A statistical model for quantification and prediction of cardiac remodelling: application to tetralogy of Fallot

Machine Learning and Statistical Shape Modelling Methodologies to Assess Vascular Morphology before and after Aortic Valve Replacement

Introduction: Statistical shape modelling (SSM) is used to analyse morphology, discover qualitatively and quantitatively unique shape features within a population, and generate mean shapes and shape modes that show morphological variability. Hierarchical agglomerative clustering is a machine learning analysis used to identify subgroups within a given population in relation to shape features. We tested the application of both methods in the clinically relevant scenario of patients undergoing aortic valve repair (AVR). Every year, around 5000 patients undergo surgical AVR in the UK. Aims: Evaluate aortic morphology and identify subgroups amongst patients who had undergone AVR, including Ozaki, Ross, and valve-sparing procedures using SSM and unsupervised hierarchical clustering analysis. This methodological framework can evaluate both pre- and post-surgical variability across subgroups undergoing different surgeries. Methods: Pre- (n = 47) and post- (n = 35) operative three-dimensional (3D) aortic models were reconstructed from computed tomography (CT) and cardiac magnetic resonance (CMR) images. Computational analyses for SSM and hierarchical clustering were run separately for the two subgroups, assessing (a) ascending aorta only and (b) the whole aorta. This allows for exploring possible variations in morphological classification related to the input shape. Results: Most patients in the Ross procedure subgroup exhibited differences in aortic morphology from other subgroups, including an elongated ascending and wide aortic arch pre-operatively, and an elongated ascending aorta with a slightly enlarged sinus post-operatively. In hierarchical clustering, the Ross aortas also appeared to cluster together compared to the other surgical procedures, both pre-operatively and post-operatively. There were significant differences between clusters in terms of clustering distance in the pre-operative analyses (p = 0.003 for ascending aortas, p = 0.016 for whole aortas). There were no significant differences between the clusters in post-operative analyses (p = 0.47 for ascending, p = 0.19 for whole aorta). Conclusions: We demonstrated the feasibility of evaluating aortic morphology before and after different aortic valve surgeries using SSM and hierarchical clustering. This framework could be used to further explore shape features associated with surgical decision-making pre-operatively and, importantly, to identify subgroups whose morphology is associated with poorer clinical outcomes post-operatively. Statistical shape modelling (SSM) and unsupervised hierarchical clustering are two statistical methods that can be used to assess morphology, show morphological variations, with the latter being able to identify subgroups within a population. These methods have been applied to the population of aortic valve replacement (AVR) patients since there are different surgical procedures (traditional AVR, Ozaki, Ross, and valve-sparing). The aim is to evaluate aortic morphology and identify subgroups within this population before and after surgery. Computed tomography and cardiac magnetic resonance images were reconstructed into 3D models of the ascending aorta and whole aorta, which were then input into SSM and hierarchical clustering. The results show that the Ross aortic morphology is quite different from the other aortas. The clustering did not classify the aortas based on the surgical procedures; however, most of the Ross group did cluster together, indicating low variability within this surgical group.

Image2Flow: A proof-of-concept hybrid image and graph convolutional neural network for rapid patient-specific pulmonary artery segmentation and CFD flow field calculation from 3D cardiac MRI data

Computational fluid dynamics (CFD) can be used for non-invasive evaluation of hemodynamics. However, its routine use is limited by labor-intensive manual segmentation, CFD mesh creation, and time-consuming simulation. This study aims to train a deep learning model to both generate patient-specific volume-meshes of the pulmonary artery from 3D cardiac MRI data and directly estimate CFD flow fields. This proof-of-concept study used 135 3D cardiac MRIs from both a public and private dataset. The pulmonary arteries in the MRIs were manually segmented and converted into volume-meshes. CFD simulations were performed on ground truth meshes and interpolated onto point-point correspondent meshes to create the ground truth dataset. The dataset was split 110/10/15 for training, validation, and testing. Image2Flow, a hybrid image and graph convolutional neural network, was trained to transform a pulmonary artery template to patient-specific anatomy and CFD values, taking a specific inlet velocity as an additional input. Image2Flow was evaluated in terms of segmentation, and the accuracy of predicted CFD was assessed using node-wise comparisons. In addition, the ability of Image2Flow to respond to increasing inlet velocities was also evaluated. Image2Flow achieved excellent segmentation accuracy with a median Dice score of 0.91 (IQR: 0.86-0.92). The median node-wise normalized absolute error for pressure and velocity magnitude was 11.75% (IQR: 9.60-15.30%) and 9.90% (IQR: 8.47-11.90), respectively. Image2Flow also showed an expected response to increased inlet velocities with increasing pressure and velocity values. This proof-of-concept study has shown that it is possible to simultaneously perform patient-specific volume-mesh based segmentation and pressure and flow field estimation using Image2Flow. Image2Flow completes segmentation and CFD in ~330ms, which is ~5000 times faster than manual methods, making it more feasible in a clinical environment.

Aortic geometry and long-term outcome in patients with a repaired coarctation

OBJECTIVE

This study aims to compare aortic morphology between repaired coarctation patients and controls, and to identify aortic morphological risk factors for hypertension and cardiovascular events (CVEs) in coarctation patients.

METHODS

Repaired coarctation patients with computed tomography angiography (CTA) or magnetic resonance angiography (MRA) were included, followed-up and compared with sex-matched and age-matched controls. Three-dimensional aortic shape was reconstructed using patients' CTA or MRA, or four-dimensional flow cardiovascular magnetic resonance in controls, and advanced geometrical characteristics were calculated and visualised using statistical shape modelling. In patients, we examined the association of geometrical characteristics with (1) baseline hypertension, using multivariable logistic regression; and (2) cardiovascular events (CVE, composite of aortic complications, coronary artery disease, ventricular arrhythmias, heart failure hospitalisation, stroke, transient ischaemic attacks and cardiovascular death), using multivariable Cox regression. The least absolute shrinkage and selection operator (LASSO) method selected the most informative multivariable model.

RESULTS

Sixty-five repaired coarctation patients (23 years (IQR 19-38)) were included, of which 44 (68%) patients were hypertensive at baseline. After a median follow-up of 8.7 years (IQR 4.8-15.4), 27 CVEs occurred in 20 patients. Aortic arch dimensions were smaller in patients compared with controls (diameter p<0.001, wall surface area p=0.026, volume p=0.007). Patients had more aortic arch torsion (p<0.001) and a higher curvature (p<0.001). No geometrical characteristics were associated with hypertension. LASSO selected left ventricular mass, male sex, tortuosity and age for the multivariable model. Left ventricular mass (p=0.014) was independently associated with CVE, and aortic tortuosity showed a trend towards significance (p=0.070).

CONCLUSION

Repaired coarctation patients have a smaller aortic arch and a more tortuous course of the aorta compared with controls. Besides left ventricular mass index, geometrical features might be of importance in long-term risk assessment in coarctation patients.

