Scalable Surrogate Deconvolution for Identification of Partially-Observable Systems and Brain Modeling

For many biophysical systems, direct measurement of all state-variables, in-vivo is not-feasible. Thus, a key challenge in biological modeling and signal processing is to reconstruct the activity and structure of interesting biological systems from indirect measurements. These measurements are often generated by approximately linear time-invariant (LTI) dynamical interactions with the hidden system and may therefore be described as a convolution of hidden state-variables with an unknown kernel. In the current work, we present an approach termed surrogate deconvolution, to directly identify such coupled systems (i.e. parameterize models). Surrogate deconvolution reframes certain nonlinear partially-observable identification problems, which are common in neuroscience/biology, as analytical objectives that are compatible with almost any user-chosen optimization procedure. We show that the proposed technique is highly scalable, low in computational complexity, and performs competitively with the current gold-standard in partially-observable system estimation: the joint Kalman Filters (Unscented and Extended). We show the benefits of surrogate deconvolution for model identification when applied to simulations of the Local Field Potential and blood oxygen level dependent (BOLD) signal. Lastly, we demonstrate the empirical stability of Hemodynamic Response Function (HRF) kernel estimates for Mesoscale Individualized NeuroDynamic (MINDy) models of individual human brains. The recovered HRF parameters demonstrate reliable individual variation as well as a stereotyped spatial distribution, on average. These results demonstrate that surrogate deconvolution promises to enhance brain-modeling approaches by simultaneously and rapidly fitting large-scale models of brain networks and the physiological processes which generate neuroscientific measurements (e.g. hemodynamics for BOLD fMRI)