Phase advance

The open-loop transfer function is third-order type 2, and is unstable for all values of open-loop gain K, as can be seen from the Nichols chart in Figure 6.33. From Figure 6.33 it can be seen that the zero modulus crossover occurs at a frequency of 1.9 rad/s, with a phase margin of —21°. A lead compensator should therefore have its maximum phase advance 0m at this frequency. Flowever, inserting the lead compensator in the loop will change (increase) the modulus crossover frequency. 

Figure 6.35 shows the Bode gain and phase for both compensated and uncompensated systems. From Figure 6.35, it can be seen that by reducing the open-loop gain by 5.4dB, the original modulus crossover frequency, where the phase advance is a maximum, can be attained. 

The frequency of maximum phase advance is to occur at the frequency that corresponds to —180° on the Bode diagram constructed in section (a). The lower break frequency XjTx is to be half this value and the upper break frequency l/r2 is to be twice this value. Evaluate T and T2 and calculate values of 0 for the frequencies specified in section (a). Construct the Bode diagram for the compensation element for the condition K = X, and read off values of modulus at the same frequencies as the calculated phase values. 

Donnio, B., Garcia-Vazquez, P., Gallani, J.-L., Guillon, D. and Terazzi, E. (2007) Dendronized Ferromagnetic Gold Nanopartides Self-Organized in a Thermotropic Cubic Phase. Advanced Materials, 19, 3534-3539. 

A number of studies have investigated the potential of melatonin to alleviate the symptoms of jet lag. Melatonin has been found to be effective in 11 placebo-controlled studies in reducing the subjective symptoms of jet lag such as sleepiness and impaired alertness (Arendt 2005). The most severe health effects of jet lag occur following eastbound flights, since this requires a phase advancement of the biological clock. In a recent study, phase advancement after melatonin administration (using 3 mg doses just before bedtime) occurred in all 11... 

One of us examined the timely use of three factors (melatonin treatment, exposure to light, physical exercise) to hasten the resynchronization of the sleep-wake cycle in a group of elite sports competitors after a transmeridian flight across 12 time zones (Cardinali et al. 2002). Outdoor light exposure and physical exercise were used to cover symmetrically the phase delay and the phase advance portions of the phase-response curve. Melatonin taken at local bedtime helped to resynchronize the circadian oscillator to the new time. Individual actograms taken from sleep log data showed that all subjects became synchronized in their sleep to the local time in 24-48 h, well in advance of what would be expected in the absence of any treatment (Cardinali et al. 2002). More recently, a retrospective analysis of the data obtained from 134 normal volunteers flying the Buenos Aires - Sydney transpolar route in the past 9 years was published this further supports such a role for exogenous melatonin in resynchronization of sleep cycles (Cardinal et al. 2006). 

A number of clinical studies have now made use of the phase advancing property of melatonin for treating delayed sleep phase syndrome (DSPS). Melatonin, at a 5 mg dose, has been found beneficial in advancing the sleep onset time and wake time in DSPS subjects (Dahlitz et al. 1991 Nagtegaal et al. 1998 Kayumov et al. 2001). Melatonin was found to be effective when given five hours before its endogenous onset or seven hours before sleep onset. 

Golombek, D. A Cardinali, D. P. (1993). Melatonin accelerates re-entrainment after phase advance of the light-dark cycle in Syrian hamsters. Antagonism by flumazenil. Chronobiol. Int. 10, 435-41. 

Hunt, A. E., A1 Ghoul, W. M., Gillette, M. U. Dubocovich, M. L. (2001). Activation of MT2 melatonin receptors in rat suprachiasmatic nucleus phase advances the circadian clock. Am. J. Physiol. Cell. Physiol. 280, 010-18. 

Polysomnographic sleep research has demonstrated that besides disturbances of sleep continuity in depression, sleep disturbance is also characterized by a reduction of slow-wave sleep and a disinhibition of REM sleep, with a shortening of REM latency, a prolongation of the first REM period, and increased REM density [62]. Most effective antidepressant agents suppress REM sleep, and depressive symptoms are at least transiently alleviated by manipulations of the sleep-wake cycle, such as sleep deprivation or a phase advance of the sleep period [63]. Thus, there appears to be a bidirectional relationship between sleep, sleep alterations and mood. 

Atkinson R, Darnall KR, Lloyd AC, et al. 1979. Kinetics and mechanisms of the reactions of the hydroxyl radical with organic compounds in the gas phase. Advances in photochemistry 11 375-488. 

