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Relationships and redundancies of selected hemodynamic and structural parameters for characterizing virtual treatment of cerebral aneurysms with flow diverter devices
Journal of Biomechanics ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Relationships and redundancies of selected hemodynamic and structural parameters for characterizing virtual treatment of cerebral aneurysms with flow diverter devices C. Karmonik a,b,n, J.R. Anderson a, J. Beilner c, J.J. Ge c, S. Partovi d, R.P. Klucznik e, O. Diaz e, Y.J. Zhang b, G.W. Britz b, R.G. Grossman b, N. Lv f, Q. Huang f a
MRI Core, Houston Methodist Research Institute, Houston, TX, USA Cerebrovascular Center, Neurosurgery, Houston Methodist, Houston, TX, USA Siemens AX, Shanghai, China d Department of Radiology, University Hospitals Case Medical Center, Case Western Reserve University, Cleveland, OH, USA e Cerebrovascular Center, Radiology, Houston Methodist, Houston, TX, USA f Neurosurgery, The Affiliated Changhai Hospital of Second Military Medical University, Shanghai, China b c
art ic l e i nf o
a b s t r a c t
Article history: Accepted 13 November 2015
Background and purpose: To quantify the relationship and to demonstrate redundancies between hemodynamic and structural parameters before and after virtual treatment with a flow diverter device (FDD) in cerebral aneurysms. Methods: Steady computational fluid dynamics (CFD) simulations were performed for 10 cerebral aneurysms where FDD treatment with the SILK device was simulated by virtually reducing the porosity at the aneurysm ostium. Velocity and pressure values proximal and distal to and at the aneurysm ostium as well as inside the aneurysm were quantified. In addition, dome-to-neck ratios and size ratios were determined. Multiple correlation analysis (MCA) and hierarchical cluster analysis (HCA) were conducted to demonstrate dependencies between both structural and hemodynamic parameters. Results: Velocities in the aneurysm were reduced by 0.14 m/s on average and correlated significantly (po0.05) with velocity values in the parent artery (average correlation coefficient: 0.70). Pressure changes in the aneurysm correlated significantly with pressure values in the parent artery and aneurysm (average correlation coefficient: 0.87). MCA found statistically significant correlations between velocity values and between pressure values, respectively. HCA sorted velocity parameters, pressure parameters and structural parameters into different hierarchical clusters. HCA of aneurysms based on the parameter values yielded similar results by either including all (n¼22) or only non-redundant parameters (n¼2, 3 and 4). Conclusion: Hemodynamic and structural parameters before and after virtual FDD treatment show strong inter-correlations. Redundancy of parameters was demonstrated with hierarchical cluster analysis. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Aneurysm Computational fluid dynamics Flow diverter
1. Introduction Endovascular treatment utilizing flow diverting devices (FDD) has recently been introduced for cerebral aneurysms (Arrese et al., 2013; Berge et al., 2012; De Vries et al., 2013; Gory et al., 2014; Murthy et al., 2014; Puffer et al., 2014; Takemoto et al., 2014; Zhou et al., 2014). Reported complications include delayed rupture (Karmonik et al., 2013; Mantha et al., 2009) and delayed n Correspondence to: Houston Methodist Research Institute, R1-309, 6565 Fannin, Houston TX 77030, USA. Tel.: þ 1 713 441 7979, fax: þ 1 713 441 0845. E-mail address: [email protected] (C. Karmonik).
parenchymal hemorrhage (Tomas et al., 2014). Simulations based on computational fluid dynamics (CFD) techniques have been postulated as an aid for gaining a better understanding of hemodynamics changes induced by FDD (Cebral et al., 2011; Darsaut et al., 2013; Karmonik et al., 2013; Kulcsar et al., 2012; Xu et al., 2013; Zhang et al., 2013), e.g. for obtaining better insights into treatment outcome before the actual intervention, or for identifying if a particular aneurysm is a good candidate for FDD treatment. To facilitate the use of CFD in clinical research, a research prototype of a dedicated CFD simulation environment was recently introduced where FDD placement is approximated by mathematically reducing the porosity of the aneurysm ostium
http://dx.doi.org/10.1016/j.jbiomech.2015.11.035 0021-9290/& 2015 Elsevier Ltd. All rights reserved.
