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Address correspondence to Bin He, University of Minnesota, 7-105 NHH, 312 Church Street SE, Minneapolis, MN 55455, U.S.A. E-mail: email@example.com
Purpose: The current gold standard for the localization of the cortical regions responsible for the initiation and propagation of the ictal activity is through the use of invasive electrocorticography (ECoG). This method is utilized to guide surgical intervention in cases of medically intractable epilepsy by identifying the location and extent of the epileptogenic focus. Recent studies have proposed mechanisms in which the activity of epileptogenic cortical networks, rather than discrete focal sources, contributes to the generation of the ictal state. If true, selective modulation of key network components could be employed for the prevention and termination of the ictal state.
Methods: Here, we have applied graph theory methods as a means to identify critical network nodes in cortical networks during both ictal and interictal states. ECoG recordings were obtained from a cohort of 25 patients undergoing presurgical monitoring for the treatment of intractable epilepsy at the Mayo Clinic (Rochester, MN, U.S.A.).
Key Findings: One graph measure, the betweenness centrality, was found to correlate with the location of the resected cortical regions in patients who were seizure-free following surgical intervention. Furthermore, these network interactions were also observed during random nonictal periods as well as during interictal spike activity. These network characteristics were found to be frequency dependent, with high frequency gamma band activity most closely correlated with improved postsurgical outcome as has been reported in previous literature.
Significance: These findings could lead to improved understanding of epileptogenesis. In addition, this theoretically allows for more targeted therapeutic interventions through the selected modulation or disruption of these epileptogenic networks.
Historically, the epileptogenic zone in human partial epilepsy has been conceptually thought to consist of one or more discrete focal sources (Luders & Comair, 2001). Recently, alternative views of epileptic brain and ictogenesis (seizure generation) have been proposed, in that the ictal activity is thought to arise from the activity of epileptogenic cortical networks (Franaszczuk et al., 1994; Franaszczuk & Bergey, 1998; Baccala et al., 2004; Worrell et al., 2004; Jirsch et al., 2006; Kramer et al., 2008; Worrell et al., 2008). It is hypothesized that the activity of these networks, rather than a single focal “pacemaker,” is responsible for the initiation and propagation of the ictal activity. As a result, this has opened the door for potential novel therapies for medically intractable epilepsy through the disruption or inhibition of these epileptogenic networks. Techniques by which to identify and characterize these networks would, therefore, have a significant impact upon the medical treatment of these patients.
In the study of epilepsy, graph theory techniques have been applied to the identification and characterization of the cortical networks giving rise to the ictal activity (Franaszczuk et al., 1994; Franaszczuk & Bergey, 1998; Baccala et al., 2004). Analysis of network connectivity in patients with epilepsy has been performed using functional data garnered from ECoG (Ortega et al., 2008a,b; Van Dellen et al., 2009), electroencephalography (EEG) (Ponten et al., 2009; Horstmann et al., 2010), magnetoencephalography (MEG) (Chavez et al., 2010), and functional magnetic resonance imaging (fMRI) (Zhang et al., 2009) measurements. These studies have demonstrated the existence of highly interconnected “hubs,” which may play a role in the initiation and propagation of the ictal activity by the epileptogenic networks (Morgan & Soltesz, 2008). Selective modulation of these hubs could, theoretically, prevent or abolish seizure activity without the need for removal of the entire network, which in turn could lead to better preoperative planning and more focused interventions.
In this study, graph theoretic measures were applied to evaluate the local and global connectivity within the network. Examination of the network properties was performed during resting interictal periods as well as during interictal spikes, in order to determine whether the network properties observed during the ictal periods could also be observed during the interictal intervals. It was observed that the functional changes in the connectivity were correlated with the seizure onset zone (SOZ) and the activity of the cortical networks affiliated with these regions was also enhanced during interictal periods as well.
