Cerebral Cortex Advance Access originally published online on August 14, 2006
Cerebral Cortex 2007 17(6):1386-1393; doi:10.1093/cercor/bhl049
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Epileptogenic Neocortical Networks Are Revealed by Abnormal Temporal Dynamics in Seizure-Free Subdural EEG
1 BioMag-Laboratory, 2 Department of Clinical Neurophysiology, Helsinki University Central Hospital, Finland, 3 Regional Epilepsy Center, Harborview Medical Center, University of Washington, Seattle, WA, USA, 4 Department of Biological and Environmental Sciences, University of Helsinki, Finland
Address correspondence to Simo Monto, BioMag-laboratory, PO Box 340, FIN-00029 HUS, Finland. Email: smonto{at}cc.hut.fi.
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Abstract |
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Long-term video electroencephalographic (EEG) recording is currently a routine procedure in the presurgical evaluation of localization-related epilepsies. Cortical epileptogenic zone is usually localized from ictal recordings with intracranial electrodes, causing a significant burden to patients and health care. Growing literature suggests that epileptogenic networks exhibit aberrant dynamics also during seizure-free periods. We examined if neocortical epileptogenic regions can be circumscribed by quantifying local long-range temporal (auto-)correlations (LRTC) with detrended fluctuation analysis of seizure-free ongoing subdural EEG activity in 4 frequency bands in 5 patients. We show here with subdural EEG recordings that the LRTC are abnormally strong near the seizure onset area. This effect was most salient in neocortical oscillations in the beta frequency band (14–30 Hz). Moreover, lorazepam, a widely used antiepileptic drug, exerted contrasting effects on LRTC (n = 2): lorazepam attenuated beta-band LRTC near the epileptic focus, whereas it strengthened LRTC in other cortical areas. Our findings demonstrate that interictal neuronal network activity near the focus of seizure onset has pathologically strong intrinsic temporal correlations. The observed effect by lorazepam on beta-band activity suggests that the antiepileptic mechanism of benzodiazepines may be related to the normalization of LRTC within the epileptic focus. We propose that this method may become a promising candidate for routine invasive and noninvasive presurgical localization of epileptic foci.
Key Words: benzodiazepines • focus localization • intracranial EEG • long-range temporal correlations • presurgical evaluation
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Introduction |
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Surgical resection of the epileptogenic brain tissue is currently a standard therapeutic option for treating patients with drug-resistant, localization-related epilepsy. A major challenge here, however, is the presurgical determination of the brain region that gives rise to seizure activity. At present, presurgical evaluation invariably involves long-term video electroencephalographic (EEG) monitoring with scalp electrodes, which is often followed by further recordings with intracranial electrodes. The epileptogenic focus is localized by identifying the cortical areas where the seizures are observed to be initiated (Wyllie 1997
). Nevertheless, in the case of neocortical epilepsies, localization of the epileptic focus can be problematical even with intracranial electrodes. This practice necessitates successful EEG acquisition of several clinical seizures considered typical for the given patient, which often prolongs the recording session up to 2 weeks and involves economic burden and risks of complications (Benbadis and others 1997). Therefore, various approaches have been tested to shorten the recording time either by lowering the seizure threshold (e.g., by drug withdrawal) or by determining the epileptogenic area from interictal epileptiform events (IIEs) (see Luders 1992; Miller and Silbergeld 2005).
Neuroimaging and neuropathology of epileptic brains have established that epileptic foci typically involve structural abnormalities and altered levels of brain metabolism even in the interictal period (Richardson 2001). Ongoing neuronal activity is characterized by large fluctuations in amplitude and synchrony throughout a wide range of frequencies (Buzsáki and Draguhn 2004; Vanhatalo and others 2004; Palva and others 2005). Yet, ongoing oscillations are remarkably stable dynamically (Freeman and others 2006). In epileptic brain areas, however, the presence of intermittent abnormalities, interictal events, and of course seizures suggest a defect in stability (Timofeev and Steriade 2004; Parra and others 2005). This run-away excitation is associated with supercriticality when viewed as a branching process in a neuronal network (Beggs and Plenz 2003). Hence, it might be possible to identify the epileptogenic networks by using analysis methods sensitive to large-scale statistical structure of ongoing activity.
