Sensitivity analysis and uncertainty quantification of 1-D models of pulmonary hemodynamics in mice under control and hypertensive conditions

Computational framework for the generation of one-dimensional vascular models accounting for uncertainty in networks extracted from medical images

One-dimensional (1D) cardiovascular models offer a non-invasive method to answer medical questions, including predictions of wave-reflection, shear stress, functional flow reserve, vascular resistance and compliance. This model type can predict patient-specific outcomes by solving 1D fluid dynamics equations in geometric networks extracted from medical images. However, the inherent uncertainty in in vivo imaging introduces variability in network size and vessel dimensions, affecting haemodynamic predictions. Understanding the influence of variation in image-derived properties is essential to assess the fidelity of model predictions. Numerous programs exist to render three-dimensional surfaces and construct vessel centrelines. Still, there is no exact way to generate vascular trees from the centrelines while accounting for uncertainty in data. This study introduces an innovative framework employing statistical change point analysis to generate labelled trees that encode vessel dimensions and their associated uncertainty from medical images. To test this framework, we explore the impact of uncertainty in 1D haemodynamic predictions in a systemic and pulmonary arterial network. Simulations explore haemodynamic variations resulting from changes in vessel dimensions and segmentation; the latter is achieved by analysing multiple segmentations of the same images. Results demonstrate the importance of accurately defining vessel radii and lengths when generating high-fidelity patient-specific haemodynamics models. KEY POINTS: This study introduces novel algorithms for generating labelled directed trees from medical images, focusing on accurate junction node placement and radius extraction using change points to provide haemodynamic predictions with uncertainty within expected measurement error. Geometric features, such as vessel dimension (length and radius) and network size, significantly impact pressure and flow predictions in both pulmonary and aortic arterial networks. Standardizing networks to a consistent number of vessels is crucial for meaningful comparisons and decreases haemodynamic uncertainty. Change points are valuable to understanding structural transitions in vascular data, providing an automated and efficient way to detect shifts in vessel characteristics and ensure reliable extraction of representative vessel radii.

Guidelines for mechanistic modeling and analysis in cardiovascular research

Computational, or in silico, models are an effective, noninvasive tool for investigating cardiovascular function. These models can be used in the analysis of experimental and clinical data to identify possible mechanisms of (ab)normal cardiovascular physiology. Recent advances in computing power and data management have led to innovative and complex modeling frameworks that simulate cardiovascular function across multiple scales. While commonly used in multiple disciplines, there is a lack of concise guidelines for the implementation of computer models in cardiovascular research. In line with recent calls for more reproducible research, it is imperative that scientists adhere to credible practices when developing and applying computational models to their research. The goal of this manuscript is to provide a consensus document that identifies best practices for in silico computational modeling in cardiovascular research. These guidelines provide the necessary methods for mechanistic model development, model analysis, and formal model calibration using fundamentals from statistics. We outline rigorous practices for computational, mechanistic modeling in cardiovascular research and discuss its synergistic value to experimental and clinical data.

Parameter subset reduction for imaging-based digital twin generation of patients with left ventricular mechanical discoordination

BACKGROUND

Integration of a patient's non-invasive imaging data in a digital twin (DT) of the heart can provide valuable insight into the myocardial disease substrates underlying left ventricular (LV) mechanical discoordination. However, when generating a DT, model parameters should be identifiable to obtain robust parameter estimations. In this study, we used the CircAdapt model of the human heart and circulation to find a subset of parameters which were identifiable from LV cavity volume and regional strain measurements of patients with different substrates of left bundle branch block (LBBB) and myocardial infarction (MI). To this end, we included seven patients with heart failure with reduced ejection fraction (HFrEF) and LBBB (study ID: 2018-0863, registration date: 2019-10-07), of which four were non-ischemic (LBBB-only) and three had previous MI (LBBB-MI), and six narrow QRS patients with MI (MI-only) (study ID: NL45241.041.13, registration date: 2013-11-12). Morris screening method (MSM) was applied first to find parameters which were important for LV volume, regional strain, and strain rate indices. Second, this parameter subset was iteratively reduced based on parameter identifiability and reproducibility. Parameter identifiability was based on the diaphony calculated from quasi-Monte Carlo simulations and reproducibility was based on the intraclass correlation coefficient ( ICC ) obtained from repeated parameter estimation using dynamic multi-swarm particle swarm optimization. Goodness-of-fit was defined as the mean squared error (χ 2 ) of LV myocardial strain, strain rate, and cavity volume.

