Yusuf Ziya Ider

Convection-Reaction Equation Based Magnetic Resonance Electrical Properties Tomography (cr-MREPT)

Images of electrical conductivity and permittivity of tissues may be used for diagnostic purposes as well as for estimating local specific absorption rate distributions. Magnetic resonance electrical properties tomography (MREPT) aims at noninvasively obtaining conductivity and permittivity images at radio-frequency frequencies of magnetic resonance imaging systems. MREPT algorithms are based on measuring the B1 field which is perturbed by the electrical properties of the imaged object. In this study, the relation between the electrical properties and the measured B1 field is formulated for the first time as a well-known convection-reaction equation. The suggested novel algorithm, called “cr-MREPT,” is based on the solution of this equation on a triangular mesh, and in contrast to previously proposed algorithms, it is applicable in practice not only for regions where electrical properties are relatively constant but also for regions where they vary. The convective field of the convection-reaction equation depends on the spatial derivatives of the B1 field, and in the regions where its magnitude is low, a spot-like artifact is observed in the reconstructed electrical properties images. For eliminating this artifact, two different methods are developed, namely “constrained cr-MREPT” and “double-excitation cr-MREPT.” Successful reconstructions are obtained using noisy and noise-free simulated data, and experimental data from phantoms.

Gradient-based electrical conductivity imaging using MR phase

To develop a fast, practically applicable, and boundary artifact free electrical conductivity imaging method that does not use transceive phase assumption, and that is more robust against the noise.

A spectrally efficient PMR system utilizing broadcast service

Different trunked Private Mobile Radio (PMR) systems have been designed over the last several decades, all of which have symmetric downlink and uplink channel capacities. Due to this symmetry, these systems may not be spectrally efficient in case of different types of services, which are specific to PMR systems, such as group and broadcast calls. In this study, a new asymmetric trunked PMR system comprising a broadband, wide-area downlink and a narrowband cellular uplink, is proposed to achieve a higher spectral efficiency than current digital trunked PMR systems. This system is spectrally more efficient because in group and broadcast calls only a single downlink channel has to be allocated in the downlink part. However, as the number of clusters in the system increases, this advantage relative to PMR systems is lost, since the latter can employ frequency reuse. Spectral efficiency of the proposed asymmetric system (a-PMR) system and a standard TETRA system are compared using numerical case studies against different traffic loads and number of clusters. The optimum point, with respect to number of clusters, up to which the proposed a-PMR system is more efficient, is determined. It is shown that a very large PMR user population can be efficiently served using the proposed a-PMR system. The issues related to implementing such a system are discussed.

Magnetic resonance electrical impedance tomography (MREIT) based on the solution of the convection equation using FEM with stabilization

Most algorithms for magnetic resonance electrical impedance tomography (MREIT) concentrate on reconstructing the internal conductivity distribution of a conductive object from the Laplacian of only one component of the magnetic flux density (∇²B(z)) generated by the internal current distribution. In this study, a new algorithm is proposed to solve this ∇²B(z)-based MREIT problem which is mathematically formulated as the steady-state scalar pure convection equation. Numerical methods developed for the solution of the more general convection-diffusion equation are utilized. It is known that the solution of the pure convection equation is numerically unstable if sharp variations of the field variable (in this case conductivity) exist or if there are inconsistent boundary conditions. Various stabilization techniques, based on introducing artificial diffusion, are developed to handle such cases and in this study the streamline upwind Petrov-Galerkin (SUPG) stabilization method is incorporated into the Galerkin weighted residual finite element method (FEM) to numerically solve the MREIT problem. The proposed algorithm is tested with simulated and also experimental data from phantoms. Successful conductivity reconstructions are obtained by solving the related convection equation using the Galerkin weighted residual FEM when there are no sharp variations in the actual conductivity distribution. However, when there is noise in the magnetic flux density data or when there are sharp variations in conductivity, it is found that SUPG stabilization is beneficial.

