1
|
Gebauer AM, Pfaller MR, Braeu FA, Cyron CJ, Wall WA. A homogenized constrained mixture model of cardiac growth and remodeling: analyzing mechanobiological stability and reversal. Biomech Model Mechanobiol 2023; 22:1983-2002. [PMID: 37482576 PMCID: PMC10613155 DOI: 10.1007/s10237-023-01747-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Accepted: 07/06/2023] [Indexed: 07/25/2023]
Abstract
Cardiac growth and remodeling (G&R) patterns change ventricular size, shape, and function both globally and locally. Biomechanical, neurohormonal, and genetic stimuli drive these patterns through changes in myocyte dimension and fibrosis. We propose a novel microstructure-motivated model that predicts organ-scale G&R in the heart based on the homogenized constrained mixture theory. Previous models, based on the kinematic growth theory, reproduced consequences of G&R in bulk myocardial tissue by prescribing the direction and extent of growth but neglected underlying cellular mechanisms. In our model, the direction and extent of G&R emerge naturally from intra- and extracellular turnover processes in myocardial tissue constituents and their preferred homeostatic stretch state. We additionally propose a method to obtain a mechanobiologically equilibrated reference configuration. We test our model on an idealized 3D left ventricular geometry and demonstrate that our model aims to maintain tensional homeostasis in hypertension conditions. In a stability map, we identify regions of stable and unstable G&R from an identical parameter set with varying systolic pressures and growth factors. Furthermore, we show the extent of G&R reversal after returning the systolic pressure to baseline following stage 1 and 2 hypertension. A realistic model of organ-scale cardiac G&R has the potential to identify patients at risk of heart failure, enable personalized cardiac therapies, and facilitate the optimal design of medical devices.
Collapse
Affiliation(s)
- Amadeus M Gebauer
- Institute for Computational Mechanics, Technical University of Munich, 85748, Garching, Germany.
| | - Martin R Pfaller
- Pediatric Cardiology, Stanford Maternal & Child Health Research Institute, and Institute for Computational and Mathematical Engineering, Stanford University, Stanford, USA
| | - Fabian A Braeu
- Ophthalmic Engineering & Innovation Laboratory, Singapore Eye Research Institute, Singapore National Eye Centre, Singapore, Singapore
- Singapore-MIT Alliance for Research and Technology, Singapore, Singapore
- Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore
| | - Christian J Cyron
- Institute of Continuum and Material Mechanics, Hamburg University of Technology, 21073, Hamburg, Germany
- Institute of Material Systems Modeling, Helmholtz-Zentrum Hereon, 21502, Geesthacht, Germany
| | - Wolfgang A Wall
- Institute for Computational Mechanics, Technical University of Munich, 85748, Garching, Germany
| |
Collapse
|
2
|
Navarrete Á, Utrera A, Rivera E, Latorre M, Celentano DJ, García-Herrera CM. An inverse fitting strategy to determine the constrained mixture model parameters: application in patient-specific aorta. Front Bioeng Biotechnol 2023; 11:1301988. [PMID: 38053847 PMCID: PMC10694237 DOI: 10.3389/fbioe.2023.1301988] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2023] [Accepted: 11/06/2023] [Indexed: 12/07/2023] Open
Abstract
The Constrained Mixture Model (CMM) is a novel approach to describe arterial wall mechanics, whose formulation is based on a referential physiological state. The CMM considers the arterial wall as a mixture of load-bearing constituents, each of them with characteristic mass fraction, material properties, and deposition stretch levels from its stress-free state to the in-vivo configuration. Although some reports of this model successfully assess its capabilities, they barely explore experimental approaches to model patient-specific scenarios. In this sense, we propose an iterative fitting procedure of numerical-experimental nature to determine material parameters and deposition stretch values. To this end, the model has been implemented in a finite element framework, and it is calibrated using reported experimental data of descending thoracic aorta. The main results obtained from the proposed procedure consist of a set of material parameters for each constituent. Moreover, a relationship between deposition stretches and residual strain measurements (opening angle and axial stretch) has been numerically proved, establishing a strong consistency between the model and experimental data.
