Bias, optimal linear estimation, and the differences between open-loop simulation and closed-loop performance of spiking-based brain–computer interface algorithms

Abstract

The activity of dozens of simultaneously recorded neurons can be used to control the movement of a robotic arm or a cursor on a computer screen. This motor neural prosthetic technology has spurred an increased interest in the algorithms by which motor intention can be inferred. The simplest of these algorithms is the population vector algorithm (PVA), where the activity of each cell is used to weight a vector pointing in that neuron’s preferred direction. Off-line, it is possible to show that more complicated algorithms, such as the optimal linear estimator (OLE), can yield substantial improvements in the accuracy of reconstructed hand movements over the PVA. We call this open-loop performance. In contrast, this performance difference may not be present in closed-loop, on-line control. The obvious difference between open and closed-loop control is the ability to adapt to the specifics of the decoder in use at the time. In order to predict performance gains that an algorithm may yield in closed-loop control, it is necessary to build a model that captures aspects of this adaptation process. Here we present a framework for modeling the closed-loop performance of the PVA and the OLE. Using both simulations and experiments, we show that (1) the performance gain with certain decoders can be far less extreme than predicted by off-line results, (2) that subjects are able to compensate for certain types of bias in decoders, and (3) that care must be taken to ensure that estimation error does not degrade the performance of theoretically optimal decoders.

Stochastic Optimal Control as a Theory of Brain-Machine Interface Operation

“…Experiments with BMI have also suggested that closed-loop control can partially compensate decoder bias, which is systematic error in the decoded velocity (Chase et al, 2009;Jarosiewicz et al, 2008;Koyama et al, 2010). To examine this possibility, we compared open-loop versus closed-loop behavior in the PVA (Georgopoulos et al, 1986), which is known to be a biased variation on the OLE (Chase et al, 2009).…”

“…To examine this possibility, we compared open-loop versus closed-loop behavior in the PVA (Georgopoulos et al, 1986), which is known to be a biased variation on the OLE (Chase et al, 2009). Error in the decoded angle of movement was averaged over multiple trials for each of eight movement directions.…”

“…Second, although the brain compensates biased decoders in closed-loop experiments (Chase et al, 2009;Jarosiewicz et al, 2008;Koyama et al, 2010), the model predicts that this capability does not necessarily come for free (see Figure 4). In our example with nongaussian neural activity, discrepancies between the PVA and OLE in terms of bias in decoded movement direction are decreased in closed-loop mode in comparison with open-loop mode.…”

“…First, closed-loop control deteriorates with increasing bin width in spike-based BMI (Cunningham et al, 2011). Second, closed-loop decoding is capable of compensating for BMI algorithms that demonstrate systematic bias in open-loop decoding (Chase, Schwartz, & Kass, 2009;Jarosiewicz et al, 2008;Koyama et al, 2010). Third, neural ensembles in motor cortex demonstrate that preferred direction of velocity tuning curves shifts between arm control and closed-loop BMI control (Carmena et al, 2003;Ganguly & Carmena, 2009;Ganguly, Dimitrov, Wallis, & Carmena, 2011;Jarosiewicz et al, 2008;Taylor et al, 2002), as well as between closed-loop operation of different BMI algorithms (Ganguly et al, 2011).…”

“…Such a model would need to generalize beyond closed-loop performance improvements to simultaneously explain various other coexisting phenomena: deterioration with increasing bin width (Cunningham et al, 2011), compensation of decoder bias (Chase et al, 2009;Jarosiewicz et al, 2008;Koyama et al, 2010), and shifting tuning curves (Carmena et al, 2003;Ganguly & Carmena, 2009;Ganguly et al, 2011;Jarosiewicz et al, 2008;Taylor et al, 2002). Here, we propose to explain these various phenomena of BMI operation by describing the brain in closed-loop mode as a stochastic optimal controller.…”