RESULTS

A subset of 270 parameters remained after MSM which produced high-quality DTs of all patients (χ 2  < 1.6), but minimum parameter reproducibility was poor (ICC min  = 0.01). Iterative reduction yielded a reproducible (ICC min  = 0.83) subset of 75 parameters, including cardiac output, global LV activation duration, regional mechanical activation delay, and regional LV myocardial constitutive properties. This reduced subset produced patient-resembling DTs (χ 2  < 2.2), while septal-to-lateral wall workload imbalance was higher for the LBBB-only DTs than for the MI-only DTs (p < 0.05).

CONCLUSIONS

By applying sensitivity and identifiability analysis, we successfully determined a parameter subset of the CircAdapt model which can be used to generate imaging-based DTs of patients with LV mechanical discoordination. Parameters were reproducibly estimated using particle swarm optimization, and derived LV myocardial work distribution was representative for the patient's underlying disease substrate. This DT technology enables patient-specific substrate characterization and can potentially be used to support clinical decision making.

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.

Application and reduction of a nonlinear hyperelastic wall model capturing ex vivo relationships between fluid pressure, area, and wall thickness in normal and hypertensive murine left pulmonary arteries

Pulmonary hypertension is a cardiovascular disorder manifested by elevated mean arterial blood pressure (>20 mmHg) together with vessel wall stiffening and thickening due to alterations in collagen, elastin, and smooth muscle cells. Hypoxia-induced (type 3) pulmonary hypertension can be studied in animals exposed to a low oxygen environment for prolonged time periods leading to biomechanical alterations in vessel wall structure. This study introduces a novel approach to formulating a reduced order nonlinear elastic structural wall model for a large pulmonary artery. The model relating blood pressure and area is calibrated using ex vivo measurements of vessel diameter and wall thickness changes, under controlled pressure conditions, in left pulmonary arteries isolated from control and hypertensive mice. A two-layer, hyperelastic, and anisotropic model incorporating residual stresses is formulated using the Holzapfel-Gasser-Ogden model. Complex relations predicting vessel area and wall thickness with increasing blood pressure are derived and calibrated using the data. Sensitivity analysis, parameter estimation, subset selection, and physical plausibility arguments are used to systematically reduce the 16-parameter model to one in which a much smaller subset of identifiable parameters is estimated via solution of an inverse problem. Our final reduced one layer model includes a single set of three elastic moduli. Estimated ranges of these parameters demonstrate that nonlinear stiffening is dominated by elastin in the control animals and by collagen in the hypertensive animals. The pressure-area relation developed in this novel manner has potential impact on one-dimensional fluids network models of vessel wall remodeling in the presence of cardiovascular disease.

Dosimetry Sensitivity in a Lower Dimensional Model of Patient-Specific Asthma Subjects

OBJECTIVE

Experimental uncertainty will impact in silico model calculations of aerosol delivery and deposition. Patient-specific dosimetry models are often parameterized based on medical imaging data, which contain inherent experimental variability.

METHODS

Here, we created and parameterized 1D models of three subject-specific asthmatic subjects and randomly assigned perturbations of up to 15 % on airway diameter, segmental volume, and defected volume. Sensitivity of imaging data experimental variability on dosimetry metrics were quantified.

RESULTS

Lobar particle delivery primarily depended on the distal segmental volumes; 15 % range of noise resulted in delivery to the upper right lobe to vary at most from 15.2 and 18.2 % for one of the severe subjects. Particle deposition was most sensitive to airway diameter; 95 % confidence intervals spanned from 8 to 10.6 % in the mild/moderate subject for 15 % variation on input metrics for 5 [Formula: see text] diameter particles. While these results provide possible ranges of dosimetry calculations for a specific subject, the perturbations were not sufficient to model the large observed inter-subject variability (8.9, 19, and 14.5 % deposition, subjects 1--3, respectively, 5 [Formula: see text] diameter particles).

