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Nightingale M, Scott MB, Sigaeva T, Guzzardi D, Garcia J, Malaisrie SC, McCarthy P, Markl M, Fedak PWM, Di Martino ES, Barker AJ. Magnetic resonance imaging-based hemodynamic wall shear stress alters aortic wall tissue biomechanics in bicuspid aortic valve patients. J Thorac Cardiovasc Surg 2024; 168:465-476.e5. [PMID: 36797175 PMCID: PMC10338641 DOI: 10.1016/j.jtcvs.2022.12.021] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/10/2022] [Revised: 12/06/2022] [Accepted: 12/22/2022] [Indexed: 01/15/2023]
Abstract
OBJECTIVE In this study we aimed to conclusively determine whether altered aortic biomechanics are associated with wall shear stress (WSS) independent of region of tissue collection. Elevated WSS in the ascending aorta of patients with bicuspid aortic valve has been shown to contribute to local maladaptive aortic remodeling and might alter biomechanics. METHODS Preoperative 4-dimensional flow magnetic resonance imaging was performed on 22 patients who underwent prophylactic aortic root and/or ascending aorta replacement. Localized elevated WSS was identified in patients using age-matched healthy atlases (n = 60 controls). Tissue samples (n = 78) were collected and categorized according to WSS (elevated vs normal) and region. Samples were subjected to planar biaxial testing. To fully quantify the nonlinear biomechanical response, the tangential modulus (local stiffness) at a low-stretch (LTM) and high-stretch (HTM) linear region and the onset (TZo) and end stress of the nonlinear transition zone were measured. A linear mixed effect models was implemented to determine statistical relationships. RESULTS A higher LTM in the circumferential and axial direction was associated with elevated WSS (P = .007 and P = .018 respectively) independent of collection region. Circumferential TZo and HTM were higher with elevated WSS (P = .024 and P = .003); whereas the collection region was associated with variations in axial TZo (P = .013), circumferential HTM (P = .015), and axial HTM (P = .001). CONCLUSIONS This study shows strong evidence that biomechanical changes in the aorta are strongly associated with hemodynamics, and not region of tissue collection for bicuspid valve aortopathy patients. Elevated WSS is associated with tissue behavior at low stretch ranges (ie, LTM and TZo).
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Affiliation(s)
- Miriam Nightingale
- Department of Biomedical Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, Canada; Libin Cardiovascular Institute of Alberta, University of Calgary, Calgary, Alberta, Canada
| | | | - Taisiya Sigaeva
- Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario, Canada
| | - David Guzzardi
- Libin Cardiovascular Institute of Alberta, University of Calgary, Calgary, Alberta, Canada; Department of Cardiac Sciences, Cummings School of Medicine, University of Calgary, Calgary, Alberta, Canada
| | - Julio Garcia
- Libin Cardiovascular Institute of Alberta, University of Calgary, Calgary, Alberta, Canada; Department of Cardiac Sciences, Cummings School of Medicine, University of Calgary, Calgary, Alberta, Canada; Department of Radiology, Cummings School of Medicine, University of Calgary, Calgary, Alberta, Canada
| | - S Chris Malaisrie
- Division of Surgery-Cardiac Surgery, Northwestern University, Evanston, Ill
| | - Patrick McCarthy
- Division of Surgery-Cardiac Surgery, Northwestern University, Evanston, Ill
| | - Michael Markl
- Department of Radiology, Northwestern University, Evanston, Ill; Department of Bioengineering, Northwestern University, Evanston, Ill
| | - Paul W M Fedak
- Libin Cardiovascular Institute of Alberta, University of Calgary, Calgary, Alberta, Canada; Department of Cardiac Sciences, Cummings School of Medicine, University of Calgary, Calgary, Alberta, Canada
| | - Elena S Di Martino
- Department of Biomedical Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, Canada; Libin Cardiovascular Institute of Alberta, University of Calgary, Calgary, Alberta, Canada
| | - Alex J Barker
- Department of Radiology, Northwestern University, Evanston, Ill; Department of Radiology, University of Colorado Anschutz Medical Campus, Aurora, Colo.
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Vianna E, Kramer B, Tarraf S, Gillespie C, Colbrunn R, Bellini C, Roselli EE. Aortic diameter is a poor predictor of aortic tissue failure metrics in patients with ascending aneurysms. J Thorac Cardiovasc Surg 2024; 167:2049-2059.e2. [PMID: 36528437 DOI: 10.1016/j.jtcvs.2022.10.021] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Revised: 09/19/2022] [Accepted: 10/13/2022] [Indexed: 11/09/2022]
Abstract
OBJECTIVES There is growing consensus that aortic diameter is a flawed predictor of aortic dissection risk. We hypothesized that aortic tissue metrics would be better predicted by clinical metrics other than aortic diameter. Our objectives were to (1) characterize circumferential aortic failure stress and stretch as a result of aortic size and patient demographics, and (2) identify the influence of bicuspid aortic valve on failure metrics. METHODS From February 2018 to January 2021, 136 aortic tissue samples were obtained from 86 adults undergoing elective ascending aorta repair. Uniaxial biomechanical testing to failure, defined as a full-thickness central tear, was performed to obtain tissue failure stress and failure stretch and compared with clinical data and preoperative computed tomography imaging. The relationships among aortic diameter, patient demographics, and failure metrics were assessed using random forest regression models. RESULTS Median failure stress was 1.46 (1.02-1.94) megapascals, and failure stretch was 1.36 (1.27-1.54). Regression models correlated moderately with failure stress (R2 = 0.557) and highly with failure stretch (R2 = 0.806). Failure stress decreased with increasing age, lower body mass index, thicker tissue, and tricuspid aortic valves, whereas failure stretch was most highly correlated with age. Aortic area-to-height index outperformed aortic diameter in all models. CONCLUSIONS Aneurysmal ascending aortic tissue failure metrics correlated with available clinical metrics. Greater tissue thickness, older age, and tricuspid aortic valve morphology outperformed aortic diameter, warranting further investigation into the role of a patient-specific multifactorial dissection risk assessment over aortic diameter as a sole marker of aortic tissue integrity.
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Affiliation(s)
- Emily Vianna
- Department of Thoracic and Cardiovascular Surgery, Aorta Center, Heart, Vascular & Thoracic Institute, Cleveland Clinic, Cleveland, Ohio
| | - Benjamin Kramer
- Department of Thoracic and Cardiovascular Surgery, Aorta Center, Heart, Vascular & Thoracic Institute, Cleveland Clinic, Cleveland, Ohio
| | - Samar Tarraf
- Department of Bioengineering, College of Engineering, Northeastern University, Boston, Mass
| | - Callan Gillespie
- Department of Biomedical Engineering, Lerner Research Institute, Cleveland Clinic, Cleveland, Ohio
| | - Robb Colbrunn
- Department of Biomedical Engineering, Lerner Research Institute, Cleveland Clinic, Cleveland, Ohio
| | - Chiara Bellini
- Department of Bioengineering, College of Engineering, Northeastern University, Boston, Mass
| | - Eric E Roselli
- Department of Thoracic and Cardiovascular Surgery, Aorta Center, Heart, Vascular & Thoracic Institute, Cleveland Clinic, Cleveland, Ohio; Department of Biomedical Engineering, Lerner Research Institute, Cleveland Clinic, Cleveland, Ohio.
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3
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Zhang Z, Xu X, Li T, Xin YF, Tong J. Region-specific delamination strength of ascending thoracic aortic aneurysm of elderly hypertensive patients with bicuspid and tricuspid aortic valves. Med Eng Phys 2024; 126:104157. [PMID: 38621853 DOI: 10.1016/j.medengphy.2024.104157] [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: 11/12/2023] [Revised: 02/18/2024] [Accepted: 03/16/2024] [Indexed: 04/17/2024]
Abstract
Both ageing and hypertension are clinical factors that may lead to a higher propensity for dissection or rupture of ascending thoracic aortic aneurysms (ATAAs). This study sought to investigate effect of valve morphology on regional delamination strength of ATAAs in the elderly hypertensive patients. Whole fresh ATAA samples were harvested from 23 hypertensive patients (age, 71 ± 8 years) who underwent elective aortic surgery. Peeling tests were performed to measure region-specific delamination strengths of the ATAAs, which were compared between patients with bicuspid aortic valve (BAV) and tricuspid aortic valve (TAV). The regional delamination strengths of the ATAAs were further correlated with patient ages and aortic diameters for BAV and TAV groups. In the anterior and right lateral regions, the longitudinal delamination strengths of the ATAAs were statistically significantly higher for BAV patients than TAV patients (33 ± 7 vs. 23 ± 8 mN/mm, p = 0.01; 30 ± 7 vs. 19 ± 9 mN/mm, p = 0.02). For both BAV and TAV patients, the left lateral region exhibited significantly higher delamination strengths in both directions than the right lateral region. Histology revealed that disruption of elastic fibers in the right lateral region of the ATAAs was more severe for the TAV patients than the BAV patients. A strong inverse correlation between longitudinal delamination strength and age was identified in the right lateral region of the ATAAs of the TAV patients. Results suggest that TAV-ATAAs are more vulnerable to aortic dissection than BAV-ATAAs for the elderly hypertensive patients. Regardless of valve morphotypes, the right lateral region may be a special quadrant which is more likely to initiate dissection when compared with other regions.
