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Wang X, Ghayesh MH, Li J, Kotousov A, Zander AC, Dawson JA, Psaltis PJ. Impact of Geometric Attributes on Abdominal Aortic Aneurysm Rupture Risk: An In Vivo FSI-Based Study. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2024; 40:e3884. [PMID: 39529502 DOI: 10.1002/cnm.3884] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2024] [Revised: 09/02/2024] [Accepted: 10/27/2024] [Indexed: 11/16/2024]
Abstract
Reported in this paper is a cutting-edge computational investigation into the influence of geometric characteristics on abdominal aortic aneurysm (AAA) rupture risk, beyond the traditional measure of maximum aneurysm diameter. A Comprehensive fluid-structure interaction (FSI) analysis was employed to assess risk factors in a range of patient scenarios, with the use of three-dimensional (3D) AAA models reconstructed from patient-specific aortic data and finite element method. Wall shear stress (WSS), and its derivatives such as time-averaged WSS (TAWSS), oscillatory shear index (OSI), relative residence time (RRT) and transverse WSS (transWSS) offer insights into the force dynamics acting on the AAA wall. Emphasis is placed on these WSS-based metrics and seven key geometric indices. By correlating these geometric discrepancies with biomechanical phenomena, this study highlights the novel and profound impact of geometry on risk prediction. This study demonstrates the necessity of a multidimensional assessment approach, future efforts should complement these findings with experimental validations for an applicable approach for clinical use.
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Affiliation(s)
- Xiaochen Wang
- School of Electrical and Mechanical Engineering, University of Adelaide, Adelaide, South Australia, Australia
| | - Mergen H Ghayesh
- School of Electrical and Mechanical Engineering, University of Adelaide, Adelaide, South Australia, Australia
| | - Jiawen Li
- School of Electrical and Mechanical Engineering, University of Adelaide, Adelaide, South Australia, Australia
| | - Andrei Kotousov
- School of Electrical and Mechanical Engineering, University of Adelaide, Adelaide, South Australia, Australia
| | - Anthony C Zander
- School of Electrical and Mechanical Engineering, University of Adelaide, Adelaide, South Australia, Australia
| | - Joseph A Dawson
- Department of Vascular & Endovascular Surgery, Royal Adelaide Hospital, Adelaide, South Australia, Australia
- Trauma Surgery Unit, Royal Adelaide Hospital, Adelaide, South Australia, Australia
- Adelaide Medical School, University of Adelaide, Adelaide, South Australia, Australia
| | - Peter J Psaltis
- Adelaide Medical School, University of Adelaide, Adelaide, South Australia, Australia
- Vascular Research Centre, Lifelong Health Theme, South Australian Health & Medical Research Institute (SAHMRI), Adelaide, South Australia, Australia
- Department of Cardiology, Central Adelaide Local Health Network, Adelaide, South Australia, Australia
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Vitásek R, Kubíček L, Schwarz D, Staffa R, Polzer S. Tension-based abdominal aortic aneurysm rupture risk assessment improves its accuracy and reduces the time of analysis. J Biomech 2024; 176:112328. [PMID: 39357344 DOI: 10.1016/j.jbiomech.2024.112328] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2024] [Revised: 07/22/2024] [Accepted: 09/12/2024] [Indexed: 10/04/2024]
Abstract
The biomechanical rupture risk assessment (BRRA) of abdominal aortic aneurysms (AAA) has higher sensitivity than maximal diameter criterion (DSEX) but its estimation is time-consuming and relies on an uncertain estimation of wall thickness. The aim of this study is to test tension-based criterion in the BRRA of AAA which removes the necessity of wall thickness measurement and should be faster. For that, we retrospectively analyzed 99 patients with intact AAA (25 females). Nineteen of them experienced a rupture later. BRRA was performed with wall tension PRRIT as a primary criterion. The ability of criterion to separate intact and ruptured AAAs at 1,3,6,9 and 12 months was estimated. Next, the receiver operating characteristics and the percentage of true negative cases for a different time to an outcome were estimated. Finally, the computational time was recorded. The results were compared to stress-based criterion PRRI and DSEX which served as a reference. All three criterions were able to discriminate between intact and ruptured AAAs up to 9 months (p < 0.05) while none of them could do for a 12 month prediction. PRRIT exhibited a significantly higher percentage of true negatives for 12 and 9 month predictions (45 % and 20 % respectively) and similar to other criteria for other prediction times. The mean computational time for estimating PRRIT was 19 h per patient compared to 67 h for PRRI. The tension- based BRRA of AAA leads to better outcomes for a 9 and 12 month prediction while the computational time drops by more than 70 % compared to PRRI.
