On the spatial phase distribution of cutaneous low-frequency perfusion oscillations

Abstract

Distributed cutaneous tissue blood volume oscillations contain information on autonomic nervous system (ANS) regulation of cardiorespiratory activity as well as dominating thermoregulation. ANS associated with low-frequency oscillations can be quantified in terms of frequencies, amplitudes, and phase shifts. The relative order between these faculties may be disturbed by conditions colloquially termed ‘stress’. Photoplethysmography imaging, an optical non-invasive diagnostic technique provides information on cutaneous tissue perfusion in the temporal and spatial domains. Using the cold pressure test (CPT) in thirteen healthy volunteers as a well-studied experimental intervention, we present a method for evaluating phase shifts in low- and intermediate frequency bands in forehead cutaneous perfusion mapping. Phase shift changes were analysed in low- and intermediate frequency ranges from 0.05 Hz to 0.18 Hz. We observed that time waveforms increasingly desynchronised in various areas of the scanned area throughout measurements. An increase of IM band phase desynchronization observed throughout measurements was comparable in experimental and control group, suggesting a time effect possibly due to overshooting the optimal relaxation duration. CPT triggered an increase in the number of points phase-shifted to the reference that was specific to the low frequency range for phase-shift thresholds defined as π/4, 3π/8, and π/2 rad, respectively. Phase shifts in forehead blood oscillations may infer changes of vascular tone due to activity of various neural systems. We present an innovative method for the phase shift analysis of cutaneous tissue perfusion that appears promising to assess ANS change processes related to physical or psychological stress. More comprehensive studies are needed to further investigate the reliability and physiological significance of findings.

Full text

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On the spatial phase distribution
of cutaneous low‑frequency
perfusion oscillations
Stefan Borik1*, Simon Lyra2, Volker Perlitz3, Micha Keller4, Steen Leonhardt2 &
Vladimir Blazek2,5
Distributed cutaneous tissue blood volume oscillations contain information on autonomic nervous
system (ANS) regulation of cardiorespiratory activity as well as dominating thermoregulation. ANS
associated with low‑frequency oscillations can be quantied in terms of frequencies, amplitudes, and
phase shifts. The relative order between these faculties may be disturbed by conditions colloquially
termed ‘stress’. Photoplethysmography imaging, an optical non‑invasive diagnostic technique
provides information on cutaneous tissue perfusion in the temporal and spatial domains. Using the
cold pressure test (CPT) in thirteen healthy volunteers as a well‑studied experimental intervention,
we present a method for evaluating phase shifts in low‑ and intermediate frequency bands in forehead
cutaneous perfusion mapping. Phase shift changes were analysed in low‑ and intermediate frequency
ranges from 0.05 Hz to 0.18 Hz. We observed that time waveforms increasingly desynchronised
in various areas of the scanned area throughout measurements. An increase of IM band phase
desynchronization observed throughout measurements was comparable in experimental and control
group, suggesting a time eect possibly due to overshooting the optimal relaxation duration. CPT
triggered an increase in the number of points phase‑shifted to the reference that was specic to the
low frequency range for phase‑shift thresholds dened as π/4, 3π/8, and π/2 rad, respectively. Phase
shifts in forehead blood oscillations may infer changes of vascular tone due to activity of various
neural systems. We present an innovative method for the phase shift analysis of cutaneous tissue
perfusion that appears promising to assess ANS change processes related to physical or psychological
stress. More comprehensive studies are needed to further investigate the reliability and physiological
signicance of ndings.
e skin is involved in multiple functions pivotal for the entire organism. Skin perfusion is thus a rich and easily
available source of information on these functions, such as the activity of the autonomic nervous system (ANS),
cardiorespiratory exercise as well as dominating thermoregulation1,2. Understandably, scientic zeal was sparked
also at the prospect of obtaining a non-invasive measure of a clinically relevant system involved in serious mental
and physical disorders. In that vein, studies of skin perfusion have a longstanding history. First published in 1937,
photoplethysmography (PPG) has been demonstrated to be an undemanding and non-invasive technology for
the study of the perfusion of supercial skin layers3. is approach has been advanced in current technologies
to non-contact instruments used in cardiovascular diagnostics4.
For long skin perfusion studies focused mostly on understanding pulsatile PPG qualities, whereas the infor-
mation on ANS processes in PPG signals remained insuciently understood. Earliest references to proprietary
oscillations in PPG signals as ‘psychomotor waves’5 had never been conrmed by objective correlates. e system-
atic analysis of frequencies and amplitudes inherent to PPG signals (or laser Doppler uxmetry, LDF) has only
as of late demonstrated that a mere 2.5% fraction of the total signal power originated in cardiovascular activity6.
is is of interest to medical elds specializing on the non-invasive and non-contact cardiovascular diagnostics4.
Scientic study of ANS inuence on cardiovascular-respiratory processes focused chiey on a low and a
high frequency band, LF and HF, resp. ose variance categories were, however, matter of scientic controversy
OPEN
1Department of Electromagnetic and Biomedical Engineering, Faculty of Electrical Engineering and Information
Technology, University of Zilina, Zilina, Slovakia. 2Medical Information Technology (MedIT), Helmholtz-Institute
for Biomedical Engineering, RWTH Aachen University, Aachen, Germany. 3Simplana GmbH, Aachen,
Germany. 4Department of Psychiatry, Psychotherapy and Psychosomatics, Medical School, RWTH Aachen
University, Aachen, Germany. 5The Czech Institute of Informatics, Robotics and Cybernetics (CIIRC), Czech
Technical University in Prague, Prague, Czech Republic. *email: stefan.borik@feit.uniza.sk
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with respect to the boundaries and physiological representations of the LF-band since it is considered to contain
sympathetic as well as parasympathetic nervous trac. While the HF-band is commonly agreed to represent
vagal (parasympathetic) activity found in respiratory sinus arrhythmia (RSA), a state of weak coupling between
cardiac and respiratory activity7, the validity of the entire approach is questionable if one of the frequency bands
evades evidence8–10. is, unfortunately, impeded its clinical use to this day.