We tested the idea that quantification of long-range temporal correlations (LRTC) of the interictal subdural EEG activity could be used to localize the epileptogenic cortical areas. Prior studies on human hippocampal depth electrode recordings have suggested that an analysis of this kind may reveal the affected hemisphere in temporal lobe epilepsy (Parish and others 2004). We recorded spontaneous neocortical EEG activity with subdural electrode grids and quantified the LRTC using detrended fluctuation analysis (DFA) (Peng and others 1995). This technique is known to be suitable for nonstationary and patchy data and effective in detecting scale-free amplitude dynamics (Linkenkaer-Hansen and others 2001; Nikulin and Brismar 2004) or fluctuations of global synchronization (Stam and de Bruin 2004) in the brain. Scale-free dynamics are often considered a hallmark of self-organized criticality. If epileptogenic networks are indeed supercritical, the DFA exponent resulting from this analysis is expected to be enhanced in epileptic regions.
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Materials and Methods |
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Subjects and Data Acquisition
Five patients (aged 22–51 years, 2 males) with medically refractory neocortical epilepsy underwent long-term intracranial video EEG recording (Nicolet BMSI, WI) as a part of their presurgical evaluation (Regional Epilepsy Center, University of Washington, Seattle, WA). The electrode grids (Ad-Tech Medical Instrument Corporation, WI) consisted of platinum electrode pads (diameter 4 mm, interelectrode distance 10 mm), with the number of electrodes in a grid ranging from 45 to 64. To investigate the spatial distribution of DFA exponents along the cortex, we selected 5 consecutive patients recorded with grid electrodes and whose seizure activity started unequivocally within the grid area. See Figure 3A for grid placement and conventionally determined seizure onset localization. We analyzed ongoing activity during seizure-free periods when the patients were awake and had eyes closed in a silent room. The lengths of the time series analyzed were 1563, 1129, 1711, 1394, and 1800 s for patients #1, #2, #3, #4, and #5, respectively. Additional data were recorded in the same condition under benzodiazepine influence from 2 of the patients (#3 and #4, data length 1370 and 1352 s, respectively) 2 and 6 h after intravenous administration of 2 mg of lorazepam. The data were referenced to a scalp electrode and digitized at 200 Hz. Further analyses were performed off-line on a custom-made analysis platform programmed in the LabView environment (National Instruments, TX). The study was approved by the University of Washington Human Subjects Review Committee.
Signal Processing
Visual Preprosessing
The EEG recordings were carefully reviewed by a clinical neurophysiologist to exclude the possibility of ictal activity during the collected epochs. Occasional interictal events (IIE) could be found in several channels in most of the patients, but these discharges were very brief in duration and not localized to the epileptic focus. In 2 patients (#1 and #3), interictal spikes were found in few channels outside the epileptogenic area. In another 2 patients (#2 and #4), prominent, nonlocalizing slow activity in the delta/alpha frequency range was observed. Rare, brief, and spatially widely distributed spike trains were found in one patient (#5), including the epileptogenic focus.
Filtering
The data were band-pass filtered with pairs of high-pass and low-pass finite impulse response (FIR) filters. The selected frequency bands roughly correspond to the traditional EEG bands of delta, alpha, and beta, and an additional broadband (BB). For the 3 narrow-band filters, the center frequencies were 2.5, 8, and 22 Hz, and the stop frequencies were 1/6.25, 4/16, and 11/44 Hz, respectively. For the high-pass and the low-pass components of the BB filter, the stop frequencies were 3 and 48 Hz, and the pass frequency for both was 12 Hz. These specifications resulted in logarithmically symmetric frequency responses with –40 dB attenuation at stop frequencies. Figure 1C shows the frequency responses of the filters, along with a power spectrum of a typical subdural EEG signal. Figure 1D displays a 5-s segment of raw signal, overlaid with the amplitude envelope of alpha-band activity. We derived 2 different time series from these data to calculate the DFA exponents: the amplitude envelope, obtained via the Hilbert transform, and the energy (square) of the narrow-band signal. The 2 approaches gave similar results, the ones presented below are based on the energy of the filtered signal.
