Combining statistical shape modeling, CFD, and meta-modeling to approximate the patient-specific pressure-drop across the aortic valve in real-time

Virtual Shape-Editing of Patient-Specific Vascular Models Using Regularized Kelvinlets

OBJECTIVE

Cardiovascular diseases, and the interventions performed to treat them, can lead to changes in the shape of patient vasculatures and their hemodynamics. Computational modeling and simulations of patient-specific vascular networks are increasingly used to quantify these hemodynamic changes, but they require modifying the shapes of the models. Existing methods to modify these shapes include editing 2D lumen contours prescribed along vessel centerlines and deforming meshes with geometry-based approaches. However, these methods can require extensive by-hand prescription of the desired shapes and often do not work robustly across a range of vascular anatomies. To overcome these limitations, we develop techniques to modify vascular models using physics-based principles that can automatically generate smooth deformations and readily apply them across different vascular anatomies.

METHODS

We adapt Regularized Kelvinlets, analytical solutions to linear elastostatics, to perform elastic shape-editing of vascular models. The Kelvinlets are packaged into three methods that allow us to artificially create aneurysms, stenoses, and tortuosity.

RESULTS

Our methods are able to generate such geometric changes across a wide range of vascular anatomies. We demonstrate their capabilities by creating sets of aneurysms, stenoses, and tortuosities with varying shapes and sizes on multiple patient-specific models.

CONCLUSION

Our Kelvinlet-based deformers allow us to edit the shape of vascular models, regardless of their anatomical locations, and parametrically vary the size of the geometric changes.

SIGNIFICANCE

These methods will enable researchers to more easily perform virtual-surgery-like deformations, computationally explore the impact of vascular shape on patient hemodynamics, and generate synthetic geometries for data-driven research.

Euclidean and Shape-Based Analysis of the Dynamic Mitral Annulus in Children using a Novel Open-Source Framework

BACKGROUND

The dynamic shape of the normal adult mitral annulus has been shown to be important to mitral valve function. However, annular dynamics of the healthy mitral valve in children have yet to be explored. The aim of this study was to model and quantify the shape and major modes of variation of pediatric mitral valve annuli in four phases of the cardiac cycle using transthoracic echocardiography.

METHODS

The mitral valve annuli of 100 children and young adults with normal findings on three-dimensional echocardiography were modeled in four different cardiac phases using the SlicerHeart extension for 3D Slicer. Annular metrics were quantified using SlicerHeart, and optimal normalization to body surface area was explored. Mean annular shapes and the principal components of variation were computed using custom code implemented in a new SlicerHeart module (Annulus Shape Analyzer). Shape was regressed over metrics of age and body surface area, and mean shapes for five age-stratified groups were generated.

RESULTS

The ratio of annular height to commissural width of the mitral valve ("saddle shape") changed significantly throughout age for systolic phases (P < .001) but within a narrow range (median range, 0.20-0.25). Annular metrics changed statistically significantly between the diastolic and systolic phases of the cardiac cycle. Visually, the annular shape was maintained with respect to age and body surface area. Principal-component analysis revealed that the pediatric mitral annulus varies primarily in size (mode 1), ratio of annular height to commissural width (mode 2), and sphericity (mode 3).

CONCLUSIONS

The saddle-shaped mitral annulus is maintained throughout childhood but varies significantly throughout the cardiac cycle. The major modes of variation in the pediatric mitral annulus are due to size, ratio of annular height to commissural width, and sphericity. The generation of age- and size-specific mitral annular shapes may inform the development of appropriately scaled absorbable or expandable mitral annuloplasty rings for children.

