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Some oscillatory phenomena of blood glucose regulation: An exploratory pilot study in pigs

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It is well-known that blood glucose oscillates with a period of approximately 15 min (900 s) and exhibits an overall complex behaviour in intact organisms. This complexity is not thoroughly studied, and thus, we aimed to decipher the frequency bands entailed in blood glucose regulation. We explored high-resolution blood glucose time-series sampled using a novel continuous intravascular sensor in four pigs under general anaesthesia for almost 24 hours. In all time series, we found several interesting oscillatory components, especially in the 5000-10000 s, 500-1000 s, and 50-100 s regions (0.0002-0.0001 Hz, 0.002-0.001 Hz, and 0.02-0.01 Hz). The presence of these oscillations is not permanent, as they come and go. This is the first report of glucose oscillations in the 50-100 s range. The origin of these oscillations and their role in overall blood glucose regulation is unknown. Although the sample size is small, we believe this finding is important for our understanding of glucose regulation and perhaps for our understanding of general homeostatic regulation in intact organisms.
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RESEARCH ARTICLE
Some oscillatory phenomena of blood
glucose regulation: An exploratory pilot study
in pigs
Nils Kristian Skjaervold
1,2
*, Kathrine Knai
1
, Nicolas Elvemo
3
1Department of Circulation and Medical Imaging, Norwegian University of Science and Technology,
Trondheim, Norway, 2Department of Cardiothoracic Anaesthesia and Intensive Care Medicine, Trondheim
University Hospital, Trondheim, Norway, 3Glucoset AS, Trondheim, Norway
*nils.k.skjaervold@ntnu.no
Abstract
It is well-known that blood glucose oscillates with a period of approximately 15 min (900 s)
and exhibits an overall complex behaviour in intact organisms. This complexity is not thor-
oughly studied, and thus, we aimed to decipher the frequency bands entailed in blood glu-
cose regulation. We explored high-resolution blood glucose time-series sampled using a
novel continuous intravascular sensor in four pigs under general anaesthesia for almost 24
hours. In all time series, we found several interesting oscillatory components, especially in
the 5000–10000 s, 500–1000 s, and 50–100 s regions (0.0002–0.0001 Hz, 0.002–0.001 Hz,
and 0.02–0.01 Hz). The presence of these oscillations is not permanent, as they come and
go. This is the first report of glucose oscillations in the 50–100 s range. The origin of these
oscillations and their role in overall blood glucose regulation is unknown. Although the sam-
ple size is small, we believe this finding is important for our understanding of glucose regula-
tion and perhaps for our understanding of general homeostatic regulation in intact
organisms.
Introduction
A key feature of physiological regulation is the oscillations and pulsations that are apparent in
all advanced organisms. These are believed to be of importance for several regulatory pro-
cesses, and are seen in different organ systems such as the endocrine system, the respiratory
system, the circulatory system, the nervous system, and others. The underlying physiological
bases for the oscillatory patterns observed in global variables, is believed to be pulsatile and
synchronization mechanisms at lower spatial and temporal levels. [13]
The pulsatile release of insulin from the beta-cells of the pancreas has been known for sev-
eral decades and has been examined in both in vitro and in vivo studies [4,5]. Insulin is released
in synchronized bursts with a periodicity of approximately five minutes. The amount of insulin
released with each burst is constantly changing depending on the current blood glucose level
(BGL). Even in periods of stable BGL, the consecutive bursts are varying, possibly due to the
system perturbing itself to fine-tune its regulation. When studying the BGL in intact organisms
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OPEN ACCESS
Citation: Skjaervold NK, Knai K, Elvemo N (2018)
Some oscillatory phenomena of blood glucose
regulation: An exploratory pilot study in pigs. PLoS
ONE 13(4): e0194826. https://doi.org/10.1371/
journal.pone.0194826
Editor: Antonio Gonzalez-Bulnes, INIA, SPAIN
Received: November 3, 2017
Accepted: March 9, 2018
Published: April 2, 2018
Copyright: ©2018 Skjaervold et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: Original data is to be
found as supporting information.
Funding: The cost of the animal experiments and
the salaries of NKS and KK were provided by
Norwegian University of Science and Technology.