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), alpha (Detrended Fluctuation Analysis
Our DFA algorithm, slightly modified from what has been used previously (Peng and others 1995; Linkenkaer-Hansen and others 2001), starts by selecting a number of window sizes or timescales 
, here ranging from 1 to 100 s. The window lengths are distributed evenly in logarithmic scale (7 windows per decade). Within each window, the signal is integrated and linearly detrended. From the resulting time series, the root-mean-square (RMS) variation in each window is calculated, followed by determination of the typical fluctuation <F> in the given timescale i, which is given by the median of RMS variation over the windows of length i (Fig. 2A). The rationale of using median instead of mean is to exclude the possible effects of large-amplitude artifacts that influence the median negligibly but may bias the mean considerably. The median fluctuations <F> are then plotted against window sizes to evaluate whether the data obey the power law <F> 
, where is called the scaling (or critical) exponent. Taking logarithms from both sides of the power-law equation yield log(<F>) = log(). Hence, in double-logarithmic coordinates, power law is a linear function with slope (see Fig. 2B). We used a least-squares linear fit to estimate . Values of 0.5 < < 1 imply self-similarity and LRTC of amplitude fluctuations. The case of = 0.5 corresponds to an uncorrelated signal (i.e., white noise) and = 1 to 1/f-type of signal.
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Deviations from Power-Law Behavior
For each , we assessed the deviation from the power law <F> by a "parabolicity index," b, that was given by b = 1–E2/E1, where E1 is the mean-squared error (MSE) of the linear (first-order polynomial) least-squares fit and E2 the MSE of the parabolic (second-order polynomial) fit in double-logarithmic coordinates (Fig. 5). The values of b range from 0 to 1. For data having a small linear fit error E1, the parabolicity index b is low as well. For large E1, b is small (close to zero) when the data have basically linear behavior (in double-logarithmic scale), that is, fluctuations obey power law but with low statistical power. On the other hand, the index b could be close to one if data did not indicate power-law scaling of fluctuations.
Statistical Analysis
The exponent data were rescaled separately for each patient and frequency band for easier comparison of the distributions. The new values were defined as ' = ( – µ)/
, where is the original exponent from DFA, µ is the mean exponent over channels, and is the standard deviation (SD) of the set of exponents (sample size equals number of channels, 45 
n 64). The SD was determined as half of the range between the 16th and the 84th percentiles of the exponent probability distribution. The sensitivity of the parameters (, E1, b) to the epileptogenic zone was quantified by the slope of a linear fit to a plot of the parameter versus distance to seizure focus.
We performed linear correlation analysis to search for possible interdependencies between DFA exponents , modeling errors b, narrow-band amplitude A, and distance from the focus d. This analysis gives the strength of correlation r, as well as the probability P that given correlation arises by chance. The P values were Bonferroni corrected (multiplied with n) to account for multiple tests. The limit for significance was P < 0.05 throughout the study.
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Results |
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Clinical Findings
The seizure onset zones were clinically determined from long-term (4–14 days) intracranial recordings by a board certified electroencephalographer (M.D.H.). Their extent varied from an area covered by 2–6 grid electrodes (see Fig. 3A). As the patients were operated after the presurgical evaluation period, we were able to use both presurgical localization of the epileptic area and the postsurgical outcome as the references for evaluating our DFA-based localization results. Magnetic resonance imaging (MRI) data were available for all patients. An MRI lesion was found in 4 patients (#2–#5) (Fig. 3A). The lesions were closely correlated with the clinically determined epileptogenic zones. The outcome from epileptic surgery was good for all the 5 patients: 3 patients were free of seizures, and in the other 2 patients (#1 and #2), the seizures were significantly reduced (by more than 75% and 90%, respectively) after a postoperative period of 23–34 months.
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LRTC in Subdural EEG
We band-pass filtered the subdural EEG (Fig. 1A,B) to 3 narrow bands (delta, alpha, and beta) and one BB (Fig. 1C,D; see Materials and Methods for details) and used DFA to evaluate the scaling behavior and LRTC in the ongoing cortical activity in these frequency bands in timescales of 1–100 s. Log–log linearity in the DFA indicates power-law scaling behavior in the data, and the DFA scaling exponent quantifies the strength of LRTC (see Materials and Methods).