CONCLUSION

This study highlights that in silico model predictions are robust in the presence of experimental uncertainty and that it continues to be necessary to perform subject-specific simulations, especially within the presence of heterogeneous airway disease.

SIGNIFICANCE

Sensitivity analysis provides confidence in calculating deposition in the airways of asthmatic subjects within the presence of experimental uncertainty.

Numerical simulation of hemodynamics in patient-specific pulmonary artery stenosis

BACKGROUND

The incidence rate of pulmonary artery stenosis is increasing year by year and its numerical simulation has become a key project of biomedical engineering.

OBJECTIVE

The purpose of this work is to study the changes of hemodynamic parameters in patient-specific pulmonary artery stenosis.

METHODS

A pulmonary artery stenosis model is established based on patient-specific computed tomography (CT) images. According to the actual anatomy of patient-specific pulmonary artery stenosis, the stenosis area is simulated using a porous medium to study its hemodynamic changes. The computational fluid dynamics (CFD) method is used to simulate the hemodynamic changes of pulmonary artery stenosis, and to explore the mechanical characteristics between blood flow and vessel wall.

RESULTS

The results suggest that the blood pressures of arterial branches increase and the pressure drop at both ends of the stenosis is higher. There is a high flow rate and wall shear stress at the stenosis.

CONCLUSION

This study shows that the hemodynamic model of pulmonary artery stenosis can be accurately reconstructed by achieving numerical simulation of the local stenosis through CT images, and this work has important implications for improving the confidence of clinical diagnosis and treatment of pulmonary artery diseases.

Data-driven computational models of ventricular-arterial hemodynamics in pediatric pulmonary arterial hypertension

Pulmonary arterial hypertension (PAH) is a complex disease involving increased resistance in the pulmonary arteries and subsequent right ventricular (RV) remodeling. Ventricular-arterial interactions are fundamental to PAH pathophysiology but are rarely captured in computational models. It is important to identify metrics that capture and quantify these interactions to inform our understanding of this disease as well as potentially facilitate patient stratification. Towards this end, we developed and calibrated two multi-scale high-resolution closed-loop computational models using open-source software: a high-resolution arterial model implemented using CRIMSON, and a high-resolution ventricular model implemented using FEniCS. Models were constructed with clinical data including non-invasive imaging and invasive hemodynamic measurements from a cohort of pediatric PAH patients. A contribution of this work is the discussion of inconsistencies in anatomical and hemodynamic data routinely acquired in PAH patients. We proposed and implemented strategies to mitigate these inconsistencies, and subsequently use this data to inform and calibrate computational models of the ventricles and large arteries. Computational models based on adjusted clinical data were calibrated until the simulated results for the high-resolution arterial models matched within 10% of adjusted data consisting of pressure and flow, whereas the high-resolution ventricular models were calibrated until simulation results matched adjusted data of volume and pressure waveforms within 10%. A statistical analysis was performed to correlate numerous data-derived and model-derived metrics with clinically assessed disease severity. Several model-derived metrics were strongly correlated with clinically assessed disease severity, suggesting that computational models may aid in assessing PAH severity.

