Biophysically constrained dynamical modelling of the brain using multimodal magnetic resonance imaging.

We propose a Biophysically Restrained Analog Integrated Neural Network (BRAINN), an analog electrical network that models the dynamics of brain function. The network interconnects analog electrical circuits that simulate two tightly coupled brain processes: (1) propagation of an action potential, and (2) regional cerebral blood flow in response to the metabolic demands of signal propagation. These two processes are modeled by two branches of an electrical circuit comprising a resistor, a capacitor, and an inductor. We estimated the electrical components from in vivo multimodal MRI together with the biophysical properties of the brain applied to state-space equations, reducing arbitrary parameters such that the dynamic behavior is determined by neuronal integrity. Electrical circuits were interconnected at Brodmann areas to form a network using neural pathways traced with diffusion tensor imaging data. We built BRAINN in Simulink, MATLAB, using longitudinal multimodal MRI data from 20 healthy controls and 19 children with leukemia. BRAINN stimulated by an impulse applied to the lateral temporal region generated sustained activity. Stimulated BRAINN functional connectivity was comparable (within ±1.3 standard deviations) to measured resting-state functional connectivity in 40 of the 55 pairs of brain regions. Control system analyses showed that BRAINN was stable for all participants. BRAINN controllability in patients relative to healthy participants was disrupted prior to treatment but improved during treatment. BRAINN is scalable as more detailed regions and fiber tracts are traced in the MRI data. A scalable BRAINN will facilitate study of brain behavior in health and illness, and help identify targets and design transcranial stimulation for optimally modulating brain activity.