The results obtained with the model for the mammalian circadian clock provide cues for circadian-rhythm-related sleep disorders in humans [117]. Thus permanent phase shifts in LD conditions could account for (a) the familial advanced sleep phase syndrome (FASPS) associated with PER hypopho-sphorylation [118, 119] and (b) the delayed sleep phase syndrome, which is also related to PER [120]. People affected by FASPS fall asleep around 7 30 p.m. and awake around 4 30 a.m. The duration of sleep is thus normal, but the phase is advanced by several hours. Moreover, the autonomous period measured for circadian rhythms in constant conditions is shorter [121]. The model shows that a decrease in the activity of the kinase responsible for PER phosphorylation is indeed accompanied by a reduction of the circadian period in continuous darkness and by a phase advance upon entrainment of the rhythm by the LD cycle [114]. 

Foster Simplistically, in entrainment the rods and cones provide transitional information at the sharp junction between a LD cycle, and the inner retinal opsins provide irradiance information. What was striking about that rodless-coneless mouse under dim LD cycles is that it was phase advanced and the onsets were bouncing all over the place. Something about the precision of entrainment is lost with the rods and cones under relatively low light conditions. 

Ishida It is possible in the case of the tau mutants that there is a mutation in a serine residue of the PER2 protein, which is considered to be a targeted sequence for CKl . It causes phase-advanced-syndrome in humans. This is clearly affected by mutation of the serine. First, our case is hPERl instead of hPER2. Thus, I cannot compare both events directly. Furthermore, our inhibitor is targeted mainly to CKls and d, so we can t conclude from these experiments which one of them (or indeed both) is important for this phosphorylation. 

Halberg (74) postulated a desynchronization of circadian rhythms in depression, whereas Goodwin and colleagues ( 75) found a phase advance in the rhythms of depressed patients, and Schulz and Lund ( 76) found a diminished amplitude. Perhaps most interesting is the ability of antidepressants to alter these rhythms, possibly by binding to receptor sites in the suprachiasmatic nucleus ( 77). 

One of the most consistent findings is the sleep disturbance that often precedes and may even trigger a manic phase ( 46). Studies on circadian rhythms have demonstrated that many aspects of the sleep cycle are phase-advanced in mania (i.e., occur earlier than normal), and often these patterns resemble the free-running rhythms seen in normal individuals who are removed from all time cues. In addition, there is a blunting of amplitude and a doubling of the sleep-wake cycle up to 48 hours. Lithium is known to delay the sleep-wake cycle and often slow such free-running rhythms, which in turn are partly modulated by neurotransmitters such as NE, 5-HT, and acetylcholine. Further, manipulation of the sleep-wake cycle may prevent a manic episode or be used to treat the depressive phase (e.g., sleep deprivation therapy see also the section Experiments in Chapter 8). 

Primary (intrinsic) Secondary (acquired) Subcategories of resistance Hematologic Chronic phase Advanced phases Cytogenetic Molecular... 

The lead compensator contributes phase advance to the system and thus increases the overall system stability (Section 7.10.4). The degree of phase advance provided is a function of frequency. At the same time this type of compensator increases the overall system amplitude ratio, which has the effect of reducing the the stability of the system. However, the major contribution of phase advance occurs at those frequencies where the open-loop polar plot is adjacent to the (-1,0) point on the complex plane. The increase in amplitude ratio takes place at lower frequencies and, consequently, the effect of this is much less significant. As the ratio of r,/r2 is increased, the maximum phase advance supplied by the lead compensator also increases, i.e. the greater is the stabilising effect of the compensating element011. 

Walsh J, Schweitzer P, Sugarman J, Muehlbach M. Transient insomnia associated with a three-hour phase advance of sleep time and treatment with zolpidem. J Clin Psychopharmacol 1990 10 184—189. 

Phase advances of the circadian system and sleep-wake activity have been reported in a number of studies, with daily administration of melatonin (180-183). Termination of melatonin administration resulted in a reversal of the phase advances, with subjects reverting to their preadministration phase. Therefore, continued administration of melatonin may provide a means for those with DSPS to maintain a normal phase, and avoid the associated sleep deprivation due to having to live on a normal schedule. It is important to note, however, that at present the effective dose of melatonin to be administered and the safety of long-term melatonin administration have yet to be established (184). Therefore, melatonin should be thought of as a research compound and not a clinical solution to DSPS. 

Bonnet MH, Mitler MM, Gillin JC, James SP, Kripke D, Mendelson W, Mitler M. The use of triazolam in phase-advanced sleep. Neuropsychopharmacology 1988 1 225-234. 

Hirai K, Kita M, Ohta H, Nishikawa H, Fujiwara Y, Ohkawa S, Miyamoto M (2005) Ramelteon (TAK-375) accelerates reentrainment of circadian rhythm after a phase advance of the light-dark cycle in rats. J Biol Rhythms 20 27-37... 

Sprouse J, Reynolds L, Braselton J, Schmidt A. Serotonin-induced phase advances of SCN neuronal firing in vitro a possibole role for 5-HT5A receptors. Synapse 2004 54 111-118. 

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