A theoretical comparison of two optimization methods for radiofrequency drive schemes in high frequency MRI resonators

In this paper, numerical simulations are used in an attempt to find optimal Source profiles for high frequency radiofrequency (RF) volume coils. Biologically loaded, shielded/unshielded circular and elliptical birdcage coils operating at 170 MHz, 300 MHz and 470 MHz are modelled using the FDTD method for both 2D and 3D cases. Taking advantage of the fact that some aspects of the electromagnetic system are linear, two approaches have been proposed for the determination of the drives for individual elements in the RF resonator. The first method is an iterative optimization technique with a kernel for the evaluation of RF fields inside an imaging plane of a human head model using pre-characterized sensitivity profiles of the individual rungs of a resonator; the second method is a regularization-based technique. In the second approach, a sensitivity matrix is explicitly constructed and a regularization procedure is employed to solve the ill-posed problem. Test simulations show that both methods can improve the B-1-field homogeneity in both focused and non-focused scenarios. While the regularization-based method is more efficient, the first optimization method is more flexible as it can take into account other issues such as controlling SAR or reshaping the resonator structures. It is hoped that these schemes and their extensions will be useful for the determination of multi-element RF drives in a variety of applications.

Asymmetric MRI magnet design using a hybrid numerical method

This paper describes a hybrid numerical method for the design of asymmetric magnetic resonance imaging magnet systems. The problem is formulated as a field synthesis and the desired current density on the surface of a cylinder is first calculated by solving a Fredholm equation of the first kind. Nonlinear optimization methods are then invoked to fit practical magnet coils to the desired current density. The field calculations are performed using a semi-analytical method. A new type of asymmetric magnet is proposed in this work. The asymmetric MRI magnet allows the diameter spherical imaging volume to be positioned close to one end of the magnet. The main advantages of making the magnet asymmetric include the potential to reduce the perception of claustrophobia for the patient, better access to the patient by attending physicians, and the potential for reduced peripheral nerve stimulation due to the gradient coil configuration. The results highlight that the method can be used to obtain an asymmetric MRI magnet structure and a very homogeneous magnetic field over the central imaging volume in clinical systems of approximately 1.2 m in length. Unshielded designs are the focus of this work. This method is flexible and may be applied to magnets of other geometries. (C) 1999 Academic Press.

A hybrid, inverse approach to the design of magnetic resonance imaging magnets

This paper describes a hybrid numerical method of an inverse approach to the design of compact magnetic resonance imaging magnets. The problem is formulated as a field synthesis and the desired current density on the surface of a cylinder is first calculated by solving a Fredholm equation of the first, kind. Nonlinear optimization methods are then invoked to fit practical magnet coils to the desired current density. The field calculations are performed using a semi-analytical method. The emphasis of this work is on the optimal design of short MRI magnets. Details of the hybrid numerical model are presented, and the model is used to investigate compact, symmetric MRI magnets as well as asymmetric magnets. The results highlight that the method can be used to obtain a compact MRI magnet structure and a very homogeneous magnetic field over the central imaging volume in clinical systems of approximately 1 m in length, significantly shorter than current designs. Viable asymmetric magnet designs, in which the edge of the homogeneous region is very close to one end of the magnet system are also presented. Unshielded designs are the focus of this work. This method is flexible and may be applied to magnets of other geometries. (C) 2000 American Association of Physicists in Medicine. [S0094-2405(00)00303-5].

Compact clinical MRI magnet design using a multilayer current density approach

In this work, a new method of optimization is successfully applied to the theoretical design of compact, actively shielded, clinical MRI magnets. The problem is formulated as a two-step process in which the desired current densities on multiple, cc-axial surface layers are first calculated by solving Fredholm equations of the first kind. Non-linear optimization methods with inequality constraints are then invoked to fit practical magnet coils to the desired current densities. The current density approach allows rapid prototyping of unusual magnet designs. The emphasis of this work is on the optimal design of short, actively-shielded MRI magnets for whole-body imaging. Details of the hybrid numerical model are presented, and the model is used to investigate compact, symmetric, and asymmetric MRI magnets. Magnet designs are presented for actively-shielded, symmetric magnets of coil length 1.0 m, which is considerably shorter than currently available designs of comparable dsv size. Novel, actively-shielded, asymmetric magnet designs are also presented in which the beginning of a 50-cm dsv is positioned just 11 cm from the end of the coil structure, allowing much improved access to the patient and reduced patient claustrophobia. Magn Reson Med 45:331540, 2001. (C) 2001 Wiley-Liss, Inc.