DeepMesh: Mesh-Based Cardiac Motion Tracking Using Deep Learning

3D motion estimation from cine cardiac magnetic resonance (CMR) images is important for the assessment of cardiac function and the diagnosis of cardiovascular diseases. Current state-of-the art methods focus on estimating dense pixel-/voxel-wise motion fields in image space, which ignores the fact that motion estimation is only relevant and useful within the anatomical objects of interest, e.g., the heart. In this work, we model the heart as a 3D mesh consisting of epi- and endocardial surfaces. We propose a novel learning framework, DeepMesh, which propagates a template heart mesh to a subject space and estimates the 3D motion of the heart mesh from CMR images for individual subjects. In DeepMesh, the heart mesh of the end-diastolic frame of an individual subject is first reconstructed from the template mesh. Mesh-based 3D motion fields with respect to the end-diastolic frame are then estimated from 2D short- and long-axis CMR images. By developing a differentiable mesh-to-image rasterizer, DeepMesh is able to leverage 2D shape information from multiple anatomical views for 3D mesh reconstruction and mesh motion estimation. The proposed method estimates vertex-wise displacement and thus maintains vertex correspondences between time frames, which is important for the quantitative assessment of cardiac function across different subjects and populations. We evaluate DeepMesh on CMR images acquired from the UK Biobank. We focus on 3D motion estimation of the left ventricle in this work. Experimental results show that the proposed method quantitatively and qualitatively outperforms other image-based and mesh-based cardiac motion tracking methods.

Generation of synthetic aortic valve stenosis geometries for in silico trials

In silico trials are a promising way to increase the efficiency of the development, and the time to market of cardiovascular implantable devices. The development of transcatheter aortic valve implantation (TAVI) devices, could benefit from in silico trials to overcome frequently occurring complications such as paravalvular leakage and conduction problems. To be able to perform in silico TAVI trials virtual cohorts of TAVI patients are required. In a virtual cohort, individual patients are represented by computer models that usually require patient-specific aortic valve geometries. This study aimed to develop a virtual cohort generator that generates anatomically plausible, synthetic aortic valve stenosis geometries for in silico TAVI trials and allows for the selection of specific anatomical features that influence the occurrence of complications. To build the generator, a combination of non-parametrical statistical shape modeling and sampling from a copula distribution was used. The developed virtual cohort generator successfully generated synthetic aortic valve stenosis geometries that are comparable with a real cohort, and therefore, are considered as being anatomically plausible. Furthermore, we were able to select specific anatomical features with a sensitivity of around 90%. The virtual cohort generator has the potential to be used by TAVI manufacturers to test their devices. Future work will involve including calcifications to the synthetic geometries, and applying high-fidelity fluid-structure-interaction models to perform in silico trials.

Automated segmentation of 3D cine cardiovascular magnetic resonance imaging

Introduction

As the life expectancy of children with congenital heart disease (CHD) is rapidly increasing and the adult population with CHD is growing, there is an unmet need to improve clinical workflow and efficiency of analysis. Cardiovascular magnetic resonance (CMR) is a noninvasive imaging modality for monitoring patients with CHD. CMR exam is based on multiple breath-hold 2-dimensional (2D) cine acquisitions that should be precisely prescribed and is expert and institution dependent. Moreover, 2D cine images have relatively thick slices, which does not allow for isotropic delineation of ventricular structures. Thus, development of an isotropic 3D cine acquisition and automatic segmentation method is worthwhile to make CMR workflow straightforward and efficient, as the present work aims to establish.

Methods

Ninety-nine patients with many types of CHD were imaged using a non-angulated 3D cine CMR sequence covering the whole-heart and great vessels. Automatic supervised and semi-supervised deep-learning-based methods were developed for whole-heart segmentation of 3D cine images to separately delineate the cardiac structures, including both atria, both ventricles, aorta, pulmonary arteries, and superior and inferior vena cavae. The segmentation results derived from the two methods were compared with the manual segmentation in terms of Dice score, a degree of overlap agreement, and atrial and ventricular volume measurements.

Results

The semi-supervised method resulted in a better overlap agreement with the manual segmentation than the supervised method for all 8 structures (Dice score 83.23 ± 16.76% vs. 77.98 ± 19.64%; P-value ≤0.001). The mean difference error in atrial and ventricular volumetric measurements between manual segmentation and semi-supervised method was lower (bias ≤ 5.2 ml) than the supervised method (bias ≤ 10.1 ml).

Discussion

The proposed semi-supervised method is capable of cardiac segmentation and chamber volume quantification in a CHD population with wide anatomical variability. It accurately delineates the heart chambers and great vessels and can be used to accurately calculate ventricular and atrial volumes throughout the cardiac cycle. Such a segmentation method can reduce inter- and intra- observer variability and make CMR exams more standardized and efficient.

Computer-aided shape features extraction and regression models for predicting the ascending aortic aneurysm growth rate

OBJECTIVE

ascending aortic aneurysm growth prediction is still challenging in clinics. In this study, we evaluate and compare the ability of local and global shape features to predict the ascending aortic aneurysm growth.

MATERIAL AND METHODS

70 patients with aneurysm, for which two 3D acquisitions were available, are included. Following segmentation, three local shape features are computed: (1) the ratio between maximum diameter and length of the ascending aorta centerline, (2) the ratio between the length of external and internal lines on the ascending aorta and (3) the tortuosity of the ascending tract. By exploiting longitudinal data, the aneurysm growth rate is derived. Using radial basis function mesh morphing, iso-topological surface meshes are created. Statistical shape analysis is performed through unsupervised principal component analysis (PCA) and supervised partial least squares (PLS). Two types of global shape features are identified: three PCA-derived and three PLS-based shape modes. Three regression models are set for growth prediction: two based on gaussian support vector machine using local and PCA-derived global shape features; the third is a PLS linear regression model based on the related global shape features. The prediction results are assessed and the aortic shapes most prone to growth are identified.

RESULTS

the prediction root mean square error from leave-one-out cross-validation is: 0.112 mm/month, 0.083 mm/month and 0.066 mm/month for local, PCA-based and PLS-derived shape features, respectively. Aneurysms close to the root with a large initial diameter report faster growth.

CONCLUSION

global shape features might provide an important contribution for predicting the aneurysm growth.

Assessment of post-infarct ventricular septal defects through 3D printing and statistical shape analysis

BACKGROUND

Post-infarct ventricular septal defect (PIVSD) is a serious complication of myocardial infarction. We evaluated 3D-printing models in PIVSD clinical assessment and the feasibility of statistical shape modeling for morphological analysis of the defects.

METHODS

Models (n = 15) reconstructed from computed tomography data were evaluated by clinicians (n = 8). Statistical shape modeling was performed on 3D meshes to calculate the mean morphological configuration of the defects.

RESULTS

Clinicians' evaluation highlighted the models' utility in displaying defects for interventional/surgical planning, education/training and device development. However, models lack dynamic representation. Morphological analysis was feasible and revealed oval-shaped (n = 12) and complex channel-like (n = 3) defects.

CONCLUSION

3D-PIVSD models can complement imaging data for teaching and procedural planning. Statistical shape modeling is feasible in this scenario.