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Affiliation(s)
- Radek Vitásek
- Department of Applied Mechanics, VSB-Technical University of Ostrava, Ostrava, Czech Republic.
| | - Luboš Kubíček
- 2nd Department of Surgery, St. Anne's University Hospital Brno and Faculty of Medicine, Masaryk University, Brno, Czech Republic.
| | - David Schwarz
- Department of Applied Mechanics, VSB-Technical University of Ostrava, Ostrava, Czech Republic.
| | - Robert Staffa
- 2nd Department of Surgery, St. Anne's University Hospital Brno and Faculty of Medicine, Masaryk University, Brno, Czech Republic.
| | - Stanislav Polzer
- Department of Applied Mechanics, VSB-Technical University of Ostrava, Ostrava, Czech Republic.
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Vander Linden K, Vanderveken E, Van Hoof L, Maes L, Fehervary H, Dreesen S, Hendrickx A, Verbrugghe P, Rega F, Meuris B, Famaey N. Stiffness matters: Improved failure risk assessment of ascending thoracic aortic aneurysms. JTCVS OPEN 2023; 16:66-83. [PMID: 38204617 PMCID: PMC10775041 DOI: 10.1016/j.xjon.2023.09.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/24/2023] [Revised: 09/07/2023] [Accepted: 09/11/2023] [Indexed: 01/12/2024]
Abstract
Objectives Rupture and dissection are feared complications of ascending thoracic aortic aneurysms caused by mechanical failure of the wall. The current method of using the aortic diameter to predict the risk of wall failure and to determine the need for surgical resection lacks accuracy. Therefore, this study aims to identify reliable and clinically measurable predictors for aneurysm rupture or dissection by performing a personalized failure risk analysis, including clinical, geometrical, histologic, and mechanical data. Methods The study cohort consisted of 33 patients diagnosed with ascending aortic aneurysms without genetic syndromes. Uniaxial tensile tests until failure were performed to determine the wall strength. Material parameters were fitted against ex vivo planar biaxial data and in vivo pressure-diameter relationships at diastole and systole, which were derived from multiphasic computed tomography (CT) scans. Using the resulting material properties and in vivo data, the maximal in vivo stress at systole was calculated, assuming a thin-walled axisymmetric geometry. The retrospective failure risk was calculated by comparing the peak wall stress at suprasystolic pressure with the wall strength. Results The distensibility coefficient, reflecting aortic compliance and derived from blood pressure measurements and multiphasic CT scans, outperformed predictors solely based on geometrical features in assessing the risk of aneurysm failure. Conclusions In a clinical setting, multiphasic CT scans followed by the calculation of the distensibility coefficient are of added benefit in patient-specific, clinical decision-making. The distensibility derived from the aneurysm volume change has the best predictive power, as it also takes the axial stretch into account.