Rapid field calculations for the effect of ferromagnetic material in MRI magnet design

Magnetic resonance imaging (MRI) magnets have very stringent constraints on the homogeneity of the static magnetic field that they generate over desired imaging regions. The magnet system also preferably generates very little stray field external to its structure, so that ease of siting and safety are assured. This work concentrates on deriving, means of rapidly computing the effect of 'cold' and 'warm' ferromagnetic material in or around the superconducting magnet system, so as to facilitate the automated design of hybrid material MR magnets. A complete scheme for the direct calculation of the spherical harmonics of the magnetic field generated by a circular ring of ferromagnetic material is derived under the conditions of arbitrary external magnetizing fields. The magnetic field produced by the superconducting coils in the system is computed using previously developed methods. The final, hybrid algorithm is fast enough for use in large-scale optimization methods. The resultant fields from a practical example of a 4 T, clinical MRI magnet containing both superconducting coils and magnetic material are presented.

Analysis of small signal stability margins using genetic optimization

Power system small signal stability analysis aims to explore different small signal stability conditions and controls, namely: (1) exploring the power system security domains and boundaries in the space of power system parameters of interest, including load flow feasibility, saddle node and Hopf bifurcation ones; (2) finding the maximum and minimum damping conditions; and (3) determining control actions to provide and increase small signal stability. These problems are presented in this paper as different modifications of a general optimization to a minimum/maximum, depending on the initial guesses of variables and numerical methods used. In the considered problems, all the extreme points are of interest. Additionally, there are difficulties with finding the derivatives of the objective functions with respect to parameters. Numerical computations of derivatives in traditional optimization procedures are time consuming. In this paper, we propose a new black-box genetic optimization technique for comprehensive small signal stability analysis, which can effectively cope with highly nonlinear objective functions with multiple minima and maxima, and derivatives that can not be expressed analytically. The optimization result can then be used to provide such important information such as system optimal control decision making, assessment of the maximum network's transmission capacity, etc. (C) 1998 Elsevier Science S.A. All rights reserved.

Structure optimization combining soft-core interaction functions, the diffusion equation method, and molecular dynamics

Smoothing the potential energy surface for structure optimization is a general and commonly applied strategy. We propose a combination of soft-core potential energy functions and a variation of the diffusion equation method to smooth potential energy surfaces, which is applicable to complex systems such as protein structures; The performance of the method was demonstrated by comparison with simulated annealing using the refinement of the undecapeptide Cyclosporin A as a test case. Simulations were repeated many times using different initial conditions and structures since the methods are heuristic and results are only meaningful in a statistical sense.

Mathematical methods for spatially cohesive reserve design

The problem of designing spatially cohesive nature reserve systems that meet biodiversity objectives is formulated as a nonlinear integer programming problem. The multiobjective function minimises a combination of boundary length, area and failed representation of the biological attributes we are trying to conserve. The task is to reserve a subset of sites that best meet this objective. We use data on the distribution of habitats in the Northern Territory, Australia, to show how simulated annealing and a greedy heuristic algorithm can be used to generate good solutions to such large reserve design problems, and to compare the effectiveness of these methods.

