Combining function and structure in a single macro-scale connectivity model of the human brain
Combining the macro-scale functional and structural connectivity matrices of the human brain could provide useful information on how various diseases and conditions affect the brain. However, it is not a simple task to combine such information as they are derived usually in very different ways with functional information typically gathered using fMRI, EEG, or MEG whereas structural information relies on robust diffusion-weighted MRI tractography methods. This work proposes a solution to this problem using an analogy to an electric circuit with the functional information being the voltage sources and the structural information resistance of the elements in the circuit. The voltage sources and resistances can be used to solve the current in the circuit using Modified Nodal Analysis, for example. In the proposed analogy, the solved electric current represents how the functional information flows in the structural brain network. This work demonstrates a connection-specific example of such analysis as well as whole-brain analysis using data from the Human Connectome Project. How this is achieved is explained in the method sections which has a complimentary Python function that can readily be applied to any project that has both functional and structural connectivity data. The main motivation for the proposed analysis method is that it could provide new information on various conditions and diseases such as Alzheimer's or multiple sclerosis that affect the human brain. In a sense, the proposed approach is a macro-scale version of the classical Hodkin-Huxley model.