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Affiliation(s)
- Zhi Zhang
- Institute for Biomedical Engineering and Nano Science, Shanghai East Hospital, Tongji University School of Medicine, Shanghai, China
| | - Xiaojuan Xu
- Institute for Biomedical Engineering and Nano Science, Shanghai East Hospital, Tongji University School of Medicine, Shanghai, China; Department of Pathology and Pathophysiology, Tongji University School of Medicine, Shanghai, China
| | - Tieyan Li
- Department of Cardiovascular Surgery, Shanghai East Hospital, Tongji University School of Medicine, Shanghai, China
| | - Yuan-Feng Xin
- Department of Cardiovascular Surgery, Shanghai East Hospital, Tongji University School of Medicine, Shanghai, China.
| | - Jianhua Tong
- Institute for Biomedical Engineering and Nano Science, Shanghai East Hospital, Tongji University School of Medicine, Shanghai, China.
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4
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Totaro P, Morganti S, Auricchio F, Pelenghi S. Aortic wall thickness in dilated ascending aorta: Comparison between tricuspid and bicuspid aortic valve. Arch Cardiovasc Dis 2023; 116:498-505. [PMID: 37770332 DOI: 10.1016/j.acvd.2023.08.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/12/2023] [Revised: 07/31/2023] [Accepted: 08/01/2023] [Indexed: 09/30/2023]
Abstract
BACKGROUND Bicuspid aortic valve (BAV) is frequently associated with dilatation of the thoracic aorta. Peculiar anatomical, histological and mechanical changes of the aortic wall in BAV aortopathy have been hypothesized to suggest an increased risk of acute aortic complications in patients with BAV. AIM In this study we tried to clarify any differences in the adaptability of the aortic wall to the mechanism of dilatation between patients with BAV and those with TAV. METHODS In total, 354 samples were taken from 71 patients undergoing elective aortic surgery and divided into two groups: BAV group (n=16; 101 samples); and TAV group (n=55; 253 samples). Aortic wall thickness was measured with a dedicated caliper. The relationship between aortic wall thickness and aortic dilatation and demographic variables was evaluated cumulatively and comparatively (BAV versus TAV). In patients with more than three samples available, intrapatient variability was also studied. Finally, potential risk factors for severely reduced aortic wall thickness were also assessed. RESULTS Analysis of preoperative characteristics revealed significant differences in patient age (54±16years for BAV and 66±11years for TAV; P=0.0011), with no differences in variables related to aortic dilatation (including phenotype). Cumulative aortic wall thickness was significantly thinner in the anterior than in the posterior wall. In the comparative analysis, aortic wall thickness was significantly thinner in patients with BAV in both the anterior and posterior regions. Furthermore, in patients with BAV, dilatation>51mm was a significant predictor of severely reduced aortic wall thickness. CONCLUSIONS In our experience, patients with BAV aortopathy reached the cut-off for the surgical indication at an early age. Careful monitoring in patients with BAV is mandatory when aortic dilatation has reached 51mm, as it is related to significant anatomical changes.
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MESH Headings
- Humans
- Middle Aged
- Male
- Bicuspid Aortic Valve Disease/diagnostic imaging
- Bicuspid Aortic Valve Disease/surgery
- Bicuspid Aortic Valve Disease/physiopathology
- Female
- Aortic Valve/abnormalities
- Aortic Valve/diagnostic imaging
- Aortic Valve/surgery
- Aortic Valve/pathology
- Aortic Valve/physiopathology
- Aged
- Adult
- Risk Factors
- Dilatation, Pathologic
- Heart Valve Diseases/diagnostic imaging
- Heart Valve Diseases/surgery
- Heart Valve Diseases/physiopathology
- Heart Valve Diseases/pathology
- Heart Valve Diseases/complications
- Tricuspid Valve/diagnostic imaging
- Tricuspid Valve/physiopathology
- Tricuspid Valve/abnormalities
- Tricuspid Valve/pathology
- Tricuspid Valve/surgery
- Retrospective Studies
- Aortic Aneurysm, Thoracic/diagnostic imaging
- Aortic Aneurysm, Thoracic/pathology
- Aortic Aneurysm, Thoracic/physiopathology
- Aortic Aneurysm, Thoracic/surgery
- Aorta, Thoracic/diagnostic imaging
- Aorta, Thoracic/pathology
- Aorta, Thoracic/surgery
- Aorta, Thoracic/physiopathology
- Aorta, Thoracic/abnormalities
- Aortic Valve Disease/diagnostic imaging
- Aortic Valve Disease/surgery
- Aortic Valve Disease/physiopathology
- Aortic Valve Disease/pathology
- Aortic Aneurysm/diagnostic imaging
- Aortic Aneurysm/pathology
- Aortic Aneurysm/surgery
- Aortic Aneurysm/etiology
- Aortic Aneurysm/physiopathology
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Affiliation(s)
- Pasquale Totaro
- Division of Cardiac Surgery, IRCCS Foundation Hospital "San Matteo", Piazzale Golgi 1, 27100 Pavia, Italy.
| | - Simone Morganti
- Department of Electrical, Computer and Biomedical Engineering, University of Pavia, 27100 Pavia, Italy
| | - Ferdinando Auricchio
- Department of Civil Engineering and Architecture, University of Pavia, 27100 Pavia, Italy
| | - Stefano Pelenghi
- Division of Cardiac Surgery, IRCCS Foundation Hospital "San Matteo", Piazzale Golgi 1, 27100 Pavia, Italy
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Durbak E, Tarraf S, Gillespie C, Germano E, Cikach F, Blackstone E, Emerton K, Colbrunn R, Bellini C, Roselli EE. Ex vivo biaxial load testing analysis of aortic biomechanics demonstrates variation in elastic energy distribution across the aortic zone zero. J Thorac Cardiovasc Surg 2023; 166:701-712.e7. [PMID: 35219518 DOI: 10.1016/j.jtcvs.2021.09.071] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/06/2021] [Revised: 08/21/2021] [Accepted: 09/01/2021] [Indexed: 10/19/2022]
Abstract
OBJECTIVES We hypothesized that tissue characteristics vary significantly along zone zero, which may be reflected by regional differences in stored elastic energy. Our objectives were to (1) characterize the regional variation in stored elastic energy within tissues of the aortic zone zero and (2) identify the association between this variation and patient characteristics. METHODS From February 2018 to January 2021, 123 aortic tissue samples were obtained from the aortic root and proximal and distal ascending aortas of 65 adults undergoing elective ascending aorta replacement. Biaxial biomechanics testing was performed to obtain tissue elastic energy at the inflection point and compared with patient demographics and preoperative computed tomography imaging. Coefficient models were fit using B-spline to interrogate the relationship among elastic energy, region, and patient characteristics. RESULTS Mean elastic energy at inflection point was 24.3 ± 15.6 kJ/m3. Elastic energy increased significantly between the root and proximal, and root and distal ascending aorta and decreased with increasing age. Differences due to history of connective tissue disorder and bicuspid aortic valve were significant but diminished when controlled for other patient characteristics. Among covariates, age and region were found to be the most important predictors for elastic energy. CONCLUSIONS Aortic tissue biomechanical metrics varied across regions and with patient characteristics within the aortic zone zero. Assessment of endovascular outcomes in the ascending aorta must closely consider the region of deployment and variable tissue qualities along the length of the landing zone. Regional variation in tissue characteristics should be incorporated into existing patient-specific models of aortic mechanics.
