Vol. 274, Issue 4, R1087-R1093, April 1998
Effects of temperature on sleep in the developing rat
Roger N.
Morrissette1,2 and
H.
Craig
Heller1
1 Department of Biological
Sciences, Stanford University, Stanford 94305;
and 2 Program in Neuroscience,
University of California at Los Angeles, California 90025
 |
ABSTRACT |
In
altricial species, such as humans and rats, much of the development of
autonomic systems occurs postnatally. Consequently, vulnerabilities
exist early in postnatal development when immature autonomic functions
are challenged by external factors such as variations in ambient
temperature (Ta).
Ta profoundly influences sleep/wake state structure in adult animals and humans, and exposure to
excessive warmth has been implicated as a risk factor in sudden infant
death syndrome. To better understand the relationship between temperature and sleep during development, we investigated the effect of
Ta variation on sleep/wake state
structure and sleep intensity in developing rats. In this experiment,
sleep intensity was measured by the intensity of slow-wave activity
during slow-wave sleep. Neonatal Long-Evans hooded rat pups were
surgically prepared for chronic sleep/wake state and brain temperature
(Tbr) recording. Two-hour
recordings of sleep/wake state and
Tbr were obtained from rats on
postnatal day
12 (P12),
P14,
P16,
P18, and
P20 at a
Ta of either 28.0-30.0,
33.0-35.0, or 38.0-40.0°C.
Ta significantly influenced
sleep/wake state structure but had little, if any, effect on sleep
intensity in developing rats.
ontogeny; neonate; slow-wave activity; delta power
| |
INTRODUCTION |
A CRITICAL FACET of the relationships between
temperature and sleep in adult animals is that temperature alters
sleep/wake state distribution (17, 36). Increased body temperature
(Tb), either by passive heating
of ambient temperature (Ta) or
through exercise leads to increased non-rapid eye movement (NREM) sleep (19). In humans, brain temperature
(Tbr) declines during the first
2-3 h after sleep onset coincident with the peak occurrence of the
deepest NREM sleep stages (32, 41). If sleep is extended to 15 h into
the early afternoon, when the circadian rhythm for Tb is rising, an increase in NREM
sleep is seen (10). It has been theorized that increases in NREM sleep
after transient increases in Tb
represent an active thermoregulatory response triggered to counter
hyperthermia (23, 31).
Sudden infant death syndrome (SIDS) has a strong association with sleep
and Ta variation. Infants who
succumb to SIDS are almost always found at the end of a sleep period
and are often found excessively bundled or close to heating units (30,
35). Likewise, the peak seasonal death rate for SIDS is during the winter months (1, 15, 30, 35). Ta
variation could affect sleep/wake state distribution or sleep depth
with concomitant increases in arousal threshold, thus preventing
infants from properly arousing from life-threatening situations such as
prolonged apneas (12).
An equally important facet of the relationships between sleep and
temperature in adult animals is that sleep/wake state distribution directly affects thermoregulation (11, 12, 18, 31). At the onset of
NREM sleep, hypothalamic thermosensitivity is diminished (18). This
coincides with a decrease in heat production, declines in
Tb, and an increase in heat
dissipation (18). In addition, Tb
has a lower level of regulation during NREM sleep than during waking
(W), while during rapid eye movement (REM) sleep, thermoregulation is
seriously inhibited (11).
During the 2- to 4-mo critical period for SIDS, a normal, healthy
infant shows increases in metabolic rate, increases in its body
mass-to-surface area ratio, a thickening of the subcutaneous fat layer,
and an increase in the effectiveness of its peripheral cold-induced
vasomotor response (6). Therefore, these infants have a reduced ability
to dissipate heat, making them vulnerable to excessive thermal loads.
SIDS victims have been shown to have significantly increased
hypothermic and hyperthermic bouts (28), and some infants have shown
evidence of excessive sweating and elevated
Tb before succumbing to SIDS (15,
28).
Neonatal rats and human infants go through similar postnatal
developmental stages. Both are born immature and, whereas rats mature
more rapidly than humans, both share a similar temporal order of
autonomic system development. Based on similar developmental changes in
sleep/wake states (7, 20, 34), thermoregulation (21, 40), circadian
rhythms (5, 22, 25), and neural development (42), we hypothesize that
rats aged postnatal day 10 (P10) through
P20 roughly equate developmentally to
human infants over the ages of 2 to 4 mo of age, which is when SIDS is
most likely to occur.