An approach which appears to overcome the dilemma on ANS-related frequency bands was introduced
with ndings on a 0.15Hz rhythm or intermediate (IM) band. Wedged between the LF and the HF frequency
band at 0.12Hz to 0.18Hz, this IM-band bridges the frequency boundaries of upper LF and lower HF band. A
rst description of the IM-band was given for skin LDF data by Smits etal. during hyperventilation11. Further
studies showed the IM-band strongly associated with profound relaxation in skin of earlobe, forehead, and
heart12. Controlled relaxation using self-control techniques such as the autogenic training (AT) exhibited dur-
ing extended IM-band prevalence cardiorespiratory phase synchronizations (CRPS) at integer number ratios,
so-called n:m—synchronizations13. In particular, these ndings suggest a series of lower and upper harmonics of
the primary IM-band frequencies covering essential LF- and HF-frequencies. is suspends the role of distinct
frequency bands as it emphasizes instead the relevance of ratios of interacting frequencies. Comparison of human
multiple physiological time series with canine experiments showed widely identical frequency characteristics in
spite of scaling dierences which suggested identical origin of the IM-band in unspecic reticular neurons in the
common brainstem system13. is is of note since Traube speculated already in 1865 on phasical ‘irradiations’
of medullary respiratory centers on brainstem nuclei controlling heart rate14.
Low-frequency oscillations exhibit spatially variable amplitudes, which depend on the site of the PPG probe.
erefore, the photoplethysmography imaging (PPGI) method, rst described in15, is ideal for the spatial analysis
of skin perfusion dynamics, which explains increased interest of this method16. PPGI enables spatial–temporal
analysis of the distribution of perfusion oscillations using a camera system17 combined with an external light
source18, or use of ambient illumination only19.
According to20, the PPGI method can be used to dierentiate low-frequency oscillations in healthy and
damaged tissues. is research group demonstrated also that slow oscillations were not phase synchronized.
In spite of open questions concerning frequencies and amplitudes in PPG-signals, the phase-shi is an
essential yet still “under-explored” parameter, which therefore mandates systematic study19. is approach was
employed by21, using a technique published rst by22 to monitor the relative phase of perfusion changes associ-
ated with the cardiac activity in migraine patients.
is research group23 validated their ndings with a novel model of light-tissue interaction when using a
reective and non-contact PPG, i.e. PPGI technique. e authors reported that the transmural pressure of the
larger arteries apparently aected locations in cutaneous areas where HR-related blood volume changes oscillate
at opposite phase to the reference signal acquired from another location on the skin. us, depending on the
wavelength used HR-related changes in the PPG signal detected with PPGI may be induced indirectly by oscil-
lations of larger arteries located even in deeper subcutaneous tissue structures24. In contrast25, another view on
light-tissue interaction for monitoring the entire experiment is given by videocapillaroscopy.
e current communication describes a novel method for mapping the phase shi of perfusion uctuations
in cutaneous tissues. In contrast to mapping cardiac activity, we focused on -frequency oscillations in the range
between 0.05Hz and 0.18Hz. We divided this frequency band into low-frequency (LF) sections and intermedi-
ate (IM) sections with boundaries according to Pfurtscheller (_Pf)26 and Keller (_Ke)27. us, we studied four
bands: LF_Pf (0.05Hz–0.10Hz), IM_Pf (0.10Hz–0.15Hz), and LF_Ke (0.05Hz–0.12Hz), and IM_Ke
(0.12Hz–0.18Hz). To stimulate ANS responses, we used the well-studied cold pressure test in young healthy
individuals to induce changes in the spatial distribution of the phase shi relative to the frontal region’s central
reference. We chose the correlation between phase synchronization of slow perfusion rhythms and possible
changes in ANS regulation caused by stress as an outcome parameter. To the best of our knowledge, this approach
has never been probed previously.
Materials and methods
Experimental protocol. A total of 16 subjects aged (27.0 ± 2.2) years participated in the study. e right- or
le-handed individuals were non-smokers and had no acute physical or mental illness, as was tested using the
German version of the patient health questionnaire (PHQ-D28;). To avoid falsifying measurement outcomes,
subjects were asked to refrain from consuming anything containing caeine on the day of the experiment. We
used a between-subject blocked protocol with seven stages in a supine position to allow internal and external
control of ANS stimulation. In 13 subjects, the following sequence was applied: (1) Eyes Open (EO), (2) Eyes
closed (EC), (3) EC + cold pressor/ambient water test (CPT, AWT), (4) EC, (5) EC + cold pressor/ambient water
test, (6) EC, (7) EO. Stages 1 and 7 lasted 180s, and stages 2, 4, and 6 lasted 300s. Stages 3 + 5 lasted 60s and
were applied in randomized order. Stage 3 or 5, CPT or AWT, was performed by immersion of the subjects’
non-dominant hand (up to the carpus) in water of either 4°C or water of ambient temperature (AWT) of 20°C
for 60s. In another group of 3 subjects, conditions of stage 2 (EC) were applied also in stages 3 and 5 to serve as
a time control group. Breathing was not controlled to avoid any unintended stress by external control. Further-
more, the head was not xed to minimize motion artifacts since this could also induce stress. e hand was dried
aerwards using a towel placed on the patient’s abdomen. Stage 6 (EC) and stage 7 (EO) nalized the recording.
An overview of all stages is illustrated in Fig.1A,B. e whole experiment lasted 23min in total and was well
tolerated by all participants. e study protocol was approved by the ethical committee of the University Hos-
pital at RWTH Aachen University (Ref. No. EK 219-21), informed consent was obtained from all subjects prior
to the study, and all methods were performed in accordance with the study protocol and with the Declaration
of Helsinki.
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Measurement setup. e measurement setup used a high-performance complementary metal-oxide-
semiconductor (CMOS) monochrome camera of type Grasshopper 3 GS3-U3-23S6 M-C (FLIR Systems, USA),
with a xed focal length lens of type Fujinon CF12.5HA-1 (Fujilm Holdings, Japan) mounted to the camera.
e recordings were performed with a spatial resolution of 1920 × 1200 pixels (12 bit per pixel) at 30 fps. Since
ambient illumination was necessary for the measurements, four organic LED (OLED) panels of type Keuka
warmwhite 24V (OLEDWorks, Germany) were mounted next to the camera. e advantages of using OLEDs
instead of LEDs for camera-based vital sign extraction were described in29. A similar setup using one OLED to
record simulated PPGI signals from an optoelectronic skin perfusion phantom was described earlier17.