The glucose sensors used were fabricated and
provided by GlucoSet AS who provided support in
the form of salaries for author NE who, as CEO and
shareholder of GlucoSet AS, was involved in study
design, analysis and interpretation of data and
writing of the paper. GlucoSet AS did not have any
additional role in the data collection or decision to
with massive repetitive measurements, oscillations with a periodicity of approximately fifteen
minutes have been found [6]. However, studies of continuous BGL measurements from subcu-
taneous sensors indicate that a normal BGL entails a complex regulatory pattern [7][8]. Fur-
thermore, this pattern seems to “decomplexify” both as patients develop diabetes mellitus and
as a consequence of critical disease [912]. This indicates that there could be several distinct
oscillatory components in the native BGL regulation that are yet to be discovered.
We have the developed a method to study BGL changes over time in animals with a highly
accurate and quickly responding continuous intravascular sensor [13]. In previous studies, we
found that this sensor was able to detect these small oscillations in the BGL [14]. Therefore, in
this study, we aimed to decipher BGL oscillations in longer time series in intact pigs.
Materials and methods
Animals, anaesthesia and study protocol
The study was approved by the Norwegian State Commission for Animal Experimentation
(Oslo, Norway). A total of four domestic pigs were used in the studies (22–28 kg), and they
were acclimatized and treated in accordance with the European Convention for the Protection
of Vertebrate Animals used for Experimental and Other Scientific Purposes. The animals were
premedicated with intramuscular diazepam 10 mg and azaperone 400 mg. Anaesthesia was
induced through an intravenous access on the external surface of theear with atropine 1.0 mg,
fentanyl 8.0 μg/kg, thiopenthal sodium 4.0 mg/kg and ketamine hydrochloride 8.0 mg/kg.
Before intubation, 5 ml of 40 mg/ml lidocaine was applied to the larynx. The animals were ven-
tilated in pressure control mode on a ventilator (Dameca, Copenhagen, Denmark) with initial
values of FiO
2
at 0.30, a tidal volume of 10 ml/kg, PEEP at 6 cmH
2
O and respiratory frequency
of 18/min adjusted as needed in order to maintain PaCO
2
at 4.5–5.5 kPa. Anaesthesia was
maintained by isoflurane 0.5–1.0%. Based on clinical response this was supplemented with
boluses of fentanyl 50 μg/ml as needed. Intravascular volume was maintained by a bolus of
acetated Ringer’s solution 10 ml/kg, followed by a continuous infusion of 10 ml/kg/h through-
out the experiment. 5000 IU heparin was administered i.v. to prevent clot formation. The
animals were kept on the ventilator for almost 24 hours before euthanasia with pentobarbital
100 mg/kg.
After surgical cut-down, the animals were fitted with a central venous line for fluid and
medicine administration in their right internal jugular vein and an arterial line in their left
carotid artery. Two intravascular glucose sensors (GlucoSet, Trondheim, Norway) were
inserted in each superficial femoral artery after surgical cut-down, and connected to the glu-
cose monitor. Details of the glucose sensor with pre-insertion two-point calibration as well as
repetitive post-insertion one-point calibrations are described in [13].
Data handling and analyses
The calibrated glucose signal was exported for analysis with the statistical software “R” version
3.3.0 with the “WaveletComp” package [15,16]. We removed the first 200 min of the sampled
data in each series since these were periods of large instability and calibration of the sensors.
The rest of the data from the entire study time until sacrifice of the animals are included in the
study and are presented in Fig 1. The rest of the data were imported into the statistical soft-
ware, and a combination of visual inspections and quantitative time-frequency analysis with
continuous wavelet analysis was applied, as described in the Results & Discussion section.
The continuous wavelet transform (CWT) is a convolution of the original signal with a
function generated from the so-called “mother wavelet” [17]. The mother wavelet is a wave-
form of limited duration with an average value of zero. In the convolution process, it is shifted
Some oscillatory phenomena of blood glucose regulation
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publish. The specific role of NE is articulated in the
‘author contributions’ section.
Competing interests: Nicolas Elvemo is CEO and
shareholder of GlucoSet AS who was involved in
study design, analysis and interpretation of data
and writing of the paper. The glucose sensors used
were fabricated and provided by GlucoSet AS.
There are no further patents, products in
development or marketed products to declare. This
does not alter our adherence to all the PLOS ONE
policies on sharing data and materials, as detailed
online in the guide for authors.
in time and stretched and shrunk through the use of a scaling function. By stretching and shift-
ing the mother wavelet in time, the CWT identifies the correlation of different frequencies at
different time points. The final wavelet power spectrum is made by making a 3D-display of the
correlation values (degree of match = power) and indicates the power by colour.
