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In the analysis of neuroscience data, the identification of task-related causal relationships between various areas of the brain gives insights about the network of physiological pathways that are active during the task. One increasingly used approach to identify causal connectivity uses the concept of Granger causality that exploits predictability of activity in one region by past activity in other regions of the brain. Owing to the complexity of the data, selecting components for the analysis of causality as a preprocessing step has to be performed. This includes predetermined—and often arbitrary—exclusion of information. Therefore, the system is confounded by latent sources. In this paper, the effect of latent confounders is demonstrated, and paths of influence among three components are studied. While methods for analysing Granger causality are commonly based on linear vector autoregressive models, the effects of latent confounders are expected to be present also in nonlinear systems. Therefore, all analyses are also performed for a simulated nonlinear system and discussed with regard to applications in neuroscience.

BackgroundArrhythmia can significantly alter the image quality of cardiovascular magnetic resonance (CMR); automatic detection and sorting of the most frequent types of arrhythmias during the CMR acquisition could potentially improve image quality. New CMR techniques, such as non-Cartesian CMR, can allow self-gating: from cardiac motion-related signal changes, we can detect cardiac cycles without an electrocardiogram. We can further use this data to obtain a surrogate for RR intervals (valley intervals: VV). Our purpose was to evaluate the feasibility of an automated method for classification of non-arrhythmic (NA) (regular cycles) and arrhythmic patients (A) (irregular cycles), and for sorting of common arrhythmia patterns between atrial fibrillation (AF) and premature ventricular contraction (PVC), using the cardiac motion-related signal obtained during self-gated free-breathing radial cardiac cine CMR with compressed sensing reconstruction (XD-GRASP).MethodsOne hundred eleven patients underwent cardiac XD-GRASP CMR between October 2015 and February 2016; 33 were included for retrospective analysis with the proposed method (6 AF, 8 PVC, 19 NA; by recent ECG). We analyzed the VV, using pooled statistics (histograms) and sequential analysis (Poincaré plots), including the median (medVV), the weighted mean (meanVV), the total number of VV values (VVval), and the total range (VVTR) and half range (VVHR) of the cumulative frequency distribution of VV, including the median to half range (medVV/VVHR) and the half range to total range (VVHR/VVTR) ratios. We designed a simple algorithm for using the VV results to differentiate A from NA, and AF from PVC.ResultsBetween NA and A, meanVV, VVval, VVTR, VVHR, medVV/VVHR and VVHR/VVTR ratios were significantly different (p values = 0.00014, 0.0027, 0.000028, 5×10−9, 0.002, respectively). Between AF and PVC, meanVV, VVval and medVV/VVHR ratio were significantly different (p values = 0.018, 0.007, 0.044, respectively). Using our algorithm, sensitivity, specificity, and accuracy were 93 %, 95 % and 94 % to discriminate between NA and A, and 83 %, 71 %, and 77 % to discriminate between AF and PVC, respectively; areas under the ROC curve were 0.93 and 0.89.ConclusionsOur study shows we can reliably detect arrhythmias and differentiate AF from PVC, using self-gated cardiac cine XD-GRASP CMR.

The proposed analysis of noise behavior and temporal fidelity establishes a theoretical basis for a quantitative evaluation of time-resolved reconstruction methods. Therefore, the presented theory allows for comparison between time-resolved parallel imaging methods and also nontime-resolved methods. Magn Reson Med 74:125-135, 2015. © 2014 Wiley Periodicals, Inc.