For electrode contacts on cortical regions far from the epileptic area, we found that ongoing activity in all frequency bands showed robust scaling behavior with = 0.68 ± 0.07 (mean ± SD, nchannels = 278, nsubjects = 5). This corroborates the scaling observed in scalp-recorded EEG and magnetoencephalography (MEG) and shows that the scaling exponents of these oscillations are very similar regardless of the scale of inspection (subdural electrode vs. scalp EEG/MEG) (Linkenkaer-Hansen and others 2001; Nikulin and Brismar 2004). To confirm that the observed scaling was not produced by an uncorrelated noise process, we created a set of control data (n = 278, length 1800 s) from white noise, which were analyzed by the same procedures as real data. The mean and the 99th percentile of the surrogate exponents were µ,s = 0.62 and 99 = 0.65 for delta band, µ,s = 0.55 and 99 = 0.58 for alpha band, µ,s = 0.52 and 99 = 0.55 for the beta band, and µ,s = 0.51 and 99 = 0.54 for the BB. These values are significantly lower than those observed for real data (cf., Fig. 3C).
In all patients, we found regions of stronger and weaker LRTC in the grid area. The exponents remained in the interval of 0.5 < < 1, as expected for LRTC of power law form, and observed for numerous complex systems. We then visualized the DFA exponents over the electrode grid for each patient and frequency band (Fig. 3). Already a visual inspection showed that the highest exponents were found near the clinically determined epileptic regions. To consolidate this finding, we plotted the exponents as a function of distance to the clinically determined epileptic focus (Fig. 3B). Correlation analyses confirmed highly significant correlations between the magnitude of DFA exponents and the distance from the epileptogenic area. This effect was present in all patients and in 9 of 20 pairs of patient and frequency band (mean correlation coefficient r = –0.41 ± 0.38, mean significance P = 0.008 ± 0.016, Bonferroni corrected with n = 4, see Materials and Methods).
Of the 4 frequency bands, the LRTC in the beta band were most consistently enhanced close to the seizure focus in every patient (r = –0.46 ± 0.16, P = 0.009 ± 0.015, n = 1) (Fig. 3B,C). The LRTCs in the alpha band, on the other hand, were found to have a spatial distribution distinct from the other frequency bands (Fig. 3). Interestingly, the spatial distribution of alpha-band DFA exponents was uncorrelated with the locus of seizure onset region (r = –0.13 ± 0.34, P = 0.11 ± 0.14, n = 1). We found that combining the information from DFA exponents in multiple bands, for example, by straightforward subtraction, may notably improve the precision of localization. This was especially true when alpha-band exponents were subtracted from the exponents in higher bands (Fig. 4). These results demonstrate that neuronal network activity in specific frequency bands, in the beta band in particular, is relevant to the mechanisms of seizure generation in epilepsy.
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Scaling Behavior in the Epileptogenic Area
The median RMS values in DFA were not always linearly dependent on the window size (in double-logarithmic coordinates), indicating that the data did not always show unequivocal power-law scaling behavior (cf., Linkenkaer-Hansen and others 2001; Parish and others 2004) (Fig. 5A). Hence, for all data, we estimated this deviation from power law with a parabolicity index, b (see Materials and Methods). This analysis is complementary to the DFA exponents because the exponents do not accurately characterize brain activity if a power law models poorly the scaling of fluctuations across timescales. Power-law fluctuations in physiological neuronal activity are robust and prominent, but the presence of scaling behavior in pathological brain activity has been less thoroughly investigated. Recent studies, however, have revealed attenuated scaling behavior of theta-band amplitude fluctuations in depression (Linkenkaer-Hansen and others 2005) and of mean global synchronization in Alzheimer's disease (Stam and others 2005).
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We found that in 6 out of 20 cases (5 patients x 4 frequency bands), the correlation between the parabolicity index b and the distance-to-focus d was statistically significant (r = 0.44 ± 0.10, P = 0.015 ± 0.017, n = 4). In each of these cases, the largest values of b were found close to the epileptic focus (Fig. 5C). However, a comparison of localization accuracies of indices b and
showed that the parabolicity index is a weaker indicator of the location of the epileptic focus than the exponent (see Fig. 5B). Nonpower-law behavior in the epileptic region was typically seen in BB data. Notably, the deviations from power law were least significant in the beta band.
Theoretically, a preferential concentration of fitting errors near the seizure focus could contribute to focus localization ability of LRTC. This is, however, unlikely, because correlation analysis between the exponent and the parabolicity index b revealed that the two were significantly correlated only in 4 cases out of 20 (r = –0.52 ± 0.037, P = 0.005 ± 0.005, n = 20). This dependence arose almost solely (3 of 4 cases) in the BB data; and b thus were independent in the beta-band data.