A Simple Analytical Expression for the Gradient Induced Potential on Active Implants During MRI

During magnetic resonance imaging, there is an interaction between the time-varying magnetic fields and the active implantable medical devices (AIMD). In this study, in order to express the nature of this interaction, simplified analytical expressions for the electric fields induced by time-varying magnetic fields are derived inside a homogeneous cylindrical volume. With these analytical expressions, the gradient induced potential on the electrodes of the AIMD can be approximately calculated if the position of the lead inside the body is known. By utilizing the fact that gradient coils produce linear magnetic field in a volume of interest, the simplified closed form electric field expressions are defined. Using these simplified expressions, the induced potential on an implant electrode has been computed approximately for various lead positions on a cylindrical phantom and verified by comparing with the measured potentials for these sample conditions. In addition, the validity of the method was tested with isolated frog leg stimulation experiments. As a result, these simplified expressions may help in assessing the gradient-induced stimulation risk to the patients with implants.

Fourier transform magnetic resonance current density imaging (FT-MRCDI) from one component of magnetic flux density

Fourier transform (FT)-based algorithms for magnetic resonance current density imaging (MRCDI) from one component of magnetic flux density have been developed for 2D and 3D problems. For 2D problems, where current is confined to the xy-plane and z-component of the magnetic flux density is measured also on the xy-plane inside the object, an iterative FT-MRCDI algorithm is developed by which both the current distribution inside the object and the z-component of the magnetic flux density on the xy-plane outside the object are reconstructed. The method is applied to simulated as well as actual data from phantoms. The effect of measurement error on the spatial resolution of the current density reconstruction is also investigated. For 3D objects an iterative FT-based algorithm is developed whereby the projected current is reconstructed on any slice using as data the Laplacian of the z-component of magnetic flux density measured for that slice. In an injected current MRCDI scenario, the current is not divergence free on the boundary of the object. The method developed in this study also handles this situation.

Feasibility of conductivity imaging using subject eddy currents induced by switching of MRI gradients.

To investigate the feasibility of low‐frequency conductivity imaging based on measuring the magnetic field due to subject eddy currents induced by switching of MRI z‐gradients.

Approximate Fourier domain expression for Bloch–Siegert shift

In this study, a new simple Fourier domain‐based analytical expression for the Bloch–Siegert (BS) shift‐based B1 mapping method is proposed to obtain |B1+| more accurately while using short BS pulse durations and small off‐resonance frequencies.

Capacity analysis of a PMR system with DAB downlink

Several trunked private mobile radio (PMR) systems have been designed over the last decade, most of which have symmetric downlink and uplink channel capacities. These systems may not be spectrally efficient in case of group or broadcast-based voice and data calls, a common feature of PMR systems. We propose a new asymmetric PMR system comprising a wideband OFDM-based downlink and a narrowband uplink, which not only achieves a better spectral efficiency but also can support high bit rate multimedia applications. The system is shown to have high trunking efficiency since all users are assumed to use the pool of channels available in the wideband downlink. In this paper, we study the performance and capacity of a private mobile radio system using a digital audio broadcasting (DAB) downlink. In particular, we study the efficiency of such a system for voice calls using voice activity detection and statistical multiplexing. Moreover, we show that, the efficiency of the system can significantly increase, if the incoming calls, which can not find an available channel, are allowed to wait a certain amount of time before occupying a channel.

Optimal multichannel transmission for improved cr-MREPT

Magnetic resonance electrical properties tomography (MR-EPT), aiming at reconstructing the EPs at radio frequencies, uses the H + field (both magnitude and phase) distribution within the object. One of the MR-EPT algorithms, cr-MREPT, accurately reconstructs the internal tissue boundaries, however, it faces an artifact which occurs at the regions where the convective field, [Formula: see text], [Formula: see text], has a low magnitude (at the noise level). This study aims to develop an artifact-free conductivity reconstruction by modifying the H + field inside the region of interest (ROI), using multiple RF transmission techniques in MRI. An eight channel multi-transmit transverse electromagnetic array is used in two different drive configurations. The first drive is the standard volume excitation configuration where all ports are driven with the same magnitude and with 45° phase increment between adjacent channels. In the second drive, the drive voltage magnitude and phases for each of the eight drive ports are modified to generate a desired H + distribution such that the low convective field region moves to another non-overlapping position. Finally, data from both drive experiments are simultaneously used to reconstruct EPs. Computer simulations using cylindrical phantoms and a brain model are conducted and it is shown that the low convective field artifact can be eliminated. It is further shown that it is not necessary to re-calculate the port drive RF voltage magnitude and phases for each patient. The implementation issues of this method are briefly discussed.