a target location in a finite-time interval. To this end dynamic optimization is applied. RESULTS: Simulations for particles in a bifurcated vessel show an increase of particle speed by 20% and a successful movement towards the targeted regions without spreading. For the dynamic optimization, simulation results demonstrate that particle collections are accurately guided with 10 times less scattering and 10 times more particles at the target than without the divergence constraint. CONCLUSIONS: The proposed methods significantly improve the steering and capturing of particles in a region of interest. They are applicable to any magnetic drug targeting configuration with electromagnets.

Model-based optimized steering and focusing of local magnetic particle concentrations for targeted drug delivery.

Magnetic drug targeting (MDT) is an application in the field of targeted drug delivery in which magnetic (nano)particles act as drug carriers. The particles can be steered toward specific regions in the human body by adapting the currents of external (electro)magnets. Accurate models of particle movement and control algorithms for the electromagnet currents are two of the many requirements to ensure effective drug targeting. In this work, a control approach for the currents is presented, based on an underlying physical model that describes the dynamics of particles in a liquid in terms of their concentration in each point in space. Using this model, the control algorithm determines the currents generating the magnetic fields that maximize the particle concentration in spots of interest over a period of time. Such an approach is computationally only feasible thanks to our innovative combination of model order reduction with the method of direct multiple shooting. Simulation results of an in-vitro targeting setup demonstrated that a particle collection can be successfully guided toward the targeted spot with limited dispersion through a surrounding liquid. As now present and future particle behavior can be taken into account, and non-stationary surrounding liquids can be dealt with, a more precise and flexible targeting is achieved compared to existing MDT methods. This proves that the presented methodology can bring MDT closer to its clinical application. Moreover, the developed model is compatible with state-of-the-art imaging methods, paving the way for theranostic platforms that combine both therapy as well as diagnostics.

On Entropy Regularized Path Integral Control for Trajectory Optimization.

In this article, we present a generalized view on Path Integral Control (PIC) methods. PIC refers to a particular class of policy search methods that are closely tied to the setting of Linearly Solvable Optimal Control (LSOC), a restricted subclass of nonlinear Stochastic Optimal Control (SOC) problems. This class is unique in the sense that it can be solved explicitly yielding a formal optimal state trajectory distribution. In this contribution, we first review the PIC theory and discuss related algorithms tailored to policy search in general. We are able to identify a generic design strategy that relies on the existence of an optimal state trajectory distribution and finds a parametric policy by minimizing the cross-entropy between the optimal and a state trajectory distribution parametrized by a parametric stochastic policy. Inspired by this observation, we then aim to formulate a SOC problem that shares traits with the LSOC setting yet that covers a less restrictive class of problem formulations. We refer to this SOC problem as Entropy Regularized Trajectory Optimization. The problem is closely related to the Entropy Regularized Stochastic Optimal Control setting which is often addressed lately by the Reinforcement Learning (RL) community. We analyze the theoretical convergence behavior of the theoretical state trajectory distribution sequence and draw connections with stochastic search methods tailored to classic optimization problems. Finally we derive explicit updates and compare the implied Entropy Regularized PIC with earlier work in the context of both PIC and RL for derivative-free trajectory optimization.

Transfer Learning in ECG Classification from Human to Horse Using a Novel Parallel Neural Network Architecture.

Automatic or semi-automatic analysis of the equine electrocardiogram (eECG) is currently not possible because human or small animal ECG analysis software is unreliable due to a different ECG morphology in horses resulting from a different cardiac innervation. Both filtering, beat detection to classification for eECGs are currently poorly or not described in the literature. There are also no public databases available for eECGs as is the case for human ECGs. In this paper we propose the use of wavelet transforms for both filtering and QRS detection in eECGs. In addition, we propose a novel robust deep neural network using a parallel convolutional neural network architecture for ECG beat classification. The network was trained and tested using both the MIT-BIH arrhythmia and an own made eECG dataset with 26.440 beats on 4 classes: normal, premature ventricular contraction, premature atrial contraction and noise. The network was optimized using a genetic algorithm and an accuracy of 97.7% and 92.6% was achieved for the MIT-BIH and eECG database respectively. Afterwards, transfer learning from the MIT-BIH dataset to the eECG database was applied after which the average accuracy, recall, positive predictive value and F1 score of the network increased with an accuracy of 97.1%.

