Multiscale entropy analysis of retinal signals reveals reduced complexity in a mouse model of Alzheimer’s disease

Alzheimer’s disease (AD) is one of the most significant health challenges of our time, affecting a growing number of the elderly population. In recent years, the retina has received increased attention as a candidate for AD biomarkers since it appears to manifest the pathological signatures of the disease. Therefore, its electrical activity may hint at AD-related physiological changes. However, it is unclear how AD affects retinal electrophysiology and what tools are more appropriate to detect these possible changes. In this study, we used entropy tools to estimate the complexity of the dynamics of healthy and diseased retinas at different ages. We recorded microelectroretinogram responses to visual stimuli of different nature from retinas of young and adult, wild-type and 5xFAD—an animal model of AD—mice. To estimate the complexity of signals, we used the multiscale entropy approach, which calculates the entropy at several time scales using a coarse graining procedure. We found that young retinas had more complex responses to different visual stimuli. Further, the responses of young, wild-type retinas to natural-like stimuli exhibited significantly higher complexity than young, 5xFAD retinas. Our findings support a theory of complexity-loss with aging and disease and can have significant implications for early AD diagnosis.


Results
Time-and frequency-domain characteristics of microelectroretinogram recordings. We recorded the microelectroretinogram ( µERG) from pieces of retina of WT and 5xFAD mice in response to visual inputs during two stimulation protocols, namely, the chirp stimulus (CS) protocol and the natural image (NI) protocol (Fig. 1). The retinal responses showed great consistency across trials and subjects. For the CS protocol, clear onset and offset responses were observed for the steps of light applied in the initial ∼ 6 s (Fig. 2a). Further, the µERG showed an oscillatory response that followed the increase in the frequency of the sinusoidal light stimulus, albeit with decreasing signal amplitude, in agreement with previous reports that showed reduced µERG amplitude for stimulus frequency beyond ∼ 10 Hz 11 . The responses recorded for the NI protocol exhibited higher variability across subjects (Fig. 3a), and a clear onset response in the transition from dark to light that resembled that for the CS protocol. For both CS and NI protocols, the power spectral density (PSD) was similar across the four groups (Figs. 2b and 3b), albeit the 5xFAD-young group had somewhat higher power in the 10-15 Hz band. In addition, the PSD showed a peak at a very low frequency ( ∼ 2 Hz). The coherence between the CS input signal and the µERG response was nonzero for frequencies ≤ 15 Hz, with a peak at ∼ 8 Hz, and was somewhat higher for young retinas in the 8-15 Hz range (Fig. 2c). In addition, µERG signals did not show any salient feature among the groups for amplitude-based variability metrics like the mean and the standard deviation (Fig. 3c). In summary, the time-and frequency-domain characteristics of the µERG responses did not show any notable difference due to condition (WT vs 5xFAD) or age (young vs adult).

Multiscale entropy analysis.
For the MSE analyses, we first calculated the fuzzy entropy (FuzzyEn) 36 of the µERG signals at different time scales, thereby obtaining a MSE curve. Next, we estimated a complexity index for each retina as the area under the MSE curve 37 . The entropy of the µERG signals increased rapidly for small scales of up to 10 (Figs. 4a and 5a). Above this scale, the entropy for the CS protocol stabilized around ∼ 0.6 for young retinas and ∼ 0.5 for adult retinas (Fig. 4a). This resulted in higher complexity-as quantified as cumulative entropy for scales from 20 to 44-for young retinas of WT and 5xFAD subjects (Fig. 4b), and the median (lower-upper quartile) complexity index for WT-young, 5xFAD-young, WT-adult and 5xFAD-adult was 14.7 (11.75-15.60), 15.04 (12.76-16.59), 12.82 (11.04-14.29) and 11.33 (10.67-12.40), respectively (Table 1). For the NI protocol, the entropy increased monotonically as the scale increased for all retinas (Fig. 5a). Further, the MSE curves reached values that were, on average, consistently higher for WT retinas as compared to 5xFAD ones, and as well, they were consistently higher for young retinas as compared to adult ones. Consequently, the complexity of retinal responses was higher for WT-young retinas (Fig. 5b), and the median (lower-upper quartile) complexity index for WT-young, 5xFAD-young, WT-adult and 5xFAD-adult was 22.72 (21.79-25.00), 21.26 A MEA was mounted on a piece of retina to record µERG signals of the electrophysiological activity of several cell types of the retinal network, including those in the outer nuclear layer (ONL), outer plexiform layer (OPL), inner nuclear layer (INL) and inner plexiform layer (IPL). The firing activity of retinal ganglion cells (GCL) was low-pass filtered of the µERG. Two types of visual stimuli were applied using a LED projector: (1) A so-called chirp stimulus (CS protocol), and (2) A sequence of natural images (NI protocol). Examples of peristimulis time histogram (PSTH) from the µERG recordings, in response to 21 repetitions of the CS and the NI protocols (on the right side), together with a fotodiode signal recorded simultaneously to keep track of the stimulus intensity. For reference, it is also shown a µERG recording during a period of no visual stimulation.

