**Purpose**:
To describe and evaluate a novel method to determine the validity of measurements made using cycle-by-cycle (CxC) recording techniques in patients with advanced retinal degenerations (RD) having low-amplitude flicker electroretinogram (ERG) responses.

**Methods**:
The method extends the original CxC recording algorithm introduced by Sieving et al., retaining the original recording setup and the preliminary analysis of raw data. Novel features include extended use of spectrum analysis, reduction of errors due to known sources, and a comprehensive statistical assessment using three different tests. The method was applied to ERG recordings from seven patients with RD and two patients with *CNGB3* achromatopsia.

**Results**:
The method was implemented as a Windows application to processes raw data obtained from a commercial ERG system, and it features a computational toolkit for statistical assessment of ERG recordings with amplitudes as low as 1 µV, commonly found in advanced RD patients. When recorded using conditions specific for eliciting cone responses, none of the CNGB3 patients had a CxC validated response, indicating that no signal artifacts were present with our recording conditions. A comparison of the presented method with conventional 30 Hz ERG was performed. Bland–Altman plots indicated good agreement (mean difference, −0.045 µV; limits of agreement, 0.193 to −0.282 µV) between the resulting amplitudes. Within-session test–retest variability was 15%, comparing favorably to the variability of standard ERG amplitudes.

**Conclusions**:
This novel method extracts highly reliable clinical recordings of low-amplitude flicker ERGs and effectively detects artifactual responses. It has potential value both as a cone outcome variable and planning tool in clinical trials on natural history and treatment of advanced RDs.

^{1}

^{–}

^{3}the electroretinogram (ERG) has evolved into standard clinical practice with protocols delineated by the International Society for Clinical Electrophysiology of Vision (ISCEV). ERGs are typically elicited using a flash stimulation of variable frequency (0.05–33 Hz) and strength (0.01–25 cd·s/m

^{2}). The selection of the stimuli characteristics depends on the contribution of retinal elements (rod, cones, bipolar cells, amacrine cells) intended for study.

^{4}

^{5}However, in advanced stages of degeneration, ERG responses can reach undetectable levels. Different approaches have been pursued to detect and quantify very small ERG amplitudes.

^{6}

^{–}

^{9}Most of these approaches make use of the flicker ERG, a retinal potential elicited by a train of evenly timed flashes or by a sinusoidally modulated light stimulus. When the stimulus frequency is in the range of 30 to 40 Hz, the resulting steady-state response is dominated by a sinusoidal component of photoreceptor/bipolar cell origin

^{10}having the same temporal frequency as the stimulus.

^{11}Nonetheless, even the computation of Fourier components is affected by noise, which introduces a random variability in amplitude and phase measurements and possibly alters the response detection in the most severe cases. Therefore, a robust statistical assessment of results is needed.

^{9}

^{9}and provides response measurements, as well as possible corrections to several common types of noise artifacts.

^{4}with stimulus frequency of 32.26 Hz and stimulus strength of 3.0 cd·s/m

^{2}. Potentials were obtained using corneal Burian–Allen electrodes (Hansen Ophthalmic Instruments, Iowa City, IA, USA). A commercial ERG system (Espion E2/ColorDome system; Diagnosys LLC, Lowell, MA, USA) provided both stimulus generation and signal recording. Settings included a total recording duration of 14.88 seconds (480 cycles), bandpass filter of 1 to 250 Hz, sampling rate of 2000 Hz, no automatic artifact rejection, and a dynamic range of 1.25 V. These settings were intended to produce a true steady-state, unaltered recording. A shorter 5-second section of optimum quality was selected for subsequent evaluation. The full recording output was exported as a text file to be processed offline with a separate software application featuring a statistical assessment toolkit. No trigger information was needed, as the system configuration guarantees a perfect synchronism between the processes of stimulus generation and signal sampling. The method was applied to ERG recordings from seven patients with advanced RD and two patients with

*CNGB3*achromatopsia. Subjects were light-adapted for 20 minutes at 30 cd/m

^{2}before each recording.

*F*-distribution.