Le Cœur en Sabot: shape associations with adverse events in repaired tetralogy of Fallot

BACKGROUND

Maladaptive remodelling mechanisms occur in patients with repaired tetralogy of Fallot (rToF) resulting in a cycle of metabolic and structural changes. Biventricular shape analysis may indicate mechanisms associated with adverse events independent of pulmonary regurgitant volume index (PRVI). We aimed to determine novel remodelling patterns associated with adverse events in patients with rToF using shape and function analysis.

METHODS

Biventricular shape and function were studied in 192 patients with rToF (median time from TOF repair to baseline evaluation 13.5 years). Linear discriminant analysis (LDA) and principal component analysis (PCA) were used to identify shape differences between patients with and without adverse events. Adverse events included death, arrhythmias, and cardiac arrest with median follow-up of 10 years.

RESULTS

LDA and PCA showed that shape characteristics pertaining to adverse events included a more circular left ventricle (LV) (decreased eccentricity), dilated (increased sphericity) LV base, increased right ventricular (RV) apical sphericity, and decreased RV basal sphericity. Multivariate LDA showed that the optimal discriminative model included only RV apical ejection fraction and one PCA mode associated with a more circular and dilated LV base (AUC = 0.77). PRVI did not add value, and shape changes associated with increased PRVI were not predictive of adverse outcomes.

CONCLUSION

Pathological remodelling patterns in patients with rToF are significantly associated with adverse events, independent of PRVI. Mechanisms related to incident events include LV basal dilation with a reduced RV apical ejection fraction.

Learned iterative segmentation of highly variable anatomy from limited data: Applications to whole heart segmentation for congenital heart disease

Training deep learning models that segment an image in one step typically requires a large collection of manually annotated images that captures the anatomical variability in a cohort. This poses challenges when anatomical variability is extreme but training data is limited, as when segmenting cardiac structures in patients with congenital heart disease (CHD). In this paper, we propose an iterative segmentation model and show that it can be accurately learned from a small dataset. Implemented as a recurrent neural network, the model evolves a segmentation over multiple steps, from a single user click until reaching an automatically determined stopping point. We develop a novel loss function that evaluates the entire sequence of output segmentations, and use it to learn model parameters. Segmentations evolve predictably according to growth dynamics encapsulated by training data, which consists of images, partially completed segmentations, and the recommended next step. The user can easily refine the final segmentation by examining those that are earlier or later in the output sequence. Using a dataset of 3D cardiac MR scans from patients with a wide range of CHD types, we show that our iterative model offers better generalization to patients with the most severe heart malformations.

Computational Modeling of Right Ventricular Motion and Intracardiac Flow in Repaired Tetralogy of Fallot

PURPOSE

Patients with repaired Tetralogy of Fallot (rTOF) will develop dilation of the right ventricle (RV) from chronic pulmonary insufficiency and require pulmonary valve replacement (PVR). Cardiac MRI (cMRI) is used to guide therapy but has limitations in studying novel intracardiac flow parameters. This pilot study aimed to demonstrate feasibility of reconstructing RV motion and simulating intracardiac flow in rTOF patients, exclusively using conventional cMRI and an immersed-boundary method computational fluid dynamic (CFD) solver.

METHODS

Four rTOF patients and three normal controls underwent cMRI including 4D flow. 3D RV models were segmented from cMRI images. Feature-tracking software captured RV endocardial contours from cMRI long-axis and short-axis cine stacks. RV motion was reconstructed via diffeomorphic mapping (Deformetrica, deformetrica.org), serving as the domain boundary for CFD. Fully-resolved direct numerical simulations were performed over several cardiac cycles. Intracardiac vorticity, kinetic energy (KE) and turbulent kinetic energy (TKE) was measured. For validation, RV motion was compared to manual tracings, results of KE were compared between CFD and 4D flow.

RESULTS

Diastolic vorticity and TKE in rTOF patients were 4.12 ± 2.42 mJ/L and 115 ± 27/s, compared to 2.96 ± 2.16 mJ/L and 78 ± 45/s in controls. There was good agreement between RV motion and manual tracings. The difference in diastolic KE between CFD and 4D flow by Bland-Altman analysis was - 0.89910 to 2 mJ/mL (95% limits of agreement: - 1.351 × 10^-2 mJ/mL to 1.171 × 10^-2 mJ/mL).

CONCLUSION

This CFD framework can produce intracardiac flow in rTOF patients. CFD has the potential for predicting the effects of PVR in rTOF patients and improve the clinical indications guided by cMRI.

Right Ventricular Flow Vorticity Relationships With Biventricular Shape in Adult Tetralogy of Fallot

Remodeling in adults with repaired tetralogy of Fallot (rToF) may occur due to chronic pulmonary regurgitation, but may also be related to altered flow patterns, including vortices. We aimed to correlate and quantify relationships between vorticity and ventricular shape derived from atlas-based analysis of biventricular shape. Adult rToF (n = 12) patients underwent 4D flow and cine MRI imaging. Vorticity in the RV was computed after noise reduction using a neural network. A biventricular shape atlas built from 95 rToF patients was used to derive principal component modes, which were associated with vorticity and pulmonary regurgitant volume (PRV) using univariate and multivariate linear regression. Univariate analysis showed that indexed PRV correlated with 3 modes (r = −0.55,−0.50, and 0.6, all p &lt; 0.05) associated with RV dilatation and an increase in basal bulging, apical bulging and tricuspid annulus tilting with more severe regurgitation, as well as a smaller LV and paradoxical movement of the septum. RV outflow and inflow vorticity were also correlated with these modes. However, total vorticity over the whole RV was correlated with two different modes (r = −0.62,−0.69, both p &lt; 0.05). Higher vorticity was associated with both RV and LV shape changes including longer ventricular length, a larger bulge beside the tricuspid valve, and distinct tricuspid tilting. RV flow vorticity was associated with changes in biventricular geometry, distinct from associations with PRV. Flow vorticity may provide additional mechanistic information in rToF remodeling. Both LV and RV shapes are important in rToF RV flow patterns.

Right-left ventricular shape variations in tetralogy of Fallot: associations with pulmonary regurgitation

BACKGROUND

Relationships between right ventricular (RV) and left ventricular (LV) shape and function may be useful in determining optimal timing for pulmonary valve replacement in patients with repaired tetralogy of Fallot (rTOF). However, these are multivariate and difficult to quantify. We aimed to quantify variations in biventricular shape associated with pulmonary regurgitant volume (PRV) in rTOF using a biventricular atlas.

METHODS

In this cross-sectional retrospective study, a biventricular shape model was customized to cardiovascular magnetic resonance (CMR) images from 88 rTOF patients (median age 16, inter-quartile range 11.8-24.3 years). Morphometric scores quantifying biventricular shape at end-diastole and end-systole were computed using principal component analysis. Multivariate linear regression was used to quantify biventricular shape associations with PRV, corrected for age, sex, height, and weight. Regional associations were confirmed by univariate correlations with distances and angles computed from the models, as well as global systolic strains computed from changes in arc length from end-diastole to end-systole.

RESULTS

PRV was significantly associated with 5 biventricular morphometric scores, independent of covariates, and accounted for 12.3% of total shape variation (p < 0.05). Increasing PRV was associated with RV dilation and basal bulging, in conjunction with decreased LV septal-lateral dimension (LV flattening) and systolic septal motion towards the RV (all p < 0.05). Increased global RV radial, longitudinal, circumferential and LV radial systolic strains were significantly associated with increased PRV (all p < 0.05).

