Computational assessment of hemodynamics-based diagnostic tools using a database of virtual subjects: Application to three case studies

One-Dimensional Blood Flow Modeling in the Cardiovascular System. From the Conventional Physiological Setting to Real-Life Hemodynamics

Research in the dynamics of blood flow is essential to the understanding of one of the major driving forces of human physiology. The hemodynamic conditions experienced within the cardiovascular system generate a highly variable mechanical environment that propels its function. Modeling this system is a challenging problem that must be addressed at the systemic scale to gain insight into the interplay between the different time and spatial scales of cardiovascular physiology processes. The vast majority of scientific contributions on systemic-scale distributed parameter-based blood flow modeling have approached the topic under relatively simple scenarios, defined by the resting state, the supine position, and, in some cases, by disease. However, the physiological states experienced by the cardiovascular system considerably deviate from such conditions throughout a significant part of our life. Moreover, these deviations are, in many cases, extremely beneficial for sustaining a healthy life. On top of this, inter-individual variability carries intrinsic complexities, requiring the modeling of patient-specific physiology. The impact of modeling hypotheses such as the effect of respiration, control mechanisms, and gravity, the consideration of other-than-resting physiological conditions, such as those encountered in exercise and sleeping, and the incorporation of organ-specific physiology and disease have been cursorily addressed in the specialized literature. In turn, patient-specific characterization of cardiovascular system models is in its early stages. As for models and methods, these conditions pose challenges regarding modeling the underlying phenomena and developing methodological tools to solve the associated equations. In fact, under certain conditions, the mathematical formulation becomes more intricate, model parameters suffer greater variability, and the overall uncertainty about the system's working point increases. This paper reviews current advances and opportunities to model and simulate blood flow in the cardiovascular system at the systemic scale in both the conventional resting setting and in situations experienced in everyday life.

Central Arterial Dynamic Evaluation from Peripheral Blood Pressure Waveforms Using CycleGAN: An In Silico Approach

Arterial stiffness is a major condition related to many cardiovascular diseases. Traditional approaches in the assessment of arterial stiffness supported by machine learning techniques are limited to the pulse wave velocity (PWV) estimation based on pressure signals from the peripheral arteries. Nevertheless, arterial stiffness can be assessed based on the pressure-strain relationship by analyzing its hysteresis loop. In this work, the capacity of deep learning models based on generative adversarial networks (GANs) to transfer pressure signals from the peripheral arterial region to pressure and area signals located in the central arterial region is explored. The studied signals are from a public and validated virtual database. Compared to other works in which the assessment of arterial stiffness was performed via PWV, in the present work the pressure-strain hysteresis loop is reconstructed and evaluated in terms of classical machine learning metrics and clinical parameters. Least-square GAN (LSGAN) and Wasserstein GAN with gradient penalty (WGAN-GP) adversarial losses are compared, yielding better results with LSGAN. LSGAN mean ± standard deviation of error for pressure and area pulse waveforms are 0.8 ± 0.4 mmHg and 0.1 ± 0.1 cm², respectively. Regarding the pressure-strain elastic modulus, it is achieved a mean absolute percentage error of 6.5 ± 5.1%. GAN-based deep learning models can recover the pressure-strain loop of central arteries while observing pressure signals from peripheral arteries.

Pulse Wave Analysis Method of Cardiovascular Parameters Extraction for Health Monitoring

OBJECTIVE

A pulse waveform is regarded as an information carrier of the cardiovascular system, which contains multiple interactive cardiovascular parameters reflecting physio-pathological states of bodies. Hence, multiple parameter analysis is increasingly meaningful to date but still cannot be easily achieved one by one due to the complex mapping between waveforms. This paper describes a new analysis method based on waveform recognition aimed for extracting multiple cardiovascular parameters to monitor public health. The objective of this new method is to deduce multiple cardiovascular parameters for a target pulse waveform based on waveform recognition to a most similar reference waveform in a given database or pattern library.

