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Various theoretical equations have been proposed to predict response rate as a function of the rate of reinforcement. If both the rate and probability of reinforcement are considered, a simple identity, defining equation, or "law" holds. This identity places algebraic constraints on the allowable forms of our mathematical models and can help identify the referents for certain empirical or theoretical coefficients. This identity can be applied to both single and compound schedules of reinforcement, absolute and relative measures, and to local, global and overall rates and probabilities. The rate matching equations of Hernstein and Catania appear to have been approximations to, and to have been evolving toward, one form of this algebraic identity. Estimates of the bias and sensitivity terms in the generalized ratio and logarithmic matching models are here held to be averaging artifacts arising from fitting procedures applied to models that violate or conceal the underlying identities.

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Throughput is a corrected response rate measure giving the number of successes per unit of discretionary time. It is a simple but general index applicable to psychomotor, behavioral, and cognitive tasks in which response times are measured. This measure has several attractive features: (1) It allows comparisons to be made across various tasks in which speed and accuracy are meaningful and measurable, independently of temporal differences in hardware, software, and procedures; (2) under conditions in which both speed and accuracy decline (or improve), throughput will be a more sensitive index of performance than either alone will be; and (3) in those tasks in which the speed-accuracy trade-off phenomenon operates, throughput will tend to be relatively less variable than either component alone will be. The measure allows both behavioral and information-processing interpretations of data and may be useful as a simple composite index, a measure of effectiveness or of cognitive efficiency [corrected] in studies investigating performance degradation or enhancement.

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This field-portable reaction time test and analysis software run on devices using the Palm operating system. It is designed to emulate a test and commercial device widely used in sleep deprivation, shift work, fatigue, and stimulant drug research but provides additional capabilities. Experimental comparisons with the standard commercial device in a 40-hour total sleep deprivation study show it to be comparably sensitive to selected experimental variables. A Pocket PC-compatible version is under developement.

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INTRODUCTION: Visual perception task, complex motor flight task, and psychomotor vigilance task performances were evaluated in U.S. Air Force pilots navigating a high-fidelity fixed wing jet simulator over 26.5 h of continuous wakefulness. METHODS: Eight military pilots on flight status performed the primary task of flying a simulated 12.5-h overnight mission in an Air Refueling Part Task Trainer (ARPTT): Response omission to presentation of single- and double-light stimuli displayed in random sequence across the cockpit instrument panel was the metric used to assess choice visual perception task (CVPT) performance. Deviation from an established azimuth heading in the ARPTT during the CVPT was the flight metric used to assess complex motor performance. Speed, lapse, false start, and anticipation were the metrics used to assess psychomotor vigilance task (PVT) performance during crew rest periods. RESULTS: Significant visual perceptual, complex motor, and psychomotor vigilance (speed and lapse) impairments occurred at 19 h awake in the eight-subject group. CVPT response omissions significantly correlated with ARPTT azimuth deviations at r = 0.97, and with PVT speed at r = -0.92 and lapses at r = 0.90. ARPTT azimuth deviations significantly correlated with PVT speed at r = -0.92 and lapses at r = 0.91. CONCLUSIONS: Acute sleep deprivation degrades visual perceptual, complex motor, and simple motor performance. Complex motor impairments strongly correlate with visual perceptual impairments. This research provides support for the use of visual perceptual measures as surrogates of complex motor performance in operational situations where the primary cognitive inputs are through the visual system.

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INTRODUCTION: Oculomotor responses related to the pupil light reflex (PLR) and saccadic velocity may be sensitive to the effects of sleepiness and therefore could be used to evaluate an individual's fitness for duty. METHODS: There were 12 normal subjects who completed an 8-d study. They were allowed 8 h in bed on the first three nights, 4 h in bed on the fourth night, and then were sleep deprived for the following 64 h. Approximately every 3 h, subjects performed a battery of tests which included a 45-s automated oculomotor test and a 40-min PC-based driving simulator task. Sleepiness was evaluated with a self-assessment instrument. Subjects were allowed 10 h of recovery sleep following sleep deprivation. RESULTS: Oculomotor results for nine subjects showed a significant increase in latency to pupil constriction and a significant decrease in saccadic velocity with total, but not partial, sleep deprivation. The most robust changes during sleep deprivation occurred for saccadic velocity. A night of recovery sleep reversed the effects of total sleep deprivation on latency to pupil constriction and saccadic velocity. Subjective sleepiness and off-road accidents were found to significantly increase over the sleep deprivation period. A significant positive correlation between increasing latency to pupil constriction and increasing sleepiness and driving accidents, and a significant negative correlation between decreasing saccadic velocity and increasing sleepiness and driving accidents during sleep deprivation were found. CONCLUSION: These findings suggest that oculomotor functions, particularly saccadic velocity, are feasible for assessing neurophysiological changes associated with and predictive of sleep deprivation-induced operational performance degradation.