Please cite this article as: Karmonik, C., et al., Relationships and redundancies of selected hemodynamic and structural parameters for characterizing virtual treatment of.... Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.035i
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(Karmonik et al., 2013, 2014). This approach represents a simplification of the actual situation where a fine mesh of stent struts is responsible for the flow diversion effect. As a result of the underlying mathematical assumptions for CFD, it is our hypothesis, that relationships between hemodynamics parameters exist which may introduce redundancies for characterizing virtual FDD treatment outcome. A better understanding of these relations is necessary for assessing the potential of CFD to characterize the hemodynamic state of a particular aneurysm. In this study, we demonstrate these relationships and consequent redundancies for pressure and velocity parameters as well as selected structural parameters, the dome–neck ratio (DNR) and the dome to parent artery radius ratio (DRR), the latter being proportional to the size ratio (SR) (Strother and Jiang, 2012). These structural parameters are of particular interest in FDD treatment as pressure values have been identified to be of interest for aneurysm rupture (Cebral et al., 2011). Velocity values can be directly assessed by non-invasive imaging (Karmonik et al., 2014). In addition to demonstrate redundancy of hemodynamic parameters, the second purpose of this study was to demonstrate that hierarchical cluster analysis (HCA) provides a means to reduce the large parametric space of hemodynamic (Mihalef et al., 2011) and structural parameters to the most significant subset. This subset is then sufficient to group or classify the investigated aneurysms.
calculated, which has to be considered when comparing the stated pressure values with values measured in the human circulation. 2.3. Pressure parameters The following pressure parameters were extracted from the simulations: pressures averaged over the entire aneurysm PRE FDD treatment (pAn) and POST FDD treatment (pAf), pressures in the parent artery proximal PRE and POST FDD treatment (pPn and pPf, respectively) as well as distal to the aneurysm before and after treatment (pDn and pDf, respectively) and pressures in the ostium at the region of inflow and at the region of outflow prior to treatment (pOp and pOm, respectively). The difference in average aneurysm pressure induced by treatment dp was calculated as dp ¼pAf–pAn. 2.4. Velocity parameters Analogous to the pressure parameters, values of the following velocity parameters were determined: velocities averaged over the entire aneurysm pre-FDD treatment (vAn) and post-FDD treatment (vAf), velocities in the parent artery proximal PRE and POST FDD treatment (vPn and vPf, respectively) as well as distal to the aneurysm before and after treatment (vDn and vDf, respectively) and velocities in the ostium at the region of inflow and at the region of outflow prior to treatment (vOp and vOm, respectively). The difference in average aneurysm velocity induced by treatment dv was calculated as dv ¼vAf-vAn. 2.5. Flow parameters Only the volumetric flow rates into the aneurysm (fOp) and out of the aneurysm after FDD treatment were included as flow changes in the parent artery are expected to be proportional to corresponding velocity changes.
2. Materials and methods 2.6. Geometrical parameters Approval of the local IRB committees was obtained for this retrospective study. 2.1. Computational simulations Further technical details describing the CFD simulations can be found in Appendix A.1. The solver that was used has been previously described (Mihalef et al., 2011) and validated (Ionasec et al., 2009) and was used to create virtual angiograms based on patient-specific angiographic image data from cerebral aneurysm (Endres et al., 2012). Diagnostic 3D digital subtraction angiography (DSA) data of 10 sidewall aneurysms of the internal carotid artery was imported into a prototype CFD workstation, version 2.0 (prototype Siemens Healthcare GmbH, Forchheim, Germany-not for clinical use). Utilizing a dedicated user interface modeled after clinical 3D visualization software, computational models of all aneurysms were created and two steady simulations, the first without a virtual FDD (PRE) and the second with a virtual FDD (POST), both with a constant inflow of 0.8 m/s and pressure zero at the outlets, were performed for each aneurysm. The velocity of 0.8 m/s was chosen to mimic systolic flow conditions in normal internal carotid arteries (Ford et al., 2005), in order to study FDD effects at maximum inflow into the aneurysm. Only steady simulations were performed as a recent comparison demonstrated good agreement of temporal means for hemodynamic parameters from transient simulations with results of steady simulations (Karmonik et al., 2015). It should be noted that using the same inflow boundary conditions for all cases leads to results, which are governed only by the geometry of the aneurysm models (Xiang et al., 2011) and the parameters characterizing the porous interface. The latter were chosen to correspond to the SILK device (Augsburger et al., 2011). These simulations, therefore, cannot take into account physiological variations of cerebral flows as no flow data from the individual patients was incorporated into the simulations (Xiang et al., 2011). Neither can they make any direct statements to aneurysm rupture risk, as rupture may not be associated with highest flows. 2.2. Hemodynamic and geometrical parameters The following naming conventions were used to consistently name the hemodynamic parameters: the first letter denotes the physical property (p: pressure, v – velocity, f: flow),the second letter denotes the location: A: aneurysm, P: proximal, D: distal, O: ostium. The last parameter specifies PRE, i.e., native (n) or POST FDD treatment (f), or, in the case of parameters derived for the ostium, the direction of the velocity/flow either into the aneurysm: p (plus) or out of the aneurysm: m (minus). The locations and techniques for extracting the values of these parameters are further illustrated in Fig. 1 and in Appendix A.2. It should be remembered though, that CFD is only able to calculate pressure up to an arbitrary constant. In our setup, outflow pressure was given by the zero pressure boundary condition and inflow pressure was given by the constant inflow velocity. This means, that effectively the pressure drop across the computational model was
DRR, proportional by a factor of two to the size ratio (DRR) and DNR were obtained from standard fluoroscopic projection images.