In this study, a comfortable patient bench was placed beneath the camera setup to locate the participants in a
supine position. e angle of the patient’s head to the camera was adjusted using a pillow. is ensured optimal
conditions for continuous measurement of facial skin perfusion. Two bowls, one with iced water (approx. 4°C),
another one with water at ambient temperature (approx. 20°C) were placed within the reach of the subject to
allow low-movement immersion of the hand. e measurement setup is shown in Fig.2a. Figure2b illustrates
the view of the camera and indicates the object detector and the point tracker used for automated region extrac-
tion explained below.
Data processing. As therst step, raw data were prepared to evaluate the spatial distribution of the PPGI
signal phase by determining the desired area of interest; here, we chose the subjects’ forehead. e following
precautions had to be taken prior to initiating an extended recording (23min), as was done in this case. First,
the subject’s lateral head movements have to be controlled since they can cause signal artifacts that are amplied
given the small kernel size used to extract temporal PPGI signals from the monitored image matrix. We decided
to track the selected area of interest, which has been previously used30–33. Second, since this tracking algorithm
can result in image jittering34, we used double tracking by combining the Viola-Jones algorithm35 with the point
detector method36–38. Here, the face detector automatically detected and extracted the face area as a bounding
box, which was then magnied by 10% to cover the entire face. ird, the image was cropped and inserted into
Figure1. (A) Stages of the experimental protocol in the experimental group (N = 13); with stages 3 and 5 being
applied in reversed order in 3 recordings to randomize intervention. (B) Stages of the control group (N = 3) with
all stages using identical conditions.
Figure2. (a) Measurement setup. (b) Example of the eld of view with an applied face detector and forehead
tracking.
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the auxiliary image layer (lled with zeros), ensuring the exact image size for subsequent processing and tracking
using the KLT point tracker. At this stage, a rectangle containing a region of interest (ROI)on the subject’s fore-
head was manually selected. Fourth, the KLTpoint tracker was initialised to track and extract the selected ROI
using minimal eigenvalue features36. In the case of angling the subject’s face o the horizontal plane, detected
ROIs were automatically reprojected into the image’s original horizontal plane perpendicular to its symmetry
axis. According to its upper edge, the process began by calculating the bounding box’s angle of inclination. e
image was then rotated back andinserted into another unied image layer and saved in *.pgm format. Prior to
data analysis, pre-processing of image data was nalized by resizing all images to the selected reference, the rst
image in the sequence of measured data. is compromise was due to the limitations of tracking and the fact
that various sized ROIs were detected as subjects moved. To minimize mixing of individual pixels, the nearest
extrapolation method was chosen. e modied image was then saved to the hard disk. Figure3 illustrates the
process of face and forehead ROI tracking.
Following pre-processing signals from suciently stable ROIs, the time courses of the PPGI signals were
extracted by analysing each recorded frame. Time waveform extraction was initiated by selecting a 10 × 10 px2
kernel moving without overlap in the selected forehead region (Fig.4). e spatial mean was then computed
for each kernel position of the processedframe. us, a three-dimensional matrix of time-domain signals was
obtained. Two dimensions encoded the extracted signal’s spatial location. e third dimension was a time vec-
tor at a length equal to the number of frames recorded (41,400 samples = 23min). Figure5 depicts a wavelet
scalogram of the unltered signal from a 10 × 10 px2 region close to the subject’s forehead showing perfusion
rhythms in the frequency domain. is image still contained primarily artifacts due to facial expressions and
changes in the geometry of the tracking area, which persisted despite image tracking (Fig.6). Suppression of
these artifacts was achieved using the stationary wavelet transform (SWT)39–41. Prior to SWT denoising, the
signal was downsampled to the sampling frequency of 5Hz.
is decomposed the signal using Daubechies – db5 wavelets—to the eight levels processing each detail
level separately using a moving window to compute the median and standard deviation. is helped to obtain
the envelope of a particular wavelet decompositiondetail. Subsequently, all values below this envelope were
adaptively ltered separately using so thresholding for each decomposition level. Finally, the signal was recon-
structed using inverse SWT. e purpose of this entire process was not to eliminate noise but to determine it.
e estimated noise was then subtracted from the original signal, eliminating other undesired artifacts, and
preparing the signal for further processing and analysis.
After removing these artifacts, defined frequency bands were extracted using finite response (FIR)
band-pass lters using the following parameter settings: low frequency (LF)_Pf band (cut-o frequencies
0.05Hz–0.10Hz); intermediate (IM)_Pf band (cut-o frequencies 0.10Hz–0.15Hz); LF_Ke band (cut-o
frequencies 0.05Hz–0.12Hz); IM_Pf band (cut-o frequencies 0.12Hz–0.18Hz).
is signal processing focused on observation of ANS regulation in those frequency ranges, which have
been recently demonstrated to be distinct processes27. ese frequency bands may contain respiration-induced
Figure3. Face and forehead ROI tracking.
Figure4. Process of obtaining PPG signals in time domain.
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perfusion changes42. However, there is evidence that while IM band activity and respiration are closely related
processes, they are yet distinct10,43. is is supported by other authors reporting LF changes associated with
waves formerly referred to as Mayer-Traube-Hering oscillations being only slightly aected by respiration44,45.
e eects of ltering using stationary wavelet transform denoising (SWTD) can be seen in Fig.7. e blue
curve represents the time-domain signal following tracking, while the red curve corresponds to the signal fol-
lowing denoising using the SWTD algorithm. As illustrated in this gure, ltering helped suppress artifacts
caused by the subject’s facial expressions, especially the forehead wrinkling visible in Fig.6. Furthermore, this
gure shows PPG signals from which ROIs were extracted. Along with suppressedartifacts, it is possible to see
a smoothed PPG curve and the oscillations corresponding to slow changes in cutaneous tissue perfusion. Aer
removing noise and artifacts, the signal reconstruction process included only wavelet levels whose frequency
corresponded with LF oscillations as dened above. Simultaneously, a frequency band for the heart rhythm up
to approx. 5Hz was included to observe possible higher harmonic components corresponding to the dicrotic
notch in the PPG signal. Figure7 shows a signal ltered this way, which exhibits artifact suppression even in the
frequency domain (Fig.8).
