Downloaded from http://jnnp.bmj.com/ on March 28, 2015 - Published by group.bmj.com
JNNP Online First, published on October 3, 2014 as 10.1136/jnnp-2014-308992 Cerebrovascular disease
RESEARCH PAPER
The network topology of aneurysmal subarachnoid haemorrhage George M Ibrahim,1,2 R Loch Macdonald1,2 ▸ Additional material is published online only. To view please visit the journal online (http://dx.doi.org/10.1136/ jnnp-2014-308992). 1
Division of Neurosurgery, St. Michael’s Hospital, Labatt Family Centre of Excellence in Brain Injury and Trauma Research, Keenan Research Centre of the Li Ka Shing Knowledge Institute of St. Michael’s Hospital, Toronto, Ontario, Canada 2 Department of Surgery, University of Toronto, Toronto, Ontario, Canada Correspondence to Dr George M Ibrahim, St. Michael’s Hospital, 30 Bond Street, Toronto, ON, Canada M5B 1W8; [email protected] Received 15 July 2014 Revised 18 August 2014 Accepted 5 September 2014
ABSTRACT Objective Network analysis is an emerging tool for the study of complex systems. In the current report, the cascade of physiological and neurological changes following aneurysmal subarachnoid haemorrhage (SAH) was modelled as a complex system of interacting parameters. Graph theoretical analysis was then applied to identify parameters at critical topological junctions of the network, which may represent the most effective therapeutic targets. Methods Correlation matrices were calculated using a combination of Pearson, polyserial and polychoric regressions among 50 variables collected from 120 participants (38 male; mean age 51 years) included in the CONSCIOUS-1 trial. Graph theoretical analysis was performed to identify important topological features within the network formed by the interactions among these variables. Non-parametric resampling was applied to determine thresholds for significance. Results Several critical network hubs were identified, including the incidence of delayed ischaemic neurological deficit (DIND), anaemia and hypoalbuminaemia/ hypoproteinaemia. While not significant hubs, World Federation of Neurosurgical Societies (WFNS) score and use of rescue therapy had widespread connections within the network. Patient sex and history of hypertension also strongly clustered with other variables. A subnetwork (module) was also identified, which was related to neurological outcomes including WFNS score, angiographic vasospasm, DIND, use of rescue therapy and hydrocephalus. Interpretation Using graph theoretical analysis, we identify critical network topologies following SAH, which may serve as useful therapeutic targets. Importantly, we demonstrate that network analysis is a robust method to model complex interactions following SAH. Trial registration number URL: http://www. clinicaltrials.gov; Identifier: NCT00111085.
INTRODUCTION
To cite: Ibrahim GM, Macdonald RL. J Neurol Neurosurg Psychiatry Published Online First: [please include Day Month Year] doi:10.1136/jnnp2014-308992
The cascade of neurological and physiological sequelae following aneurysmal subarachnoid haemorrhage (SAH) represents a complex system of interacting clinical parameters. The term ‘complex’ does not simply denote a complicated system, but rather one that is characterised by constantly changing, non-linear relations among multiple components and with variable reliance on historical behaviour.1 Interventions aimed at improving outcomes following SAH suffer from a major limitation, in that it is unclear how changing a single or multiple concurrent parameters may alter this network of physiological interactions. Indeed,
while many previous works have evaluated the statistical contributions of a given indicator or patient phenotype to overall outcome,2–4 there has been no concerted effort to identify variables that lie at critical junctions of the system of interacting parameters, which, in theory, represent the most effective therapeutic targets. Efforts to model interactions among multiple clinical indicators may benefit from the application of network analysis. This approach involves decomposing complex interactions into a set of mathematical structures (termed graphs), and modelling their topological features using graph theoretical analysis.5 Increasingly, such an approach is employed in brain connectivity analysis to define structure–function relations and their alterations in pathological disease states.5–7 By describing multidimensional interactions as graphs, important summary statistics may be calculated that provide novel insights into the inter-relations among different parameters and their relative importance. The current study applies a novel analysis approach, graph theory, to clinical data from patients with SAH in order to identify parameters that are topologically important within the network of interacting variables. Using graph theory, we model a network of 50 parameters collected from a large database derived from Clazosentan to Overcome Neurological iSChemia and Infarction Occurring after Subarachnoid haemorrhage (CONSCIOUS-1) trial. The topological features of each component and their significance are calculated in order to identify variables that, if modified, would drastically alter the network topology.
