Minimum maximum temperature gradient coil design.

Ohmic heating is a serious problem in gradient coil operation. A method is presented for redesigning cylindrical gradient coils to operate at minimum peak temperature, while maintaining field homogeneity and coil performance. To generate these minimaxT coil windings, an existing analytic method for simulating the spatial temperature distribution of single layer gradient coils is combined with a minimax optimization routine based on sequential quadratic programming. Simulations are provided for symmetric and asymmetric gradient coils that show considerable improvements in reducing maximum temperature over existing methods. The winding patterns of the minimaxT coils were found to be heavily dependent on the assumed thermal material properties and generally display an interesting "fish-eye" spreading of windings in the dense regions of the coil. Small prototype coils were constructed and tested for experimental validation and these demonstrate that with a reasonable estimate of material properties, thermal performance can be improved considerably with negligible change to the field error or standard figures of merit.

Chemical kinetics of a bipalladium complex.

A theoretical model is presented, for reductive elimination in a bipalladium complex, based on the model of Ariafard et al. (2011). This reaction is of particular interest due to the novel Pd(III) intermediate. A thermo-kinetic model is proposed for this reaction scheme, and the rate laws and energy balance are given as a system of ordinary differential equations. A simplified model is then derived that only involves two key variables, so that the system can be analyzed completely in a phase plane. It is shown that kinetic oscillations do not occur, but that there are multiple steady states for the reaction. These new features are confirmed by a numerical analysis of the full model scheme. The predictions provide a mechanism to test the model and the underlying computational chemistry.

Minimizing hot spot temperature in asymmetric gradient coil design.

Heating caused by gradient coils is a considerable concern in the operation of magnetic resonance imaging (MRI) scanners. Hot spots can occur in regions where the gradient coil windings are closely spaced. These problem areas are particularly common in the design of gradient coils with asymmetrically located target regions. In this paper, an extension of an existing coil design method is described, to enable the design of asymmetric gradient coils with reduced hot spot temperatures. An improved model is presented for predicting steady-state spatial temperature distributions for gradient coils. A great amount of flexibility is afforded by this model to consider a wide range of geometries and system material properties. A feature of the temperature distribution related to the temperature gradient is used in a relaxed fixed point iteration routine for successively altering coil windings to have a lower hot spot temperature. Results show that significant reductions in peak temperature are possible at little or no cost to coil performance when compared to minimum power coils of equivalent field error.

3D gradient coil design for open MRI systems.

Existing gradient coil design methods typically require some predetermined surface to be specified upon which the precise locations of coil windings are optimised with respect to gradient homogeneity and other measures of coil performance. In contrast, in this paper an analytic inverse method is presented for the theoretical design of 3D gradient coils in which the precise 3D geometry of the coils is obtained as part of the optimisation process. This method has been described previously for cylindrical whole-body gradients and is extended here for open MRI systems. A 3D current density solution is obtained using Fourier series combined with Tikhonov regularisation. The examples presented involve a minimum power penalty function and an optional shielding constraint. A discretised set of 3D coil windings is obtained using an equi-flux streamline seeding method. Results for an unshielded example display a concentration of windings within the portion of the coil volume nearest the imaging region and looped return path windings taken away from this region. However, for a shielded example the coil windings are found to lie almost exclusively on biplanar surfaces, suggesting that this is the optimum geometry for a shielded minimum power open coil.

Designing gradient coils with reduced hot spot temperatures.

Gradient coil temperature is an important concern in the design and construction of MRI scanners. Closely spaced gradient coil windings cause temperature hot spots within the system as a result of Ohmic heating associated with large current being driven through resistive material, and can strongly affect the performance of the coils. In this paper, a model is presented for predicting the spatial temperature distribution of a gradient coil, including the location and extent of temperature hot spots. Subsequently, a method is described for designing gradient coils with improved temperature distributions and reduced hot spot temperatures. Maximum temperature represents a non-linear constraint and a relaxed fixed point iteration routine is proposed to adjust coil windings iteratively to minimise this coil feature. Several examples are considered that assume different thermal material properties and cooling mechanisms for the gradient system. Coil winding solutions are obtained for all cases considered that display a considerable drop in hot spot temperature (>20%) when compared to standard minimum power gradient coils with equivalent gradient homogeneity, efficiency and inductance. The method is semi-analytical in nature and can be adapted easily to consider other non-linear constraints in the design of gradient coils or similar systems.

3D Gradient coil design - toroidal surfaces.

Gradient coil design typically involves optimisation of current densities or coil windings on familiar cylindrical, planar, spherical or conical surfaces. In this paper, an analytic inverse method is presented for the theoretical design of toroidal transverse gradient coils. This novel geometry is based on previous work involving a 3D current density solution, in which the precise geometry of the gradient coils was obtained as part of the optimisation process. Regularisation is used to solve for the toroidal current densities, whereby the field error is minimised in conjunction with the total power of the coil. The method is applied to the design of unshielded and shielded, whole-body and head coil gradient systems. Preliminary coil windings displaying high gradient homogeneity, low inductance, high efficiency and good force balancing are displayed and discussed. Potential benefits associated with this morphology include self-shielding gradient sets, greater access to cooling mechanisms, a reduction in acoustic noise due to force-balancing, a lessening of patient claustrophobia and greater patient access for clinicians.

3-D gradient coil design--initial theoretical framework.

An analytic inverse method is presented for the theoretical design of 3-D transverse gradient coils. Existing gradient coil design methods require the basic geometry of the coil to be predetermined before optimization. Typically, coil windings are constrained to lie on cylindrical, planar, spherical, or conical surfaces. In this paper, a fully 3-D region in the solution space is explored and the precise geometry of the gradient coils is obtained as part of the optimization process. Primary interest lies in minimizing the field error between induced and target gradient fields within a spherical target region. This is achieved using regularization, in which the field error is minimized along with the total coil power, to obtain a 3-D current density solution within the coil volume. A novel priority streamline technique is used to create 3-D coil windings that approximate this current density, and a secondary optimization is performed to obtain appropriate coil currents. The 3-D coil windings display an interesting general geometric form involving sets of closed loops plus spiral-type coils, and a number of examples are presented and discussed. The corresponding induced magnetic field is found to be highly linear within the region of interest, and a shielding constraint may be implemented to minimize the field outside the coil volume.

Electromagnetic fields in the human body due to switched transverse gradient coils in MRI.

Magnetic resonance imaging scans impose large gradient magnetic fields on the patient. Modern imaging techniques require this magnetic field to be switched rapidly for good resolution. However, it is believed that this can also lead to the unwanted side effect of peripheral nerve stimulation, which proves to be a limiting factor to the advancement of MRI technology. This paper establishes an analytical model for the fields produced within an MRI scanner by transverse gradient coils of known current density. Expressions are obtained for the magnetic induction vector and the electric field vector, as well as for the surface charge and current densities that are induced on the patient's body. The expressions obtained are general enough to allow the study of any combination of gradient coils whose behaviour can be approximated by Fourier series. For a realistic example coil current density and switching function, it is found that spikes of surface charge density are induced on the patient's body as the gradient field is switched, as well as loops of surface current density that mimic the coil current density. For a 10 mT m(-1) gradient field with a rise time of 100 micros, the magnitude of the radial electric field at the body is found to be 10.3 V m(-1). It is also found that there is a finite limit to radial electric field strength as rise time approaches zero.