Likelihood ratio test results for the linear mixed effects model.

Likelihood ratio test results for the linear mixed effects model.</p

Comparison of data with the model (n = 10) for different velocities with noise held constant (zero noise) and different levels of noise with a velocity held constant at (16˚/s).

A. Solid black line is the mean bar angle across participants whereas the shaded area is the standard deviation of participant's mean response. The segmented line displays the model's behaviour. At low velocities the model slightly underestimates the bar angle and it appears to have a shorter time constant than participant's responses. Model fit to the grand mean is displayed as the r2 value on each plot. B. We simulated gain changes with visual noise by multiplying the visual pathway gains (Ko, Go) by one minus the percentage of noise (1, 0.75, 0.5, 0.4, 0.3, 0.2). Model correspondence to the grand mean is displayed as the r2 value on each plot. Shaded area is the standard deviation of participant's mean response.</p

Linear multilevel mixed effects model with sample mean and individual data displaying the effect of adding noise on perceived vertical.

Noise decreased the influence on visual motion on perceived vertical but the size of the effect depends on the velocity. Each subject's mean bar angle for the last 13s of visual motion in each trial are shown as grey circles. Sample means are black circles (n = 10). The error bars are standard deviations. The segmented line is the bootstrapped linear multilevel mixed effects model mean and the shaded regions are the 68% and 95% confidence intervals for the mean.</p

Point of subjective equality between the reference 6 ˚/s stimulus (horizontal grey dotted line) and a comparison stimulus with different levels of noise (n = 8).

With the addition of noise, the point of subjective equality becomes much more variable across participants and exhibits a non-significant (β = -1.6, t(10) = -1.96, p = 0.078) decreasing trend, opposite of what is expected if participants perceived the stimulus as slower with added noise. Each subject has its own symbol, the dotted line indicates the mean, and large filled dark circles are the means at each noise level. The shaded region is the 95% confidence interval for the mean.</p

Grand mean bar angle for each condition and their standard deviations (n = 10) derived from the shaded region in Fig 1C.

Grand mean bar angle for each condition and their standard deviations (n = 10) derived from the shaded region in Fig 1C.</p

Linear multilevel mixed effects model with sample mean and individual data displaying the effect of increasing velocity on perceived vertical.

Higher velocities biased vertical more than lower velocities and the size of the effect depends on the noise level. Each subject's mean bar angle for the last 13s of visual motion in each trial are shown as grey circles. Sample means are black circles (n = 10). The error bars are standard deviations. The segmented line is the bootstrapped linear multilevel mixed effects model mean and the shaded regions are the 68% and 95% confidence intervals for the mean.</p

Schematic of the mechanistic model describing the transformation of visual and vestibular motion to a change in bar angle.

Visual motion (Vis) is encoded as retinal slip (rSL), the difference between the internal estimate of the head's velocity and scenes velocity. The retinal slip information is multiplied by gain Ko (0.11*{1-percent noise}) and integrated overtime with vestibular signals (V) multiplied by gain Kv (0.2). The integration process is leaky with time constant Tvs (15) and is influenced by rotation feedback derived from the cross product of the Gravitoinertial acceleration signal (GIA) and the inferred orientation of gravity (G) multiplied by gain Kf (0.0). This integration process has been broadly described as velocity storage process. The output of the velocity storage is then summed with the rSL, multiplied by gain Go (0.16 *{1-percent noise}), and V, multiplied by gain Gv (0.43), to infer the angular velocity of the head (Ω). The cross-product of the inferred angular velocity of the head and the inferred gravity vector is then integrated to estimate the gravitational vector. This cross-product ensures that only rotations orthogonal to gravity are integrated. The difference between GIA and G is then used to estimate linear acceleration of the head (A) and acts as a negative feedback loop, that models the somatogravic effect, acting to pull G back into alignment with GIA (with gain factor Ts {0.74 }). For a more detailed description of this model see Laurens and Angelaki 2011 and Laurens et al., 2013a.</p

Methods and experimental set up.

A. Participants sat in front of an annulus of colored dots B. The dots rotated clockwise (CW) or counter-clockwise (CCW) while participants controlled the angle of a dotted line in the center using a handheld potentiometer. C. Grand means (N = 10) time-course of bar bias for the zero noise conditions at each velocity. Time-period used to estimate mean bar bias during visual motion for each trial was from 27s to 40 seconds (shaded region).</p

DataSheet1_Predicting occupant head displacements in evasive maneuvers; tuning and comparison of a rotational based and a translational based neck muscle controller.docx

Objective: Real-life car crashes are often preceded by an evasive maneuver, which can alter the occupant posture and muscle state. To simulate the occupant response in such maneuvers, human body models (HBMs) with active muscles have been developed. The aim of this study was to implement an omni-directional rotational head-neck muscle controller in the SAFER HBM and compare the bio-fidelity of the HBM with a rotational controller to the HBM with a translational controller, in simulations of evasive maneuvers.Methods: The rotational controller was developed using an axis-angle representation of head rotations, with x, y, and z components in the axis. Muscle load sharing was based on rotational direction in the simulation and muscle activity recorded in three volunteer experiments in these directions. The gains of the rotational and translational controller were tuned to minimize differences between translational and rotational head displacements of the HBM and volunteers in braking and lane change maneuvers using multi-objective optimizations. Bio-fidelity of the model with tuned controllers was evaluated objectively using CORrelation and Analysis (CORA).Results: The results indicated comparable performance for both controllers after tuning, with somewhat higher bio-fidelity for rotational kinematics with the translational controller. After tuning, good or excellent bio-fidelity was indicated for both controllers in the loading direction (forward in braking, and lateral in lane change), with CORA scores of 0.86−0.99 and 0.93−0.98 for the rotational and translational controllers, respectively. For rotational displacements, and translational displacements in the other directions, bio-fidelity ranged from poor to excellent, with slightly higher average CORA scores for the HBM with the translational controller in both braking and lane changing. Time-averaged muscle activity was within one standard deviation of time-averaged muscle activity from volunteers.Conclusion: Overall, the results show that when tuned, both the translational and rotational controllers can be used to predict the occupant response to an evasive maneuver, allowing for the inclusion of evasive maneuvers prior to a crash in evaluation of vehicle safety. The rotational controller shows potential in controlling omni-directional head displacements, but the translational controller outperformed the rotational controller. Thus, for now, the recommendation is to use the translational controller with tuned gains.</p