METHODS

The first part of the methodology includes building the sub-pattern libraries and training classifier. This provides a trained classifier and the sub-pattern library with reference pulse waveforms and known parameters. The second part is waveform analysis. The target waveform will be classified and output a state category being used to select the corresponding sub-pattern library with the same state. This will reduce subsequent recognition scope and computation costs. The mainstay of this new analysis method is improved dynamic time warping (DTW). This improved DTW and K-Nearest Neighbors (KNN) were applied to recognize the most similar waveform in the pattern library. Hence, cardiovascular parameters can be assigned accordingly from the most similar waveform in the pattern library.

RESULTS

Four hundred and thirty eight (438) randomly selected pulse waveforms were tested to verify the effectiveness of this method. The results show that the classification accuracy is 96.35%. Using statistical analysis to compare the target sample waveforms and the recognized reference ones from within the pattern library, most correlation coefficients are beyond 0.99. Each set of cardiovascular parameters was assessed using the Bland-Altman plot. The extracted cardiovascular parameters are in strong agreement with the original verifying the effectiveness of this new approach.

CONCLUSION

This new method using waveform recognition shows promising results that can directly extract multiple cardiovascular parameters from waveforms with high accuracy. This new approach is efficient and effective and is very promising for future continuous monitoring of cardiovascular health.

The effect of cardiac properties on arterial pulse waves: An in-silico study

This study investigated the effects of cardiac properties variability on arterial pulse wave morphology using blood flow modelling and pulse wave analysis. A lumped-parameter model of the left part of the heart was coupled to a one-dimensional model of the arterial network and validated using reference pulse waveforms in turn verified by comparison with in vivo measurements. A sensitivity analysis was performed to assess the effects of variations in cardiac parameters on central and peripheral pulse waveforms. Results showed that left ventricle contractility, stroke volume, cardiac cycle duration, and heart valves impairment are determinants of central waveforms morphology, pulse pressure and its amplification. Contractility of the left atrium has negligible effects on arterial pulse waves. Results also suggested that it might be possible to infer left ventricular dysfunction by analysing the timing of the dicrotic notch and cardiac function by analysing PPG signals. This study has identified cardiac properties that may be extracted from in vivo central and peripheral pulse waves to assess cardiac function.

Association of Local Arterial Stiffness and Windkessel Model Parameters with Ageing in Normotensives and Hypertensives

Computation of arterial stiffness is a well-established, widely accepted method for estimating vascular age. Although carotid-femoral pulse wave velocity is typically used for vascular age assessment, most recent studies have reported the need to consider a combination of local and regional stiffness indices possessing distinct association with the vascular structure and/or function for better prediction of early vascular ageing syndrome. In this work, we investigate the association of clinically validated local stiffness (obtained using biomechanical relations), global stiffness (obtained from 3-element Windkessel modelling), and pulse contour indices from the aorta with ageing and their distribution in normotensives and hypertensives. The analysis was performed on 420 (virtual) subjects (age: 65 ± 11 years) with an equal proportion of hypertensive (age: 65 ± 11 years) and normotensive (age: 65 ± 11 years) subjects. Multivariate linear regression analysis revealed an independent association of each of the indices with age (Adjusted r = 0.75 p < 0.01). Specific stiffness index (r = 0.67, p < 0.001), Augmentation index (r = 0.55, p< 0.001) and total arterial compliance (r = -0.50, p < 0.001) depicted highest correlation with age. There was a significant difference (> 16%, p < 0.001) in mean values of the measured indices between hypertensive and normotensive subjects. The study findings further emphasize the need to combine multiple non-invasive vascular markers to capture the unique aspects of age-induced arterial wall remodelling for reliable monitoring and management of the early vascular ageing syndrome. Clinical Relevance- This study demonstrates an independent and combined predictive role of local/global stiffness and pulse contour indices in ageing.

Wave Intensity Analysis Combined With Machine Learning can Detect Impaired Stroke Volume in Simulations of Heart Failure