CONCLUSION

A biventricular atlas of rTOF patients quantified multivariate relationships between left-right ventricular morphometry and wall motion with pulmonary regurgitation. Regional RV dilation, LV reduction, LV septal-lateral flattening and increased RV strain were all associated with increased pulmonary regurgitant volume. Morphometric scores provide simple metrics linking mechanisms for structural and functional alteration with important clinical indices.

Computational analysis of cardiac structure and function in congenital heart disease: Translating discoveries to clinical strategies

Increased availability and access to medical image data has enabled more quantitative approaches to clinical diagnosis, prognosis, and treatment planning for congenital heart disease. Here we present an overview of long-term clinical management of tetralogy of Fallot (TOF) and its intersection with novel computational and data science approaches to discovering biomarkers of functional and prognostic importance. Efforts in translational medicine that seek to address the clinical challenges associated with cardiovascular diseases using personalized and precision-based approaches are then discussed. The considerations and challenges of translational cardiovascular medicine are reviewed, and examples of digital platforms with collaborative, cloud-based, and scalable design are provided.

Linking statistical shape models and simulated function in the healthy adult human heart

Cardiac anatomy plays a crucial role in determining cardiac function. However, there is a poor understanding of how specific and localised anatomical changes affect different cardiac functional outputs. In this work, we test the hypothesis that in a statistical shape model (SSM), the modes that are most relevant for describing anatomy are also most important for determining the output of cardiac electromechanics simulations. We made patient-specific four-chamber heart meshes (n = 20) from cardiac CT images in asymptomatic subjects and created a SSM from 19 cases. Nine modes captured 90% of the anatomical variation in the SSM. Functional simulation outputs correlated best with modes 2, 3 and 9 on average (R = 0.49 ± 0.17, 0.37 ± 0.23 and 0.34 ± 0.17 respectively). We performed a global sensitivity analysis to identify the different modes responsible for different simulated electrical and mechanical measures of cardiac function. Modes 2 and 9 were the most important for determining simulated left ventricular mechanics and pressure-derived phenotypes. Mode 2 explained 28.56 ± 16.48% and 25.5 ± 20.85, and mode 9 explained 12.1 ± 8.74% and 13.54 ± 16.91% of the variances of mechanics and pressure-derived phenotypes, respectively. Electrophysiological biomarkers were explained by the interaction of 3 ± 1 modes. In the healthy adult human heart, shape modes that explain large portions of anatomical variance do not explain equivalent levels of electromechanical functional variation. As a result, in cardiac models, representing patient anatomy using a limited number of modes of anatomical variation can cause a loss in accuracy of simulated electromechanical function.

Direct Numerical Simulations of a Great Horn Owl in Flapping Flight

The fluid dynamics of owls in flapping flight is studied by coordinated experiments and computations. The great horned owl was selected, which is nocturnal, stealthy, and relatively large sized raptor. On the experimental side, perch-to-perch flight was considered in an open wind tunnel. The owl kinematics was captured with multiple cameras from different view angles. The kinematic extraction was central in driving the computations, which were designed to resolve all significant spatio-temporal scales in the flow with an unprecedented level of resolution. The wing geometry was extracted from the planform image of the owl wing and a three-dimensional model, the reference configuration, was reconstructed. This configuration was then deformed in time to best match the kinematics recorded during flights utilizing an image-registration technique based on the large deformation diffeomorphic metric mapping framework. All simulations were conducted using an eddy-resolving, high-fidelity, solver, where the large displacements/deformations of the flapping owl model were introduced with an immersed boundary formulation. We report detailed information on the spatio-temporal flow dynamics in the near wake including variables that are challenging to measure with sufficient accuracy, such as aerodynamic forces. At the same time, our results indicate that high-fidelity computations over smooth wings may have limitations in capturing the full range of flow phenomena in owl flight. The growth and subsequent separation of the laminar boundary layers developing over the wings in this Reynolds number regime is sensitive to the surface micro-features that are unique to each species.

Statistical Shape Analysis of Ascending Thoracic Aortic Aneurysm: Correlation between Shape and Biomechanical Descriptors

An ascending thoracic aortic aneurysm (ATAA) is a heterogeneous disease showing different patterns of aortic dilatation and valve morphologies, each with distinct clinical course. This study aimed to explore the aortic morphology and the associations between shape and function in a population of ATAA, while further assessing novel risk models of aortic surgery not based on aortic size. Shape variability of n = 106 patients with ATAA and different valve morphologies (i.e., bicuspid versus tricuspid aortic valve) was estimated by statistical shape analysis (SSA) to compute a mean aortic shape and its deformation. Once the computational atlas was built, principal component analysis (PCA) allowed to reduce the complex ATAA anatomy to a few shape modes, which were correlated to shear stress and aortic strain, as determined by computational analysis. Findings demonstrated that shape modes are associated to specific morphological features of aneurysmal aorta as the vessel tortuosity and local bulging of the ATAA. A predictive model, built with principal shape modes of the ATAA wall, achieved better performance in stratifying surgically operated ATAAs versus monitored ATAAs, with respect to a baseline model using the maximum aortic diameter. Using current imaging resources, this study demonstrated the potential of SSA to investigate the association between shape and function in ATAAs, with the goal of developing a personalized approach for the treatment of the severity of aneurysmal aorta.

Artificial intelligence in pediatric and adult congenital cardiac MRI: an unmet clinical need

Cardiac MRI (CMR) allows non-invasive, non-ionizing assessment of cardiac function and anatomy in patients with congenital heart disease (CHD). The utility of CMR as a non-invasive imaging tool for evaluation of CHD have been growing exponentially over the past decade. The algorithms based on artificial intelligence (AI), and in particular, deep learning, have rapidly become a methodology of choice for analyzing CMR. A wide range of applications for AI have been developed to tackle challenges in various aspects of CMR, and significant advances have also been made from image acquisition to image analysis and diagnosis. We include an overview of AI definitions, different architectures, and details on well-known methods. This paper reviews the major deep learning concepts used for analyses of patients with CHD. In the end, we have summarized a list of open challenges and concerns to be considered for future studies.

Ventricle stress/strain comparisons between Tetralogy of Fallot patients and healthy using models with different zero-load diastole and systole morphologies

Patient-specific in vivo ventricle mechanical wall stress and strain conditions are important for cardiovascular investigations and should be calculated from correct zero-load ventricle morphologies. Cardiac magnetic resonance (CMR) data were obtained from 6 healthy volunteers and 12 Tetralogy of Fallot (TOF) patients with consent obtained. 3D patient-specific CMR-based ventricle models with different zero-load diastole and systole geometries due to myocardium contraction and relaxation were constructed to qualify right ventricle (RV) diastole and systole stress and strain values at begin-filling, end-filling, begin-ejection, and end-ejection, respectively. Our new models (called 2G models) can provide end-diastole and end-systole stress/strain values which models with one zero-load geometries (called 1G models) could not provide. 2G mean end-ejection stress value from the 18 participants was 321.4% higher than that from 1G models (p = 0.0002). 2G mean strain values was 230% higher than that of 1G models (p = 0.0002). TOF group (TG) end-ejection mean stress value was 105.4% higher than that of healthy group (HG) (17.54±7.42kPa vs. 8.54±0.92kPa, p = 0.0245). Worse outcome group (WG, n = 6) post pulmonary valve replacement (PVR) begin-ejection mean stress was 57.4% higher than that of better outcome group (BG, 86.94±26.29 vs. 52.93±22.86 kPa; p = 0.041). Among 7 selected parameters, End-filling stress was the best predictor to differentiate BG patients from WG patients with prediction accuracy = 0.8208 and area under receiver operating characteristic curve (AUC) value at 0.8135 (EE stress). Large scale studies are needed to further validate our findings.