In adult rats, there are three sleep/wake states: W, REM sleep, and
NREM sleep. W is characterized by desynchronous electroencephalographic (EEG) activity and enhanced electromyographic (EMG) activity. REM sleep
has similar desynchronous activity in the EEG, but the EMG is
significantly reduced due to the presence of muscle atonia (20). In
humans, REM sleep is also characterized by irregularity of heart rate
and respiration and phasic occurrences of myoclonic jerks, rapid eye
movements, and pontogeniculooccipital waves (33, 34). Similar
characteristics have been found for rats and other mammals (7, 13, 20).
NREM sleep is distinguished from REM and W by the presence of
synchronized activity, called slow waves, in the EEG. Hence, NREM sleep
is also referred to as slow-wave sleep (SWS). NREM sleep is also
characterized by a decrease in EMG activity to a level below W but
above REM sleep (7, 13, 20, 33, 34).
Before the appearance of differential EEG patterns in neonates,
neonatal arousal states are divided into either W, active sleep (AS),
or quiet sleep (QS) based on behavioral observations of body movement.
Distinct EEG patterns begin to appear at
P10-P11 in the rat (3, 7, 13). At P12, slow
waves (0.75-4.0 Hz), as well as faster synchronized EEG activity,
can be discriminated from desynchronized activity, making state
distinctions based on adultlike EEG patterns possible (3, 7, 13). In
this study we used EEG and EMG to determine sleep states.
Rat pups within the
P12-P20
age range show distinct features of both AS and adult REM sleep (7).
The prominent muscle twitches seen during AS slowly decline in
intensity with increasing age but are still present at
P20. Likewise, several but not all of the phasic features of adult REM sleep are present by
P20 (7). For this reason we chose to
call this REM-like state "AS/REM," because it contains
characteristics of both AS and adult REM sleep. The term SWS will be
used to define the QS/NREM-like state, because the presence of slow
waves in the EEG was the main defining criteria of this state.
Through spectral analysis of the EEG, the intensity of slow waves or
slow-wave activity (SWA) can be quantified. SWA within NREM sleep has
been shown to increase as a function of prior waking and is therefore
believed to reflect a homeostatic sleep restorative process (39).
Likewise, SWA can be considered a measure of NREM sleep intensity or
depth of sleep (39). This experiment was designed to determine how 3 h
of a specific chronic Ta exposure affects sleep/wake state structure and intensity in neonatal rat pups
age
P12-P20.
| |
METHODS |
Housing conditions. All Long-Evans
hooded male rats were housed in the colony room with one dam and litter
per cage. The animals were maintained at a
Ta of 22 ± 0.5°C on a
12:12-h light-dark cycle. Food and water were available ad libitum.
During data collection, animals were placed into double-walled
recording chambers made of clear acrylic (22 × 16 × 18 cm).
The walls were perfused with heated water to control the
Ta inside the recording chamber.
The recording chamber floor was made of a taut piece of neoprene. The
Ta and
Tbr thermocouples and cable
commutators were secured to the top of the recording chambers.
Surgeries. A total of 29 male
Long-Evans hooded rat pups were chronically implanted for sleep/wake
state and Tbr recording at
P10. Animals were anesthetized with
methoxyfluorane (Metofane; Pitman-Moore). A dorsal midline incision in
the skin was made on the top of the skull. The skull was then cleaned
with hydrogen peroxide solution (3%). To record the frontal-parietal
EEG, four miniature stainless steel screws were soldered to
Teflon-coated stainless steel wire and implanted into the skull (0.0 mm
anterior and ±2.0 mm lateral to bregma, 0.0 mm anterior and
±2.0 mm lateral to lambda). Three Teflon-coated stainless steel
stranded wire electrodes were inserted bilaterally and at midline into
the dorsal nuchal muscle to record EMG activity. To record
Tbr, a sealed stainless steel
guide cannula or reentrant tube (0.65 mm OD), was inserted into the
skull (0.5 mm anterior, 0.5 mm lateral, and 4.0 mm ventral to bregma)
to allow thermocouple placement into the brain. All electrodes were
soldered to a seven-pin gold connector (MicroTech) that was affixed to
the skull along with the reentrant tube via dental acrylic (Hygenic).