The most frequently used mother wavelet and the one used in this paper, the Morlet wave,
is by mathematical definition a Gaussian enveloped cosine wave [17,18]. To illustrate the oscil-
latory phenomena, the presence of which varied, we performed the CWT on selections of the
time series. Instead of illustrating frequency in Hz (number of cycles per second), we use
period (the duration of time of one cycle), specified in seconds.
Results & discussion
All recordings were mainly performed with BGLs in the range of 4 to 6.5 mmol/l; however, as
seen from Fig 1, the BGLs of all animals slowly declined throughout the studies. Some of the
BGLs of the animals were very low at the end of the experiment, and the data for these periods
were discarded before analysis. When qualitatively studying the BGLs of the four animals (Fig
1) a few oscillatory periods can clearly be seen. In Pig 1 and to some extent in Pig 3, one can
Fig 1. Time series of the glucose values for the four animals. The length of the time series and thus the scaling on the x-axes different between individual animals
(BGL = Blood glucose level).
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see a very slow wave with a period of somewhere between 5000 and 10000 sec (0.0001–0.0002
Hz 1½h period). In particular, in some parts of Pigs 2, very distinct oscillations with a peri-
odicity of approximately 1000 sec (0.01 Hz 15 min) can be observed.
When examining the data in details, as we will below, there are oscillatory components to
be found with periodicity ranging from 50 to 5000 sec. These oscillations constitute time-
changing properties and should therefore be analysed by a time-frequency method such as the
CWT. However, since the oscillatory components are not present throughout the recording
and the power of the oscillations compared to the overall signal is so low, it is difficult to
merely analyse the signal in its entirety. We subjected the entire time series of Pig 1 to a CWT,
looking for periodicity from 30 to 10000 sec, but we had difficulty in deciphering any mean-
ingful information apart from very slow oscillations at a periodicity of approximately 8000 sec
(Fig 2A). When repeating the analysis only for the slowest period, we obtained a clearer visual-
ization of this 8000-sec oscillation (Fig 2B). We then repeated the procedure for the shortest
periods we studied, 50–100 sec. For these periods, the analysis did not perform well, only indi-
cating some interesting periods in the high frequency range, especially between 10000 and
20000 sec and at 40000 sec in the time series (Fig 2C).
Before going deeper into the faster frequencies, we created a complete time series CWT of
the slowest frequencies and performed these analyses for Pigs 2, 3, and 4. Pig 2 also had a low-
frequency component at 5000–10000 sec throughout the series, although with larger time-vari-
ations than Pig 1. Pig 3 had a very complex oscillatory pattern with an increasing decay in BGL
Fig 2. Wavelet power spectrum from the continuous wavelet transform (CWT) of the entire time series from Pig 1. The plot depicts the presence of distinct periods
throughout the time series, with the time in the experiment in seconds at the abscissa, the time of the respective periods on a logarithmic scale at the ordinate, and the
“power” of distinct periods as a function of the time-series shown in colours according to the scale next to the plots. The CWT covering the whole range of periods from
30–10000 sec only reveals the slow oscillation at approximately 8000 sec (A), which is highlighted when focusing in on the slow periods (B). The CWT of the whole time-
series focusing on the high-frequency oscillations at 30–300 sec does not yield any meaningful result (C).
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throughout the time-series, that seems to disturb the analysis; however, the 5000–10000-sec
oscillatory component can to some extent be seen at the beginning and end of the series. In
Pig 4, this component is also present and is most visible in the first and last part of the CWT
analysis but less evident in the middle of the analysis period. The lack of such a component in
the middle could be caused by several large abrupt changes, artefacts, and the presence of
other, more powerful higher-frequency oscillations (Fig 3).
As seen from Fig 1, Pig 2 had very distinct oscillations with a periodicity of some 1000 sec
throughout the second quarter of the time series. We therefore specifically searched for this
Fig 3. Wavelet power spectrum of the continuous wavelet transform of slow oscillations (1000–10000 seconds) of
Pig 2, Pig 3 and Pig 4.
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component in this one animal to quantify this component, looking in the range from 500 to
2000 sec. The CWT result is somewhat interesting as it shows both some of the strengths and
the weaknesses of the method. One can see the approximately 1000-sec oscillation between
1000 and 3000 sec in the time series, but it does not stand out as very powerful and clear (Fig
4). This is probably caused by a combination of edge effects, artefacts, and other oscillatory
components somewhat overshadowing the period we are examining.
