Efficient estimation of three-dimensional curves and their derivatives by free-knot regression splines, applied to the analysis of inner carotid artery centrelines

Residence time in complex left main bifurcation disease after stenting

BACKGROUND

Data regarding the mean resident time (RT) after left main (LM) bifurcation stenting are scant. In the present study we performed a patient-specific computational fluid dynamic (CFD) analysis to investigate the different post-stenting mean RT values in LM patients treated with single-or double stenting techniques.

METHODS

Patients were identified after reviewing the local Optical Coherence Tomography (OCT) scans database. Overall, 27 patients (mean age 65.5 ± 12.4, 21 males) [10 patients treated with provisional cross-over stenting, 7 with the double kissing crush (DK crush) and 10 with the nano-inverted T (NIT) technique, respectively] with isolated and significant LM bifurcation disease were analyzed.

RESULTS

After LM bifurcation stenting, the NIT showed a higher averages WSS values at all bifurcation sites compared to DK crush and provisional cross-over stenting. Moreover, the mean RT resulted lower after NIT compared to provisional or DK crush. During the diastolic phase, the average RT of the entire LM bifurcation was 0.46 s, 0.38 s and 0.33 s after using the provisional stenting, DK crush and NIT, respectively. Moreover, the average RT in the LM bifurcation decreased by 17.1 % using the DK crush and by 28.2 % using the NIT compared to the Provisional.

CONCLUSION

The present OCT-derived CFD analysis revealed that, in patients with complex bifurcation LM disease, the provisional approach resulted in lower WSS values, while double stenting techniques, especially the NIT technique, resulted in a marked reduction of average RT compared to the provisional approach.

CONDENSED ABSTRACT

In the present study we performed a patient-specific Optical coherence tomography (OCT)-based computational fluid dynamic (CFD) analysis to investigate the different post-stenting mean RT values in 27 patients treated with provisional cross-over stenting, DK crush and Nano-inverted-T (NIT) stenting. The NIT showed a higher averages WSS values at all bifurcation sites compared to DK crush and Provisional. The mean RT resulted lower in NIT compared to Provisional or DK crush. During the entire diastolic phase, the average RT of the entire LM bifurcation was 0.46 s, 0.38 s and 0.33 s after using the provisional stenting, DK crush and NIT, respectively. Moreover, the average RT in the entire LM bifurcation decreased by 17.1 % using the DK crush and by 28.2 % using the NIT compared to the Provisional.

Modeling and hexahedral meshing of cerebral arterial networks from centerlines

Computational fluid dynamics (CFD) simulation provides valuable information on blood flow from the vascular geometry. However, it requires extracting precise models of arteries from low-resolution medical images, which remains challenging. Centerline-based representation is widely used to model large vascular networks with small vessels, as it encodes both the geometric and topological information and facilitates manual editing. In this work, we propose an automatic method to generate a structured hexahedral mesh suitable for CFD directly from centerlines. We addressed both the modeling and meshing tasks. We proposed a vessel model based on penalized splines to overcome the limitations inherent to the centerline representation, such as noise and sparsity. The bifurcations are reconstructed using a parametric model based on the anatomy that we extended to planar n-furcations. Finally, we developed a method to produce a volume mesh with structured, hexahedral, and flow-oriented cells from the proposed vascular network model. The proposed method offers better robustness to the common defects of centerlines and increases the mesh quality compared to state-of-the-art methods. As it relies on centerlines alone, it can be applied to edit the vascular model effortlessly to study the impact of vascular geometry and topology on hemodynamics. We demonstrate the efficiency of our method by entirely meshing a dataset of 60 cerebral vascular networks. 92% of the vessels and 83% of the bifurcations were meshed without defects needing manual intervention, despite the challenging aspect of the input data. The source code is released publicly.

Is spontaneous coronary artery dissection (SCAD) related to local anatomy and hemodynamics? An exploratory study

AIMS

Spontaneous coronary artery dissection (SCAD) is an increasingly diagnosed cause of myocardial infarction with unclear pathophysiology. The aim of the study was to test if vascular segments site of SCAD present distinctive local anatomy and hemodynamic profiles.

