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Wu W, Daneker M, Turner KT, Jolley MA, Lu L. Identifying Heterogeneous Micromechanical Properties of Biological Tissues via Physics-Informed Neural Networks. SMALL METHODS 2024:e2400620. [PMID: 39091065 DOI: 10.1002/smtd.202400620] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2024] [Revised: 07/19/2024] [Indexed: 08/04/2024]
Abstract
The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying full-field heterogeneous elastic properties of soft materials using traditional engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in data-driven models for learning full-field mechanical responses, such as displacement and strain, from experimental or synthetic data. However, research studies on inferring full-field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, a physics-informed machine learning approach is proposed to identify the elasticity map in nonlinear, large deformation hyperelastic materials. This study reports the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) in inferring the heterogeneous elasticity maps across materials with structural complexity that closely resemble real tissue microstructure, such as brain, tricuspid valve, and breast cancer tissues. Further, the improved architecture is applied to three hyperelastic constitutive models: Neo-Hookean, Mooney Rivlin, and Gent. The improved network architecture consistently produces accurate estimations of heterogeneous elasticity maps, even when there is up to 10% noise present in the training data.
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Affiliation(s)
- Wensi Wu
- Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, PA, 19104, USA
- Division of Cardiology, Children's Hospital of Philadelphia, Philadelphia, PA, 19104, USA
| | - Mitchell Daneker
- Department of Statistics and Data Science, Yale University, New Haven, CT, 06511, USA
- Department of Chemical and Biochemical Engineering, University of Pennsylvania, Philadelphia, PA, 19104, USA
| | - Kevin T Turner
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, 19104, USA
| | - Matthew A Jolley
- Department of Anesthesiology and Critical Care Medicine, Children's Hospital of Philadelphia, Philadelphia, PA, 19104, USA
- Division of Cardiology, Children's Hospital of Philadelphia, Philadelphia, PA, 19104, USA
| | - Lu Lu
- Department of Statistics and Data Science, Yale University, New Haven, CT, 06511, USA
- Wu Tsai Institute, Yale University, New Haven, CT, 06510, USA
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Wu W, Daneker M, Turner KT, Jolley MA, Lu L. Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks. ARXIV 2024:arXiv:2402.10741v3. [PMID: 38745694 PMCID: PMC11092874] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Subscribe] [Scholar Register] [Indexed: 05/16/2024]
Abstract
The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying full-field heterogeneous elastic properties of soft materials using traditional engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in using data-driven models to learn full-field mechanical responses such as displacement and strain from experimental or synthetic data. However, research studies on inferring full-field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, we propose a physics-informed machine learning approach to identify the elasticity map in nonlinear, large deformation hyperelastic materials. We evaluate the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) by inferring the heterogeneous elasticity maps across three materials with structural complexity that closely resemble real tissue patterns, such as brain tissue and tricuspid valve tissue. We further applied our improved architecture to three additional examples of breast cancer tissue and extended our analysis to three hyperelastic constitutive models: Neo-Hookean, Mooney Rivlin, and Gent. Our selected network architecture consistently produced highly accurate estimations of heterogeneous elasticity maps, even when there was up to 10% noise present in the training data.