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Affiliation(s)
- Emily Durbak
- Department of Thoracic and Cardiovascular Surgery, Aortic Center, Heart, Vascular & Thoracic Institute, Cleveland Clinic, Cleveland, Ohio
| | - Samar Tarraf
- Department of Bioengineering, College of Engineering, Northeastern University, Boston, Mass
| | - Callan Gillespie
- Department of Biomedical Engineering, BioRobotics and Mechanical Testing Core, Lerner Research Institute, Cleveland Clinic, Cleveland, Ohio
| | - Emidio Germano
- Department of Thoracic and Cardiovascular Surgery, Aortic Center, Heart, Vascular & Thoracic Institute, Cleveland Clinic, Cleveland, Ohio
| | - Frank Cikach
- Department of Thoracic and Cardiovascular Surgery, Aortic Center, Heart, Vascular & Thoracic Institute, Cleveland Clinic, Cleveland, Ohio
| | - Eugene Blackstone
- Department of Thoracic and Cardiovascular Surgery, Aortic Center, Heart, Vascular & Thoracic Institute, Cleveland Clinic, Cleveland, Ohio
| | - Kelly Emerton
- Department of Thoracic and Cardiovascular Surgery, Aortic Center, Heart, Vascular & Thoracic Institute, Cleveland Clinic, Cleveland, Ohio
| | - Robb Colbrunn
- Department of Biomedical Engineering, BioRobotics and Mechanical Testing Core, Lerner Research Institute, Cleveland Clinic, Cleveland, Ohio
| | - Chiara Bellini
- Department of Bioengineering, College of Engineering, Northeastern University, Boston, Mass
| | - Eric E Roselli
- Department of Thoracic and Cardiovascular Surgery, Aortic Center, Heart, Vascular & Thoracic Institute, Cleveland Clinic, Cleveland, Ohio.
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6
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Li Z, Pei M, Zhang J, Liu N, Wang J, Zou D. A study to characterize the mechanical properties and material constitution of adult descending thoracic aorta based on uniaxial tensile test and digital image correlation. Front Bioeng Biotechnol 2023; 11:1178199. [PMID: 37388776 PMCID: PMC10306407 DOI: 10.3389/fbioe.2023.1178199] [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: 03/02/2023] [Accepted: 06/05/2023] [Indexed: 07/01/2023] Open
Abstract
The mechanical properties and material constitution of the aorta are important in forensic science and clinical medicine. Existing studies on the material constitution of the aorta do not satisfy the practical requirements of forensic and clinical medicine, as the reported failure stress and failure strain values for human aortic materials have a high dispersion. In this study, descending thoracic aortas were obtained from 50 cadavers (dead within 24 h) free of thoracic aortic disease, aged from 27 to 86 years old, which were divided into six age groups. The descending thoracic aorta was divided into proximal and distal segments. A customized 4-mm cutter was used to punch a circumferential and an axial dog-bone-shaped specimen from each segment; the aortic ostia and calcification were avoided. Instron 8,874 and digital image correlation were used to perform a uniaxial tensile test on each sample. Four samples from each descending thoracic aorta produced ideal stress-strain curves. All parameter-fitting regressions from the selected mathematical model converged, and the best-fit parameters of each sample were obtained. The elastic modulus of collagen fiber, failure stress, and the strain showed a decreasing trend with age, while the elastic modulus of elastic fiber showed an increasing trend with age. The elastic modulus of collagen fiber, failure stress, and strain of circumferential tensile were all greater than those for axial tensile. There was no statistical difference in model parameters and physiological moduli between the proximal and distal segments. The failure stress and strain in the proximal circumferential, distal circumferential, and distal axial tensile were all greater for the male group than for the female group. Finally, the Fung-type hyperelastic constitutive equations were fitted for the different segments in different age groups.
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Affiliation(s)
- Zhengdong Li
- Shanghai Key Laboratory of Forensic Medicine, Key Laboratory of Forensic Science, Ministry of Justice, Shanghai Forensic Service Platform, Academy of Forensic Science, Shanghai, China
| | - Ming Pei
- Institute of Forensic Science, Xuzhou Public Security Bureau, Xuzhou, Jiangsu, China
| | - Jianhua Zhang
- Shanghai Key Laboratory of Forensic Medicine, Key Laboratory of Forensic Science, Ministry of Justice, Shanghai Forensic Service Platform, Academy of Forensic Science, Shanghai, China
| | - Ningguo Liu
- Shanghai Key Laboratory of Forensic Medicine, Key Laboratory of Forensic Science, Ministry of Justice, Shanghai Forensic Service Platform, Academy of Forensic Science, Shanghai, China
| | - Jinming Wang
- Shanghai Key Laboratory of Forensic Medicine, Key Laboratory of Forensic Science, Ministry of Justice, Shanghai Forensic Service Platform, Academy of Forensic Science, Shanghai, China
| | - Donghua Zou
- Shanghai Key Laboratory of Forensic Medicine, Key Laboratory of Forensic Science, Ministry of Justice, Shanghai Forensic Service Platform, Academy of Forensic Science, Shanghai, China
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7
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Tong J, Xin YF, Zhang Z, Xu X, Li T. Effect of hypertension on the delamination and tensile strength of ascending thoracic aortic aneurysm with a focus on right lateral region. J Biomech 2023; 154:111615. [PMID: 37178496 DOI: 10.1016/j.jbiomech.2023.111615] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Revised: 04/18/2023] [Accepted: 05/02/2023] [Indexed: 05/15/2023]
Abstract
Hypertension is a major predisposing factor to initiate thoracic aortopathy. The objective of this study is to investigate effect of hypertension on delamination and tensile strength of ascending thoracic aortic aneurysms (ATAAs). A total of 35 fresh ATAA samples were harvested from 19 hypertensive and 16 non-hypertensive patients during elective aortic surgery. Peeling tests with two extension rates were performed to determine delamination strength, while uniaxial tensile (UT) tests were employed to measure failure stresses. The delamination strength and failure stresses of the ATAAs were further correlated with patient ages for hypertensive and non-hypertensive groups. The delamination strength to peel apart the ATAA tissue along the longitudinal direction was statistically significantly lower for the hypertensive patients than that of the non-hypertensive patients (35 ± 11 vs. 49 ± 9 mN/mm, p = 0.02). A higher delamination strength was measured if peeling was performed with a higher extension rate. The circumferential failure stresses were significantly lower for the hypertensive ATAAs than those of the non-hypertensive ATAAs (1.03 ± 0.27 vs. 1.43 ± 0.38 MPa, p = 0.02). Histology showed that laminar structures of elastic fibers were mainly disrupted in the hypertensive ATAAs. The longitudinal delamination strength of the ATAAs was significantly decreased and strongly correlated with ages for the hypertensive patients. Strong inverse correlations were also identified between the circumferential and longitudinal failure stresses of the ATAAs and ages for the hypertensive patients. Results suggest that the ATAAs of the elderly hypertensive patients may have a higher propensity for dissection or rupture. The dissection properties of the ATAA tissue are rate dependent.
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Affiliation(s)
- Jianhua Tong
- Institute for Biomedical Engineering and Nano Science, Shanghai East Hospital, Tongji University School of Medicine, Shanghai, PR China.