Cardiac Motion Evolution Model for Analysis of Functional Changes Using Tensor Decomposition and Cross-Sectional Data

Cardiac disease can reduce the ability of the ventricles to function well enough to sustain long-term pumping efficiency. Recent advances in cardiac motion tracking have led to improvements in the analysis of cardiac function. We propose a method to study cohort effects related to age with respect to cardiac function. The proposed approach makes use of a recent method for describing cardiac motion of a given subject using a polyaffine model, which gives a compact parameterization that reliably and accurately describes the cardiac motion across populations. Using this method, a data tensor of motion parameters is extracted for a given population. The partial least squares method for higher order arrays is used to build a model to describe the motion parameters with respect to age, from which a model of motion given age is derived. Based on the cross-sectional statistical analysis with the data tensor of each subject treated as an observation along time, the left ventricular motion over time of Tetralogy of Fallot patients is analysed to understand the temporal evolution of functional abnormalities in this population compared to healthy motion dynamics.

Statistical shape modeling of the left ventricle: myocardial infarct classification challenge

Statistical shape modeling is a powerful tool for visualizing and quantifying geometric and functional patterns of the heart. After myocardial infarction (MI), the left ventricle typically remodels in response to physiological challenges. Several methods have been proposed in the literature to describe statistical shape changes. Which method best characterizes left ventricular remodeling after MI is an open research question. A better descriptor of remodeling is expected to provide a more accurate evaluation of disease status in MI patients. We therefore designed a challenge to test shape characterization in MI given a set of three-dimensional left ventricular surface points. The training set comprised 100 MI patients, and 100 asymptomatic volunteers (AV). The challenge was initiated in 2015 at the Statistical Atlases and Computational Models of the Heart workshop, in conjunction with the MICCAI conference. The training set with labels was provided to participants, who were asked to submit the likelihood of MI from a different (validation) set of 200 cases (100 AV and 100 MI). Sensitivity, specificity, accuracy and area under the receiver operating characteristic curve were used as the outcome measures. The goals of this challenge were to (1) establish a common dataset for evaluating statistical shape modeling algorithms in MI, and (2) test whether statistical shape modeling provides additional information characterizing MI patients over standard clinical measures. Eleven groups with a wide variety of classification and feature extraction approaches participated in this challenge. All methods achieved excellent classification results with accuracy ranges from 0.83 to 0.98. The areas under the receiver operating characteristic curves were all above 0.90. Four methods showed significantly higher performance than standard clinical measures. The dataset and software for evaluation are available from the Cardiac Atlas Project website1.

Statistical shape modelling to aid surgical planning: associations between surgical parameters and head shapes following spring-assisted cranioplasty

PURPOSE

Spring-assisted cranioplasty is performed to correct the long and narrow head shape of children with sagittal synostosis. Such corrective surgery involves osteotomies and the placement of spring-like distractors, which gradually expand to widen the skull until removal about 4 months later. Due to its dynamic nature, associations between surgical parameters and post-operative 3D head shape features are difficult to comprehend. The current study aimed at applying population-based statistical shape modelling to gain insight into how the choice of surgical parameters such as craniotomy size and spring positioning affects post-surgical head shape.

METHODS

Twenty consecutive patients with sagittal synostosis who underwent spring-assisted cranioplasty at Great Ormond Street Hospital for Children (London, UK) were prospectively recruited. Using a nonparametric statistical modelling technique based on mathematical currents, a 3D head shape template was computed from surface head scans of sagittal patients after spring removal. Partial least squares (PLS) regression was employed to quantify and visualise trends of localised head shape changes associated with the surgical parameters recorded during spring insertion: anterior-posterior and lateral craniotomy dimensions, anterior spring position and distance between anterior and posterior springs.

RESULTS

Bivariate correlations between surgical parameters and corresponding PLS shape vectors demonstrated that anterior-posterior (Pearson's [Formula: see text]) and lateral craniotomy dimensions (Spearman's [Formula: see text]), as well as the position of the anterior spring ([Formula: see text]) and the distance between both springs ([Formula: see text]) on average had significant effects on head shapes at the time of spring removal. Such effects were visualised on 3D models.

CONCLUSIONS

Population-based analysis of 3D post-operative medical images via computational statistical modelling tools allowed for detection of novel associations between surgical parameters and head shape features achieved following spring-assisted cranioplasty. The techniques described here could be extended to other cranio-maxillofacial procedures in order to assess post-operative outcomes and ultimately facilitate surgical decision making.

Quantitative analysis of fetal facial morphology using 3D ultrasound and statistical shape modeling: a feasibility study

BACKGROUND

The antenatal detection of facial dysmorphism using 3-dimensional ultrasound may raise the suspicion of an underlying genetic condition but infrequently leads to a definitive antenatal diagnosis. Despite advances in array and noninvasive prenatal testing, not all genetic conditions can be ascertained from such testing.

OBJECTIVES

The aim of this study was to investigate the feasibility of quantitative assessment of fetal face features using prenatal 3-dimensional ultrasound volumes and statistical shape modeling. STUDY DESIGN: Thirteen normal and 7 abnormal stored 3-dimensional ultrasound fetal face volumes were analyzed, at a median gestation of 29⁺⁴ weeks (25⁺⁰ to 36⁺¹). The 20 3-dimensional surface meshes generated were aligned and served as input for a statistical shape model, which computed the mean 3-dimensional face shape and 3-dimensional shape variations using principal component analysis.

RESULTS

Ten shape modes explained more than 90% of the total shape variability in the population. While the first mode accounted for overall size differences, the second highlighted shape feature changes from an overall proportionate toward a more asymmetric face shape with a wide prominent forehead and an undersized, posteriorly positioned chin. Analysis of the Mahalanobis distance in principal component analysis shape space suggested differences between normal and abnormal fetuses (median and interquartile range distance values, 7.31 ± 5.54 for the normal group vs 13.27 ± 9.82 for the abnormal group) (P = .056).

CONCLUSION

This feasibility study demonstrates that objective characterization and quantification of fetal facial morphology is possible from 3-dimensional ultrasound. This technique has the potential to assist in utero diagnosis, particularly of rare conditions in which facial dysmorphology is a feature.

