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Szafron JM, Yang W, Feinstein JA, Rabinovitch M, Marsden AL. A computational growth and remodeling framework for adaptive and maladaptive pulmonary arterial hemodynamics. Biomech Model Mechanobiol 2023; 22:1935-1951. [PMID: 37658985 PMCID: PMC10929588 DOI: 10.1007/s10237-023-01744-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2023] [Accepted: 07/05/2023] [Indexed: 09/05/2023]
Abstract
Hemodynamic loading is known to contribute to the development and progression of pulmonary arterial hypertension (PAH). This loading drives changes in mechanobiological stimuli that affect cellular phenotypes and lead to pulmonary vascular remodeling. Computational models have been used to simulate mechanobiological metrics of interest, such as wall shear stress, at single time points for PAH patients. However, there is a need for new approaches that simulate disease evolution to allow for prediction of long-term outcomes. In this work, we develop a framework that models the pulmonary arterial tree through adaptive and maladaptive responses to mechanical and biological perturbations. We coupled a constrained mixture theory-based growth and remodeling framework for the vessel wall with a morphometric tree representation of the pulmonary arterial vasculature. We show that non-uniform mechanical behavior is important to establish the homeostatic state of the pulmonary arterial tree, and that hemodynamic feedback is essential for simulating disease time courses. We also employed a series of maladaptive constitutive models, such as smooth muscle hyperproliferation and stiffening, to identify critical contributors to development of PAH phenotypes. Together, these simulations demonstrate an important step toward predicting changes in metrics of clinical interest for PAH patients and simulating potential treatment approaches.
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Affiliation(s)
- Jason M Szafron
- Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, 94305, USA
- Cardiovascular Institute, Stanford University, Palo Alto, CA, 94305, USA
| | - Weiguang Yang
- Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, 94305, USA
| | - Jeffrey A Feinstein
- Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, 94305, USA
- Cardiovascular Institute, Stanford University, Palo Alto, CA, 94305, USA
| | - Marlene Rabinovitch
- Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, 94305, USA
- Cardiovascular Institute, Stanford University, Palo Alto, CA, 94305, USA
| | - Alison L Marsden
- Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, 94305, USA.
- Cardiovascular Institute, Stanford University, Palo Alto, CA, 94305, USA.
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Muhl L, Mocci G, Pietilä R, Liu J, He L, Genové G, Leptidis S, Gustafsson S, Buyandelger B, Raschperger E, Hansson EM, Björkegren JL, Vanlandewijck M, Lendahl U, Betsholtz C. A single-cell transcriptomic inventory of murine smooth muscle cells. Dev Cell 2022; 57:2426-2443.e6. [DOI: 10.1016/j.devcel.2022.09.015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Revised: 09/12/2022] [Accepted: 09/27/2022] [Indexed: 11/28/2022]
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Colebank MJ, Umar Qureshi M, Olufsen MS. Sensitivity analysis and uncertainty quantification of 1-D models of pulmonary hemodynamics in mice under control and hypertensive conditions. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3242. [PMID: 31355521 DOI: 10.1002/cnm.3242] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2019] [Revised: 07/01/2019] [Accepted: 07/14/2019] [Indexed: 06/10/2023]
Abstract
Pulmonary hypertension (PH), defined as an elevated mean blood pressure in the main pulmonary artery (MPA) at rest, is associated with vascular remodeling of both large and small arteries. PH has several sub-types that are all linked to high mortality rates. In this study, we use a one-dimensional (1-D) fluid dynamics model driven by in vivo measurements of MPA flow to understand how model parameters and network size influence MPA pressure predictions in the presence of PH. We compare model predictions with in vivo MPA pressure measurements from a control and a hypertensive mouse and analyze results in three networks of increasing complexity, extracted from micro-computed tomography (micro-CT) images. We introduce global scaling factors for boundary condition parameters and perform local and global sensitivity analysis to calculate parameter influence on model predictions of MPA pressure and correlation analysis to determine a subset of identifiable parameters. These are inferred using frequentist optimization and Bayesian inference via the Delayed Rejection Adaptive Metropolis (DRAM) algorithm. Frequentist and Bayesian uncertainty is computed for model parameters and MPA pressure predictions. Results show that MPA pressure predictions are most sensitive to distal vascular resistance and that parameter influence changes with increasing network complexity. Our outcomes suggest that PH leads to increased vascular stiffness and decreased peripheral compliance, congruent with clinical observations.