Validated respiratory drug deposition predictions from 2D and 3D medical images with statistical shape models and convolutional neural networks

For the one billion sufferers of respiratory disease, managing their disease with inhalers crucially influences their quality of life. Generic treatment plans could be improved with the aid of computational models that account for patient-specific features such as breathing pattern, lung pathology and morphology. Therefore, we aim to develop and validate an automated computational framework for patient-specific deposition modelling. To that end, an image processing approach is proposed that could produce 3D patient respiratory geometries from 2D chest X-rays and 3D CT images. We evaluated the airway and lung morphology produced by our image processing framework, and assessed deposition compared to in vivo data. The 2D-to-3D image processing reproduces airway diameter to 9% median error compared to ground truth segmentations, but is sensitive to outliers of up to 33% due to lung outline noise. Predicted regional deposition gave 5% median error compared to in vivo measurements. The proposed framework is capable of providing patient-specific deposition measurements for varying treatments, to determine which treatment would best satisfy the needs imposed by each patient (such as disease and lung/airway morphology). Integration of patient-specific modelling into clinical practice as an additional decision-making tool could optimise treatment plans and lower the burden of respiratory diseases.

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.

Impact of the Spatial Velocity Inlet Distribution on the Hemodynamics of the Thoracic Aorta

The impact of the distribution in space of the inlet velocity in the numerical simulations of the hemodynamics in the thoracic aorta is systematically investigated. A real healthy aorta geometry, for which in-vivo measurements are available, is considered. The distribution is modeled through a truncated cone shape, which is a suitable approximation of the real one downstream of a trileaflet aortic valve during the systolic part of the cardiac cycle. The ratio between the upper and the lower base of the truncated cone and the position of the center of the upper base are selected as uncertain parameters. A stochastic approach is chosen, based on the generalized Polynomial Chaos expansion, to obtain accurate response surfaces of the quantities of interest in the parameter space. The selected parameters influence the velocity distribution in the ascending aorta. Consequently, effects on the wall shear stress are observed, confirming the need to use patient-specific inlet conditions if interested in the hemodynamics of this region. The surface base ratio is globally the most important parameter. Conversely, the impact on the velocity and wall shear stress in the aortic arch and descending aorta is almost negligible.

A parametric geometry model of the aortic valve for subject-specific blood flow simulations using a resistive approach

Cardiac valves simulation is one of the most complex tasks in cardiovascular modeling. Fluid-structure interaction is not only highly computationally demanding but also requires knowledge of the mechanical properties of the tissue. Therefore, an alternative is to include valves as resistive flow obstacles, prescribing the geometry (and its possible changes) in a simple way, but, at the same time, with a geometry complex enough to reproduce both healthy and pathological configurations. In this work, we present a generalized parametric model of the aortic valve to obtain patient-specific geometries that can be included into blood flow simulations using a resistive immersed implicit surface (RIIS) approach. Numerical tests are presented for geometry generation and flow simulations in aortic stenosis patients whose parameters are extracted from ECG-gated CT images.

Modelling blood flow in patients with heart valve disease using deep learning: A computationally efficient method to expand diagnostic capabilities in clinical routine

Introduction

The computational modelling of blood flow is known to provide vital hemodynamic parameters for diagnosis and treatment-support for patients with valvular heart disease. However, most diagnosis/treatment-support solutions based on flow modelling proposed utilize time- and resource-intensive computational fluid dynamics (CFD) and are therefore difficult to implement into clinical practice. In contrast, deep learning (DL) algorithms provide results quickly with little need for computational power. Thus, modelling blood flow with DL instead of CFD may substantially enhances the usability of flow modelling-based diagnosis/treatment support in clinical routine. In this study, we propose a DL-based approach to compute pressure and wall-shear-stress (WSS) in the aorta and aortic valve of patients with aortic stenosis (AS).

Methods

A total of 103 individual surface models of the aorta and aortic valve were constructed from computed tomography data of AS patients. Based on these surface models, a total of 267 patient-specific, steady-state CFD simulations of aortic flow under various flow rates were performed. Using this simulation data, an artificial neural network (ANN) was trained to compute spatially resolved pressure and WSS using a centerline-based representation. An unseen test subset of 23 cases was used to compare both methods.

Results

ANN and CFD-based computations agreed well with a median relative difference between both methods of 6.0% for pressure and 4.9% for wall-shear-stress. Demonstrating the ability of DL to compute clinically relevant hemodynamic parameters for AS patients, this work presents a possible solution to facilitate the introduction of modelling-based treatment support into clinical practice.