Modeling transcranial magnetic stimulation from the induced electric fields to the membrane potentials along tractography-based white matter fiber tracts.

OBJECTIVE: Transcranial magnetic stimulation (TMS) is a promising non-invasive tool for modulating the brain activity. Despite the widespread therapeutic and diagnostic use of TMS in neurology and psychiatry, its observed response remains hard to predict, limiting its further development and applications. Although the stimulation intensity is always maximum at the cortical surface near the coil, experiments reveal that TMS can affect deeper brain regions as well. APPROACH: The explanation of this spread might be found in the white matter fiber tracts, connecting cortical and subcortical structures. When applying an electric field on neurons, their membrane potential is altered. If this change is significant, more likely near the TMS coil, action potentials might be initiated and propagated along the fiber tracts towards deeper regions. In order to understand and apply TMS more effectively, it is important to capture and account for this interaction as accurately as possible. Therefore, we compute, next to the induced electric fields in the brain, the spatial distribution of the membrane potentials along the fiber tracts and its temporal dynamics. MAIN RESULTS: This paper introduces a computational TMS model in which electromagnetism and neurophysiology are combined. Realistic geometry and tissue anisotropy are included using magnetic resonance imaging and targeted white matter fiber tracts are traced using tractography based on diffusion tensor imaging. The position and orientation of the coil can directly be retrieved from the neuronavigation system. Incorporating these features warrants both patient- and case-specific results. SIGNIFICANCE: The presented model gives insight in the activity propagation through the brain and can therefore explain the observed clinical responses to TMS and their inter- and/or intra-subject variability. We aspire to advance towards an accurate, flexible and personalized TMS model that helps to understand stimulation in the connected brain and to target more focused and deeper brain regions.

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.

Computational evaluation of amplitude modulation for enhanced magnetic nanoparticle hyperthermia.

Magnetic nanoparticles (MNPs) can interact with alternating magnetic fields (AMFs) to deposit localized energy for hyperthermia treatment of cancer. Hyperthermia is useful in the context of multimodality treatments with radiation or chemotherapy to enhance disease control without increased toxicity. The unique attributes of heat deposition and transfer with MNPs have generated considerable attention and have been the focus of extensive investigations to elucidate mechanisms and optimize performance. Three-dimensional (3D) simulations are often conducted with the finite element method (FEM) using the Pennes' bioheat equation. In the current study, the Pennes' equation was modified to include a thermal damage-dependent perfusion profile to improve model predictions with respect to known physiological responses to tissue heating. A normal distribution of MNPs in a model liver tumor was combined with empirical nanoparticle heating data to calculate tumor temperature distributions and resulting survival fraction of cancer cells. In addition, calculated spatiotemporal temperature changes were compared among magnetic field amplitude modulations of a base 150-kHz sinusoidal waveform, specifically, no modulation, sinusoidal, rectangular, and triangular modulation. Complex relationships were observed between nanoparticle heating and cancer tissue damage when amplitude modulation and damage-related perfusion profiles were varied. These results are tantalizing and motivate further exploration of amplitude modulation as a means to enhance efficiency of and overcome technical challenges associated with magnetic nanoparticle hyperthermia (MNH).

Robustness assessment of 1-d electron paramagnetic resonance for improved magnetic nanoparticle reconstructions.