Statistical Shape Modeling for Cavopulmonary Assist Device Development: Variability of Vascular Graft Geometry and Implications for Hemodynamics

Patients born with a single functional ventricle typically undergo three-staged surgical palliation in the first years of life, with the last stage realizing a cross-like total cavopulmonary connection (TCPC) of superior and inferior vena cavas (SVC and IVC) with both left and right pulmonary arteries, allowing all deoxygenated blood to flow passively back to the lungs (Fontan circulation). Even though within the past decades more patients survive into adulthood, the connection comes at the prize of deficiencies such as chronic systemic venous hypertension and low cardiac output, which ultimately may lead to Fontan failure. Many studies have suggested that the TCPC's inherent insufficiencies might be addressed by adding a cavopulmonary assist device (CPAD) to provide the necessary pressure boost. While many device concepts are being explored, few take into account the complex cardiac anatomy typically associated with TCPCs. In this study, we focus on the extra cardiac conduit vascular graft connecting IVC and pulmonary arteries as one possible landing zone for a CPAD and describe its geometric variability in a cohort of 18 patients that had their TCPC realized with a 20mm vascular graft. We report traditional morphometric parameters and apply statistical shape modeling to determine the main contributors of graft shape variability. Such information may prove useful when designing CPADs that are adapted to the challenging anatomical boundaries in Fontan patients. We further compute the anatomical mean 3D graft shape (template graft) as a representative of key shape features of our cohort and prove this template graft to be a significantly better approximation of population and individual patient's hemodynamics than a commonly used simplified tube geometry. We therefore conclude that statistical shape modeling results can provide better models of geometric and hemodynamic boundary conditions associated with complex cardiac anatomy, which in turn may impact on improved cardiac device development.

Detecting Clinically Meaningful Shape Clusters in Medical Image Data: Metrics Analysis for Hierarchical Clustering Applied to Healthy and Pathological Aortic Arches

OBJECTIVE

Today's growing medical image databases call for novel processing tools to structure the bulk of data and extract clinically relevant information. Unsupervised hierarchical clustering may reveal clusters within anatomical shape data of patient populations as required for modern precision medicine strategies. Few studies have applied hierarchical clustering techniques to three-dimensional patient shape data and results depend heavily on the chosen clustering distance metrics and linkage functions. In this study, we sought to assess clustering classification performance of various distance/linkage combinations and of different types of input data to obtain clinically meaningful shape clusters.

METHODS

We present a processing pipeline combining automatic segmentation, statistical shape modeling, and agglomerative hierarchical clustering to automatically subdivide a set of 60 aortic arch anatomical models into healthy controls, two groups affected by congenital heart disease, and their respective subgroups as defined by clinical diagnosis. Results were compared with traditional morphometrics and principal component analysis of shape features.

RESULTS

Our pipeline achieved automatic division of input shape data according to primary clinical diagnosis with high F-score (0.902 ± 0.042) and Matthews correlation coefficient (0.851 ± 0.064) using the correlation/weighted distance/linkage combination. Meaningful subgroups within the three patient groups were obtained and benchmark scores for automatic segmentation and classification performance are reported.

CONCLUSION

Clustering results vary depending on the distance/linkage combination used to divide the data. Yet, clinically relevant shape clusters and subgroups could be found with high specificity and low misclassification rates.

SIGNIFICANCE

Detecting disease-specific clusters within medical image data could improve image-based risk assessment, treatment planning, and medical device development in complex disease.

Investigating Cardiac Motion Patterns Using Synthetic High-Resolution 3D Cardiovascular Magnetic Resonance Images and Statistical Shape Analysis

Diagnosis of ventricular dysfunction in congenital heart disease is more and more based on medical imaging, which allows investigation of abnormal cardiac morphology and correlated abnormal function. Although analysis of 2D images represents the clinical standard, novel tools performing automatic processing of 3D images are becoming available, providing more detailed and comprehensive information than simple 2D morphometry. Among these, statistical shape analysis (SSA) allows a consistent and quantitative description of a population of complex shapes, as a way to detect novel biomarkers, ultimately improving diagnosis and pathology understanding. The aim of this study is to describe the implementation of a SSA method for the investigation of 3D left ventricular shape and motion patterns and to test it on a small sample of 4 congenital repaired aortic stenosis patients and 4 age-matched healthy volunteers to demonstrate its potential. The advantage of this method is the capability of analyzing subject-specific motion patterns separately from the individual morphology, visually and quantitatively, as a way to identify functional abnormalities related to both dynamics and shape. Specifically, we combined 3D, high-resolution whole heart data with 2D, temporal information provided by cine cardiovascular magnetic resonance images, and we used an SSA approach to analyze 3D motion per se. Preliminary results of this pilot study showed that using this method, some differences in end-diastolic and end-systolic ventricular shapes could be captured, but it was not possible to clearly separate the two cohorts based on shape information alone. However, further analyses on ventricular motion allowed to qualitatively identify differences between the two populations. Moreover, by describing shape and motion with a small number of principal components, this method offers a fully automated process to obtain visually intuitive and numerical information on cardiac shape and motion, which could be, once validated on a larger sample size, easily integrated into the clinical workflow. To conclude, in this preliminary work, we have implemented state-of-the-art automatic segmentation and SSA methods, and we have shown how they could improve our understanding of ventricular kinetics by visually and potentially quantitatively highlighting aspects that are usually not picked up by traditional approaches.

Combination of visual and symbolic knowledge: A survey in anatomy

In medicine, anatomy is considered as the most discussed field and results in a huge amount of knowledge, which is heterogeneous and covers aspects that are mostly independent in nature. Visual and symbolic modalities are mainly adopted for exemplifying knowledge about human anatomy and are crucial for the evolution of computational anatomy. In particular, a tight integration of visual and symbolic modalities is beneficial to support knowledge-driven methods for biomedical investigation. In this paper, we review previous work on the presentation and sharing of anatomical knowledge, and the development of advanced methods for computational anatomy, also focusing on the key research challenges for harmonizing symbolic knowledge and spatial 3D data.

Computational modelling for congenital heart disease: how far are we from clinical translation?

Computational models of congenital heart disease (CHD) have become increasingly sophisticated over the last 20 years. They can provide an insight into complex flow phenomena, allow for testing devices into patient-specific anatomies (pre-CHD or post-CHD repair) and generate predictive data. This has been applied to different CHD scenarios, including patients with single ventricle, tetralogy of Fallot, aortic coarctation and transposition of the great arteries. Patient-specific simulations have been shown to be informative for preprocedural planning in complex cases, allowing for virtual stent deployment. Novel techniques such as statistical shape modelling can further aid in the morphological assessment of CHD, risk stratification of patients and possible identification of new ‘shape biomarkers’. Cardiovascular statistical shape models can provide valuable insights into phenomena such as ventricular growth in tetralogy of Fallot, or morphological aortic arch differences in repaired coarctation. In a constant move towards more realistic simulations, models can also account for multiscale phenomena (eg, thrombus formation) and importantly include measures of uncertainty (ie, CIs around simulation results). While their potential to aid understanding of CHD, surgical/procedural decision-making and personalisation of treatments is undeniable, important elements are still lacking prior to clinical translation of computational models in the field of CHD, that is, large validation studies, cost-effectiveness evaluation and establishing possible improvements in patient outcomes.

