Generating wall shear stress for coronary artery in real-time using neural networks: Feasibility and initial results based on idealized models

Rapid prediction of wall shear stress in stenosed coronary arteries based on deep learning

There is increasing evidence that coronary artery wall shear stress (WSS) measurement provides useful prognostic information that allows prediction of adverse cardiovascular events. Computational Fluid Dynamics (CFD) has been extensively used in research to measure vessel physiology and examine the role of the local haemodynamic forces on the evolution of atherosclerosis. Nonetheless, CFD modelling remains computationally expensive and time-consuming, making its direct use in clinical practice inconvenient. A number of studies have investigated the use of deep learning (DL) approaches for fast WSS prediction. However, in these reports, patient data were limited and most of them used synthetic data generation methods for developing the training set. In this paper, we implement 2 approaches for synthetic data generation and combine their output with real patient data in order to train a DL model with a U-net architecture for prediction of WSS in the coronary arteries. The model achieved 6.03% Normalised Mean Absolute Error (NMAE) with inference taking only 0.35 s; making this solution time-efficient and clinically relevant.

Mesh neural networks for SE(3)-equivariant hemodynamics estimation on the artery wall

Computational fluid dynamics (CFD) is a valuable asset for patient-specific cardiovascular-disease diagnosis and prognosis, but its high computational demands hamper its adoption in practice. Machine-learning methods that estimate blood flow in individual patients could accelerate or replace CFD simulation to overcome these limitations. In this work, we consider the estimation of vector-valued quantities on the wall of three-dimensional geometric artery models. We employ group-equivariant graph convolution in an end-to-end SE(3)-equivariant neural network that operates directly on triangular surface meshes and makes efficient use of training data. We run experiments on a large dataset of synthetic coronary arteries and find that our method estimates directional wall shear stress (WSS) with an approximation error of 7.6% and normalised mean absolute error (NMAE) of 0.4% while up to two orders of magnitude faster than CFD. Furthermore, we show that our method is powerful enough to accurately predict transient, vector-valued WSS over the cardiac cycle while conditioned on a range of different inflow boundary conditions. These results demonstrate the potential of our proposed method as a plugin replacement for CFD in the personalised prediction of hemodynamic vector and scalar fields.

A physics-informed deep learning framework for modeling of coronary in-stent restenosis

Machine learning (ML) techniques have shown great potential in cardiovascular surgery, including real-time stenosis recognition, detection of stented coronary anomalies, and prediction of in-stent restenosis (ISR). However, estimating neointima evolution poses challenges for ML models due to limitations in manual measurements, variations in image quality, low data availability, and the difficulty of acquiring biological quantities. An effective in silico model is necessary to accurately capture the mechanisms leading to neointimal hyperplasia. Physics-informed neural networks (PINNs), a novel deep learning (DL) method, have emerged as a promising approach that integrates physical laws and measurements into modeling. PINNs have demonstrated success in solving partial differential equations (PDEs) and have been applied in various biological systems. This paper aims to develop a robust multiphysics surrogate model for ISR estimation using the physics-informed DL approach, incorporating biological constraints and drug elution effects. The model seeks to enhance prediction accuracy, provide insights into disease progression factors, and promote ISR diagnosis and treatment planning. A set of coupled advection-reaction-diffusion type PDEs is constructed to track the evolution of the influential factors associated with ISR, such as platelet-derived growth factor (PDGF), the transforming growth factor- β (TGF- β ), the extracellular matrix (ECM), the density of smooth muscle cells (SMC), and the drug concentration. The nature of PINNs allows for the integration of patient-specific data (procedure-related, clinical and genetic, etc.) into the model, improving prediction accuracy and assisting in the optimization of stent implantation parameters to mitigate risks. This research addresses the existing gap in predictive models for ISR using DL and holds the potential to enhance patient outcomes through predictive risk assessment.

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.

Non-invasive fractional flow reserve derived from reduced-order coronary model and machine learning prediction of stenosis flow resistance

BACKGROUND AND OBJECTIVE

Recently, computational fluid dynamics enables the non-invasive calculation of fractional flow reserve (FFR) based on 3D coronary model, but it is time-consuming. Currently, machine learning technique has emerged as an efficient and reliable approach for prediction, which allows saving a lot of analysis time. This study aimed at developing a simplified FFR prediction model for rapid and accurate assessment of functional significance of stenosis.

METHODS

A reduced-order lumped parameter model (LPM) of coronary system and cardiovascular system was constructed for rapidly simulating coronary flow, in which a machine learning model was embedded for accurately predicting stenosis flow resistance at a given flow from anatomical features of stenosis. Importantly, the LPM was personalized in both structures and parameters according to coronary geometries from computed tomography angiography and physiological measurements such as blood pressure and cardiac output for personalized simulations of coronary pressure and flow. Coronary lesions with invasive FFR ≤ 0.80 were defined as hemodynamically significant.