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Affiliation(s)
- Wensi Wu
- Department of Anesthesiology and Critical Care Medicine, Children’s Hospital of Philadelphia, Philadelphia, PA 19104
- Division of Cardiology, Children’s Hospital of Philadelphia, Philadelphia, PA 19104
| | - Mitchell Daneker
- Department of Statistics and Data Science, Yale University, New Haven, CT 06511
- Department of Chemical and Biochemical Engineering, University of Pennsylvania, Philadelphia, PA 19104
| | - Kevin T. Turner
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104
| | - Matthew A. Jolley
- Department of Anesthesiology and Critical Care Medicine, Children’s Hospital of Philadelphia, Philadelphia, PA 19104
- Division of Cardiology, Children’s Hospital of Philadelphia, Philadelphia, PA 19104
| | - Lu Lu
- Department of Statistics and Data Science, Yale University, New Haven, CT 06511
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Dux-Santoy L, Rodríguez-Palomares JF, Teixidó-Turà G, Garrido-Oliver J, Carrasco-Poves A, Morales-Galán A, Ruiz-Muñoz A, Casas G, Valente F, Galian-Gay L, Fernández-Galera R, Oliveró R, Cuéllar-Calabria H, Roque A, Burcet G, Barrabés JA, Ferreira-González I, Guala A. Three-dimensional aortic geometry mapping via registration of non-gated contrast-enhanced or gated and respiratory-navigated MR angiographies. J Cardiovasc Magn Reson 2024; 26:100992. [PMID: 38211655 PMCID: PMC11211222 DOI: 10.1016/j.jocmr.2024.100992] [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: 12/04/2023] [Accepted: 12/21/2023] [Indexed: 01/13/2024] Open
Abstract
BACKGROUND The measurement of aortic dimensions and their evolution are key in the management of patients with aortic diseases. Manual assessment, the current guideline-recommended method and clinical standard, is subjective, poorly reproducible, and time-consuming, limiting the capacity to track aortic growth in everyday practice. Aortic geometry mapping (AGM) via image registration of serial computed tomography angiograms outperforms manual assessment, providing accurate and reproducible 3D maps of aortic diameter and growth rate. This observational study aimed to evaluate the accuracy and reproducibility of AGM on non-gated contrast-enhanced (CE-) and cardiac- and respiratory-gated (GN-) magnetic resonance angiographies (MRA). METHODS Patients with thoracic aortic disease followed with serial CE-MRA (n = 30) or GN-MRA (n = 15) acquired at least 1 year apart were retrospectively and consecutively identified. Two independent observers measured aortic diameters and growth rates (GR) manually at several thoracic aorta reference levels and with AGM. Agreement between manual and AGM measurements and their inter-observer reproducibility were compared. Reproducibility for aortic diameter and GR maps assessed with AGM was obtained. RESULTS Mean follow-up was 3.8 ± 2.3 years for CE- and 2.7 ± 1.6 years for GN-MRA. AGM was feasible in the 93% of CE-MRA pairs and in the 100% of GN-MRA pairs. Manual and AGM diameters showed excellent agreement and inter-observer reproducibility (ICC>0.9) at all anatomical levels. Agreement between manual and AGM GR was more limited, both in the aortic root by GN-MRA (ICC=0.47) and in the thoracic aorta, where higher accuracy was obtained with GN- than with CE-MRA (ICC=0.55 vs 0.43). The inter-observer reproducibility of GR by AGM was superior compared to manual assessment, both with CE- (thoracic: ICC= 0.91 vs 0.51) and GN-MRA (root: ICC=0.84 vs 0.52; thoracic: ICC=0.93 vs 0.60). AGM-based 3D aortic size and growth maps were highly reproducible (median ICC >0.9 for diameters and >0.80 for GR). CONCLUSION Mapping aortic diameter and growth on MRA via 3D image registration is feasible, accurate and outperforms the current manual clinical standard. This technique could broaden the possibilities of clinical and research evaluation of patients with aortic thoracic diseases.
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Affiliation(s)
| | - Jose F Rodríguez-Palomares
- Vall d'Hebron Institut de Recerca (VHIR), Barcelona, Spain; CIBER de Enfermedades Cardiovasculares, CIBER-CV, Instituto de Salud Carlos III, Madrid, Spain; Department of Cardiology, Hospital Universitari Vall d'Hebron, Barcelona, Spain; Departament of Medicine, Universitat Autònoma de Barcelona, Bellaterra, Spain.