METHODS

Coronary arteries with spontaneously healed SCAD (confirmed by follow-up angiography) underwent three-dimensional reconstruction, morphometric analysis with definition of vessel local curvature and torsion, and computational fluid dynamics (CFD) simulations with derivation of time-averaged wall shear stress (TAWSS) and topological shear variation index (TSVI). The (reconstructed) healed proximal SCAD segment was visually inspected for co-localization with curvature, torsion, and CFD-derived quantities hot spots.

RESULTS

Thirteen vessels with healed SCAD underwent the morpho-functional analysis. Median time between baseline and follow-up coronary angiograms was 57 (interquartile range [IQR] 45-95) days. In seven cases (53.9%), SCAD was classified as type 2b and occurred in the left anterior descending artery or near a bifurcation. In all cases (100%), at least one hot spot co-localized within the healed proximal SCAD segment, in 9 cases (69.2%) ≥3 hot spots were identified. Healed SCAD in proximity of a coronary bifurcation presented lower TAWSS peak values (6.65 [IQR 6.20-13.2] vs. 3.81 [2.53-5.17] Pa, p = 0.008) and hosted less frequently TSVI hot spots (100% vs. 57.1%, p = 0.034).

CONCLUSION

Vascular segments of healed SCAD were characterized by high curvature/torsion and WSS profiles reflecting increased local flow disturbances. Hence, a pathophysiological role of the interaction between vessel anatomy and shear forces in SCAD is hypothesized.

Classification of EEG signals: An interpretable approach using functional data analysis

Electroencephalography (EEG) is a noninvasive method to record electrical activity of the brain. The EEG data is continuous flow of voltages, in this paper, we consider them as functional data, and propose a three-stage algorithm based on functional data analysis, with the advantage of interpretability. Specifically, the time and frequency information are extracted by wavelet transform in the first stage. Then, functional testing is utilized to select EEG channels and frequencies that show significant differences for different human behaviors. In the third stage, we propose to use penalized multiple functional logistic regression to interpretably classify human behaviors. With simulation and a scalp EEG data as validation set, we show that the proposed three-stage algorithm provides an interpretable classification of the scalp EEG signals.

Comparison of Swine and Human Computational Hemodynamics Models for the Study of Coronary Atherosclerosis

Coronary atherosclerosis is a leading cause of illness and death in Western World and its mechanisms are still non completely understood. Several animal models have been used to 1) study coronary atherosclerosis natural history and 2) propose predictive tools for this disease, that is asymptomatic for a long time, aiming for a direct translation of their findings to human coronary arteries. Among them, swine models are largely used due to the observed anatomical and pathophysiological similarities to humans. However, a direct comparison between swine and human models in terms of coronary hemodynamics, known to influence atherosclerotic onset/development, is still lacking. In this context, we performed a detailed comparative analysis between swine- and human-specific computational hemodynamic models of coronary arteries. The analysis involved several near-wall and intravascular flow descriptors, previously emerged as markers of coronary atherosclerosis initiation/progression, as well as anatomical features. To do that, non-culprit coronary arteries (18 right–RCA, 18 left anterior descending–LAD, 13 left circumflex–LCX coronary artery) from patients presenting with acute coronary syndrome were imaged by intravascular ultrasound and coronary computed tomography angiography. Similarly, the three main coronary arteries of ten adult mini-pigs were also imaged (10 RCA, 10 LAD, 10 LCX). The geometries of the imaged coronary arteries were reconstructed (49 human, 30 swine), and computational fluid dynamic simulations were performed by imposing individualized boundary conditions. Overall, no relevant differences in 1) wall shear stress-based quantities, 2) intravascular hemodynamics (in terms of helical flow features), and 3) anatomical features emerged between human- and swine-specific models. The findings of this study strongly support the use of swine-specific computational models to study and characterize the hemodynamic features linked to coronary atherosclerosis, sustaining the reliability of their translation to human vascular disease.

