Proper Orthogonal Decomposition Analysis of the Flow Downstream of a Dysfunctional Bileaflet Mechanical Aortic Valve

Deriving phenotype-representative left ventricular flow patterns by reduced-order modeling and classification

BACKGROUND

Extracting phenotype-representative flow patterns and their associated numerical metrics is a bottleneck in the clinical translation of advanced cardiac flow imaging modalities. We hypothesized that reduced-order models (ROMs) are a suitable strategy for deriving simple and interpretable clinical metrics of intraventricular flow suitable for further assessments. Combined with machine learning (ML) flow-based ROMs could provide new insight to help diagnose and risk-stratify patients.

METHODS

We analyzed 2D color-Doppler echocardiograms of 81 non-ischemic dilated cardiomyopathy (DCM) patients, 51 hypertrophic cardiomyopathy (HCM) patients, and 77 normal volunteers (Control). We applied proper orthogonal decomposition (POD) to build patient-specific and cohort-specific ROMs of LV flow. Each ROM aggregates a low number of components representing a spatially dependent velocity map modulated along the cardiac cycle by a time-dependent coefficient. We tested three classifiers using deliberately simple ML analyses of these ROMs with varying supervision levels. In supervised models, hyperparameter grid search was used to derive the ROMs that maximize classification power. The classifiers were blinded to LV chamber geometry and function. We ran vector flow mapping on the color-Doppler sequences to help visualize flow patterns and interpret the ML results.

RESULTS

POD-based ROMs stably represented each cohort through 10-fold cross-validation. The principal POD mode captured >80 % of the flow kinetic energy (KE) in all cohorts and represented the LV filling/emptying jets. Mode 2 represented the diastolic vortex and its KE contribution ranged from <1 % (HCM) to 13 % (DCM). Semi-unsupervised classification using patient-specific ROMs revealed that the KE ratio of these two principal modes, the vortex-to-jet (V2J) energy ratio, is a simple, interpretable metric that discriminates DCM, HCM, and Control patients. Receiver operating characteristic curves using V2J as classifier had areas under the curve of 0.81, 0.91, and 0.95 for distinguishing HCM vs. Control, DCM vs. Control, and DCM vs. HCM, respectively.

CONCLUSIONS

Modal decomposition of cardiac flow can be used to create ROMs of normal and pathological flow patterns, uncovering simple interpretable flow metrics with power to discriminate disease states, and particularly suitable for further processing using ML.

4D Flow Patterns and Relative Pressure Distribution in a Left Ventricle Model by Shake-the-Box and Proper Orthogonal Decomposition Analysis

PURPOSE

Intraventricular blood flow dynamics are associated with cardiac function. Accurate, noninvasive, and easy assessments of hemodynamic quantities (such as velocity, vortex, and pressure) could be an important addition to the clinical diagnosis and treatment of heart diseases. However, the complex time-varying flow brings many challenges to the existing noninvasive image-based hemodynamic assessments. The development of reliable techniques and analysis tools is essential for the application of hemodynamic biomarkers in clinical practice.

METHODS

In this study, a time-resolved particle tracking method, Shake-the-Box, was applied to reconstruct the flow in a realistic left ventricle (LV) silicone model with biological valves. Based on the obtained velocity, 4D pressure field was calculated using a Poisson equation-based pressure solver. Furthermore, flow analysis by proper orthogonal decomposition (POD) of the 4D velocity field has been performed.

RESULTS

As a result of the Shake-the-Box algorithm, we have extracted: (i) particle positions, (ii) particle tracks, and finally, (iii) 4D velocity fields. From the latter, the temporal evolution of the 3D pressure field during the full cardiac cycle was obtained. The obtained maximal pressure difference extracted along the base-to-apex was about 2.7 mmHg, which is in good agreement with those reported in vivo. The POD analysis results showed a clear picture of different scale of vortices in the pulsatile LV flow, together with their time-varying information and corresponding kinetic energy content. To reconstruct 95% of the kinetic energy of the LV flow, only the first six POD modes would be required, leading to significant data reduction.

CONCLUSIONS

This work demonstrated Shake-the-Box is a promising technique to accurately reconstruct the left ventricle flow field in vitro. The good spatial and temporal resolutions of the velocity measurements enabled a 4D reconstruction of the pressure field in the left ventricle. The application of POD analysis showed its potential in reducing the complexity of the high-resolution left ventricle flow measurements. For future work, image analysis, multi-modality flow assessments, and the development of new flow-derived biomarkers can benefit from fast and data-reducing POD analysis.

Deriving Explainable Metrics of Left Ventricular Flow by Reduced-Order Modeling and Classification

Background

Extracting explainable flow metrics is a bottleneck to the clinical translation of advanced cardiac flow imaging modalities. We hypothesized that reduced-order models (ROMs) of intraventricular flow are a suitable strategy for deriving simple and interpretable clinical metrics suitable for further assessments. Combined with machine learning (ML) flow-based ROMs could provide new insight to help diagnose and risk-stratify patients.

