| ObjectiveThe study developed sparse non-negative matrix factorization (SNMF) based sparse coding and Granger causality analysis method to study how working memory was encoded by energy of θ band and γ band of multi-channel local field potentials (LFPs) and the functional connectivity of LFPs and sparse source components, which provide an innovative methods to study neural coding and functional connectivity.Methods1. Experimental data:The rats were implanted with16-channel nickel-cadmium microelectrode array (impedance less than1MΩ) targeting the prefrontal cortex PFC under aseptic conditions and chloral hydrate (350mg/kg) anesthesia. When the rats were in rest and during Y maze working memory task, the experimental data were recorded. The length of each data used in this study was6s which was used to represent the entire process of working memory event.2. Preprocessing of original data:the raw data are filtered with low-pass filter (0.3-500Hz) to obtain the LFPs. Then reject power interference and baseline wander for each LFP.3. After preprocessing, short-time Fourier transform (STFT) was used to obtain the time frequency representation of the LFPs.4. Constructed the input matrix X of SNMF from the time frequency representation of LFPs data. After SNMF, a basis matrix,A and a sparse source components matrix S were gotten. Each sparse source component is a time series.5. Coding of working memory by energy of θ and γ band:We determined the approximate time of the working memory event from matrix S. Selected sparse source components in which power increased suddenly during the time as working memory related sparse source components. Reconstruct working memory related sparse source components using the inverse operation of SNMF and the time frequency representation of the working memory related sparse source components was gotten. Then calculated the energy of θ and γ band of working memory related sparse source components. 6. The functional connectivity of LFPs and sparse source components:Granger causality analysis was used to LFPs and sparse source components. Two measures of causal interactivity,’causal density (CD)’ and ’causal flow (CF)’ were used to determine the functional connectivity of LFPs and sparse source components during working memory task and in rest with Granger causality analysis.(1) Causal densityCalculated the averaged CD values of LFPs and sparse source components for each rat in both working memory state and rest state. Compared the functional connectivity between two states.(2) Causal FlowCalculated the averaged CF value of each node of LFPs causal networks. After that, t test was used to determine the causal sources and causal sinks related channels for each rat in both working memory state and rest state.Calculated the CF value of each node of sparse source components causal networks, and determined causal sources and causal sinks related sparse source components for every trial. Reconstruct causal sources and causal sinks related sparse source components using the inverse operation of SNMF respectively and the time frequency representation of the causal sources and causal sinks related sparse source components was gotten. Then Calculated averaged time frequency representation of the causal sources and causal sinks respectively for each rat.Results1. Coding of working memory by energy of θ and γ band:(1) We analyzed LFPs recorded from4Sprague-Dawley (SD) rats’prefrontal cortex (PFC) during working memory task in Y maze, with10trials for each rat. We calculated the energy of θ and y band in working memory state and rest state in a second when the LFPs power of both two state peaks. Group statistics showed that the energy of θ and y band in the working memory state were greater than in the rest state in the second (t test, p<0.01).(2) We calculated the energy of θ and y band in working memory related sparse source components for each rat. The energy of θ and y band was significantly greater than zero (t test, p<0.01). The energy of θ band was significantly greater than that of γ band (t test, p<0.01).2. The functional connectivity of LFPs in working memory state:(1) Causal densityThe averaged CD values of LFPs for rat1, rat2, rat3and rat4in working memory state are0.1467±0.0320,0.0971±0.0313,0.1721±0.0296and0.1496±0.0427respectively. The averaged CD values of LFPs for rat1, rat2, rat3and rat4in rest state are0.0353±0.0127,0.0462±0.0159,0.0784±0.0375and0.0904±0.0354respectively. The averaged CD values in working memory state were significantly greater than that in rest state (t test, p<0.01).(2) Causal flowThe causal sources for rat1in working memory state were corresponding to No.2and No.14channels; the causal sinks for rat1in working memory state were corresponding to No.l, No.6, No.8, No.9, No.10and No.11channels. There was no channel related causal sources for rat1in rest state; the causal sinks for rat1in rest state were corresponding to No.9, No.13and No.14channels.The causal sources for rat2in working memory state were corresponding to No.13and No.16channels; the causal sinks for rat2in working memory state were corresponding to No.1, No.4, No.5and No.10channels. The causal sources for rat2in rest state were corresponding to No.16channel; the causal sinks for rat2in rest state were corresponding to No.3and No.6channels.The causal sources for rat3in working memory state were corresponding to No.13and No.14channels; the causal sinks for rat3in working memory state were corresponding to No.l, No.11, No.15and No.16channels. The causal sources for rat3in rest state were corresponding to No.13and No.14channels; the causal sinks for rat3in rest state were corresponding to No.4, No.5, No.8, No.12, No.15and No.16channels.The causal sources for rat4in working memory state were corresponding to No.3, No.12and No.13channels; the causal sinks for rat4in working memory state were corresponding to No.6, No.7and No.8channels. The causal sources for rat4in rest state were corresponding to No.2channel; the causal sinks for rat4in rest state were corresponding to No.8, No.14and No.16channels. 3. The functional connectivity of sparse sources components in working memory state(1) Causal densityThe averaged CD values of sparse sources components for rat1, rat2, rat3and rat4in working memory state are0.2315±0.0452,1697±0.0331,0.1894±0.0360, and0.2004±0.0485and0.1496±0.0427respectively. The averaged CD values of sparse sources components for rat1, rat2, rat3and rat4in rest state are0.1456±0.0094,0.1177±0.0266,0.1098±0.0142and0.1423±0.0168respectively. The averaged CD values in working memory state were significantly greater than that in rest state (t test,p<0.01).(2) Causal flowWe got the averaged time-frequency representation and amplitude frequency diagram of causal sources and causal sinks in both working memory state and rest state (the result was averaged up all10trails and all channels). It shows a great difference of time-frequency representation of causal sources and causal sinks between the two groups. The amplitude frequency lines of working memory group are higher in theta band (4-12Hz) than rest group. And we found that the amplitude of causal sources of working memory group peaks at about10Hz from amplitude frequency diagram.Conclusions1. Energy of θ and y band was meaningful to support working memory. There was more energy of0band than that of y band to encode working memory.2. The functional connectivity of LFPs and sparse sources components in working memory state was stronger than in rest states. The causal interactivity of neural activity strengthened in work memory state than in rest state.3. Our result showed that0band may play an important role of Granger cause in working memory. |
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