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The “stationarity time” (ST) of neuronal spontaneous activity signals of rat embryonic cortical cells, measured by means of a planar Multielectrode Array (MEA), was estimated based on the “Detrended Fluctuation Analysis” (DFA). The ST is defined as the mean time interval during which the signal under analysis keeps its statistical characteristics constant. An upgrade on the DFA method is proposed, leading to a more accurate procedure. Strong statistical correlation between the ST, estimated from the Absolute Amplitude of Neural Spontaneous Activity (AANSA) signals and the Mean Interburst Interval (MIB), calculated by classical spike sorting methods applied to the interspike interval time series, was obtained. In consequence, the MIB may be estimated by means of the ST, which further includes relevant biological information arising from basal activity. The results point out that the average ST of MEA signals lies between 2-3 seconds. Furthermore, it was shown that a neural culture presents signals that lead to different statistical behaviors, depending on the relative geometric position of each electrode and the cells. Such behaviors may disclose physiological phenomena, which are possibly associated with different adaptation/facilitation mechanisms.

The digital processing of biological signals may be considered a challenging task [

A classical mathematical procedure in neuronal signal processing consists of the detection of spikes connected with action potentials, which requires the establishment of an amplitude threshold, above which any potential is considered a spike [

Multielectrode Arrays (MEAs) emerged during the 1990's, in order to measure the electrical activity of cultured neurons [

On the other hand, neuropathologies may be considered relevant deseases from a clinical viewpoint. Particularly, epilepsy disturbs 1% of the world population, corresponding to 50 million people. From this amount, at least the seizures of 30% of patients can not be well managed by conventional treatments based on anticonvulsivant drugs [

Consequently, MEA devices should be capable to process both cellular-level signals, such as action potentials, as well as electroencephalographic (EEG) data in real time, to minimize epileptic seizures [

For these reasons, the neuroprosthesis implementation requires simple statistical tools of low computational complexity, leading to real-time signal processing. To our knowledge, these practical constraints have been very fewly addressed by literature connected with MEA-signal analysis, especially regarding the estimation of optimal data windowing, taking into consideration the non-stationary behavior of the signal. Notice that such procedure is essential for any operation linked to the MEA-signal processing [

A possible strategy to establish optimal windowing is based on the concept of “Stationarity Time” (ST), defined as the time interval during which the signal measured by MEA keeps its statistical characteristics constant [

In brief, the study of the stationary behavior of MEA signals can disclose important features of culture neurodynamics, as well as enabling the definition of optimal windowing, which is mandatory for efficient neuroprosthesis implementation. In this context, this paper develops the estimation of the ST of a set of spontaneous activity signals. An upgrade on DFA technique is proposed, leading to an accurate tool that is able to process the absolute amplitudes of neuronal spontaneous activity. The results are compared to classical quantities that are currently used to characterize the culture dynamics, such as the Mean-Interburst Interval, pointing out strong statiscal correlations. Finally, the neurodynamics of the culture is discussed in terms of the ST diagram, leading to physiological interpretations of the results.

MEA signals are characterized by the absolute amplitude of neural spontaneous activity (AANSA), collected from primary cultures of cortical neurons, extracted from rat embryos of 17-18 days. These cells were plated on planar MEAs containing 60 microelectrodes (

MEA signals were analyzed by means of the plataform

The following quantities are defined through (

DFA method [

In the second step, the signal

It should be noticed that (

In the third step, the detrended walk variance is calculated for each segment, and, finally, all these variances are averaged, considering all segments, as shown by (

In the following, the classical methodology for the ST estimation based on the variance

Example of the classical methodology for ST estimation through DFA [

The ST is estimated as the

The ST characterizes the signal time-variation profile as discussed in the following. Since ST is estimated as particular value of the window length

In brief, the ST estimation procedure previously described [

In order to highlight all the changes of the first derivative of

The ST estimation for one single electrode is performed based on the plot

Hypothetical illustration of a second-derivative generic plot, associated with a function

Considering just one single five-minute experiment, the average ST of each electrode was estimated based on (

Table

Average results of ISI analysis.