Immediately after surgery, animals were returned to their home cages
with their nursing dams and littermates. All animals were allowed at
least 2 days to recover from surgery. At
P21, rats were given a lethal overdose
with 4% halothane gas, their implants were removed, and the surgical
area was inspected for pathology.
Recording procedure. At 1 h after
lights-on in the colony room, pups were removed from their home cages
and given a light dose of methoxyfluorane anesthesia to facilitate
attachment to recording cables. The pups were then placed in recording
chambers with Ta preset to either
28.0-30.0, 33.0-35.0, or 38.0-40.0°C. Animals were
allowed 1 h of chamber acclimation and recovery from anesthesia.
Starting at 2 h after lights-on, sleep/wake state and
Tbr data were collected for the
next 2 h. Animals were then returned to their home cages with their
nursing dams and littermates.
Data analysis. The
Tbr and
Ta thermocouple signals were
amplified to a 0.1 V/1.0°C signal and stored by computer in 10-s
epochs. The differential output between frontal-parietal EEG electrodes was amplified to a 
5.0- to +5.0-V signal band filtered between a
0.3-Hz high-pass and 30-Hz low-pass filter (Grass Instruments). The
amplified signal was then digitized by a data acquisition computer
system (Data Translation) at 100 Hz. A fast Hartley transform was used
to transform the digitized input in the frequency domain of consecutive
10-s epochs. EEG power spectra from 0 to 20 Hz were then calculated and
stored. The EMG signal was collected by amplifying the differential
output between two of the three EMG electrodes to a 5.0- to
+5.0-V signal band filtered between a 3.0-Hz high-pass and 75-Hz
low-pass filter (Grass Instruments). The EMG signal was integrated per
epoch so that a single quantified EMG value could be assigned to each
epoch. EEG power spectra were then averaged for delta (0.75-4.0
Hz), theta (6.0-9.0 Hz), and sigma (10.0-14.0 Hz) frequency
ranges as previously described (2).
Sleep/wake states were scored algorithmically using integrated EMG
values and EEG power spectra values (2). Waking was first separated
from the two sleep states by generating a scatterplot using sigma × theta by integrated EMG values for each 10-s epoch. A high
integrated EMG value and a low sigma × theta value would represent waking epochs. Second, to determine SWS from REM sleep, a
scatterplot using the integrated EMG and delta values was used. Low EMG
values and low delta activity would indicate REM epochs, whereas low
EMG and high delta activity would indicate SWS epochs. State scoring
confirmation and artifact removal was done by visually reviewing each
epoch of data. Age-dependent changes in power spectra did not affect
the state scoring criteria.
The amount of time an animal spent in each arousal state (W, AS/REM,
SWS) is expressed as the percentage of total recording time (%TRT).
The %TRT, number of bouts of each state, mean bout length, number of
brief arousals
(nBA), and SWS SWA
were determined for each animal. Because rat pups can change from sleep
to wake and back to sleep in <10 s, a 10-s minimum was used to define a bout length. Likewise, a brief arousal was scored as any waking state
that lasted <20 s. Due to wide variance in absolute EEG power values
between animals, SWS SWA scores were standardized to
z scores and then to
T scores before analysis across
developmental age. For analysis across
Ta condition, SWS SWA was
normalized to SWS total EEG power to control for changes in EEG power
across development. Data were statistically analyzed by a two-way ANOVA repeated-measures test with Fisher's test applied for post hoc pairwise comparisons.
| |
RESULTS |
Effect of Ta on
Tbr. As expected,
when data were pooled across age,
Ta had a highly significant effect
on Tbr
[F(2,66) = 89.698, P = 0.0001, n = 24], with
Tbr generally increasing with
Ta. There was also a significant
age-dependent effect on Tbr when
data were pooled across Ta
condition [F(4,66) = 2.872, P = 0.0296, n = 14]. Post hoc analyses
revealed significant differences between
P12 and
P18
(P = 0.0093),
P12 and
P20
(P = 0.0377), and
P14 and
P18 (P = 0.0283). Figure
1 displays mean
Tbr values for each
Ta condition and across each
developmental age. These data demonstrate that the range of
Ta did not produce a cold thermal
stress but did produce a warm thermal stress. This is evident by the
fact that Tbr did not drop below
normal ranges in the coolest Ta
but was elevated to hyperthermic levels during the warmest
Ta condition (37, 38).