| | - Yuan-Feng Xin
- Department of Cardiovascular Surgery, Shanghai East Hospital, Tongji University School of Medicine, Shanghai, PR China
| | - Zhi Zhang
- Institute for Biomedical Engineering and Nano Science, Shanghai East Hospital, Tongji University School of Medicine, Shanghai, PR China
| | - Xiaojuan Xu
- Institute for Biomedical Engineering and Nano Science, Shanghai East Hospital, Tongji University School of Medicine, Shanghai, PR China; Department of Pathology and Pathophysiology, Tongji University School of Medicine, Shanghai, PR China
| | - Tieyan Li
- Department of Cardiovascular Surgery, Shanghai East Hospital, Tongji University School of Medicine, Shanghai, PR China
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8
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Tarraf SA, Kramer B, Vianna E, Gillespie C, Germano E, Emerton KB, Amini R, Colbrunn R, Hargrave J, Roselli EE, Bellini C. Lengthwise regional mechanics of the human aneurysmal ascending thoracic aorta. Acta Biomater 2023; 162:266-277. [PMID: 36944405 PMCID: PMC10148908 DOI: 10.1016/j.actbio.2023.03.023] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Revised: 02/16/2023] [Accepted: 03/15/2023] [Indexed: 03/23/2023]
Abstract
The prognosis of patients undergoing emergency endovascular repair of ascending thoracic aortic aneurysm (ATAA) depends on defect location, with root disease bearing worse outcomes than proximal or distal aortopathy. We speculate that a spatial gradient in aneurysmal tissue mechanics through the length of the ascending thoracic aorta may fuel noted survival discrepancies. To this end, we performed planar biaxial testing on 153 root, proximal, and distal segments of ATAA samples collected from 80 patients receiving elective open surgical repair. Following data averaging via surface fitting-based interpolation of strain-controlled protocols, we combined in-vitro and in-vivo measurements of loads and geometry to resolve inflation-extension kinematics and evaluate mechanical metrics of stress, stiffness, and energy at consistent deformation levels. Representative (averaged) experimental data and simulated in-vivo conditions revealed significantly larger biaxial stiffness at the root compared to either proximal or distal tissues, which persisted as the entire aorta stiffened during aging. Advancing age further reduced biaxial stretch and energy storage, a measure of aortic function, across all ATAA segments. Importantly, age emerged as a stronger predictor of tissue mechanics in ATAA disease than either bicuspid aortic valve or connective tissue disorders. Besides strengthening the general understanding of aneurysmal disease, our findings provide specifications to customize the design of stent-grafts for the treatment of ATAA disease. Optimization of deployment and interaction of novel endovascular devices with the local native environment is expected to carry significant potential for improving clinical outcomes. STATEMENT OF SIGNIFICANCE: Elucidating the lengthwise regional mechanics of ascending thoracic aortic aneurysms (ATAAs) is critical for the design of endovascular devices tailored to the ascending aorta. Stent-grafts provide a less invasive alternative to support the long-term survival of ATAA patients ineligible for open surgical repair. In this study, we developed a numerical framework that combines semi-inverse constitutive and forward modeling with in-vitro and in-vivo data to extract mechanical descriptors of ATAA tissue behavior at physiologically meaningful deformation. Moving distally from the aortic root to the first ascending aortic branch, we observed a progressive decline in biaxial stiffness. Furthermore, we showed that aging leads to reduced aortic function and is a stronger predictor of mechanics than either valve morphology or underlying syndromic disorder.
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Affiliation(s)
- Samar A Tarraf
- Department of Bioengineering, Northeastern University, 360 Huntington Ave., Boston, MA, 02125 USA
| | - Benjamin Kramer
- Aortic Center, Department of Thoracic and Cardiovascular Surgery, Cleveland Clinic, Cleveland, OH, USA
| | - Emily Vianna
- Aortic Center, Department of Thoracic and Cardiovascular Surgery, Cleveland Clinic, Cleveland, OH, USA
| | - Callan Gillespie
- Department of Biomedical Engineering, BioRobotics and Mechanical Testing Core, Cleveland Clinic, Cleveland, OH, USA
| | - Emídio Germano
- Aortic Center, Department of Thoracic and Cardiovascular Surgery, Cleveland Clinic, Cleveland, OH, USA
| | - Kelly B Emerton
- Aortic Center, Department of Thoracic and Cardiovascular Surgery, Cleveland Clinic, Cleveland, OH, USA
| | - Rouzbeh Amini
- Department of Bioengineering, Northeastern University, 360 Huntington Ave., Boston, MA, 02125 USA; Department of Mechanical and Industrial Engineering, Northeastern University, 360 Huntington Ave., Boston, MA, 02125 USA
| | - Robb Colbrunn
- Department of Biomedical Engineering, BioRobotics and Mechanical Testing Core, Cleveland Clinic, Cleveland, OH, USA
| | - Jennifer Hargrave
- Department of Cardiothoracic Anesthesiology, Cleveland Clinic, Cleveland, OH, USA
| | - Eric E Roselli
- Aortic Center, Department of Thoracic and Cardiovascular Surgery, Cleveland Clinic, Cleveland, OH, USA; Department of Biomedical Engineering, BioRobotics and Mechanical Testing Core, Cleveland Clinic, Cleveland, OH, USA
| | - Chiara Bellini
- Department of Bioengineering, Northeastern University, 360 Huntington Ave., Boston, MA, 02125 USA.
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9
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What Are the Biomechanical Properties of an Aortic Aneurysm Associated with Quadricuspid Aortic Valve? J Clin Med 2022; 11:jcm11164897. [PMID: 36013136 PMCID: PMC9410111 DOI: 10.3390/jcm11164897] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2022] [Revised: 07/26/2022] [Accepted: 07/30/2022] [Indexed: 11/18/2022] Open
Abstract
Association of quadricuspid aortic valve (QAV) with ascending aortic aneurysms (AsAA) is rare. A 63-year-old female with hypertension was found (on MRI) to have an ascending aortic aneurysm (52 mm in maximum diameter) and dilatation at the level of the sinotubular junction (38 mm in diameter) associated with quadricuspid aortic valve. An ascending aortic wall replacement surgery was performed. In this study, we focus on the behavior of the aorta associated with QAV considering the in vitro biomechanical characteristics and histology. The properties of QAV are closer to bicuspid aortic valve than tricuspid aortic valve, but with higher wall thickness.
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10
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Cheng H, Li G, Dai J, Zhang K, Xu T, Wei L, Zhang X, Ding D, Hou J, Li J, Zhuang J, Tan K, Guo R. A fluid-structure interaction model accounting arterial vessels as a key part of the blood-flow engine for the analysis of cardiovascular diseases. Front Bioeng Biotechnol 2022; 10:981187. [PMID: 36061431 PMCID: PMC9438578 DOI: 10.3389/fbioe.2022.981187] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2022] [Accepted: 07/28/2022] [Indexed: 11/13/2022] Open
Abstract
According to the classical Windkessel model, the heart is the only power source for blood flow, while the arterial system is assumed to be an elastic chamber that acts as a channel and buffer for blood circulation. In this paper we show that in addition to the power provided by the heart for blood circulation, strain energy stored in deformed arterial vessels in vivo can be transformed into mechanical work to propel blood flow. A quantitative relationship between the strain energy increment and functional (systolic, diastolic, mean and pulse blood pressure) and structural (stiffness, diameter and wall thickness) parameters of the aorta is described. In addition, details of blood flow across the aorta remain unclear due to changes in functional and other physiological parameters. Based on the arterial strain energy and fluid-structure interaction theory, the relationship between physiological parameters and blood supply to organs was studied, and a corresponding mathematical model was developed. The findings provided a new understanding about blood-flow circulation, that is, cardiac output allows blood to enter the aorta at an initial rate, and then strain energy stored in the elastic arteries pushes blood toward distal organs and tissues. Organ blood supply is a key factor in cardio-cerebrovascular diseases (CCVD), which are caused by changes in blood supply in combination with multiple physiological parameters. Also, some physiological parameters are affected by changes in blood supply, and vice versa. The model can explain the pathophysiological mechanisms of chronic diseases such as CCVD and hypertension among others, and the results are in good agreement with epidemiological studies of CCVD.