Further ltering of spectral components helped avoid inaccuracies in determining the phases of LF oscilla-
tions, which might possibly be aected by other physiological oscillators, such as cardiac activity or respiration.
e Hilbert transform was chosen to provide information on the instantaneous phase of the signal as this is a
computationally undemanding yet robust and well studied approach. e phase is determined separately for each
time waveform of the PPGI matrix. Applying the Hilbert transform yielded an analytical signal:
where xr represents the original signal and xi is its imaginary part shied by 90°.
e information on the instantaneous phase is:
(1)
x(t)=xr+jxi,
Figure5. Continuous wavelet scalogram aer tracking.
Figure6. Mimics and light change comparison (at the start—frame 1, in the middle of cold pressure test—
frame 25,989). Blue colour depicts motion estimated by optical ow.
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where ϕ(t) has the form of a sawtooth signal carrying information on changes of the phase of the signal within a
given cycle. is allowed calculation of the instantaneous phase of each time course of the PPGI matrix, creating
a three-dimensional instantaneous phase matrix carrying spatial-temporal information on phase distribution in
the forehead region and changes over time.
Selection of a suitable reference signal was essential to create a planar map of phase changes. Here, the axis
of symmetry was determined using the central vertical line of the forehead region. is reference signal was
always central element for each row of the phasematrix, which consisted here of a uniform size of 12 rows and
35 columns (Fig.9).
e algorithm used to create this map started by computing the phase dierence between the reference point
and all other points (column positions) in any given row. is allowed to estimate the relative phase shi across
all phase matrix points. us, a matrix of dimensions 12 × 35 was obtained, with the points on the symmetry
axis naturally equal to zero radians.
e phase shi between the reference and the corresponding matrix point was calculated as the absolute value
of their instantaneous phase dierences within a specied time window.
We chose a 10∙Fs window size to avoid sudden and undesirable phase changes caused, for example, by insuf-
cient artifact suppression. is window of 3000 samples (100s) moved acrosss the entire signal, calculating
the median
φmed,
r
,
c
(t)
of the dierence between the absolute phase value of the reference signal
φref ,
r
(t)
and the
signal of the corresponding point
φ
r
,
c
(t)
of the phase shi matrix:
(2)
φ(
t)=atan
x
i
x
r
,
(3)
φmed,
r
,
c(t)=|β|=


φ
ref,
r(t)−φr,c(t)

,
Figure7. Signal before and aer stationary wavelet transform denoising.
Figure8. Filtered scalogram showing heart rate (HR) and low frequency (LF) bands and experimental stages.
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where r andc represent rows and columns of the phase matrix, respectively.
An example of this process is shown in Fig.10, depicting changes in the phase synchronization between the
reference point and a selected point of the phase matrix corresponding to the forehead region of the subject
under investigation.
To create a temporal sequence of phase maps and visualize the actual phase shi changes and their spatial
distribution, a moving window of 60s was used to calculate the average phase shi value
β
for each point of
the phase matrix. Since averaging failed to correct averaging of circular quantities, a method incorporating its
vector properties was used instead:
where
βn
is the relative phase of selected points of the phase matrix, n corresponds to the frame number and W
corresponds to the moving averaging window length.
is logic was followed when selecting phase thresholds to analyse the synchronisation of spatial changes
in perfusion. First, we wanted to use intervals that would not overlap, as is usually the case, for example, when
selecting frequency bands in amplitude analysis of signals. However, instead of this approach, we used phase
thresholds and thus intervals with overlaps, i.e., from the le, each interval is bounded by a π value. is choice
is supported by the assumption that the relative temporal position between the reference and the observed signal
is tracked at a selected point in a matrix containing information about the spatial distribution of perfusion in
the low-frequency domain when working with phase shis. Furthermore, we assume that the perfusion signals
(due to their nature) are not perfectly aligned, and even in the case of resting state, some initial phase shi is
present between them (here considered as background). By gradually narrowing the interval towards the π value,
the responses to the intervention (CPT or AWT) become apparent and are dierentiable from the background.
us, to map spatiotemporal variation of phase, the values with an average phase shi less than π/4 were
marked blue, which corresponded to zero, and phase shi values in the range of π/4 to πwere colour coded
from green to red, indicating counterphase to the reference. is approach was also used for colour coding of
the 3π/8-π and π/2-π intervals. e spatiotemporal variation in reciprocal phase shis is illustrated in Fig.11,
which depicts minute-by-minute changes. e y-axis included information on the measured subjects. Another
technique of representing the relative phase shis was to encode them following their time course. is was
(4)
β
=atan2
W

n=1
sinβn,
W

n=1
cosβn

, or in complex numbers β=arg
W

n=1
ejβn
,
Figure9. Example of map creation. Reference points in the matrix are placed in the middle of each row.
Figure10. Detection of desynchronization based on the Hilbert transform. Blue and red signals represent ROIs
from dierent parts of the forehead. ere are low-frequency oscillations obtained from the signal by SWTD,
similar to initial denoising. e dashed black line is the instantaneous phase calculated in the moving window
with a length of 10s. e area marked yellow corresponds to the desynchronization threshold used for further
analysis.
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achieved by counting the number of phase matrix points with a relative phase shi to the reference exceeding
a predened threshold in a given row. Here, three dierent threshold values (thrs) π/4, 3π/8 and π/2rad were
dened. Subsequently, the ratio of phase matrix points exceeding the pre-set threshold to the total number of
phase matrix points was calculated for each frame and, thus, for the associated phase matrix. is process is
mathematically described by equation:
where N = r × c is the total number of phase matrix points and
Nφ>thrs
is the number of points exceeding the
predened threshold.
