Winding patterns for biplanar MRI shim coils with rectangular and circular target-field regions

A method is presented for calculating the winding patterns required to design independent zonal and tesseral biplanar shim coils for magnetic resonance imaging. Streamline, target-field, Fourier integral and Fourier series methods are utilized. For both Fourier-based methods, the desired target field is specified on the surface of the conducting plates. For the Fourier series method it is possible to specify the target field at additional depths interior to the two conducting plates. The conducting plates are confined symmetrically in the xy plane with dimensions 2a x 2b, and are separated by 2d in the z direction. The specification of the target field is symmetric for the Fourier integral method, but can be over some asymmetric portion pa < x < qa and sb < y < tb of the coil dimensions (-1 < p < q < 1 and -1 < s < t < 1) for the Fourier series method. Arbitrary functions are used in the outer sections to ensure continuity of the magnetic field across the entire coil face. For the Fourier series case, the entire field is periodically extended as double half-range sine or cosine series. The resultant Fourier coefficients are substituted into the Fourier series and integral expressions for the internal and external magnetic fields, and stream functions on both the conducting surfaces. A contour plot of the stream function directly gives the required coil winding patterns. Spherical harmonic analysis of field calculations from a ZX shim coil indicates that example designs and theory are well matched.

Novel target-field method for designing shielded biplanar shim and gradient coils

A new method is presented here for the systematic design of biplanar shielded shim and gradient coils, for use in magnetic resonance imaging (MRI) and other applications. The desired target field interior to the coil is specified in advance, and a winding pattern is then designed to produce a field that matches the target as closely as possible. Both gradient and shim coils can be designed by this approach, and the target region can be located asymmetrically within the coil. The interior target field may be matched at two or more interior locations, to improve accuracy. When shields are present, the winding patterns are designed so that the fields exterior to the biplanar coil are made as small as possible. The method is illustrated here by the design of some transverse gradient and shim coils.

A target-field method to design circular biplanar coils for asymmetric shim and gradient fields

The paper presents a method for designing circular, shielded biplanar coils that can generate any desired field. A particular feature of these coils is that the target field may be located asymmetrically within the coil. A transverse component of the magnetic field produced by the coil is made to match a prescribed target field over the surfaces of two concentric spheres (the diameter of spherical volume) that define the target field location. The paper shows winding patterns and fields for several gradient and shim coils. It examines the effect that the finite coil size has on the winding patterns, using a Fourier-transform calculation for comparison.

A time-harmonic target-field method for designing unshielded RF coils in MRI

Time-harmonic methods are required in the accurate design of RF coils as operating frequency increases. This paper presents such a method to find a current density solution on the coil that will induce some desired magnetic field upon an asymmetrically located target region within. This inverse method appropriately considers the geometry of the coil via a Fourier series expansion, and incorporates some new regularization penalty functions in the solution process. A new technique is introduced by which the complex, time-dependent current density solution is approximated by a static coil winding pattern. Several winding pattern solutions are given, with more complex winding patterns corresponding to more desirable induced magnetic fields.

An inverse method for designing loaded RF coils in MRI

Radio-frequency ( RF) coils are designed such that they induce homogeneous magnetic fields within some region of interest within a magnetic resonance imaging ( MRI) scanner. Loading the scanner with a patient disrupts the homogeneity of these fields and can lead to a considerable degradation of the quality of the acquired image. In this paper, an inverse method is presented for designing RF coils, in which the presence of a load ( patient) within the MRI scanner is accounted for in the model. To approximate the finite length of the coil, a Fourier series expansion is considered for the coil current density and for the induced fields. Regularization is used to solve this ill-conditioned inverse problem for the unknown Fourier coefficients. That is, the error between the induced and homogeneous target fields is minimized along with an additional constraint, chosen in this paper to represent the curvature of the coil windings. Smooth winding patterns are obtained for both unloaded and loaded coils. RF fields with a high level of homogeneity are obtained in the unloaded case and a limit to the level of homogeneity attainable is observed in the loaded case.

