Computation of inertial motion: neural strategies to resolve ambiguous otolith information

Abstract

According to Einstein's equivalence principle, inertial accelerations during translational motion are physically indistinguishable from gravitational accelerations experienced during tilting movements. Nevertheless, despite ambiguous sensory representation of motion in primary otolith afferents, primate oculomotor responses are appropriately compensatory for the correct translational component of the head movement. The neural computational strategies used by the brain to discriminate the two and to reliably detect translational motion were investigated in the primate vestibulo-ocular system. The experimental protocols consisted of either lateral translations, roll tilts, or combined translation-tilt paradigms. Results using both steady-state sinusoidal and transient motion profiles in darkness or near target viewing demonstrated that semicircular canal signals are necessary sensory cues for the discrimination between different sources of linear acceleration. When the semicircular canals were inactivated, horizontal eye movements (appropriate for translational motion) could no longer be correlated with head translation. Instead, translational eye movements totally reflected the erroneous primary otolith afferent signals and were correlated with the resultant acceleration, regardless of whether it resulted from translation or tilt. Therefore, at least for frequencies in which the vestibulo-ocular reflex is important for gaze stabilization (>0.1 Hz), the oculomotor system discriminates between head translation and tilt primarily by sensory integration mechanisms rather than frequency segregation of otolith afferent information. Nonlinear neural computational schemes are proposed in which not only linear acceleration information from the otolith receptors but also angular velocity signals from the semicircular canals are simultaneously used by the brain to correctly estimate the source of linear acceleration and to elicit appropriate oculomotor responses.

Fig. 1.

Schematic diagram outlining the main experimental protocol of lateral motion and/or roll tilt oscillations at 0.5 Hz.a, Pure translation [black arrow, gravitational acceleration (g); gray arrow, translational acceleration (f)]. b, Pure roll tilt. c, Combined roll tilt and translation with relative phases such that the translational component added to the gravity component along the IA axis, generating a resultant IA acceleration of 0.74G (thick arrow). d, Combined roll tilt and translation with relative phases such that the translational and gravitational components along the IA axis canceled each other (i.e., IA acceleration, 0G).

Fig. 2.

Tilt–translation discrimination in a labyrinthine-intact rhesus monkey. Torsional, vertical, and horizontal components of eye position (E_tor,E_ver, and E_hor, respectively) and slow phase eye velocity (Ω_tor, Ω_ver, andΩ_hor, respectively) of the right eye during lateral translation and/or roll tilt at 0.5 Hz in complete darkness.Left to Right, The stimuli consisted ofTranslation motion only, Roll tilt only,Roll tilt + Translation motion, and Roll tilt − Translation motion. Dotted linesare zero position (straight-ahead gaze) and zero eye velocity. The stimulus traces (bottom) show sled position (H_trans, positive direction to the left) and roll tilt position (H_roll, positive tilt toward right ear-down). Positive eye movement directions are leftward, downward, and clockwise (upper pole of the eye toward the right ear).

Fig. 3.

Comparison of horizontal eye velocity elicited during roll and translation. Mean ± SD peak horizontal eye velocity sensitivity (expressed in degrees/second/gravity, where G = 9.81 m/sec²) and phase have been plotted separately for earth-horizontal and earth-vertical roll oscillations (filled and open symbols, respectively). Roll oscillations: squares, ±90° (0.01–0.2 Hz); circles, ±22° (0.1–0.5 Hz) and ±5° (1 Hz); lateral translations: triangles(Angelaki, 1998, Fig. 6, average data from five animals replotted).

Fig. 4.

Translational (horizontal) VOR as a function of stimulus type in labyrinthine-intact animals. Mean ± SD peak horizontal eye velocity from four monkeys with intact semicircular canals, tested at 1, 0.5, and 0.16 Hz (stimulus parameters are shown in Table 1A). Note that primate VOR correctly discriminates between tilt and translation at all tested frequencies.