To quantify relative phase changes within each group and phase shi threshold value (π/4, 3π/8 and π/2rad),
separate 2 (LF_Pf, IM_Pf and LF_Ke, IM_Ke) × 7 (Repetition) repeated measures analyses of variance (ANOVAs)
of relative phase desynchronization were computed. e main experimental and random group were analysed
together aer adapting the order of AWT and CPT as well as subsequent EC stages of the random group to match
(5)
R
φ>thrs(t)=
Nφ>thrs
N,thrs =

π
4
,3π
8
,π
2,
Figure11. Spatial phase shi distribution matrices indexing desynchronization for low and intermediate
frequency (LF, and IM, resp.) bands according to boundaries used by Pfurtscheller (Pf, le column) or Keller
(Ke, right column) for individual participants (horizontal lines of squares) of the main group (n = 10). EO = eyes
open, EC = eyes closed; orange bar at top: cold water test, blue bar at top: ambient water test. From top to
bottom, colour coded points display thresholds for relative phase shi intervals from π/4rad to π rad, 3π/8rad
to π rad, and π/2rad to π rad: dark blue < blue < green < yellow. Red indexing counterphase with the reference.
Plots show only minute dierences between Pfurtscheller and Keller frequency denitions.
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the order of the main group. Despite lack of power due to a small sample size, the control group was also analysed
using a repeated measures ANOVA. A p-value of < 0.05 was considered signicant. Post-hoc paired t-tests were
computed for (1) the contrast stage 1 versus 7 to test whether our experimental conditions were followed by an
increase in phase desynchronization, and (2) contrasting AWT and CPT (stage 3 vs 5) to test dierences in phase
desynchronization. ese post-hoc tests were conducted separately for phase shis, groups as well as frequency
band denitions. Bonferroni corrections were applied for each frequency band denition pair (LF_Pf/IM_Pf
and LF_Ke/IM_Ke) and separately for each phase shi, resulting in an α = 0.05/4 = 0.0125.
Results
e matrices of spatial phase shi distribution indexing desynchronization for low and intermediate frequency
are shown for the experimental (main) group in Fig.11 and for control and random groups in Fig.12, resp.
(results based on Eqs. (3) and (4)). ese plots exhibit various patterns for phase shi threshold ranges, frequency
bands, and experimental time. Pattern dierences for Pf and Ke boundary denitions appear rather insignicant.
Furthermore, phase shi distributions were plotted for π/4, 3π/8 and π/2 thresholds, and they were more promi-
nent in either IM band as in LF bands. us, desynchronization was strongest in π/4 in the IM band. Conversely,
there was almost complete synchronization with reference for π/2 in the LF band.
To quantify individual ndings, using Eq.(5) we computed the median (red graphs) for phase shi changes
(desynchronization compared to reference) for π/4, 3π/8, and π/2rad thresholds in the main and the random
group combined, and for the time control group. is was computed separately for LF and IM frequency bands
at varying boundary denitions according to Pfurtscheller (Pf) and Keller (Ke). e increase in phase desyn-
chronization can be interpreted as an increase in the number of matrix points above the predened threshold,
with a value of 1 equal to 100% phase shied points compared to reference.
Figures13 and 14 shows the time courses of phase desynchronizations for the main and control groups for
frequency boundaries dened as IM_Pf band (0.10Hz–0.15Hz) and IM_Ke (0.12Hz–0.18Hz), respectively.
Two patterns are obvious in both groups and both frequency denitions. Firstly, the levels of phase desynchroni-
zations decreased for thresholds with π/4 > 3π/8 > π/2rad. In the IM_Pf band the smallest phase window (π/2rad)
underlines the upward trend throughout measurements pointed out by a more specic response. Secondly,
phase desynchronizations increased over time for all three thresholds and both groups. However, there were
fewer prominent oscillations in the main group during the entire experimental time course than in control. In
the main group, phase desynchronization due to CPT were of magnitudes comparable with non-experimentally
induced uctuations in all thresholds. In controls, there were prominent spontaneous oscillations. Opening the
eyes (stage 7) was followed by a transient increase in phase desynchronization in all thresholds. Here, the increase
in phase desynchronization appeared to be strongest as of the 17 min. is may have been due to the length of
the relaxation causing some discomfort for participants.
Figure15 shows the time courses of the phase desynchronizations for the main and the control groups for
frequency boundaries dened as LF_Pf frequency band (0.05Hz–0.10Hz). In the main group, there were still
few pronounced uctuations. Here, too, the level of phase desynchronization decreased with each threshold.
In all thresholds, a comparable course was found in CPT: stable conditions during CPT, then rapid increases
in phase desynchronization, then continuous decreases in phase desynchronization for 3min. Occasionally in
all 3 thresholds dierently pronounced oscillations of shorter frequency and amplitude appeared. Opening the
eyes was accompanied by hardly any changes in phase desynchronization. e control group showed very stable
conditions. ere were distinct oscillations about every 7min, most pronounced at π/4 > 3π/8 > π/2rad. ere
was no evidence of increases in phase desynchronization with time.
Figure16 shows the time courses of the phase desynchronizations for the main and the control groups for
frequency boundaries dened as LF_Ke frequency band (0.05Hz–0.12Hz). In the main group, largely identi-
cal conditions are found as in the LF_PF frequency band. e response to CPT appears overall at a comparable
course as in LF-Pf. During CPT there is a stable course of phase desynchronization in all thresholds, followed
by rapid increases, and slow decays for approx. 3min. Here, however, oscillations of shorter frequency and
amplitude are missing. In the control group, spontaneous oscillations of comparable period duration are found,
but not only of stronger amplitude, but also of somewhat dierent dynamics. Here, steep rising edges are found,
followed by slow continuous decay of this activity. is is found roughly three times: in the eighth minute, the
12th minute, and in the 17th minute.
Statistical analyses. For each phase threshold and group (main + random group, control group), 2 (LF and
IM band for each frequency denition) × 7 (Repetition) repeated measures ANOVAs were computed. Mauchly’s
test indicated that the assumption of sphericity had been violated in the experimental group for
Rφ>π/2
in
Pfurtscheller (χ2(20) = 34.3, p = 0.03) and Keller frequency band denitions (χ2(20) = 32.7, p = 0.04) as well as for
Keller denition of
Rφ>π/4
(χ2(20) = 32.5, p = 0.047). erefore, degrees of freedom were corrected using Green-
house–Geisser estimates of sphericity (ε = 0.48, ε = 0.43 and ε = 0.41). In the experimental group, the repeated
measures ANOVAs for
Rφ>π/4
,
Rφ>3π/8
, and
Rφ>π/2
, respectively, revealed signicant main eects for the fac-
tor repetition (all p < 0.05; Table1). is indicates that phase desynchronization values of all relative phase shis
showed a signicant increase throughout measurements. e main eects of the factor band as well as the inter-
action band × repetition did not yield signicant results for any frequency band denition and phase shi (all
p > 0.05; see Table1).