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Affiliation(s)
- Heming Cheng
- Department of Mechanics, Kunming University of Science and Technology, Kunming, China
- *Correspondence: Heming Cheng, ; Ke Zhang,
| | - Gen Li
- Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, China
| | - Jifeng Dai
- Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, China
| | - Ke Zhang
- Department of Mechanics, Kunming University of Science and Technology, Kunming, China
- Department of Hydraulic Engineering, Kunming University of Science and Technology, Kunming, China
- *Correspondence: Heming Cheng, ; Ke Zhang,
| | - Tianrui Xu
- Faculty of Life Science and Technology, Kunming University of Science and Technology, Kunming, China
| | - Liuchuang Wei
- Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, China
| | - Xue Zhang
- Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, China
| | - Dongfang Ding
- Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, China
| | - Jie Hou
- Department of Mechanics, Kunming University of Science and Technology, Kunming, China
| | - Jianyun Li
- Department of Mechanics, Kunming University of Science and Technology, Kunming, China
| | - Jiangping Zhuang
- Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, China
| | - Kaijun Tan
- Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming, China
| | - Ran Guo
- Department of Mechanics, Kunming University of Science and Technology, Kunming, China
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11
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Xu X, Zhang Z, Abudupataer M, Yang F, Wang C, Zhu K, Tong J. Mechanical characterization and material modeling of ascending aortic aneurysm with different bicuspid aortic cusp fusion morphologies. J Mech Behav Biomed Mater 2022; 132:105295. [DOI: 10.1016/j.jmbbm.2022.105295] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2022] [Revised: 04/27/2022] [Accepted: 05/21/2022] [Indexed: 10/18/2022]
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12
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Lin S, Morgant MC, Marín-Castrillón DM, Walker PM, Glélé LSA, Boucher A, Presles B, Bouchot O, Lalande A. Aortic local biomechanical properties in ascending aortic aneurysms. Acta Biomater 2022; 149:40-50. [PMID: 35714897 DOI: 10.1016/j.actbio.2022.06.019] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2021] [Revised: 06/08/2022] [Accepted: 06/09/2022] [Indexed: 11/01/2022]
Abstract
Ascending aortic aneurysm (AsAA) is a high-risk cardiovascular disease with an increased incidence over years. In this study, we compare different risk factors based on the pre-failure behavior (from a biomechanical point of view) obtained ex-vivo from an equi-biaxial tensile test. A total of 100 patients (63 ± 12 years, 72 males) with AsAA replacement, were recruited. Equi-biaxial tensile tests of AsAA walls were performed on freshly sampled aortic wall tissue after ascending aortic replacement. The aneurysmal aortic walls were divided into four quadrants (medial, anterior, lateral, and posterior) and two directions (longitudinal and circumferential) were considered. The stiffness was represented by the maximum Young Modulus (MYM). Based on patient information, the following subgroups were considered: age, gender, hypertension, obesity, dyslipidemia, diabetes, smoking history, aortic insufficiency, aortic stenosis, coronary artery disease, aortic diameter and aortic valve type. In general, when the aortic diameter increased, the aortic wall became thicker. In terms of the MYM, the longitudinal direction was significantly higher than that in the circumferential direction. In the multivariant analysis, the impact factors of age (p = 0.07), smoking (p = 0.05), diabetes (p = 0.03), aortic stenosis (p = 0.02), coronary artery disease (p < 10-3), and aortic diameters (p = 0.02) were significantly influencing the MYM. There was no significant MYM difference when the patients presented arterial hypertension, dyslipidemia, obesity, or bicuspid aortic valve. To conclude, the pre-failure aortic stiffness is multi-factorial, according to our population of 100 patients with AsAA. STATEMENT OF SIGNIFICANCE: : Our research on the topic of "Aortic local biomechanical properties in case of ascending aortic aneurysms" is about the biomechanical properties on one hundred aortic samples according to the aortic wall quadrants and the direction. More than ten factors and risks which may impact ascending aortic aneurysms have been studied. According to our knowledge, so far, this article involved the largest population on this topic. It will be our pleasure to share this information with all the readers.
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Affiliation(s)
- Siyu Lin
- ImViA laboratory, University of Burgundy, Dijon, France.
| | - Marie Catherine Morgant
- ImViA laboratory, University of Burgundy, Dijon, France; Department of Cardio-Vascular and Thoracic Surgery, University Hospital of Dijon, Dijon, France
| | | | - Paul M Walker
- ImViA laboratory, University of Burgundy, Dijon, France; Department of Medical Imaging, University Hospital of Dijon, Dijon, France
| | | | | | | | - Olivier Bouchot
- ImViA laboratory, University of Burgundy, Dijon, France; Department of Cardio-Vascular and Thoracic Surgery, University Hospital of Dijon, Dijon, France
| | - Alain Lalande
- ImViA laboratory, University of Burgundy, Dijon, France; Department of Medical Imaging, University Hospital of Dijon, Dijon, France
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13
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Kefalidi E, Angouras DC, Sokolis DP. Regional and directional variations in the layer-specific resistance to tear propagation in ascending thoracic aortic aneurysms. J Biomech 2022; 138:111133. [DOI: 10.1016/j.jbiomech.2022.111133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2022] [Revised: 04/29/2022] [Accepted: 05/04/2022] [Indexed: 10/18/2022]
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14
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Biomechanics in ascending aortic aneurysms correlate with tissue composition and strength. JTCVS OPEN 2022; 9:1-10. [PMID: 36003475 PMCID: PMC9390473 DOI: 10.1016/j.xjon.2021.12.001] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/19/2021] [Accepted: 12/03/2021] [Indexed: 12/12/2022]
Abstract
Objective This study correlates low strain tangential modulus (LTM) and transition zone onset (TZo) stress, biomechanical parameters that occur within the physiological range of stress seen in vivo, with tissue strength and histopathologic changes in aneurysmal ascending aortic tissue. Method Ascending aortic aneurysm tissue samples were collected from 41 patients undergoing elective resection. Samples were subjected to planar biaxial testing to quantify LTM and TZo. These were then correlated with strength assessed from uniaxial testing and with histopathologic quantification of pathologic derangements in elastin, collagen, and proteoglycan (PG). Results Decreased LTM and TZo were correlated with reduced strength (P < .05), PG content (P < .05), and elastin content (P < .05). Reduced TZo also was correlated with increased elastin fragmentation (P < .05). Conclusions LTM and TZo are correlated with common biomechanical and histopathologic alterations in ascending aortic aneurysm tissue that are thought to relate to the risk of acute aortic syndromes. LTM and TZo are measured under conditions approximating in vivo physiology and have the potential to be obtained noninvasively using medical imaging techniques. Therefore, they represent parameters that warrant future study as potential contributors to our growing knowledge of pathophysiology, disease progression, and risk stratification of aortic disease.
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Wang Y, Bai L, Yang J, Lu Y, Fan W, Nie Z, Yu J, Wen K, Wang R, He L, Yang F, Qi B. Artificial intelligence measuring the aortic diameter assist in identifying adverse blood pressure status including masked hypertension. Postgrad Med 2021; 134:111-121. [PMID: 34762815 DOI: 10.1080/00325481.2021.2003150] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Abstract
INTRODUCTION AND OBJECTIVES Artificial intelligence (AI) made it achievable that aortic dilation could be measured in CT images indirectly, while aortic diameter (AD) has the certain relationship with blood pressure. It was potential that the blood pressure condition be determined by AD measurement using the data obtained from a CT scanning especially in identifying masked hypertension and predicting the risk of poor control of blood pressure (BP) which was easy to elude diagnosis in clinic. We aimed to evaluate the possibility of utilizing AD by AI for predicting the risk of adverse BP status (including masked hypertension or poor BP control) and the optimal thoracic aortic position in measurement as well as the cutoff value for predicting the risk. METHODS Eight hundred and one patients were enrolled in our study. AI-Rad Companion Cardiovascular (K183268 FDA approved) was used to perform automatic aorta measurement in thoracic CT images at nine key positions based on AHA guidelines. Data was post processed by software from AI-Rad Companion undergone rigorous clinical validation by both FDA and CE as verification of its efficacy and usability. The AD's risk and diagnostic value was assessed in identifying hypertension in the general population, in identifying the poor BP controlled in the hypertension population, and in screening masked hypertension in the general population respectively by multiple regression analysis and receiver operating curve analysis. RESULTS AD measured by AI was a risk factor for adverse BP status after clinical covariates adjustment (OR = 1.02 ~ 1.26). The AD at mid descending aorta was mostly affected by BP particularly, which is optimal indicator in identifying hypertension in the general population (AUC = 0.73) and for screening masked hypertension (AUC = 0.78). CONCLUSION Using AI to measure the AD of the aorta, particularly at the position of mid descending aorta, is greatly valuable for identifying people with poor BP status. It will be possible to reveal more clinical information reflected by ordinary CT images and enrich the screening methods for hypertension, especially masked hypertension.PLAIN LANGUAGE SUMMARYHTN has a significant adverse effect on arterial deformation. BP and arterial dilation promote each other in a vicious circle. Arterial dilation may not be restricted by apparent fluctuations in BP and is objective evidence of an undesirable BP state. The accuracy of AD measurements by AI on chest CT images has been verified. There has not been the application of AD measurement by AI in the scene of poor BP status in clinical practice.In this study, we applied AI to measure the diameter of the aorta in nine consecutive positions. We explored the association between AD at various positions and BP levels and the possibility that AD in identifying poor BP status in different populations. We found that the AD at the MD is of great value in screening MH and evaluating the control state of BP in HTN. It will be possible to significantly expand the clinical information reflected by ordinary CT images and enrich the screening methods for HTN, especially MH.