Discussion
We performed MSE analyses of µERG signals recorded in retinas of healthy and 5xFAD -an animal model of AD-mice of different ages in response to two types of light stimuli. The µERG signals exhibited non-decreasing entropy values for a wide range of time scales, which is a signature of the dynamics of complex systems 22,37 . These results illustrate the complex nature of the electrophysiological activity of the retina exposed to high-information visual fields as those encountered in a natural environment. Further, the responses of young, healthy retinas to natural-like stimuli were more complex than those of 5xFAD retinas regardless of age. For deterministic sinusoidal stimuli, the responses of young retinas were more complex regardless of condition. These findings agree with the theory of complexity-loss with aging and disease 24 , though in our measurements age appeared as a more determinant factor in the reduction of complexity. Our results suggest that complexity differences due to age are more inherent and less responsive to the nature of the stimulus than those observed under disease. The loss of complexity was first postulated as an age-related phenomenon such that impairment of functional components and/or altered coupling between these components would lead to a progressive decline in adaptability to physiologic stress 38 . Since then, mounting evidence in  www.nature.com/scientificreports/ various physiological outputs showed complexity reductions with age and disease 24,26,31,37,39 . Our measurements of retinal µERG bring additional evidence of age-related loss of complexity, a feature that, in this case, emerged for diverse visual inputs. We also observed reductions of complexity in 5xFAD retinas, however, detecting it via MSE analysis required a more complex stimulus that triggered a more complex response in all retinas (21.65 and 13.23 median complexity for NI and CS protocol, respectively). Thus, for entropy tools to be used in early AD diagnosis, it is first necessary to find visual stimuli that elicit complex responses, as it may be the case for white noise inputs 40 . In addition, to use MSE tools for diagnosis and discriminate individual cases in clinical applications, machine learning tools may be used to classify MSE-based complexity indexes in a per patient basis using a rich set of visual inputs. However, such an approach would require sufficient data for algorithm training, and further research is needed to determine the most appropriate parameters and classification methods for this task. Taken together, our findings demonstrate that certain changes in retinal function can be elicited using specific visual inputs, and therefore, different groups based on age and/or condition may be discriminated against by selecting appropriate stimuli. Future work should determine what stimulus' features are more determinant for group separation according to age, condition and possibly other factors. In addition, our results suggest that MSE tools are more powerful during a specific time window (young ages for the animals in this study), which may pose a challenge for translational research. Still, whether and how such age-related differences manifest in signals recorded from AD patients and healthy people is yet to be determined. Here, we did not aim at finding a precise time window in which AD produces lower complexity but at presenting a candidate retinal measure that may be used as an AD early biomarker. Future work should determine whether MSE tools yield similar results in humans. For this, the different nature of the signals should be taken into account since, in contrast with the in-vivo-recorded and clinically used ERG, the µERG used in this study   www.nature.com/scientificreports/ is an ex vivo measure. Finally, we note that an approach to assess the age effects on the complexity of clinical ERG is to measure the MSE in a broad time window during the patient's life course, using complex visual stimuli.