Recordings were obtained from a group of 25 patients with medically intractable neocortical-onset epilepsy for use in the present study. All patients underwent presurgical monitoring in the Epilepsy Monitoring Unit at the Mayo Clinic (Rochester, MN, U.S.A.). Long-term intracranial EEG (iEEG) recordings were obtained from subdural silastic grids (4 mm diameter electrode contacts; 10 mm interelectrode spacing) implanted on the cortical surface. The recordings were referenced to a scalp suture electrode placed at the vertex, passed through a 125 Hz anti-aliasing filter and sampled at 500 Hz (Xltek EMU128; Natus Medical Inc, Oakville, ON, Canada). Following acquisition of the data, offline preprocessing was performed and included additional band-pass filtering (0.1–50 Hz) and automated artifact rejection. Visual inspection was also performed upon the data and channels exhibiting the presence of artifact were discarded from the analysis. The study was approved by the institutional review boards at the University of Minnesota and the Mayo Clinic.
Sections of the data corresponding to ictal, interictal spikes, and resting interictal periods were obtained for each of the analyzed patients. A detailed summary of the epoch selection is given in the supplemental material.
DTF connectivity calculations
The directed transfer function (DTF) was calculated for each windowed ictal and resting interictal dataset as described previously (Babiloni et al., 2005; Wilke et al., 2009a). Here, the DTF was calculated over the theta (3–7 Hz), alpha (8–12 Hz), beta (13–29 Hz), and gamma (30–50 Hz) frequency bands. The strongest 5% of the total possible causal connections (corresponding to approximately 200 connections in a 64-electrode montage) within each frequency band were identified for further analysis. This was performed to maintain a similar average degree distribution between subjects, since the betweenness centrality can be affected by the degree of a network. A range of thresholds (1–10%) was examined in several patients, but these thresholds were not found to significantly alter the properties of the examined networks. The path lengths were determined by taking the inverse of the strength of each DTF connection. Therefore, nodes that were tightly coupled by evidence of strong DTF connections had short path lengths, whereas those that were more weakly coupled had longer path lengths.
ADTF connectivity calculations
The adaptive directed transfer function (ADTF) was calculated for each interictal spike (Wilke et al., 2007, 2009b). Time-frequency representations were made from the interictal spike recordings, and the frequency bands containing ≥50% of the maximum power during the peak point of the interictal spike were identified. The ADTF was then used to identify the time-varying causal activity within these frequency bands. The causal network identified during the peak point of the interictal spike was selected for analysis. The path lengths were calculated by taking the inverse of the strength of the ADTF connection similar to the previously described DTF method.
The betweenness centrality (Goh et al., 2003; Yoon et al., 2006; Puzis et al., 2007; Wang et al., 2008) for each node in a network is defined as the ratio of the number of shortest paths that pass through a specified node to the total number of shortest paths in the network. Given the causal network identified by the DTF method, the betweenness centrality can be defined mathematically as:
where σij is the number of shortest paths between nodes i and j and σij(v) is the number of these shortest paths that pass through node v. In effect, the betweenness centrality is a measure of the “importance” of each node to the transit of information across the network. Nodes that have a high betweenness centrality act as centralized hubs in a network, and removal of these nodes will have the most significant deleterious effect on the network performance. This method has been used to identify critical nodes in a variety of communication, neuronal-based, biologically derived and social networks (Wang et al., 2006; Sporns et al., 2007; Chen & Duan, 2008; Goni et al., 2008; Ueno & Masuda, 2008; Mukherjee & Gupte, 2009; Perkins et al., 2009). Unlike other measures that quantify the information that arises from each node, the betweenness centrality depends not only on the primary efferent and afferent connections to a node, but also on the secondary and tertiary connections to the node. Figure 1 demonstrates the betweenness centrality values for a simulated cortical ECoG network.
The cortical regions were delineated into a bivariate distribution through the use of K-means clustering. The betweenness centrality was calculated for each ECoG channel from ictal onset to cessation; therefore, a time-varying betweenness-centrality value was obtained for each node over the course of the seizure. Because the betweenness centrality was a function of time, the K-means algorithm was utilized to identify the group of nodes within each network that contained significantly higher betweenness centrality values over the course of the seizure compared to the background activity. The K-means algorithm was subsequently used to stratify the cortical regions as either “active,” that is, those regions exhibiting high amounts of betweenness centrality during the ictal period, or “inactive” pertaining to the regions with low betweenness centrality values during the ictal activity.