Machine Learning for Cardiovascular Biomechanics Modeling: Challenges and Beyond

Recent progress in machine learning (ML), together with advanced computational power, have provided new research opportunities in cardiovascular modeling. While classifying patient outcomes and medical image segmentation with ML have already shown significant promising results, ML for the prediction of biomechanics such as blood flow or tissue dynamics is in its infancy. This perspective article discusses some of the challenges in using ML for replacing well-established physics-based models in cardiovascular biomechanics. Specifically, we discuss the large landscape of input features in 3D patient-specific modeling as well as the high-dimensional output space of field variables that vary in space and time. We argue that the end purpose of such ML models needs to be clearly defined and the tradeoff between the loss in accuracy and the gained speedup carefully interpreted in the context of translational modeling. We also discuss several exciting venues where ML could be strategically used to augment traditional physics-based modeling in cardiovascular biomechanics. In these applications, ML is not replacing physics-based modeling, but providing opportunities to solve ill-defined problems, improve measurement data quality, enable a solution to computationally expensive problems, and interpret complex spatiotemporal data by extracting hidden patterns. In summary, we suggest a strategic integration of ML in cardiovascular biomechanics modeling where the ML model is not the end goal but rather a tool to facilitate enhanced modeling.

The impact of shape uncertainty on aortic-valve pressure-drop computations

Patient-specific image-based computational fluid dynamics (CFD) is widely adopted in the cardiovascular research community to study hemodynamics, and will become increasingly important for personalized medicine. However, segmentation of the flow domain is not exact and geometric uncertainty can be expected which propagates through the computational model, leading to uncertainty in model output. Seventy-four aortic-valves were segmented from computed tomography images at peak systole. Statistical shape modeling was used to obtain an approximate parameterization of the original segmentations. This parameterization was used to train a meta-model that related the first five shape mode coefficients and flowrate to the CFD-computed transvalvular pressure-drop. Consequently, shape uncertainty in the order of 0.5 and 1.0 mm was emulated by introducing uncertainty in the shape mode coefficients. A global variance-based sensitivity analysis was performed to quantify output uncertainty and to determine relative importance of the shape modes. The first shape mode captured the opening/closing behavior of the valve and uncertainty in this mode coefficient accounted for more than 90% of the output variance. However, sensitivity to shape uncertainty is patient-specific, and the relative importance of the fourth shape mode coefficient tended to increase with increases in valvular area. These results show that geometric uncertainty in the order of image voxel size may lead to substantial uncertainty in CFD-computed transvalvular pressure-drops. Moreover, this illustrates that it is essential to assess the impact of geometric uncertainty on model output, and that this should be thoroughly quantified for applications that wish to use image-based CFD models.

Data-driven cardiovascular flow modelling: examples and opportunities

High-fidelity blood flow modelling is crucial for enhancing our understanding of cardiovascular disease. Despite significant advances in computational and experimental characterization of blood flow, the knowledge that we can acquire from such investigations remains limited by the presence of uncertainty in parameters, low resolution, and measurement noise. Additionally, extracting useful information from these datasets is challenging. Data-driven modelling techniques have the potential to overcome these challenges and transform cardiovascular flow modelling. Here, we review several data-driven modelling techniques, highlight the common ideas and principles that emerge across numerous such techniques, and provide illustrative examples of how they could be used in the context of cardiovascular fluid mechanics. In particular, we discuss principal component analysis (PCA), robust PCA, compressed sensing, the Kalman filter for data assimilation, low-rank data recovery, and several additional methods for reduced-order modelling of cardiovascular flows, including the dynamic mode decomposition and the sparse identification of nonlinear dynamics. All techniques are presented in the context of cardiovascular flows with simple examples. These data-driven modelling techniques have the potential to transform computational and experimental cardiovascular research, and we discuss challenges and opportunities in applying these techniques in the field, looking ultimately towards data-driven patient-specific blood flow modelling.