In this study, we used the 5xFAD transgenic mouse that, in contrast to other AD mouse models, presents AD-like symptoms early in its lifetime, and so it has been compared with early-onset ( ∼ 60 years-old) AD in humans 41 . 5xFAD animals start to aggregate amyloid-β plaques in brain regions such as the subiculum and the hippocampus at as early as 1.5 months old 42 , and this feature would be similar to early stages in AD patients. The early manifestation of symptoms in the 5xFAD mouse allows studying the disease at stages for which other aging effects may be minimal. Further, 6-7 months old mice, the oldest group in this study, are in fact considered "adult" rather than "aged" or "old" (12-14 months) 43 . Since the 5xFAD mouse manifests AD-like symptoms at relatively young ages, it is expected that little to none aging effects are observed in, for example, retinal function. In future studies, the use of another AD mouse model could give more insights into age effects, e.g. APP/PSEN starts to aggregate amyloid-β protein at 5-6 months in their brains, allowing the broadest range of time window. Finally, to separate aging and disease effects in AD patients, retinal function and bioelectric signal complexity should be assessed at various ages in a long-term clinical study.
Gender is a confounding factor in AD, and its prevalence is greater in the female population 44 . In AD animal models, recent studies have demonstrated sex differences in 5xFAD mice manifested in gene expression at 4 months old 45 and behavior and molecular pathology at 5 months old 46 , but it is unclear whether these differences can manifest at 2-3 months old, the young group in our study. In this study, we had much less males in the 5xFAD-young group, and much more males in the WT-young group (Table 3), and so it is possible that the differences in complexity for the young animals were affected by gender disparities (for the NI protocol, the median complexity index for males was 22.73, 25.36, 23.49 and 19.94 for WT-young, 5xFAD-young, WT-adult and 5xFAD-adult, respectively, whereas the median complexity index for females was 23.36, 20.64, 20.19 and 18.89 for WT-young, 5xFAD-young, WT-adult and 5xFAD-adult, respectively). Future studies should more exhaustively analyze gender differences using a greater number of subjects of each sex, quantifying differences in the µERG of males and females and their impact on MSE and complexity metrics.
The MSE curves calculated for the retinal responses showed entropy values close to zero for very small scales, implying that µERG signals had no significant variability at these scales. Variations at small time scales correspond to high frequency components, and since the signals were low-pass filtered at 30 Hz, low entropy values for time scales < ⌈200/30⌉ = 7 were expected. Further, retinal µERG seems to function at temporal scales <∼ 10 Hz 11 , supporting the notion of low variability at lower scales. In addition, for FuzzyEn calculation we used sequences of length 2 ( m = 2 ), in agreement with previous work 47 , due to the limited length of the signals. We also used a distance threshold of 0.2 times the standard deviation of signals ( r = 0.2 ), a common value used in previous reports 47 . However, we note that FuzzyEn changes smoothly with r 36 , and in fact, our MSE curves did not substantially change with r between 0.1 and 0.5.
In our experiments, small pieces of the retina were placed on microelectrodes to capture, after low-pass filtering, the overall contribution of photoreceptors, bipolar cells, and amacrine cells. Previous work showed that ERG responses in 5xFAD retinas were altered at certain ages 20 . More specifically, 5xFAD retinas older than 6 months-old exhibited reductions, as compared to healthy ones, in traditional ERG features, namely P3, P2 and OP, associated with photoreceptors, bipolar cells and amacrine cells, respectively. However, no changes were detected at 6 months-old (the youngest age analyzed in this study), although a retinal ganglion cell-mediated response was reduced at this age. This indicates that amplitude-based tools are able to detect physiological changes in the retina only during advanced stages of the disease. Conversely, in our measurements we observed significant reductions in the complexity of 5xFAD retinas as compared to healthy ones for the younger group (i.e., 2-3 months-old), whereas for the adult group (i.e. 6-7 months-old) the differences were not significant. This suggests that MSE analyses may be able to detected physiological changes early in the development of the disease that go otherwise undetected by traditional amplitude-based tools.
Our findings support the theory of complexity-loss with aging and disease and demonstrate that MSE analyses may be a valuable tool to detect physiological changes in senescence or during illness. Our results also present additional evidence of the electrophysiological changes in the retina of a transgenic animal model of AD and can have great implications for early AD diagnosis. Future work should determine whether similar effects are observed in AD patients, and what type of visual stimuli should be used to elicit retinal behaviors with enough complexity to detect differences.

