Feedback Gain Indicates the Preferred Direction in Optimal Feedback Control Theory

We investigated the role of feedback gain in optimal feedback control (OFC) theory using a neuromotor system. Neural studies have shown that directional tuning, known as the "preferred direction" (PD), is a basic functional property of cell activity in the primary motor cortex (M1). However, it is not clear which directions the M1 codes for, because neural activities can correlate with several directional parameters, such as joint torque and end-point motion. Thus, to examine the computational mechanism in the M1, we modeled the isometric motor task of a musculoskeletal system required to generate the desired joint torque. Then, we computed the optimal feedback gain according to OFC. The feedback gain indicated directional tunings of the joint torque and end-point motion in Cartesian space that were similar to the M1 neuron PDs observed in previous studies. Thus, we suggest that the M1 acts as a feedback gain in OFC.