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Affiliation(s)
| | - Emma Vanderveken
- Department of Cardiovascular Sciences, KU Leuven, Leuven, Belgium
| | - Lucas Van Hoof
- Department of Cardiac Surgery, University Hospitals Leuven, Leuven, Belgium
| | - Lauranne Maes
- Department of Mechanical Engineering, KU Leuven, Leuven, Belgium
| | - Heleen Fehervary
- Department of Mechanical Engineering, KU Leuven, Leuven, Belgium
- FIBEr, KU Leuven Core Facility for Biomechanical Experimentation, Leuven, Belgium
| | - Silke Dreesen
- Department of Mechanical Engineering, KU Leuven, Leuven, Belgium
| | - Amber Hendrickx
- Department of Cardiovascular Sciences, KU Leuven, Leuven, Belgium
| | - Peter Verbrugghe
- Department of Cardiac Surgery, University Hospitals Leuven, Leuven, Belgium
| | - Filip Rega
- Department of Cardiac Surgery, University Hospitals Leuven, Leuven, Belgium
| | - Bart Meuris
- Department of Cardiac Surgery, University Hospitals Leuven, Leuven, Belgium
| | - Nele Famaey
- Department of Mechanical Engineering, KU Leuven, Leuven, Belgium
- FIBEr, KU Leuven Core Facility for Biomechanical Experimentation, Leuven, Belgium
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Gasser TC, Miller C, Polzer S, Roy J. A quarter of a century biomechanical rupture risk assessment of abdominal aortic aneurysms. Achievements, clinical relevance, and ongoing developments. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2023; 39:e3587. [PMID: 35347895 DOI: 10.1002/cnm.3587] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2021] [Revised: 01/28/2022] [Accepted: 03/03/2022] [Indexed: 05/12/2023]
Abstract
Abdominal aortic aneurysm (AAA) disease, the local enlargement of the infrarenal aorta, is a serious condition that causes many deaths, especially in men exceeding 65 years of age. Over the past quarter of a century, computational biomechanical models have been developed towards the assessment of AAA risk of rupture, technology that is now on the verge of being integrated within the clinical decision-making process. The modeling of AAA requires a holistic understanding of the clinical problem, in order to set appropriate modeling assumptions and to draw sound conclusions from the simulation results. In this article we summarize and critically discuss the proposed modeling approaches and report the outcome of clinical validation studies for a number of biomechanics-based rupture risk indices. Whilst most of the aspects concerning computational mechanics have already been settled, it is the exploration of the failure properties of the AAA wall and the acquisition of robust input data for simulations that has the greatest potential for the further improvement of this technology.
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Affiliation(s)
- T Christian Gasser
- Department of Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden
- Faculty of Health Sciences, University of Southern Denmark, Odense, Denmark
| | - Christopher Miller
- Department of Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden
| | - Stanislav Polzer
- Department of Applied Mechanics, VSB-Technical University of Ostrava, Ostrava-Poruba, Czech Republic
| | - Joy Roy
- Department of Molecular Medicine and Surgery, Karolinska Institutet, Stockholm, Sweden
- Department of Vascular Surgery, Karolinska University Hospital, Stockholm, Sweden
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Dynamic Loading-A New Marker for Abdominal Aneurysm Growth? MEDICINA (KAUNAS, LITHUANIA) 2023; 59:medicina59020404. [PMID: 36837605 PMCID: PMC9967562 DOI: 10.3390/medicina59020404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Revised: 02/07/2023] [Accepted: 02/16/2023] [Indexed: 02/22/2023]
Abstract
The growing possibilities of non-invasive heart rate and blood pressure measurement with mobile devices allow vital data to be continuously collected and used to assess patients' health status. When it comes to the risk assessment of abdominal aortic aneurysms (AAA), the continuous tracking of blood pressure and heart rate could enable a more patient-specific approach. The use of a load function and an energy function, with continuous blood pressure, heart rate, and aneurysm stiffness as input parameters, can quantify dynamic load on AAA. We hypothesise that these load functions correlate with aneurysm growth and outline a possible study procedure in which the hypothesis could be tested for validity. Subsequently, uncertainty quantification of input quantities and derived quantities is performed.