Transformers on-load exciting current Park`s vector approach as a tool for winding faults diagnostics

This paper presents the development of a new approach for diagnosing the occurrence of inter-turn short-circuits in the windings of three-phase transformers, which is based on the on-line monitoring of the on-load exciting current Park's Vector patterns. Experimental and simulated results demonstrate the effectiveness of the proposed technique for detecting winding inter-turn insulation faults in operating three-phase transformers.

Detection of trasformer intermittent winding faults by the on-load exciting current Park`s vector approach

This paper presents the application of the on-load exciting current Park's Vector Approach for diagnosing permanent and intermittent turn-to-turn winding faults in operating power transformers. First, an experimental investigation of the behaviour of the transformer under the occurrence of both permanent and intermittent winding faults is presented. Finally, experimental test results demonstrate the effectiveness of the proposed diagnostic technique, which is based on the on-line monitoring of the on-load exciting current Park's Vector patterns.

Geometric diagnostics of complex patterns: Spiral defect chaos

Motivated by the observation of spiral patterns in a wide range of physical, chemical, and biological systems, we present an automated approach that aims at characterizing quantitatively spiral-like elements in complex stripelike patterns. The approach provides the location of the spiral tip and the size of the spiral arms in terms of their arc length and their winding number. In addition, it yields the number of pattern components (Betti number of order 1), as well as their size and certain aspects of their shape. We apply the method to spiral defect chaos in thermally driven Rayleigh- Bénard convection and find that the arc length of spirals decreases monotonically with decreasing Prandtl number of the fluid and increasing heating. By contrast, the winding number of the spirals is nonmonotonic in the heating. The distribution function for the number of spirals is significantly narrower than a Poisson distribution. The distribution function for the winding number shows approximately an exponential decay. It depends only weakly on the heating, but strongly on the Prandtl number. Large spirals arise only for larger Prandtl numbers. In this regime the joint distribution for the spiral length and the winding number exhibits a three-peak structure, indicating the dominance of Archimedean spirals of opposite sign and relatively straight sections. For small Prandtl numbers the distribution function reveals a large number of small compact pattern components.

Quantitative electroencephalographic comodulation : an investigation of patterns in chronic fatigue syndrome

Introduction. This is a pilot study of quantitative electro-encephalographic (QEEG) comodulation analysis, which is used to assist in identifying regional brain differences in those people suffering from chronic fatigue syndrome (CFS) compared to a normative database. The QEEG comodulation analysis examines spatial-temporal cross-correlation of spectral estimates in the resting dominant frequency band. A pattern shown by Sterman and Kaiser (2001) and referred to as the anterior posterior dissociation (APD) discloses a significant reduction in shared functional modulation between frontal and centro-parietal areas of the cortex. This research attempts to examine whether this pattern is evident in CFS. Method. Eleven adult participants, diagnosed by a physician as having CFS, were involved in QEEG data collection. Nineteen-channel cap recordings were made in five conditions: eyes-closed baseline, eyes-open, reading task one, math computations task two, and a second eyes-closed baseline. Results. Four of the 11 participants showed an anterior posterior dissociation pattern for the eyes-closed resting dominant frequency. However, seven of the 11 participants did not show this pattern. Examination of the mean 8-12 Hz amplitudes across three cortical regions (frontal, central and parietal) indicated a trend of higher overall alpha levels in the parietal region in CFS patients who showed the APD pattern compared to those who did not have this pattern. All patients showing the pattern were free of medication, while 71% of those absent of the pattern were using antidepressant medications. Conclusions. Although the sample is small, it is suggested that this method of evaluating the disorder holds promise. The fact that this pattern was not consistently represented in the CFS sample could be explained by the possibility of subtypes of CFS, or perhaps co-morbid conditions. Further, the use of antidepressant medications may mask the pattern by altering the temporal characteristics of the EEG. The results of this pilot study indicate that further research is warranted to verify that the pattern holds across the wider population of CFS sufferers.