The Effect of Geometric and Hemodynamic Parameters on Blood Flow Efficiency in Repaired Tetralogy of Fallot Patients

Surgical repair of Tetralogy of Fallot (TOF) involves a series of steps to remove right ventricular outflow tract and pulmonary artery obstruction. However, the large degree of anatomic variability among preoperative TOF patients may impact the effectiveness of different repair strategies and, subsequently, different geometric modifications for different patients. This study investigates the relationships between geometric and hemodynamic parameters and mechanical energy efficiency for a patient-specific dataset of 16 postoperative TOF repairs, using morphometric and statistical shape analyses, as well as computational fluid dynamics simulations with physiologically-relevant inlet and outlet boundary conditions. Quantitatively, negative correlations were found between the right and left pulmonary artery centerline tract cumulative torsion and energy efficiency (r = - 0.65, p = 0.01, for both). A positive correlation was also found for a statistical shape mode associated with skewing of the geometric sub-regions (r = 0.61, p = 0.01). Qualitatively, medium- and low-efficiency geometries exhibit disturbed flow and much more proximal vortex formation as compared to a high-efficiency geometry. Thus, it is recommended, as much as possible, to both relieve and avoid the introduction of torsion into the patient's anatomy during surgical repair of TOF.

Feature extraction of EEG signals based on functional data analysis and its application to recognition of driver fatigue state

OBJECTIVE

Our objective is to study how to obtain features which can reflect the continuity and internal dynamic changes of electroencephalography (EEG) signals and study an effective method for fatigued driving state recognition based on the obtained features.

APPROACH

A method of EEG signalfeature extraction based on functional data analysis is proposed. Combined with kernel principal component analysis method, the obtained features are applied to the recognition of driver fatigue state, and a corresponding recognition model of fatigued driving state is constructed.

MAIN RESULTS

The recognition model is tested on the real collected driver fatigue EEG signals by selecting a suitable classifier. The test results show that the proposed driver fatigue state recognition method has good recognition effect, especially on the classifier based on decision tree, with an average accuracy of 99.50%.

SIGNIFICANCE

The extracted features well reflect the continuityand internal dynamic changes of the EEG signals, and it is of great significance and application value to study an effective method of fatigued driver state recognition based on the features.

A penalized spline fitting method to optimize geometric parameters of arterial centerlines extracted from medical images

In order to grasp the spatial and temporal evolution of vascular geometry, three-dimensional (3D) arterial bending structure and geometrical changes of arteries and stent grafts (SG) must be quantified using geometrical parameters such as curvature and torsion along the vasculature centerlines extracted from medical images. Here, we develop a robust method for constructing smooth centerlines based on a spline fitting method (SFM) such that the optimized geometric parameters of curvature and torsion can be obtained independently of digitization noise in the images. Conventional SFM consists of the 3rd degree spline basis function and 2nd derivative penalty term. In contrast, the present SFM uses the 5th degree spline basis function and 3rd and 4th derivative penalty terms, the coefficients of which are derived by the Akaike information criterion. The results show that the developed SFM can reduce the errors of curvature and torsion compared to conventional SFM. We then apply the present SFM to the centerline of the SG in an abdominal aortic aneurysm (AAA), and those of bilateral internal carotid arteries (ICA) in 6 cases: 3 cases with aneurysms and 3 cases without any aneurysm. The SG centerlines were obtained from temporal medical images at three scan times. The strong peak of the curvature could be clearly observed in the distal area of the SG, the inversion of the torsion at 0 months in the middle area of SG disappeared over time, and the torsions around the SG bifurcation at the three time periods were inverted. The curvature-torsion graphs along the ICA centerlines superimposing five aneurysmal positions were useful for investigating the relationship between arterial bending structure and aneurysmal positions. Both ICAs had curvature peak values higher than 0.4 within the ICA syphons. The ICA torsion graphs indicated that left and right ICA tended to be a right- and left-handed helix, respectively. In the left ICA syphon, the biggest aneurysm could be observed downstream of the salient torsion inversion. All aneurysms for 3 cases were positioned at the downstream of the inverted torsion.

Comparison of Qualitative and Quantitative Assessments of Iliac Artery Tortuosity and Calcification

Introduction:

During endovascular aneurysm repair, the iliac artery typically serves as a conduit for device delivery. The degree of tortuosity and calcification in the iliac artery ultimately determines whether the device can successfully traverse the vessel. These 2 parameters can be assessed using qualitative approaches or calculated using quantitative methods based on the Society for Vascular Surgery (SVS) reporting standards. The objective of this study was to determine whether qualitative methods are sufficient to accurately assess iliac artery tortuosity and calcification by calculating interobserver variability and comparing them to the SVS Reporting Standards.

