Squid

Using a 151 SQUID (Superconducting QUantum Interference Device) array system, we collected 39 fMCG data between 30 and 37 weeks of gestation from 27 pregnant women who delivered healthy singleton neonates at term. This study was approved by the local Institutional Review Board and all subjects gave their informed written consent to participate in the study. Each study lasted approximately 20–30 min depending on maternal comfort and the data was recorded with a sampling rate of 312.5 Hz. The data was bandpass filtered between 1 and 50 Hz using the Butterworth filter with zero-phase distortion and the interfering maternal cardiac signal was attenuated using the signal space projection technique.30 (link) The fetal R-waves were calculated using the Hilbert transform approach32 (link) and was followed by an adaptive scheme to correct for the missed and extra beats.27 (link)
The different steps involved in the identifying the R-wave are shown in a flowchart (see Fig. 1). After attenuation of the maternal cardiac signals using the orthogonal projection technique, we computed the Fourier transform of the resulting signals from all the sensors and selected only the 10 sensors (C_1,10) with the highest Fourier peak power in the 1–60 Hz band. Then, for the data x(t) from a sensor we computed Hilbert transform h(t) using the “Hilbert” function in Matlab (Mathwork, Inc.). We define R(n), the rate of change of Hilbert amplitude (RHA) as follows:
$$R(n)=\sqrt{{[x(n)-x(n-1)]}^2+{[h(n)-h(n-1)]}^2},$$
R(n) is positive definite and using this property, we linearly combined the RHA from all the 10 sensors with highest spectral content (cRHA).

In this paper, the summed RHA method, FastICA, RHA applied to two or more FastICA components, and simple filtering are considered postprocessing steps designed to simplify the extraction of the fetal R-waves. Since the maternal cardiac signal is dominant over the fetal signal, the maternal MCG was first removed from all SQUID channels by a signal space projection algorithm [31 ] before applying any of the methods tested. To further reduce the influence of the residual maternal MCG, only data from the lower 82 channels of the SARA system, far from the maternal heart but nearer to the fetal heart, were used in our analysis. To be clear, the FastICA was not used to separate the fetal and maternal MCGs in this study, but rather it was only used to separate the fMCG from background signal. After removal of the maternal MCG, each dataset was postprocessed in four ways: 1) compute the RHA of each channel and sum (Hilbert); 2) apply the FastICA and select the dominant fetal component (ICA); 3) compute the RHA of all FastICA components containing fMCG and sum (ICA+Hilbert); and 4) manually select the channel with the largest fMCG signal (filtered). The label “filtered” refers to the 1–100 Hz bandwidth imposed by the initial filtering operations. Ideally, after applying any of the earlier postprocessing methods, the fiducial points may be identified by simply extracting all of the maxima and testing which maxima fall above a selected threshold.
To illustrate this process, the results from a single recording are presented in Fig. 4. Here, the local maxima from each method were extracted and normalized by the largest positive value, and then, used to build the histograms shown in Fig. 4(A)–(D). For clarity, the histograms were scaled by taking the log(n+1) of each histogram bin. Fig. 4(E)–(H) shows the resulting RR intervals obtained after selecting a threshold between 0 and 1 and then extracting the remaining maxima. For this dataset, the ICA and Hilbert method (RHA) separate the maxima into two nonoverlapping distributions, as shown in Fig. 4(B) and (D), where the histograms indicate a completely resolved distribution of R-wave maxima separated from the distribution of lower amplitude maxima arising from noise and/or other fMCG components. Fig. 4(F) and (H) are the graphs of the corresponding RR intervals for any value of threshold falling between the two resolved distributions. In contrast, Fig. 4(A) and (C) shows overlapping distributions. In these two cases, a single threshold cannot be selected that cleanly separates the maxima of R-waves from maxima originating from other sources. As an example, Fig. 4(E) shows an upward spike in the graph of RR intervals near the beginning of the dataset indicating that at least one true R-wave maxima fell below the threshold. We refer to this case as a “missed” beat. Fig. 4(G) shows several downward spikes indicating that a few maxima were falsely classified as R-waves. We refer to this case as “extra” beat.