Collapse
Affiliation(s)
- Álvaro Navarrete
- Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, USACH, Santiago de Chile, Chile
| | - Andrés Utrera
- Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, USACH, Santiago de Chile, Chile
| | - Eugenio Rivera
- Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, USACH, Santiago de Chile, Chile
| | - Marcos Latorre
- Center for Research and Innovation in Bioengineering, Universitat Politècnica de València, València, Spain
| | - Diego J. Celentano
- Departamento de Ingeniería Mecánica y Metalúrgica, Pontificia Universidad Católica de Chile, Santiago de Chile, Chile
| | - Claudio M. García-Herrera
- Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, USACH, Santiago de Chile, Chile
| |
Collapse
|
3
|
Dalbosco M, Terzano M, Carniel TA, Fancello EA, Holzapfel GA. A two-scale numerical study on the mechanobiology of abdominal aortic aneurysms. J R Soc Interface 2023; 20:20230472. [PMID: 37907092 PMCID: PMC10618057 DOI: 10.1098/rsif.2023.0472] [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: 08/14/2023] [Accepted: 10/11/2023] [Indexed: 11/02/2023] Open
Abstract
Abdominal aortic aneurysms (AAAs) are a serious condition whose pathophysiology is related to phenomena occurring at different length scales. To gain a better understanding of the disease, this work presents a multi-scale computational study that correlates AAA progression with microstructural and mechanical alterations in the tissue. Macro-scale geometries of a healthy aorta and idealized aneurysms with increasing diameter are developed on the basis of existing experimental data and subjected to physiological boundary conditions. Subsequently, microscopic representative volume elements of the abluminal side of each macro-model are employed to analyse the local kinematics at the cellular scale. The results suggest that the formation of the aneurysm disrupts the micromechanics of healthy tissue, which could trigger collagen growth and remodelling by mechanosensing cells. The resulting changes to the macro-mechanics and microstructure of the tissue seem to establish a new homeostatic state at the cellular scale, at least for the diameter range investigated.
Collapse
Affiliation(s)
- Misael Dalbosco
- Institute of Biomechanics, Graz University of Technology, Graz, Austria
- GRANTE—Department of Mechanical Engineering, Federal University of Santa Catarina, Florianópolis, Santa Catarina, Brazil
| | - Michele Terzano
- Institute of Biomechanics, Graz University of Technology, Graz, Austria
| | - Thiago A. Carniel
- Polytechnic School, Community University of Chapecó Region, Chapecó, Santa Catarina, Brazil
- Graduate Program in Health Sciences, Community University of Chapecó Region, Chapecó, Santa Catarina, Brazil
| | - Eduardo A. Fancello
- GRANTE—Department of Mechanical Engineering, Federal University of Santa Catarina, Florianópolis, Santa Catarina, Brazil
- LEBm—University Hospital, Federal University of Santa Catarina, Florianópolis, Santa Catarina, Brazil
| | - Gerhard A. Holzapfel
- Institute of Biomechanics, Graz University of Technology, Graz, Austria
- Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| |
Collapse
|
4
|
Parikh S, Moerman KM, Ramaekers MJFG, Schalla S, Bidar E, Delhaas T, Reesink K, Huberts W. Biomechanical Characterisation of Thoracic Ascending Aorta with Preserved Pre-Stresses. Bioengineering (Basel) 2023; 10:846. [PMID: 37508873 PMCID: PMC10376551 DOI: 10.3390/bioengineering10070846] [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: 06/07/2023] [Revised: 07/07/2023] [Accepted: 07/11/2023] [Indexed: 07/30/2023] Open
Abstract
Mechanical properties of an aneurysmatic thoracic aorta are potential markers of future growth and remodelling and can help to estimate the risk of rupture. Aortic geometries obtained from routine medical imaging do not display wall stress distribution and mechanical properties. Mechanical properties for a given vessel may be determined from medical images at different physiological pressures using inverse finite element analysis. However, without considering pre-stresses, the estimation of mechanical properties will lack accuracy. In the present paper, we propose and evaluate a mechanical parameter identification technique, which recovers pre-stresses by determining the zero-pressure configuration of the aortic geometry. We first validated the method on a cylindrical geometry and subsequently applied it to a realistic aortic geometry. The verification of the assessed parameters was performed using synthetically generated reference data for both geometries. The method was able to estimate the true mechanical properties with an accuracy ranging from 98% to 99%.