Nine time points corresponding to 5, 3, and 1 min prior to ictal onset; early, mid, and late ictal periods; and 1, 3, and 5 min following seizure termination were selected for analysis. The length of each analyzed seizure was normalized to 1, and the early, mid, and late ictal segments corresponded to 0–0.2, 0.4–0.6, and 0.8–1 of the ictal length, respectively. The betweenness centrality within both the active and inactive cortical regions was calculated for all nine periods. The results were normalized for each analyzed seizure, and a composite map of the activity was obtained. The Wilcoxon rank test was used to calculate significant changes in activity between time periods (p < 0.01).
In 15 of the 25 patients, surgical resection of the presumed ictal focus was performed resulting in either cessation or a significant reduction in seizure frequency. The remaining patients were either determined to not be viable surgical candidates or follow-up information was not available. For the 15 surgical patients, the locations of the “active” cortical regions identified through the K-means analysis were compared with the surgically resected SOZ identified by conventional clinical means. Both the amount of overlap between the cortical regions with high betweenness centrality and the SOZ as well as the total spatial area (the spatial extent) of the active regions were examined in the theta, alpha, beta, and gamma frequency bands. This procedure was not performed in the remaining 10 patients, as a surgical SOZ was not available for this subset.
K-means clustering was similarly used to separate active and inactive cortical regions during the selected interictal periods in the theta, alpha, beta, and gamma frequency bands. Spatial maps of the active networks were constructed and compared with the SOZ identified clinically. The amount of overlap between the SOZ and the activated network regions was identified in each of the frequencies and was also compared with the results obtained from the ictal data.
Interictal spike analysis
The time-varying causal networks were obtained during the time course of each interictal spike. The causal network corresponding to the average peak point of each interictal spike was identified and the betweenness centrality was estimated for each network node from this selected network. The nodes that displayed ≥50% of the normalized maximum betweenness centrality were identified as the active networks corresponding to the interictal spike activity (Wilke et al., 2009b). As with the ictal and interictal analysis, these activated networks were subsequently compared to the surgical SOZs identified by conventional clinical means.
For each patient, the causal networks were obtained by means of the DTF method. A 6-s moving window was applied to the ECoG recordings beginning 5 min prior to ictal onset and lasting until 5 min following ictal cessation. During the seizure, K-means clustering was used to identify the activated nodes of the epileptogenic network using the betweenness centrality metric. Examples of the spatial extents of the ictal betweenness centrality networks in the theta, alpha, beta, and gamma frequency bands are shown for a representative patient in Fig. 2. In this particular patient, the spatial distributions of the nodes identified by K-means using the betweenness centrality metrics were nearly identical across the four analyzed frequency bands. The betweenness centrality in all four frequencies identified a primary region overlapping and adjacent to the posterior aspect of the SOZ identified by the epileptologist. The theta, alpha, and beta frequencies, however, also identified regions within the frontal lobe that were spatially removed from the clinically identified SOZ.
ECoG recordings were analyzed in 65 seizures obtained from the 25 patients undergoing presurgical evaluation. The activities from the “active” nodes identified by the K-means clustering algorithm as well as those from the “inactive” background nodes were compared at 9 time points: 5, 3, and 1 min prior to, and following ictal onset and offset, respectively, as well as the early ictal, midictal, and late ictal periods corresponding to 0–0.2, 0.4–0.6, and 0.8–1.0 of the normalized seizure length. The composite results obtained for the betweenness centrality networks during these time points are shown in Fig. 3. As can be observed from this figure, the activity of the identified “active” nodes decreased during the ictal propagation and the betweenness centrality of the active nodes reached a minimum 1 min after ictal cessation with the active nodes displaying significantly diminished betweenness centrality levels during this time point compared to the preictal baseline in all four frequency bands (Wilcoxon p < 0.05). The betweenness centrality of the active nodes subsequently increased toward baseline preictal levels and no significant differences between the pre-ictal levels and the betweenness centrality at the 5-min postictal time point were observed. A decrease in the background activity (“inactive” nodes) was also observed during the early, mid, and late ictal periods, which was significantly diminished in all four frequency bands during the early, mid, and late ictal periods (Wilcoxon p < 0.01). The background activity of the networks in the theta, alpha, and beta bands returned to preictal baseline following ictal cessation, with the background activity of the gamma band networks remaining significantly depressed at 1-min postictal (Wilcoxon p < 0.01).