An in-silico analysis of experimental designs to study ventricular function: A focus on the right ventricle

In-vivo studies of pulmonary vascular disease and pulmonary hypertension (PH) have provided key insight into the progression of right ventricular (RV) dysfunction. Additional in-silico experiments using multiscale computational models have provided further details into biventricular mechanics and hemodynamic function in the presence of PH, yet few have assessed whether model parameters are practically identifiable prior to data collection. Moreover, none have used modeling to devise synergistic experimental designs. To address this knowledge gap, we conduct a practical identifiability analysis of a multiscale cardiovascular model across four simulated experimental designs. We determine a set of parameters using a combination of Morris screening and local sensitivity analysis, and test for practical identifiability using profile likelihood-based confidence intervals. We employ Markov chain Monte Carlo (MCMC) techniques to quantify parameter and model forecast uncertainty in the presence of noise corrupted data. Our results show that model calibration to only RV pressure suffers from practical identifiability issues and suffers from large forecast uncertainty in output space. In contrast, parameter and model forecast uncertainty is substantially reduced once additional left ventricular (LV) pressure and volume data is included. A comparison between single point systolic and diastolic LV data and continuous, time-dependent LV pressure-volume data reveals that at least some quantitative data from both ventricles should be included for future experimental studies.

A multiscale model of vascular function in chronic thromboembolic pulmonary hypertension

Chronic thromboembolic pulmonary hypertension (CTEPH) is caused by recurrent or unresolved pulmonary thromboemboli, leading to perfusion defects and increased arterial wave reflections. CTEPH treatment aims to reduce pulmonary arterial pressure and reestablish adequate lung perfusion, yet patients with distal lesions are inoperable by standard surgical intervention. Instead, these patients undergo balloon pulmonary angioplasty (BPA), a multisession, minimally invasive surgery that disrupts the thromboembolic material within the vessel lumen using a catheter balloon. However, there still lacks an integrative, holistic tool for identifying optimal target lesions for treatment. To address this insufficiency, we simulate CTEPH hemodynamics and BPA therapy using a multiscale fluid dynamics model. The large pulmonary arterial geometry is derived from a computed tomography (CT) image, whereas a fractal tree represents the small vessels. We model ring- and web-like lesions, common in CTEPH, and simulate normotensive conditions and four CTEPH disease scenarios; the latter includes both large artery lesions and vascular remodeling. BPA therapy is simulated by simultaneously reducing lesion severity in three locations. Our predictions mimic severe CTEPH, manifested by an increase in mean proximal pulmonary arterial pressure above 20 mmHg and prominent wave reflections. Both flow and pressure decrease in vessels distal to the lesions and increase in unobstructed vascular regions. We use the main pulmonary artery (MPA) pressure, a wave reflection index, and a measure of flow heterogeneity to select optimal target lesions for BPA. In summary, this study provides a multiscale, image-to-hemodynamics pipeline for BPA therapy planning for patients with inoperable CTEPH. NEW & NOTEWORTHY This article presents novel computational framework for predicting pulmonary hemodynamics in chronic thromboembolic pulmonary hypertension. The mathematical model is used to identify the optimal target lesions for balloon pulmonary angioplasty, combining simulated pulmonary artery pressure, wave intensity analysis, and a new quantitative metric of flow heterogeneity.

Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation

This study uses Bayesian inference to quantify the uncertainty of model parameters and haemodynamic predictions in a one-dimensional pulmonary circulation model based on an integration of mouse haemodynamic and micro-computed tomography imaging data. We emphasize an often neglected, though important source of uncertainty: in the mathematical model form due to the discrepancy between the model and the reality, and in the measurements due to the wrong noise model (jointly called 'model mismatch'). We demonstrate that minimizing the mean squared error between the measured and the predicted data (the conventional method) in the presence of model mismatch leads to biased and overly confident parameter estimates and haemodynamic predictions. We show that our proposed method allowing for model mismatch, which we represent with Gaussian processes, corrects the bias. Additionally, we compare a linear and a nonlinear wall model, as well as models with different vessel stiffness relations. We use formal model selection analysis based on the Watanabe Akaike information criterion to select the model that best predicts the pulmonary haemodynamics. Results show that the nonlinear pressure-area relationship with stiffness dependent on the unstressed radius predicts best the data measured in a control mouse.

