Median recognition scores obtained by the cochlear implanted groups and the normal-hearing group.

<p>Median recognition scores of (A) phonemes, (B) lexical tones and (C) words obtained by the prelingual group, the postlingual group and the normal-hearing (NH) group in audiovisual (AV) and auditory-only (AO) modes at the 3 presentation levels. The asterisk marks indicate significant difference between AV and AO modes. The horizontal bars indicate significant difference between groups. The vertical error bars represent 95% confidence interval.</p

Demographical background of the prelingually deaf group, the postlingually deaf group and the normal-hearing (NH) group.

<p>IQR: Interquartile range; ImpSide: Side of ear with a implant; OnsetDeaf: Onset of deafness; DuraDeaf: Duration of deafness; AgeImp: Age at implantation; DuraImp: Duration of implant use; SDT: Speech detection threshold; SRT: Speech recognition threshold; ImpPTA: Pure tone average of the implanted ear; NonImpPTA: Pure tone average of the non-implanted or normal-hearing ear; VisionCon: Vision condition.</p><p>Demographical background of the prelingually deaf group, the postlingually deaf group and the normal-hearing (NH) group.</p

Spearman correlation coefficients between deafness-related parameters, test conditions and recognition scores.

<p>OnsetDeaf: Onset of deafness; DuraDeaf: Duration of deafness; AgeImp: Age at implantation; DuraImp: Duration of implant use; n/s: Not significant; n/a: Not applicable.</p><p>*Spearman's correlation coefficients adjusted by sex and age.</p>1<p>Scoring type coded as word  = 1, tone  = 2, phoneme  = 3.</p>2<p>Mode coded as auditory-only  = 1, audiovisual  = 2.</p><p>Only significant correlations are shown.</p><p>Spearman correlation coefficients between deafness-related parameters, test conditions and recognition scores.</p

BPWP method output spectra compared with reference distribution built from 1,000 iterations.

Significant peaks in the output power spectra from the simulated data, participants 1, 2, and 3 are shown in sections (A), (B), (C), and (D) respectively. In i, the reference distribution for significance calculations was the result of re-running the model with re-shuffled input data 100 times. In ii, the model was re-run 1,000 times. (TIF)</p

Supplementary methods.

Numerous physiological processes are cyclical, but sampling these processes densely enough to perform frequency decomposition and subsequent analyses can be challenging. Mathematical approaches for decomposition and reconstruction of sparsely and irregularly sampled signals are well established but have been under-utilized in physiological applications. We developed a basis pursuit denoising with polynomial detrending (BPWP) model that recovers oscillations and trends from sparse and irregularly sampled timeseries. We validated this model on a unique dataset of long-term inter-ictal epileptiform discharge (IED) rates from human hippocampus recorded with a novel investigational device with continuous local field potential sensing. IED rates have well established circadian and multiday cycles related to sleep, wakefulness, and seizure clusters. Given sparse and irregular samples of IED rates from multi-month intracranial EEG recordings from ambulatory humans, we used BPWP to compute narrowband spectral power and polynomial trend coefficients and identify IED rate cycles in three subjects. In select cases, we propose that random and irregular sampling may be leveraged for frequency decomposition of physiological signals.Trial Registration:NCT03946618.</div

Impact of varying sample density on Basis Pursuit with Polynomial Detrending (BPWP) outputs, participant 1.

(A) Raw data showing hourly rate of inter-ictal epileptiform discharges (IED) detected from the left hippocampus, updated every 20 minutes. Timeseries consists of over 20,000 samples. (Bi) Raw data are in gray and one random sample per day is in orange. (Bii) Raw data are in gray and the reconstructed signal using BPWP outputs based on input data of one random sample per day is in orange. (C) Average complex wavelet transform (CWT) spectrum from the raw data in (A) is in gray. The BPWP spectrum based on one sample per day input is shown in orange. Black stars denote significant peaks; peaks whose amplitude was above the 99th percentile of the distribution created by shuffling the input data and re-calculating the method 100 times. Random samples, signal reconstructions, and BPWP spectra are shown again for sampling rates of three and five per day in (D) and (E) and in (F) and (G) respectively. Agreement between BPWP output and raw data and CWT spectra improves as the signal is sampled more densely. Part (H) shows agreement between the BPWP and CWT spectra as a function of frequency of random sampling. For each sampling frequency, the raw data were resampled and BPWP was re-calculated 10 times. For each peak in the CWT spectrum, the offset between the period of the CWT peak and the nearest BPWP peak was calculated in terms of days and divided by the period of the CWT peak. This offset-to-cycle-length ratio was averaged across the 10 iterations and plotted as a log value on the y axis. The associated frequency of random sampling was plotted on the x axis. Shaded areas denote 95% confidence intervals. The offset ratio decreases and stabilizes as sampling density increases.</p

Description of method objectives and signal assumptions.

