Mathematical Modeling of Aortic Diseases

A special issue of Bioengineering (ISSN 2306-5354).

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 9682

Special Issue Editors


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Guest Editor
Department of Biomedical Engineering, National University of Singapore, Singapore 117583, Singapore
Interests: computational and experimental biofluid mechanics; heart valve engineering; artificial liver device; In vitro drug screening platform

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Guest Editor
Department of Biomedical Engineering and Imaging Sciences, King’s College London, London, UK
Interests: computational fluid dynamics; computational and experimental biofluid mechanics; reduced-order modeling; uncertainty quantification; particle tracking in biological systems

Special Issue Information

Dear Colleagues,

Recent advances in computational and experimental software and hardware provided researchers with valuable approaches to investigate complex aortic pathological conditions. The mathematical modeling of aortic diseases could fill the existing gap in our understanding of these diseases, improve surgical approaches, and predict complications.

This Special Issue of Bioengineering titled “Mathematical Modeling of Aortic Diseases” will focus on original research and comprehensive review articles addressing the advanced mathematical modeling and analysis of the experimental investigation of complex cases of aortic diseases. Topics of interest for this Special Issue include, but are not limited to:

  • Blood flow modeling in the pathological aorta;
  • Novel multifidelity approaches to model blood flow in the aorta and large arteries;
  • Blood–vessel interaction;
  • Uncertainty quantification in image-based patient-specific simulations;
  • Aortic valve modeling;
  • Remodeling of the aorta;
  • Novel mathematical analysis of advanced imaging techniques in the aorta;
  • Blood coagulation modeling in the aorta and large arteries;
  • Simulation of various aortic surgical procedures.

Dr. Hwa Liang Leo
Dr. Hamed Keramati
Guest Editors

Manuscript Submission Information

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Keywords

  • aortic diseases
  • remodeling
  • blood–vessel interaction
  • patient-specific modeling

Published Papers (5 papers)

