Sources of path integration error in young and aging humans

Abstract

Path integration plays a vital role in navigation: it enables the continuous tracking of one's position in space by integrating self-motion cues. Path integration abilities vary widely across individuals, and tend to deteriorate in old age. The specific causes of path integration errors, however, remain poorly characterized. Here, we combine tests of path integration performance in participants of different ages with an analysis based on the Langevin equation for diffusive dynamics, which allows us to decompose errors into distinct causes that can corrupt path integration computations. We show that, across age groups, the dominant error source is unbiased noise that accumulates with travel distance not elapsed time, suggesting that the noise originates in the velocity input rather than within the integrator. Age-related declines are primarily traced to a growth in this noise. These findings shed light on the contributors to path integration error and the mechanisms underlying age-related navigational deficits.

Fig. 1. Path integration task.

a Example path from top-down perspective. Participants began at the starting point (green dot) and then walked along the path (curved black line). There were four stopping points (red dots) along each path; at these points, participants were asked to report their estimate of the direct distance and angle to the path’s starting point. b During the experiment, participants saw a virtual environment from first-person perspective via a head-mounted display (HMD). Movements in the real world were tracked with a motion tracking system and translated to movements (i.e., changes in location and viewing orientation) in the virtual environment. Participants held a wooden stick and were guided by the experimenter along a path. At each stopping point, the direct distance to the starting point had to be estimated verbally in meters and centimeters, and participants turned their body on the spot to indicate the orientation to the starting point. c Three different virtual environments (left panel) used in the path integration task. Each environment comprised a ground plane and distant landmark cues. Landmark cues were rendered at infinity, in order to allow participants to determine their heading direction, but not position or distance information. One tile of each environment's ground plane is shown in the right panel. These tiles were textured to provide optic flow during movement, but were seamless (no visible border between adjacent tiles) and provided no fixed cues with positional information. d Overview of the 10 different paths used in the experiment. Each path contained three turns, and turn directions (i.e., left “L” and right “R” turns) were counter-balanced between paths. e Participants performed three blocks of the path integration task. Each block consisted of 16 paths (paths #1–10, and paths #1–6 repeated without intermediate stopping at stopping points 1–3). In addition, after the 4th and 12th path of each block, participants performed so-called “standardization-paths” (i.e., straight lines with a length of 2, 6, and 10 m), which were used to correct for each participant’s bias in converting their internal location estimate to a verbal response. Text in bold in panel e indicates the phases used for data analyses. See “Methods” section for more details.

Fig. 2. Path integration performance across both age groups.

a Absolute path integration errors over four stopping points for young and older adults. Average errors per stopping point are shown for each participant separately by blue (young adults) and orange (older adults) dots, connected with lines between stopping points. b Each participant’s location estimate (y-axis) versus their true location (x-axis) at each of the four stopping points (columns), separately for x-coordinates (top row) and y-coordinates (bottom row). Plots show data from all participants and all paths. The diagonal (dashed line) indicates perfect response (estimated location = true location). All correlation coefficients are statistically significant (all p < 0.00001). Units are meters. c Absolute path integration errors of young and older adults versus errors with shuffled responses. It is evident that the mean absolute path integration error of both groups (solid lines) is much lower than the errors obtained from shuffling each participant’s responses across trials. Error bars indicate group mean ± SEM.

Fig. 3. Computational modeling results.

a Path integration errors of two example participants (error bars) versus model fits (solid lines). Error bars represent mean ± SEM over trials. See Supplementary Fig. 2 for all participants. b Average path integration errors per age group (error bars) versus model fits (solid lines). Error bars represent mean ± SEM over participants. c Single-trial path integration error vectors versus error vectors predicted by the model. Predicted position is computed individually per participant per trajectory; datapoints show the per-trajectory predicted position, averaged across participants of the same age group on the same trajectory and trial (to reduce scatter). Error bars represent mean ± SEM at a single trial across participants. Dashed black lines indicate perfect prediction; solid lines represent the best-fitting linear regression fit. Units are meters. d Model comparison: negative log-likelihood scores using LOOCV between models, with higher bars indicating a poorer model fit. *** Denotes “very strong” evidence against the model relative to the full model (ΔBIC or ΔLOOCV ≫ 10; see also “Methods” section on model comparison, and Supplementary Fig. 3). Key to model names: The “full model” (Full) is our default, with ongoing “accumulating noise” (AN) that is proportional to the length of the traveled path, nonzero additive bias (AB) and velocity gain bias parameters, and reporting noise (RN) that is proportional to the magnitude of the reported variable. CN refers to when the non-reporting portion of the noise is constant rather than accumulating. +/− refers to the addition/removal of that contribution to the model, respectively. e Impact of model parameters on the predicted path integration error. Relative influence measures the predicted reduction in square error by setting a parameter to its ideal value corresponding to noiseless and unbiased integration. Note that due to the nonlinearity of the model, the relative influences do not have to sum to 100%, and that a parameter’s relative influence can be negative if the reduced square error is larger than the square error of the full model (see “Methods” section).

Fig. 4. Time-scaling versus distance-scaling of accumulating noise.

a Model comparison using LOOCV between the full model with accumulated error proportional to total travel distance versus total time in trajectory. For both age groups, the full model is better supported by the data. Higher bars indicate poorer model-fit. *** Denotes “very strong” evidence against the model with poorer fit (ΔBIC or ΔLOOCV ≫ 10; see “Methods” section on model comparison, and Supplementary Fig. 7). b Average path integration error at the last stopping point, in trials with and without intermediate stopping points. The path integration error is very similar even though trials with stopping take much more time, indicating that the path integration error mainly scales with distance rather than time. Error bars indicate mean ± SEM (young adults: n = 540 trials without stopping vs. 900 trials with stopping; older adults: n = 468 trials without stopping vs. 780 trials with stopping). c Walking velocity versus path integration error for trials with and without stopping and for both age groups.

Fig. 5. Path integration in older versus young adults.

a On average, older adults showed a higher absolute path integration error than young adults at all stopping points. Blue and orange shaded lines indicate group mean ± SEM, error bars indicate SD. b The incremental path integration error (i.e., the additional contribution to the path integration error for each segment between adjacent stopping points), averaged across stopping points, was higher for older than young adults (p = 0.001). c Model parameter values, averaged over participants of the same age group. Parameter values for leak, accumulating unbiased noise, and additive bias were significantly higher in older relative to young adults. Individual parameter values for single participants are shown in Supplementary Fig. 1. d Each model parameter’s contribution to the absolute square error, averaged over participants of the same age group. Only the accumulating unbiased noise resulted in a significant difference in error contribution between age groups. A parameter’s contribution is calculated by measuring the reduction in square error when setting the parameter to its ideal value corresponding to unbiased, noiseless integration; note that due to the non-linearity of the model a parameter's contribution can be negative (see “Methods” section for more details). Dots indicate data for individual participants. Error bars in panels b–d indicate mean ± SEM (n = 30 young vs. 26 older participants). * Denotes a significant difference between age groups (p < 0.05) in a one-sided permutation test with 10,000 permutations.