Fig. 5.

Tilt–translation discrimination after all semicircular canals were inactivated by plugging the canal lumen. Responses, stimuli, and figure organization as in Figure 2. Note that there is no horizontal response during Roll tilt − Translation motion (IA acceleration, 0G).

Fig. 6.

Translational (horizontal) VOR as a function of stimulus type in two canal-plugged animals. Mean ± SD peak horizontal eye velocity elicited during lateral translation and/or roll tilt oscillations at 1, 0.5, and 0.16 Hz. Notice the large differences when compared with labyrinthine-intact animals (Fig. 4), particularly during Roll only and Roll tilt − Translation stimuli.

Fig. 7.

Combined roll–translational motion stimuli. Constant peak amplitude roll oscillations (θ_o = 21.8°) were paired with varying peak amplitude and in phase or out of phase translational oscillations (Table 1B). As peak translational acceleration amplitude (f) was varied between 0 and ±0.37G, the resultant IA acceleration changed between 0 and 0.74G. Horizontal slow phase velocity has been separately plotted for three intact (A) and two canal-plugged (B) animals (differentsymbols are used for different animals). Open symbols, Data obtained during pure translational motion (0.37G).

Fig. 8.

Combined roll–translational motion stimuli. Constant peak amplitude translational oscillations (39.4 cm; i.e.,f_o = 0.4G) were paired with varying peak amplitude, in phase or out of phase roll oscillations (Table 1B), such that the resultant IA acceleration varied between 0 and 0.74G. Horizontal slow phase velocity has been separately plotted for three intact (A) and two canal-plugged (B) animals (differentsymbols are used for different animals).

Fig. 9.

Combined roll–translational motion stimuli. Constant peak amplitude roll oscillations (θ_o = 21.8°) were paired with constant peak amplitude translational oscillations (39.8 cm; i.e., f_o = 0.4G) and variable phase. A, Mean ± SD horizontal slow phase velocity amplitude and phase from intact animals (open circles) are compared with data from two canal-plugged animals (filled circles and squares).B, Theoretical predictions of the dependence of the resultant and the translational component of acceleration along the IA axis, according to Equations 1 and 2 (solid anddotted lines, respectively).

Fig. 10.

Transient Roll tilt − Translation motion profiles in an animal with intact and inactivated semicircular canals (SCC). The stimulus consisted of a subtractive combination of a 15° roll tilt toward the animal’s right ear and linear translation to the right. Horizontal eye position (top) and eye velocity (middle) of both the right and left eyes (mean ± SD; left, nine trials; right, 26 trials). Dotted lines are zero eye position (straight-ahead gaze) and zero eye velocity. Bottom, Translational component and resultant IA acceleration measured as the outputs of two linear accelerometers mounted on the linear sled and on the animal’s head, respectively. The IA acceleration trace was not measured for the Inactivated SCC plot and is therefore duplicated from the Intact SCC condition.

Fig. 11.

A four-neuron network, the simplest model that would implement the computations described by the differential Equation4. ω_SSC, Primary semicircular canal afferents;α, α˙, static and dynamic otolith signals, respectively; x,Σ, ∫, vector multiplication, summation, and signal integration, respectively.

Fig. 12.

Schematic diagram summarizing the two main computations necessary to transform primary vestibular signals into inertial motion parameters. Angular velocity signals from the semicircular canals (ω) are used to segregate the resultant linear acceleration signals coded by primary otolith afferents (α) into gravitational (g, orientation) and translational (f) components. Gravitational estimates are also used to transform head-fixed angular velocity signals from the semicircular canals (ω) into inertial velocity, i.e., space-referenced angular velocity (ω_S) (Angelaki and Hess, 1994, 1995, 1996b).

Fig. 13.

Tilt–translation paradigm. x,y, z, Head-fixed coordinates.X, Y, Z, Space-fixed coordinates. θ, Roll tilt angle (about the x-axis).