3. Data analysis For additional technical details of the data analysis please refer to Appendix A.2.
3.1. Multiple correlation analysis A correlation matrix of all parameters was created to identify statistical significant (statistical significance was defined as po 0.05) relationships between parameters. Parameters that are dependent on each other will introduce redundancy when used to describe the hemodynamic state of a particular aneurysm.
3.2. Hierarchical cluster analysis Two separate HCA steps were performed. In the first step, the hemodynamic and structural parameters were clustered whereby each parameter was described by its values derived from the simulation result for each aneurysm. Clusters identified in this step will contain each a set of redundant parameters. In contract to MCA introduced on the previous section, moving up in the hierarchy of clusters in the HCA dendogram allows to reduce the parameter set thereby eliminating redundant parameters (i.e. by choosing one representative parameter for each cluster). This is further illustrated in the second HCA step, where all aneurysms were clustered using either the entire parameter set (n ¼22) or reduced sets of n ¼4,3, and 2 with redundant parameters eliminated. Similarity of the obtained aneurysm clusters is then indicative of successfully removing redundant parameters.
Please cite this article as: Karmonik, C., et al., Relationships and redundancies of selected hemodynamic and structural parameters for characterizing virtual treatment of.... Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.035i
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Fig. 1. Left panel: upper left shows the 3D surface reconstruction of aneurysm #8 together with the virtual flow diverter (blue, A) and upper right the velocity field obtained from the CFD simulations (B). In the center (C), surface normal vectors (in red) are displayed as calculated within Paraview. The lower panel (D) shows the velocity components perpendicular to the surface of the virtual FDD (red/orange: inflow into the aneurysm, blue: outflow out of the aneurysm), the values of which were calculated using the inner vector product between the velocity vectors and the surface normals. Right panel: on top (E), cut planes and rectangular box from which hemodynamic parameters for the parent and distal artery as well as for the aneurysm was extracted. Below (F), inflow and outflow areas at the virtual FDD surface from which hemodynamic parameters for the ostium were extracted (units of the velocities are in mm/s). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
4. Results
4.3. First HCA step
4.1. Comparison of CFD simulation results with and without FDD
HCA identified a separation into groups containing only pressure values of the aneurysm and the parent artery, only velocities of the parent artery as well as two ‘mixed’ groups with the remaining parameters (Fig. 3a).
The mean value over all cases for vAf was 0.14 m/s lower than vAn, range: 0 to 0.37 m/s, corresponding to a mean reduction of 4% (range: 0–10.8%). Mean values and distributions for vPn and vPf were identical (average: 0.82 m/s, range: 0.18–1.6 m/s). Mean values for vDn (0.82 m/s, range: 0.19–1.7 m/s) and vDf (0.82 m/s, range: 0.17–1.7 m/s) were in good agreement with absolute relative sum of differences being 21%. Mean difference between fOp and fOm was 6%.
4.2. Multiple correlation analysis Several relationship separating the investigated parameters in different groups are identifiable in the correlation matrix (Fig. 2): velocities in the parent artery segment and inside the aneurysm correlated significantly with each other as did pressures. Similarly, velocity at the aneurysm ostium (inflow and outflow) correlated with each other and with PRE–POST velocities in the aneurysm. DNR and DRR correlated significantly with each other as did fOp and fOm. No significant inter-group correlations were observed. Reduction in aneurysm velocity dv inversely correlated significantly with the velocity in the parent artery segments before and after virtual treatment (vPf: 0.73; vPn: 0.73; vDf: 0.66 and vDn: 0.68, Fig. 2).
4.4. Second HCA step Applying hierarchical clustering including all parameters (n ¼22) identified 5 groups of aneurysms with similar hemodynamics (group 1: aneurysm #7, group 2: #5 and #8, group 3: #4, #1, #6 and #9, group 4: #2 and group 5: #3 and #10, Fig. 3b). Reducing the parameter set by choosing representative parameters for each cluster in the parameter cluster hierarchy obtained in the first HCA step (four parameters: pAn, vPn, dp and vAn and three parameters: pAn, vPn, dp ) yielded identical groups (albeit a small variation in group 3 between aneurysm #1 and #4, Fig. 3b). Further reducing the parameter set (two parameters pAn and vPn) resulted in similar groups but with a different structure of the HCA dendogram (Fig. 3b).