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Kubicek L, Vitasek R, Schwarz D, Staffa R, Strakos P, Polzer S. Biomechanical Rupture Risk Assessment in Management of Patients with Abdominal Aortic Aneurysm in COVID-19 Pandemic. Diagnostics (Basel) 2022; 13:132. [PMID: 36611424 PMCID: PMC9818825 DOI: 10.3390/diagnostics13010132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2022] [Revised: 10/18/2022] [Accepted: 12/27/2022] [Indexed: 01/04/2023] Open
Abstract
Background: The acute phase of the COVID-19 pandemic requires a redefinition of healthcare system to increase the number of available intensive care units for COVID-19 patients. This leads to the postponement of elective surgeries including the treatment of abdominal aortic aneurysm (AAA). The probabilistic rupture risk index (PRRI) recently showed its advantage over the diameter criterion in AAA rupture risk assessment. Its major improvement is in increased specificity and yet has the same sensitivity as the maximal diameter criterion. The objective of this study was to test the clinical applicability of the PRRI method in a quasi-prospective patient cohort study. Methods: Nineteen patients (fourteen males, five females) with intact AAA who were postponed due to COVID-19 pandemic were included in this study. The PRRI was calculated at the baseline via finite element method models. If a case was diagnosed as high risk (PRRI > 3%), the patient was offered priority in AAA intervention. Cases were followed until 10 September 2021 and a number of false positive and false negative cases were recorded. Results: Each case was assessed within 3 days. Priority in intervention was offered to two patients with high PRRI. There were four false positive cases and no false negative cases classified by PRRI. In three cases, the follow-up was very short to reach any conclusion. Conclusions: Integrating PRRI into clinical workflow is possible. Longitudinal validation of PRRI did not fail and may significantly decrease the false positive rate in AAA treatment.
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Affiliation(s)
- Lubos Kubicek
- 2nd Department of Surgery, St. Anne’s University Hospital Brno and Faculty of Medicine, Masaryk University, 612 00 Brno, Czech Republic
| | - Radek Vitasek
- Department of Applied Mechanics, VSB-Technical University of Ostrava, 708 00 Ostrava, Czech Republic
| | - David Schwarz
- Department of Applied Mechanics, VSB-Technical University of Ostrava, 708 00 Ostrava, Czech Republic
| | - Robert Staffa
- 2nd Department of Surgery, St. Anne’s University Hospital Brno and Faculty of Medicine, Masaryk University, 612 00 Brno, Czech Republic
| | - Petr Strakos
- IT4Innovations, VSB—Technical University of Ostrava, 708 00 Ostrava, Czech Republic
| | - Stanislav Polzer
- Department of Applied Mechanics, VSB-Technical University of Ostrava, 708 00 Ostrava, Czech Republic
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An improved parameter fitting approach of a planar biaxial test including the experimental prestretch. J Mech Behav Biomed Mater 2022; 134:105389. [DOI: 10.1016/j.jmbbm.2022.105389] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Revised: 07/11/2022] [Accepted: 07/17/2022] [Indexed: 11/21/2022]
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Philip NT, Patnaik BSV, Sudhir BJ. Hemodynamic simulation of abdominal aortic aneurysm on idealised models: Investigation of stress parameters during disease progression. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2022; 213:106508. [PMID: 34800807 DOI: 10.1016/j.cmpb.2021.106508] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Accepted: 10/25/2021] [Indexed: 06/13/2023]
Abstract
