Delayed Sleep Phase Syndrome (DSPS)

From supermemo.guru
Jump to: navigation, search

This text is part of: "Science of sleep" by Piotr Wozniak (2017)

DSPS Problem

When a tendency to go to sleep later each day is strongly pronounced, it may become a serious problem. People with a particularly long circadian cycle or with an insufficient sensitivity to zeitgebers are classified as suffering from Delayed Sleep Phase Syndrome (DSPS for short). Sometimes the abbreviation DSPD is used where syndrome is replaced with disorder. The terms non 24-hour sleep/wake syndrome (N24, N-24, Non-24) or hypernychthemeral syndrome (with a few spelling variants) are occasionally used to refer to the most severe cases. I will consistently stick with the label DSPS to emphasize that these are all variants of the same problem expressed differently in different circumstances. This quarrels with the established definitions used by other authors, which I will disrespectfully ignore due to the fact that the established terminology leads to a harmful confusion and the sense of disabling inevitability.

In DSPS, an individual finds it difficult to fall asleep late in the night, and sleeps well into the afternoon if not awakened. DSPS has only been characterized in 1982, but increasing data indicates that various degrees of DSPS occur with epidemic frequency, esp. among high school and university students. DSPS individuals often like to keep on learning late into the night, go to sleep very late (for example, 4-6 am), and find it very hard to wake up early on a regular basis. For example, regular getting up at 7 am is a pure torture for individuals affected with DSPS. They often fail to keep jobs that require them to perform early in the morning. Very often, they tend to split the day sleep into two components. For example, DSPS students often get a short sleep in the night, wake up early with an alarm clock, go to school where they are semi-conscious and perform poorly, get a solid nap after school and only late in the evening they regain vigor and their full mental powers. DSPS students feel best after midnight when everyone else is asleep and they can focus on learning or other activities (reading, Internet, watching TV, computer games, etc.).

The main factors contributing to DSPS:

  • increased period of the body clock (well above 25 hours)
  • reduced or increased sensitivity to factors that reset or advance body clock (e.g. light, activity, stress, exercise, etc.)
  • electric lighting, 24-hour economy and the resulting "want to do more" lifestyle

A normal individual has a body clock running with a period slightly longer than 24 hours. The clock is reset in the morning with activity and bright light. Thus a normal individual easily adjusts to the standard day-night cycle. However, DSPS individuals may have their clocks running periods long enough to find it hard to fit to 24 hours. They also push their clocks ahead by activity late in the evening (the process opposite to the morning reset synchronization). DSPS individuals, when given a chance to sleep when they want, will tend to go to sleep later and later. They will also wake up later and later. DSPS people do not have problems with sleep if they sleep in their favorite hours. Most mild DSPS cases can be remedied by changes in lifestyle, but rarely are those changes painless to individuals affected by the condition. If this description fits your problem, you may diagnose the degree of your DSPS with SleepChart freeware.

DSPS in teenagers

Research shows that DSPS is very frequent in adolescence (Carskadon 1995[1]). Teenagers with DSPS will often find it difficult to adapt to normal school time. They will experience maximum daytime sleepiness at 10 am (in the middle of the school day) and a peak in alertness right after the school. For many teenagers with a natural tendency to go to sleep late, school becomes a torture and a true waste of time! Educators have already taken on this subject; however, students dozing off during classes are still a norm! Sleepy students learn little, and may naturally develop strong negative feelings for the school in general. This is a problem of colossal proportions! If you are a parent of a teenager who finds it difficult to wake up for school, you will need to act now! Otherwise young man's school years will be a period of monumentally wasted time! It won't be enough to demand an early hour for going to bed. If you ban the late evening Internet surfing, you will just swap a dose of evening education for an idle tossing and turning in bed. Actually, there is only one simple solution, let the kids get up at their natural time but... this may not be realistic in most cases. Your sleep therapist may not be able to help either. The whole school system might need to be changed to accommodate the prevalence of DSPS among adolescents. There have been positive results noted in schools that decided to start classes 1-2 hours later. However, long circadian cycles may result in students staying up yet later in the long-run. Researchers suggest schedule stabilization and gradual realignment. Those measures may still be largely ineffective. Homeschooling and free running sleep could be a great option for those kids.