To further examine the signicant main eect of factor repetition in the experimental group, paired t-tests
were computed for each frequency band denition and phase threshold. e LF_Ke band showed for
Rφ>π/4
,
Rφ>3π/8
, and
Rφ>π/2
a signicant increase from stage 1 to 7 aer Bonferroni correction (p < 0.0125). e LF_
Pf band showed a signicant increase from stage 1 to 7 for
Rφ>π/4
and
Rφ>3π/8
at p < 0.05 and
Rφ>π/2
aer
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Bonferroni correction (p < 0.0125). Furthermore, the increase from stage 1 to 7 was signicant at p < 0.05 for
Rφ>3π/8
, and
Rφ>π/2
. Further paired t-tests showed a signicantly higher phase desynchronization during CPT
compared to AWT at p < 0.05 for LF_Ke at
φ>3π/8
and
φ > π/2
threshold as well as for LF_Pf at
φ > π/2
.
is indicates that CPT aected phase desynchronization particularly in the low frequency range.
Further 2 (LF and IM band for each frequency denition) × 7 (Repetition) repeated measures ANOVAs were
computed for the control group. Neither the main eects of factor repetition and band nor the interaction of
repetition × band showed a signicant eect for any threshold (all p > 0.05; see Table2). However, descriptively,
the IM band denitions displayed an increase of phase desynchronization across stages pointing at a possible
time eect (see Fig.17).
Figure12. Spatial phase shi distribution matrices indexing desynchronization for low and intermediate
frequency (LF, and IM, resp.) bands according to boundaries used by Pfurtscheller (Pf, le column) or Keller
(Ke, right column) for individual participants (horizontal lines of squares) control and random groups.
EO = eyes open, EC = eyes closed; orange bar at top: cold water test, blue bar at top: ambient water test. From
top to bottom, colour coded points display thresholds for relative phase shi intervals from π/4rad to π rad,
3π/8rad to π rad, and π/2rad to π rad: dark blue < blue < green < yellow. Red indexing counterphase with the
reference.
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Figure13. Phase desynchronization for dierent thresholds for main and control groups in the IM_Pf band
(0.1Hz–0.15Hz) including 0.1Hz activity. ere were only few oscillations in the main group. e increases in
phase desynchronization due to CPT were of magnitudes comparable to other non-experimental oscillations. In
controls, few prominent spontaneous oscillations. In both groups, phase desynchronization increased over time.
Levels of phase desynchronization were π/4 > 3π/8 > π/2rad in both groups. Red: median curve, black vertical
lines: stages of the experiment, grey area bounds: 25th and 75th percentiles; blue dashed lines: min and max
values.
Figure14. Phase desynchronization for dierent thresholds for main and control groups in the IM_Ke band
(0.12Hz–0.18Hz) excluding 0.1Hz activity. In the main group, there were hardly any obvious responses to
CPT. is group showed also only a slight increase of phase desynchronizations over time. Of note, the control
group exhibits for all phase thresholds distinct peaks in phase desynchronizations of approx. 100s length at
minute 4 and 11. Phase desynchronizations increased distinctly at the end of the recordings in 3π/8 and π/2
thresholds. Red: median curve, black vertical lines: stages of the experiment, grey area bounds: 25th and 75th
percentiles; blue dashed lines: min and max values.
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Figure15. Phase desynchronization for dierent thresholds for main and control groups in the LF_Pf band
(0.05Hz–0.1Hz) possibly curtailing 0.1Hz activity. In the main group, few pronounced oscillations; the level
of phase desynchronization decreased with each threshold. Comparable course of phase desynchronizations
in all thresholds for CPT: stable course during CPT, rapid increases, slow decreases for about 3min. Few
dierently pronounced oscillations of shorter frequency and amplitude in all 3 thresholds. EO (stage 7)
accompanied by hardly any changes in phase desynchronization. Stable conditions in the control group:
distinct oscillations approx. every 7min, most pronounced at π/4 > 3π/8 > π/2rad. No evidence of increases in
phase desynchronization with time. Red: median curve, black vertical lines: stages of the experiment, grey area
bounds: 25th and 75th percentiles; blue dashed lines: min and max values.
Figure16. Phase desynchronization for dierent thresholds for all groups in the LF_Ke band
(0.05Hz–0.12Hz) completely including 0.1Hz activity. Widely identical conditions in the main group as in the
LF_PF frequency band. Phase desynchronizations in all thresholds for CPT as in LF_Pf frequency band. Stable
course during CPT, rapid increases, slow decreases for about 3min. Here no oscillations of higher frequency
and amplitude. Increases of phase desynchronizations with time in all thresholds. In controls oscillations of
comparable period duration, yet of dierent dynamics: steep rising edges followed by slow continuous activity
(8min, 12min, 17 min). No increases with time in controls. Red: median curve, black vertical lines: stages of the
experiment, grey area bounds: 25th and 75th percentiles; blue dashed lines: min and max values.
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Bar graph analysis underpins these ndings. In both LF bands there is a general trend of increasing phase
desynchronization over time from stage 1 to 7 in
Rφ>π/4
. For
Rφ>3π/8
and for
Rφ>π/2
this is shown also in
IM_Ke. ere is a signicant dierence between AWT and CPT for LF_PF and LF_Ke (Fig.18).