BACKGROUND AND OBJECTIVE Analysis and prediction of rupture risk of abdominal aortic aneurysms (AAA) facilitates planning for surgical interventions and assessment of plausible treatment modalities. Present approach of using maximum diameter criterion, is giving way to hemodynamic and bio-mechanical based predictors in conjunction with Computational fluid dynamic (CFD) simulations. Detailed studies on hemodynamic and bio-mechanical parameters at the stage of maximum growth/rupture is of practical importance to the clinical community. However, understanding the changes in these parameters at different stages of growth, will be useful for clinicians, in planning routine monitoring to reduce the risk of sudden rupture. This is particularly useful in medical resource starved nations. Present study investigates the hemodynamic and bio-mechanical changes occurring during the growth stages of aortic aneurysms using fluid structure interaction (FSI) studies. METHOD Six idealized fusiform aneurysm models spanning high (shorter) and low (longer) values of the shape index (DHr), have been analysed at three different stages of growth viz, a Dmax of 3.5cm, 4.25cm, 5cm. Pulsatile Newtonian blood flow, passing through an elastic arterial vessel wall with uniform thickness is assumed. Two-way coupled fluid structure interaction have been employed for the numerical simulation of blood flow dynamics and arterial wall mechanics. RESULTS Wall shear stress (WSS) parameters and vonmises stress indicators, co-relating rupture and thrombus formation, have been extracted and reported, at each growth stage. When the aneurysm progresses in diameter, the areas recording abnormally low TAWSS, as well as areas of high/low OSI were found to increase at different rates for shorter and longer aneurysms. Moreover, drastic increase in the maximum wall stresses (MWS) and wall displacement were observed as the aneurysm approached the critical diameter. CONCLUSION Hemodynamic predictors were found to be highly dependent on the shape index (DHr), when the aneurysm was small, whereas significant influence of DHr on the wall stresses happens, as the aneurysm approaches the critical diameter. Inconsistent variation of these indicators exhibited by shorter aneurysms (high DHr) at different growth stages, demands routine monitoring (using scans), of such aneurysms, to prevent unexpected rupture.
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Affiliation(s)
- Nimmy Thankom Philip
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, 600036, India
| | - B S V Patnaik
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, 600036, India
| | - B J Sudhir
- Sree Chitra Tirunal Institute for Medical Sciences and Technology, Trivandrum, 695011, Kerala.
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Galloy AE, Raghuram A, Nino MA, Varon Miller A, Sabotin R, Osorno-Cruz C, Samaniego EA, Raghavan SML, Hasan D. Analysis of Cerebral Aneurysm Wall Tension and Enhancement Using Finite Element Analysis and High-Resolution Vessel Wall Imaging. Front Neurol 2021; 12:764063. [PMID: 34956050 PMCID: PMC8702555 DOI: 10.3389/fneur.2021.764063] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 11/12/2021] [Indexed: 12/02/2022] Open
Abstract
Biomechanical computational simulation of intracranial aneurysms has become a promising method for predicting features of instability leading to aneurysm growth and rupture. Hemodynamic analysis of aneurysm behavior has helped investigate the complex relationship between features of aneurysm shape, morphology, flow patterns, and the proliferation or degradation of the aneurysm wall. Finite element analysis paired with high-resolution vessel wall imaging can provide more insight into how exactly aneurysm morphology relates to wall behavior, and whether wall enhancement can describe this phenomenon. In a retrospective analysis of 23 unruptured aneurysms, finite element analysis was conducted using an isotropic, homogenous third order polynomial material model. Aneurysm wall enhancement was quantified on 2D multiplanar views, with 14 aneurysms classified as enhancing (CRstalk≥0.6) and nine classified as non-enhancing. Enhancing aneurysms had a significantly higher 95th percentile wall tension (μ = 0.77 N/cm) compared to non-enhancing aneurysms (μ = 0.42 N/cm, p < 0.001). Wall enhancement remained a significant predictor of wall tension while accounting for the effects of aneurysm size (p = 0.046). In a qualitative comparison, low wall tension areas concentrated around aneurysm blebs. Aneurysms with irregular morphologies may show increased areas of low wall tension. The biological implications of finite element analysis in intracranial aneurysms are still unclear but may provide further insights into the complex process of bleb formation and aneurysm rupture.