| | - Gisela Teixidó-Turà
- Vall d'Hebron Institut de Recerca (VHIR), Barcelona, Spain; CIBER de Enfermedades Cardiovasculares, CIBER-CV, Instituto de Salud Carlos III, Madrid, Spain; Department of Cardiology, Hospital Universitari Vall d'Hebron, Barcelona, Spain
| | - Juan Garrido-Oliver
- Vall d'Hebron Institut de Recerca (VHIR), Barcelona, Spain; Departament of Medicine, Universitat Autònoma de Barcelona, Bellaterra, Spain
| | - Alejandro Carrasco-Poves
- Vall d'Hebron Institut de Recerca (VHIR), Barcelona, Spain; Departament of Medicine, Universitat Autònoma de Barcelona, Bellaterra, Spain
| | | | - Aroa Ruiz-Muñoz
- Vall d'Hebron Institut de Recerca (VHIR), Barcelona, Spain; CIBER de Enfermedades Cardiovasculares, CIBER-CV, Instituto de Salud Carlos III, Madrid, Spain
| | - Guillem Casas
- Department of Cardiology, Hospital Universitari Vall d'Hebron, Barcelona, Spain
| | - Filipa Valente
- Department of Cardiology, Hospital Universitari Vall d'Hebron, Barcelona, Spain
| | - Laura Galian-Gay
- CIBER de Enfermedades Cardiovasculares, CIBER-CV, Instituto de Salud Carlos III, Madrid, Spain; Department of Cardiology, Hospital Universitari Vall d'Hebron, Barcelona, Spain
| | | | - Ruperto Oliveró
- Department of Cardiology, Hospital Universitari Vall d'Hebron, Barcelona, Spain
| | - Hug Cuéllar-Calabria
- Vall d'Hebron Institut de Recerca (VHIR), Barcelona, Spain; Departament of Medicine, Universitat Autònoma de Barcelona, Bellaterra, Spain; Department of Radiology, Hospital Universitari Vall d'Hebron, Barcelona, Spain
| | - Albert Roque
- Vall d'Hebron Institut de Recerca (VHIR), Barcelona, Spain; Departament of Medicine, Universitat Autònoma de Barcelona, Bellaterra, Spain; Department of Radiology, Hospital Universitari Vall d'Hebron, Barcelona, Spain
| | - Gemma Burcet
- Vall d'Hebron Institut de Recerca (VHIR), Barcelona, Spain; Departament of Medicine, Universitat Autònoma de Barcelona, Bellaterra, Spain; Department of Radiology, Hospital Universitari Vall d'Hebron, Barcelona, Spain
| | - José A Barrabés
- Vall d'Hebron Institut de Recerca (VHIR), Barcelona, Spain; CIBER de Enfermedades Cardiovasculares, CIBER-CV, Instituto de Salud Carlos III, Madrid, Spain; Department of Cardiology, Hospital Universitari Vall d'Hebron, Barcelona, Spain; Departament of Medicine, Universitat Autònoma de Barcelona, Bellaterra, Spain
| | - Ignacio Ferreira-González
- Vall d'Hebron Institut de Recerca (VHIR), Barcelona, Spain; Department of Cardiology, Hospital Universitari Vall d'Hebron, Barcelona, Spain; Departament of Medicine, Universitat Autònoma de Barcelona, Bellaterra, Spain; CIBER de Epidemiología y Salud Pública, CIBERESP, Instituto de Salud Carlos III, Madrid, Spain.
