Sensing linear acceleration

To understand how accelerations are sensed, we start with the case of the otolith system. Figure 8.5 shows a schematic representation of an otolith organ, which may be either the utricle or saccule. Mechanoreceptors, in the form of hair cells, convert acceleration into neural signals. Each hair cell has cilia that are embedded in a gelatinous matrix. Heavy weights lie on top of the matrix so that when acceleration occurs laterally, the shifting weight applies a shearing force that causes the cilia to bend. The higher the acceleration magnitude, the larger the bending, and a higher rate of neural impulses become transmitted. Two dimensions of lateral deflection are possible. For example, in the case of the utricle, linear acceleration in any direction in the $ xz$ plane would cause the cilia to bend. To distinguish between particular directions inside of this plane, the cilia are polarized so that each cell is sensitive to one particular direction. This is accomplished by a thicker, lead hair called the kinocilium, to which all other hairs of the cell are attached by a ribbon across their tips so that they all bend together.

Figure 8.6: Because of the Einstein equivalence principle, the otolith organs cannot distinguish linear acceleration of the head from tilt with respect to gravity. In either case, the cilia deflect in the same way, sending equivalent signals to the neural structures.

One major sensing limitation arises because of a fundamental law from physics: The Einstein equivalence principle. In addition to the vestibular system, it also impacts VR tracking systems (see Section 9.2). The problem is gravity. If we were deep in space, far away from any gravitational forces, then linear accelerations measured by a sensor would correspond to pure accelerations with respect to a fixed coordinate frame. On the Earth, we also experience force due to gravity, which feels as if we were on a rocket ship accelerating upward at roughly $ 9.8$m/s$ ^2$. The equivalence principle states that the effects of gravity and true linear accelerations on a body are indistinguishable. Figure 8.6 shows the result in terms of the otolith organs. The same signals are sent to the brain whether the head is tilted or it is linearly accelerating. If you close your eyes or wear a VR headset, then you should not be able to distinguish tilt from acceleration. In most settings, we are not confused because the vestibular signals are accompanied by other stimuli when accelerating, such as vision and a revving engine.

Steven M LaValle 2020-01-06