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BACKGROUND: High-frequency EEG (HFE) as a potential predictor of alertness/drowsiness was first proposed by Kaplan and Loparo. Sampling EEG at 950 Hz, they established an HFE bandwidth of interest ranging from 100-475 Hz. We extend their work by applying discrete Fourier transform (DFT) of HFE signals sampled at 1000 Hz and partitioned into spectral bands along specific frequency ranges for the assessment of sleep-wake state transition, sleep, and active cognitive engagement. METHODS: There were 13 volunteers (6 men, 7 women, 30 +/- 3 yr) who participated in a 40-h sleep-deprivation study, during which time they performed multiple cognitive tasks. EEG, in synchrony with other physiological signals, was collected at a sampling rate of 1000 Hz. EEG and task performance results from two volunteers are discussed in this preliminary analysis of the C3-C4 region data. Spectral components obtained from DFT are delineated into five main frequency bands: low, (LFB, 1-15 Hz); intermediate (IFB, 16-50 Hz); and 3 high frequency bands: HFB1 (51-100 Hz); HFB2 (101-200 Hz); and HFB3 (201-500 Hz) for analysis purposes. RESULTS: LFB in the 1-15 Hz range at 0.40 spectrum proportion indicated declining alertness; LFB above 0.50 signals transition to sleep; and LFB at 0.70 indicates Stage 2/3 sleep. HFB3 in the 201-500 Hz range at 0.25 and above was a marker of cognitive function and/or capacity. CONCLUSIONS: HFE may provide a quantitative measure of cognitive function capacity. LFB may provide a measure for awake, asleep, or awake-sleep transition, and HFB3 an estimate of cognitive task engagement. HFE may be applied for electroencephalographic monitoring of cognitive performance.

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As both military and commercial operations increasingly become continuous, 24-h-per-day enterprises, the likelihood of operator errors or inefficiencies caused by sleep loss and/or circadian desynchrony also increases. Avoidance of such incidents requires the timely application of appropriate interventions--which, in turn, depend on the ability to measure and monitor the performance capacity of individuals in the operational environment. Several factors determine the potential suitability of candidate measures, including their relative sensitivity, reliability, content validity, intrusiveness and cumbersomeness/fieldability. In the present study, the relative sensitivity (defined as the ratio of effect size to 95% confidence interval) of several measures to the effects of sleep loss was compared in a sleep restriction experiment, in which groups were allowed 3, 5, 7, or 9 h time in bed (TIB) across seven consecutive nights. Of the measures compared, the Psychomotor Vigilance Test was among the most sensitive to sleep restriction, was among the most reliable with no evidence of learning over repeated administrations, and possesses characteristics that make it among the most practical for use in the operational environment.

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INTRODUCTION: The extent to which modafinil and caffeine reverse fatigue effects (defined as performance decrements with time on task) during total sleep deprivation was investigated. METHODS: There were 50 healthy young adults who remained awake for 54.5 h (06:30 day 1 to 13:00 day 3). A 10-min vigilance test was administered bi-hourly from 08:00 day 1 until 22:00 day 2. At 23:55 day 2 (after 41.5 h awake), double-blind administration of one of five drug doses (placebo; modafinil 100, 200, or 400 mg; or caffeine 600 mg; n = 10 per group) was followed by hourly testing from 00:00 through 12:00 day 3. Response speed (reciprocal of reaction time) across the 10-min task (by 1-min block) was analyzed prior to and after drug administration. RESULTS: A fatigue effect (response speed degradation across the 10-min task) was exacerbated by sleep deprivation and circadian rhythmicity. Prior to the drug, this effect was maximal between 08:00 and 12:00 day 3 (24-28 h sleep deprivation). Modafinil 400 mg attenuated fatigue in a manner comparable to that seen with caffeine 600 mg; these effects were especially salient during the circadian nadir of performance (06:00 through 10:00); modafinil 200 mg also reversed fatigue, but for a shorter duration (3 min) than modafinil 400 mg (8 min) or caffeine 600 mg (6 min). DISCUSSION AND CONCLUSIONS: Time-on-task effects contributed to the performance degradation seen during sleep deprivation; effects which were reversed by caffeine and, at appropriate doses, by modafinil. Because the duration of efficacy for reversing time-on-task effects was shorter at lower drug dosages, the latter must be considered when determining the appropriate dose to use during sustained operations.

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The U.S. Department of Defense (DOD) has long pursued applied research concerning fatigue in sustained and continuous military operations. In 1996, Hursh developed a simple homeostatic fatigue model and programmed the model into an actigraph to give a continuous indication of performance. Based on this initial work, the Army conducted a study of 1 wk of restricted sleep in 66 subjects with multiple measures of performance, termed the Sleep Dose-Response Study (SDR). This study provided numerical estimation of parameters for the Walter Reed Army Institute of Research Sleep Performance Model (SPM) and elucidated the relationships among several sleep-related performance measures. Concurrently, Hursh extended the original actigraph modeling structure and software expressions for use in other practical applications. The model became known as the Sleep, Activity, Fatigue, and Task Effectiveness (SAFTE) Model, and Hursh has applied it in the construction of a Fatigue Avoidance Scheduling Tool. This software is designed to help optimize the operational management of aviation ground and flight crews, but is not limited to that application. This paper describes the working fatigue model as it is being developed by the DOD laboratories, using the conceptual framework, vernacular, and notation of the SAFTE Model. At specific points where the SPM may differ from SAFTE, this is discussed. Extensions of the SAFTE Model to incorporate dynamic phase adjustment for both transmeridian relocation and shift work are described. The unexpected persistence of performance effects following chronic sleep restriction found in the SDR study necessitated some revisions of the SAFTE Model that are also described. The paper concludes with a discussion of several important modeling issues that remain to be addressed.