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Affiliation(s)
- Adam E Galloy
- Roy J. Carver Department of Biomedical Engineering, University of Iowa, Iowa City, IA, United States
| | - Ashrita Raghuram
- Department of Neurology, The University of Iowa Hospitals and Clinics, University of Iowa, Iowa City, IA, United States
| | - Marco A Nino
- Roy J. Carver Department of Biomedical Engineering, University of Iowa, Iowa City, IA, United States
| | - Alberto Varon Miller
- Department of Neurology, The University of Iowa Hospitals and Clinics, University of Iowa, Iowa City, IA, United States
| | - Ryan Sabotin
- Department of Neurology, The University of Iowa Hospitals and Clinics, University of Iowa, Iowa City, IA, United States
| | - Carlos Osorno-Cruz
- Department of Neurosurgery, The University of Iowa Hospitals and Clinics, University of Iowa, Iowa City, IA, United States
| | - Edgar A Samaniego
- Department of Neurology, The University of Iowa Hospitals and Clinics, University of Iowa, Iowa City, IA, United States.,Department of Neurosurgery, The University of Iowa Hospitals and Clinics, University of Iowa, Iowa City, IA, United States.,Department of Radiology, The University of Iowa Hospitals and Clinics, University of Iowa, Iowa City, IA, United States
| | - Suresh M L Raghavan
- Roy J. Carver Department of Biomedical Engineering, University of Iowa, Iowa City, IA, United States
| | - David Hasan
- Department of Neurosurgery, The University of Iowa Hospitals and Clinics, University of Iowa, Iowa City, IA, United States
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Avril S, Gee MW, Hemmler A, Rugonyi S. Patient-specific computational modeling of endovascular aneurysm repair: State of the art and future directions. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3529. [PMID: 34490740 DOI: 10.1002/cnm.3529] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2021] [Accepted: 08/30/2021] [Indexed: 06/13/2023]
Abstract
Endovascular aortic repair (EVAR) has become the preferred intervention option for aortic aneurysms and dissections. This is because EVAR is much less invasive than the alternative open surgery repair. While in-hospital mortality rates are smaller for EVAR than open repair (1%-2% vs. 3%-5%), the early benefits of EVAR are lost after 3 years due to larger rates of complications in the EVAR group. Clinicians follow instructions for use (IFU) when possible, but are left with personal experience on how to best proceed and what choices to make with respect to stent-graft (SG) model choice, sizing, procedural options, and their implications on long-term outcomes. Computational modeling of SG deployment in EVAR and tissue remodeling after intervention offers an alternative way of testing SG designs in silico, in a personalized way before intervention, to ultimately select the strategies leading to better outcomes. Further, computational modeling can be used in the optimal design of SGs in cases of complex geometries. In this review, we address some of the difficulties and successes associated with computational modeling of EVAR procedures. There is still work to be done in all areas of EVAR in silico modeling, including model validation, before models can be applied in the clinic, but much progress has already been made. Critical to clinical implementation are current efforts focusing on developing fast algorithms that can achieve (near) real-time solutions, as well as ways of dealing with inherent uncertainties related to patient aortic wall degradation on an individualized basis. We are optimistic that EVAR modeling in the clinic will soon become a reality to help clinicians optimize EVAR interventions and ultimately reduce EVAR-associated complications.
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Affiliation(s)
- Stéphane Avril
- Mines Saint-Étienne, Univ Lyon, Univ Jean Monnet, INSERM, Saint-Étienne, France
| | - Michael W Gee
- Mechanics & High Performance Computing Group, Department of Mechanical Engineering, Technical University of Munich, Garching, Germany
| | - André Hemmler
- Mechanics & High Performance Computing Group, Department of Mechanical Engineering, Technical University of Munich, Garching, Germany
| | - Sandra Rugonyi
- Biomedical Engineering Department, Oregon Health & Science University, Portland, Oregon, USA
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