Discussion and conclusion
In this study we present an innovative method for the phase shi analysis of cutaneous tissue perfusion that
appears promising to assess ANS change processes related to physical or psychological stress. Non-contact
mapping of forehead skin perfusion was used to detect spatial phase changes in photoplethysmography imaging
(PPGI) data. irteen healthy participants were exposed to an ambient/cold pressure water test (AWT, CPT)
in randomized order with intermittent resting blocks and compared to three time-control participants who
underwent no intervention. Relative phase desynchronization was investigated using three dierent thresholds
Table 1. Repeated measures ANOVAs in experimental groups (N = 13) for dierent thresholds and frequency
band denitions.
reshold Parameter Source F P
φ > π/4
LF_Pf
IM_Pf
Repetition 3.57 0.004
Band 0.003 0.96
Repetition × Band 1.46 0.20
LF_Ke
IM_Ke
Repetition 3.66 0.03
Band 1.26 0.28
Repetition × Band 0.91 0.50
φ>3π/8
LF_Pf
IM_Pf
Repetition 4.25 0.001
Band 0.04 0.85
Repetition × Band 1.39 0.23
LF_Ke
IM_Ke
Repetition 3.94 0.002
Band 0.83 0.38
Repetition × Band 0.64 0.70
φ > π/2
LF_Pf
IM_Pf
Repetition 4.203 0.013
Band 0.025 0.878
Repetition × Band 0.81 0.57
LF_Ke
IM_Ke
Repetition 3.93 0.022
Band 0.39 0.54
Repetition × Band 0.61 0.73
Table 2. Repeated measures ANOVAs in control group (N = 3) for dierent thresholds and frequency band
denitions.
reshold Parameter Source F p
ϕ > π⁄4
LF_Pf
IM_Pf
Repetition 0.62 0.71
Band 1.38 0.36
Repetition × Band 1.04 0.45
LF_Ke
IM_Ke
Repetition 0.51 0.79
Band 0.05 0.85
Repetition × Band 2.78 0.06
ϕ > 3π⁄8
LF_Pf
IM_Pf
Repetition 0.43 0.85
Band 1.66 0.33
Repetition × Band 2.01 0.14
LF_Ke
IM_Ke
Repetition 1.09 0.42
Band 2.02 0.29
Repetition × Band 2.5 0.08
ϕ > π⁄2
LF_Pf
IM_Pf
Repetition 0.52 0.79
Band 0.61 0.52
Repetition × Band 2.59 0.08
LF_Ke
IM_Ke
Repetition 1.76 0.32
Band 1.76 0.19
Repetition × Band 1.00 0.46
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(
φ > π/4
,
φ>3π/8
, and
φ > π/2
). PPGI data was initially ltered using pooled low frequency (LF) and inter-
mediate (IM) frequencies (data not shown). is, however, did not supply sucient sensitivity for the detection
of experimental changes. Following recent evidence showing that LF band activity is better explained by using
two subcomponents, data was ltered based on frequency boundaries dened by Pfurtscheller46 and Keller27.
Pfurtscheller etal. suggested to separate LF bands as LFa: 0.05Hz–0.1Hz (referred to by us as LF_Pf), and LFb:
0.1Hz–0.15Hz, whereas Keller etal., used LF_Ke (0.05Hz–0.12Hz) as well as and IM_Ke (0.12Hz–0.18Hz)
bands. us, Keller LF boundaries included all 0.1Hz activity reported to exhibit individual variation between
0.075Hz and 0.12 Hz26, which therefore LF_Pf might fall short to reect. In the same vein, IM_Pf may confound
IM activity by including 0.1Hz activity, which is excluded when starting IM boundaries at 0.12Hz. Overall, we
observed an increase of phase desynchronization throughout the measurement for both LF and IM frequency
band denitions in the experimental group and for all phase shi thresholds. A non-signicant increase in IM
bands of the control group suggests this increase be related to time eects in this frequency range.
CPT compared to AWT signicantly enhanced phase desynchronization in both LF bands, though to a larger
extent for LF_Ke. Spontaneous increases at seemingly regular intervals unrelated to intervention observed in the
control group may indeed indicate that phase desynchronizations were specic for the LF_Pf and LF_Ke bands
during CPT. is nding is also of relevance since it supports the notion that the LF_Ke band includes 0.1Hz
activity to a larger extent. Yet, there is ample evidence that LF frequencies reect activity of dierent physiological
processes. At profound rest, it was shown to contain subharmonics of primary IM band activity13. It has been
much disputed that conventional LF represents also sympathetic activity47. erefore, measures such as the ratio
between LF and HF supposedly indexing autonomic balance have been challenged long8,48 and investigating
subcomponents of the LF band seems crucial for understanding autonomic dynamics.
Malpas already pointed out that “one must use care in relating changes in the strength of an oscillation in
blood pressure and heart rate as denitively due to a change in autonomic control”. But even for ANS con-
trol, there are still not all questions suciently resolved. Slow oscillations at 0.1Hz may represent primarily
Figure17. Bar graphs of phase desynchronization for LF and IM frequency band denitions based on
Pfurtscheller (Pf) and Keller (Ke), and dierent thresholds in the main group (N = 13). (A) Ratio
Rφ>π/4
shows
a general increasing trend of phase desynchronization and a signicant increase from stage 1 to 7 for LF_Pf and
LF_Ke. (B) Ratio
Rφ>
3
π/
8 showing general increasing trend throughout measurement and signicant increase
from stage 1 to 7 for IM_Ke, LF_Pf and LF_Ke exhibit signicantly higher phase desynchronization during CPT.
(C) Ratio
Rφ>π/2
showing general increasing trend and signicant increase from stage 1 to 7 for IM_Ke, LF_Pf
and LF_Ke. ere is a signicant dierence between AWT and CPT for LF_PF and LF_Ke. Asterisks indicate (*)
p-value < .05 or (**) p-value signicant aer Bonferroni correction at p < .0125. Error bars show standard error of
the mean.
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baroreceptor-mediated blood pressure regulation via sympathetic nerve bres47. However, other authors con-
vincingly demonstrated 0.1Hz oscillations in HRV might rather reect activity of the unmyelinated vagus nerve
originating in the dorsal lateral vagal complex49, which was supported by ndings that those oscillations were
abolished by vagal blockade but only little unaected by sympathetic blockade50. Following other authors who
presented a model of frequency-power distribution in skin blood ow6, we herewith seem to be able to provide
a promising approach to the methodological toolbox needed to improve capturing dynamic ANS regulation on
the level of the skin.
According to von Holst51, relative coordination is the rule in biological systems, while absolute coordination is
the exception. Further, frequency and amplitude responses to various stressors have long been known to exhibit
great variation51. is has been conrmed more recently in multiple skin locations for IM band frequencies
showing great variation with respect to presence of IM band52. is has led to the description of these opera-
tions as the meshing of cogs and the observed frequencies as clanking of the cogs53. erefore, a more recent
study suggested to include ideally a minimum of 2 biological systems in parallel when studying cardiovascular
system oscillations54.