Interval training program optimization in highly trained endurance cyclists

Purpose: The purpose of this study was to examine the influence of three different high-intensity interval training (HIT) regimens on endurance performance in highly trained endurance athletes. Methods: Before, and after 2 and 4 wk of training, 38 cyclists and triathletes (mean +/- SD; age = 25 +/- 6 yr; mass = 75 +/- 7 kg; (V)over dot O-2peak = 64.5 +/- 5.2 mL.kg(-1).min(-1)) performed: 1) a progressive cycle test to measure peak oxygen consumption ((V)over dotO(2peak)) and peak aerobic power output (PPO), 2) a time to exhaustion test (T-max) at their (V)over dotO(2peak) power output (P-max), as well as 3) a 40-kin time-trial (TT40). Subjects were matched and assigned to one of four training groups (G(1), N = 8, 8 X 60% T-max P-max, 1:2 work:recovery ratio; G(2), N = 9, 8 X 60% T-max at P-max, recovery at 65% HRmax; G(3), N = 10, 12 X 30 s at 175% PPO, 4.5-min recovery; G(CON), N = 11). In addition to G(1) G(2), and G(3) performing HIT twice per week, all athletes maintained their regular low-intensity training throughout the experimental period. Results: All HIT groups improved TT40 performance (+4.4 to +5.8%) and PPO (+3.0 to +6.2%) significantly more than G(CON) (-0.9 to + 1.1 %; P < 0.05). Furthermore, G(1) (+5.4%) and G(2) (+8.1%) improved their (V)over dot O-2peak significantly more than G(CON) (+ 1.0%; P < 0.05). Conclusion: The present study has shown that when HIT incorporates P-max as the interval intensity and 60% of T-max as the interval duration, already highly trained cyclists can significantly improve their 40-km time trial performance. Moreover, the present data confirm prior research, in that repeated supramaximal HIT can significantly improve 40-km time trial performance.

A genetic algorithm/method of moments approach to the optimization of an RF coil for MRI applications - Theoretical considerations - Abstract

A Combined Genetic Algorithm and Method of Moments design methods is presented for the design of unusual near-field antennas for use in Magnetic Resonance Imaging systems. The method is successfully applied to the design of an asymmetric coil structure for use at 190MHz and demonstrates excellent radiofrequency field homogeneity.

Area-under-the-curve monitoring of prednisolone for dose optimization in a stable renal transplant population

Background: Renal transplant recipients were noted to appear cushingoid while on low doses of steroid as part of a triple therapy immunosuppression of cyclosporin A (CsA), prednisolone, and azathioprine. Methods: The study group comprised adult renal transplant recipients with stable graft function who had received their renal allograft a minimum of 1 year previously (43 studies undertaken in 22 men and 20 women) with median daily prednisone dose of 7 mg (range 3-10). The control group was healthy nontransplant subjects [median dose 10 mg (10-30)]. Prednisolone bioavailability was measured using a limited 6-hour area under the curve (AUC), with prednisolone measured using specific HPLC assay. Results: The median prednisolone AUC/mg dose for all transplant recipients was significantly greater than the control group by approximately 50% (316 nmol(.)h/L/mg prednisolone versus 218). AUC was significantly higher in female recipients (median 415 versus 297 for men) and in recipients receiving cyclospotin (348 versus 285). The highest AUC was in women on estrogen supplements who were receiving cyclosporin (median 595). A significantly higher proportion of patients on triple therapy had steroid side effects compared with those on steroid and azathioprine (17/27 versus 4/15), more women than men had side effects (14/16 versus 7/22), and the AUC/mg prednisone was greater in those with side effects than without (median 377 versus 288 nmol-h/L/mg). Discussion: The results are consistent with the hypothesis that CsA increases the bioavailability of prednisolone, most likely through inhibition of beta-glycoprotein. The increased exposure to steroid increased the side-effect profile of steroids in the majority of patients. Because the major contributor to AUC is the maximum postdose concentration, it may be possible to use single-point monitoring (2 hours postdose) for routine clinical studies.

Population-based continuous optimization, probabilistic modelling and mean shift

Evolutionary algorithms perform optimization using a population of sample solution points. An interesting development has been to view population-based optimization as the process of evolving an explicit, probabilistic model of the search space. This paper investigates a formal basis for continuous, population-based optimization in terms of a stochastic gradient descent on the Kullback-Leibler divergence between the model probability density and the objective function, represented as an unknown density of assumed form. This leads to an update rule that is related and compared with previous theoretical work, a continuous version of the population-based incremental learning algorithm, and the generalized mean shift clustering framework. Experimental results are presented that demonstrate the dynamics of the new algorithm on a set of simple test problems.

Multiresolution query optimization in an online environment

Multiresolution (or multi-scale) techniques make it possible for Web-based GIS applications to access large dataset. The performance of such systems relies on data transmission over network and multiresolution query processing. In the literature the latter has received little research attention so far, and the existing methods are not capable of processing large dataset. In this paper, we aim to improve multiresolution query processing in an online environment. A cost model for such query is proposed first, followed by three strategies for its optimization. Significant theoretical improvement can be observed when comparing against available methods. Application of these strategies is also discussed, and similar performance enhancement can be expected if implemented in online GIS applications.