Methods
The data analyzed in this work were described with more details in a previous publication of our group 21 , and thus we provide here only a brief description of how the recordings were obtained. The entropy/complexity analyses of µERG signals presented here have not been the subject of previous analyses or publications, and thus we provide a more detailed description of the entropy tools used in this work.
Animal care and use. All experimental procedures followed protocols approved by the bioethics committee of Universidad de Santiago de Chile (report #457), following the international guidelines on animal handling and manipulation and the Chilean National Agency for Research and Development (ANID) bioethics and biosecurity standards. All experiments and methods were conducted in accordance with the ARRIVE guidelines. 5xFAD mice (Jackson laboratory, Bar Harbor, Maine, USA) and WT mice (B6SJLF1/J) were used in this study 21 . These animals were maintained in Universidad de Valparaíso, with a time routine of 12:12 hrs light/dark cycle, with controlled temperature, and water and food ad libitum. The animals were grouped into young subjects (2-3 months-old), age at which the animals start exhibiting amyloid-β brain aggregation, and adult subjects (6-7 months-old), which present thorough accumulation of plaques in the brain and behavior alterations 42 . µERG recordings from mice retina. The protocol for µERG recordings was performed using a Multi-Electrode Array (MEA) (USB256, Multichannel Systems GmbH, Reutlingen, Germany) with 252 electrode channels and a sampling rate of 20 kHz, which recorded the responses of a small piece of the retina ( n =13, 12, 11 and 11 for WT-young, 5xFAD-young, WT-adult and 5xFAD-adult, respectively, taken from 9, 9, 8 and 9 animals, respectively, with no more than two pieces of retina from the same animal). In brief, all the recordings were stored in a computer for offline analysis. Before the experiments, the animals were dark-adapted for 30 min, and then profoundly anesthetized with Isofluorane (Baxter, Deerfield, Illinois, USA) and euthanized. Eyes were removed and enucleated under dim red light, and eyecups were maintained in Ames medium (Sigma-Aldrich, San Luis, Missouri, USA) at 32 C and pH 7.4 and oxygenated with a mixture of 95% O2 & 5% CO2. Small pieces of the retina were positioned on an o-ring (MWCO-25000, Spectrumlabs, Rancho Dominguez, California, USA) with polylysine treatment (Product P4707, Sigma-Aldrich, San Luis, Missouri, USA).The retina was stimulated with different visual stimuli created on MATLAB software (Natick, Massachusetts, USA), projected on it using a LED projector (PB60G-JE, LG, Soul, South Korea), mounted in an inverted microscope (Eclipse T200, Nikon, Minato, Tokyo, Japan). The average radiance of each stimulus was 70 nW/mm 2 (Newport Corporation, Irvine, California, USA) with a spectral content ranging between 460 and 520 nm (Ocean Optics Inc, Dunedin, Florida, USA). All stimuli thoroughly covered the piece of the retina. We applied two visual stimulation protocols consisting of 21 repetitions each of: 1) a chirp stimulus (CS) protocol, and 2) a natural image (NI) protocol. The CS protocol consisted of an ON-light flash (3s) and an OFFdark period (3s) followed by a sinusoidal light stimulus of increasing frequency (1 to 10 Hz) and fixed maximum intensity, and followed by a sinusoidal light stimulus of 1 Hz with increasing intensity. Each repetition of the CS protocol lasted ∼ 35 s ( ∼ 12 min total). The NI protocol consisted of a sequence of images recorded in natural habitat and presented at a refresh rate of 60 fps 21 . Each repetition of the NI protocol lasted ∼ 11 s ( ∼ 5 min total). In the experiments, we used a fotodiode (PDA100A-EC, Thorlabs, Newton, New Jersey, United States) to control the retinal illumination stimulation (Fig. 1).