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Fig. 1.
Mean ± SE brain temperatures
(Tbr) at different postnatal
ages [postnatal day 1 (P1), etc.] and ambient
temperature (Ta).
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Effect of age and
Ta on state percentages
(%TRT). State percentages changed significantly with
age. %SWS significantly increased with age
[F(4,68) = 7.596, P < 0.0001, n = 15], whereas %AS/REM significantly decreased [F(4,68) = 7.336, P < 0.0001, n = 15]. %W showed no
significant change across age
[F(4,68) = 1.034, P = 0.3964, n = 15]. Figure
2A
displays the changes in sleep/wake state percentages across age.
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Fig. 2.
A: mean ± SE state percentages by
age pooled across Ta condition.
abc Significantly different
(P < 0.05) from
P12,
P14, and
P16, respectively.
B: Mean ± SE state percentages by
Ta condition pooled across age.
ef Significantly different
(P < 0.05) 28-30 or
33-35°C, respectively.
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|
State percentages were significantly affected by
Ta. %SWS was significantly higher
in the two warmest Ta conditions
[F(2,68) = 10.928, P < 0.0001, n = 26], whereas %AS/REM was
significantly higher at 33.0-35.0°C
[F(2,68) = 15.422, P < 0.0001, n = 26]. %W was significantly
lowest at 33.0-35.0°C and significantly highest at
28.0-30.0°C [F(2,68) = 18.805, P < 0.0001, n = 26]. Figure 2B shows changes in sleep/wake state
percentages across the three different
Ta conditions.
Effect of Tbr
on state percentages.
Tbr was positively correlated with
%SWS (r = 0.478, P < 0.0001, n = 83) and negatively correlated with
%AS/REM (r = 0.258,
P < 0.05, n = 83). Figure 3A
displays the scatterplot for Tbr
and %SWS while Fig. 3B shows the
scatterplot for Tbr and %AS/REM.
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Fig. 3.
A: scatterplot with regression line
(±SE) showing the relationship between mean
Tbr and percentage slow-wave sleep
(%SWS). B: scatterplot showing the
relationship between mean Tbr and
percentage active sleep/rapid eye movement sleep (%AS/REM). Both
scatterplots pool Ta conditions
and ages. * Significant difference
(P < 0.05).
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The significant positive correlation between
Tbr and %SWS is both
Ta condition dependent and age
dependent. Individual analyses revealed a significant correlation at a
Ta of 33-35°C
(r = 0.517, P < 0.01, n = 27) and at age
P14
(r = 0.591, P < 0.005, n = 20) and
P16
(r = 0.715, P < 0.005, n = 17). No other significant
Ta-specific or age-specific
correlations were found between
Tbr and %SWS.
The significant negative correlation between
Tbr and %AS/REM is
Ta condition dependent but shows
no significant age-dependent relationship. Individual analyses revealed
a significant correlation at a Ta
of 33-35°C (r = 0.587,
P < 0.005, n = 27) and 38-40°C (r = 0.646,
P < 0.0005, n = 30).
Effect of age and
Ta on bout
number. There was a significant age-dependent
effect on state bout number when pooled across all
Ta conditions. Both SWS
[F(4,68) = 3.617, P = 0.0099, n = 15] and AS/REM
[F(4,68) = 4.047, P = 0.0053, n = 15] showed a significant
decrease in the number of bouts from
P12 to
P16. Waking showed no significant age
effects [F(4,68) = 1.175, P = 0.3298, n = 15]. Figure
4A
displays the changes in state bout number with age.
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Fig. 4.
A: mean ± SE state bout number by
age pooled across Ta condition.
B: mean ± SE state bout number by
Ta condition pooled across age.
C: mean ± SE bout length by age
pooled across Ta condition.
D: mean ± SE bout length by
Ta condition pooled across age.
abc Significantly different
from P12,
P14,
P16, respectively.
ef Significantly different
from 28-30 or 33-35°C, respectively.