5. Discussion CFD simulations of FDD treatment in cerebral aneurysm were performed where the actual treatment was simulated by replacing the ostium surface by a porous media. This approach has been reported to successfully model the effects of FDD where results
Please cite this article as: Karmonik, C., et al., Relationships and redundancies of selected hemodynamic and structural parameters for characterizing virtual treatment of.... Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.035i
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Fig. 2. Correlation matrix of the hemodynamic parameters (listed at the diagonal). The lower triangular matrix shows scatterplots with red lines as guides to the eye, blue color denotes positive correlation, red color negative correlation. The upper triangular matrix gives absolute value of correlation coefficient together with statistical significance as follows: *p o0.1, **po 0.05, ***p o 0.01. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
showed good agreement with clinical findings (Augsburger et al., 2011; Zhang et al., 2013). The prototype of a dedicated simulation environment was employed. Previously, it has been demonstrated that this prototype is capable of reproducing major hemodynamic features in cerebral aneurysms by direct comparison with velocities measured with 2D phase contrast magnetic resonance imaging (2D pcMRI) (Karmonik et al., 2014). The advantage of this prototype consists in its optimized user interface for creating the computational model of the aneurysm as well as the standardization of the CFD simulations, which might be of importance when comparing simulation results from multiple centers. The potential significance of our findings is that, MCA revealed orthogonal parameter spaces of velocities and pressure with high intra-group correlations. The orthogonal nature of the velocity and pressure subspaces suggests that velocity measurements cannot serve as a surrogate marker for pressure changes inside the aneurysm. Still, the high correlation between velocity values in the parent artery and the change in velocities in the aneurysm itself may be of interest, as blood flow velocities can be measured noninvasively by Doppler ultrasound or by phase contrast magnetic resonance. The techniques are non-invasive and clinically available towards providing boundary conditions and validation for CFD. While the former is limited to find a suitable transmission window through the skull bones, the latter suffers from artifacts in the vicinity of metal implants. Measuring the velocity in the parent artery away from the FDD may in this respect be of advantage. Velocities inside the aneurysm after FDD treatment have recently
been related to degree of local occlusion (Cebral et al., 2014; Kulcsar et al., 2012). Currently, absolute pressure values are only accessible by invasive means (pressure catheters) and thus cannot be appreciated or estimated non-invasively prior to treatment. CFD simulations therefore remain an appealing alternative for calculating pressures based on patient-derived computational models without the need for invasive catherization, associated with significant risk for adverse events. A further significant point is that, our sensitivity analysis of the HCA results demonstrated that the CFD parameters are not necessarily independent from each other and their number can be markedly reduced to yield the same measure of aneurysm similarity. Our analysis was limited to steady simulations thereby excluding inherent transient effects and parameters such as the oscillatory shear index. Recent studies have demonstrated stable flow patterns at the aneurysm ostium for transient conditions (Mantha et al., 2009) and comparable behavior of temporally averaged parameters with those from steady simulations (Karmonik et al., 2015), thereby justifying our approach. As it is well known, flow in the ICA varies between healthy individuals, within one side usually being the dominant side, but also with age (Ford et al., 2005; Amin-Hanjani et al., 2015). Here, each computational model served as its own control (before and after virtual treatment) with inflow values in the normal physiological range. For simulating an individual aneurysm, ideally flow measurements
Please cite this article as: Karmonik, C., et al., Relationships and redundancies of selected hemodynamic and structural parameters for characterizing virtual treatment of.... Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.035i
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Fig. 3. (A) HCA dendrogram for all 22 parameters for the first HCA step. Of note is the separation of pressures from other parameters. Colored lines visualize the approach for reducing the parameter set by only including a representative parameter of a cluster in the higher hierarchy of the dendogram. (red: two clusters, parameters used: pAn and vPn; green: three clusters, parameters used: pAn, vPn and dp; blue: four clusters: parameters used: pAn, vPn, dp and vAn). Results of the second HCA step implementing clustering with these reduced parameters are shown in (B). (B) Results of the second HCA step performed with the entire parameter set (left) and reduced parameter sets (A). n: number of parameters which are explicitly given in the boxes. Color-coding of boxes corresponds to colors in (A). On left: Aneurysm models used in this study together with virtual FDD (dark color) and regions of ostium inflow (red/orange) and outflow (blue) as introduced in Fig. 1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
either with MRI or transcranial Doppler should be used to enhance the fidelity of the computation results. The porous media approach employed here may be considered sufficient to capture the main features of flow, which was the intent of this study. For detailed flow features, in particular around the stent struts of the SILK FDD, a more detailed analysis may be necessary by actually simulating the deployment of the stent using finite element analysis. First reported results of this kind of studies are promising and yield great potential albeit increased computational complexity and time requirements are drawbacks (Ma et al., 2012, 2014).
knowledge or beliefs) in the subject matter or materials discussed in this manuscript. J Beilner and JJ Ge are employees of Siemens.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jbiomech.2015.11.035.
References 6. Conclusion The goal of the present study was to demonstrate that due to the underlying mathematical assumptions of the CFD technique, calculated hemodynamic parameters are expected to exhibit relations between each other, which consequently introduces redundancies. These relations and redundancies, as described here for velocities and pressure parameters in the virtual treatment of cerebral aneurysms using FDD are important for adequately assessing the potential but also the limitations of CFD.
