Abstract Purpose The rapid switching of the gradient fields induces eddy currents in neighboring metallic structures, causing undesirable effects. Numerical computations are thus required to understand eddy-currents effects for designing/implementing mitigation (involving passive shielding) and compensating techniques (using pre-emphasis). Previously, the network-analysis (NA) method was introduced to compute z-gradient eddy currents, although limited to a circularly symmetric and unconnected coil. Multi-layer integral method (MIM) method was recently introduced, modifying the circuit equation involving stream functions. We tailor MIM (TMIM) for a more general eddy-currents analysis in thin structures. Z-gradient eddy currents are analyzed and then compared using three methods (NA, TMIM, and Ansys). The analysis helps to evaluate the efficiency of passive shielding and to compensate eddy currents. Methods NA and TMIM computational frameworks for harmonic and transient eddy-currents analysis were implemented and cross-validated against Ansys Maxwell. A pre-emphasis pulse was modeled for compensating eddy currents. Results Eddy-currents analysis of an unconnected z-gradient coil in both the passive shield and cryostat were computed, and results were comparable to the least computationally efficient Ansys simulations. Although NA computations are fast, TMIM is implemented with reasonable efficiency and applied to circularly unsymmetric geometries. TMIM computations were further validated against Ansys using a connected z-gradient. Our computations allowed the effective evaluation of the performance of three various passive-shielding configurations, non-capped, capped, and slitted (for the first time), and an effective pre-emphasis compensation model was computed. Conclusion Three eddy-currents analysis methods were studied and compared. Computationally efficient TMIM allows both harmonic and transient eddy-currents analysis involving different/complex gradient configurations/situations as well as involved shielding structures. Eddy-currents pre-emphasis compensation was demonstrated.
Large and fast electrical current pulses are typically applied to conventional single-channel transverse MR gradient coils. However, these pulses result in a significant amount of power losses and heating of the coils. Previously, we presented a cylindrical multi-channel Z-gradient coil design that has better power efficiency compared to the single-channel design. In this work, we further investigate the DC power advantage for a two-channel actively-shielded transverse cylindrical gradient coil over the single-channel design. The conventional coil quadrants are radially divided into two sections, one for each channel, for both the primary and shielding surfaces. The symmetric inner sections of both the primary and shielding coils are assigned to the first channel, while the outer enclosing sections for each quadrant are assigned to the second channel. Discrete wire design is employed, where quasi-elliptic functions are used to parameterize the turns of each section. The coil geometric parameters, section size, number of turns, and turn locations are used as the design optimization parameters. The coils are optimized to maximize the coil’s efficiency while keeping the linearity error less than 10% and the shielding ratio above 85%. The design procedure is employed to design both the single and two-channel transverse gradient coils for comparison. Eleven different two-channel configurations having different section sizes were investigated. Results show that the power used to drive the most power-efficient two-channel coil is less than that of the single-channel design by ∼25%. Moreover, the two-channel configuration showed slightly better shielding efficiency.
Eddy currents are induced in the metallic structures of MRI machines due to the rapid switching of gradient fields generated by gradient coils. Several undesirable effects are associated with the induced eddy currents such as heat, acoustic noise, and MR image distortions. Accurate transient eddy currents numerical computations are required to predict and ameliorate such effects. Spiral gradient waveforms are of importance, particularly for fast MRI acquisition applications. For mathematical convenience, previously published work is mostly concerned with transient eddy currents computations associated with trapezoidal gradient waveforms; where spiral gradient waveforms were not considered. We recently presented preliminary transient eddy currents computations induced by an amplitude-modulated sinusoidal pulse in the scanner’s cryostat. In this work, we present a full computational framework for transient eddy currents induced by a spiral gradient waveform. A mathematical model for transient eddy currents involving the spiral pulse was derived and presented in detail using the circuit equation. Computations were implemented using a tailored multilayer integral method (TMIM) and results were compared to Ansys eddy currents analysis for cross-validation. The transient response of resultant fields generated by both an unshielded transverse coil driven by a spiral waveform was computed showing high agreement between Ansys and TMIM; albeit with high computational efficiency concerning time and memory. For further validation, computations for a shielded transverse coil were performed showing how eddy currents effects are reduced.
The creatine kinase (CK) reaction is central to muscle energetics, buffering ATP levels during periods of intense activity via consumption of phosphocreatine (PCr). PCr is believed to serve as a spatial shuttle of high-energy phosphate between sites of energy production in the mitochondria and sites of energy utilization in the myofibrils via diffusion. Knowledge of the diffusion coefficient of PCr (D(PCr)) is thus critical for modeling and understanding energy transport in the myocyte, but D(PCr) has not been measured in humans. Using localized phosphorus magnetic resonance spectroscopy, we measured D(PCr) in the calf muscle of 11 adults as a function of direction and diffusion time. The results show that the diffusion of PCr is anisotropic, with significantly higher diffusion along the muscle fibers, and that the diffusion of PCr is restricted to a ∼28-μm pathlength assuming a cylindrical model, with an unbounded diffusion coefficient of ∼0.69 × 10(-3) mm(2)/s. This distance is comparable in size to the myofiber radius. On the basis of prior measures of CK reaction kinetics in human muscle, the expected diffusion distance of PCr during its half-life in the CK reaction is ∼66 μm. This distance is much greater than the average distances between mitochondria and myofibrils. Thus these first measurements of PCr diffusion in human muscle in vivo support the view that PCr diffusion is not a factor limiting high-energy phosphate transport between the mitochondria and the myofibrils in healthy resting myocytes.
Cardiac phosphorus magnetic resonance spectroscopy (MRS) with surface coils promises better quantification at 3 Tesla (T) from improved signal-to-noise ratios and spectral resolution compared with 1.5 T. However, Bloch equation and field analyses at 3T show that for efficient quantitative MRS protocols using small-angle adiabatic (BIR4/BIRP) pulses the excitation-field is limited by radiofrequency (RF) power requirements and power deposition. When BIR4/BIRP pulse duration is increased to reduce power levels, T2-decay can introduce flip-angle dependent errors in the steady-state magnetization, causing errors in saturation corrections for metabolite quantification and in T1s measured by varying the flip-angle. A new dual-repetition-time (2TR) T1 method using frequency-sign-cycled adiabatic-half-passage pulses is introduced to alleviate power requirements, and avoid the problem related to T2 relaxation during the RF pulse. The 2TR method is validated against inversion-recovery in phantoms using a practical transmit/receive coil set designed for phosphorus MRS of the heart at depths of 9-10 cm with 4 kW of pulse power. The T1s of phosphocreatine (PCr) and adenosine triphosphate (gamma-ATP) in the calf-muscle (n=9) at 3 T are 6.8+/-0.3 s and 5.4+/-0.6 s, respectively. For heart (n=10) the values are 5.8+/-0.5 s (PCr) and 3.1+/-0.6 s (gamma-ATP). The 2TR protocol measurements agreed with those obtained by conventional methods to within 10%.