Ventricular structure in ARVC: going beyond volumes as a measure of risk

BACKGROUND

Altered right ventricular structure is an important feature of Arrhythmogenic Right Ventricular Cardiomyopathy (ARVC), but is challenging to quantify objectively. The aim of this study was to go beyond ventricular volumes and diameters and to explore if the shape of the right and left ventricles could be assessed and related to clinical measures. We used quantifiable computational methods to automatically identify and analyse malformations in ARVC patients from Cardiovascular Magnetic Resonance (CMR) images. Furthermore, we investigated how automatically extracted structural features were related to arrhythmic events.

METHODS

A retrospective cross-sectional feasibility study was performed on CMR short axis cine images of 27 ARVC patients and 21 ageing asymptomatic control subjects. All images were segmented at the end-diastolic (ED) and end-systolic (ES) phases of the cardiac cycle to create three-dimensional (3D) bi-ventricle shape models for each subject. The most common components to single- and bi-ventricular shape in the ARVC population were identified and compared to those obtained from the control group. The correlations were calculated between identified ARVC shapes and parameters from the 2010 Task Force Criteria, in addition to clinical outcomes such as ventricular arrhythmias.

RESULTS

Bi-ventricle shape for the ARVC population showed, as ordered by prevalence with the percent of total variance in the population explained by each shape: global dilation/shrinking of both ventricles (44 %), elongation/shortening at the right ventricle (RV) outflow tract (15 %), tilting at the septum (10 %), shortening/lengthening of both ventricles (7 %), and bulging/shortening at both the RV inflow and outflow (5 %). Bi-ventricle shapes were significantly correlated to several clinical diagnostic parameters and outcomes, including (but not limited to) correlations between global dilation and electrocardiography (ECG) major criteria (p = 0.002), and base-to-apex lengthening and history of arrhythmias (p = 0.003). Classification of ARVC vs. control using shape modes yielded high sensitivity (96 %) and moderate specificity (81 %).

CONCLUSION

We presented for the first time an automatic method for quantifying and analysing ventricular shapes in ARVC patients from CMR images. Specific ventricular shape features were highly correlated with diagnostic indices in ARVC patients and yielded high classification sensitivity. Ventricular shape analysis may be a novel approach to classify ARVC disease, and may be used in diagnosis and in risk stratification for ventricular arrhythmias.

A Bayesian framework for joint morphometry of surface and curve meshes in multi-object complexes

We present a Bayesian framework for atlas construction of multi-object shape complexes comprised of both surface and curve meshes. It is general and can be applied to any parametric deformation framework and to all shape models with which it is possible to define probability density functions (PDF). Here, both curve and surface meshes are modelled as Gaussian random varifolds, using a finite-dimensional approximation space on which PDFs can be defined. Using this framework, we can automatically estimate the parameters balancing data-terms and deformation regularity, which previously required user tuning. Moreover, it is also possible to estimate a well-conditioned covariance matrix of the deformation parameters. We also extend the proposed framework to data-sets with multiple group labels. Groups share the same template and their deformation parameters are modelled with different distributions. We can statistically compare the groups'distributions since they are defined on the same space. We test our algorithm on 20 Gilles de la Tourette patients and 20 control subjects, using three sub-cortical regions and their incident white matter fiber bundles. We compare their morphological characteristics and variations using a single diffeomorphism in the ambient space. The proposed method will be integrated with the Deformetrica software package, publicly available at www.deformetrica.org.

A statistical shape modelling framework to extract 3D shape biomarkers from medical imaging data: assessing arch morphology of repaired coarctation of the aorta

BACKGROUND

Medical image analysis in clinical practice is commonly carried out on 2D image data, without fully exploiting the detailed 3D anatomical information that is provided by modern non-invasive medical imaging techniques. In this paper, a statistical shape analysis method is presented, which enables the extraction of 3D anatomical shape features from cardiovascular magnetic resonance (CMR) image data, with no need for manual landmarking. The method was applied to repaired aortic coarctation arches that present complex shapes, with the aim of capturing shape features as biomarkers of potential functional relevance. The method is presented from the user-perspective and is evaluated by comparing results with traditional morphometric measurements.

METHODS

Steps required to set up the statistical shape modelling analyses, from pre-processing of the CMR images to parameter setting and strategies to account for size differences and outliers, are described in detail. The anatomical mean shape of 20 aortic arches post-aortic coarctation repair (CoA) was computed based on surface models reconstructed from CMR data. By analysing transformations that deform the mean shape towards each of the individual patient's anatomy, shape patterns related to differences in body surface area (BSA) and ejection fraction (EF) were extracted. The resulting shape vectors, describing shape features in 3D, were compared with traditionally measured 2D and 3D morphometric parameters.

RESULTS

The computed 3D mean shape was close to population mean values of geometric shape descriptors and visually integrated characteristic shape features associated with our population of CoA shapes. After removing size effects due to differences in body surface area (BSA) between patients, distinct 3D shape features of the aortic arch correlated significantly with EF (r = 0.521, p = .022) and were well in agreement with trends as shown by traditional shape descriptors.

CONCLUSIONS

The suggested method has the potential to discover previously unknown 3D shape biomarkers from medical imaging data. Thus, it could contribute to improving diagnosis and risk stratification in complex cardiac disease.

Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics

With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.

Systems approaches in integrative cardiac biology: illustrations from cardiac heterocellular signalling studies

Understanding the complexity of cardiac physiology requires system-level studies of multiple cardiac cell types. Frequently, however, the end result of published research lacks the detail of the collaborative and integrative experimental design process, and the underlying conceptual framework. We review the recent progress in systems modelling and omics analysis of the heterocellular heart environment through complementary forward and inverse approaches, illustrating these conceptual and experimental frameworks with case studies from our own research program. The forward approach begins by collecting curated information from the niche cardiac biology literature, and connecting the dots to form mechanistic network models that generate testable system-level predictions. The inverse approach starts from the vast pool of public omics data in recent cardiac biological research, and applies bioinformatics analysis to produce novel candidates for further investigation. We also discuss the possibility of combining these two approaches into a hybrid framework, together with the benefits and challenges. These interdisciplinary research frameworks illustrate the interplay between computational models, omics analysis, and wet lab experiments, which holds the key to making real progress in improving human cardiac wellbeing.

Geodesic shape regression in the framework of currents

Shape regression is emerging as an important tool for the statistical analysis of time dependent shapes. In this paper, we develop a new generative model which describes shape change over time, by extending simple linear regression to the space of shapes represented as currents in the large deformation diffeomorphic metric mapping (LDDMM) framework. By analogy with linear regression, we estimate a baseline shape (intercept) and initial momenta (slope) which fully parameterize the geodesic shape evolution. This is in contrast to previous shape regression methods which assume the baseline shape is fixed. We further leverage a control point formulation, which provides a discrete and low dimensional parameterization of large diffeomorphic transformations. This flexible system decouples the parameterization of deformations from the specific shape representation, allowing the user to define the dimensionality of the deformation parameters. We present an optimization scheme that estimates the baseline shape, location of the control points, and initial momenta simultaneously via a single gradient descent algorithm. Finally, we demonstrate our proposed method on synthetic data as well as real anatomical shape complexes.