Heart failure is treatable, but in the United Kingdom, the 1-, 5- and 10-year mortality rates are 24.1, 54.5 and 75.5%, respectively. The poor prognosis reflects, in part, the lack of specific, simple and affordable diagnostic techniques; the disease is often advanced by the time a diagnosis is made. Previous studies have demonstrated that certain metrics derived from pressure-velocity-based wave intensity analysis are significantly altered in the presence of impaired heart performance when averaged over groups, but to date, no study has examined the diagnostic potential of wave intensity on an individual basis, and, additionally, the pressure waveform can only be obtained accurately using invasive methods, which has inhibited clinical adoption. Here, we investigate whether a new form of wave intensity based on noninvasive measurements of arterial diameter and velocity can detect impaired heart performance in an individual. To do so, we have generated a virtual population of two-thousand elderly subjects, modelling half as healthy controls and half with an impaired stroke volume. All metrics derived from the diameter-velocity-based wave intensity waveforms in the carotid, brachial and radial arteries showed significant crossover between groups-no one metric in any artery could reliably indicate whether a subject's stroke volume was normal or impaired. However, after applying machine learning to the metrics, we found that a support vector classifier could simultaneously achieve up to 99% recall and 95% precision. We conclude that noninvasive wave intensity analysis has significant potential to improve heart failure screening and diagnosis.

Transfer-function-free technique for the noninvasive determination of the human arterial pressure waveform

The estimation of central aortic blood pressure is a cardinal measurement, carrying effective physiological, and prognostic data beyond routine peripheral blood pressure. Transfer function-based devices effectively estimate aortic systolic and diastolic blood pressure from peripheral pressure waveforms, but the reconstructed pressure waveform seems to preserve features of the peripheral waveform. We sought to develop a new method for converting the local diameter distension waveform into a pressure waveform, through an exponential function whose parameters depend on the local wave speed. The proposed method was then tested at the common carotid artery. Diameter and blood velocity waveforms were acquired via ultrasound at the right common carotid artery while simultaneously recording pressure at the left common carotid artery via tonometer in 203 people (122 men, 50 ± 18 years). The wave speed was noninvasively estimated via the lnDU-loop method and then used to define the exponential function to convert the diameter into pressure. Noninvasive systolic and mean pressures estimated by the new technique were 3.8 ± 21.8 (p = 0.015) and 2.3 ± 9.6 mmHg (p = 0.011) higher than those obtained using tonometery. However, differences were much reduced and not significant in people >35 years (0.6 ± 18.7 and 0.8 ± 8.3 mmHg, respectively). This proof of concept study demonstrated that local wave speed, estimated from noninvasive local measurement of diameter and flow velocity, can be used to determine an exponential function that describes the relationship between local pressure and diameter. This pressure-diameter function can then be used for the noninvasive estimation of local arterial pressure.

Comparison of arterial wave intensity analysis by pressure-velocity and diameter-velocity methods in a virtual population of adult subjects

Pressure-velocity-based analysis of arterial wave intensity gives clinically relevant information about the performance of the heart and vessels, but its utility is limited because accurate pressure measurements can only be obtained invasively. Diameter-velocity-based wave intensity can be obtained noninvasively using ultrasound; however, due to the nonlinear relationship between blood pressure and arterial diameter, the two wave intensities might give disparate clinical indications. To test the magnitude of the disagreement, we have generated an age-stratified virtual population to investigate how the two dominant nonlinearities viscoelasticity and strain-stiffening cause the two formulations to differ. We found strong agreement between the pressure-velocity and diameter-velocity methods, particularly for the systolic wave energy, the ratio between systolic and diastolic wave heights, and older subjects. The results are promising regarding the introduction of noninvasive wave intensities in the clinic.

Noninvasive estimation of aortic hemodynamics and cardiac contractility using machine learning

Cardiac and aortic characteristics are crucial for cardiovascular disease detection. However, noninvasive estimation of aortic hemodynamics and cardiac contractility is still challenging. This paper investigated the potential of estimating aortic systolic pressure (aSBP), cardiac output (CO), and end-systolic elastance (E_es) from cuff-pressure and pulse wave velocity (PWV) using regression analysis. The importance of incorporating ejection fraction (EF) as additional input for estimating E_es was also assessed. The models, including Random Forest, Support Vector Regressor, Ridge, Gradient Boosting, were trained/validated using synthetic data (n = 4,018) from an in-silico model. When cuff-pressure and PWV were used as inputs, the normalized-RMSEs/correlations for aSBP, CO, and E_es (best-performing models) were 3.36 ± 0.74%/0.99, 7.60 ± 0.68%/0.96, and 16.96 ± 0.64%/0.37, respectively. Using EF as additional input for estimating E_es significantly improved the predictions (7.00 ± 0.78%/0.92). Results showed that the use of noninvasive pressure measurements allows estimating aSBP and CO with acceptable accuracy. In contrast, E_es cannot be predicted from pressure signals alone. Addition of the EF information greatly improves the estimated E_es. Accuracy of the model-derived aSBP compared to in-vivo aSBP (n = 783) was very satisfactory (5.26 ± 2.30%/0.97). Future in-vivo evaluation of CO and E_es estimations remains to be conducted. This novel methodology has potential to improve the noninvasive monitoring of aortic hemodynamics and cardiac contractility.

