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Gharahi H, Filonova V, Mullagura HN, Nama N, Baek S, Figueroa CA. A multiscale framework for defining homeostasis in distal vascular trees: applications to the pulmonary circulation. Biomech Model Mechanobiol 2023; 22:971-986. [PMID: 36917305 DOI: 10.1007/s10237-023-01693-7] [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: 08/10/2021] [Accepted: 01/11/2023] [Indexed: 03/16/2023]
Abstract
Pulmonary arteries constitute a low-pressure network of vessels, often characterized as a bifurcating tree with heterogeneous vessel mechanics. Understanding the vascular complexity and establishing homeostasis is important to study diseases such as pulmonary arterial hypertension (PAH). The onset and early progression of PAH can be traced to changes in the morphometry and structure of the distal vasculature. Coupling hemodynamics with vessel wall growth and remodeling (G&R) is crucial for understanding pathology at distal vasculature. Accordingly, the goal of this study is to provide a multiscale modeling framework that embeds the essential features of arterial wall constituents coupled with the hemodynamics within an arterial network characterized by an extension of Murray's law. This framework will be used to establish the homeostatic baseline characteristics of a pulmonary arterial tree, including important parameters such as vessel radius, wall thickness and shear stress. To define the vascular homeostasis and hemodynamics in the tree, we consider two timescales: a cardiac cycle and a longer period of vascular adaptations. An iterative homeostatic optimization, which integrates a metabolic cost function minimization, the stress equilibrium, and hemodynamics, is performed at the slow timescale. In the fast timescale, the pulsatile blood flow dynamics is described by a Womersley's deformable wall analytical solution. Illustrative examples for symmetric and asymmetric trees are presented that provide baseline characteristics for the normal pulmonary arterial vasculature. The results are compared with diverse literature data on morphometry, structure, and mechanics of pulmonary arteries. The developed framework demonstrates a potential for advanced parametric studies and future G&R and hemodynamics modeling of PAH.
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Affiliation(s)
- Hamidreza Gharahi
- Section of Vascular Surgery, Department of Surgery, University of Michigan, Ann Arbor, MI, USA.
| | - Vasilina Filonova
- Section of Vascular Surgery, Department of Surgery, University of Michigan, Ann Arbor, MI, USA
| | - Haritha N Mullagura
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA
| | - Nitesh Nama
- Department of Mechanical & Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, USA
| | - Seungik Baek
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA
| | - C Alberto Figueroa
- Section of Vascular Surgery, Department of Surgery, University of Michigan, Ann Arbor, MI, USA
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA
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Kharche SR, So A, Salerno F, Lee TY, Ellis C, Goldman D, McIntyre CW. Computational Assessment of Blood Flow Heterogeneity in Peritoneal Dialysis Patients' Cardiac Ventricles. Front Physiol 2018; 9:511. [PMID: 29867555 PMCID: PMC5968396 DOI: 10.3389/fphys.2018.00511] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2018] [Accepted: 04/20/2018] [Indexed: 01/28/2023] Open
Abstract
Dialysis prolongs life but augments cardiovascular mortality. Imaging data suggests that dialysis increases myocardial blood flow (BF) heterogeneity, but its causes remain poorly understood. A biophysical model of human coronary vasculature was used to explain the imaging observations, and highlight causes of coronary BF heterogeneity. Post-dialysis CT images from patients under control, pharmacological stress (adenosine), therapy (cooled dialysate), and adenosine and cooled dialysate conditions were obtained. The data presented disparate phenotypes. To dissect vascular mechanisms, a 3D human vasculature model based on known experimental coronary morphometry and a space filling algorithm was implemented. Steady state simulations were performed to investigate the effects of altered aortic pressure and blood vessel diameters on myocardial BF heterogeneity. Imaging showed that stress and therapy potentially increased mean and total BF, while reducing heterogeneity. BF histograms of one patient showed multi-modality. Using the model, it was found that total coronary BF increased as coronary perfusion pressure was increased. BF heterogeneity was differentially affected by large or small vessel blocking. BF heterogeneity was found to be inversely related to small blood vessel diameters. Simulation of large artery stenosis indicates that BF became heterogeneous (increase relative dispersion) and gave multi-modal histograms. The total transmural BF as well as transmural BF heterogeneity reduced due to large artery stenosis, generating large patches of very low BF regions downstream. Blocking of arteries at various orders showed that blocking larger arteries results in multi-modal BF histograms and large patches of low BF, whereas smaller artery blocking results in augmented relative dispersion and fractal dimension. Transmural heterogeneity was also affected. Finally, the effects of augmented aortic pressure in the presence of blood vessel blocking shows differential effects on BF heterogeneity as well as transmural BF. Improved aortic blood pressure may improve total BF. Stress and therapy may be effective if they dilate small vessels. A potential cause for the observed complex BF distributions (multi-modal BF histograms) may indicate existing large vessel stenosis. The intuitive BF heterogeneity methods used can be readily used in clinical studies. Further development of the model and methods will permit personalized assessment of patient BF status.
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Affiliation(s)
- Sanjay R Kharche
- Kidney Clinical Research Unit, Lawson's Health Research Institute, Victoria Hospital, London, ON, Canada.,Department of Medical Biophysics, Schulich School of Medicine and Dentistry, University of Western Ontario, London, ON, Canada
| | - Aaron So
- Department of Medical Biophysics, Schulich School of Medicine and Dentistry, University of Western Ontario, London, ON, Canada.,Robarts Research Institute, University of Western Ontario, London, ON, Canada
| | - Fabio Salerno
- Kidney Clinical Research Unit, Lawson's Health Research Institute, Victoria Hospital, London, ON, Canada
| | - Ting-Yim Lee
- Robarts Research Institute, University of Western Ontario, London, ON, Canada
| | - Chris Ellis
- Department of Medical Biophysics, Schulich School of Medicine and Dentistry, University of Western Ontario, London, ON, Canada
| | - Daniel Goldman
- Department of Medical Biophysics, Schulich School of Medicine and Dentistry, University of Western Ontario, London, ON, Canada
| | - Christopher W McIntyre
- Kidney Clinical Research Unit, Lawson's Health Research Institute, Victoria Hospital, London, ON, Canada.,Department of Medical Biophysics, Schulich School of Medicine and Dentistry, University of Western Ontario, London, ON, Canada
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