Solution to the DSPS problem

Free running sleep is usually an instant solution to sleep problems in DSPS, however, it inevitably results in a "shifting" sleep pattern (see below). Other than free running sleep, the best known remedy is to:

  1. cycle the sleep phase to alignment with the desired hour bracket and
  2. battle to reset the cycle (see: Curing DSPS and insomnia)

In other words, if possible, you could use your natural tendency to go to sleep 1-2 hours later, until you align with the desired sleep rhythm. At that point, the real battle begins by efforts to provide strong morning resetting stimuli (e.g. bright light, stress, exhaustive exercise, etc.). Those can be enhanced by evening measures such as melatonin and the avoidance of phase delaying factors such as light, stimulation, stress, Internet, etc. In general, you need to provide resetting stimuli in the morning, and avoid evening delay factors such as computers, TV, artificial lighting, etc. For most people, a degree of sleep deprivation is more acceptable than several futile inactive hours in the evening in a dark room.

Is DSPS a disease?

Probably, most of the cases of DSPS can be explained by a lack of compatibility between the genetically determined sleep control system and the lifestyle. For some people, the degree of the problem may be greater than for others (see: Clock genes and mutations affecting the clock period (Golombek and Rosenstein 2010[2])). Everyone can easily cure the disorder with a decision to drastically change one's habits (e.g. a return to a farmer's lifestyle). However, such a change is usually not feasible due to the type of employment or family life conditions. This means that DSPS sufferers are probably, for a while, sentenced to wage a constant battle with their body clock.

Officially, 0.2% of adults suffer from DSPS. Using numerous SleepChart data submissions, I see a true epidemic of DSPS. Moreover, there is a large hidden DSPS population. I have seen cases where people started showing DSPS sleep patterns as soon as they gave up an alarm clock after years on a normal schedule with a seemingly normal life contaminated somewhat with a degree of sleep deprivation.

Admittedly, people who write to me are already a pre-selected population, but the numbers are really staggering. I am pretty sure that most of those DSPS cases are lifestyle related. As the term "syndrome" might suggest DSPS is a disease, I keep emphasizing that DSPS is rather a reflection of our modern electricity-based lifestyle than an actual disorder. Interestingly, I received very few ASPS submissions. It seems that it is DSPS people that hang out late in the night googling on their PC for solutions to their sleep problem. In the end, they arrive to SleepChart and the concept of free running sleep that can be their magic cure (if ever truly affordable).

DSPS epidemic can be considered a civilizational disorder in which the pressure of a modern lifestyle stands in disagreement with millions of years of evolution. In the long run, once we fully understand all biochemical and hormonal processes underlying sleep, it is possible that mild pharmacological intervention will make it possible to regulate the circadian cycle.

Asynchronous DSPS

Combating phase shift

People suffering from DSPS find it difficult to synchronize with the 24-hour clock. In the picture below, an adolescent female with a mild DSPS suffers disintegration of the sleeping rhythm due to the failed efforts to synchronize with "the rest of the world":

Sleep timeline of an adolescent female suffering from a mild DSPS

After the vacation period, she begins in early September well-synchronized with the "rest of the world". She wakes up between 6:30 and 10:00. However, her body clock experiences continuous shift in her subjective night period. Soon she wakes up at 12:00 and begins a struggle against the further shift. This results in the disintegration of the sleep cycle, short sleep periods below her preferred average (e.g. 4 hours) and frequent bouts of tiredness. SleepChart attempts to plot the extent of the subjective night (i.e. the hours of maximum natural sleepiness). The statistically predicted subjective night is bracketed between the red and blue lines. Circadian acrophase (middle-of-the-night) is plotted in yellow. Circadian sleep propensity is expressed by the shades of red. Sleep blocks terminated with an alarm clock are marked in aqua. Clearly, the greatest disruption in the sleep pattern occurs at the point where the "natural" rhythm departs furthest from the "desired" rhythm. Mild DSPS cases are able to force the body clock to remain more or less in the desired bracket at the cost of a constant struggle with sleepiness. In more severe cases, the circadian variables will run a 24 hour cycle and the individual will experience return to "good sleep" when free running variables align again with the "desired" sleep period.

The average sleep length is 6.8 hours but total sleep changes widely from day to day. The average DSPS shift is difficult to determine due to the battle against the natural rhythm. However, it is likely that the shift is around 60 minutes as evidenced by the average progression of the circadian acrophase estimate (in yellow). Without the use of an alarm clock, the advancing sleep phase would likely complete a full 24h turnaround in 3-4 weeks.