Deep learning for prediction of cardiac indices from photoplethysmographic waveform: A virtual database approach

Deep learning methods combined with large datasets have recently shown significant progress in solving several medical tasks. However, collecting and annotating large datasets can be a very cumbersome and expensive task. We tackle these problems with a virtual database approach where training data is generated using computer simulations of related phenomena. Specifically, we concentrate on the following problem: can cardiovascular indices such as aortic elasticity, diastolic and systolic blood pressures, and blood flow from heart be predicted continuously using wearable photoplethysmographic sensors? We simulate the blood flow using a haemodynamic model consisting of the entire human circulation. Repeated evaluation of the simulator allows us to create a database of "virtual subjects" with size that is only limited by available computational resources. Using this database, we train neural networks to predict the cardiac indices from photoplethysmographic signal waveform. We consider two approaches: neural networks based on predefined input features and deep convolutional neural networks taking waveform directly as the input. The performance of the methods is demonstrated using numerical examples, thus carrying out a preliminary assessment of the approaches. The results show improvements in accuracy compared with the previous methods. The improvements are especially significant with indices related to aortic elasticity and maximum blood flow. The proposed approach would provide new means to measure cardiovascular health continuously, for example, with a simple wrist device.

Computational hemodynamics in arteries with the one-dimensional augmented fluid-structure interaction system: viscoelastic parameters estimation and comparison with in-vivo data

Mathematical models are widely recognized as a valuable tool for cardiovascular diagnosis and the study of circulatory diseases, especially to obtain data that require otherwise invasive measurements. To correctly simulate body hemodynamics, the viscoelastic properties of vessels walls are a key aspect to be taken into account as they play an essential role in cardiovascular behavior. The present work aims to apply the augmented fluid-structure interaction system of blood flow to real case studies to assess the validity of the model as a valuable resource to improve cardiovascular diagnostics and the treatment of pathologies. Main contributions of the paper include the evaluation of viscoelastic tube laws, estimation of viscoelastic parameters and comparison of models with literature results and in-vivo experiments. The ability of the model to correctly simulate pulse waveforms in single arterial segments is verified using literature benchmark test cases, designed taking into account a simple elastic behavior of the wall in the upper thoracic aorta and in the common carotid artery. Furthermore, in-vivo pressure waveforms, extracted from tonometric measurements performed on four human common carotid arteries and two common femoral arteries, are compared to numerical solutions. It is highlighted that the viscoelastic damping effect of arterial walls is required to avoid an overestimation of pressure peaks. Finally, an effective procedure to estimate the viscoelastic parameters of the model is herein proposed, which returns hysteresis curves of the common carotid arteries dissipating energy fractions in line with values calculated from literature hysteresis loops in the same vessel.

Modeling arterial pulse waves in healthy aging: a database for in silico evaluation of hemodynamics and pulse wave indexes

