Analysis of artificial gravity paradigms using a mathematical model of spatial orientation

Highlights

• Linear sled hybrid concept provides alternative approach to artificial gravity.

• The cross-coupled illusion scales non-linearly with head tilt angle and spin rate.

• Linear sled artificial gravity is not likely to be disorientating to the rider.

Abstract

Artificial gravity (AG) is a promising approach to reduce the physiological deconditioning experienced by astronauts. Here we propose the linear sled hybrid AG system as an alternative to the typical centrifuge approach to creating AG. In this paradigm, the rider is briefly linearly accelerated towards their head, then rotated 180° around, then decelerated. This sequence is repeated creating footward loading during the linear acceleration and deceleration phases, replicating standing upright on Earth, without any gravity gradient or Coriolis forces. The 180° rotation also produces gradient centripetal acceleration, for a “hybrid” approach. We simulated the well-validated observer model to predict the rider's orientation perception and potential disorientation in response to these two AG paradigms. Particularly, we simulated head tilts to investigate the cross-coupled illusion. For the centrifuge, as expected, we found head tilts caused the cross-coupled illusion and an illusory sense of tilt. As a novel prediction, we found the head tilt angle and centrifuge spin rate to interact non-linearly, producing an inflection point in the peak perceived tilt of the cross-coupled illusion. We found the linear sled paradigm to be well perceived and, as expected, head tilts did not produce the cross-coupled illusion. While the observer model predicted the linear sled paradigm to not be disorienting, future experimental work is necessary for validation. Comfort and motion sickness feasibility, as well as countermeasure efficacy, should be studied experimentally.

Introduction

During space exploration missions, astronauts are exposed to increased radiation as well as microgravity for long durations. Extended microgravity exposure results in physiological deconditioning including, but not limited to, musculoskeletal, cardiovascular, sensorimotor, cerebrovascular, as well as ocular changes (see Ref. [1] for a summary). This physiological deconditioning poses concerns not only over the duration of the crew's lifetimes, but also risks for the safety and success of the crew on a particular mission (e.g. [2]).

Various physiological countermeasures to this deconditioning have been proposed or are in use (e.g., resistive and aerobic exercise, fluid loading, diet and pharmaceuticals, etc.). However, most countermeasures focus on a single or a few physiological systems and in some cases have not been found to be fully effective [3]. Though recent exercise and nutrition countermeasures have been effective for mitigating musculoskeletal deconditioning [4] for up to 6 months stays on the International Space Station (ISS). Alternatively, artificial gravity (AG) has been proposed as a comprehensive countermeasure (i.e., addresses nearly all physiological systems) for extended exposure to weightlessness [3,5]. Presumably, AG will not have a direct benefit towards protecting against radiation-induced effects.

Typically, AG concepts have proposed using a centrifuge to create sustained centripetal acceleration. The required centripetal acceleration level (or G-level) for optimally protecting an astronaut from spaceflight-induced physiological deconditioning remains an open research question [5]. We define G as the ratio of the gravito-inertial acceleration to the standard g = 9.81 m/s² experienced on Earth. As such, forces expressed in G's are specific forces throughout this paper. The magnitude of centripetal acceleration is equal to the product of the radius and the spin rate squared. Thus, for a desired acceleration level, this leads to a tradeoff between a long-radius centrifuge that spins slowly versus a shorter radius that must spin more quickly. Lower mass, short-radius centrifuge concepts (there is no strict definition, but approximately <3 m radius) are generally deemed more practical for early exploration missions and the Low Earth Orbit research required prior to them [5].