Resynchronizing the cycle

In the next example, a middle-aged female with a severe case of DSPS experienced a similar struggle in stabilizing her sleep rhythm within socially acceptable limits:

Sleep timeline of a middle-aged female with a severe case of DSPS

Subjective sleepiness was minimum when the body succumbed to the progression of the sleep phase (Sep 16 - Sep 23), daytime tiredness increased markedly at the time of the battle with the progression (Oct 2 - Oct 11) where light aqua blue sleep blocks were blocks artificially terminated with an alarm clock. Finally, daytime drowsiness peaked in the period of lost synchrony between sleep periods and the circadian phase (Oct 19 - Oct 22). The breakthrough came with the religious adherence to free running sleep. The next log shows the same female on a well-managed free running schedule:

Sleep timeline of a middle-aged female who decided to free run their sleep after she had been diagnosed as a severe case of DSPS

A perfect alignment of sleep periods with the circadian acrophase (yellow line in the middle of the subjective night) resulted in tripled energy and a sense of well-being.

Social life in DSPS

Naturally, only people who are telecommuting, self-employed, or working from home office can afford to let their sleep run free in DSPS. Even then, the shifting sleep phase is a serious predicament. A legally blind DSPS sufferer from the Netherlands wrote about the pain of the shifting sleep pattern: "I am free running my sleep. I had an appointment at 17:30. I expected to wake up around 15:00 as in the previous three days. Instead I woke up around 17:00 still a bit tired. I had to skip my morning routine (meditation, breakfast, SuperMemo, etc.). FRS works really well for me. But today sucked. It was really stressing having to run due to waking up later than expected". After a medical consultation, this subject was prescribed evening melatonin and was able to stabilize his cycle (for at least a few weeks at the moment of writing these words). The torturous battle of the same subject with phase shifts before running free and before administration of melatonin is shown in this graph:

Sleep timeline of a legally blind DSPS sufferer showing torturous battle with phase shifts before running free and before administration of melatonin

This example illustrates the major dilemma of all more severe DSPS cases. Free running sleep will often produce a phase shift. Anyone who tends to wake up very late is also highly likely to tend to wake up later each day in free running sleep. This is a hallmark symptom of the DSPS. DSPS, however severe, is never a health problem on its own if the sleep is run free. It is the scheduling problems that are most bothersome. The choice is between the two extremes:

  1. either make one's life less dependent on meetings and appointments that can collide with your sleep schedule, or
  2. study DSPS remedies that can stabilize your sleep-wake cycle.

If you happen to always wake up late, waking up always at the same time makes scheduling much easier. If you do not opt for one of the above extremes (free schedule vs. stabilization battle), you will risk collisions that will make life pretty hard. What is even more dangerous, if one disrupts a circadian rhythm on a free running schedule, there can be a loss of synchrony between various circadian variables. This will result in a situation in which for a day or even a few days one is not sure of the optimum bedtime. Even SleepChart may be unable to make a good prediction. This will inevitably result in poor quality sleep, and a few days of low productivity.

DSPS: genes or lifestyle?

Even though I keep repeating that the DSPS epidemic is a reflection of a modern lifestyle, genetic factors clearly play a role and the "creative personality" can also be at the root of the problem. Here is an interesting story of a writer mom whose parents and two kids do not show any signs of sleep problems, however, she suffers from a severe case of DSPS and so does her 20-year-old son:

My mother claims I have had sleep issues from the day I was born. In those days "rooming in" was new as most babies were kept in the nursery and it was the norm for both baby and mother to stay in the hospitals for a week after a normal birth. She enjoys telling the story of how the nurses forced her to have me "room in" with her during hospital stay because I was "keeping up all the other babies in the nursery all night long" because I refused to sleep during nighttime hours. She said that after she and my father brought me home, I was afforded one night in the room with them but I was up all night so I had to "cry it out" alone from then on because I simply would not sleep at night. When I was a few years old, one night, exasperated, my parents said, "Fine. If you want to stay up, you can sit here and watch Johnny Carson." Apparently I was happy to do so! I did, however, have very unhappy memories dating back to the beginnings of my recall of being put to bed at around 20:00 every night and lying up awake and with nothing to do for hours and hours in my darkened, boring room. Back in those days, there was no Internet, no cable TV, no video games, no cell phones, etc. I simply could not get myself to sleep at a decent hour ever in my entire life! I'd often sing myself to sleep and it would take hours to do so. Sometimes I would run out of songs to sing and have to repeat a few until I passed out."