The spatial locations of the activated regions were identified and compared with the SOZ determined by the epileptologists. In addition, the spatial extents of the networks were analyzed in each of the four frequency bands. The results from the networks obtained using the betweenness centrality metric are shown in Fig. 4. The spatial extent of the active cortical regions in each of the four analyzed frequency bands is shown in Fig. 4A. For each analyzed seizure, the extent of the network containing the greatest cortical area was normalized to one. The spatial extents of the cortical networks in the other frequency bands were subsequently denoted as fractions of the frequency with the greatest spatial extent. As can be observed from Fig. 4a, a frequency-dependent relationship was seen with progressively more focal spatial extents at increased frequencies. Compared to the theta networks, the gamma band networks were found to be significantly more focal in extent (Wilcoxon p < 0.01).
The percentage overlap between the activated regions and the SOZ is shown in Fig. 4B. From this figure, a frequency-dependent effect on the amount of overlap between the clinically identified SOZ and the activated betweenness centrality network nodes was observed, with the theta band networks having the least amount of overlap and the gamma band networks displaying the greatest amount of overlap. This difference, as well as the increased overlap observed in the beta band compared to the theta activity, was found to be statistically significant (Wilcoxon p < 0.01). The percentage of overlap based upon chance alone was calculated for the various seizures and SOZs and was found to be 0.16 ± 0.06. The overlap in the beta and gamma frequencies was found to be significantly greater than chance alone (p < 0.01).
Of the 25 patients analyzed in the current study, surgical resection was performed on 15 of the patients. The majority of the remaining patients were determined to not be viable surgical candidates based upon the number or cortical locations of the ictal foci. For the 15 patients who underwent surgical resection of the presumed ictal focus/foci, five patients were seizure-free, class 1, and the remaining 10 had significant reductions in seizure frequency following surgery, Engel class 2–4 (see Supplementary Tables S1 and S2) (Wieser, et al. 2001). The amount of overlap between the clinical SOZ and the betweenness centrality networks was obtained for each of these two groups—the seizure-free patients and those who continued to have seizures. The average distance from the active nodes to the SOZ was calculated for each seizure in each patient and the composite results are shown in Figure 5. In this analysis, if an active node was within the SOZ, it was assigned a value of 0 cm, whereas an active node outside of the SOZ was assigned a value based upon the distance to the nearest border of the SOZ. The patients who were seizure-free and the patients who continued to have seizures following surgery, albeit at a reduced frequency, had similar average distance measures in the theta, alpha, and beta frequencies. The patients who were seizure-free, however, had SOZs that were more significantly overlapped with the active nodes in the gamma frequency band compared to their non–seizure-free counterparts (Wilcoxon p < 0.05).
The betweenness centrality was also calculated from 15-min–long interictal segments several hours removed from an ictal event. The spatial extent of the activated networks in the gamma frequency band were obtained and compared to the SOZ. In addition, the causal source activity was also obtained from interictal spikes in these patients as described previously. Qualitatively, it was observed that the spatial locations of the activated gamma networks were similar between the spikes, interictal periods, and ictal events, although the networks present during the interictal periods tended to have a slightly higher spatial variance. These results are consistent with previous literature, which has shown increased gamma band activity within the SOZ during nonictal periods (Worrell et al., 2004, 2008; Jirsch et al., 2006). Examples of these activated networks in two representative patients are shown in Supplementary Figs S1 and S2. For qualitative comparison of the colocalization of the identified networks with the SOZs, the average distance of the activated nodes was calculated for the ictal, interictal spike, and interictal periods temporally removed from the ictal events. As can be observed in Fig. 6, no significant difference was observed in the average distance of the active nodes to the SOZ for the interictal spike and ictal recordings. The cortical locations identified during the interictal periods were significantly more diffuse than those obtained during either the interictal spike or ictal activity (Wilcoxon p < 0.01); however, they remained in close approximation to the clinically identified SOZs (average distance <1.6 cm).
This study examined the properties of the epileptogenic networks that give rise to the ictal activity in patients with medically intractable neocortical-onset epilepsy. In particular, connectivity tools were used to assess the cortical interactions that occur during both ictal and interictal periods. A measure of the complex network interactions was analyzed in the current study: namely, the betweenness centrality. The betweenness centrality provides an indicator of network performance that takes into account the causal network connections on a holistic basis. Using this measure, epileptogenic network activity was evaluated and compared to the locations of the SOZs identified using conventional clinical methods.