The arterial pulse wave (PW) is a rich source of information on cardiovascular (CV) health. It is widely measured by both consumer and clinical devices. However, the physical determinants of the PW are not yet fully understood, and the development of PW analysis algorithms is limited by a lack of PW data sets containing reference CV measurements. Our aim was to create a database of PWs simulated by a computer to span a range of CV conditions, representative of a sample of healthy adults. The typical CV properties of 25-75 yr olds were identified through a literature review. These were used as inputs to a computational model to simulate PWs for subjects of each age decade. Pressure, flow velocity, luminal area, and photoplethysmographic PWs were simulated at common measurement sites, and PW indexes were extracted. The database, containing PWs from 4,374 virtual subjects, was verified by comparing the simulated PWs and derived indexes with corresponding in vivo data. Good agreement was observed, with well-reproduced age-related changes in hemodynamic parameters and PW morphology. The utility of the database was demonstrated through case studies providing novel hemodynamic insights, in silico assessment of PW algorithms, and pilot data to inform the design of clinical PW algorithm assessments. In conclusion, the publicly available PW database is a valuable resource for understanding CV determinants of PWs and for the development and preclinical assessment of PW analysis algorithms. It is particularly useful because the exact CV properties that generated each PW are known.NEW & NOTEWORTHY First, a comprehensive literature review of changes in cardiovascular properties with age was performed. Second, an approach for simulating pulse waves (PWs) at different ages was designed and verified against in vivo data. Third, a PW database was created, and its utility was illustrated through three case studies investigating the determinants of PW indexes. Fourth, the database and tools for creating the database, analyzing PWs, and replicating the case studies are freely available.

Pulse transit time estimation of aortic pulse wave velocity and blood pressure using machine learning and simulated training data

Recent developments in cardiovascular modelling allow us to simulate blood flow in an entire human body. Such model can also be used to create databases of virtual subjects, with sizes limited only by computational resources. In this work, we study if it is possible to estimate cardiovascular health indices using machine learning approaches. In particular, we carry out theoretical assessment of estimating aortic pulse wave velocity, diastolic and systolic blood pressure and stroke volume using pulse transit/arrival timings derived from photopletyshmography signals. For predictions, we train Gaussian process regression using a database of virtual subjects generated with a cardiovascular simulator. Simulated results provides theoretical assessment of accuracy for predictions of the health indices. For instance, aortic pulse wave velocity can be estimated with a high accuracy (r > 0.9) when photopletyshmography is measured from left carotid artery using a combination of foot-to-foot pulse transmit time and peak location derived for the predictions. Similar accuracy can be reached for diastolic blood pressure, but predictions of systolic blood pressure are less accurate (r > 0.75) and the stroke volume predictions are mostly contributed by heart rate.

Recently there has been a strong trend for self-monitoring of your cardiovascular health and new wearable sport trackers and mobile applications are coming to the market everyday. However, such solutions are mostly taking advantage of heart rate measurement. Other health indices such as blood pressure and pulse wave velocity reflecting to the condition of cardiovascular system would also be of great interest, but such solutions for continuous monitoring are barely existing or are at least unreliable. In this paper, we use computational modelling to assess theoretical capabilities of such measurements. We concentrate on predicting health indices using on pulse transmit time type of measurements. Such measurements could be carried out, for example, with photopletyshmography sensor or an optical sensor already found from several wearable sport trackers. We use cardiovascular modelling to create a database of “virtual subjects”, which is applied with machine learning to construct predictors for health indices. Our findings suggest that aortic pulse wave velocity and diastolic blood pressured could be predicted with a high accuracy, but predictions of systolic blood pressure are less accurate.

Computational assessment of model-based wave separation using a database of virtual subjects

The quantification of arterial wave reflection is an important area of interest in arterial pulse wave analysis. It can be achieved by wave separation analysis (WSA) if both the aortic pressure waveform and the aortic flow waveform are known. For better applicability, several mathematical models have been established to estimate aortic flow solely based on pressure waveforms. The aim of this study is to investigate and verify the model-based wave separation of the ARCSolver method on virtual pulse wave measurements. The study is based on an open access virtual database generated via simulations. Seven cardiac and arterial parameters were varied within physiological healthy ranges, leading to a total of 3325 virtual healthy subjects. For assessing the model-based ARCSolver method computationally, this method was used to perform WSA based on the aortic root pressure waveforms of the virtual patients. Asa reference, the values of WSA using both the pressure and flow waveforms provided by the virtual database were taken. The investigated parameters showed a good overall agreement between the model-based method and the reference. Mean differences and standard deviations were -0.05±0.02AU for characteristic impedance, -3.93±1.79mmHg for forward pressure amplitude, 1.37±1.56mmHg for backward pressure amplitude and 12.42±4.88% for reflection magnitude. The results indicate that the mathematical blood flow model of the ARCSolver method is a feasible surrogate for a measured flow waveform and provides a reasonable way to assess arterial wave reflection non-invasively in healthy subjects.