Tomographic imaging of electrical conductivity and permittivity of tissues may be used for diagnostic purposes as well as for estimating local specific absorption rate (SAR) distributions. Magnetic Resonance Electrical Properties Tomography (MREPT) aims at noninvasively obtaining conductivity and permittivity images at RF frequencies of MRI systems. MREPT algorithms are based on measuring the B 1 field which is perturbed by the electrical properties of the imaged object. In this study, the relation between the electrical properties and the measured B + 1 field is formulated, for the first time as, the well-known convection-reaction equation. The suggested novel algorithm, called "cr-MREPT", is based on the solution of this equation, 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 convection-reaction equation is solved using a triangular mesh based finite difference method and also finite element method (FEM).The convective field of the convection-reaction equation depends on the spatial derivatives of the B + 1 field. In the regions where the magnitude of convective field is low, a spot-like artifact is observed in the reconstructed conductivity and dielectric permittivity images. For eliminating this artifact, two different methods are developed, namely "constrained cr-MREPT" and "double-excitation cr-MREPT". In the constrained cr-MREPT method, in the region where the magnitude of convective field is low, the electrical properties are reconstructed by neglecting the convective term in the equation. The obtained solution is used as a constraint for solving electrical properties in the whole domain. In the double-excitation cr-MREPT method, two B 1 excitations, which create two convective field distributions having low magnitude of convective field in different iii iv locations, are applied separately. The electrical properties are then reconstructed simultaneously using data from these two applied B + 1 field.These methods are tested with both simulation and experimental data from phantoms. As seen from results, successful electrical property reconstructions are obtained in all regions including electrical property transition region. The performance of cr-MREPT method against noise is also investigated.

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.

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.

Purpose: Arterial spin labeling (ASL) is an established noninvasive MRI technique used for cerebral blood flow measurement, which generally suffers from a low signal-to-noise ratio (SNR). The use of ultra-high fields to enhance sensitivity inevitably results in an increase in TR because of specific absorption rate (SAR) constraints, causing inadequate sampling of hemodynamic response in functional MRI, and adversely affecting concurrent measurement such as blood oxygen level dependent. To address this problem, variable-rate selective excitation (VERSE) radiofrequency (RF) pulses were used. Methods: The conventional (sinc) selective RF pulses of the Q2TIPS block in the PICORE pulsed ASL (PASL) sequence used for blood saturation were replaced by their equivalent VERSE RF waveforms. Nine healthy volunteers were scanned using the conventional and VERSE PASL sequences on a head-only 7T scanner operating in parallel transmit mode. Results: VERSE PASL sequence provides perfusion images similar to the conventional version, with comparable perfusion SNR (conventional, 3.33 ± 0.48; VERSE, 3.26 ± 0.55) and temporal SNR (conventional, 1.02 ± 0.20; VERSE, 1.05 ± 0.12) for TR = 3.5 seconds and 70 measurements. With shorter acquisition time (TR = 2.5 seconds), VERSE PASL sequence still provides similar results to those acquired using the conventional PASL sequence with longer TR = 3.5 seconds. Conclusion: The use of VERSE RF pulses in the Q2TIPS block of a PASL sequence allowed for the reduction of RF power deposition and, consequently, an increase in the temporal resolution and/or perfusion SNR. K E Y W O R D Sarterial spin labeling, cerebral blood flow, radiofrequency pulse, ultra-high field imaging

Purpose: 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 zgradients. Methods: We developed a simulation model for calculating subject eddy currents and the magnetic fields they generate (subject eddy fields). The inverse problem of obtaining conductivity distribution from subject eddy fields was formulated as a convection-reaction partial differential equation. For measuring subject eddy fields, a modified spin-echo pulse sequence was used to determine the contribution of subject eddy fields to MR phase images. Results: In the simulations, successful conductivity reconstructions were obtained by solving the derived convectionreaction equation, suggesting that the proposed reconstruction algorithm performs well under ideal conditions. However, the level of the calculated phase due to the subject eddy field in a representative object indicates that this phase is below the noise level and cannot be measured with an uncertainty sufficiently low for accurate conductivity reconstruction. Furthermore, some artifacts other than random noise were observed in the measured phases, which are discussed in relation to the effects of system imperfections during readout. Conclusion: Low-frequency conductivity imaging does not seem feasible using basic pulse sequences such as spin-echo on a clinical MRI scanner. Magn Reson