Channels were selected using the Neuroexplorer software (Plexon, Inc, Dallas, TX, USA) and according to a quality criterion (QI) 21 , and selected channels were averaged to obtain a single µERG signal for each piece of retina stimulated with the CS and NI protocols. The median number of selected channels (± 25-75% interquartile range) for the WT-young, 5xFAD-young, WT-adult and 5xFAD-adult groups was: 197.5 (± 64), 206 (± 116), 186 (± 78) and 203.5 (± 99), respectively. The averaged µERG signal was LP-filtered at 30 Hz, then subsampled at 200 Hz, and for each stimulation protocol, the recorded µERG signal was averaged over 21 repetitions. Only animals for which QI ≤ 0.45 were selected in this study, regardless of sex (Table 3).

Spectrum and coherence.
We calculated the power spectral density (PSD) of signals for frequencydomain characterization by means of Welch's method 48 . This method estimates PSD as an average of the periodogram of multiple overlapping segments, thereby reducing noise in PSD estimation at the cost of frequency resolution. We used a Hann window of size 256 and an overlap of 128. In addition, for the CS protocol, we calculated the coherence, C xy , between the chirp stimulus and the µERG response by means of the cross-spectral density, P xy , and the PSD of each signal: Here, P xy can be viewed as the PSD of the cross-correlation signal, and it is estimated using Welch's method. For both PSD and coherence calculation we used the Scipy Python library v1.6.2.
Multiscale entropy. In this study, we used the concept of entropy as a measure of signal uncertainty or disorder. The sample entropy 49 , SampEn, is a regularity statistics so that higher SampEn values are assigned to less predictable, more irregular time series. Given a time series X of length N, SampEn counts, for each subset sequence i of length m, the number of sequences of the same length that are at a distance smaller than r from the sequence i. Let this number be U m i (r) , then: (1) C xy = |P xy | 2 P x · P y Scientific Reports | (2022) 12:8900 | https://doi.org/10.1038/s41598-022-12208-2 www.nature.com/scientificreports/ Here, U m i (r) excludes the comparison of sequence i with itself. SampEn overcomes some difficulties of other entropy measures, namely, the need of many samples, and sensitivity to noise. SampEn resembles the so-called approximate entropy, ApEn, but it is a less biased statistic since, differently to ApEn, it eliminates the self-matching in the counting process. However, SampEn shows high sensitivity to parameter selection since, when comparing a pair of subsets, a Heaviside function is applied as a similarity metric after taking the distance -the contribution of such a pair is 1 if the distance between the subsets is less than r, and 0 otherwise. In contrast, the fuzzy entropy (FuzzyEn) 36 uses a fuzzy degree of similarity, D m ij , which instead of being binary, depends on the distance between the pairs, d m ij , through a continuous, concave function, typically quadratic exponential: The MSE method was proposed to account for the multiple time scales present in physiological processes 22,37 . Under this framework, a metric of entropy, e.g., the FuzzyEn, is calculated for the original time series, i.e., time scale 1, and for coarse-grained time series constructed by averaging as many samples as the current scale, in non-overlapping windows. For example, for time scale 2, the corresponding coarse-grained series is of length N/2, and each sample corresponds to the average of two consecutive samples of the original time series. This coarse-graining procedure is illustrated in Fig. 6 for two types of noise and for an electrophysiological signal. The coarse-grained time series appears less irregular for larger scales due to averaging for uniform noise. However, pink noise (a complex signal example) and the example µERG signal exhibit a degree of irregularity that appears to persist across all scales. Note that when coarse-graining a time series for a given scale τ , the resulting reduced series depends on the choice of the starting position for the initial window, so that there are τ possible coarse-grained resulting series. In the composite MSE (CMSE), the entropies of all these coarse-grained time series corresponding to scale τ are calculated and then averaged to obtain a single entropy value for τ . This procedure ensures more reliable results for larger scales 50 . Further, in the refined CMSE (RCMSE), the logarithm for entropy calculation is taken after computing the number of similar sequences, which reduces the probability of obtaining undefined entropy and increases the accuracy of entropy estimation 51 . In this study, we calculated the RCMSE of µERG responses with the FuzzyEn using the Neurokit2 toolbox for Python 52  Complexity. More complex signals have consistently higher entropy values across different time scales 22,37,53 , and accordingly, the area under the MSE curve has been used to quantify complexity 27,31,37 . We calculated a complexity index, C i , as the cumulative sum of the RCMSE for scales 20 − 44 , noting that (1) at the time scale of 20