METHODS Study population A post hoc analysis was performed of 413 participants enrolled in the CONSCIOUS-1 trial, a prospective, randomised, double-blinded phase IIb trial evaluating the efficacy of clazosentan in preventing angiographic vasospasm, which has been previously published.8 The trial was registered and the ethics committee at each institution reviewed and approved the protocol before study initiation. The study was conducted in compliance with the Declaration of Helsinki or with laws and regulations of the country in which the research was conducted. Of the participants included in the original trial, a sample of 120 participants with complete data for all the variables analysed was extracted for analysis. Because all relations tested are based on pair-wise associations between covariates, the
Ibrahim GM,employer) et al. J Neurol Neurosurg 2014;0:1–7. doi:10.1136/jnnp-2014-308992 Copyright Article author (or their 2014. Psychiatry Produced by BMJ Publishing Group Ltd under licence.
1
Downloaded from http://jnnp.bmj.com/ on March 28, 2015 - Published by group.bmj.com
Cerebrovascular disease population provides an ample sample size for the subsequent analyses.
Clinical variables The clinical variables included in the analysis include participants’ ages, sex and whether or not they had a history of hypertension or nicotine use. Variables that were collected on presentation include the initial systolic blood pressure, mean arterial pressure and heart rate. The World Federation of Neurosurgical Societies (WFNS) score was used to quantify the severity of the participants’ presentations.9 It was also recorded whether the patients underwent neurosurgical clipping or endovascular coiling of the ruptured aneurysm, as deemed appropriate by the respective treating physicians. Clinical variables describing the patients’ course following SAH were also recorded. The first of these was the incidence of delayed ischaemic neurological deficit (DIND), which was defined by the investigators as angiographic vasospasm on catheter angiography or transcranial Doppler ultrasound associated with neurological worsening lasting longer than 2 h after exclusion of other causes. Neurological worsening was defined as a decline of at least two points in the modified Glasgow Coma Scale, or an increase of two points in the abbreviated National Institutes of Health Stroke Scale (NIHSS).10 The use of rescue therapy was also recorded, defined as any intervention used to treat DIND (including haemodynamic therapy and mechanical or pharmacological angioplasty). Long-term neurological outcome was indexed by the modified Rankin Scale measured at 3 months post-SAH.11
Radiology Radiographic variables analysed include the extent of subarachnoid clot on presentation, which was quantified using the Hijdra scale on CT.12 This parameter evaluates the amount of clot in 10 fissures and cisterns using a scoring system as follows: 0 (no blood), 1 (small amount of blood), 2 (moderately filled with blood) or 3 (completely filled with blood) for a range of scores from 0 to 30.12 We also included a measure of the change in Hijdra score between the baseline CT and one performed after the aneurysm securing procedure. Intraventricular haemorrhage on the baseline CT was measured using a modification of the Graeb score, whereby a score of 0 (no blood), 1 (sedimentation, less than 25% filled), 2 (moderately filled) or 3 (completely filled) was given to each ventricle for a maximum possible score of 12.13 14 We also included parameters describing the frequency of intracerebral haemorrhage, subdural haematoma and the extent of hydrocephalus (ventriculocranial ratio, VCR, the ratio of the width of the frontal horns of the lateral ventricles at the level of the foramen of Monroe to the distance between the inner tables of the skull on the same CT scan slice).15 The participants included in the original trial universally underwent digital subtraction angiography (DSA) within 48 h of the aneurysm rupture and again within the angiographic vasospasm/DIND risk period (7–11 days). The aneurysm size and location were evaluated using baseline DSA. The extent of angiographic vasospasm was calculated based on the change in arterial diameter between the baseline and follow-up scans as follows: none (0–25%), mild (26–50%), moderate (51–75%) and severe (76–100%).