Effect of an Antiepileptic Drug on LRTCs
Two of the patients (#3 and #4) underwent an additional recording with 2 mg of lorazepam, a widely used antiepileptic drug, administered intravenously before the recording session. These recordings were performed in the same conditions and the data were processed by the same way as described above. We asked whether the antiepileptic effect of lorazepam medication would be reflected in LRTC.
A comparison of DFA exponents before and after lorazepam administration showed that lorazepam enhanced the DFA exponents in most parts of the cortex. Strikingly, however, lorazepam attenuated the exponents in areas closest to the epileptic focus. Correlation analyses showed that especially in the beta band, this intercondition difference in DFA exponents was strongly correlated with the distance from the focus (subject #3: r = 0.47, P = 0.0002; subject #4: r = 0.62, P < 0.00001; Fig. 6). In other frequencies, the effect was similar but far less or not at all significant.
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Effect of Signal Amplitude
The recordings used in this study were examined by a clinical neurophysiologist (S.V.) to exclude ictal epileptiform activity or technical artifacts. Mean signal amplitude, however, could have an impact on calculated exponents through influencing the signal-to-noise ratio (SNR). This is because the ambient noise biases the exponents toward = 0.5 of uncorrelated noise. To evaluate whether the SNR was an issue in our data, we plotted the amplitude–exponent pairs from all patients, channels, and frequencies (Fig. 7). The distribution was roughly spherical, and only in 1 out of 20 subject–frequency band pairs did we observe a correlation between the DFA exponent and signal amplitude (alpha band of subject #2, P < 0.0004). Thus, the DFA exponents can be considered largely independent of signal amplitude in our study, which is in line with the excellent SNR of subdurally recorded EEG.
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To further corroborate the importance of LRTC in localization of the epileptic focus, we correlated the mean amplitude in each frequency band with the distance to focus. We found that they were correlated in 8 of 20 pairs of patient and frequency band. However, the significances of correlations were remarkably lower, often for several orders of magnitude, than for correlation of LRTC with the distance to focus. In addition, in 5 cases the correlation was positive and in 3 cases negative. The correlations also were distributed to all frequency bands. Thus, the mean amplitude of oscillations is not suitable for use as an indicator of the epileptic focus.
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Discussion |
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To the best of our knowledge, this is the first report of LRTC in subdurally recorded human EEG. We observed robust scaling behavior throughout the inspected frequency range in all subjects. Interestingly, the scaling exponents in our direct cortical recordings were quantitatively very close to those recorded noninvasively from the human brain. Furthermore, we showed that highly significant, albeit visually nondetectable, features in cortical activity revealed by estimation of LRTC separate epileptic from healthy areas with centimeter precision. The observed spread of abnormally large long-range correlations suggests that the epileptic focus is associated with significant changes in network behavior even in the cortical areas immediately surrounding the clinically determined focus. The enhancement of LRTCs observed in this study may either reflect a compensatory mechanism around the ictal focus or be a persistent abnormality in this network due to exposure of the neuronal networks to epileptic activity. The change may reflect permanent functional pathology independent of other features of ongoing activity, such as amplitude or synchrony of oscillations. In addition, we found that specific frequencies were sensitive to the epileptic focus (beta band), whereas others were not (alpha band). This finding suggests that the epileptic condition affects the activity in neuronal networks in a frequency-specific manner.
Present study is based on the idea that the brain shows properties typical of self-organizing complex systems (Bak and others 1988; Freeman 2005). These properties include scaling and LRTC of healthy human cortical activity (Linkenkaer-Hansen and others 2001), and scaling behavior in epileptic hippocampus (Worrell and others 2002), as well as power-law scaling and avalanche-like dynamics in mammalian brain both in vitro (Jung and others 1998; Beggs and Plenz 2003) and in vivo (Leopold and others 2003).
Epileptic Processes and LRTC
Unlike the phasic and, hence, temporally limited epileptiform phenomena (interictal and ictal events), LRTC do not arise from an instantaneous state of the cortex, but rather describe longer term statistical properties of ongoing activity in large-scale neuronal networks. Here we quantified LRTC using DFA, in which larger values of the scaling exponent indicate stronger (auto)correlations in the timescales where the power-law assumption is valid, approximately 1–100 s in our data (Peng and others 1995).
