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.

A magnetization mapping approach for passive shim design in MRI

A new passive shim design method is presented which is based on a magnetization mapping approach. Well defined regions with similar magnetization values define the optimal number of passive shims, their shape and position. The new design method is applied in a shimming process without prior-axial shim localization; this reduces the possibility of introducing new errors. The new shim design methodology reduces the number of iterations and the quantity of material required to shim a magnet. Only a few iterations (1-5) are required to shim a whole body horizontal bore magnet with a manufacturing error tolerance larger than 0.1 mm and smaller than 0.5 mm. One numerical example is presented

Left-right information flow in the brain during EEG arousals

In disorders such as sleep apnea, sleep is fragmented with frequent EEG-arousal (EEGA) as determined via changes in the sleep-electroencephalogram. EEGA is a poorly understood, complicated phenomenon which is critically important in studying the mysteries of sleep. In this paper we study the information flow between the left and right hemispheres of the brain during the EEGA as manifested through inter-hemispheric asynchrony (IHA) of the surface EEG. EEG data (using electrodes A1/C4 and A2/C3 of international 10-20 system) was collected from 5 subjects undergoing routine polysomnography (PSG). Spectral correlation coefficient (R) was computed between EEG data from two hemispheres for delta-delta(0.5-4 Hz), theta-thetas(4.1-8 Hz), alpha-alpha(8.1-12 Hz) & beta-beta(12.1-25 Hz) frequency bands, during EEGA events. EEGA were graded in 3 levels as (i) micro arousals (3-6 s), (ii) short arousals (6.1-10 s), & (iii) long arousals (10.1-15 s). Our results revealed that in beta band, IHA increases above the baseline after the onset of EEGA and returns to the baseline after the conclusion of event. Results indicated that the duration of EEGA events has a direct influence on the onset of IHA. The latency (L) between the onset of arousals and IHA were found to be L=2plusmn0.5 s (for micro arousals), 4plusmn2.2 s (short arousals) and 6.5plusmn3.6 s (long arousals)

Tailoring magnetic field gradient design to magnet cryostat geometry

Eddy currents induced within a magnetic resonance imaging (MRI) cryostat bore during pulsing of gradient coils can be applied constructively together with the gradient currents that generate them, to obtain good quality gradient uniformities within a specified imaging volume over time. This can be achieved by simultaneously optimizing the spatial distribution and temporal pre-emphasis of the gradient coil current, to account for the spatial and temporal variation of the secondary magnetic fields due to the induced eddy currents. This method allows the tailored design of gradient coil/magnet configurations and consequent engineering trade-offs. To compute the transient eddy currents within a realistic cryostat vessel, a low-frequency finite-difference time-domain (FDTD) method using total-field scattered-field (TFSF) scheme has been performed and validated