Laboratory investigations Various laboratory parameters were also collected and analysed within this data set, including complete blood count, extended 2
electrolytes, renal and liver function tests as well as markers of coagulation. Calcium concentrations were corrected for albumin levels, where corrected calcium was defined as: measured calcium [mmol/L]+0.02 (40−serum albumin [g/L]), where 40 represents the average albumin concentration in g/L.
Graph theoretical analysis The complete data set of 50 variables was organised into an n-by-m matrix with n rows indicating observations (participants) and m columns representing 50 parameters. Because the range of values of the parameters differed considerably, data centreing was performed to ensure that parameters with large values did not bias the subsequent analysis. A z-score was derived for the laboratory values to represent their deviation from normal ranges published by the Canadian Medical Council. As we have shown previously, this approach places greater weights on values that deviate from normal ranges.2 To centre the means of other dimensions (such as subarachnoid and intraventricular clot burden), a z-score was derived from the sample distribution. By measuring deviation from the mean, different physiological parameters may be directly compared irrespective of their absolute value. An m-by-m correlation matrix was then calculated from the centred data set (figure 1A). A correlation, rather than covariance matrix, was calculated in order to allow the variables to have unit variances, again to prevent certain parameters from dominating the analysis due to their large numerical values. The heterogeneous correlation matrix consisted of Pearson productmoment correlations between numeric variables, polyserial correlations between numeric and ordinal variables, and polychoric correlations between ordinal variables.16 17 The matrix was calculated using the hetcor function of the polycor package of R statistical software. The fundamental mathematical relationships in network analysis are contained in graphs, which are structures that describe the relations among elements within a system. Graphs contain nodes, which are the elements of interest as well as edges, which are pair-wise relationships between any two nodes. The latter may be binary or weighted and directed or undirected. In the current report, each clinical variable was considered a node. Because the magnitude of the pair-wise relation was more important than the direction, the absolute value of each correlation value was considered an edge, creating a weighted, undirected graph (figure 1B).
Network properties Graph theoretical properties were then derived from mathematical relationships in graph, as previously described (figure 1C).5 Three important characteristics of a node within a network are strength, clustering coefficient and eigenvector centrality (table 1). Strength is, simply, the sum of weighted edges that surround a certain node. The clustering coefficient is calculated by dividing the number of connections between a node and its neighbours by the number of possible connections between them.18 19 Conceptually, it is a measure of the number of closed triads surrounding a given node. A high clustering coefficient indicates that the neighbours of a node are also often directly connected (therefore clustered). Eigenvector centrality is a metric that facilitates the identification of hubs within a network.20 Nodes that are considered to be hubs play a disproportionately important role within a given network. Finally, we identified non-overlapping communities (subnetworks) within the graph by defining unique modules.21 22
Ibrahim GM, et al. J Neurol Neurosurg Psychiatry 2014;0:1–7. doi:10.1136/jnnp-2014-308992
Downloaded from http://jnnp.bmj.com/ on March 28, 2015 - Published by group.bmj.com
Cerebrovascular disease
Figure 1 Schematic of data processing pipeline. (A) Correlation matrices were created using a combination of Pearson, polyserial and polychoric regressions among 50 clinical parameters. (B) The absolute value of the matrices was calculated to index the strength of relations among covariates. (C) Graphs were constructed from the correlation matrices by considering each variable as a node and the pair-wise correlation between each variable as an edge. Graph theoretical parameters describing topological features of the network were calculated. (D) Non-parametric resampling was performed by shuffling the edges of the network and recalculating the graph theoretical parameters with each permutation. The deviation of the observed value from the surrogate distribution was used to identify significant topologies.