When looking into the individual time series in more detail, especially searching for faster
oscillatory periods, some interesting features appear. Pig 1 has quite a few periods with distinct
oscillations in the 50–100 sec range, and Fig 5 depicts some of the most impressive periods. As
shown, the exact periodicity varies some, and sometimes it changes in a linear fashion within
small time periods; for example, in Fig 5 panel B, there is a quickly oscillating component that
seems to have a linear increase in periodicity. Fig 6 depicts a CWT of this individual time
period. Here, we have both an average power spectrum that does not consider the time dimen-
sion and therefore does not yield much information (left panel), and a time-frequency plot
where the oscillatory component is very visible. The latter plot clearly shows how the oscil-
latory component linearly increases its period from 50 to 300 sec.
Often, one oscillatory component precedes another, or different oscillatory components are
present at the same time in a fractal-like pattern. For example, in Pig 2, there is a distinct
period of 50–100-sec oscillations followed by the very characteristic 1000 sec oscillation (Fig 7)
Fig 4. Wavelet power spectrum of the continuous wavelet transform of Pig 2 with a periodicity set to 500–2000 sec to identify the 1000-sec oscillatory
component in the second quarter of the time series. This period is somewhat visualized in orange colour in the plot. The high power seen at 35000–40000 sec in
the time series is caused by the steep decay in BGL at this time period.
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Fig 5. Some interesting periods from Pig 1 with oscillations in the 50–100 sec period range.
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Fig 6. Continuous wavelet transform of the time series from Fig 5B where the periodicity appears to be constantly changing. The average power plot to the left only
indicates that there are some periodicities in the 100–300 sec range while the wavelet power spectrum plot to the right clearly shows how the main oscillatory component
has a linear rising periodicity from 50 to 300 sec throughout the time series. The abrupt drop in the middle of the series, seen in Fig 5B, yields the large artefact in the
middle of the wavelet power spectrum plot.
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However, the fractal nature is most clearly seen in Pig 3, where Fig 8 depicts two illustrative
situations in which both the 100-sec and the-1000 sec oscillations are present at the same time.
In Pig 4, we found several oscillatory components, especially in the 50–100-sec range and
the 1000-sec region, as shown in Fig 9.
The current study was exploratory in its nature, and should be interpreted as hypothesis
generating. We also kept in mind that we studied pigs, not humans, and the very limited num-
ber of animals observed. The results of this pilot animal study need to be confirmed in larger
future studies, preferably in humans, to draw clearer conclusions. Nevertheless, these examples
Fig 7. A period from Pig 2 in which two different oscillatory components follows each other. In Fig 7A, the 500–1000-sec slow oscillating component in the second
half of the time series is shown. A period (marked in red, enlarged in panel B) seems to have a fast oscillating component at 50–100 sec. The wavelet power spectrum
from the continuous wavelet transform of the time series in 7 B is displayed in 7 C, and this clearly showsthe 50–100 sec oscillatory component.
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show several oscillatory components in the time series of all four pigs. In our study, we find
clear oscillations in the 5000–10000-sec, 500–1000-sec, and 50–100-sec regions (0.0002–0.0001
Hz, 0.002–0.001 Hz, and 0.02–0.01 Hz). This could indicate that there are three distinct oscilla-
tors within the organism that regulate the BGL. It is beyond the scope of this exploratory study
to speculate regarding the physiological origin of these oscillations. However, based on our
previous studies on the effect of intravenous insulin boluses on BGL changes in pigs, where the
effect of each bolus has an approximately 15-min BGL-lowering effect [19], the fastest oscilla-
tions are unlikely to be caused by the pulsatile oscillation release by the beta-cells. The two
slowest effects, in contrast, could be caused by such pulsatility.
The current study confirms observations of previously described oscillations using a novel
sensing system, and describes a previously undescribed high-frequency oscillatiory phenome-
non. There have been some concerns that the observed differences in complexity in continu-
ous glucose measurements in different clinical situations could be caused by limitations in the
Fig 8. The fractal nature of blood glucose oscillations illustrated with two examples from Pig 3. Panels A and D depicts the time series from two situations in which
the 1000-sec oscillation is clearly seen. Panels B and E depicts the wavelet power spectrum from the continuous wavelet transform from A and D, respectively, clearly
showing the 1000-sec oscillatory component. However, the 50–100-sec componentis poorly depicted in thesefigures due to the low power in the high-frequency
oscillations compared with the low-frequency oscillations. Thus, panels C and F depicts the 50–100-sec components from A and D, respectively. (BGL = blood glucose
level).