Composite maps were obtained of the betweenness centrality activity in each of the 65 analyzed seizures. For each network, K-means clustering was used to identify the activated network nodes. Through the K-means clustering, the ECoG electrodes were identified as either “active” or “inactive” and the time courses of these networks pertaining to the betweenness centrality metric were subsequently evaluated to identify generalized temporal change in the network structure during seizure initiation, propagation, and termination.
Graph results during seizure activity
From the results it was observed that the betweenness centrality of the identified activated nodes decreased from the onset of the ictal activity and reached a minimum approximately 1 min after ictal cessation. This finding is not unexpected, however, given the nature of the ictal initiation and propagation. A study performed by Schindler et al. observed a decrease in the zero-lag coherence of the ECoG signal at ictal onset, which the authors hypothesized arose from the time-lagged propagation of information from the ictal-onset site (Schindler et al., 2007). They observed that the coherence of the intracranial recordings increased immediately prior to ictal cessation and extended to the postictal period. The authors theorized that the increase in coherence prior to and following ictal cessation could potentially be an active neural mechanism for seizure termination. The decrease in betweenness centrality observed in the analyzed seizures agrees with these prior findings by Schindler et al. concerning temporal changes in coherence structure during the ictal activity and immediately following its cessation. From a network perspective, as the seizures progressed, the nodes of the cortical network became more highly synchronous and the network architecture became more regular. As a result, the betweenness centrality of the active “hubs” of the network correspondingly decreased. This is in agreement with prior studies that have shown the path length and synchronizability of the cortical networks to increase during the ictal activity (Ponten et al., 2007, 2009).
At the ictal onset, a decrease was observed in the betweenness centrality measured in all four of the frequency bands. From the time course of the betweenness centrality measured in the gamma band, however, it was observed that there was initially a slight increase (albeit not reaching statistical significance from baseline) at the onset of the seizures that was not observed in the other three frequency bands. This observation could potentially be due to preferential information transfer in the gamma frequency band during ictal onset. Several studies have shown that gamma band and high frequency oscillations are preferentially associated with the SOZ in patients with focal onset epilepsy (Worrell et al., 2004, 2008; Jirsch et al., 2006). These high frequency networks could potentially be catalysts for the onset of the ictal activity in these patients.
Spatial distribution of epileptic networks
From the spatial analysis of the identified activated networks, it was observed that the betweenness centrality was highly dependent upon the frequency of the analyzed network. The networks identified using the betweenness centrality in the gamma band was more localized and significantly more focal in extent compared to the networks identified in the theta frequencies. In addition, group analysis was performed on the patients who were seizure-free following surgery and those who were not. For the two groups, it was shown that the patients who were seizure-free after surgery had a significantly greater amount of the activated nodes in the gamma band resected compared to the patients who continued to have seizures following surgery. From the results of the spatial analysis of the gamma band networks as well as the observed time course of these networks, it is hypothesized that the causal activity within the gamma band may play a significant role in the epileptogenesis and propagation of the ictal activity. Specifically, the results suggest that these gamma networks are active during the onset of the ictal activity and, furthermore, resection of these activated network nodes appears to have a significantly beneficial effect on postoperative outcome in these patients. Additional work is needed to fully address this issue.
Time course of network activity
The final portion of this study attempted to ascertain whether these networks were present only during ictal activity or if they were constitutively active during interictal periods as well. From the composite results of the betweenness centrality in the 65 analyzed seizures, it can be observed that the preictal baseline for the “activated” regions identified by K-means clustering is significantly higher than the background activity of the remaining nodes. Both interictal spikes and interictal periods temporally removed from the seizure activity were analyzed to discern if they could be useful surrogates of the network activity during ictal events.