Number of spikes/second within one burst | Average duration of one burst | Average number of spikes during one burst | Average duration of one spike within the burst |
---|---|---|---|

78.02 | 161.16 seconds | 12570 | 12.82 milliseconds |

The processing of all MEA channels, considering all the four experiments, leads to the estimation of the overall log(

Overall average log(

The second derivative _{2} = 3.35 seconds, which is slightly different from ST = 3.2 seconds estimated by the classical approach (see Figure

Overall average value of

Table

Average values for each experiment, considering all the 60 channels, based on (

Experiment number | ST [s] – AANSA signals | ST [s] – ISI time series | MIB [s] | MFR [spikes/s] | MBR [bursts/min] |
---|---|---|---|---|---|

1 | 2.29 | 3.10 | 3.26 | 10.01 | 19.07 |

2 | 2.41 | 4.93 | 5.03 | 6.63 | 13.63 |

3 | 2.50 | 6.12 | 6.44 | 5.69 | 11.77 |

4 | 2.42 | 5.53 | 5.61 | 7.17 | 13.57 |

Overall average | 2.40 | 4.92 | 5.09 | 7.38 | 14.51 |

Figure

Spatial variation of the amplitude of the overall-average ST (AANSA) along the MEA electrodes, upper view

Colour scale representing the amplitude of the overall-average ST, in seconds

In order to get further insights on the relationship of the several quantities of Table

Pearson Correlation Coefficients (

Comparison in terms of | ||||
---|---|---|---|---|

Channels, considering four experiments | ||||

Experiments (5 minutes, all channels at a time) | ||||

Dispersion plot involving ST and MFR for 60 channels, four experiments;

Dispersion plot involving ST and MIB for 60 channels, four experiments;

Dispersion plot involving ST and MFR, average for 60 channels, four experiments;

Dispersion plot involving ST and MIB, average for 60 channels, four experiments;

Dispersion plot involving ST estimated for AANSA signals and ST estimated for ISI time series, average for 60 channels, four experiments;

The last line of Table

Consider now Table

Results of Figures

There is a significant statistical correlation between ST (AANSA) and MIB, at the channel level (see second line of Table

There is a very strong and significant statistical correlation between ST (AANSA) and MFR, MBR and MIB, at the experiment level (see third line of Table

There is a very strong and significant statistical correlation between ST estimated for the AANSA signals and the ST estimated for ISI time series, even if their absolute amplitudes are different from each other.

Particularly regarding the first conclusion above, based on Table

There are, however, several relevant issues involving the results of the statistical analysis presented in Figures

Consider now results of Figure

Furthermore, the results shown in Table

According to Table

Figure

Figure

Among these components, there are those characterized by a quick dynamics, which can change in the scale of hundreds of milliseconds, known as “brief components”. There are also other ones, presenting slower action, which will influence neurophysiological phenomena in the time scale of seconds [

Finally, comparing the results and discussions in this paper, in [

The upgraded DFA method allowed the detection of nonstationarities of the neural-culture signals throughout the time. Our proposition enables a more accurate and systematic detection of signal ruptures, if compared to the classical straight-line rough approach [

Results based on experiments and on a rigorous statistical analysis discussed the relationships among the ST (which was estimated for both AANSA signals and ISI time series) and the classical spike analysis quantities MIB, MFR, and MBR, which are generally calculated to assess the global physiological state of the culture. It was shown that ST (AANSA) does not present any correlation with both MFR and MBR. However, ST (AANSA), ST (ISI), and MIB (which is also calculated from ISI) do present a strong statistical correlation, so that it is possible to estimate MIB(ISI) as the ST (AANSA) divided by 0.6, as shown in (

The upgrade on the DFA technique proposed in this paper leads to the estimation of the overall-average ST within the range 2-3 seconds, pointing out that the optimal windowing of signals arising from the neural culture is about 2-3 seconds. According to literature [

Future work involves the use of the upgraded DFA method for the development of efficient spike classification and neural connectivity techniques, based on the concept of ST. White-noise theory plays also an important role according to previous works of literature, suggesting its association with DFA. Finally, deeper studies about the role of ionic channels involved in the physiological mechanisms of adaptation/facilitation should be performed to evaluate the association of these channel dynamics with the ST profile of the neuronal culture.

This work was funded by the Research Council of Minas Gerais Province (FAPEMIG) and by the Brazilian Research Council (CNPq). Special thanks are addressed to undergraduate student Leandro Cordeiro (School of Medicine/UFU), for his valuable help with the physiological bibliographic research, as well as to Danilo R. Campos, for the initial work on the DFA method. The authors are also indebted to the editor and reviewers for their comprehension during the development of the publication process.