Methods:

Three vascular surgeons reviewed preoperative computed tomography scans for 50 patients who underwent fenestrated endovascular aneurysm repair and qualitatively assessed left and right iliac artery tortuosity and calcification. Iliac artery geometries were segmented from these image sets. Tortuosity index and calcification length ratio were calculated and categorized based on the SVS Reporting Standards.

Results:

Interobserver variability was calculated for the qualitative assessments using interclass correlation coefficients. For tortuosity index, among the 3 observers, good agreement was found for the left iliac artery and fair agreement was found for the right. For calcification length ratio, excellent agreement was found for both iliac arteries. When compared to the quantitative assessment, the qualitative assessments underpredicted tortuosity in 2.3% of cases, matched the quantitative values in 16.7% of cases, and overpredicted tortuosity in 81.0% of cases. The qualitative assessments underpredicted calcification in 46.3% of cases, matched the quantitative values in 49.3% of cases, and overpredicted calcification in 4.3% of cases.

Conclusion:

Qualitative assessment of iliac artery tortuosity showed fair-to-good interobserver agreement and poor agreement to SVS Reporting Standards. Qualitative assessment of iliac artery calcification showed excellent interobserver agreement and fair agreement to SVS Reporting Standards. These trends should be considered when qualitative reporting methodologies are used.

Abdominal aortic aneurysm endovascular repair: profiling post-implantation morphometry and hemodynamics with image-based computational fluid dynamics

Endovascular aneurysm repair (EVAR) has disseminated rapidly as an alternative to open surgical repair for the treatment of abdominal aortic aneurysms (AAAs), because of its reduced invasiveness, low mortality and morbidity rate. The effectiveness of the endovascular devices used in EVAR is always at question as postoperative adverse events can lead to re-intervention or to a possible fatal scenario for the circulatory system. Motivated by the assessment of the risks related to thrombus formation, here the impact of two different commercial endovascular grafts on local hemodynamics is explored through 20 image-based computational hemodynamic models of EVAR-treated patients (N=10 per each endograft model). Hemodynamic features, susceptible to promote thrombus formation, such as flow separation and recirculation, are quantitatively assessed and compared with the local hemodynamics established in image-based infrarenal abdominal aortic models of healthy subjects (N=10). The hemodynamic analysis is complemented by a geometrical characterization of the EVAR-induced reshaping of the infrarenal abdominal aortic vascular region. The findings of this study indicate that: (1) the clinically observed propensity to thrombus formation in devices used in EVAR strategies can be explained in terms of local hemodynamics by means of image-based computational hemodynamics approach; (2) reportedly pro-thrombotic hemodynamic structures are strongly correlated with the geometry of the aortoiliac tract postoperatively. In perspective, our study suggests that future clinical follow up studies could include a geometric analysis of the region of the implant, monitoring shape variations that can lead to hemodynamic disturbances of clinical significance.

Derivative estimation for longitudinal data analysis: Examining features of blood pressure measured repeatedly during pregnancy

Estimating velocity and acceleration trajectories allows novel inferences in the field of longitudinal data analysis, such as estimating change regions rather than change points, and testing group effects on nonlinear change in an outcome (ie, a nonlinear interaction). In this article, we develop derivative estimation for 2 standard approaches-polynomial mixed models and spline mixed models. We compare their performance with an established method-principal component analysis through conditional expectation through a simulation study. We then apply the methods to repeated blood pressure (BP) measurements in a UK cohort of pregnant women, where the goals of analysis are to (i) identify and estimate regions of BP change for each individual and (ii) investigate the association between parity and BP change at the population level. The penalized spline mixed model had the lowest bias in our simulation study, and we identified evidence for BP change regions in over 75% of pregnant women. Using mean velocity difference revealed differences in BP change between women in their first pregnancy compared with those who had at least 1 previous pregnancy. We recommend the use of penalized spline mixed models for derivative estimation in longitudinal data analysis.

Analysis of Iliac Artery Geometric Properties in Fenestrated Aortic Stent Graft Rotation

Introduction:

A complication of fenestrated endovascular aneurysm repair is the potential for stent graft rotation during deployment causing fenestration misalignment and branch artery occlusion. The objective of this study is to demonstrate that this rotation is caused by a buildup of rotational energy as the device is delivered through the iliac arteries and to quantify iliac artery geometric properties associated with device rotation.