Methods

We analyzed 2D color-Doppler echocardiograms of 81 non-ischemic dilated cardiomyopathy (DCM) patients, 51 hypertrophic cardiomyopathy (HCM) patients, and 77 normal volunteers (Control). We applied proper orthogonal decomposition (POD) to build patient-specific and cohort-specific ROMs of LV flow. Each ROM aggregates a low number of components representing a spatially dependent velocity map modulated along the cardiac cycle by a time-dependent coefficient. We tested three classifiers using deliberately simple ML analyses of these ROMs with varying supervision levels. In supervised models, hyperparameter gridsearch was used to derive the ROMs that maximize classification power. The classifiers were blinded to LV chamber geometry and function. We ran vector flow mapping on the color-Doppler sequences to help visualize flow patterns and interpret the ML results.

Results

POD-based ROMs stably represented each cohort through 10-fold cross-validation. The principal POD mode captured >80% of the flow kinetic energy (KE) in all cohorts and represented the LV filling/emptying jets. Mode 2 represented the diastolic vortex and its KE contribution ranged from <1% (HCM) to 13% (DCM). Semi-unsupervised classification using patient-specific ROMs revealed that the KE ratio of these two principal modes, the vortex-to-jet (V2J) energy ratio, is a simple, interpretable metric that discriminates DCM, HCM, and Control patients. Receiver operating characteristic curves using V2J as classifier had areas under the curve of 0.81, 0.91, and 0.95 for distinguishing HCM vs. Control, DCM vs. Control, and DCM vs. HCM, respectively.

Conclusions

Modal decomposition of cardiac flow can be used to create ROMs of normal and pathological flow patterns, uncovering simple interpretable flow metrics with power to discriminate disease states, and particularly suitable for further processing using ML.

Aneurysmal growth in type-B aortic dissection: assessing the impact of patient-specific inlet conditions on key haemodynamic indices

Type-B aortic dissection is a cardiovascular disease in which a tear develops in the intimal layer of the descending aorta, allowing pressurized blood to delaminate the layers of the vessel wall. In medically managed patients, long-term aneurysmal dilatation of the false lumen (FL) is considered virtually inevitable and is associated with poorer disease outcomes. While the pathophysiological mechanisms driving FL dilatation are not yet understood, haemodynamic factors are believed to play a key role. Computational fluid dynamics (CFD) and 4D-flow MRI (4DMR) analyses have revealed correlations between flow helicity, oscillatory wall shear stress and aneurysmal dilatation of the FL. In this study, we compare CFD simulations using a patient-specific, three-dimensional, three-component inlet velocity profile (4D IVP) extracted from 4DMR data against simulations with flow rate-matched uniform and axial velocity profiles that remain widely used in the absence of 4DMR. We also evaluate the influence of measurement errors in 4DMR data by scaling the 4D IVP to the degree of imaging error detected in prior studies. We observe that oscillatory shear and helicity are highly sensitive to inlet velocity distribution and flow volume throughout the FL and conclude that the choice of IVP may greatly affect the future clinical value of simulations.

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.

Body Acoustics for the Non-Invasive Diagnosis of Medical Conditions

In the past few decades, many non-invasive monitoring methods have been developed based on body acoustics to investigate a wide range of medical conditions, including cardiovascular diseases, respiratory problems, nervous system disorders, and gastrointestinal tract diseases. Recent advances in sensing technologies and computational resources have given a further boost to the interest in the development of acoustic-based diagnostic solutions. In these methods, the acoustic signals are usually recorded by acoustic sensors, such as microphones and accelerometers, and are analyzed using various signal processing, machine learning, and computational methods. This paper reviews the advances in these areas to shed light on the state-of-the-art, evaluate the major challenges, and discuss future directions. This review suggests that rigorous data analysis and physiological understandings can eventually convert these acoustic-based research investigations into novel health monitoring and point-of-care solutions.

Spectral Decomposition of the Flow and Characterization of the Sound Signals through Stenoses with Different Levels of Severity

Treatments of atherosclerosis depend on the severity of the disease at the diagnosis time. Non-invasive diagnosis techniques, capable of detecting stenosis at early stages, are essential to reduce associated costs and mortality rates. We used computational fluid dynamics and acoustics analysis to extensively investigate the sound sources arising from high-turbulent fluctuating flow through stenosis. The frequency spectral analysis and proper orthogonal decomposition unveiled the frequency contents of the fluctuations for different severities and decomposed the flow into several frequency bandwidths. Results showed that high-intensity turbulent pressure fluctuations appeared inside the stenosis for severities above 70%, concentrated at plaque surface, and immediately in the post-stenotic region. Analysis of these fluctuations with the progression of the stenosis indicated that (a) there was a distinct break frequency for each severity level, ranging from 40 to 230 Hz, (b) acoustic spatial-frequency maps demonstrated the variation of the frequency content with respect to the distance from the stenosis, and (c) high-energy, high-frequency fluctuations existed inside the stenosis only for severe cases. This information can be essential for predicting the severity level of progressive stenosis, comprehending the nature of the sound sources, and determining the location of the stenosis with respect to the point of measurements.