Today, this self-employed female is experimenting with free running sleep and claims that, except for her social life that suffers as a result, the new schedule brought her back from the "hell of perpetual drowsiness".

Chronotherapy and its perils

Chronotherapy makes it easy to fit the circadian phase into a desired time bracket, e.g. after an intercontinental flight, in circadian disorders, or for the sake of shiftwork. For most people, shifting the cycle forward by inducing phase delays is easier. It is possible to go to sleep 40-70 min. later each day and to cycle throughout the day until the desired sleep phase is reached. Pushing one's circadian cycle should always be the last resort. All artificial forms of sleep control should be avoided if possible as they are not healthwise neutral. However, some reports in the literature suggest that chronotherapy may have serious long-term cycle synchronization consequences. Wehr reports (Wehr et al. 1992[3]): "In 1983, one of us described a 28-year-old man with DSPS who underwent chronotherapy and found himself unable to stop his sleep period from rotating around the clock or restore his rhythm to a 24-hour schedule. Instead, hypernyctohemeral syndrome developed, with a persisting 25-hour sleep-wake cycle. This rare syndrome is extremely debilitating in that it is incompatible with most social and professional obligations".

I have personally witnessed numerous cases of phase delays upon switching to free running sleep in seemingly normal people, and have a different interpretation. People differ in the degree of difficulty in sustaining a balanced 24h cycle in free running sleep. That difficulty is well expressed in circadian graphs by the angle of the sleep maintenance curve in reference to the breakeven line that determine a balanced 24h cycle. Most adolescents will experience a degree of difficulty in maintaining the balance if they are allowed to engage in their hobbies and passions late into the night. Once they are allowed to do as they wish, they will often induce phase delays by a simple unwillingness to go to bed "in time". Even though the progressive 24.5 hour cycle may seem unsettling at first, resulting in sleeping in unusual hours, the convenience of running free with extended waking days may outweigh the negative side effects. For people suffering from DSPS, running free may provide an unusual degree of comfort that is difficult to forfeit. No wonder that many DSPS sufferers, who enjoy a progressively shifting circadian cycle in free running sleep, often give up the battle to reset the cycle, or even discover that their natural phase shift is far larger than originally diagnosed.

As the medical and psychiatric terminology of severe cases of DSPS is very confusing, I need to yet attempt to explain cases of "irregular Non-24-hour sleep-wake syndrome", by which I mean a severe DSPS where sleep episodes do not fall into a regular pattern. I have presented some cases in the Asynchronous DSPS section. I have little doubt that most of such irregularities come from subject's own ignorance of his or her sleep preferences, as well as the rules of a healthy free running sleep regimen in circadian disorders. Once a sufferer is instructed on the rules of healthy free running sleep, perhaps with some assistance from SleepChart, the sleep pattern becomes regular.

My personal stance on chronotherapy is therefore as follows:

Chronotherapy is the best approach to repositioning the phase of the circadian cycle. It should always be the last resort as it is not neutral for the quality of sleep. However, long term consequences of occasional use of moderate chronotherapy are probably negligible.

Synchronous DSPS

When a DSPS sufferer attempts free running sleep, sleep phase delays are inevitable. There have been cases in literature that documented people living along such a shifting DSPS schedule for decades without major health side effects (Neubauer 2000[4]). For an exemplary report see this blog[5]. Some authors claim that a shifting schedule may increase the incidence of depression, alcoholism, or dependence on sedatives (as a result of attempts to induce sleep at the "appropriate" time).