Methods:

A retrospective clinical study was undertaken in which iliac artery geometric properties were assessed from preoperative imaging for 42 cases divided into 2 groups: 27 in the nonrotation group and 15 in the rotation group. Preoperative computed tomography scans were segmented, and the iliac artery centerlines were determined. Iliac artery tortuosity, curvature, torsion, and diameter were calculated from the centerline and the segmented vessel geometry.

Results:

The total iliac artery net torsion was found to be higher in the rotation group compared to the nonrotation group (23.5 ± 14.7 vs 14.6 ± 12.8 mm−1; P = .05). No statistically significant differences were found for the mean values of tortuosity, curvature, torsion, or diameter between the 2 groups.

Conclusion:

Stent graft rotation occurred in 36% of the cases considered in this study. Cases with high iliac artery total net torsion were found to be more likely to have stent graft rotation upon deployment. This retrospective study provides a framework for prospectively studying the influence of iliac artery geometric properties on fenestrated stent graft rotation.

A computational framework to characterize and compare the geometry of coronary networks

This work presents a computational framework to perform a systematic and comprehensive assessment of the morphometry of coronary arteries from in vivo medical images. The methodology embraces image segmentation, arterial vessel representation, characterization and comparison, data storage, and finally analysis. Validation is performed using a sample of 48 patients. Data mining of morphometric information of several coronary arteries is presented. Results agree to medical reports in terms of basic geometric and anatomical variables. Concerning geometric descriptors, inter-artery and intra-artery correlations are studied. Data reported here can be useful for the construction and setup of blood flow models of the coronary circulation. Finally, as an application example, similarity criterion to assess vasculature likelihood based on geometric features is presented and used to test geometric similarity among sibling patients. Results indicate that likelihood, measured through geometric descriptors, is stronger between siblings compared with non-relative patients. Copyright © 2016 John Wiley & Sons, Ltd.

Automatic extraction of three-dimensional thoracic aorta geometric model from phase contrast MRI for morphometric and hemodynamic characterization

PURPOSE

To propose and assess a new method that automatically extracts a three-dimensional (3D) geometric model of the thoracic aorta (TA) from 3D cine phase contrast MRI (PCMRI) acquisitions.

METHODS

The proposed method is composed of two steps: segmentation of the TA and creation of the 3D geometric model. The segmentation algorithm, based on Level Set, was set and applied to healthy subjects acquired in three different modalities (with and without SENSE reduction factors). Accuracy was evaluated using standard quality indices. The 3D model is characterized by the vessel surface mesh and its centerline; the comparison of models obtained from the three different datasets was also carried out in terms of radius of curvature (RC) and average tortuosity (AT).

RESULTS

In all datasets, the segmentation quality indices confirmed very good agreement between manual and automatic contours (average symmetric distance < 1.44 mm, DICE Similarity Coefficient > 0.88). The 3D models extracted from the three datasets were found to be comparable, with differences of less than 10% for RC and 11% for AT.

CONCLUSION

Our method was found effective on PCMRI data to provide a 3D geometric model of the TA, to support morphometric and hemodynamic characterization of the aorta.

A rational approach to defining principal axes of multidirectional wall shear stress in realistic vascular geometries, with application to the study of the influence of helical flow on wall shear stress directionality in aorta

The distribution of arterial lesions is attributed by the prevalent mechanistic theory to the proatherogenic role played by low and oscillatory wall shear stress (WSS). However, discrepancies observed when comparing WSS distribution with location of regions with lesion prevalence challenge this theory and have recently stimulated the idea that a role in endothelial mechanosensing is played by WSS multidirectionality, which could contribute to explain the observed discrepancies. Here an approach is presented for analyzing the multidirectional nature of WSS in complex vascular geometries. Using an essential geometric attribute of the vessel (its centerline), the local WSS vector is projected along an "axial" direction (aligned with the tangent to the vessel׳s centerline), and "secondary" direction (orthogonal to centerline׳s tangent), which is related to secondary flow. The WSS projection scheme is applied: (1) to a realistic computational hemodynamic model of human aorta, with the aim to come up with a plausibility checking regarding its consistency; and (2) to investigate if an aortic hemodynamics characterized by different amount and topology of helical flow (HF) could influence WSS directionality. The projection scheme confirmed its consistency and plausibility in realistic arterial geometries and allowed to get insight into the relationship between aortic intravascular fluid structures and WSS directionality. The findings of this study clearly show the potential of the projection scheme as quantitative tool for an in depth investigation of the WSS multidirectional nature. The proposed approach enriches the arsenal of tools available to study and exploit the role played by local hemodynamics in vascular disease.

