A Unified Model of Performance for Predicting the Effects of Sleep and Caffeine

Abstract

Study objectives: Existing mathematical models of neurobehavioral performance cannot predict the beneficial effects of caffeine across the spectrum of sleep loss conditions, limiting their practical utility. Here, we closed this research gap by integrating a model of caffeine effects with the recently validated unified model of performance (UMP) into a single, unified modeling framework. We then assessed the accuracy of this new UMP in predicting performance across multiple studies.

Methods: We hypothesized that the pharmacodynamics of caffeine vary similarly during both wakefulness and sleep, and that caffeine has a multiplicative effect on performance. Accordingly, to represent the effects of caffeine in the UMP, we multiplied a dose-dependent caffeine factor (which accounts for the pharmacokinetics and pharmacodynamics of caffeine) to the performance estimated in the absence of caffeine. We assessed the UMP predictions in 14 distinct laboratory- and field-study conditions, including 7 different sleep-loss schedules (from 5 h of sleep per night to continuous sleep loss for 85 h) and 6 different caffeine doses (from placebo to repeated 200 mg doses to a single dose of 600 mg).

Results: The UMP accurately predicted group-average psychomotor vigilance task performance data across the different sleep loss and caffeine conditions (6% < error < 27%), yielding greater accuracy for mild and moderate sleep loss conditions than for more severe cases. Overall, accounting for the effects of caffeine resulted in improved predictions (after caffeine consumption) by up to 70%.

Conclusions: The UMP provides the first comprehensive tool for accurate selection of combinations of sleep schedules and caffeine countermeasure strategies to optimize neurobehavioral performance.

Keywords: PVT; biomathematical model; caffeine model; chronic sleep restriction; total sleep deprivation.

© 2016 Associated Professional Sleep Societies, LLC.

Figures

Figure 1

Group-averaged and standard errors of psychomotor vigilance task (PVT) lapse data (A) and mean response time (RT) data (B), along with unified model of performance (UMP) predictions on baseline (day 1), chronic sleep restriction (CSR; days 2–6), and recovery (days 7–9) phases in study V1. The solid blue circles and thick blue dash-dotted lines correspond to the measured data and caffeine-free UMP predictions (P0), respectively, for the placebo condition (study condition 1; Table 1). The solid red squares and thick red lines correspond to the measured data and UMP predictions (Pc), respectively, for the caffeine condition (study condition 2; Table 1). The gray-shaded vertical bars represent sleep episodes. Thin dotted vertical lines denote caffeine intake (d1 = 200 mg and d2 = 200 mg). The blue and red shaded regions correspond to the 95% prediction interval ranges, respectively, for P0 and Pc (after the first caffeine dose). Also shown are root mean squared errors (RMSEs) between measured data and UMP predictions. (Numbers within parentheses correspond to the RMSEs that result when the UMP does not account for the effects of caffeine.) For lapses, δ = –0.1 lapses, RMSE1 = 1.5 lapses, and RMSEr = 1.3 lapses. For mean RT, δ = 56 msec, RMSE1 = 15 msec, and RMSEr = 30 msec. (See Methods for description of δ, RMSE1, and RMSEr.)

Figure 2

Group-averaged and standard errors of psychomotor vigilance task (PVT) lapse data (A) and mean response time (RT) data (B), along with unified model of performance (UMP) predictions for study conditions 3 and 4 (Table 1) in study V2. Thin dotted vertical lines denote caffeine intake (d1 = 200 mg, d2 = 200 mg, d3 = 200 mg, and d4 = 200 mg). Other descriptors are identical to those in Figure 1. For lapses, δ = 2.8 lapses, RMSE1 = 1.6 lapses, and RMSEr = 2.5 lapses. For mean RT, δ = 107 msec, RMSE1 = 25 msec, and RMSEr = 59 msec.

Figure 3

Group-averaged and standard errors of psychomotor vigilance task (PVT) lapse data (A) and mean response time (RT) data (B), along with unified model of performance (UMP) predictions for study conditions 5 and 6 (Table 1) in study V3. Thin dotted vertical lines denote caffeine intake (d1 = 100 mg, d2 = 200 mg, d3 = 100 mg, and d4 = 200 mg). Other descriptors are identical to those in Figure 1. For lapses, δ = 4.9 lapses, RMSE1 = 1.9 lapses, and RMSEr = 5.5 lapses. For mean RT, δ = 142 msec, RMSE1 = 43 msec, and RMSEr = 98 msec.

Figure 4

Group-averaged and standard errors of transformed psychomotor vigilance task (PVT) lapse (lapses+lapses+1) data, along with unified model of performance (UMP) predictions for study conditions 7 and 8 (Table 1) in study V4., Thin dotted vertical lines denote caffeine intake (d1 = 200 mg and d2 = 200 mg). Other descriptors are identical to those in Figure 1. δ = −2.3 lapses, RMSE1 = 0.2 lapses, and RMSEr = 0.7 lapses.

Figure 5

Group-averaged and standard errors of psychomotor vigilance task (PVT) lapse data (A) and mean response time (RT) data (B), along with unified model of performance (UMP) predictions for study conditions 9 and 10 (Table 1) in study V5. Thin dotted vertical lines denote caffeine intake (d1 = 400 mg, d2 = 100 mg, and d3 = 100 mg). Other descriptors are identical to those in Figure 1. For lapses, δ = 2.1 lapses, RMSE1 = 0.7 lapses, and RMSEr = 2.7 lapses. For mean RT, δ = 90 msec, RMSE1 = 7 msec, and RMSEr = 52 msec.

Figure 6

Group-averaged and standard errors of psychomotor vigilance task (PVT) lapse data (A) and mean response time (RT) data (B), along with unified model of performance (UMP) predictions for study conditions 11 and 12 (Table 1) in study V6. Thin dotted vertical line denotes caffeine intake (d1 = 600 mg). Other descriptors are identical to those in Figure 1. For lapses, δ = 0.6 lapses, RMSE1 = 2.2 lapses, and RMSEr = 7.1 lapses. For mean RT, δ = 70 msec, RMSE1 = 18 msec, and RMSEr = 84 msec.

Figure 7

Group-averaged and standard errors of psychomotor vigilance task (PVT) lapse data (A) and mean response time (RT) data (B), along with unified model of performance (UMP) predictions for study conditions 13 and 14 (Table 1) in study V7. Thin dotted vertical line denotes caffeine intake (d1 = 600 mg). Other descriptors are identical to those in Figure 1. For lapses, δ = 1.1 lapses, RMSE1 = 1.9 lapses, and RMSEr = 7.7 lapses. For mean RT, δ = 77 msec, RMSE1 = 15 msec, and RMSEr = 94 msec.

Figure 8

Unified model of performance (UMP) simulations for baseline (day 1) and chronic sleep restriction (CSR; days 2–6) phases for study condition 2 (Table 1) in study V1. The red solid, green dashed, and purple dash-dotted lines represent the simulations of case A (10-h sleep/night on baseline nights), case B (7-h sleep/night on baseline nights), and case C (7-h sleep/night on baseline nights and additional 200 mg of caffeine on days 2–6), respectively. (UMP predictions for cases B and C are superimposed on day 1.) The dotted black horizontal line corresponds to maximum basal level (20% beyond the maximum impairment on day 1 under case A). Gray-shaded vertical bars represent sleep episodes. Thin dotted vertical lines denote caffeine intake (d1 = 200 mg, d2 = 200 mg, and d3 = 200 mg). Percentage values within parentheses indicate the fraction of time for which UMP predictions exceed maximum basal level. RT, response time.