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.

Impact of gender on risk stratification by exercise and dobutamine stress echocardiography: long-term mortality in 4234 women and 6898 men

Aims Prior research is limited with regard to the diagnostic and prognostic accuracy of commonplace cardiac imaging modalities in women. The aim of this study was to examine 5-year mortality in 4234 women and 6898 men undergoing exercise or dobutamine stress echocardiography at three hospitals. Methods and results Univariable and multivariable Cox proportional hazards models were used to estimate time to cardiac death in this multi-centre, observational registry. Of the 11 132 patients, women had a greater frequency of cardiac risk factors (P < 0.0001). However, men more often had a history of coronary disease including a greater frequency of echocardiographic wall motion abnormalities (P < 0.0001). During 5 years of follow-up, 103 women and 226 men died from ischaernic heart disease (P < 0.0001). Echocardiographic estimates of left ventricular function (P < 0.0001) and the extent of ischaernic watt motion abnormalities (P < 0.0001) were highly predictive of cardiac death. Risk-adjusted 5-year survival was 99.4, 97.6, and 95% for exercising women with no, single, and multi-vessel ischaemia (P < 0.0001). For women undergoing dobutamine stress, 5-year survival was 95, 89, and 86.6% for those with 0, 1, and 2-3 vessel ischaemia (P < 0.0001). Exercising men had a 2.0-fold higher risk at every level of worsening ischaemia (P < 0.0001). Significantly worsening cardiac survival was noted for the 1568 men undergoing dobutamine stress echocardiography (P < 0.0001); no ischaemia was associated with 92% 5-year survival as compared with death rates of &GE; 16% for men with ischaemia on dobutamine stress echocardiography (P < 0.0001). Conclusion Echocardiographic measures of inducible wall motion abnormalities and global and regional left ventricutar function are highly predictive of long-term outcome for women and men alike.