| | - Andrea Guala
- Vall d'Hebron Institut de Recerca (VHIR), Barcelona, Spain; CIBER de Enfermedades Cardiovasculares, CIBER-CV, Instituto de Salud Carlos III, Madrid, Spain
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Rodríguez-Palomares JF, Dux-Santoy L, Guala A, Galian-Gay L, Evangelista A. Mechanisms of Aortic Dilation in Patients With Bicuspid Aortic Valve: JACC State-of-the-Art Review. J Am Coll Cardiol 2023; 82:448-464. [PMID: 37495282 DOI: 10.1016/j.jacc.2022.10.042] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Revised: 10/07/2022] [Accepted: 10/20/2022] [Indexed: 07/28/2023]
Abstract
Bicuspid aortic valve is the most common congenital heart disease and exposes patients to an increased risk of aortic dilation and dissection. Aortic dilation is a slow, silent process, leading to a greater risk of aortic dissection. The prevention of adverse events together with optimization of the frequency of the required lifelong imaging surveillance are important for both clinicians and patients and motivated extensive research to shed light on the physiopathologic processes involved in bicuspid aortic valve aortopathy. Two main research hypotheses have been consolidated in the last decade: one supports a genetic basis for the increased prevalence of dilation, in particular for the aortic root, and the second supports the damaging impact on the aortic wall of altered flow dynamics associated with these structurally abnormal valves, particularly significant in the ascending aorta. Current opinion tends to rule out mutually excluding causative mechanisms, recognizing both as important and potentially clinically relevant.
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Affiliation(s)
- Jose F Rodríguez-Palomares
- Department of Cardiology, Hospital Universitari Vall d'Hebron, Barcelona, Spain; Vall d'Hebron Institut de Recerca, Barcelona, Spain; Biomedical Research Networking Center on Cardiovascular Diseases, Instituto de Salud Carlos III, Madrid, Spain; Departament of Medicine, Universitat Autònoma de Barcelona, Bellaterra, Spain.
| | | | - Andrea Guala
- Vall d'Hebron Institut de Recerca, Barcelona, Spain; Biomedical Research Networking Center on Cardiovascular Diseases, Instituto de Salud Carlos III, Madrid, Spain.
| | - Laura Galian-Gay
- Department of Cardiology, Hospital Universitari Vall d'Hebron, Barcelona, Spain
| | - Arturo Evangelista
- Department of Cardiology, Hospital Universitari Vall d'Hebron, Barcelona, Spain; Vall d'Hebron Institut de Recerca, Barcelona, Spain; Biomedical Research Networking Center on Cardiovascular Diseases, Instituto de Salud Carlos III, Madrid, Spain; Departament of Medicine, Universitat Autònoma de Barcelona, Bellaterra, Spain; Instituto del Corazón, Quirónsalud-Teknon, Barcelona, Spain
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Kim T, Tjahjadi NS, He X, van Herwaarden JA, Patel HJ, Burris NS, Figueroa CA. Three-Dimensional Characterization of Aortic Root Motion by Vascular Deformation Mapping. J Clin Med 2023; 12:4471. [PMID: 37445507 DOI: 10.3390/jcm12134471] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2023] [Revised: 06/29/2023] [Accepted: 07/02/2023] [Indexed: 07/15/2023] Open
Abstract
The aorta is in constant motion due to the combination of cyclic loading and unloading with its mechanical coupling to the contractile left ventricle (LV) myocardium. This aortic root motion has been proposed as a marker for aortic disease progression. Aortic root motion extraction techniques have been mostly based on 2D image analysis and have thus lacked a rigorous description of the different components of aortic root motion (e.g., axial versus in-plane). In this study, we utilized a novel technique termed vascular deformation mapping (VDM(D)) to extract 3D aortic root motion from dynamic computed tomography angiography images. Aortic root displacement (axial and in-plane), area ratio and distensibility, axial tilt, aortic rotation, and LV/Ao angles were extracted and compared for four different subject groups: non-aneurysmal, TAA, Marfan, and repair. The repair group showed smaller aortic root displacement, aortic rotation, and distensibility than the other groups. The repair group was also the only group that showed a larger relative in-plane displacement than relative axial displacement. The Marfan group showed the largest heterogeneity in aortic root displacement, distensibility, and age. The non-aneurysmal group showed a negative correlation between age and distensibility, consistent with previous studies. Our results revealed a strong positive correlation between LV/Ao angle and relative axial displacement and a strong negative correlation between LV/Ao angle and relative in-plane displacement. VDM(D)-derived 3D aortic root motion can be used in future studies to define improved boundary conditions for aortic wall stress analysis.