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Affiliation(s)
- Yaoling Wang
- Department of Geriatrics, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China
| | - Lijuan Bai
- Department of Geriatrics, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China
| | - Jinrong Yang
- Department of Radiology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China
| | - Yichen Lu
- Digital Health, Siemens Healthineers Digital Technology(Shanghai)Co., Ltd, Shanghai, China
| | - Wenliang Fan
- Department of Software Engineering and Data Technology, School of Software & Microelectronics, Peking University, Beijing, China
| | - Zhuang Nie
- Department of Radiology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China
| | - Jie Yu
- Department of Radiology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China
| | - Kai Wen
- Department of Software Engineering and Data Technology, School of Software & Microelectronics, Peking University, Beijing, China
| | - Ruiyun Wang
- Department of Geriatrics, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China
| | - Linfeng He
- Department of Geriatrics, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China
| | - Fan Yang
- Department of Radiology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China
| | - Benling Qi
- Department of Geriatrics, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China
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He X, Auricchio F, Morganti S, Lu J. Uniaxial properties of ascending aortic aneurysms in light of effective stretch. Acta Biomater 2021; 136:306-313. [PMID: 34560300 DOI: 10.1016/j.actbio.2021.09.029] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Revised: 09/07/2021] [Accepted: 09/16/2021] [Indexed: 01/15/2023]
Abstract
A constitutive model that explicitly considers the gradual recruitment of collagen fibers is applied to investigate the uniaxial properties of human ascending aortic aneurysms. The model uses an effective stretch, which is a continuum scale kinematic variable measuring the true stretch of the tissue, to formulate the fiber stress. The constitutive equation contains two shape parameters characterizing the stochastic distribution of fiber waviness, and two elastic parameters accounting for, respectively, the elastic properties of ground substance and the straightened collagen fibers. The model is applied to 156 sets of uniaxial stress-stretch data obtained from 52 aneurysm samples. Major findings include (1) the uniaxial response can be well described by a quadratic strain energy function of the effective strain; (2) the ultimate stretches, when measured in terms of the effective stretch, are closely clustered around 1.1, in contrast to a much wider range in the original stretch; and (3) the ultimate stress correlates positively with the fiber stiffness. The age dependence and directional differences of constitutive parameters are also investigated. Results indicate that only the waviness depends strongly on age; no clear alterations occur in elastic parameters. Further, the fibers are wavier and stiffer in the circumferential direction than in the longitudinal direction. No other parameters exhibit significant direction difference. STATEMENT OF SIGNIFICANCE: We introduced a constitutive model which explicitly accounts for collagen fiber recruitment to investigate the uniaxial properties of human ascending aortic aneurysm tissues. Uniaxial response data from 156 specimens were considered in the study. It was found that the seemingly dissimilar response curves are, in fact, similar if we measure the deformation using an effective stretch which factors out the uncrimping deformation. The rupture stretches in terms of the effective stretch are closely packed around 1.1. And the stress-stretch curves collapse to a canonical curve after a transformation.
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Affiliation(s)
- Xuehuan He
- Department of Mechanical Engineering, The University of Iowa, Iowa City, IA 52242, USA
| | - Ferdinando Auricchio
- Department of Civil Engineering and Architecture, University of Pavia, Pavia 27100, Italy
| | - Simone Morganti
- Department of Electrical, Computer, and Biomedical Engineering, University of Pavia, Pavia 27100, Italy
| | - Jia Lu
- Department of Mechanical Engineering, The University of Iowa, Iowa City, IA 52242, USA.
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17
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Bhat SK, Yamada H. Mechanical characterization of dissected and dilated human ascending aorta using Fung-type hyperelastic models with pre-identified initial tangent moduli for low-stress distensibility. J Mech Behav Biomed Mater 2021; 125:104959. [PMID: 34800890 DOI: 10.1016/j.jmbbm.2021.104959] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2020] [Revised: 10/24/2021] [Accepted: 11/06/2021] [Indexed: 10/19/2022]
Abstract
Ascending aortic dissection (AD) is a potentially fatal vascular disease associated with degradation and fragmentation of the elastic fibers in the aortic media, increasing low-stress distensibility, and a dilated aorta may lead to dissection. In this study, a Fung-type hyperelastic model was formulated incorporating the initial tangent moduli (ITM) of stress-strain curves as an index of low-stress distensibility. ITM were correlated with the material constants by linearizing incompressible stress-strain relationships at zero strain. For uniaxial loading tests, the robustness of the material constants was examined in the stress ranges of 0-200, 0-180, and 0-160 kPa and to the ITM values of 100%, 95%, and 90%. Examination revealed stable changes in the material constants of 80% of the specimens. For equibiaxial stretch tests, the material constants were determined for each curve of the isotropic and anisotropic deformation groups by pre-identifying the ITM and minimizing fitting errors using isotropic or anisotropic models. The errors for all groups were <6% using a transversely isotropic model, and <10% for an orthotropic model. Comparisons with experimental curves showed that Fung-type models described both the ITM and significant stiffening at high stress levels. The mechanical characteristics of the aorta in the stage prior/posterior to dissection is such that while hardening occurs under both low- and high-stress levels with an increase in collagen content as an aging response, softening occurs under low-stress conditions due to histological abnormalities such as elastin deficiency and fragmentation. Numerical simulations using Fung-type models implied that elastic fiber degeneration and fragmentation in AD tissues reduced not only the low-stress stiffness but also the elastic stiffness with superimposed shear. The latter stiffness was modulated by the stiffening at high stress levels in tensile deformation behavior and normal-strain state under physiological loading conditions, and therefore provides further insight into wall rupture.
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Affiliation(s)
- Subraya Krishna Bhat
- Department of Biological Functions Engineering, Kyushu Institute of Technology, 2-4 Hibikino, Wakamatsu-ku, Kitakyushu, 808-0196, Japan.
| | - Hiroshi Yamada
- Department of Biological Functions Engineering, Kyushu Institute of Technology, 2-4 Hibikino, Wakamatsu-ku, Kitakyushu, 808-0196, Japan.
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18
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Sokolis DP, Angouras DC. Failure properties of ascending thoracic aortic aneurysms with dysfunctional tricuspid aortic valves. Interact Cardiovasc Thorac Surg 2021; 33:949-958. [PMID: 34333633 DOI: 10.1093/icvts/ivab184] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Revised: 04/28/2021] [Accepted: 06/03/2021] [Indexed: 11/14/2022] Open
Abstract
OBJECTIVES Ascending thoracic aortic aneurysms (ATAAs) often coexist with dysfunctional tricuspid aortic valves (TAVs). How valvular pathology relates to the aortic wall mechanical properties requires detailed examination. METHODS Intact-wall and layer-specific mechanical properties from 40 and 21 patients with TAV-ATAAs, respectively, were studied using uniaxial tensile testing, longitudinally and circumferentially. Failure stress (tensile strength), failure stretch (extensibility) and peak elastic modulus (stiffness) measurements, along with histological assays of thickness and elastin/collagen contents, were compared among patients with no valvular pathology (NVP), aortic stenosis (AS) or aortic insufficiency (AI). RESULTS Intact-wall stiffness longitudinally and medial strength and stiffness, in either direction, were significantly lower in AI patients than in AS and NVP patients. Intact-wall/medial thickness and extensibility in either direction were significantly lower in AS patients than in AI and NVP patients. In contrast, intact-wall/medial stiffness circumferentially was significantly higher in AS patients than in NVP patients, consistent with the significantly increased medial collagen in AS patients. Failure properties and medial thickness and elastin/collagen contents were significantly lower (more impaired) in females. The left lateral was the thickest quadrant in NVP patients, but the 4 quadrants were equally thick in AS and AI patients. There were significant differences in strength and stiffness among quadrants, which varied however in the 3 patient groups. CONCLUSIONS The aortic wall load-bearing capacity was impaired in patients with ATAA in the presence of TAV stenosis or insufficiency. These findings lend biomechanical support to the current guidelines suggesting lower thresholds for elective ascending aorta replacement in cases of aortic valve surgery.
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Affiliation(s)
- Dimitrios P Sokolis
- Laboratory of Biomechanics, Center of Clinical, Experimental Surgery, and Translational Research, Biomedical Research Foundation of the Academy of Athens, 11527 Athens, Greece
| | - Dimitrios C Angouras
- Department of Cardiac Surgery, Attikon University Hospital, School of Medicine, National and Kapodistrian University of Athens, 12462 Athens, Greece
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Lu J, He X. Incorporating fiber recruitment in hyperelastic modeling of vascular tissues by means of kinematic average. Biomech Model Mechanobiol 2021; 20:1833-1850. [PMID: 34173928 DOI: 10.1007/s10237-021-01479-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2021] [Accepted: 06/08/2021] [Indexed: 12/26/2022]
Abstract
We present a framework for considering the gradual recruitment of collagen fibers in hyperelastic constitutive modeling. An effective stretch, which is a response variable representing the true stretch at the tissue-scale, is introduced. Properties of the effective stretch are discussed in detail. The effective stretch and strain invariants derived from it are used in selected hyperelastic constitutive models to describe the tissue response. This construction is investigated in conjunction with Holzapfel-Gasser-Ogden family strain energy functions. The ensuing models are validated against a large body of uniaxial and bi-axial stress-strain response data from human aortic aneurysm tissues. Both the descriptive and the predictive capabilities are examined. The former is evaluated by the quality of constitutive fitting, and the latter is assessed using finite element simulation. The models significantly improve the quality of fitting, and reproduce the experiment displacement, stress, and strain distributions with high fidelity in the finite element simulation.