Electron paramagnetic resonance (EPR) is a sensitive measurement technique which can be used to recover the 1-D spatial distribution of magnetic nanoparticles (MNP) noninvasively. This can be achieved by solving an inverse problem that requires a numerical model for interpreting the EPR measurement data. This paper assesses the robustness of this technique by including different types of errors such as setup errors, measurement errors, and sample positioning errors in the numerical model. The impact of each error is estimated for different spatial MNP distributions. Additionally, our error models are validated by comparing the simulated impact of errors to the impact on lab EPR measurements. Furthermore, we improve the solution of the inverse problem by introducing a combination of truncated singular value decomposition and nonnegative least squares. This combination enables to recover both smooth and discontinuous MNP distributions. From this analysis, conclusions are drawn to improve MNP reconstructions with EPR and to state requirements for using EPR as a 2-D and 3-D imaging technique for MNP.

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.

Optimizing bipolar radiofrequency ablation treatment by means of pulsed currents.

Given the high mortality rate, liver cancer is considered to be a difficult cancer to treat. Consequently, alternative strategies are being developed such as radiofrequency ablation (RFA). RFA applies radiofrequent currents leading to local heating of the tumoral tissue. Accurate numerical modeling contributes to a better knowledge of the physical phenomena and allows optimizations. In this work, the bipolar radiofrequency ablation technique is explored followed by an optimization by means of pulsed currents. Numerical results clearly show the larger ablation zones due to the pulsed currents. Hence, pulsed bipolar RFA increases the efficacy and has the potential to be incorporated in clinical practice.

Subspace electrode selection methodology for EEG multiple source localization error reduction due to uncertain conductivity values.

This paper proposes a modification of the subspace correlation cost function and the Recursively Applied and Projected Multiple Signal Classification (RAP-MUSIC) method for electroencephalography (EEG) source analysis in epilepsy. This enables to reconstruct neural source locations and orientations that are less degraded due to the uncertain knowledge of the head conductivity values. An extended linear forward model is used in the subspace correlation cost function that incorporates the sensitivity of the EEG potentials to the uncertain conductivity value parameter. More specifically, the principal vector of the subspace correlation function is used to provide relevant information for solving the EEG inverse problems. A simulation study is carried out on a simplified spherical head model with uncertain skull to soft tissue conductivity ratio. Results show an improvement in the reconstruction accuracy of source parameters compared to traditional methodology, when using conductivity ratio values that are different from the actual conductivity ratio.

Quantifying the effect of repetitive transcranial magnetic stimulation in the rat brain by µSPECT CBF scans.

BACKGROUND: Repetitive transcranial magnetic stimulation (rTMS) is used to treat neurological and psychiatric disorders such as depression and addiction amongst others. Neuro-imaging by means of SPECT is a non-invasive manner of evaluating regional cerebral blood flow (rCBF) changes, which are assumed to reflect changes in neural activity. OBJECTIVE: rCBF changes induced by rTMS are evaluated by comparing stimulation on/off in different stimulation paradigms using microSPECT of the rat brain. METHODS: Rats (n = 6) were injected with 10 mCi of (99m)Tc-HMPAO during application of two rTMS paradigms (1 Hz and 10 Hz, 1430 A at each wing of a 20 mm figure-of-eight coil) and sham. SPM- and VOI-based analysis was performed. RESULTS: rTMS caused widespread significant hypoperfusion throughout the entire rat brain. Differences in spatial extent and intensity of hypoperfusion were observed between both stimulation paradigms: 1 Hz caused significant hypoperfusion (P < 0.05) in 11.9% of rat brain volume while 10 Hz caused this in 23.5%; the minimal t-value induced by 1 Hz was -24.77 while this was -17.98 due to 10 Hz. Maximal percentage of hypoperfused volume due to 1 Hz and 10 Hz was reached at tissue experiencing 0.03-0.15 V/m. CONCLUSION: High-frequency (10 Hz) stimulation causes more widespread hypoperfusion, while 1 Hz induces more pronounced hypoperfusion. The effect of rTMS is highly dependent on the electric field strength in the brain tissue induced by the TMS coil. This innovative imaging approach can be used as a fast screening tool in quantifying and evaluating the effect of various stimulation paradigms and coil designs for TMS and offers a means for research and development.