(A) The core assumption of the model is that the underlying signal (ii) is the linear sum of (i) oscillations, a polynomial trend, and noise. Part (B) describes the overall workflow including (i) data input to the model, (ii) outputs, and (iii) estimated signal reconstructions. (Ci) Equation representing the core signal assumption that the observations come from a combination of oscillations, a polynomial trend, and noise or error. Notation includes y (m x 1 vector of observed data), Ψ (n x n discrete cosine transform (DCT) basis), Φ (m x n binary row subsampling matrix), x (n x 1 DCT coefficients), Τ (n x p Vandermonde matrix), z (p x 1 polynomial coefficients), (m x 1 error terms). (Cii) Expression for basis pursuit denoising containing x and z as unknowns, yielding a 2D minimization problem that is reduced to a 1D minimization problem (Ciii) by variable projection. (D) Schematic representation of the equations and sampling approach in (C).</p

Basis Pursuit with Polynomial Detrending (BPWP) of real-world inter-ictal epileptiform discharges (IED) timeseries, participant 1.

(A) Raw data showing hourly rate of IEDs detected from the left hippocampus, updated every 20 minutes. Timeseries consists of over 20,000 samples. (B) Complex wavelet transform (CWT) spectrogram of the timeseries in A showing power in different cycles. Strong cycles are evident at one day and around on month. (C) Average of CWT spectrum (averaged over time from the spectrogram in) (B) shows cycles of IED rate including periods around one day, two-three weeks, one month, fifty days, and 100 days. (D) Random samples from the raw data in A averaging at 5 samples per day. Timeseries consists of 1,800 total samples. (E) Underlying raw data are shown in gray. The method’s estimated reconstruction of the underlying data based on the sparse samples in (D) is shown in orange. (F) The CWT spectrum for the raw data is shown in gray. The method’s spectral output is shown in orange. Black stars denote significant peaks; peaks whose amplitude was above the 99th percentile of the distribution created by shuffling the input data and re-calculating the method 100 times. The insert shows the spectral outputs from the reshuffling in purple. The amplitude of this noise floor is an order of magnitude smaller than the spectral output from the correctly ordered input data. The narrowband peaks from the method align with the central tendencies of the broadband CWT peaks. (G) The method’s estimated reconstruction of the underlying signal using only significant peaks from F with a period longer than two days is in orange. Overlayed black circles denote when seizures occurred. Seizures appear to prefer the peaks of the combined slow cycles derived from the method. (H) The method-based reconstruction was filtered in cycle ranges around one day, one week, two to three weeks, and one month then the signal Hilbert transform was used to identify the phase at which seizures occurred for each of these cycles. Polar histograms denoting the phase at which seizures occurred for each of these cycles indicate a cycle-specific phase preference for seizures. Stars denote p < 0.001 on the Omnibus test for uniformity, indicating that seizure phase is not uniformly distributed.</p

Impact of data drops on Basis Pursuit with Polynomial Detrending (BPWP) outputs, participant 1.

(A) Raw data showing hourly rate of inter-ictal epileptiform discharges (IED) detected from the left hippocampus, updated every 20 minutes. Timeseries consists of over 20,000 samples. (Bi) Raw data are in gray and random sampling excluding 12-day data drops are in orange. (Bii) Raw data are in gray and the reconstructed signal using model output based on input data with 12-day data drops is in orange. (C) Average complex wavelet transform (CWT) spectrum from the raw data in (A) is in gray. The BPWP spectral output based on the sampling in Bi input is shown in orange. Black stars denote significant peaks; peaks whose amplitude was above the 99th percentile of the distribution created by shuffling the input data and re-calculating the method 100 times. Data drops of thirty- and sixty- days duration, signal reconstructions, and method spectra are shown in (D) and (E) and in (F) and (G) respectively. The total number of samples for BPWP is fixed across the conditions at n = 1307 which is approximately 4 samples per day assuming no drops.</p

Impact of data drops on BPWP outputs, participant 3.

(A) Raw data showing hourly rate of IEDs detected from the left hippocampus, updated every 20 minutes. Timeseries consists of over 20,000 samples. (Bi) Raw data are in gray and random sampling excluding 12-day data drops are in orange. (Bii) Raw data are in gray and the reconstructed signal using model output based on input data with 12-day data drops is in orange. (C) Average complex wavelet transform (CWT) spectrum from the raw data in (A) is in gray. The BPWP spectral output based on the sampling in (Bi) input is shown in orange. Black stars denote significant peaks; peaks whose amplitude was above the 99th percentile of the distribution created by shuffling the input data and re-calculating BPWP 100 times. Data drops of thirty- and sixty- days duration, signal reconstructions, and method spectra are shown in (D) and (E) and in (F) and (G) respectively. The total number of samples for BPWP is fixed across the conditions at n = 1307 which is approximately 4 samples per day assuming no drops. (TIF)</p