Background The article is focused on the brain connectivity extensions and expansions, with the introductory elements in this section. Method In Causality measures and brain connectivity models, the necessary, basic properties demanded in the problem are summerized, which is followed by short introduction to Granger causality, Geweke developments, PDC, DTF measures, and short reflections on computation and comparison of measures. Results Analyzing model semantic stability, certain criteria are mandatory, formulated in preservation/coherence properties. In the sequel, a shorter addition to earlier critical presentation of brain connectivity measures, together with their computation and comparison is given, with special attention to Partial Directed Coherence, PDC and Directed Transfer Function, DTF, complementing earlier exposed errors in the treatment of these highly renowned authors and promoters of these broadly applied connectivity measures. Somewhat more general complementary methods are introduced in brain connectivity modeling in order to reach faithful and more realistic models of brain connectivity; this approach is applicable to the extraction of common information in multiple signals, when those are masked by, or embedded in noise and are elusive for the connectivity measures in current use; the methods applied are: Partial Linear Dependence and the method of recognition of (small) features in images contaminated with noise. Results are well illustrated with earlier published experiments of renowned authors, together with experimental material illustrating method extension and expansion in time. Conclusion Critical findings, mainly addressing the connectivity model stability, together with the positive effects of method extension with weak connectivity are summarized.
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