Physiologically, pronounced temporal correlations may result from clustering of periods of oscillatory activity, in a way that a period of high level of activity is more probably followed by another such period. This effect has a major impact on network stability, a central concept in epilepsy research for decades, as high amplitude oscillations reflect coordinated neuronal synchronization. Therefore, clustering of strong oscillatory activity may point to a link between increased LRTC and susceptibility to seizure initiation. Furthermore, our observation opens new perspectives to mechanisms of seizure prevention. The antiepileptic effect of benzodiazepines seems to be related to neuronal dynamics that is adjusted in a spatially and spectrally selective manner. The drop in LRTC in beta frequency activity in the seizure-generating zone is a system-level consequence of drug-induced low-level changes. Some effects of lorazepam have been previously documented in humans, but they have been of global nature (Link and others 1991; Schreckenberger and others 2004; Jensen and others 2005).
One possible explanation for inverted effect of lorazepam in the epileptic focus is the altered function of 
-aminobutyric acidergic (GABAergic) cells, most likely interneurons (Cossart and others 2005). The neuronal networks are known to undergo profound rearrangement during epileptogenesis. These include a partial transition from inhibitory GABAergic transmission to excitatory one (Ben-Ari and Holmes 2005), probably due to changes in chloride extrusion mechanisms (Payne and others 2003). It is thus not inconceivable that the opposite effects of lorazepam, a GABAA-agonist, on LRTC near and far away from the focus would be related to this transition in GABAergic function.
Previous studies on epileptic patients have monitored phase synchronization between cortical networks prior to interictal-to-ictal transition (Mormann and others 2003; Le Van Quyen and others 2001, 2003). Synchrony was reported to decrease preictally even tens of minutes before seizure initiation, especially in the beta frequency band and close to the epileptic focus. Moreover, a frequency-specific entrainment of photo-sensitive seizures by flashes at 15–20 Hz has been reported (Drury 1997; Parra and others 2003). Our finding of focus-related abnormalities in beta frequency band LRTC thus add on to the accumulating evidence showing that activity in the beta band may be relevant in the neuronal mechanisms of epilepsy.
Methodological Issues
Although the present results were essentially similar with a wide range of analysis parameters (using amplitude or energy of the narrow-band signal, varying fitting interval in DFA, taking mean or median of fluctuations in DFA, FIR filtering parameters), further studies with larger patient groups are needed for optimized and standardized analysis. For instance, the interval of linear regression, here fixed to 1–100 s, could be adjusted to fit into more limited regions of scale-free behavior. Deviations from power-law behavior observed in our study have been previously attributed to multiscaling or crossover phenomena (Peng and others 1995; Ivanov and others 1999), but in some cases also to insufficient amounts of data.
The strength of LRTC in the beta band was robustly correlated with the proximity to seizure focus, but the underpinnings of topology of LRTC in other frequency bands remain unclear. If related to epilepsy, they could be due to aspects such as characteristic frequencies at seizure onset, cortical regions involved, or etiology. However, it is notable that mutually conflicting localizations between frequency bands were not observed in any patient and that combining the information from different frequency bands augmented localization (Fig. 4).
Clinical Perspectives
Scalp-recorded and intracranial EEG have traditionally been used in the presurgical assessment of the epileptic area. The accuracy of using source modeling of IIEs for localization of the region of seizure initiation is, however, limited because IIE waveforms do not necessarily arise from the seizure onset zone (Luders 1992; Barkley and Baumgartner 2003). Whereas ictal intracranial recording (with depth and subdural electrodes) is currently considered to provide the most reliable localization of the seizure focus, invasive recordings of this kind are always associated with significant health risks (e.g., bleeding, infections) as well as psychological and economical burden. It is hence obvious that limiting the need and duration of invasive monitoring is currently an important clinical challenge, which may be pursued by exploiting several independent, complementary analysis methods.
LRTC analysis used in the present study is both technically and physiologically rather straightforward, and it appears to hold promise for becoming a part of a clinical toolbox for surgical treatment of localization-related epilepsies and their basic research. This technique may also be directly extended to noninvasive localization of the seizure focus with EEG/MEG, which would constitute a significant improvement to the present clinical practice.
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Acknowledgments |
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SM has been supported by Jenny and Antti Wihuri Foundation, Farmos Science and Research Foundation, and The Finnish Foundation for Economic and Technology Sciences. The study was also supported by grants from the Academy of Finland and Arvo and Lea Ylppö Foundation. Conflict of Interest: None declared.
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