  The quest for a scientific description of consciousness has given rise to new
theoretical and empirical paradigms for the investigation of phenomenological
contents as well as clinical disorders of consciousness. An outstanding
challenge in the field is to develop measures that uniquely quantify global
brain states tied to consciousness. In particular, information-theoretic
complexity measures such as integrated information have recently been proposed
as measures of conscious awareness. This suggests a new framework to
quantitatively classify states of consciousness. However, it has proven
increasingly difficult to apply these complexity measures to realistic brain
networks. In part, this is due to high computational costs incurred when
implementing these measures on realistically large network dimensions.
Nonetheless, complexity measures for quantifying states of consciousness are
important for assisting clinical diagnosis and therapy. This article is meant
to serve as a lookup table of measures of consciousness, with particular
emphasis on clinical applicability of these measures. We consider both,
principle-based complexity measures as well as empirical measures tested on
patients. We address challenges facing these measures with regard to realistic
brain networks, and where necessary, suggest possible resolutions.