Image-based scaling laws for somatic growth and pulmonary artery morphometry from infancy to adulthood

Pulmonary artery (PA) morphometry has been extensively explored in adults, with particular focus on intra-acinar arteries. However, scaling law relationships for length and diameter of extensive preacinar PAs by age have not been previously reported for in vivo human data. To understand preacinar PA growth spanning children to adults, we performed morphometric analyses of all PAs visible in the computed tomography (CT) and magnetic resonance (MR) images from a healthy subject cohort [n = 16; age: 1-51 yr; body surface area (BSA): 0.49-2.01 m²]. Subject-specific anatomic PA models were constructed from CT and MR images, and morphometric information-diameter, length, tortuosity, bifurcation angle, and connectivity-was extracted and sorted into diameter-defined Strahler orders. Validation of Murray's law, describing optimal scaling exponents of radii for branching vessels, was performed to determine how closely PAs conform to this classical relationship. Using regression analyses of vessel diameters and lengths against orders and patient metrics (BSA, age, height), we found that diameters increased exponentially with order and allometrically with patient metrics. Length increased allometrically with patient metrics, albeit weakly. The average tortuosity index of all vessels was 0.026 ± 0.024, average bifurcation angle was 28.2 ± 15.1°, and average Murray's law exponent was 2.92 ± 1.07. We report a set of scaling laws for vessel diameter and length, along with other morphometric information. These provide an initial understanding of healthy structural preacinar PA development with age, which can be used for computational modeling studies and comparison with diseased PA anatomy.NEW & NOTEWORTHY Pulmonary artery (PA) morphometry studies to date have focused primarily on large arteries and intra-acinar arteries in either adults or children, neglecting preacinar arteries in both populations. Our study is the first to quantify in vivo preacinar PA morphometry changes spanning infants to adults. For preacinar arteries > 1 mm in diameter, we identify scaling laws for vessel diameters and lengths with patient metrics of growth and establish a healthy PA morphometry baseline for most preacinar PAs.

Structural and hemodynamic properties of murine pulmonary arterial networks under hypoxia-induced pulmonary hypertension

Detection and monitoring of patients with pulmonary hypertension, defined as a mean blood pressure in the main pulmonary artery above 25 mmHg, requires a combination of imaging and hemodynamic measurements. This study demonstrates how to combine imaging data from microcomputed tomography images with hemodynamic pressure and flow waveforms from control and hypertensive mice. Specific attention is devoted to developing a tool that processes computed tomography images, generating subject-specific arterial networks in which one-dimensional fluid dynamics modeling is used to predict blood pressure and flow. Each arterial network is modeled as a directed graph representing vessels along the principal pathway to ensure perfusion of all lobes. The one-dimensional model couples these networks with structured tree boundary conditions representing the small arteries and arterioles. Fluid dynamics equations are solved in this network and compared to measurements of pressure in the main pulmonary artery. Analysis of microcomputed tomography images reveals that the branching ratio is the same in the control and hypertensive animals, but that the vessel length-to-radius ratio is significantly lower in the hypertensive animals. Fluid dynamics predictions show that in addition to changed network geometry, vessel stiffness is higher in the hypertensive animal models than in the control models.

Influence of image segmentation on one-dimensional fluid dynamics predictions in the mouse pulmonary arteries

Computational fluid dynamics (CFD) models are emerging tools for assisting in diagnostic assessment of cardiovascular disease. Recent advances in image segmentation have made subject-specific modelling of the cardiovascular system a feasible task, which is particularly important in the case of pulmonary hypertension, requiring a combination of invasive and non-invasive procedures for diagnosis. Uncertainty in image segmentation propagates to CFD model predictions, making the quantification of segmentation-induced uncertainty crucial for subject-specific models. This study quantifies the variability of one-dimensional CFD predictions by propagating the uncertainty of network geometry and connectivity to blood pressure and flow predictions. We analyse multiple segmentations of a single, excised mouse lung using different pre-segmentation parameters. A custom algorithm extracts vessel length, vessel radii and network connectivity for each segmented pulmonary network. Probability density functions are computed for vessel radius and length and then sampled to propagate uncertainties to haemodynamic predictions in a fixed network. In addition, we compute the uncertainty of model predictions to changes in network size and connectivity. Results show that variation in network connectivity is a larger contributor to haemodynamic uncertainty than vessel radius and length.