AUTO-ENCODING OF DISCRIMINATING MORPHOMETRY FROM CARDIAC MRI

We propose a fully-automatic morphometric encoding targeted towards differentiating diseased from healthy cardiac MRI. Existing encodings rely on accurate segmentations of each scan. Segmentation generally includes labour-intensive editing and increases the risk associated with intra- and inter-rater variability. Our morphometric framework only requires the segmentation of a template scan. This template is non-rigidly registered to the other scans. We then confine the resulting deformation maps to the regions outlined by the segmentations. We learn a manifold for each region and identify the most informative coordinates with respect to distinguishing diseased from healthy scans. Compared with volumetric measurements and a deformation-based score, this encoding is much more accurate in capturing morphometric patterns distinguishing healthy subjects from those with Tetralogy of Fallot, diastolic dysfunction, and hypertrophic cardiomyopathy.

Quantifying anatomical shape variations in neurological disorders

We develop a multivariate analysis of brain anatomy to identify the relevant shape deformation patterns and quantify the shape changes that explain corresponding variations in clinical neuropsychological measures. We use kernel Partial Least Squares (PLS) and formulate a regression model in the tangent space of the manifold of diffeomorphisms characterized by deformation momenta. The scalar deformation momenta completely encode the diffeomorphic changes in anatomical shape. In this model, the clinical measures are the response variables, while the anatomical variability is treated as the independent variable. To better understand the "shape-clinical response" relationship, we also control for demographic confounders, such as age, gender, and years of education in our regression model. We evaluate the proposed methodology on the Alzheimer's Disease Neuroimaging Initiative (ADNI) database using baseline structural MR imaging data and neuropsychological evaluation test scores. We demonstrate the ability of our model to quantify the anatomical deformations in units of clinical response. Our results also demonstrate that the proposed method is generic and generates reliable shape deformations both in terms of the extracted patterns and the amount of shape changes. We found that while the hippocampus and amygdala emerge as mainly responsible for changes in test scores for global measures of dementia and memory function, they are not a determinant factor for executive function. Another critical finding was the appearance of thalamus and putamen as most important regions that relate to executive function. These resulting anatomical regions were consistent with very high confidence irrespective of the size of the population used in the study. This data-driven global analysis of brain anatomy was able to reach similar conclusions as other studies in Alzheimer's disease based on predefined ROIs, together with the identification of other new patterns of deformation. The proposed methodology thus holds promise for discovering new patterns of shape changes in the human brain that could add to our understanding of disease progression in neurological disorders.

WESD--Weighted Spectral Distance for measuring shape dissimilarity

This paper presents a new distance for measuring shape dissimilarity between objects. Recent publications introduced the use of eigenvalues of the Laplace operator as compact shape descriptors. Here, we revisit the eigenvalues to define a proper distance, called Weighted Spectral Distance (WESD), for quantifying shape dissimilarity. The definition of WESD is derived through analyzing the heat trace. This analysis provides the proposed distance with an intuitive meaning and mathematically links it to the intrinsic geometry of objects. We analyze the resulting distance definition, present and prove its important theoretical properties. Some of these properties include: 1) WESD is defined over the entire sequence of eigenvalues yet it is guaranteed to converge, 2) it is a pseudometric, 3) it is accurately approximated with a finite number of eigenvalues, and 4) it can be mapped to the [0,1) interval. Last, experiments conducted on synthetic and real objects are presented. These experiments highlight the practical benefits of WESD for applications in vision and medical image analysis.

Computational modelling of the right ventricle in repaired tetralogy of Fallot: can it provide insight into patient treatment?

AIMS

Pulmonary regurgitation (PR) causes progressive right ventricle (RV) dilatation and dysfunction in repaired tetralogy of Fallot (rToF). Declining RV function is often insidious and the timing of pulmonary valve replacement remains under debate. Quantifying the pathophysiology of adverse RV remodelling due to worsening PR may help in defining the best timing for pulmonary valve replacement. Our aim was to identify whether complex three-dimensional (3D) deformations of RV shape, as assessed with computer modelling, could constitute an anatomical biomarker that correlated with clinical parameters in rToF patients.

METHODS AND RESULTS

We selected 38 rToF patients (aged 10-30 years) who had complete data sets and had not undergone PVR from a population of 314 consecutive patients recruited in a collaborative study of four hospitals. All patients underwent cardiovascular magnetic resonance (CMR) imaging: PR and RV end-diastolic volumes were measured. An unbiased shape analysis framework was used with principal component analysis and linear regression to correlate shape with indexed PR volume. Regurgitation severity was significantly associated with RV dilatation (P = 0.01) and associated with bulging of the outflow tract (P = 0.07) and a dilatation of the apex (P = 0.08).

CONCLUSION

In this study, we related RV shape at end-diastole to clinical metrics of PR in rToF patients. By considering the entire 3D shape, we identified a link between PR and RV dilatation, outflow tract bulging, and apical dilatation. Our study constitutes a first attempt to correlate 3D RV shape with clinical metrics in rToF, opening new ways to better quantify 3D RV change in rToF.

A new approach to kinematic feature extraction from the human right ventricle for classification of hypertension: a feasibility study

This work presents a novel approach to analyze the function of the human right ventricle (RV) by deriving kinematic features of the relative change in shape throughout the cardiac cycle. The approach is anatomically consistent, allows direct comparison across populations of individuals, and potentially provides new metrics to improve the diagnosis and understanding of cardiovascular diseases such as pulmonary hypertension (PH). The details of the approach are presented, which includes a variation of harmonic topological mapping and proper orthogonal decomposition techniques, with particular focus on their applicability with respect to untagged cardiac imaging data. Results are shown for the decomposition of a collection of clinically obtained human RV endocardial surfaces segmented from cardiac computed tomography imaging into the fundamental shape change features for individuals both with and without PH. The features are shown to be consistent and converging towards intrinsically physiological components for the heart, and may potentially represent a new set of features for classifying the progressive change in RV function caused by PH, particularly in comparison to traditional clinical metrics.

Regression-based cardiac motion prediction from single-phase CTA

State of the art cardiac computed tomography (CT) enables the acquisition of imaging data of the heart over the entire cardiac cycle at concurrent high spatial and temporal resolution. However, in clinical practice, acquisition is increasingly limited to 3-D images. Estimating the shape of the cardiac structures throughout the entire cardiac cycle from a 3-D image is therefore useful in applications such as the alignment of preoperative computed tomography angiography (CTA) to intra-operative X-ray images for improved guidance in coronary interventions. We hypothesize that the motion of the heart is partially explained by its shape and therefore investigate the use of three regression methods for motion estimation from single-phase shape information. Quantitative evaluation on 150 4-D CTA images showed a small, but statistically significant, increase in the accuracy of the predicted shape sequences when using any of the regression methods, compared to shape-independent motion prediction by application of the mean motion. The best results were achieved using principal component regression resulting in point-to-point errors of 2.3±0.5 mm, compared to values of 2.7±0.6 mm for shape-independent motion estimation. Finally, we showed that this significant difference withstands small variations in important parameter settings of the landmarking procedure.