Resampling statistics In order to determine the significance of the graph theoretical measures, resampling was performed, whereby edges within the graph were shuffled 1000 times and the measures recalculated at each permutation (figure 1D). Such an approach preserves the degree distribution (the distribution of edge weights), while randomising their position. According to the central limit theorem, a random, Gaussian resampling distribution of network parameters was generated. Significant deviations from this distribution were quantified. Statistical significance was set at p
JNNP Online First, published on October 3, 2014 as 10.1136/jnnp-2014-308992 Cerebrovascular disease
RESEARCH PAPER
The network topology of aneurysmal subarachnoid haemorrhage George M Ibrahim,1,2 R Loch Macdonald1,2 ▸ Additional material is published online only. To view please visit the journal online (http://dx.doi.org/10.1136/ jnnp-2014-308992). 1
Division of Neurosurgery, St. Michael’s Hospital, Labatt Family Centre of Excellence in Brain Injury and Trauma Research, Keenan Research Centre of the Li Ka Shing Knowledge Institute of St. Michael’s Hospital, Toronto, Ontario, Canada 2 Department of Surgery, University of Toronto, Toronto, Ontario, Canada Correspondence to Dr George M Ibrahim, St. Michael’s Hospital, 30 Bond Street, Toronto, ON, Canada M5B 1W8; [email protected] Received 15 July 2014 Revised 18 August 2014 Accepted 5 September 2014
ABSTRACT Objective Network analysis is an emerging tool for the study of complex systems. In the current report, the cascade of physiological and neurological changes following aneurysmal subarachnoid haemorrhage (SAH) was modelled as a complex system of interacting parameters. Graph theoretical analysis was then applied to identify parameters at critical topological junctions of the network, which may represent the most effective therapeutic targets. Methods Correlation matrices were calculated using a combination of Pearson, polyserial and polychoric regressions among 50 variables collected from 120 participants (38 male; mean age 51 years) included in the CONSCIOUS-1 trial. Graph theoretical analysis was performed to identify important topological features within the network formed by the interactions among these variables. Non-parametric resampling was applied to determine thresholds for significance. Results Several critical network hubs were identified, including the incidence of delayed ischaemic neurological deficit (DIND), anaemia and hypoalbuminaemia/ hypoproteinaemia. While not significant hubs, World Federation of Neurosurgical Societies (WFNS) score and use of rescue therapy had widespread connections within the network. Patient sex and history of hypertension also strongly clustered with other variables. A subnetwork (module) was also identified, which was related to neurological outcomes including WFNS score, angiographic vasospasm, DIND, use of rescue therapy and hydrocephalus. Interpretation Using graph theoretical analysis, we identify critical network topologies following SAH, which may serve as useful therapeutic targets. Importantly, we demonstrate that network analysis is a robust method to model complex interactions following SAH. Trial registration number URL: http://www. clinicaltrials.gov; Identifier: NCT00111085.
INTRODUCTION
To cite: Ibrahim GM, Macdonald RL. J Neurol Neurosurg Psychiatry Published Online First: [please include Day Month Year] doi:10.1136/jnnp2014-308992
The cascade of neurological and physiological sequelae following aneurysmal subarachnoid haemorrhage (SAH) represents a complex system of interacting clinical parameters. The term ‘complex’ does not simply denote a complicated system, but rather one that is characterised by constantly changing, non-linear relations among multiple components and with variable reliance on historical behaviour.1 Interventions aimed at improving outcomes following SAH suffer from a major limitation, in that it is unclear how changing a single or multiple concurrent parameters may alter this network of physiological interactions. Indeed,
while many previous works have evaluated the statistical contributions of a given indicator or patient phenotype to overall outcome,2–4 there has been no concerted effort to identify variables that lie at critical junctions of the system of interacting parameters, which, in theory, represent the most effective therapeutic targets. Efforts to model interactions among multiple clinical indicators may benefit from the application of network analysis. This approach involves decomposing complex interactions into a set of mathematical structures (termed graphs), and modelling their topological features using graph theoretical analysis.5 Increasingly, such an approach is employed in brain connectivity analysis to define structure–function relations and their alterations in pathological disease states.5–7 By describing multidimensional interactions as graphs, important summary statistics may be calculated that provide novel insights into the inter-relations among different parameters and their relative importance. The current study applies a novel analysis approach, graph theory, to clinical data from patients with SAH in order to identify parameters that are topologically important within the network of interacting variables. Using graph theory, we model a network of 50 parameters collected from a large database derived from Clazosentan to Overcome Neurological iSChemia and Infarction Occurring after Subarachnoid haemorrhage (CONSCIOUS-1) trial. The topological features of each component and their significance are calculated in order to identify variables that, if modified, would drastically alter the network topology.