Conflict of interest statement All authors except J Beilner and JJ Ge certify that they have no affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations,
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Relationships and redundancies of selected hemodynamic and structural parameters for characterizing virtual treatment of cerebral aneurysms with flow diverter devices C. Karmonik a,b,n, J.R. Anderson a, J. Beilner c, J.J. Ge c, S. Partovi d, R.P. Klucznik e, O. Diaz e, Y.J. Zhang b, G.W. Britz b, R.G. Grossman b, N. Lv f, Q. Huang f a
MRI Core, Houston Methodist Research Institute, Houston, TX, USA Cerebrovascular Center, Neurosurgery, Houston Methodist, Houston, TX, USA Siemens AX, Shanghai, China d Department of Radiology, University Hospitals Case Medical Center, Case Western Reserve University, Cleveland, OH, USA e Cerebrovascular Center, Radiology, Houston Methodist, Houston, TX, USA f Neurosurgery, The Affiliated Changhai Hospital of Second Military Medical University, Shanghai, China b c
art ic l e i nf o
a b s t r a c t
Article history: Accepted 13 November 2015
Background and purpose: To quantify the relationship and to demonstrate redundancies between hemodynamic and structural parameters before and after virtual treatment with a flow diverter device (FDD) in cerebral aneurysms. Methods: Steady computational fluid dynamics (CFD) simulations were performed for 10 cerebral aneurysms where FDD treatment with the SILK device was simulated by virtually reducing the porosity at the aneurysm ostium. Velocity and pressure values proximal and distal to and at the aneurysm ostium as well as inside the aneurysm were quantified. In addition, dome-to-neck ratios and size ratios were determined. Multiple correlation analysis (MCA) and hierarchical cluster analysis (HCA) were conducted to demonstrate dependencies between both structural and hemodynamic parameters. Results: Velocities in the aneurysm were reduced by 0.14 m/s on average and correlated significantly (po0.05) with velocity values in the parent artery (average correlation coefficient: 0.70). Pressure changes in the aneurysm correlated significantly with pressure values in the parent artery and aneurysm (average correlation coefficient: 0.87). MCA found statistically significant correlations between velocity values and between pressure values, respectively. HCA sorted velocity parameters, pressure parameters and structural parameters into different hierarchical clusters. HCA of aneurysms based on the parameter values yielded similar results by either including all (n¼22) or only non-redundant parameters (n¼2, 3 and 4). Conclusion: Hemodynamic and structural parameters before and after virtual FDD treatment show strong inter-correlations. Redundancy of parameters was demonstrated with hierarchical cluster analysis. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Aneurysm Computational fluid dynamics Flow diverter
1. Introduction Endovascular treatment utilizing flow diverting devices (FDD) has recently been introduced for cerebral aneurysms (Arrese et al., 2013; Berge et al., 2012; De Vries et al., 2013; Gory et al., 2014; Murthy et al., 2014; Puffer et al., 2014; Takemoto et al., 2014; Zhou et al., 2014). Reported complications include delayed rupture (Karmonik et al., 2013; Mantha et al., 2009) and delayed n Correspondence to: Houston Methodist Research Institute, R1-309, 6565 Fannin, Houston TX 77030, USA. Tel.: þ 1 713 441 7979, fax: þ 1 713 441 0845. E-mail address: [email protected] (C. Karmonik).
parenchymal hemorrhage (Tomas et al., 2014). Simulations based on computational fluid dynamics (CFD) techniques have been postulated as an aid for gaining a better understanding of hemodynamics changes induced by FDD (Cebral et al., 2011; Darsaut et al., 2013; Karmonik et al., 2013; Kulcsar et al., 2012; Xu et al., 2013; Zhang et al., 2013), e.g. for obtaining better insights into treatment outcome before the actual intervention, or for identifying if a particular aneurysm is a good candidate for FDD treatment. To facilitate the use of CFD in clinical research, a research prototype of a dedicated CFD simulation environment was recently introduced where FDD placement is approximated by mathematically reducing the porosity of the aneurysm ostium
http://dx.doi.org/10.1016/j.jbiomech.2015.11.035 0021-9290/& 2015 Elsevier Ltd. All rights reserved.
Please cite this article as: Karmonik, C., et al., Relationships and redundancies of selected hemodynamic and structural parameters for characterizing virtual treatment of.... Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.035i
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(Karmonik et al., 2013, 2014). This approach represents a simplification of the actual situation where a fine mesh of stent struts is responsible for the flow diversion effect. As a result of the underlying mathematical assumptions for CFD, it is our hypothesis, that relationships between hemodynamics parameters exist which may introduce redundancies for characterizing virtual FDD treatment outcome. A better understanding of these relations is necessary for assessing the potential of CFD to characterize the hemodynamic state of a particular aneurysm. In this study, we demonstrate these relationships and consequent redundancies for pressure and velocity parameters as well as selected structural parameters, the dome–neck ratio (DNR) and the dome to parent artery radius ratio (DRR), the latter being proportional to the size ratio (SR) (Strother and Jiang, 2012). These structural parameters are of particular interest in FDD treatment as pressure values have been identified to be of interest for aneurysm rupture (Cebral et al., 2011). Velocity values can be directly assessed by non-invasive imaging (Karmonik et al., 2014). In addition to demonstrate redundancy of hemodynamic parameters, the second purpose of this study was to demonstrate that hierarchical cluster analysis (HCA) provides a means to reduce the large parametric space of hemodynamic (Mihalef et al., 2011) and structural parameters to the most significant subset. This subset is then sufficient to group or classify the investigated aneurysms.