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Affiliation(s)
- Jia Lu
- Department of Mechanical Engineering, and Iowa Technology Institute, The University of Iowa, Iowa City, IA, 52242, USA.
| | - Xuehuan He
- Department of Mechanical Engineering, and Iowa Technology Institute, The University of Iowa, Iowa City, IA, 52242, USA
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20
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Biomechanical properties of ascending aortic aneurysms: Quantification of inter- and intra-patient variability. J Biomech 2021; 125:110542. [PMID: 34237660 DOI: 10.1016/j.jbiomech.2021.110542] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2020] [Revised: 04/19/2021] [Accepted: 05/31/2021] [Indexed: 12/14/2022]
Abstract
This study investigates the biomechanical properties of ascending aortic aneurysms focusing on the inter-patient differences vs. the heterogeneity within a patient's aneurysm. Each specimen was tested on a biaxial testing device and the resulting stress-strain response was fitted to a four-parameter Fung constitutive model. We postulate that the inter-patient variability (differences between patients) blurs possible intra-patient variability (regional heterogeneity) and, thus, that both effects must be considered to shed light on the role of heterogeneity in aneurysm progression. We propose, demonstrate, and discuss two techniques to assess differences by, first, comparing conventional biomechanical properties and, second, the overall constitutive response. Results show that both inter- and intra-patient variability contribute to errors when using population averaged models to fit individual tissue behaviour. When inter-patient variability was accounted for and its effects excluded, intra-patient heterogeneity could be assessed, showing a wide degree of heterogeneity at the individual patient level. Furthermore, the right lateral region (from the patient's perspective) appeared different (stiffer) than the other regions. We posit that this heterogeneity could be a consequence of maladaptive remodelling due to altered loading conditions that hastens microstructural changes naturally occurring with age. Further validation of these results should be sought from a larger cohort study.
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21
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Estimating aortic thoracic aneurysm rupture risk using tension-strain data in physiological pressure range: an in vitro study. Biomech Model Mechanobiol 2021; 20:683-699. [PMID: 33389275 DOI: 10.1007/s10237-020-01410-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Accepted: 12/02/2020] [Indexed: 12/17/2022]
Abstract
Previous studies have shown that the rupture properties of an ascending thoracic aortic aneurysm (ATAA) are strongly correlated with the pre-rupture response features. In this work, we present a two-step machine learning method to predict where the rupture is likely to occur in ATAA and what safety reserve the structure may have. The study was carried out using ATAA specimens from 15 patients who underwent surgical intervention. Through inflation test, full-field deformation data and post-rupture images were collected, from which the wall tension and surface strain distributions were computed. The tension-strain data in the pressure range of 9-18 kPa were fitted to a third-order polynomial to characterize the response properties. It is hypothesized that the region where rupture is prone to initiate is associated with a high level of tension buildup. A machine learning method is devised to predict the peak risk region. The predicted regions were found to match the actual rupture sites in 13 samples out of the total 15. In the second step, another machine learning model is utilized to predict the tissue's rupture strength in the peak risk region. Results suggest that the ATAA rupture risk can be reasonably predicted using tension-strain response in the physiological range. This may open a pathway for evaluating the ATAA rupture propensity using information of in vivo response.
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22
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Prediction of local strength of ascending thoracic aortic aneurysms. J Mech Behav Biomed Mater 2020; 115:104284. [PMID: 33348213 DOI: 10.1016/j.jmbbm.2020.104284] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2019] [Revised: 12/08/2020] [Accepted: 12/14/2020] [Indexed: 12/12/2022]
Abstract
Knowledges of both local stress and strength are needed for a reliable evaluation of the rupture risk for ascending thoracic aortic aneurysm (ATAA). In this study, machine learning is applied to predict the local strength of ATAA tissues based on tension-strain data collected through in vitro inflation tests on tissue samples. Inputs to machine learning models are tension, strain, slope, and curvature values at two points on the low strain region of the tension-strain curve. The models are trained using data from locations where the tissue ruptured, and subsequently applied to data from intact sites to predict the local rupture strength. The predicted strengths are compared with the known strength at rupture sites as well as the highest tension the tissues experienced at the intact sites. A local rupture index, which is the ratio of the end tension to the predicted rupture strength, is computed. The 'hot spots' of the rupture index are found to match the rupture sites better than those of the peak tension. The study suggests that the strength of ATAA tissue could be reliably predicted from early phase response features defined in this work.
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Iliopoulos DC, Sokolis DP. Ascending aorta mechanics in bicuspid aortopathy: controversy or fact? Asian Cardiovasc Thorac Ann 2020; 29:592-604. [PMID: 32447961 DOI: 10.1177/0218492320928731] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Bicuspid aortic valve is the most common congenital cardiovascular defect, often associated with proximal aortic dilatation, and the ideal management strategy is debated. The inconsistency in previous and present guideline recommendations emphasizes the insufficiency of the maximal diameter as the sole criterion for prophylactic repair. Our ability to guide clinical decisions may improve through an understanding of the mechanical properties of ascending thoracic aortic aneurysms in bicuspid compared to tricuspid aortic valve patients and non-aneurysmal aortas, because dissection and rupture are aortic wall mechanical failures. Such an understanding of the mechanical properties has been attempted by several authors, and this article addresses whether there is a controversy in the accumulated knowledge. The available mechanical studies are briefly reviewed, discussing factors such as age, sex, and the region of mechanical examination that may be responsible for the lack of unanimity in the reported findings. The rationale for acquiring layer-specific properties is presented along with the main results from our recent study. No mechanical vulnerability of ascending thoracic aortic aneurysms was evidenced in bicuspid aortic valve patients, corroborating present conservative guidelines concerning the management of bicuspid aortopathy. Weakening and additional vulnerability was evidenced in aged patients and those with coexisting valve pathology, aortic root dilatation, hypertension, and hyperlipidemia. Discussion of these results from age- and sex-matched subjects, accounting for the region- and layer-specific aortic heterogeneity, in relation to intact wall results and histologic confirmation, helps to reconcile previous findings and affords a universal interpretation of ascending aorta mechanics in bicuspid aortopathy.
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Affiliation(s)
- Dimitrios C Iliopoulos
- Department of Cardiac Surgery, National and Kapodistrian University of Athens, and 4th Cardiac Surgery Department, Hygeia Hospital, Athens, Greece
| | - Dimitrios P Sokolis
- Biomechanics Laboratory, Center of Clinical, Experimental Surgery, and Translational Research, Biomedical Research Foundation of the Academy of Athens, Athens, Greece
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Sherifova S, Holzapfel GA. Biomechanics of aortic wall failure with a focus on dissection and aneurysm: A review. Acta Biomater 2019; 99:1-17. [PMID: 31419563 PMCID: PMC6851434 DOI: 10.1016/j.actbio.2019.08.017] [Citation(s) in RCA: 81] [Impact Index Per Article: 16.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2019] [Revised: 08/05/2019] [Accepted: 08/08/2019] [Indexed: 12/12/2022]
Abstract
Aortic dissections and aortic aneurysms are fatal events characterized by structural changes to the aortic wall. The maximum diameter criterion, typically used for aneurysm rupture risk estimations, has been challenged by more sophisticated biomechanically motivated models in the past. Although these models are very helpful for the clinicians in decision-making, they do not attempt to capture material failure. Following a short overview of the microstructure of the aorta, we analyze the failure mechanisms involved in the dissection and rupture by considering also traumatic rupture. We continue with a literature review of experimental studies relevant to quantify tissue strength. More specifically, we summarize more extensively uniaxial tensile, bulge inflation and peeling tests, and we also specify trouser, direct tension and in-plane shear tests. Finally we analyze biomechanically motivated models to predict rupture risk. Based on the findings of the reviewed studies and the rather large variations in tissue strength, we propose that an appropriate material failure criterion for aortic tissues should also reflect the microstructure in order to be effective. STATEMENT OF SIGNIFICANCE: Aortic dissections and aortic aneurysms are fatal events characterized by structural changes to the aortic wall. Despite the advances in medical, biomedical and biomechanical research, the mortality rates of aneurysms and dissections remain high. The present review article summarizes experimental studies that quantify the aortic wall strength and it discusses biomechanically motivated models to predict rupture risk. We identified contradictory observations and a large variation within and between data sets, which may be due to biological variations, different sample sizes, differences in experimental protocols, etc. Based on the findings of the reviewed literature and the rather large variations in tissue strength, it is proposed that an appropriate criterion for aortic failure should also reflect the microstructure.