*T*

^{2}test, the multivariate counterpart of Student's

*t*-test. We tested the hypothesis that the vector mean is different from zero. Assuming zero covariance, as is the case for Fourier components of random noise,

^{12}

^{,}

^{13}the test statistic

*T*

^{2}is simply

*x*and

*y*are the components of the 1F mean amplitude, σ

*x*

^{2}and σ

*y*

^{2}are the associated variances, and

*n*is the number of points. If a normalized form of

*T*

^{2}is used, the

*P*value for the observed mean may be computed using

*pF*, the cumulative probability distribution of

*F*, as follows

^{14}:

*pF*is the cumulative probability distribution of

*F*with 2 and n – 2 degrees of freedom.

*n*= 160, α = 0.05), we obtain

*Q*= 2.479, which is a close approximation of the limit value 2.448 obtained when

*n*tends to infinity.

*T*=

*Q*defines an elliptical confidence region in canonical form, with semi-axes

*a*and

*b*given by

*a*and

*b*depend on the standard error of the mean of cosine and sine components, as described previously.

^{9}The test is passed if the test ratio

*T*/

*Q*is greater than 1, a condition having the geometrical meaning that the ellipse does not include the origin.

^{15}

^{,}

^{16}The signal is divided into four segments of 40 cycles, and the corresponding time averages are computed. The number of segments was chosen in order to have a sufficient number of samples to perform subsequent statistics while keeping the minimum segment length that is necessary to have independent spectral estimates.

^{12}The traces of partial and total averages are displayed, as in any clinical electrophysiology system. The Fourier analysis in this case produces only four vectors, whose mean is tested against the

*H*

_{0}hypothesis using the

*T*

^{2}

*statistic,*

_{circ}^{13}a method better suited than

*T*

^{2}when only small samples are available. In this statistic, the variances of sine and cosine components are assumed to be equal, and the test statistic

*T*

^{2}is defined as follows:

*P*value is obtained by a direct application of the

*F*cumulative distribution

^{12}:

*T*is therefore

*F*is doubled, giving the method a specific advantage when small samples are used. Using the actual values (

*n*= 4, α = 0.05), we obtain

*Q*= 2.268.

*R*may be regarded as an amplitude threshold for significance. A circle of confidence of radius

*R*may also be traced and used as in the case of the ellipse.

^{17}aimed at detecting a periodical signal hidden in noise. Afterward, it was adapted and improved in many ways, but in the present case, where the signal frequency is known a priori, the simplest form may be used. If we assume that the spectral power density of noise is constant in a small frequency band centered around the test frequency (a hypothesis that is usually well verified), then the amplitude of the Fourier sine and cosine components included in this band will have a normal distribution with equal variance and a mean of zero.

^{12}The test statistic

*T*is obtained using this set of noise components plus the signal component, in the form of a signal-to-noise ratio, expressed in terms of power:

*Nx*and

_{k}*Ny*are the noise components at

_{k}*n*frequency bins around the stimulation frequency, excluding it or its harmonics. As the numerator is the sum of two squared orthogonal components (sine and cosine) and likewise in the numerator there is a sum of 2

*N*squared components, it follows from definitions that

*T*

^{2}is distributed as

*F*with 2 and 2

*n*degrees of freedom in the numerator and denominator.

^{18}The

*P*value is therefore simply

*T*is

*Q*= 1.798, given α = 0.05. A test ratio,

*T*/

*Q*, is then computed as for other tests, and

*T*=

*Q*now represents a signal-to-noise threshold (for power values).

*T*ratio is now distributed in a very specific way. For

*N*≤ 2, it may be expressed by a closed formula,

^{19}but for

*N*> 2 no solution is available, to our knowledge. It is possible to use an approximate solution

^{20}and numerically calculate the critical value for a given confidence level. In this case, we obtain

*Q*= 2.02 for the parameters previously used, and the extra material includes the algorithms used to compute approximate values of

*Q*for

*n*> 2.

*T*=

*Q*defines a critical threshold for 1F amplitude traced as a line, and in the

*x*,

*y*plot a circular confidence region appears.