calculated, which has to be considered when comparing the stated pressure values with values measured in the human circulation. 2.3. Pressure parameters The following pressure parameters were extracted from the simulations: pressures averaged over the entire aneurysm PRE FDD treatment (pAn) and POST FDD treatment (pAf), pressures in the parent artery proximal PRE and POST FDD treatment (pPn and pPf, respectively) as well as distal to the aneurysm before and after treatment (pDn and pDf, respectively) and pressures in the ostium at the region of inflow and at the region of outflow prior to treatment (pOp and pOm, respectively). The difference in average aneurysm pressure induced by treatment dp was calculated as dp ¼pAf–pAn. 2.4. Velocity parameters Analogous to the pressure parameters, values of the following velocity parameters were determined: velocities averaged over the entire aneurysm pre-FDD treatment (vAn) and post-FDD treatment (vAf), velocities in the parent artery proximal PRE and POST FDD treatment (vPn and vPf, respectively) as well as distal to the aneurysm before and after treatment (vDn and vDf, respectively) and velocities in the ostium at the region of inflow and at the region of outflow prior to treatment (vOp and vOm, respectively). The difference in average aneurysm velocity induced by treatment dv was calculated as dv ¼vAf-vAn. 2.5. Flow parameters Only the volumetric flow rates into the aneurysm (fOp) and out of the aneurysm after FDD treatment were included as flow changes in the parent artery are expected to be proportional to corresponding velocity changes.
2. Materials and methods 2.6. Geometrical parameters Approval of the local IRB committees was obtained for this retrospective study. 2.1. Computational simulations Further technical details describing the CFD simulations can be found in Appendix A.1. The solver that was used has been previously described (Mihalef et al., 2011) and validated (Ionasec et al., 2009) and was used to create virtual angiograms based on patient-specific angiographic image data from cerebral aneurysm (Endres et al., 2012). Diagnostic 3D digital subtraction angiography (DSA) data of 10 sidewall aneurysms of the internal carotid artery was imported into a prototype CFD workstation, version 2.0 (prototype Siemens Healthcare GmbH, Forchheim, Germany-not for clinical use). Utilizing a dedicated user interface modeled after clinical 3D visualization software, computational models of all aneurysms were created and two steady simulations, the first without a virtual FDD (PRE) and the second with a virtual FDD (POST), both with a constant inflow of 0.8 m/s and pressure zero at the outlets, were performed for each aneurysm. The velocity of 0.8 m/s was chosen to mimic systolic flow conditions in normal internal carotid arteries (Ford et al., 2005), in order to study FDD effects at maximum inflow into the aneurysm. Only steady simulations were performed as a recent comparison demonstrated good agreement of temporal means for hemodynamic parameters from transient simulations with results of steady simulations (Karmonik et al., 2015). It should be noted that using the same inflow boundary conditions for all cases leads to results, which are governed only by the geometry of the aneurysm models (Xiang et al., 2011) and the parameters characterizing the porous interface. The latter were chosen to correspond to the SILK device (Augsburger et al., 2011). These simulations, therefore, cannot take into account physiological variations of cerebral flows as no flow data from the individual patients was incorporated into the simulations (Xiang et al., 2011). Neither can they make any direct statements to aneurysm rupture risk, as rupture may not be associated with highest flows. 2.2. Hemodynamic and geometrical parameters The following naming conventions were used to consistently name the hemodynamic parameters: the first letter denotes the physical property (p: pressure, v – velocity, f: flow),the second letter denotes the location: A: aneurysm, P: proximal, D: distal, O: ostium. The last parameter specifies PRE, i.e., native (n) or POST FDD treatment (f), or, in the case of parameters derived for the ostium, the direction of the velocity/flow either into the aneurysm: p (plus) or out of the aneurysm: m (minus). The locations and techniques for extracting the values of these parameters are further illustrated in Fig. 1 and in Appendix A.2. It should be remembered though, that CFD is only able to calculate pressure up to an arbitrary constant. In our setup, outflow pressure was given by the zero pressure boundary condition and inflow pressure was given by the constant inflow velocity. This means, that effectively the pressure drop across the computational model was
DRR, proportional by a factor of two to the size ratio (DRR) and DNR were obtained from standard fluoroscopic projection images.