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BACKGROUND: In most current sleep/performance models, the homeostatic process is generally conceived as a simple reservoir in which performance capacity increases exponentially during sleep and decays either linearly or exponentially during wakefulness. Models that include this notional homeostatic process have been successful for describing sleep-performance data under conditions of irregular sleep schedules, jet lag, and short periods of total sleep loss. However, recently described data from sleep restriction studies indicate that recovery following chronically restricted sleep is considerably slower than would be predicted by these models. These findings suggest that chronic sleep restriction induces relatively long-term, slow-recovering changes in brain physiology that affect alertness and performance. METHODS: This paper describes, both conceptually and mathematically, a generic modification to sleep/performance models that facilitates the ability to predict the rate at which alertness and performance restoration occurs during recovery sleep following chronic sleep restriction. Weighted nonlinear least-squares methods were used to compare the proposed modulated homeostatic model with recent sleep/performance observations during chronic sleep restriction and recovery. RESULTS: When compared with the classical Walter Reed homeostatic model, this proposed model was found to provide a better description of sleep restriction and recovery observations. The proposed model was also found to be consistent with the data from a recent University of Pennsylvania study. CONCLUSIONS: These two models make significantly different predictions of performance during both the recovery phase and the chronic sleep restriction phase.

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Daytime performance changes were examined during chronic sleep restriction or augmentation and following subsequent recovery sleep. Sixty-six normal volunteers spent either 3 (n = 18), 5 (n= 16), 7 (n = 16), or 9 h (n = 16) daily time in bed (TIB) for 7 days (restriction/augmentation) followed by 3 days with 8 h daily TIB (recovery). In the 3-h group, speed (mean and fastest 10% of responses) on the psychomotor vigilance task (PVT) declined, and PVT lapses (reaction times greater than 500 ms) increased steadily across the 7 days of sleep restriction. In the 7- and 5-h groups speed initially declined, then appeared to stabilize at a reduced level; lapses were increased only in the 5-h group. In the 9-h group, speed and lapses remained at baseline levels. During recovery, PVT speed in the 7- and 5-h groups (and lapses in the 5-h group) remained at the stable, but reduced levels seen during the last days of the experimental phase, with no evidence of recovery. Speed and lapses in the 3-h group recovered rapidly following the first night of recovery sleep; however, recovery was incomplete with speed and lapses stabilizing at a level comparable with the 7- and 5-h groups. Performance in the 9-h group remained at baseline levels during the recovery phase. These results suggest that the brain adapts to chronic sleep restriction. In mild to moderate sleep restriction this adaptation is sufficient to stabilize performance, although at a reduced level. These adaptive changes are hypothesized to restrict brain operational capacity and to persist for several days after normal sleep duration is restored, delaying recovery.

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RATIONALE: The performance and alertness effects of modafinil were evaluated to determine whether modafinil should replace caffeine for restoring performance and alertness during total sleep deprivation in otherwise healthy adults. OBJECTIVES: Study objectives were to determine (a) the relative efficacy of three doses of modafinil versus an active control dose of caffeine 600 mg; (b) whether modafinil effects are dose-dependent; and (c) the extent to which both agents maintain performance and alertness during the circadian trough. METHODS: Fifty healthy young adults remained awake for 54.5 h (from 6:30 a.m. day 1 to 1:00 p.m. on day 3) and performance and alertness tests were administered bi-hourly from 8:00 a.m. day 1 until 10:00 p.m. day 2. At 11:55 p.m. on day 2 (after 41.5 h awake), subjects received double blind administration of one of five drug doses: placebo; modafinil 100, 200, or 400 mg; or caffeine 600 mg ( n=10 per group), followed by hourly testing from midnight through 12:00 p.m. on day 3. RESULTS: Performance and alertness were significantly improved by modafinil 200 and 400 mg relative to placebo, and effects were comparable to those obtained with caffeine 600 mg. Although a trend toward better performance at higher modafinil doses suggested a dose-dependent effect, differences between modafinil doses were not significant. Performance enhancing effects were especially salient during the circadian nadir (6:00 a.m. through 10:00 a.m.). Few instances of adverse subjective side effects (nausea, heart pounding) were reported. CONCLUSIONS: Like caffeine, modafinil maintained performance and alertness during the early morning hours, when the combined effects of sleep loss and the circadian trough of performance and alertness trough were manifest. Thus, equivalent performance- and alertness-enhancing effects were obtained with drugs possessing different mechanisms of action. However, modafinil does not appear to offer advantages over caffeine (which is more readily available and less expensive) for improving performance and alertness during sleep loss in otherwise normal, healthy adults.

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