Ground water model calibration using pilot points and regularization

Use of nonlinear parameter estimation techniques is now commonplace in ground water model calibration. However, there is still ample room for further development of these techniques in order to enable them to extract more information from calibration datasets, to more thoroughly explore the uncertainty associated with model predictions, and to make them easier to implement in various modeling contexts. This paper describes the use of pilot points as a methodology for spatial hydraulic property characterization. When used in conjunction with nonlinear parameter estimation software that incorporates advanced regularization functionality (such as PEST), use of pilot points can add a great deal of flexibility to the calibration process at the same time as it makes this process easier to implement. Pilot points can be used either as a substitute for zones of piecewise parameter uniformity, or in conjunction with such zones. In either case, they allow the disposition of areas of high and low hydraulic property value to be inferred through the calibration process, without the need for the modeler to guess the geometry of such areas prior to estimating the parameters that pertain to them. Pilot points and regularization can also be used as an adjunct to geostatistically based stochastic parameterization methods. Using the techniques described herein, a series of hydraulic property fields can be generated, all of which recognize the stochastic characterization of an area at the same time that they satisfy the constraints imposed on hydraulic property values by the need to ensure that model outputs match field measurements. Model predictions can then be made using all of these fields as a mechanism for exploring predictive uncertainty.

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.

A comparison of different choices for the regularization parameter in inverse electrocardiography models

Calculating the potentials on the heart’s epicardial surface from the body surface potentials constitutes one form of inverse problems in electrocardiography (ECG). Since these problems are ill-posed, one approach is to use zero-order Tikhonov regularization, where the squared norms of both the residual and the solution are minimized, with a relative weight determined by the regularization parameter. In this paper, we used three different methods to choose the regularization parameter in the inverse solutions of ECG. The three methods include the L-curve, the generalized cross validation (GCV) and the discrepancy principle (DP). Among them, the GCV method has received less attention in solutions to ECG inverse problems than the other methods. Since the DP approach needs knowledge of norm of noises, we used a model function to estimate the noise. The performance of various methods was compared using a concentric sphere model and a real geometry heart-torso model with a distribution of current dipoles placed inside the heart model as the source. Gaussian measurement noises were added to the body surface potentials. The results show that the three methods all produce good inverse solutions with little noise; but, as the noise increases, the DP approach produces better results than the L-curve and GCV methods, particularly in the real geometry model. Both the GCV and L-curve methods perform well in low to medium noise situations.