Reduced conductivity dependence method for increase of dipole localization accuracy in the EEG inverse problem.

The EEG is a neurological diagnostic tool with high temporal resolution. However, when solving the EEG inverse problem, its localization accuracy is limited because of noise in measurements and available uncertainties of the conductivity value in the forward model evaluations. This paper proposes the reduced conductivity dependence (RCD) method for decreasing the localization error in EEG source analysis by limiting the propagation of the uncertain conductivity values to the solutions of the inverse problem. We redefine the traditional EEG cost function, and in contrast to previous approaches, we introduce a selection procedure of the EEG potentials. The selected potentials are, as low as possible, affected by the uncertainties of the conductivity when solving the inverse problem. We validate the methodology on the widely used three-shell spherical head model with a single electrical dipole and multiple dipoles as source model. The proposed RCD method enhances the source localization accuracy with a factor ranging between 2 and 4, dependent on the dipole location and the noise in measurements.

An efficient 3-D eddy-current solver using an independent impedance method for transcranial magnetic stimulation.

In many important bioelectromagnetic problem settings, eddy-current simulations are required. Examples are the reduction of eddy-current artifacts in magnetic resonance imaging and techniques, whereby the eddy currents interact with the biological system, like the alteration of the neurophysiology due to transcranial magnetic stimulation (TMS). TMS has become an important tool for the diagnosis and treatment of neurological diseases and psychiatric disorders. A widely applied method for simulating the eddy currents is the impedance method (IM). However, this method has to contend with an ill conditioned problem and consequently a long convergence time. When dealing with optimal design problems and sensitivity control, the convergence rate becomes even more crucial since the eddy-current solver needs to be evaluated in an iterative loop. Therefore, we introduce an independent IM (IIM), which improves the conditionality and speeds up the numerical convergence. This paper shows how IIM is based on IM and what are the advantages. Moreover, the method is applied to the efficient simulation of TMS. The proposed IIM achieves superior convergence properties with high time efficiency, compared to the traditional IM and is therefore a useful tool for accurate and fast TMS simulations.

Low-parametric induced current - magnetic resonance electrical impedance tomography for quantitative conductivity estimation of brain tissues using a priori information: a simulation study.

Accurate estimation of the human head conductivity is important for the diagnosis and therapy of brain diseases. Induced Current - Magnetic Resonance Electrical Impedance Tomography (IC-MREIT) is a recently developed non-invasive technique for conductivity estimation. This paper presents a formulation where a low number of material parameters need to be estimated, starting from MR eddy-current field maps. We use a parameterized frequency dependent 4-Cole-Cole material model, an efficient independent impedance method for eddy-current calculations and a priori information through the use of voxel models. The proposed procedure circumvents the ill-posedness of traditional IC-MREIT and computational efficiency is obtained by using an efficient forward eddy-current solver.

A hybrid algorithm for solving the EEG inverse problem from spatio-temporal EEG data.

Epilepsy is a neurological disorder caused by intense electrical activity in the brain. The electrical activity, which can be modelled through the superposition of several electrical dipoles, can be determined in a non-invasive way by analysing the electro-encephalogram. This source localization requires the solution of an inverse problem. Locally convergent optimization algorithms may be trapped in local solutions and when using global optimization techniques, the computational effort can become expensive. Fast recovery of the electrical sources becomes difficult that way. Therefore, there is a need to solve the inverse problem in an accurate and fast way. This paper performs the localization of multiple dipoles using a global-local hybrid algorithm. Global convergence is guaranteed by using space mapping techniques and independent component analysis in a computationally efficient way. The accuracy is locally obtained by using the Recursively Applied and Projected-MUltiple Signal Classification (RAP-MUSIC) algorithm. When using this hybrid algorithm, a four times faster solution is obtained.