RESULTS

A total of 91 patients (93 lesions) who underwent invasive FFR were involved in FFR derived from machine learning (FFRML) calculation. Of the 93 lesions, 27 lesions (29.0%) showed lesion-specific ischemia. The average time of FFRML simulation was about 10 min. On a per-vessel basis, the FFRML and FFR were significantly correlated (r = 0.86, p < 0.001). The diagnostic accuracy, sensitivity, specificity, positive predictive value and negative predictive value were 91.4%, 92.6%, 90.9%, 80.6% and 96.8%, respectively. The area under the receiver-operating characteristic curve of FFRML was 0.984.

CONCLUSION

In this selected cohort of patients, the FFRML improves the computational efficiency and ensures the accuracy. The favorable performance of FFRML approach greatly facilitates its potential application in detecting hemodynamically significant coronary stenosis in future routine clinical practice.

Mechanism Analysis of Vascular Calcification Based on Fluid Dynamics

Vascular calcification is the abnormal deposition of calcium phosphate complexes in blood vessels, which is regarded as the pathological basis of multiple cardiovascular diseases. The flowing blood exerts a frictional force called shear stress on the vascular wall. Blood vessels have different hydrodynamic properties due to discrepancies in geometric and mechanical properties. The disturbance of the blood flow in the bending area and the branch point of the arterial tree produces a shear stress lower than the physiological magnitude of the laminar shear stress, which can induce the occurrence of vascular calcification. Endothelial cells sense the fluid dynamics of blood and transmit electrical and chemical signals to the full-thickness of blood vessels. Through crosstalk with endothelial cells, smooth muscle cells trigger osteogenic transformation, involved in mediating vascular intima and media calcification. In addition, based on the detection of fluid dynamics parameters, emerging imaging technologies such as 4D Flow MRI and computational fluid dynamics have greatly improved the early diagnosis ability of cardiovascular diseases, showing extremely high clinical application prospects.

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.

Deep learning-based hemodynamic prediction of carotid artery stenosis before and after surgical treatments

Hemodynamic prediction of carotid artery stenosis (CAS) is of great clinical significance in the diagnosis, prevention, and treatment prognosis of ischemic strokes. While computational fluid dynamics (CFD) is recognized as a useful tool, it shows a crucial issue that the high computational costs are usually required for real-time simulations of complex blood flows. Given the powerful feature-extraction capabilities, the deep learning (DL) methodology has a high potential to implement the mapping of anatomic geometries and CFD-driven flow fields, which enables accomplishing fast and accurate hemodynamic prediction for clinical applications. Based on a brain/neck CT angiography database of 280 subjects, image based three-dimensional CFD models of CAS were constructed through blood vessel extraction, computational domain meshing and setting of the pulsatile flow boundary conditions; a series of CFD simulations were undertaken. A DL strategy was proposed and accomplished in terms of point cloud datasets and a DL network with dual sampling-analysis channels. This enables multimode mapping to construct the image-based geometries of CAS while predicting CFD-based hemodynamics based on training and testing datasets. The CFD simulation was validated with the mass flow rates at two outlets reasonably agreed with the published results. Comprehensive analysis and error evaluation revealed that the DL strategy enables uncovering the association between transient blood flow characteristics and artery cavity geometric information before and after surgical treatments of CAS. Compared with other methods, our DL-based model trained with more clinical data can reduce the computational cost by 7,200 times, while still demonstrating good accuracy (error<12.5%) and flow visualization in predicting the two hemodynamic parameters. In addition, the DL-based predictions were in good agreement with CFD simulations in terms of mean velocity in the stenotic region for both the preoperative and postoperative datasets. This study points to the capability and significance of the DL-based fast and accurate hemodynamic prediction of preoperative and postoperative CAS. For accomplishing real-time monitoring of surgical treatments, further improvements in the prediction accuracy and flexibility may be conducted by utilizing larger datasets with specific real surgical events such as stent intervention, adopting personalized boundary conditions, and optimizing the DL network.

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.

Deep Learning Based Centerline-Aggregated Aortic Hemodynamics: An Efficient Alternative to Numerical Modelling of Hemodynamics

Image-based patient-specific modelling of hemodynamics are gaining increased popularity as a diagnosis and outcome prediction solution for a variety of cardiovascular diseases. While their potential to improve diagnostic capabilities and thereby clinical outcome is widely recognized, these methods require considerable computational resources since they are mostly based on conventional numerical methods such as computational fluid dynamics (CFD). As an alternative to the numerical methods, we propose a machine learning (ML) based approach to calculate patient-specific hemodynamic parameters. Compared to CFD based methods, our approach holds the benefit of being able to calculate a patient-specific hemodynamic outcome instantly with little need for computational power. In this proof-of-concept study, we present a deep artificial neural network (ANN) capable of computing hemodynamics for patients with aortic coarctation in a centerline aggregated (i.e. locally averaged) form. Considering the complex relation between vessels shape and hemodynamics on the one hand and the limited availability of suitable clinical data on the other, a sufficient accuracy of the ANN may however not be achieved with available data only. Another key aspect of this study is therefore the successful augmentation of available clinical data. Using a statistical shape model, additional training data was generated which substantially increased the ANNs accuracy, showcasing the ability of ML based methods to perform in-silico modelling tasks previously requiring resource intensive CFD simulations.