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Ta significantly affected state
bout number. All three states, AS/REM
[F(2,68) = 47.453, P < 0.0001, n = 26], SWS
[F(2,68) = 65.464, P < 0.0001, n = 26], and W
[F(2,68) = 37.575, P < 0.0001, n = 26], showed significant
increases in bout number at 38.0-40.0°C compared with the
other two Ta conditions. AS/REM
bout number also showed a significant increase at 33.0-35.0°C
compared with 28.0-30.0°C. A significant interaction between
developmental age and Ta was found
for AS/REM bout number [F(8,68) = 2.968, P = 0.0066], so
interpretations of main treatment effects should be made with caution.
Figure 4B shows changes in state bout
number across Ta condition.
Effect of age and
Ta on mean bout
length. Developmental age had a significant effect on
mean bout length. Both SWS
[F(4,68) = 3.951, P = 0.0061, n = 15] and AS/REM
[F(4,68) = 4.411, P = 0.0031, n = 15] showed a significant
increase in mean bout length with specific ages,
P14 and
P16 for SWS and
P14 for AS/REM. Waking showed no
significant differences in mean bout length across age [F(4,68) = 0.724, P = 0.5787, n = 15]. Figure
4C demonstrates the changes in state
mean bout length across age.
Ta had a significant effect on
mean bout length. As with number of bouts, all three states, SWS
[F(2,68) = 13.985, P < 0.0001, n = 26], AS/REM
[F(2,68) = 20.822, P < 0.0001, n = 26], and W [F(2,68) = 21.114, P < 0.0001, n = 26], showed significant
effects at 38.0-40.0°C. In this case, all three state mean
bout lengths were decreased in the 38.0-40.0°C
Ta condition. Waking mean bout length was also significantly decreased at 33.0-35.0°C
relative to 28.0-30.0°C. See Fig.
4D for relative changes in state mean bout length across Ta.
Effect of age and
Ta on nBA.
Although nBA was not affected by age
[F(4,68) = 1.290, P = 0.2827, n = 15] significant increases in
nBA
[F(2,68) = 33.42, P < 0.0001, n = 26] were seen with increases in Ta. Figure
5, A and
B, demonstrates these relationships.
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Fig. 5.
A: mean ± SE number of brief
arousals across age. B: mean ± SE
number of brief arousals by Ta
condition. ef Significantly
different from 28-30 or 33-35°C, respectively.
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Effect of age and
Ta on SWS SWA.
SWS SWA showed no significant effect across the
Ta conditions
[F(2,68) = 0.655, P = 0.5229, n = 26] but showed a significant
effect across age. SWS SWA significantly increased with age
[F(4,40) = 138.752, P < 0.0001, n = 11] and showed significant
differences at each age group. Figure 6,
A and
B, demonstrates these relationships.
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Fig. 6.
A: mean ± SE SWS slow-wave
activity (SWA) across age. SWS SWA values are standardized and
converted to T scores.
B: mean ± SE SWS SWA by
Ta condition. SWS SWA values are
normalized and presented as a ratio of absolute SWS SWA to SWS total
power. abcd Significantly
different from P12,
P14,
P16, and
P18, respectively.
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| |
DISCUSSION |
This study was designed to determine how 3 h of a specific
Ta exposure affects sleep/wake
state structure and SWS intensity in the developing rat.
Ta variations had a significant
effect on sleep/wake state structure. %AS/REM peaked at
33.0-35.0°C, whereas %SWS was high at both 33.0-35.0 and
38.0-40.0°C. It has been shown in adult rats that the amount
of time an animal spends in REM sleep is maximal within the
Ta range at which metabolic rate
is not elevated by energy expenditure for thermoregulation, the
thermoneutral zone (TNZ; Ref. 36). Because %AS/REM peaks at the
33-35°C Ta condition,
this suggests that the TNZ for these developing rats may fall within
this Ta range. These results agree with other estimates of the TNZ in neonatal rats (37, 38). There was
also a significant increase in the number of AS/REM bouts at this same
Ta. In adult rats, as
Ta is moved toward the TNZ, there
are more transitions into REM sleep (18). Likewise, as
Ta deviates away from the TNZ,
NREM sleep accounts for a larger percentage of total sleep time (TST)
than REM sleep (18). This is seen at 38.0-40.0°C, where
%AS/REM is significantly less than at 33.0-35.0°C, whereas
%SWS remains high. Although both
Ta conditions of 33.0-35.0
and 38.0-40.0°C suppress %W, the former does so by promoting
both AS/REM and SWS, whereas the latter does so by promoting SWS alone.
Both of these effects are similar to responses seen in adult rats (27,
36).