3. Data analysis For additional technical details of the data analysis please refer to Appendix A.2.
3.1. Multiple correlation analysis A correlation matrix of all parameters was created to identify statistical significant (statistical significance was defined as po 0.05) relationships between parameters. Parameters that are dependent on each other will introduce redundancy when used to describe the hemodynamic state of a particular aneurysm.
3.2. Hierarchical cluster analysis Two separate HCA steps were performed. In the first step, the hemodynamic and structural parameters were clustered whereby each parameter was described by its values derived from the simulation result for each aneurysm. Clusters identified in this step will contain each a set of redundant parameters. In contract to MCA introduced on the previous section, moving up in the hierarchy of clusters in the HCA dendogram allows to reduce the parameter set thereby eliminating redundant parameters (i.e. by choosing one representative parameter for each cluster). This is further illustrated in the second HCA step, where all aneurysms were clustered using either the entire parameter set (n ¼22) or reduced sets of n ¼4,3, and 2 with redundant parameters eliminated. Similarity of the obtained aneurysm clusters is then indicative of successfully removing redundant parameters.
Please cite this article as: Karmonik, C., et al., Relationships and redundancies of selected hemodynamic and structural parameters for characterizing virtual treatment of.... Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.035i
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Fig. 1. Left panel: upper left shows the 3D surface reconstruction of aneurysm #8 together with the virtual flow diverter (blue, A) and upper right the velocity field obtained from the CFD simulations (B). In the center (C), surface normal vectors (in red) are displayed as calculated within Paraview. The lower panel (D) shows the velocity components perpendicular to the surface of the virtual FDD (red/orange: inflow into the aneurysm, blue: outflow out of the aneurysm), the values of which were calculated using the inner vector product between the velocity vectors and the surface normals. Right panel: on top (E), cut planes and rectangular box from which hemodynamic parameters for the parent and distal artery as well as for the aneurysm was extracted. Below (F), inflow and outflow areas at the virtual FDD surface from which hemodynamic parameters for the ostium were extracted (units of the velocities are in mm/s). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
4. Results
4.3. First HCA step
4.1. Comparison of CFD simulation results with and without FDD
HCA identified a separation into groups containing only pressure values of the aneurysm and the parent artery, only velocities of the parent artery as well as two ‘mixed’ groups with the remaining parameters (Fig. 3a).
The mean value over all cases for vAf was 0.14 m/s lower than vAn, range: 0 to 0.37 m/s, corresponding to a mean reduction of 4% (range: 0–10.8%). Mean values and distributions for vPn and vPf were identical (average: 0.82 m/s, range: 0.18–1.6 m/s). Mean values for vDn (0.82 m/s, range: 0.19–1.7 m/s) and vDf (0.82 m/s, range: 0.17–1.7 m/s) were in good agreement with absolute relative sum of differences being 21%. Mean difference between fOp and fOm was 6%.
4.2. Multiple correlation analysis Several relationship separating the investigated parameters in different groups are identifiable in the correlation matrix (Fig. 2): velocities in the parent artery segment and inside the aneurysm correlated significantly with each other as did pressures. Similarly, velocity at the aneurysm ostium (inflow and outflow) correlated with each other and with PRE–POST velocities in the aneurysm. DNR and DRR correlated significantly with each other as did fOp and fOm. No significant inter-group correlations were observed. Reduction in aneurysm velocity dv inversely correlated significantly with the velocity in the parent artery segments before and after virtual treatment (vPf: 0.73; vPn: 0.73; vDf: 0.66 and vDn: 0.68, Fig. 2).
4.4. Second HCA step Applying hierarchical clustering including all parameters (n ¼22) identified 5 groups of aneurysms with similar hemodynamics (group 1: aneurysm #7, group 2: #5 and #8, group 3: #4, #1, #6 and #9, group 4: #2 and group 5: #3 and #10, Fig. 3b). Reducing the parameter set by choosing representative parameters for each cluster in the parameter cluster hierarchy obtained in the first HCA step (four parameters: pAn, vPn, dp and vAn and three parameters: pAn, vPn, dp ) yielded identical groups (albeit a small variation in group 3 between aneurysm #1 and #4, Fig. 3b). Further reducing the parameter set (two parameters pAn and vPn) resulted in similar groups but with a different structure of the HCA dendogram (Fig. 3b).