Previous work has shown that the network activity observed during the interictal spike events is in relatively good agreement with the clinically identified SOZ. If these networks were also found to be active during resting interictal periods, the invasive intracranial monitoring procedures could be reduced or potentially eliminated altogether. In this study, 15-min interictal recordings were obtained that were temporally removed from the ictal events, and the betweenness centrality pertaining to the networks in the gamma band were analyzed and compared to the ictal networks. It was observed that these networks were fairly robust over time and were spatially correlated with the networks identified as corresponding to both the interictal spikes and ictal activity. This is an important finding as it indicates that these epileptogenic networks can be identified during periods of nonictal activity. Therefore, it is possible that, in the future, these techniques could be utilized to reduce the necessity for long-term monitoring in patients with intractable neocortical-onset epilepsy. In fact, it is plausible that such techniques could potentially eliminate the need for long-term intracranial recording altogether with the identification and resection of the epileptogenic networks performed during a single operation.
There are a few drawbacks to the current method, namely, the limitation of the analysis to the number of recorded ECoG channels. An inherent assumption in this method is that the spatial distribution of the ECoG electrodes spans the extent of the SOZ. This method will not be able to identify portions of the epileptogenic network if they lay outside of the region covered by the ECoG grid. This limitation, however, exists with standard presurgical monitoring techniques and is not unique to the technique presented here. In this particular study, care was taken to ensure that the patients selected for analysis had epileptogenic foci that were covered by the implanted electrodes.
In addition to the location of the recording sites with respect to the epileptic foci, the DTF method used to obtain the connectivity pattern of the ictal networks requires that the analyzed data be quasi-stationary. The Schwarz Bayesian Criterion (SBC) has been utilized in previous studies to determine the appropriate quasi-stationary properties of the system (Kaminski & Blinowska, 1991; Franaszczuk et al., 1994; Franaszczuk & Bergey, 1998; Wilke et al., 2007, 2009a). Here, the SBC was used to verify that the selected time windows in the study satisfied the quasi-stationary assumption. If a minimum was not observed in the SBC plots, the selected time series was judged to not fulfill the quasi-stationary criterion and was not used in the current study. In addition to the betweenness centrality metric utilized in this study, other alternatives to the identification of hubs through centrality measures such as the node degree and the eigenvector centrality (Lohmann et al., 2010) can potentially be used. A comparative examination of these techniques, however, is beyond the scope of the current work.
The major limitations with the DTF/ADTF techniques employed in the present study lie in the intracranial recordings. The current method is limited to the identification of cortical sources that are in proximity to the recording sites. If the cortical generator responsible for the initiation of the interictal spike is located outside of the area covered by the ECoG, the DTF/ADTF method will produce erroneous results. In this case, the methods will identify the proximal recording site as the source of the observed activity, although this identified “source” may in fact be spatially removed from the true source of the observed activity. For this reason, care must be given in the interpretation of the result when a source is identified as confined to an edge of the recorded field. Similarly, when the source is located within a deep portion of the brain, the DTF/ADTF method may identify the cortical manifestations of the source activity. However, this problem can be solved through the use of stereotactic EEG (sEEG) recordings if deeper regions of the brain are responsible for the activity, as in mesial temporal lobe epilepsy. The connectivity methods presented in this study can be applied readily to accommodate these recordings as well. The previously described limitations are not confined to these methods, however, as they are applicable to any analysis that utilizes intracranial recordings. In the present study, patients were selected in which the ictal generators were in close contact with the ECoG electrodes, thereby minimizing or avoiding altogether the aforementioned limitations.
Although these results have been obtained from invasive intracranial recordings, such techniques could also be applied to cortical potentials obtained from noninvasive methods such as high-resolution EEG recordings. Previous studies have shown that the DTF-based connectivity techniques can be successfully applied to reconstructed cortical potentials (Astolfi et al., 2005, 2007; Babiloni et al., 2005). The connectivity techniques described here could be applied to these or similar noninvasive functional imaging techniques. Such a technique, in which the cortical networks are estimated from high-resolution EEG, would allow for the noninvasive identification of these neocortical epileptogenic networks. This would significantly advance the medical state-of-the-art, as the presurgical monitoring could be potentially moved from the intensive care unit to an outpatient setting.
The authors would like to thank Dr. Matt Stead for technical assistance in data mining. This work was supported in part by NIH RO1EB007920, NIH RO1EB006433, NIH R01-NS63039, and a grant from the Minnesota Partnership for Biotechnology and Medical Genomics. C.W. was supported in part by NIH T32 EB008389.
We confirm that we have read the Journal’s position on issues involved in ethical publication and affirm that this report is consistent with those guidelines. None of the authors have any conflict of interest to disclose.