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Affiliation(s)
- Mitchel J Colebank
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina
| | - M Umar Qureshi
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina
| | - Mette S Olufsen
- Department of Mathematics, North Carolina State University, Raleigh, North Carolina
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Paun LM, Colebank MJ, Olufsen MS, Hill NA, Husmeier D. Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation. J R Soc Interface 2020; 17:20200886. [PMID: 33353505 PMCID: PMC7811590 DOI: 10.1098/rsif.2020.0886] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
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.
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Affiliation(s)
- L Mihaela Paun
- School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QQ, UK
| | - Mitchel J Colebank
- Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
| | - Mette S Olufsen
- Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
| | - Nicholas A Hill
- School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QQ, UK
| | - Dirk Husmeier
- School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QQ, UK
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Dong M, Yang W, Tamaresis JS, Chan FP, Zucker EJ, Kumar S, Rabinovitch M, Marsden AL, Feinstein JA. Image-based scaling laws for somatic growth and pulmonary artery morphometry from infancy to adulthood. Am J Physiol Heart Circ Physiol 2020; 319:H432-H442. [PMID: 32618514 DOI: 10.1152/ajpheart.00123.2020] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
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.
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Affiliation(s)
- Melody Dong
- Department of Bioengineering, Stanford University, Stanford, California
| | - Weiguang Yang
- Department of Pediatrics-Cardiology, Stanford University, Stanford, California
| | - John S Tamaresis
- Department of Biomedical Data Science, Stanford University, Stanford, California
| | - Frandics P Chan
- Department of Radiology, Stanford University, Stanford, California
| | - Evan J Zucker
- Department of Radiology, Stanford University, Stanford, California
| | - Sahana Kumar
- Department of Pediatrics-Cardiology, Stanford University, Stanford, California
| | - Marlene Rabinovitch
- Department of Pediatrics-Cardiology, Stanford University, Stanford, California
| | - Alison L Marsden
- Department of Bioengineering, Stanford University, Stanford, California.,Department of Pediatrics-Cardiology, Stanford University, Stanford, California
| | - Jeffrey A Feinstein
- Department of Bioengineering, Stanford University, Stanford, California.,Department of Pediatrics-Cardiology, Stanford University, Stanford, California
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Multiscale modeling of ventricular–vascular dysfunction in pulmonary arterial hypertension. CURRENT OPINION IN BIOMEDICAL ENGINEERING 2019. [DOI: 10.1016/j.cobme.2019.09.004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Hemodynamics and Wall Mechanics after Surgical Repair of Aortic Arch: Implication for Better Clinical Decisions. APPLIED SCIENCES-BASEL 2019. [DOI: 10.3390/app9040807] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Graft repair of aortic coarctation is commonly used to mimic the physiological aortic arch shape and function. Various graft materials and shapes have been adopted for the surgery. The goal of this work is to quantitatively assess the impact of graft materials and shapes in the hemodynamics and wall mechanics of the restored aortic arch and its correlation with clinical outcomes. A three-dimensional aortic arch model was reconstructed from magnetic resonance images. The fluid–structure interaction (FSI) analysis was performed to characterize the hemodynamics and solid wall mechanics of the repaired aortic arch. Two graft shapes (i.e., a half-moon shape and a crescent one) were considered. Material choices of the aortic arch repair included three commonly used graft materials (i.e., polytetrafluoroethylene (PTFE) synthetic graft, CorMatrix extracellular matrix, and pulmonary homograft) as well as one native tissue serving as a control. The pathological hemodynamic parameters, in terms of the percentage area of low wall shear stress (WSS), high oscillatory shear index (OSI), and high relative residence time (RRT), were quantified to be associated with potential clinical outcomes. Results have shown that the peak von Mises stress for the aortic arch repaired by the crescent graft was 76% less than that of the half-moon graft. Flow disturbance and recirculation were also minimized with the crescent graft. Moreover, pathological hemodynamic parameters were significantly reduced with the crescent graft. The graft material mismatch with the surrounding tissue aggregated the stress concentration on the aortic wall, but had minimal impact on flow dynamics. The present work demonstrated the role and importance of the graft geometry and materials on hemodynamics and wall mechanics, which could guide optimal graft decisions towards better clinical outcomes.