The following graph presents a sleep pattern of a free running middle-aged self-employed male:

A regular DSPS pattern with a daily phase shift of 64-68 minutes

A very clear and regular DSPS pattern visible in the graph with a daily phase shift of 64-68 minutes. Although sleeping in "unnatural" hours is certainly less beneficial healthwise than normal sleep, for a DSPS subject, free running sleep rhythm may by far less stressful and disruptive than any attempt to fit to "standard" lifestyle. A very reliable determinant of synchronous DSPS is the loss of the link between the sleep onset hour and sleep duration (see: Preference for night sleep). As the duration of sleep is determined by the circadian phase, well-synchronized sleep schedule shows little variability in the sleep length (6.6 hours in the presented graph). In particular, the sleep length is independent of the sleep onset hour. Whenever the subject makes any attempt at synchronization with daylight or daylight-related activities, the link between sleep length and the onset hour will be reconstituted. Mistakenly, DSPS people are often called "owls" for their tendency to stay up late, while ASPS people are called "larks". The graph illustrates why this is a misnomer.

A similar graph shows a DSPS case with an even greater degree of phase shift (84-90 min):

A regular DSPS pattern with a daily phase shift of 84-90 minutes

Due to a better sleep efficiency in episodes well aligned with the circadian cycle, people on a regular free running DSPS schedule report a much higher subjective alertness and energy as compared with those on an irregular DSPS schedule. This difference also shows up in data collected with SuperMemo.

28 hour day schedule

28 hour day schedule was proposed for those who seek higher productivity and more hours in a day. An example of a 28h sleep pattern design shows a phase shift that needs to reach the daily extreme of 4 hours per day for anyone to be able to sustain that schedule for a longer period of time:

An example of a 28h sleep pattern design showing a phase shift that needs to reach the daily extreme of 4 hours

28h day schedule design

The advantages of a 28 hour schedule supposedly include longer working days, regular 6 day week, repeatability, long weekends, increased energy, unlimited sleep, etc. (for more see: 28 hour day). This proposition is the other extreme of a spectrum of propositions that begins with polyphasic sleep. However, it seems far easier to sustain as it does not need to involve an alarm clock. Sleep researches believe that this schedule is so extreme that nobody should be able to sustain it in a long run. 4 hour phase shifts are so unlikely that researchers choose it for their experimental forced desynchrony protocols. These are experimental protocols in which the body is supposed to fail to adapt to the timing of zeitgebers. Such an entrainment failure is beneficial in studying free running circadian variables. 4 hours shifts have been used in both advancing and delaying protocols (20 hour days (Wyatt et al. 1999[6]) and 28 hour days (Carskadon et al. 1999[7])). All research to-date seems to indicate that the circadian cycle keeps running free in the background in forced desynchrony protocols due to the fact that resetting stimuli cancel each other out and sleep episode intersect with the circadian variables in unpredictable patterns that result in segmented sleep, premature awakening, shortened sleep, reduced REM, and other symptoms of asynchrony. In short, 28 hour day is considered extreme enough to cause perpetual lack of synchrony between the timing of sleep and the circadian cycle.

28 hour day in DSPS

Some sufferers from DSPS report feeling better on the 28 hour schedule than on a conventional 24 hour sleep schedule. I do not think it is likely there are individuals out there with an innate ~28 hour circadian cycle, however, it is conceivable that the effort to squeeze a DSPS cycle into 24 hours is more painful than the alternative in the form of stretching the cycle to 28 hours. The main difference is that the shortening of the cycle usually involves the painful use of an alarm clock, while stretching the cycle requires "only" extra 2-3 hours of zombified wakefulness. Even in severe DSPS, it should be pretty hard to adapt one circadian cycle to the 28 hour schedule as the phase response curve indicates that the sleep phase does not respond strongly enough to strongly delayed bedtime, which may, in extreme cases, cause a phase advance. Phase delays beyond 2 hours should be extremely rare.

For most people, it is pretty hard to tolerate even minor deviations from one's optimum cycle period. For this reason, all designer schedules should be avoided unless they come from a strict analysis of one's own sleep preferences. Again, free running sleep is a better option, even though it may be less predictable and less convenient in planning one's social or professional life.

Let us consider an exemplary case of Subject S, and compare her sleep efficiency on conventional, 28 hour, and free running schedules.

Conventional schedule in severe DSPS

When S attempts to adhere to a conventional sleep schedule, under medical supervision, with the help of sleep medication (incl. melatonin), the sleep is strongly fragmented, short, unrefreshing, and the schedule is unsustainable:

Subject S on an unsustainable conventional schedule.

Subject S on an unsustainable conventional schedule.

This type of sleep is tantamount to mental torture, and all individuals with a similar degree of entrainment failure should always be allowed to let their sleep run free on the grounds of severe disability.

