Simulating brain signals with predefined mutual correlations - a technical note

ObjectiveWhen modeling task-related human brain activity it is often necessary to simulate brain signals with specific mutual correlations between them. The signals should resemble those observed in practice, and consist of an "evoked" ("phase-locked") component and a random oscillatory part. To be neurophysiologically plausible their waveforms must be shaped in a certain way or exhibit specific global features; in technical terms - they should be modulated by a certain envelope function. The goal of this technical note is to describe a simple way of how such signal sets can be obtained. MethodsWe derive a procedure which allows generating multi-epoch signals with the above properties. This is done by mixing a "seed" set of waveforms typically reflecting particular qualities of the target brain activity. As an example, the seed set can consist of realizations of colored noise with desired power spectrum, or can be obtained from real brain measurements. ResultsThe algorithm yields a set of n multi-epoch signals with specified mutual correlations. Evoked parts, oscillatory parts and global envelopes of the signals can be controlled independently in order to obtain desired properties of the generated time courses. ConclusionThe procedure provides versatile sets of mutually correlated signals suitable for modeling task-related brain activity. SignificanceIn contrast to other methods often relying on complicated computations, the suggested approach is straightforward and easy to apply in everyday practical work, yet yielding realistic "functionally connected" simulated brain signals.