METHODS Study population A post hoc analysis was performed of 413 participants enrolled in the CONSCIOUS-1 trial, a prospective, randomised, double-blinded phase IIb trial evaluating the efficacy of clazosentan in preventing angiographic vasospasm, which has been previously published.8 The trial was registered and the ethics committee at each institution reviewed and approved the protocol before study initiation. The study was conducted in compliance with the Declaration of Helsinki or with laws and regulations of the country in which the research was conducted. Of the participants included in the original trial, a sample of 120 participants with complete data for all the variables analysed was extracted for analysis. Because all relations tested are based on pair-wise associations between covariates, the
Ibrahim GM,employer) et al. J Neurol Neurosurg 2014;0:1–7. doi:10.1136/jnnp-2014-308992 Copyright Article author (or their 2014. Psychiatry Produced by BMJ Publishing Group Ltd under licence.
1
Downloaded from http://jnnp.bmj.com/ on March 28, 2015 - Published by group.bmj.com
Cerebrovascular disease population provides an ample sample size for the subsequent analyses.
Clinical variables The clinical variables included in the analysis include participants’ ages, sex and whether or not they had a history of hypertension or nicotine use. Variables that were collected on presentation include the initial systolic blood pressure, mean arterial pressure and heart rate. The World Federation of Neurosurgical Societies (WFNS) score was used to quantify the severity of the participants’ presentations.9 It was also recorded whether the patients underwent neurosurgical clipping or endovascular coiling of the ruptured aneurysm, as deemed appropriate by the respective treating physicians. Clinical variables describing the patients’ course following SAH were also recorded. The first of these was the incidence of delayed ischaemic neurological deficit (DIND), which was defined by the investigators as angiographic vasospasm on catheter angiography or transcranial Doppler ultrasound associated with neurological worsening lasting longer than 2 h after exclusion of other causes. Neurological worsening was defined as a decline of at least two points in the modified Glasgow Coma Scale, or an increase of two points in the abbreviated National Institutes of Health Stroke Scale (NIHSS).10 The use of rescue therapy was also recorded, defined as any intervention used to treat DIND (including haemodynamic therapy and mechanical or pharmacological angioplasty). Long-term neurological outcome was indexed by the modified Rankin Scale measured at 3 months post-SAH.11
Radiology Radiographic variables analysed include the extent of subarachnoid clot on presentation, which was quantified using the Hijdra scale on CT.12 This parameter evaluates the amount of clot in 10 fissures and cisterns using a scoring system as follows: 0 (no blood), 1 (small amount of blood), 2 (moderately filled with blood) or 3 (completely filled with blood) for a range of scores from 0 to 30.12 We also included a measure of the change in Hijdra score between the baseline CT and one performed after the aneurysm securing procedure. Intraventricular haemorrhage on the baseline CT was measured using a modification of the Graeb score, whereby a score of 0 (no blood), 1 (sedimentation, less than 25% filled), 2 (moderately filled) or 3 (completely filled) was given to each ventricle for a maximum possible score of 12.13 14 We also included parameters describing the frequency of intracerebral haemorrhage, subdural haematoma and the extent of hydrocephalus (ventriculocranial ratio, VCR, the ratio of the width of the frontal horns of the lateral ventricles at the level of the foramen of Monroe to the distance between the inner tables of the skull on the same CT scan slice).15 The participants included in the original trial universally underwent digital subtraction angiography (DSA) within 48 h of the aneurysm rupture and again within the angiographic vasospasm/DIND risk period (7–11 days). The aneurysm size and location were evaluated using baseline DSA. The extent of angiographic vasospasm was calculated based on the change in arterial diameter between the baseline and follow-up scans as follows: none (0–25%), mild (26–50%), moderate (51–75%) and severe (76–100%).