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Research

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14 pages, 5126 KiB  
Article
The Impact of Left Ventricular Performance and Afterload on the Evaluation of Aortic Valve Stenosis: A 1D Mathematical Modeling Approach
by Cemre Çelikbudak Orhon, Nikolaos Stergiopulos, Stéphane Noble, Georgios Giannakopoulos, Hajo Müller and Dionysios Adamopoulos
Bioengineering 2023, 10(4), 425; https://doi.org/10.3390/bioengineering10040425 - 28 Mar 2023
Viewed by 1563
Abstract
The transaortic valvular pressure gradient (TPG) plays a central role in decision-making for patients suffering from severe aortic stenosis. However, the flow-dependence nature of the TPG makes the diagnosis of aortic stenosis challenging since the markers of cardiac performance and afterload present high [...] Read more.
The transaortic valvular pressure gradient (TPG) plays a central role in decision-making for patients suffering from severe aortic stenosis. However, the flow-dependence nature of the TPG makes the diagnosis of aortic stenosis challenging since the markers of cardiac performance and afterload present high physiological interdependence and thus, isolated effects cannot be measured directly in vivo. We used a validated 1D mathematical model of the cardiovascular system, coupled with a model of aortic stenosis, to assess and quantify the independent effect of the main left ventricular performance parameters (end-systolic (Ees) and end-diastolic (Eed) elastance) and principal afterload indices (total vascular resistance (TVR) and total arterial compliance (TAC)) on the TPG for different levels of aortic stenosis. In patients with critical aortic stenosis (aortic valve area (AVA) ≤ 0.6 cm2), a 10% increase of Eed from the baseline value was associated with the most important effect on the TPG (−5.6 ± 0.5 mmHg, p < 0.001), followed by a similar increase of Ees (3.4 ± 0.1 mmHg, p < 0.001), in TAC (1.3 ±0.2 mmHg, p < 0.001) and TVR (−0.7 ± 0.04 mmHg, p < 0.001). The interdependence of the TPG left ventricular performance and afterload indices become stronger with increased aortic stenosis severity. Disregarding their effects may lead to an underestimation of stenosis severity and a potential delay in therapeutic intervention. Therefore, a comprehensive evaluation of left ventricular function and afterload should be performed, especially in cases of diagnostic challenge, since it may offer the pathophysiological mechanism that explains the mismatch between aortic severity and the TPG. Full article
(This article belongs to the Special Issue Mathematical Modeling of Aortic Diseases)
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26 pages, 7948 KiB  
Article
CFD Computation of Flow Fractional Reserve (FFR) in Coronary Artery Trees Using a Novel Physiologically Based Algorithm (PBA) Under 3D Steady and Pulsatile Flow Conditions
by Nursultan Alzhanov, Eddie Y. K. Ng, Xiaohui Su and Yong Zhao
Bioengineering 2023, 10(3), 309; https://doi.org/10.3390/bioengineering10030309 - 28 Feb 2023
Cited by 1 | Viewed by 1661
Abstract
A novel physiologically based algorithm (PBA) for the computation of fractional flow reserve (FFR) in coronary artery trees (CATs) using computational fluid dynamics (CFD) is proposed and developed. The PBA was based on an extension of Murray’s law and additional inlet conditions prescribed [...] Read more.
A novel physiologically based algorithm (PBA) for the computation of fractional flow reserve (FFR) in coronary artery trees (CATs) using computational fluid dynamics (CFD) is proposed and developed. The PBA was based on an extension of Murray’s law and additional inlet conditions prescribed iteratively and was implemented in OpenFOAM v1912 for testing and validation. 3D models of CATs were created using CT scans and computational meshes, and the results were compared to invasive coronary angiographic (ICA) data to validate the accuracy and effectiveness of the PBA. The discrepancy between the calculated and experimental FFR was within 2.33–5.26% in the steady-state and transient simulations, respectively, when convergence was reached. The PBA was a reliable and physiologically sound technique compared to a current lumped parameter model (LPM), which is based on empirical scaling correlations and requires nonlinear iterative computing for convergence. The accuracy of the PBA method was further confirmed using an FDA nozzle, which demonstrated good alignment with the CFD-validated values. Full article
(This article belongs to the Special Issue Mathematical Modeling of Aortic Diseases)
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19 pages, 37727 KiB  
Article
Mild Paravalvular Leak May Pose an Increased Thrombogenic Risk in Transcatheter Aortic Valve Replacement (TAVR) Patients-Insights from Patient Specific In Vitro and In Silico Studies
by Brandon J. Kovarovic, Oren M. Rotman, Puja B. Parikh, Marvin J. Slepian and Danny Bluestein
Bioengineering 2023, 10(2), 188; https://doi.org/10.3390/bioengineering10020188 - 1 Feb 2023
Cited by 4 | Viewed by 1825
Abstract
In recent years, the treatment of aortic stenosis with TAVR has rapidly expanded to younger and lower-risk patients. However, persistent thrombotic events such as stroke and valve thrombosis expose recipients to severe clinical complications that hamper TAVR’s rapid advance. We presented a novel [...] Read more.
In recent years, the treatment of aortic stenosis with TAVR has rapidly expanded to younger and lower-risk patients. However, persistent thrombotic events such as stroke and valve thrombosis expose recipients to severe clinical complications that hamper TAVR’s rapid advance. We presented a novel methodology for establishing a link between commonly acceptable mild paravalvular leak (PVL) levels through the device and increased thrombogenic risk. It utilizes in vitro patient-specific TAVR 3D-printed replicas evaluated for hydrodynamic performance. High-resolution µCT scans are used to reconstruct in silico FSI models of these replicas, in which multiple platelet trajectories are studied through the PVL channels to quantify thrombogenicity, showing that those are highly dependent on patient-specific flow conditions within the PVL channels. It demonstrates that platelets have the potential to enter the PVL channels multiple times over successive cardiac cycles, increasing the thrombogenic risk. This cannot be reliably approximated by standard hemodynamic parameters. It highlights the shortcomings of subjectively ranked PVL commonly used in clinical practice by indicating an increased thrombogenic risk in patient cases otherwise classified as mild PVL. It reiterates the need for more rigorous clinical evaluation for properly diagnosing thrombogenic risk in TAVR patients. Full article
(This article belongs to the Special Issue Mathematical Modeling of Aortic Diseases)
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Review

