Safety, Vol. 8, Pages 85: Objective Evaluation of the Somatogravic Illusion from Flight Data of an Airplane Accident

2.1. Vestibular ModelsDetails and block diagrams of the SOMS and the Observer model can be found in [9] and [11,16], respectively. Both models consider inputs from the otolith organs and the semicircular canals: the two sub-systems that constitute the equilibrium organ in the inner ear. The otolith organs respond to the GIA, which is the vector sum of the gravitational acceleration (g) and inertial accelerations associated with linear motion (a); hence, GIA = g + a (note that GIA in this vector addition is marked in bold, while in the text GIA is just phrased as abbreviation). The semicircular canals respond to angular accelerations of the head and are thus insensitive to a constant, or slowly varying, angular velocity (such as a sustained aircraft turn). In the frequency range of natural head movements, the response of the semicircular canals is, however, proportional to angular velocity (see, for example, [17]). Hence, both vestibular models use angular velocity as an input signal for the semicircular canals. Mathematically, the behavior of the semicircular canals can be described by a high-pass filter that transmits relatively quick changes in head rotation and filters out low-frequency angular motions. A high-pass filter also predicts the decay in the rotation sensation, which is typically reported by blindfolded subjects in response to an angular velocity “step” (i.e., a vestibular stimulus consisting of a sudden increase in angular velocity that is then held constant). For roll and pitch rotations, the time constant of this decay has been estimated between 4 and 7 s [18]. In the SOMS model, this time constant is set to 4.2 s, and in the Observer model, it is 5.7 s. Note there is a longer time constant for yaw rotations to account for a neural process known as “velocity storage” [19,20], which prolongs the perception of yaw rotations. However, because yaw rotations play a minor role in the control of fixed-wing aircraft, we here focus on pitch and roll rotations.There is one, more fundamental, difference between the models with respect to the perception of (roll and pitch) rotations about a non-vertical axis. Whereas the predicted perception in the SOMS model is purely based on the characteristics of the semicircular canals, the Observer model also takes otolith inputs into account, which respond to the changing orientation of the head relative to gravity. As a consequence, the Observer model predicts a more sustained perception of roll or pitch rotations than the SOMS model, which is shown in Figure 1. for a roll stimulus. Figure 1 also shows that, because of the decaying response during prolonged rotation, we perceive an after-sensation of rotation in the opposite direction when the rotation stops, which is larger in the SOMS model output compared to the Observer model output. In flight, this after-sensation may occur after a slow roll motion and is known as the post-roll illusion [19]. With regard to the input signals to the otolith organs, both models assume that the peripheral otolith organs respond to a wide frequency range, which can be represented by a simple unity matrix [17]. However, the models differ in the way the otolith-sensed GIA is disambiguated into an (internal) estimate of gravity. A key assumption in the SOMS model is that our brain “knows” that Earth gravity is constant and that accelerations due to head motion are variable [17]. Hence, it is assumed that the neural process to determine an internal estimate of gravity from the GIA can be approximated by a low-pass filter. The time for this low-pass filter was set at tau = 2 s based on [15]. As gravity is constant in an Earth-fixed reference frame and the GIA is sensed in a head-fixed reference frame, the latter must first be transferred into Earth coordinates before applying the low-pass filter. This transformation is performed by a rotation matrix using angular velocity information from the semicircular canals. The result must be rotated back into head coordinates by the inverse matrix to obtain the internal, head-referenced estimate of gravity. In contrast to the SOMS model, the Observer model does not explicitly use frequency segregation to disambiguate the otolith stimulation into gravity (i.e., tilt) and linear acceleration (i.e., translation). Instead, the model hypothesizes that the brain generates expected sensory measurements, enabling the computation of “sensory conflict”. This framework is inspired by the engineering estimation structure of the classic Luenburger observer [20] and is implicit in Kalman filtering [21]. Specifically, it is hypothesized that the brain uses internal models of sensory dynamics and physical laws to produce the expected sensory afferent signals [10,22]. These are compared to produce sensory conflict signals that are then weighted with a gain. These gains serve as free parameters, defined once by the modeler to explain spatial orientation perception across a range of motion paradigms [11]. While the Observer model does not explicitly utilize frequency segregation, the canal–otolith integration produces similar behaviors for many motion paradigms (i.e., low-frequency otolith stimulation is accurately predicted to be perceived as tilt). As shown in Figure 2, both models predict that the longitudinal acceleration (gray line in the upper plot), representing a static takeoff run, results in a brief perception of forward motion (colored lines in the upper plot) followed by a sustained perception of nose-up pitch (colored lines in the bottom plot). This pitch-up sensation reflects the somatogravic illusion. The green line in the middle plot shows the perceived angular velocity component computed by the Observer model based on the rotating GIA vector on the otoliths, which is not present in the SOMS model. This illusory angular velocity explains why the Observer model predicts a larger somatogravic illusion than the SOMS model (bottom plot).

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