5. Discussion CFD simulations of FDD treatment in cerebral aneurysm were performed where the actual treatment was simulated by replacing the ostium surface by a porous media. This approach has been reported to successfully model the effects of FDD where results
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Fig. 2. Correlation matrix of the hemodynamic parameters (listed at the diagonal). The lower triangular matrix shows scatterplots with red lines as guides to the eye, blue color denotes positive correlation, red color negative correlation. The upper triangular matrix gives absolute value of correlation coefficient together with statistical significance as follows: *p o0.1, **po 0.05, ***p o 0.01. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
showed good agreement with clinical findings (Augsburger et al., 2011; Zhang et al., 2013). The prototype of a dedicated simulation environment was employed. Previously, it has been demonstrated that this prototype is capable of reproducing major hemodynamic features in cerebral aneurysms by direct comparison with velocities measured with 2D phase contrast magnetic resonance imaging (2D pcMRI) (Karmonik et al., 2014). The advantage of this prototype consists in its optimized user interface for creating the computational model of the aneurysm as well as the standardization of the CFD simulations, which might be of importance when comparing simulation results from multiple centers. The potential significance of our findings is that, MCA revealed orthogonal parameter spaces of velocities and pressure with high intra-group correlations. The orthogonal nature of the velocity and pressure subspaces suggests that velocity measurements cannot serve as a surrogate marker for pressure changes inside the aneurysm. Still, the high correlation between velocity values in the parent artery and the change in velocities in the aneurysm itself may be of interest, as blood flow velocities can be measured noninvasively by Doppler ultrasound or by phase contrast magnetic resonance. The techniques are non-invasive and clinically available towards providing boundary conditions and validation for CFD. While the former is limited to find a suitable transmission window through the skull bones, the latter suffers from artifacts in the vicinity of metal implants. Measuring the velocity in the parent artery away from the FDD may in this respect be of advantage. Velocities inside the aneurysm after FDD treatment have recently
been related to degree of local occlusion (Cebral et al., 2014; Kulcsar et al., 2012). Currently, absolute pressure values are only accessible by invasive means (pressure catheters) and thus cannot be appreciated or estimated non-invasively prior to treatment. CFD simulations therefore remain an appealing alternative for calculating pressures based on patient-derived computational models without the need for invasive catherization, associated with significant risk for adverse events. A further significant point is that, our sensitivity analysis of the HCA results demonstrated that the CFD parameters are not necessarily independent from each other and their number can be markedly reduced to yield the same measure of aneurysm similarity. Our analysis was limited to steady simulations thereby excluding inherent transient effects and parameters such as the oscillatory shear index. Recent studies have demonstrated stable flow patterns at the aneurysm ostium for transient conditions (Mantha et al., 2009) and comparable behavior of temporally averaged parameters with those from steady simulations (Karmonik et al., 2015), thereby justifying our approach. As it is well known, flow in the ICA varies between healthy individuals, within one side usually being the dominant side, but also with age (Ford et al., 2005; Amin-Hanjani et al., 2015). Here, each computational model served as its own control (before and after virtual treatment) with inflow values in the normal physiological range. For simulating an individual aneurysm, ideally flow measurements
Please cite this article as: Karmonik, C., et al., Relationships and redundancies of selected hemodynamic and structural parameters for characterizing virtual treatment of.... Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.035i
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Fig. 3. (A) HCA dendrogram for all 22 parameters for the first HCA step. Of note is the separation of pressures from other parameters. Colored lines visualize the approach for reducing the parameter set by only including a representative parameter of a cluster in the higher hierarchy of the dendogram. (red: two clusters, parameters used: pAn and vPn; green: three clusters, parameters used: pAn, vPn and dp; blue: four clusters: parameters used: pAn, vPn, dp and vAn). Results of the second HCA step implementing clustering with these reduced parameters are shown in (B). (B) Results of the second HCA step performed with the entire parameter set (left) and reduced parameter sets (A). n: number of parameters which are explicitly given in the boxes. Color-coding of boxes corresponds to colors in (A). On left: Aneurysm models used in this study together with virtual FDD (dark color) and regions of ostium inflow (red/orange) and outflow (blue) as introduced in Fig. 1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
either with MRI or transcranial Doppler should be used to enhance the fidelity of the computation results. The porous media approach employed here may be considered sufficient to capture the main features of flow, which was the intent of this study. For detailed flow features, in particular around the stent struts of the SILK FDD, a more detailed analysis may be necessary by actually simulating the deployment of the stent using finite element analysis. First reported results of this kind of studies are promising and yield great potential albeit increased computational complexity and time requirements are drawbacks (Ma et al., 2012, 2014).
knowledge or beliefs) in the subject matter or materials discussed in this manuscript. J Beilner and JJ Ge are employees of Siemens.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jbiomech.2015.11.035.
References 6. Conclusion The goal of the present study was to demonstrate that due to the underlying mathematical assumptions of the CFD technique, calculated hemodynamic parameters are expected to exhibit relations between each other, which consequently introduces redundancies. These relations and redundancies, as described here for velocities and pressure parameters in the virtual treatment of cerebral aneurysms using FDD are important for adequately assessing the potential but also the limitations of CFD.
Conflict of interest statement All authors except J Beilner and JJ Ge certify that they have no affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations,
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Please cite this article as: Karmonik, C., et al., Relationships and redundancies of selected hemodynamic and structural parameters for characterizing virtual treatment of.... Journal of Biomechanics (2015), http://dx.doi.org/10.1016/j.jbiomech.2015.11.035i