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Affiliation(s)
- Selda Sherifova
- Institute of Biomechanics, Graz University of Technology, Stremayrgasse 16/2, 8010 Graz, Austria
| | - Gerhard A Holzapfel
- Institute of Biomechanics, Graz University of Technology, Stremayrgasse 16/2, 8010 Graz, Austria; Department of Structural Engineering, Norwegian Institute of Science and Technology (NTNU), 7491 Trondheim, Norway.
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25
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Cavinato C, Molimard J, Curt N, Campisi S, Orgéas L, Badel P. Does the Knowledge of the Local Thickness of Human Ascending Thoracic Aneurysm Walls Improve Their Mechanical Analysis? Front Bioeng Biotechnol 2019; 7:169. [PMID: 31380360 PMCID: PMC6646470 DOI: 10.3389/fbioe.2019.00169] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2019] [Accepted: 07/02/2019] [Indexed: 12/22/2022] Open
Abstract
Ascending thoracic aortic aneurysm (ATAA) ruptures are life threatening phenomena which occur in local weaker regions of the diseased aortic wall. As ATAAs are evolving pathologies, their growth represents a significant local remodeling and degradation of the microstructural architecture and thus their mechanical properties. To address the need for deeper study of ATAAs and their failure, it is required to analyze the mechanical behavior at the sub-millimeter scale by making use of accurate geometrical and kinematical measurements during their deformation. For this purpose, we propose a novel methodology that combined an accurate tool for thickness distribution measurement of the arterial wall, digital image correlation to assess local strain fields and bulge inflation to characterize the physiological and failure response of flat unruptured human ATAA specimens. The analysis of the heterogeneity of the local thickness and local physiological stress and strain was carried out for each investigated subject. At the subject level, our results state the presence of a non-consistent relationship between the local wall thickness and the local physiological strain field and high heterogeneity of the variables. At the inter-subject level, thicknesses were studied in relation to physiological strain and stress and load at rupture. The rupture pressure was correlated with neither the average thickness nor the lowest thickness of the specimens. Our results confirm that intrinsic material strength (hence structure) differs a lot from a subject to another and even within the same subject.
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Affiliation(s)
- Cristina Cavinato
- Mines Saint-Etienne, Centre CIS, INSERM, U 1059 Sainbiose, Univ Lyon, Univ Jean Monnet, Saint-Etienne, France
| | - Jerome Molimard
- Mines Saint-Etienne, Centre CIS, INSERM, U 1059 Sainbiose, Univ Lyon, Univ Jean Monnet, Saint-Etienne, France
| | - Nicolas Curt
- Mines Saint-Etienne, Centre CIS, INSERM, U 1059 Sainbiose, Univ Lyon, Univ Jean Monnet, Saint-Etienne, France
| | - Salvatore Campisi
- Department of CardioVascular Surgery, CHU Hôpital Nord Saint-Etienne, Saint-Etienne, France
| | - Laurent Orgéas
- UMR 5521, Univ. Grenoble Alpes, CNRS, Grenoble INP, 3SR Lab, Grenoble, France
| | - Pierre Badel
- Mines Saint-Etienne, Centre CIS, INSERM, U 1059 Sainbiose, Univ Lyon, Univ Jean Monnet, Saint-Etienne, France
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26
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Liu T, Xie M, Lv Q, Li Y, Fang L, Zhang L, Deng W, Wang J. Bicuspid Aortic Valve: An Update in Morphology, Genetics, Biomarker, Complications, Imaging Diagnosis and Treatment. Front Physiol 2019; 9:1921. [PMID: 30761020 PMCID: PMC6363677 DOI: 10.3389/fphys.2018.01921] [Citation(s) in RCA: 45] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2018] [Accepted: 12/20/2018] [Indexed: 12/19/2022] Open
Abstract
The bicuspid aortic valve, a kind of heart disease that comes from parents, has been paid attention around the world. Although most bicuspid aortic valve (BAV) patients will suffer from some complications including aortic stenosis, aortic regurgitation, endocarditis, and heart dysfunction in the late stage of the disease, there is none symptom in the childhood, which restrains us to diagnose and treatment in the onset phase of BAV. Hemodynamic abnormalities induced by the malformations of the valves in BAV patients for a long time will cause BAV-associated aortopathy: including progress aortic dilation, aneurysm, dissection and rupture, cardiac cyst and even sudden death. At present, preventive surgical intervention is the only effective method used in this situation and the diameter of the aorta is the primary reference criterion for surgery. And the treatment effects are always not satisfactory for patients and clinicians. Therefore, we need more methods to evaluate the progression of BAV and the surgery value and the appropriate intervention time by combining basic research with clinical treatment. In this review, advances in morphology, genetic, biomarkers, diagnosis and treatments are summarized, which expects to provide an update about BAV. It is our supreme expectations to provide some evidences for BAV early screening and diagnosis, and in our opinion, personalized surgical strategy is the trend of future BAV treatment.
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Affiliation(s)
- Tianshu Liu
- Department of Ultrasound, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China.,Hubei Province Key Laboratory of Molecular Imaging, Wuhan, China
| | - Mingxing Xie
- Department of Ultrasound, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China.,Hubei Province Key Laboratory of Molecular Imaging, Wuhan, China
| | - Qing Lv
- Department of Ultrasound, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China.,Hubei Province Key Laboratory of Molecular Imaging, Wuhan, China
| | - Yuman Li
- Department of Ultrasound, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China.,Hubei Province Key Laboratory of Molecular Imaging, Wuhan, China
| | - Lingyun Fang
- Department of Ultrasound, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China.,Hubei Province Key Laboratory of Molecular Imaging, Wuhan, China
| | - Li Zhang
- Department of Ultrasound, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China.,Hubei Province Key Laboratory of Molecular Imaging, Wuhan, China
| | - Wenhui Deng
- Department of Ultrasound, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China.,Hubei Province Key Laboratory of Molecular Imaging, Wuhan, China
| | - Jing Wang
- Department of Ultrasound, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China.,Hubei Province Key Laboratory of Molecular Imaging, Wuhan, China
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Luo Y, Fan Z, Baek S, Lu J. Machine learning-aided exploration of relationship between strength and elastic properties in ascending thoracic aneurysm. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2018; 34:e2977. [PMID: 29504264 DOI: 10.1002/cnm.2977] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2017] [Revised: 02/07/2018] [Accepted: 02/23/2018] [Indexed: 06/08/2023]
Abstract
Machine learning was applied to classify tension-strain curves harvested from inflation tests on ascending thoracic aneurysm samples. The curves were classified into rupture and nonrupture groups using prerupture response features. Two groups of features were used as the basis for classification. The first was the constitutive parameters fitted from the tension-strain data, and the second was geometric parameters extracted from the tension-strain curve. Based on the importance scores provided by the machine learning, implications of some features were interrogated. It was found that (1) the value of a constitutive parameter is nearly the same for all members in the rupture group and (2) the strength correlates strongly with a tension in the early phase of response as well as with the end stiffness. The study suggests that the strength, which is not available without rupturing the tissue, may be indirectly inferred from prerupture response features.
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Affiliation(s)
- Yuanming Luo
- Department of Mechanical and Industrial Engineering, The University of Iowa, Iowa City, IA 52242, USA
| | - Zhiwei Fan
- Department of Computer Sciences, University of Wisconsin-Madison, 1210 W. Dayton St, Madison, WI 53706-1613, USA
| | - Stephen Baek
- Department of Mechanical and Industrial Engineering, The University of Iowa, Iowa City, IA 52242, USA
| | - Jia Lu
- Department of Mechanical and Industrial Engineering, The University of Iowa, Iowa City, IA 52242, USA
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