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Affiliation(s)
- Taeouk Kim
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
| | - Nic S Tjahjadi
- Department of Cardiac Surgery, University of Michigan, Ann Arbor, MI 48109, USA
| | - Xuehuan He
- Department of Radiology, University of Michigan, Ann Arbor, MI 48109, USA
| | - J A van Herwaarden
- Department of Vascular Surgery, University Medical Center Utrecht, 3584 CX Utrecht, The Netherlands
| | - Himanshu J Patel
- Department of Cardiac Surgery, University of Michigan, Ann Arbor, MI 48109, USA
| | - Nicholas S Burris
- Department of Radiology, University of Michigan, Ann Arbor, MI 48109, USA
| | - C Alberto Figueroa
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
- Department of Surgery, University of Michigan, Ann Arbor, MI 48109, USA
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Mastrodicasa D, Willemink MJ, Turner VL, Hinostroza V, Codari M, Hanneman K, Ouzounian M, Ocazionez Trujillo D, Afifi RO, Hedgire S, Burris NS, Yang B, Lacomis JM, Gleason TG, Pacini D, Folesani G, Lovato L, Hinzpeter R, Alkadhi H, Stillman AE, Chen EP, van Kuijk SMJ, Schurink GWH, Sailer AM, Bäumler K, Miller DC, Fischbein MP, Fleischmann D. Registry of Aortic Diseases to Model Adverse Events and Progression (ROADMAP) in Uncomplicated Type B Aortic Dissection: Study Design and Rationale. Radiol Cardiothorac Imaging 2022; 4:e220039. [PMID: 36601455 PMCID: PMC9806732 DOI: 10.1148/ryct.220039] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2022] [Revised: 09/01/2022] [Accepted: 11/09/2022] [Indexed: 12/24/2022]
Abstract
Purpose To describe the design and methodological approach of a multicenter, retrospective study to externally validate a clinical and imaging-based model for predicting the risk of late adverse events in patients with initially uncomplicated type B aortic dissection (uTBAD). Materials and Methods The Registry of Aortic Diseases to Model Adverse Events and Progression (ROADMAP) is a collaboration between 10 academic aortic centers in North America and Europe. Two centers have previously developed and internally validated a recently developed risk prediction model. Clinical and imaging data from eight ROADMAP centers will be used for external validation. Patients with uTBAD who survived the initial hospitalization between January 1, 2001, and December 31, 2013, with follow-up until 2020, will be retrospectively identified. Clinical and imaging data from the index hospitalization and all follow-up encounters will be collected at each center and transferred to the coordinating center for analysis. Baseline and follow-up CT scans will be evaluated by cardiovascular imaging experts using a standardized technique. Results The primary end point is the occurrence of late adverse events, defined as aneurysm formation (≥6 cm), rapid expansion of the aorta (≥1 cm/y), fatal or nonfatal aortic rupture, new refractory pain, uncontrollable hypertension, and organ or limb malperfusion. The previously derived multivariable model will be externally validated by using Cox proportional hazards regression modeling. Conclusion This study will show whether a recent clinical and imaging-based risk prediction model for patients with uTBAD can be generalized to a larger population, which is an important step toward individualized risk stratification and therapy.Keywords: CT Angiography, Vascular, Aorta, Dissection, Outcomes Analysis, Aortic Dissection, MRI, TEVAR© RSNA, 2022See also the commentary by Rajiah in this issue.