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Qureshi MU, Colebank MJ, Paun LM, Ellwein Fix L, Chesler N, Haider MA, Hill NA, Husmeier D, Olufsen MS. Hemodynamic assessment of pulmonary hypertension in mice: a model-based analysis of the disease mechanism. Biomech Model Mechanobiol 2018; 18:219-243. [DOI: 10.1007/s10237-018-1078-8] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2018] [Accepted: 09/17/2018] [Indexed: 12/26/2022]
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D'Souza GA, Taylor MD, Banerjee RK. Evaluation of pulmonary artery wall properties in congenital heart disease patients using cardiac magnetic resonance. PROGRESS IN PEDIATRIC CARDIOLOGY 2017. [DOI: 10.1016/j.ppedcard.2017.09.005] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
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Arnold A, Battista C, Bia D, German YZ, Armentano RL, Tran H, Olufsen MS. Uncertainty Quantification in a Patient-Specific One-Dimensional Arterial Network Model: EnKF-Based Inflow Estimator. JOURNAL OF VERIFICATION, VALIDATION, AND UNCERTAINTY QUANTIFICATION 2017; 2:0110021-1100214. [PMID: 35832352 PMCID: PMC8597574 DOI: 10.1115/1.4035918] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2016] [Revised: 01/31/2017] [Indexed: 11/09/2023]
Abstract
Successful clinical use of patient-specific models for cardiovascular dynamics depends on the reliability of the model output in the presence of input uncertainties. For 1D fluid dynamics models of arterial networks, input uncertainties associated with the model output are related to the specification of vessel and network geometry, parameters within the fluid and wall equations, and parameters used to specify inlet and outlet boundary conditions. This study investigates how uncertainty in the flow profile applied at the inlet boundary of a 1D model affects area and pressure predictions at the center of a single vessel. More specifically, this study develops an iterative scheme based on the ensemble Kalman filter (EnKF) to estimate the temporal inflow profile from a prior distribution of curves. The EnKF-based inflow estimator provides a measure of uncertainty in the size and shape of the estimated inflow, which is propagated through the model to determine the corresponding uncertainty in model predictions of area and pressure. Model predictions are compared to ex vivo area and blood pressure measurements in the ascending aorta, the carotid artery, and the femoral artery of a healthy male Merino sheep. Results discuss dynamics obtained using a linear and a nonlinear viscoelastic wall model.
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Affiliation(s)
- Andrea Arnold
- Department of Mathematics, North Carolina State University, 2108 SAS Hall, 2311 Stinson Drive, Box 8205, Raleigh, NC 27695-8205 e-mail:
| | - Christina Battista
- DILIsym Services, Inc., Six Davis Drive, Research Triangle Park, NC 27709 e-mail:
| | - Daniel Bia
- Department of Physiology, Universidad de la República, Montevideo 11800, Uruguay e-mail:
| | - Yanina Zócalo German
- Department of Physiology, Universidad de la República, Montevideo 11800, Uruguay e-mail:
| | - Ricardo L Armentano
- Department of Biological Engineering, CENUR Litoral Norte-Paysandú, Universidad de la República, Montevideo 11800, Uruguay e-mail:
| | - Hien Tran
- Department of Mathematics, North Carolina State University, 2108 SAS Hall, 2311 Stinson Drive, Box 8205, Raleigh, NC 27695-8205 e-mail:
| | - Mette S Olufsen
- Department of Mathematics, North Carolina State University, 2108 SAS Hall, 2311 Stinson Drive, Box 8205, Raleigh, NC 27695-8205 e-mail:
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