A physiologically realistic virtual patient database for the study of arterial haemodynamics

An in silico study of the effects of cardiovascular aging on carotid flow waveforms and indexes in a virtual population

Cardiovascular aging is strongly associated with increased risk of cardiovascular disease and mortality. Moreover, health and lifestyle factors may accelerate age-induced alterations, such as increased arterial stiffness and wall dilation, beyond chronological age, making the clinical assessment of cardiovascular aging an important prompt for preventative action. Carotid flow waveforms contain information about age-dependent cardiovascular properties, and their ease of measurement via noninvasive Doppler ultrasound (US) makes their analysis a promising tool for the routine assessment of cardiovascular aging. In this work, the impact of different aging processes on carotid waveform morphology and derived indexes is studied in silico, with the aim of establishing the clinical potential of a carotid US-based assessment of cardiovascular aging. One-dimensional (1-D) hemodynamic modeling was employed to generate an age-specific virtual population (VP) of N = 5,160 realistic carotid hemodynamic waveforms. The resulting VP was statistically validated against in vivo aging trends in waveforms and indexes from the literature, and simulated waveforms were studied in relation to age and underlying cardiovascular parameters. In our study, the carotid flow augmentation index (FAI) significantly increased with age (with a median increase of 50% from the youngest to the oldest age group) and was strongly correlated to local arterial stiffening (r = 0.94). The carotid pulsatility index (PI), which showed less pronounced age variation, was inversely correlated with the reflection coefficient at the carotid branching (r = -0.88) and directly correlated with carotid net forward wave energy (r = 0.90), corroborating previous literature where it was linked to increased risk of cerebrovascular damage in the elderly. There was a high correlation between corrected carotid flow time (ccFT) and cardiac output (CO) (r = 0.99), which was not affected by vascular age. This study highlights the potential of carotid waveforms as a valuable tool for the assessment of cardiovascular aging.NEW & NOTEWORTHY An age-specific virtual population was generated based on a 1-D model of the arterial circulation, including newly defined literature-based specific age variations in carotid vessel properties. Simulated carotid flow/velocity waveforms, indexes, and age trends were statistically validated against in vivo data from the literature. A comprehensive study of the impact of aging on carotid flow waveform morphology was performed, and the mechanisms influencing different carotid indexes were elucidated. Notably, flow augmentation index (FAI) was found to be a strong indicator of local carotid stiffness.

Hemodynamics of vascular shunts: trends, challenges, and prospects

Vascular bypass surgery takes a significant place in the treatment of vascular disease. According to various assessments, this type of surgery is associated with almost 20 % of all vascular surgery episodes (up to 23 % according to the Federal Neurosurgical Center of Novosibirsk). Even though the problem of using of vascular grafts is obvious and natural, many problems associated with them are not still elucidated. From the mechanics' point of view, a vascular bypass is a converging or diverging tee, and the functioning of such structures still does not have strict mathematical formulations and proofs in the general case, which forces many researchers to solve specific engineering problems associated with shunting. Mathematical modeling, which is the gold standard for virtual simulations of industrial and medical problems, faces great difficulties and limitations in solving problems for vascular bypasses. Complications in the treatment of the vascular disease may follow the difficulties in mathematical modeling, and the price can be a cardiac arrest or a stroke. This work is devoted to the main aspects of the medical application of vascular bypasses and their functioning as a mechanical system, as well the mathematical aspects of their possible setup.

First blood: An efficient, hybrid one- and zero-dimensional, modular hemodynamic solver

Low-dimensional (1D or 0D) models can describe the whole human blood circulation, for example, 1D distributed parameter model for the arterial network and 0D concentrated models for the heart or other organs. This paper presents a combined 1D-0D solver, called first_blood, that solves the governing equations of fluid dynamics to model low-dimensional hemodynamic effects. An extended method of characteristics is applied here to solve the momentum, and mass conservation equations and the viscoelastic wall model equation, mimicking the material properties of arterial walls. The heart and the peripheral lumped models are solved with a general zero-dimensional (0D) nonlinear solver. The model topology can be modular, that is, first_blood can solve any 1D-0D hemodynamic model. To demonstrate the applicability of first_blood, the human arterial system, the heart and the peripherals are modelled using the solver. The simulation time of a heartbeat takes around 2 s, that is, first_blood requires only twice the real-time for the simulation using an average PC, which highlights the computational efficiency. The source code is available on GitHub, that is, it is open source. The model parameters are based on the literature suggestions and on the validation of output data to obtain physiologically relevant results.

Sensitivity Analysis of a Mathematical Model Simulating the Post-Hepatectomy Hemodynamics Response

Recently a lumped-parameter model of the cardiovascular system was proposed to simulate the hemodynamics response to partial hepatectomy and evaluate the risk of portal hypertension (PHT) due to this surgery. Model parameters are tuned based on each patient data. This work focuses on a global sensitivity analysis (SA) study of such model to better understand the main drivers of the clinical outputs of interest. The analysis suggests which parameters should be considered patient-specific and which can be assumed constant without losing in accuracy in the predictions. While performing the SA, model outputs need to be constrained to physiological ranges. An innovative approach exploits the features of the polynomial chaos expansion method to reduce the overall computational cost. The computed results give new insights on how to improve the calibration of some model parameters. Moreover the final parameter distributions enable the creation of a virtual population available for future works. Although this work is focused on partial hepatectomy, the pipeline can be applied to other cardiovascular hemodynamics models to gain insights for patient-specific parameterization and to define a physiologically relevant virtual population.