In general, the coordination of blood ow and intravascular blood volume mandatory for intravascular blood
pressure may alter with changes in windkessel properties or with local redistribution of blood ow. is may
result in delays reected as phase dierences detected e.g., in cutaneous blood ow. In hard vessels this phase
dierence may be very small or vanish altogether, whereas so (dilatated) vessels may exhibit ’large’ phase dif-
ference. Shiing phases may therefore allow to infer changes in vascular tone. In PPG signals, this may index
changes in the tone of pre- and postcapillary sphincters, arterioles or venioles. Given the prominent function of
skin temperature regulation, cold pressure test may have had a signicant impact.
When combined with established high-resolution algorithms for the analysis of frequencies (e.g., continu-
ous wavelet scalograms), our novel methodology presented here on high resolution of dynamic phase changes
should greatly expand and therefore improve the study of rhythmic coordination processes. e improvement
comes with transforming the time-domain PPGI signal into an instantaneous phase waveform using the Hilbert
transform. Furthermore, the advantage of the non-contact and camera-based approach allows for high spatial
resolution of blood volume changes in cutaneous tissues. e matrix of PPGI signals transformed into a matrix of
instantaneous phases contained colour coded information on phases relative to the reference point. Determining
Figure18. Phase desynchronization for LF and IM frequency band denitions based on Pfurtscheller (Pf) and
Keller (Ke), and dierent thresholds in the control group (N = 3). R atio
Rφ>π/
4 , (B)
Rφ>
3
π/
8 and (C)
Rφ>π/
2
shows a general increasing trend of phase desynchronization, however, no signicant eects. Error bars show
standard error of the mean.
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the number of points of phase shis on the forehead region exceeding a predened threshold, allowed evaluation
of ANS responses found to be sensitive and capable of determining the state of the subject’s autonomic system.
is is supported by our control group which, however, due to its small sample size should be viewed with
caution. e control group showed a clear increase for IM band phase desynchronizations by the end of the
experimental session which may be related to the duration of relaxation experienced as tedious since the optimal
duration of relaxation should be limited to 7 min55. is is reason to assume the present methodology ideally
sensitive for the analysis of cutaneous responses qualifying it as a complementary tool for non-invasive diagnosis
compared to other evaluation methods, e.g., in the spectral amplitude domain56,57, or time-domain analysis58.
Our current results rest on analysis of primary cutaneous blood ow rhythmicity. More recently, PPG signals
frequently served as an undemanding source for the study of rhythms related to cardiac and respiratory activ-
ity (see59). On the other hand, methods such as laser Doppler devices proved valuable in physiological studies
investigating frequency response characteristics of sympathetically mediated vasomotor activity60. Analysis of
phase responses are of sound physiological relevance since changes observed in the frequency domain have
been burdened by various shortcomings. Among the most important ones are inherent frequency variations
or instabilities in biological systems. In systems with low complexity such as medulla sh, inherent frequency
variations may amount up to 35% of variation in either direction51, and up to 20% in humans reported in osteo-
pathic medicine61.
e current ndings present a novel technological approach of investigating phase changes in PPGI data.
However, reliability of ndings should further be investigated in larger samples to dierentiate e.g. the long-
disputed 0.1Hz activity in the contexts of LF and IM bands. Furthermore, a variety of physiological factors
are known to modulate cardiovascular oscillations. ese include the hormonal circuits (HPA axis) regulating
blood volume, blood pressure, and vascular tone (renin—angiotensin system; epinephrine and norepinephrine;
etc.). Some of these factors can be partly inuenced by experimental paradigms, e.g., orthostasis stress (tilt table
experiments), physical activity, mental activity (arithmetic tests). Other factors require testing specic patient
populations to investigate deviations from physiologic controls. Furthermore, in the present study, we used PPG
of the center of the forehead as a reference. In further studies, however, e.g., respiration should be included,
since blood ow to the skin and respiration are known to interact intensively6. Lastly, physiological changes
should be investigated only in a psychometrically validated manner. Essentially, the results of Keller etal. on
peripheral 0.15Hz activity demonstrate the urgent need to interpret physiological measurements with respect
to interoceptive processes. is has also been demonstrated by recent results of Pfurtscheller etal. who showed
that dierent levels of fear processing occur at LFa and LFb26. Questionnaires such as the Multidimensional
Assessment of Interoceptive Awareness62 or the state and trait anxiety questionnaire63 are important tools for
psychophysiological interpretation of phase analyses.
Outlook. ANS responses at the full scale should be studied further using spatial phase changes as a highly
promising method. It will undoubtedly be worthwhile to further investigate these phenomena through a series
of additional, comprehensive experiments that could help develop a highly eective tool for evaluating ANS
responses. is will eventually help our understanding of the still enigmatic concert of physiological rhythms.
Received: 13 September 2021; Accepted: 24 March 2022
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Acknowledgements
is work was supported by the National Scholarship Programme of the Slovak Republic (Application No. 29417).
Dr. Volker Perlitz and Micha Keller received nancial support from the HEAD Genuit Foundation, Herzogen-
rath/Germany, grant number: HGS-03S-18072016. e authors are indebted to Prof. Dr. Dipl.-Ing. Reinhard
Grebe, Babeuf/France for his valuable assistance in the writing of the reviewed manuscript.
Author contributions
Conceptualization—S.B., S.L., V.P., V.B.; Data curation—S.B., S.L.; Formal analysis—S.B., M.K.; Investigation—
S.B., S.L.; Methodology—S.B., V.P., V.B.; Resources—St.L., V.B.; Soware—S.B., S.L.; Supervision—V.B.; Vali-
dation—S.L., V.P., M.K., St.L., V.B.; Visualization—S.B., S.L.; Writing—original dra—S.B., S.L., V.P.; Writing—
review and editing—S.B., S.L., V.P., M.K., St.L., V.B.
Funding
Open Access funding enabled and organized by Projekt DEAL.
Competing interests
e authors declare no competing interests.
Additional information
Correspondence and requests for materials should be addressed to S.B.
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