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Bian Z, Zhong J, Dominic J, Christensen GE, Hatt CR, Burris NS. Validation of a robust method for quantification of three-dimensional growth of the thoracic aorta using deformable image registration. Med Phys 2022; 49:2514-2530. [PMID: 35106769 PMCID: PMC9305918 DOI: 10.1002/mp.15496] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Revised: 12/14/2021] [Accepted: 01/10/2022] [Indexed: 11/06/2022] Open
Abstract
PURPOSE Accurate assessment of thoracic aortic aneurysm (TAA) growth is important for appropriate clinical management. Maximal aortic diameter is the primary metric that is used to assess growth, but it suffers from substantial measurement variability. A recently proposed technique, termed vascular deformation mapping (VDM), is able to quantify three-dimensional aortic growth using clinical computed tomography angiography (CTA) data using an approach based on deformable image registration (DIR). However, the accuracy and robustness of VDM remains undefined given the lack of ground truth from clinical CTA data, and, furthermore, the performance of VDM relative to standard manual diameter measurements is unknown. METHODS To evaluate the performance of the VDM pipeline for quantifying aortic growth, we developed a novel and systematic evaluation process to generate 76 unique synthetic CTA growth phantoms (based on 10 unique cases) with variable degrees and locations of aortic wall deformation. Aortic deformation was quantified using two metrics: area ratio (AR), defined as the ratio of surface area in triangular mesh elements and the magnitude of deformation in the normal direction (DiN) relative to the aortic surface. Using these phantoms, we further investigated the effects on VDM's measurement accuracy resulting from factors that influence the quality of clinical CTA data such as respiratory translations, slice thickness, and image noise. Lastly, we compare the measurement error of VDM TAA growth assessments against two expert raters performing standard diameter measurements of synthetic phantom images. RESULTS Across our population of 76 synthetic growth phantoms, the median absolute error was 0.063 (IQR: 0.073-0.054) for AR and 0.181 mm (interquartile range [IQR]: 0.214-0.143 mm) for DiN. Median relative error was 1.4% for AR and3.3 % $3.3\%$ for DiN at the highest tested noise level (contrast-to-noise ratio [CNR] = 2.66). Error in VDM output increased with slice thickness, with the highest median relative error of 1.5% for AR and 4.1% for DiN at a slice thickness of 2.0 mm. Respiratory motion of the aorta resulted in maximal absolute error of 3% AR and 0.6 mm in DiN, but bulk translations in aortic position had a very small effect on measured AR and DiN values (relative errors< 1 % $< 1\%$ ). VDM-derived measurements of magnitude and location of maximal diameter change demonstrated significantly high accuracy and lower variability compared to two expert manual raters (p < 0.03 $p<0.03$ across all comparisons). CONCLUSIONS VDM yields an accurate, three-dimensional assessment of aortic growth in TAA patients and is robust to factors such as image noise, respiration-induced translations, and differences in patient position. Further, VDM significantly outperformed two expert manual raters in assessing the magnitude and location of aortic growth despite optimized experimental measurement conditions. These results support validation of the VDM technique for accurate quantification of aortic growth in patients and highlight several important advantages over diameter measurements.
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Affiliation(s)
- Zhangxing Bian
- Department of RadiologyUniversity of MichiganAnn ArborMIUSA
- Department of Electrical Engineering and Computer ScienceUniversity of MichiganAnn ArborMIUSA
| | - Jiayang Zhong
- Department of RadiologyUniversity of MichiganAnn ArborMIUSA
- Department of Electrical Engineering and Computer ScienceUniversity of MichiganAnn ArborMIUSA
| | - Jeffrey Dominic
- Department of RadiologyUniversity of MichiganAnn ArborMIUSA
- Department of Electrical Engineering and Computer ScienceUniversity of MichiganAnn ArborMIUSA
| | - Gary E. Christensen
- Department of Electrical and Computer EngineeringUniversity of IowaIowa CityIowaUSA
| | - Charles R. Hatt
- Department of RadiologyUniversity of MichiganAnn ArborMIUSA
- ImbioLLCMinneapolisMinnesotaUSA
| | - Nicholas S. Burris
- Department of RadiologyUniversity of MichiganAnn ArborMIUSA
- Department of Biomedical EngineeringUniversity of MichignaAnn ArborMIUSA
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