Sleep consolidation is disrupted at 38.0-40.0°C compared with
the other two Ta conditions. The
number of bouts for AS/REM, SWS, and W are significantly increased at
38.0-40.0°C, whereas mean bout lengths are significantly
decreased for all three states. The number of brief arousals is another
measure of sleep consolidation or fragmentation of sleep. As with
number of bouts, number of brief arousals is significantly higher at
38.0-40.0°C than at either 28.0-30.0 or
33.0-35.0°C. Although a
Ta of both 33.0-35.0 and
38.0-40.0°C increases TST in developing rat pups, these
temperatures also increase the fragmentation of sleep and so disrupt
sleep/wake state structure.
Sleep intensity or depth of sleep was measured by SWS SWA. No
significant Ta effects were seen
for sleep intensity, as measured by SWS SWA. These results do not
support our hypothesis that an increase in
Ta may increase sleep depth or
intensity and run contradictory to the increases in SWS SWA seen after
hypothalamic warming in adult rats (24). One factor that may be behind
these results is the fact that we waited 1 h after the initial
Ta condition exposure to record
SWA. This was necessary to allow for anesthesia recovery but may have
masked the true response of SWS SWA to an increase in
Ta. It may be that the greatest
increase in SWS SWA occurs after the initial exposure to an increase in
Ta. After sleep deprivation in
adult rats, the first 4 h of recovery results in enhanced SWS SWA and a
subsequent reduction in nBA (9). This
inverse relationship between SWS SWA and
nBA in adults was not seen in our rat
pups and suggests that the two elements, SWS SWA and
nBA do not have the same relationship
during development as they do in adulthood.
Developmental changes in sleep/wake state percentages are similar to
those found by other authors (20, 26). There was a steady increase in
%SWS coincident with a decrease in %AS/REM. Likewise, SWS SWA showed
a steady increase coincident with brain maturation in developing rats
(13). No significant effects of number of brief arousals were found
across developmental age, but state bout number and mean bout length
showed age-dependent effects. SWS showed significant decreases in bout
number, with significant increases in mean bout length at
P14 and
P16, whereas AS/REM mean bout length
was significantly increased at P14
only. Recent data suggest that, in neonatal rats
P20 and younger, SWS SWA may not be
influenced by sleep deprivation, as is seen in adults (8). This means
that SWS SWA may not be regulated at these ages. Age-specific increases
in state bout length may prove to be a better measure of sleep
intensity or depth of sleep than SWS SWA. Arousal threshold experiments
across varied state bout lengths need to be conducted to answer this
question.
Perspectives
Sleep/wake state characteristics have been collected from infants that
have been rescued from a SIDS event. In these near-miss infants,
increases from controls are seen for %AS/TST (14, 29), AS mean bout
length (29), QS mean bout length (29), and %TST (4, 14, 29). Near-miss
infants show a decrease in %QS/TST (14, 16) and in the number of
awakenings from sleep (4). These data suggest that near-miss SIDS
infants spend more time sleeping, with increased mean bout lengths of
both AS and QS, and thus awaken less frequently (4, 14, 29). Our
developing rats age P14 and
P16 also show an increase in %AS/REM,
AS/REM and SWS mean bout length, and %TST when exposed to a
Ta of 33-35°C. The
results from this study suggest that rats age
P14-P16
exposed to a Ta of
33-35°C share similar sleep/wake state characteristics as SIDS
near-miss infants. It is concluded that subtle changes in
Ta variation can significantly
affect sleep/wake state structure, specifically state percentages and
sleep consolidation in developing rats. Manipulations of
Ta at specific ages in the
developing rat can mimic the sleep/wake state structure changes seen in
infants at risk for SIDS.
| |
ACKNOWLEDGEMENTS |
The authors thank Joel Benington for assistance with software.
| |
FOOTNOTES |
This research was supported by a National Research Service Award
predoctoral fellowship from the National Institute of Child Health and
Human Development (NICHHD) to R. Morrissette (5 F31 HD-07895-02)
and by an NICHHD Perinatal Emphasis Research Center grant (5 P50
HD-29732).
Address for reprint requests: R. N. Morrissette, Dept. of Biological
Sciences, Stanford Univ., Stanford, CA 94305-5020.
Received 17 April 1997; accepted in final form 7 January 1998.
| |
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