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sensors [20]. However, the novel sensing system used in this study has a very low signal-to-
noise ratio, as seen in the figures containing unprocessed raw data (Figs 1,5,7and 8). The
high-frequency phenomenon is unlikely to have been picked up with slower glucose sensors.
Nevertheless, the sensors used in this study have a time constant to stepwise change of some
two minutes. The amplitudes of the measured oscillations are therefore likely larger than those
that we measure in these experiments due to damping caused by this time-delay.
A limitation of using a novel sensing system is that it is not as well-described as a more
mature system and that the results could be caused by an unknown interference or other phe-
nomenon in the sensing system. However, the non-stationarity and physiological appearance
of the oscillations make them unlikely to be caused from some unknown properties of the opti-
cal signal processing. Prior to this study, the sensors were tested in in vitro studies to examine
interference by other physiological and pharmacological chemical factorss, and they were
found to be sensitive to interferents, mainly temperature and pH. However, while these
measures can change quickly in experimental conditions [21], no changes in the experimen-
tal protocol varied with the same frequency as the oscillations. Alternatively, could the
observed BGL oscillations be caused by some other natural oscillatory phenomena or iatro-
genic interference from medications or other interventions? All medication given
Fig 9. Some interesting periods from Pig 4 with oscillations in the 50–100-sec range and the 1000-sec range.
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throughout a study can theoretically have some unappreciated effect on the physiological
outcome studied [22], for example, isoflurane is known to interfere with the insulin/glucose
system, albeit not in an oscillatory manner [23]. It is also unlikely that the oscillatory nature
of the respirator with a periodicity of three to four seconds or occasional changes in anaes-
thesia could cause the rhythmicity observed in the BGL. Nevertheless, the current study
cannot rule out that the observed oscillations were in fact caused by some previously unde-
scribed non-glucose, high-frequency phenomenon.
Conclusion
In this exploratory study of continuous intraarterial BGL measurements in four domestic pigs
under general anaesthesia, we found several interesting oscillatory components, especially in
the 5000–10000-sec, 500–1000-sec, and 50–100-sec regions (0.0002–0.0001 Hz, 0.002–0.001
Hz, and 0.02–0.01 Hz). The origin of these oscillations is unknown. Further studies are needed
to confirm the novel findings described in this study and to elucidate any underlying physio-
logical mechanism of the phenomena.
Supporting information
S1 Text. A table of time (sec) in column 1 and blood glucose values (mmol/l) in column 2
from the entire recording in Pig 1.
(TXT)
S2 Text. A table of time (sec) in column 1 and blood glucose values (mmol/l) in column 2
from the entire recording in Pig 2.
(TXT)
S3 Text. A table of time (sec) in column 1 and blood glucose values (mmol/l) in column 2
from the entire recording in Pig 3.
(TXT)
S4 Text. A table of time (sec) in column 1 and blood glucose values (mmol/l) in column 2
from the entire recording in Pig 4.
(TXT)
Acknowledgments
We wish to thank Tine Hunt (GlucoSet) and Oddveig Lyng (NTNU) for invaluable help with
the animal studies and Dag Roar Hjelme (GlucoSet & NTNU) for the pre-processing of signal
recordings.
Author Contributions
Conceptualization: Nils Kristian Skjaervold, Kathrine Knai, Nicolas Elvemo.
Data curation: Nils Kristian Skjaervold.
Formal analysis: Nils Kristian Skjaervold.
Investigation: Nils Kristian Skjaervold, Kathrine Knai.
Methodology: Nils Kristian Skjaervold.
Writing – original draft: Nils Kristian Skjaervold.
Writing – review & editing: Kathrine Knai, Nicolas Elvemo.
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Some oscillatory phenomena of blood glucose regulation
PLOS ONE | https://doi.org/10.1371/journal.pone.0194826 April 2, 2018 13 / 13
... Indeed, oscillatory BG phenomena in the range of 0.01 to 0.02 Hz have been recently shown in the pig [58]. Thus, it would be of importance to confirm that calculations on nonsmoothed signals could account for improved accuracy and more informative complexity analysis. ...
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