Laboratory investigations Various laboratory parameters were also collected and analysed within this data set, including complete blood count, extended 2
electrolytes, renal and liver function tests as well as markers of coagulation. Calcium concentrations were corrected for albumin levels, where corrected calcium was defined as: measured calcium [mmol/L]+0.02 (40−serum albumin [g/L]), where 40 represents the average albumin concentration in g/L.
Graph theoretical analysis The complete data set of 50 variables was organised into an n-by-m matrix with n rows indicating observations (participants) and m columns representing 50 parameters. Because the range of values of the parameters differed considerably, data centreing was performed to ensure that parameters with large values did not bias the subsequent analysis. A z-score was derived for the laboratory values to represent their deviation from normal ranges published by the Canadian Medical Council. As we have shown previously, this approach places greater weights on values that deviate from normal ranges.2 To centre the means of other dimensions (such as subarachnoid and intraventricular clot burden), a z-score was derived from the sample distribution. By measuring deviation from the mean, different physiological parameters may be directly compared irrespective of their absolute value. An m-by-m correlation matrix was then calculated from the centred data set (figure 1A). A correlation, rather than covariance matrix, was calculated in order to allow the variables to have unit variances, again to prevent certain parameters from dominating the analysis due to their large numerical values. The heterogeneous correlation matrix consisted of Pearson productmoment correlations between numeric variables, polyserial correlations between numeric and ordinal variables, and polychoric correlations between ordinal variables.16 17 The matrix was calculated using the hetcor function of the polycor package of R statistical software. The fundamental mathematical relationships in network analysis are contained in graphs, which are structures that describe the relations among elements within a system. Graphs contain nodes, which are the elements of interest as well as edges, which are pair-wise relationships between any two nodes. The latter may be binary or weighted and directed or undirected. In the current report, each clinical variable was considered a node. Because the magnitude of the pair-wise relation was more important than the direction, the absolute value of each correlation value was considered an edge, creating a weighted, undirected graph (figure 1B).
Network properties Graph theoretical properties were then derived from mathematical relationships in graph, as previously described (figure 1C).5 Three important characteristics of a node within a network are strength, clustering coefficient and eigenvector centrality (table 1). Strength is, simply, the sum of weighted edges that surround a certain node. The clustering coefficient is calculated by dividing the number of connections between a node and its neighbours by the number of possible connections between them.18 19 Conceptually, it is a measure of the number of closed triads surrounding a given node. A high clustering coefficient indicates that the neighbours of a node are also often directly connected (therefore clustered). Eigenvector centrality is a metric that facilitates the identification of hubs within a network.20 Nodes that are considered to be hubs play a disproportionately important role within a given network. Finally, we identified non-overlapping communities (subnetworks) within the graph by defining unique modules.21 22
Ibrahim GM, et al. J Neurol Neurosurg Psychiatry 2014;0:1–7. doi:10.1136/jnnp-2014-308992
Downloaded from http://jnnp.bmj.com/ on March 28, 2015 - Published by group.bmj.com
Cerebrovascular disease
Figure 1 Schematic of data processing pipeline. (A) Correlation matrices were created using a combination of Pearson, polyserial and polychoric regressions among 50 clinical parameters. (B) The absolute value of the matrices was calculated to index the strength of relations among covariates. (C) Graphs were constructed from the correlation matrices by considering each variable as a node and the pair-wise correlation between each variable as an edge. Graph theoretical parameters describing topological features of the network were calculated. (D) Non-parametric resampling was performed by shuffling the edges of the network and recalculating the graph theoretical parameters with each permutation. The deviation of the observed value from the surrogate distribution was used to identify significant topologies.
Resampling statistics In order to determine the significance of the graph theoretical measures, resampling was performed, whereby edges within the graph were shuffled 1000 times and the measures recalculated at each permutation (figure 1D). Such an approach preserves the degree distribution (the distribution of edge weights), while randomising their position. According to the central limit theorem, a random, Gaussian resampling distribution of network parameters was generated. Significant deviations from this distribution were quantified. Statistical significance was set at p
