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.

How to include the variability of TMS responses in simulations: a speech mapping case study.

When delivered over a specific cortical site, TMS can temporarily disrupt the ongoing process in that area. This allows mapping of speech-related areas for preoperative evaluation purposes. We numerically explore the observed variability of TMS responses during a speech mapping experiment performed with a neuronavigation system. We selected four cases with very small perturbations in coil position and orientation. In one case (E) a naming error occurred, while in the other cases (NEA, B, C) the subject appointed the images as smoothly as without TMS. A realistic anisotropic head model was constructed of the subject from T1-weighted and diffusion-weighted MRI. The induced electric field distributions were computed, associated to the coil parameters retrieved from the neuronavigation system. Finally, the membrane potentials along relevant white matter fibre tracts, extracted from DTI-based tractography, were computed using a compartmental cable equation. While only minor differences could be noticed between the induced electric field distributions of the four cases, computing the corresponding membrane potentials revealed different subsets of tracts were activated. A single tract was activated for all coil positions. Another tract was only triggered for case E. NEA induced action potentials in 13 tracts, while NEB stimulated 11 tracts and NEC one. The calculated results are certainly sensitive to the coil specifications, demonstrating the observed variability in this study. However, even though a tract connecting Broca's with Wernicke's area is only triggered for the error case, further research is needed on other study cases and on refining the neural model with synapses and network connections. Case- and subject-specific modelling that includes both electromagnetic fields and neuronal activity enables demonstration of the variability in TMS experiments and can capture the interaction with complex neural networks.

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.

Effective electric fields along realistic DTI-based neural trajectories for modelling the stimulation mechanisms of TMS.

In transcranial magnetic stimulation (TMS), an applied alternating magnetic field induces an electric field in the brain that can interact with the neural system. It is generally assumed that this induced electric field is the crucial effect exciting a certain region of the brain. More specifically, it is the component of this field parallel to the neuron's local orientation, the so-called effective electric field, that can initiate neuronal stimulation. Deeper insights on the stimulation mechanisms can be acquired through extensive TMS modelling. Most models study simple representations of neurons with assumed geometries, whereas we embed realistic neural trajectories computed using tractography based on diffusion tensor images. This way of modelling ensures a more accurate spatial distribution of the effective electric field that is in addition patient and case specific. The case study of this paper focuses on the single pulse stimulation of the left primary motor cortex with a standard figure-of-eight coil. Including realistic neural geometry in the model demonstrates the strong and localized variations of the effective electric field between the tracts themselves and along them due to the interplay of factors such as the tract's position and orientation in relation to the TMS coil, the neural trajectory and its course along the white and grey matter interface. Furthermore, the influence of changes in the coil orientation is studied. Investigating the impact of tissue anisotropy confirms that its contribution is not negligible. Moreover, assuming isotropic tissues lead to errors of the same size as rotating or tilting the coil with 10 degrees. In contrast, the model proves to be less sensitive towards the not well-known tissue conductivity values.

Reduction of the impact of multiple uncertain conductivity values on EEG dipole source analysis.

It is well known that the uncertain knowledge of the conductivity values of the head tissues has an important impact upon the accuracy of the electroencephalogram source reconstruction. Assuming a certain value of the conductivity often leads to high reconstruction error values when solving the inverse problem. It is possible to quantify the impact of multiple uncertain conductivity values on the localization accuracy. We propose an approach that reduces the impact of these multiple uncertainties on the reconstruction accuracy of the dipole parameters. This paper elaborates the numerical method and shows results of localization accuracy in a five-shell spherical head model. Sensitivity analysis, when considering multiple layers in the head model, shows the different scales of the influence of the various uncertain conductivity values on the potential values. We propose a cost function that reduces the impact of multiple uncertainties of the conductivity value on the electroencephalogram dipole reconstruction and two strategies for selecting potential values on the basis of the sensitivity analysis. Numerical simulations, when considering multiple uncertainties in the model, provide results with higher reconstruction accuracy compared with the case where only a single uncertainty is taken into account.

A DTI-based model for TMS using the independent impedance method with frequency-dependent tissue parameters.

Accurate simulations on detailed realistic head models are necessary to gain a better understanding of the response to transcranial magnetic stimulation (TMS). Hitherto, head models with simplified geometries and constant isotropic material properties are often used, whereas some biological tissues have anisotropic characteristics which vary naturally with frequency. Moreover, most computational methods do not take the tissue permittivity into account. Therefore, we calculate the electromagnetic behaviour due to TMS in a head model with realistic geometry and where realistic dispersive anisotropic tissue properties are incorporated, based on T1-weighted and diffusion-weighted magnetic resonance images. This paper studies the impact of tissue anisotropy, permittivity and frequency dependence, using the anisotropic independent impedance method. The results show that anisotropy yields differences up to 32% and 19% of the maximum induced currents and electric field, respectively. Neglecting the permittivity values leads to a decrease of about 72% and 24% of the maximum currents and field, respectively. Implementing the dispersive effects of biological tissues results in a difference of 6% of the maximum currents. The cerebral voxels show limited sensitivity of the induced electric field to changes in conductivity and permittivity, whereas the field varies approximately linearly with frequency. These findings illustrate the importance of including each of the above parameters in the model and confirm the need for accuracy in the applied patient-specific method, which can be used in computer-assisted TMS.

Subspace electrode selection methodology for the reduction of the effect of uncertain conductivity values in the EEG dipole localization: a simulation study using a patient-specific head model.

The simulation of the electroencephalogram (EEG) using a realistic head model needs the correct conductivity values of several tissues. However, these values are not precisely known and have an influence on the accuracy of the EEG source analysis problem. This paper presents a novel numerical methodology for the increase of accuracy of the EEG dipole source localization problem. The presented subspace electrode selection (SES) methodology is able to limit the effect of uncertain conductivity values on the solution of the EEG inverse problem, yielding improved source localization accuracy. We redefine the traditional cost function associated with the EEG inverse problem and introduce a selection procedure of EEG potentials. In each iteration of the presented EEG cost function minimization procedure, potentials are selected that are affected as little as possible by the uncertain conductivity value. Using simulation data, the proposed SES methodology is able to enhance the neural source localization accuracy dependent on the dipole location, the assumed versus actual conductivity and the possible noise in measurements.

A system approach modelling of the three-stage non-linear kinetics in biological ageing.

There is a widely observed non-linear kinetics in the ageing of biological systems, which is characterised by three successive stages, (1) the ageing rate is firstly high, but decreases quickly to a minimum, from which (2) it remains nearly constant during the major part of the process until (3) it starts increasing again up to the final collapse of the system. Such kinetics are also encountered in the ageing of inert systems. It is shown that a model useful for the follow-up of operating inert systems allows to find back typical curves and laws related to the ageing of biological systems (mortality rate curves, survival curves, growth curves, Gompertz law, ...). In this model, ageing is seen as a multifactorial process. The classical concepts of lifespan, longevity and life expectancy are given new light using the model, which also gives clues to explain both the discrepancy in the age of death of individuals in a given population and the wide range of lifespans of species encountered in nature. Finally, the model shows in which directions accelerated senescence testing protocols should be orientated for a better understanding of the underlying phenomena and for life prediction purposes.