In the presented chart, a pattern of possible free running circadian cycle can be noticed in the chart with the subjective night leaving the conventional night bracket around April 6, 2011. This is more noticeable upon sleep episode consolidation:

Subject S on an unsustainable conventional schedule (sleep episodes consolidated).

Subject S on an unsustainable conventional schedule (sleep episodes consolidated).

Needless to say, the conventional schedule, if maintained for longer, may lead to serious health problems due to the state of persistent sleep deprivation compounded by medication. Even though the presented case is pretty drastic, the number of people suffering from similar sleep problems is constantly increasing and is definitely affecting overall population health and productivity.

28 hour schedule in severe DSPS

When S attempts to adhere to a 28h day schedule, her subjective sleep quality increases dramatically along with the total sleep achieved. Detailed analysis of the sleep chart, however, shows that sleep fragmentation is still substantial showing strains in the sleep control system:

Subject S on a 28h day schedule.

Subject S on a 28h day schedule.

Segmented sleep starts showing after two cycles which might indicate that the actual phase shift lags behind the planned phase delays. Segmented sleep is often a sign of premature bedtime and shows up when the 28h schedule bedtime falls ahead of the presumed free running subjective night. When the sleep schedule undergoes an eventual collapse, the positioning of lengthy recovery sleep episodes seems to indicate that the average daily phase shift might have actually been much less than 4 hours. In an extreme case, large disparity between the subjective night and the planned nighttime might result in self-cancelling phase shifts that might paradoxically stabilize the sleep cycle.

Circadian graph for the same 28h day schedule illustrates the degree of chaos in the sleep control system:

Circadian graph for Subject S on a 28h day schedule.

Circadian graph for Subject S on a 28h day schedule.
Free running sleep in severe DSPS

When the sleep chart of Subject S running free just a few months earlier is inspected, the sleep phase shift is closer to a mere 41 min per day (as opposed to 240 minutes needed to smoothly sustain the 28h day schedule):

Subject S on a free running schedule.

Subject S on a free running schedule.

However, the chart shows that even in that period sleep was strongly fragmented and irregular. Similar analyses are often misleading due to compounding circumstances such as a disease, family problems, medication, and even a wrong choice of bedtime (e.g. in an attempt to stabilize or accelerate the cycle).

In similar cases, it is paramount to chart one's precise circadian preferences. For this reason, a few weeks of uninterrupted free running sleep would be precious to determine one's natural innate daily phase shift. Once this is done, more can be said about the sustainability of a 28h day schedule for a given individual. However, continual free running sleep is always the best option for those who are absolutely unable to balance the cycle and those who can afford the sleep schedule that is hard to reconcile with the rhythm of the outside world. See: Curing DSPS and insomnia.

References

  1. Carskadon M.A., "Early school schedules modify adolescent sleepiness," Sleep Research / Volume 24: 92
  2. Golombek D.A. and Rosenstein R.E., Physiology of Circadian Entrainment," Physiological Reviews / Volume 90 / Issue 3: 1063-1102, doi: 10.1152/physrev.00009.2009
  3. Oren D.A., M.D., Wehr T.A., M.D., "Hypernyctohemeral Syndrome after Chronotherapy for Delayed Sleep Phase Syndrome," The New England Journal of Medicine / Volume 327 / Issue 24 (December 10, 1992): 1762
  4. Neubauer D.N., "Delayed sleep phase syndrome: Analysis of a 10-year sleep log," Johns Hopkins Sleep Disorders Center (2000)
  5. LivingWithN24, "Charting the course of N24," DSPS, a sleep disorder (October 27, 2010)
  6. Wyatt J.K., Ritz-De Cecco A., Czeisler C.A., and Dijk D.J., Circadian temperature and melatonin rhythms, sleep, and neurobehavioral function in humans living on a 20-h day," American Journal of Physiology - Regulatory, Integrative and Comparative Physiology / Volume 277 / Issue 4 (October 1999): 1152-1163
  7. Carskadon M.A., Labyak S.E., Acebo C., and Seifer R., Intrinsic circadian period of adolescent humans measured in conditions of forced desynchrony, Neuroscience Letters / Volume 260 / Issue 2 (January 29, 1999): 129–132, doi: 10.1016/S0304-3940(98)00971-9