A Unified Model of Performance: Validation of its Predictions across Different Sleep/Wake Schedules

Abstract

Study objectives: Historically, mathematical models of human neurobehavioral performance developed on data from one sleep study were limited to predicting performance in similar studies, restricting their practical utility. We recently developed a unified model of performance (UMP) to predict the effects of the continuum of sleep loss-from chronic sleep restriction (CSR) to total sleep deprivation (TSD) challenges-and validated it using data from two studies of one laboratory. Here, we significantly extended this effort by validating the UMP predictions across a wide range of sleep/wake schedules from different studies and laboratories.

Methods: We developed the UMP on psychomotor vigilance task (PVT) lapse data from one study encompassing four different CSR conditions (7 d of 3, 5, 7, and 9 h of sleep/night), and predicted performance in five other studies (from four laboratories), including different combinations of TSD (40 to 88 h), CSR (2 to 6 h of sleep/night), control (8 to 10 h of sleep/night), and nap (nocturnal and diurnal) schedules.

Results: The UMP accurately predicted PVT performance trends across 14 different sleep/wake conditions, yielding average prediction errors between 7% and 36%, with the predictions lying within 2 standard errors of the measured data 87% of the time. In addition, the UMP accurately predicted performance impairment (average error of 15%) for schedules (TSD and naps) not used in model development.

Conclusions: The unified model of performance can be used as a tool to help design sleep/wake schedules to optimize the extent and duration of neurobehavioral performance and to accelerate recovery after sleep loss.

Keywords: PVT; biomathematical model; chronic sleep restriction; naps; total sleep deprivation; two-process model.

© 2016 Associated Professional Sleep Societies, LLC.

Figures

Figure 1

Group-averaged lapse data (standard errors) and unified model of performance (UMP) fits on baseline (B2–B3), chronic sleep restriction (CSR; C1–C7), and recovery (R1–R3) phases in Study T1. The four panels A-D correspond to the 3-, 5-, 7-, and 9-h time in bed (TIB) study conditions (1–4; Table 1) in Study T1, respectively. Gray-shaded vertical bars represent sleep episodes. Also shown are root mean squared errors (RMSE; lapses) between measured data and UMP fits, and 95% prediction intervals (PI) of the model outputs (dashed black lines).

Figure 2

Group-averaged lapse data (standard errors) and unified model of performance (UMP) predictions on baseline (B7), total sleep deprivation (TSD; T1–T2)/chronic sleep restriction (CSR; C1–C7), and recovery (R1–R3) phases in Study V1. Panels A and B correspond to the 64-h TSD and 3-h time in bed CSR study conditions (5–6; Table 1) in Study V1, respectively. Gray-shaded vertical bars represent sleep episodes. Also shown are root mean squared errors (RMSE; lapses) between measured data and UMP predictions, and 95% prediction intervals (PI) of the model outputs (dashed black lines).

Figure 4

Group-averaged transformed lapse (lapses + lapses+1) data (standard errors) and unified model of performance (UMP) predictions averaged over each day on baseline (B1), total sleep deprivation (T1)/chronic sleep restriction (C1–C5), and recovery (R1) phases in Study V3. Panels A and B correspond to the 40-h TSD and 4-h time in bed CSR study conditions (9–10; Table 1) in Study V3, respectively.

Figure 3

Group-averaged lapse data (standard errors) and unified model of performance (UMP) predictions on baseline (B1–B2), total sleep deprivation (TSD; T1–T2)/control (C1–C2), and recovery (R1–R2) phases in Study V2. Panels A and B correspond to the 62-h TSD and 10-h time in bed control study conditions (7–8; Table 1) in Study V2, respectively. Other descriptors are identical to those in Figure 2.

Figure 5

Group-averaged lapse data and unified model of performance (UMP) predictions on baseline (B2), chronic sleep restriction (CSR; C1–C5), and six different recovery time in bed (TIB) phases in Study V4. Panel A shows the measured data (averaged across all 142 subjects in the six study conditions 11–16; Table 1) and the UMP prediction for the baseline and CSR phases. Panels B–G show daily-averaged measured data (standard errors) and UMP predictions during recovery night of 0, 2, 4, 6, 8, and 10 h TIB (study conditions 11–16; Table 1), respectively. Other descriptors are identical to those in Figure 2. (Standard errors of the measured data were not available for the baseline and CSR phases.)

Figure 6

Group-averaged lapse data (standard errors) and unified model of performance (UMP) predictions on baseline (B3), no naps (T1–T3), and 2-h naps every 12 h (C1–C3) phases in Study V5. Panels A and B correspond to the 88-h TSD and 2-h naps study conditions (17–18; Table 1) in Study V5, respectively. The dark- and light-gray shaded vertical bars represent the nocturnal and diurnal sleep episodes, respectively. Other descriptors are identical to those in Figure 2.

Figure 7

Unified model of performance (UMP) simulations for baseline (B1–B7), total sleep deprivation (TSD; T1–T2)/chronic sleep restriction (CSR; C1–C7), and recovery (R1–R10) phases under two different recovery scenarios for Study V1. Panels A and B correspond to the 64-h TSD and 3-h time in bed (TIB) CSR study conditions (5–6; Table 1), respectively. Black solid lines represent the UMP predictions up to the first recovery night. Solid red and dashed blue lines represent UMP predictions during the recovery nights for the 8- and 10-h TIB recovery scenarios, respectively. The dotted green horizontal line corresponds to the threshold used to define complete recovery (within 20% of the maximum basal performance level). Gray-shaded vertical bars represent the sleep episodes. Also indicated, within red and dashed blue circles, are the number of recovery nights required for complete recovery under the 8- and 10-h TIB recovery scenarios, respectively.

Figure 8

Unified model of performance (UMP) simulations for baseline (B1–B7), chronic sleep restriction (CSR; C1–C7), and recovery (R1–R10) phases under two different baseline conditions for Study V1. Panels A and B correspond to the 64-h TSD and 3-h time in bed (TIB) CSR study conditions (5–6; Table 1), respectively. Solid red and dashed blue lines represent UMP predictions for the 10- and 7-h TIB baseline conditions, respectively. The dotted green horizontal line corresponds to the threshold used to define complete recovery (within 20% of the maximum basal performance level). Gray-shaded vertical bars represent the sleep episodes. Also indicated, within the red circle, is the number of recovery nights required for complete recovery under the 10-h TIB baseline condition.

Figure 9

Unified model of performance (UMP) simulations for baseline (B3) and three 4-h time in bed (TIB)/day schedules (C1–C3) across 88 h: (1) solid red line: split sleep with 2-h naps (one every 12 h) as in Study V5 (study condition 18; Table 1); (2) dashed green line: consolidated 4 h nocturnal sleep (01:45 to 05:45); and (3) dotted blue line: consolidated 4 h diurnal sleep (13:45 to 17:45). The dark- and light-gray-shaded vertical bars represent the nocturnal and diurnal sleep episodes, respectively, corresponding to the split-sleep schedule.