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23 pages, 3460 KiB  
Review
Evaluating the Haemodynamic Performance of Endografts for Complex Aortic Arch Repair
by Sampad Sengupta, Yu Zhu, Mohamad Hamady and Xiao Yun Xu
Bioengineering 2022, 9(10), 573; https://doi.org/10.3390/bioengineering9100573 - 18 Oct 2022
Cited by 6 | Viewed by 2486
Abstract
Thoracic endovascular aortic repair (TEVAR) of aortic aneurysms and dissections involving the arch has evolved over the last two decades. Compared to conventional surgical methods, endovascular repair offers a less invasive treatment option with lower risk and faster recovery. Endografts used in TEVAR [...] Read more.
Thoracic endovascular aortic repair (TEVAR) of aortic aneurysms and dissections involving the arch has evolved over the last two decades. Compared to conventional surgical methods, endovascular repair offers a less invasive treatment option with lower risk and faster recovery. Endografts used in TEVAR vary in design depending on the procedure and application. Novel endografts (e.g., branched stent-graft) were developed to ensure perfusion of blood to the supra-aortic vessels, but their haemodynamic performance and long-term durability have not been adequately studied. This review focuses on the use of computational modelling to study haemodynamics in commercially available endografts designed for complex aortic arch repair. First, we summarise the currently adopted workflow for computational fluid dynamics (CFD) modelling, including geometry reconstruction, boundary conditions, flow models, and haemodynamic metrics of interest. This is followed by a review of recently (2010-present) published CFD studies on complex aortic arch repair, using both idealized and patient-specific models. Finally, we introduce some of the promising techniques that can be potentially applied to predict post-operative outcomes. Full article
(This article belongs to the Special Issue Mathematical Modeling of Aortic Diseases)
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Other

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12 pages, 3693 KiB  
Brief Report
Feasibility of Wave Intensity Analysis from 4D Cardiovascular Magnetic Resonance Imaging Data
by Froso Sophocleous, Kiril Delchev, Estefania De Garate, Mark C. K. Hamilton, Massimo Caputo, Chiara Bucciarelli-Ducci and Giovanni Biglino
Bioengineering 2023, 10(6), 662; https://doi.org/10.3390/bioengineering10060662 - 31 May 2023
Viewed by 1262
Abstract
Congenital heart defects (CHD) introduce haemodynamic changes; e.g., bicuspid aortic valve (BAV) presents a turbulent helical flow, which activates aortic pathological processes. Flow quantification is crucial for diagnostics and to plan corrective strategies. Multiple imaging modalities exist, with phase contrast magnetic resonance imaging [...] Read more.
Congenital heart defects (CHD) introduce haemodynamic changes; e.g., bicuspid aortic valve (BAV) presents a turbulent helical flow, which activates aortic pathological processes. Flow quantification is crucial for diagnostics and to plan corrective strategies. Multiple imaging modalities exist, with phase contrast magnetic resonance imaging (PC-MRI) being the current gold standard; however, multiple predetermined site measurements may be required, while 4D MRI allows for measurements of area (A) and velocity (U) in all spatial dimensions, acquiring a single volume and enabling a retrospective analysis at multiple locations. We assessed the feasibility of gathering hemodynamic insight into aortic hemodynamics by means of wave intensity analysis (WIA) derived from 4D MRI. Data were collected in n = 12 BAV patients and n = 7 healthy controls. Following data acquisition, WIA was successfully derived at three planes (ascending, thoracic and descending aorta) in all cases. The values of wave speed were physiological and, while the small sample limited any clinical interpretation of the results, the study shows the possibility of studying wave travel and wave reflection based on 4D MRI. Below, we demonstrate for the first time the feasibility of deriving wave intensity analysis from 4D flow data and open the door to research applications in different cardiovascular scenarios. Full article
(This article belongs to the Special Issue Mathematical Modeling of Aortic Diseases)
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