Classification and regression of stenosis using an in-vitro pulse wave data set: Dependence on heart rate, waveform and location

BACKGROUND

Data-based approaches promise to use the information in cardiovascular signals to diagnose cardiovascular diseases. Considerable effort has been undertaken in the field of pulse-wave analysis to harness this information. However, the inverse problem, inferring arterial properties from waveform measurements, is not well understood today. Consequently, uncertainties within the estimation hinder the diagnostic application of such methods.

METHOD

This work contributes a publicly available data set measured at an in-vitro cardiovascular simulator, focusing on a set of input conditions (heart rate, waveform) and stenosis locations. Furthermore, a first attempt is undertaken to perform classification and regression on this data set using standard machine learning methods on features extracted from four peripheral pressure signals.

RESULTS

The locations of six different stenoses could be distinguished at high accuracy of 93%, where transfer function-based features outperformed features based solely on signal shape in almost all cases. Furthermore, regression on the stenosis position could be performed with a root mean square error of 2.4 cm along a 20 cm section of the arterial system using a shallow neural network. However, the performance difference between shape and transfer function features was not clear for this task.

CONCLUSION

The data set contains 800 measurements and allows investigating the influence of different heart boundary conditions, such as heart rate and waveform shape, on classification and regression tasks. Extracting features that minimise this influence is a promising way of improving the performance of these tasks.

A physiologically realistic virtual patient database for the study of arterial haemodynamics

This study creates a physiologically realistic virtual patient database (VPD), representing the human arterial system, for the primary purpose of studying the effects of arterial disease on haemodynamics. A low dimensional representation of an anatomically detailed arterial network is outlined, and a physiologically realistic posterior distribution for its parameters constructed through the use of a Bayesian approach. This approach combines both physiological/geometrical constraints and the available measurements reported in the literature. A key contribution of this work is to present a framework for including all such available information for the creation of virtual patients (VPs). The Markov Chain Monte Carlo (MCMC) method is used to sample random VPs from this posterior distribution, and the pressure and flow-rate profiles associated with each VP computed through a physics based model of pulse wave propagation. This combination of the arterial network parameters (representing a virtual patient) and the haemodynamics waveforms of pressure and flow-rates at various locations (representing functional response and potential measurements that can be acquired in the virtual patient) makes up the VPD. While 75,000 VPs are sampled from the posterior distribution, 10,000 are discarded as the initial burn-in period of the MCMC sampler. A further 12,857 VPs are subsequently removed due to the presence of negative average flow-rate, reducing the VPD to 52,143. Due to undesirable behaviour observed in some VPs-asymmetric under- and over-damped pressure and flow-rate profiles in left and right sides of the arterial system-a filter is proposed to remove VPs showing such behaviour. Post application of the filter, the VPD has 28,868 subjects. It is shown that the methodology is appropriate by comparing the VPD statistics to those reported in literature across real populations. Generally, a good agreement between the two is found while respecting physiological/geometrical constraints.

Machine learning for detection of stenoses and aneurysms: application in a physiologically realistic virtual patient database

This study presents an application of machine learning (ML) methods for detecting the presence of stenoses and aneurysms in the human arterial system. Four major forms of arterial disease-carotid artery stenosis (CAS), subclavian artery stenosis (SAS), peripheral arterial disease (PAD), and abdominal aortic aneurysms (AAA)-are considered. The ML methods are trained and tested on a physiologically realistic virtual patient database (VPD) containing 28,868 healthy subjects, adapted from the authors previous work and augmented to include disease. It is found that the tree-based methods of Random Forest and Gradient Boosting outperform other approaches. The performance of ML methods is quantified through the [Formula: see text] score and computation of sensitivities and specificities. When using six haemodynamic measurements (pressure in the common carotid, brachial, and radial arteries; and flow-rate in the common carotid, brachial, and femoral arteries), it is found that maximum [Formula: see text] scores larger than 0.9 are achieved for CAS and PAD, larger than 0.85 for SAS, and larger than 0.98 for both low- and high-severity AAAs. Corresponding sensitivities and specificities are larger than 90% for CAS and PAD, larger than 85% for SAS, and larger than 98% for both low- and high-severity AAAs. When reducing the number of measurements, performance is degraded by less than 5% when three measurements are used, and less than 10% when only two measurements are used for classification. For AAA, it is shown that [Formula: see text] scores larger than 0.85 and corresponding sensitivities and specificities larger than 85% are achievable when using only a single measurement. The results are encouraging to pursue AAA monitoring and screening through wearable devices which can reliably measure pressure or flow-rates.