*P*values of the tests, critical values, and test ratio

*T*/

*Q*); the associated confidence regions plot; and the recorded data in the time and frequency domains, as well as 1F and 2F harmonic amplitudes, noise amplitude, and signal-to-noise ratio (Figs. 1–3)

^{19}The ideal model of a periodical signal hidden in random noise is then well matched, and a meaningful high-resolution spectrogram may be obtained from the recording. Moreover, the test–retest reliability is improved. The distinctive feature of our method is the use of a purposely designed statistical assessment toolkit that provides a comprehensive and contextual assessment of the quality of the recording and the reliability of the results.

*T*

^{2}

*test and may produce an altered statistic result.*

_{circ}^{21}and it is possible to compute the relationship between the underlying signal

*v*and the observed response, as showed in Figure 5, where both signal and response are normalized to the noise amplitude. The mean response magnitude (central curve) was obtained from the analytic formulas of the moments of Rice's distribution and the confidence limits and the detection probability were obtained using the Marcum

*Q*-function for the cumulative probability

^{22}and the critical value

*Q*= 2.02 previously described.

*v*reduces itself as

*v*increases, becoming negligible for

*v*> 2.56 (bias error <5%). At the same time, the detection probability increases, attaining almost certainty (95% level) when

*v*is greater than 3.2. Meanwhile, the spread range of the measured magnitudes reduces very little in absolute values, so that at the

*v*= 3.2 level it is still +43.6% and −37.0%. of the mean. If an accuracy of ±20% is needed, the signal-to-noise ratio must be greater than 7.

*v*values previously considered may be translated into actual voltages so that, using the chart in Figure 5, it is possible to forecast the detection probability and the average dispersion of the results for the cohort to be studied. This capacity may be of value for the rational planning of the clinical activity and the efficient design of clinical trials.

**A. Fadda**, None;

**F. Martelli**, None;

**W.M. Zein**, None;

**B. Jeffrey**, None;

**G. Placidi**, None;

**P.A. Sieving**, None;

**B. Falsini**, None

*J Physiol*. 1933; 77(3): 207–239. [CrossRef] [PubMed]

*Ophthalmologica*. 1958; 135(4): 327–348. [CrossRef] [PubMed]

*The Retina: An Approachable Part of the Brain*. 2nd ed. Cambridge, MA: Harvard University Press; 2012.

*Doc Ophthalmol*. 2022; 144(3): 165–177. [CrossRef] [PubMed]

*JCI Insight*. 2023; 8(15): 167546. [CrossRef]

*Am J Ophthalmol*. 1988; 105(5): 500–503. [CrossRef] [PubMed]

*Doc Ophthalmol*. 1996; 92(4): 269–280. [CrossRef] [PubMed]

*Clin Neurophysiol*. 2009; 120(10): 1828–1834. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 1998; 39(8): 1462–1469. [PubMed]

*Invest Ophthalmol Vis Sci*. 2001; 42(1): 305–312. [PubMed]

*J Ophthalmic Vis Res*. 2012; 7(1): 34–38. [PubMed]

*Electroencephalogr Clin Neurphysiol*. 1991; 78(5): 389–401. [CrossRef]

*Electroencephalogr Clin Neurphysiol*. 1991; 78(5): 378–388. [CrossRef]

*Statistics of Directional Data*. Vol. 5. London: Academic Press; 1972.

*Clin Neurophysiol*. 2013; 124(8): 1652–1658. [CrossRef] [PubMed]

*Comput Methods Programs Biomed*. 1989; 28(1): 45–50. [CrossRef] [PubMed]

*Proc R Soc London*. 1897; 61(369–377): 455–465.

*Comput Methods Programs Biomed*. 2000; 61(2): 125–150. [CrossRef] [PubMed]

*Doc Ophthalmol*. 1999; 99(1): 69–82. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2010; 51(5): 1491.

*Vision Res*. 1989; 29(5): 627–637. [CrossRef] [PubMed]

*IEEE Trans Inf Theory*. 1960; 6(2): 59–267. [CrossRef]