However, short-radius centrifugation, and the associated fast spin rate, leads to three confounding challenges. First, the short radius leads to a “gravity-gradient” where the portions of the astronaut's body farther from the center of rotation experience relatively higher G's. This alters fluid distribution and cardiovascular responses [6] and can also present sensorimotor/coordination challenges (e.g., an astronaut's arm becomes “heavier” as it is moved radially outward/footward). Second, a mass moving linearly in the spinning environment experiences Coriolis forces, except if moving exactly parallel to the centrifuge spin axis. This leads to sensorimotor errors where, for example, a reaching arm movement is unexpectedly perturbed [7]. Third, and the focus of this paper, is that if the astronaut makes any “out of plane” head tilts/rotations (i.e., not parallel to the centrifuge spin axis), they will experience the cross-coupled illusion [8]. This illusion, sometimes called the Coriolis illusion (though it is independent of the Coriolis force issue described earlier), results in an illusory perception of tumbling that can be very disorientating and typically leads to motion sickness [9,10].

A detailed description of the cross-coupled illusion can be found elsewhere [8]. Briefly, the semicircular canals of the vestibular system in the inner ear sense angular rotation, but are insensitive at lower frequencies. For example, during the sustained, constant spin rate of a centrifuge, the endolymph fluid in the stimulated semicircular canal(s) of the vestibular system equilibrates and the sense of rotation ceases (in the dark or with a centrifuge-fixed visual reference). When the head is then tilted/rotated, the physical centrifuge spin instantly stimulates the canal(s) now aligned with the spin axis. Furthermore, the equilibrated axis is no longer aligned with the spin axis causing a reversal in stimulation leading to the tumbling sensation. The axis of the illusory tumbling sensation follows a right hand rule (e.g., a yaw head tilt during roll centrifuge spin causes an illusory pitch perception). During the head tilt, the otolith organs of the vestibular system provide a generally veridical cue of gravito-inertial acceleration, which is inconsistent with the tumbling sensation and eventually leads to its decay. During the illusion, humans typically report a paradoxical sensation of only moderate illusory tilt despite a large sense of tumbling (“I feel like I am spinning but not going anywhere”).

We now transition to introducing a novel, alternative approach to creating AG, the “linear sled hybrid AG system”. Fig. 1 shows the stimulation pattern of the system. Instead of constantly spinning like on a centrifuge, the rider is linearly accelerated to create AG. This linear acceleration cannot continue indefinitely as the required displacement will grow unconstrained. Instead, the rider is then quickly rotated 180° around and then linearly decelerated to a stop. The pattern then repeats, with the rider being linearly accelerated back in the opposite direction. Between the acceleration/deceleration phases and the 180° rotation, a constant linear velocity coast phase is included. This may be important either for the mechanical design (i.e., to allow transfer of energy between translational and rotational actuators) or for rider tolerance. As discussed below, different values may be considered, but for an initial analysis we considered each phase to be 1s in duration (for 5s total going from left to right, 10s for a complete cycle) and the acceleration/deceleration phases to produce 1G. The black lines in Fig. 5, show a quantitative time-history of the linear sled sequence.

In both the linear acceleration and deceleration phases, the rider experiences an applied “gravitational” force towards their feet (footward), replicating that experienced when standing upright here on Earth. Critically, during these linear acceleration/deceleration phases, the rider would experience “pure” AG: there is no gravity gradient (i.e., the rider's entire body experiences the same G-level determined by the acceleration rate), there are no Coriolis forces, and presumably the rider would not experience the cross-coupled illusion in response to head tilts. During the 180° rotation phase, the rider would also experience AG in the lower portions of their body due to centripetal acceleration, hence the “hybrid” portion of the name. The rider would also experience lateral tangential accelerations due to the angular acceleration and deceleration of the rotation. During the rotation, there would be a gravity-gradient and Coriolis forces (if a portion of the body is moved with a sizable linear velocity), similar to on a centrifuge. However, presumably the cross-coupled illusion would not occur since the brief rotation does not allow for the canal signal to decay. With the rotation axis at the subject's head level, there would not be centripetal or tangential acceleration stimulation to the otoliths.

The aim of this paper was to quantitatively investigate the orientation perceptions riders are likely to experience in a centrifuge AG system as well as the novel linear sled hybrid AG system. Specifically, we simulated the two motion profiles using a well-validated mathematical model for human spatial orientation, known as the observer model [[11], [12], [13], [14]]. As a particular focus, we simulated scenarios where the rider made head tilts to potentially induce the cross-coupled illusion.