A role for neuromorphic processors in therapeutic nervous system stimulation

Abstract

The motivations behind the development of many neuromorphic processors have been dominated by either the creation of better artificial intelligence, or novel non-von Neumann computing paradigms. A result of this impetus has been a number of low-power processors capable of simulating many different biological features of the nervous system. Power efficiency is crucial for deployed neuromorphic systems, but it also opens this technology up to other energy restricted applications. In this opinion, we suggest two such applications pertaining to therapeutic stimulation of the nervous system where closing the control loop could be assisted by advances in neuromorphic architectures: (1) deep brain stimulation (DBS) in the treatment of Parkinson's disease and (2) epidural spinal cord stimulation (ESS) for restoring voluntary motor functions. Though there are still questions that must be addressed before this would be feasible, but we are suggesting that the technological barriers—in both the algorithms and hardware—can be overcome with directed funding and research. Neuromorphic processor research is centered around the creation of brain-like intelligence through power-efficient circuits that borrow elements directly from biology (Mead, 1989). The applications for these projects range from brain-scale simulations (Gao et al., 2012; Benjamin et al., 2014) and in silica experimentation (Schemmel et al., 2010; Furber et al., 2012), to brain-like computing and learning (Merolla et al., 2011; Srinivasa and Cruz-Albrecht, 2012; Cruz-Albrecht et al., 2013; Rahimi Azghadi et al., 2014; Schmuker et al., 2014). These projects promise unrivaled access to large-scale models of the brain as well as insight into the unique non-von Neumann computation that biological systems appear to achieve. Regardless of the motivation, the tangible result of these efforts has been an accumulation of low-power circuits capable of emulating various elements of the nervous system. Although these are essential for embodying robotic systems and augmenting current super-computing paradigms, they also have the potential to assist in nervous system stimulation control. This application is outside the scope of the currently funded neuromorphic hardware projects, but with new insights and technological advances, it is one that will be particularly beneficial. In our current capacity to monitor neural circuits, most system variables are unobservable. One strategy for estimating these unknown system variables and parameters is by employing an Unscented Kalman Filter (UKF) to combine the observable and unobservable states. The UKF employs a set of known dynamical equations and observation functions with the measurable data to update an approximation of the state and its uncertainty. At each update, sigma points—system states that are consistent with the current state uncertainty—are selected and used to integrate the system. These are combined with estimated mean state values and the approximate uncertainty. A gain matrix then updates the new most likely state of the system. The schematic for this organization is illustrated in Figure 1A. Applying this kind of feedback control to biological systems was initially demonstrated by Voss et al. (2004) but has since been demonstrated on a number of control and estimation problems (Abarbanel et al., 2008; Li et al., 2009; Ullah and Schiff, 2009, 2010; Schiff, 2010; ODoherty et al., 2011; Aprasoff and Donchin, 2012; Schiff, 2012; Liu et al., 2014). Figure 1. Example therapeutic applications of model based control. (A) The system dynamics are described by a model, F, and the observations are described by a function, A. In most systems those observations are going to be noisy, so a covariance matrix, R, will account for that. After one step of F, using the resulting sigma points will provide ${\tilde{X}}_i$ = F(X_i). A new set of observations can then be found, Ỹ_i = A(X_i). The means over these two matrices are the a priori state and measurement estimates. The a posteriori state estimate, $\widehat{x}$, is now dependent on the state estimate, $\tilde{x}$, the measurement estimate, ỹ, the actual measurement, y, and the Kalman gain matrix, G. (B) Diagram of deep brain stimulation in the treatment of Parkinson's disease. Adapted from Thibeault and Srinivasa (2013). (C) Example epidural spinal cord stimulation for restoring voluntary motor functions. By using a model of the area under stimulation, both the activity and state of that area can be approximated—something that is not directly measurable. The model, constructed from the current understanding of the anatomy, can then be used to find an optimal set of stimulation parameters. In addition, the model output can be used as the feedback into a control system that can not only dynamically tune the stimulation parameters but also adapt to the physiological circuit remodeling—providing the highest possible therapeutic benefit. Embedding these models in low-power neuromorphic hardware would facilitate a transition into implantable devices. A discussion of control inherently implies observability of the system. However, observability alone is useful to current nervous system stimulation strategies. Observing the unknown—or unreachable—states of the physical system, would provide a way to automatically tune the stimulation...