Quantification and geometric analysis of coiling patterns in gastropod shells based on 3D and 2D image data

The morphology of gastropod shells has been a focus of analyses in ecology and evolution. It has recently emerged as an important issue in developmental biology, thanks to recent advancements in molecular biological techniques. The growing tube model is a theoretical morphological model for describing various coiling patterns of molluscan shells, and it is a useful theoretical tool to relate local tissue growth with global shell morphology. However, the growing tube model has rarely been adopted in empirical research owing to the difficulty in estimating the parameters of the model from morphological data. In this article, I solve this problem by developing methods of parameter estimation when (1) 3D Computed Tomography (CT) data are available and (2) only 2D image data (such as photographs) are available. When 3D CT data are available, the parameters can be estimated by fitting an analytical solution of the growing tube model to the data. When only 2D image data are available, we first fit Raup׳s model to the 2D image data and then convert the parameters of Raup׳s model to those of the growing tube model. To illustrate the use of these methods, I apply them to data generated by a computer simulation of the model. Both methods work well, except when shells grow without coiling. I also demonstrate the effectiveness of the methods by applying the model to actual 3D CT data and 2D image data of land snails. I conclude that the method proposed in this article can reconstruct the coiling pattern from observed data.

Object Oriented Data Analysis: A few methodological challenges

This is a discussion of the paper "Overview of object oriented data analysis" by J. Steve Marron and Andrés M. Alonso.

More on functional data analysis and other aspects in OODA

This is a discussion of the paper "Overview of object oriented data analysis" by J. Steve Marron and Andrés M. Alonso.

An introduction with medical applications to functional data analysis

Functional data are data that can be represented by suitable functions, such as curves (potentially multi-dimensional) or surfaces. This paper gives an introduction to some basic but important techniques for the analysis of such data, and we apply the techniques to two datasets from biomedicine. One dataset is about white matter structures in the brain in multiple sclerosis patients; the other dataset is about three-dimensional vascular geometries collected for the study of cerebral aneurysms. The techniques described are smoothing, alignment, principal component analysis, and regression.

Geometry of the Internal Carotid Artery and Recurrent Patterns in Location, Orientation, and Rupture Status of Lateral Aneurysms: An Image-Based Computational Study

BACKGROUND:

Intracranial aneurysm development and rupture may be associated to the morphology of the parent vessel.

OBJECTIVE:

To quantitatively characterize the geometry of the internal carotid artery (ICA) in relation to the location and orientation of lateral aneurysms and to identify recurrent patterns associated with their rupture status.

METHODS:

The geometry of 54 ICAs hosting lateral aneurysms was analyzed by means of computational geometry techniques. The ICA was split into individual bends, and the bend hosting the aneurysm was described in terms of curvature, torsion, length, and radius. Aneurysm position and orientation with respect to the parent vessel and specifically the hosting bend were characterized, as well as angles between the portions of the parent artery immediately upstream of and downstream from the aneurysm and the aneurysm ostium. Differences in geometric parameters with respect to rupture status and their performance as classifiers were evaluated.

RESULTS:

ICA bends hosting ruptured aneurysms were shorter with a smaller radius, lower maximum curvature, and lower proximal torsion compared with those hosting unruptured lesions. Ruptured aneurysms occurred in more distal portions of the ICA, along the outer wall of the vessel, and closer to the curvature peak within the hosting bend than unruptured ones. The proximal portions of ICAs hosting ruptured aneurysms approached the ostium region at a smaller angle.

CONCLUSION:

Geometric factors relative to the ICA were associated with the distribution of aneurysms and their rupture status. The present work has potential implications in the quest for hemodynamic factors contributing to the development, progression, and rupture of intracranial aneurysms.