Collapse
Affiliation(s)
- Shaiv Parikh
- Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, 6229 ER Maastricht, The Netherlands
| | - Kevin M Moerman
- Department of Mechanical Engineering, University of Galway, H91 TK33 Galway, Ireland
| | - Mitch J F G Ramaekers
- Department of Cardiology, Heart & Vascular Centre, Maastricht University Medical Centre, 6229 HX Maastricht, The Netherlands
- Department of Radiology and Nuclear Medicine, Maastricht University Medical Centre, 6229 HX Maastricht, The Netherlands
| | - Simon Schalla
- Department of Cardiology, Heart & Vascular Centre, Maastricht University Medical Centre, 6229 HX Maastricht, The Netherlands
- Department of Radiology and Nuclear Medicine, Maastricht University Medical Centre, 6229 HX Maastricht, The Netherlands
| | - Elham Bidar
- Department of Cardiothoracic Surgery, Heart & Vascular Centre, Maastricht University Medical Centre, 6229 HX Maastricht, The Netherlands
| | - Tammo Delhaas
- Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, 6229 ER Maastricht, The Netherlands
| | - Koen Reesink
- Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, 6229 ER Maastricht, The Netherlands
| | - Wouter Huberts
- Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, 6229 ER Maastricht, The Netherlands
- Department of Biomedical Engineering, Cardiovascular Biomechanics, Eindhoven University of Technology, 5612 AE Eindhoven, The Netherlands
| |
Collapse
|
5
|
Wang X, Ghayesh MH, Kotousov A, Zander AC, Dawson JA, Psaltis PJ. Fluid-structure interaction study for biomechanics and risk factors in Stanford type A aortic dissection. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2023:e3736. [PMID: 37258411 DOI: 10.1002/cnm.3736] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Revised: 04/04/2023] [Accepted: 05/16/2023] [Indexed: 06/02/2023]
Abstract
Aortic dissection is a life-threatening condition with a rising prevalence in the elderly population, possibly as a consequence of the increasing population life expectancy. Untreated aortic dissection can lead to myocardial infarction, aortic branch malperfusion or occlusion, rupture, aneurysm formation and death. This study aims to assess the potential of a biomechanical model in predicting the risks of a non-dilated thoracic aorta with Stanford type A dissection. To achieve this, a fully coupled fluid-structure interaction model was developed under realistic blood flow conditions. This model of the aorta was developed by considering three-dimensional artery geometry, multiple artery layers, hyperelastic artery wall, in vivo-based physiological time-varying blood velocity profiles, and non-Newtonian blood behaviours. The results demonstrate that in a thoracic aorta with Stanford type A dissection, the wall shear stress (WSS) is significantly low in the ascending aorta and false lumen, leading to potential aortic dilation and thrombus formation. The results also reveal that the WSS is highly related to blood flow patterns. The aortic arch region near the brachiocephalic and left common carotid artery is prone to rupture, showing a good agreement with the clinical reports. The results have been translated into their potential clinical relevance by revealing the role of the stress state, WSS and flow characteristics as the main parameters affecting lesion progression, including rupture and aneurysm. The developed model can be tailored for patient-specific studies and utilised as a predictive tool to estimate aneurysm growth and initiation of wall rupture inside the human thoracic aorta.
Collapse
Affiliation(s)
- Xiaochen Wang
- School of Mechanical Engineering, University of Adelaide, Adelaide, Australia
| | - Mergen H Ghayesh
- School of Mechanical Engineering, University of Adelaide, Adelaide, Australia
| | - Andrei Kotousov
- School of Mechanical Engineering, University of Adelaide, Adelaide, Australia
| | - Anthony C Zander
- School of Mechanical Engineering, University of Adelaide, Adelaide, Australia
| | - Joseph A Dawson
- Department of Vascular & Endovascular Surgery, Royal Adelaide Hospital, Adelaide, Australia
- Trauma Surgery Unit, Royal Adelaide Hospital, Adelaide, Australia
- Adelaide Medical School, University of Adelaide, Adelaide, Australia
| | - Peter J Psaltis
- Adelaide Medical School, University of Adelaide, Adelaide, Australia
- Vascular Research Centre, Lifelong Health Theme, South Australian Health & Medical Research Institute (SAHMRI), Adelaide, Australia
- Department of Cardiology, Central Adelaide Local Health Network, Adelaide, Australia
| |
Collapse
|
6
|
Nolte D, Bertoglio C. Inverse problems in blood flow modeling: A review. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2022; 38:e3613. [PMID: 35526113 PMCID: PMC9541505 DOI: 10.1002/cnm.3613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/17/2021] [Revised: 12/29/2021] [Accepted: 03/18/2022] [Indexed: 06/14/2023]
Abstract
Mathematical and computational modeling of the cardiovascular system is increasingly providing non-invasive alternatives to traditional invasive clinical procedures. Moreover, it has the potential for generating additional diagnostic markers. In blood flow computations, the personalization of spatially distributed (i.e., 3D) models is a key step which relies on the formulation and numerical solution of inverse problems using clinical data, typically medical images for measuring both anatomy and function of the vasculature. In the last years, the development and application of inverse methods has rapidly expanded most likely due to the increased availability of data in clinical centers and the growing interest of modelers and clinicians in collaborating. Therefore, this work aims to provide a wide and comparative overview of literature within the last decade. We review the current state of the art of inverse problems in blood flows, focusing on studies considering fully dimensional fluid and fluid-solid models. The relevant physical models and hemodynamic measurement techniques are introduced, followed by a survey of mathematical data assimilation approaches used to solve different kinds of inverse problems, namely state and parameter estimation. An exhaustive discussion of the literature of the last decade is presented, structured by types of problems, models and available data.
Collapse
Affiliation(s)
- David Nolte
- Bernoulli InstituteUniversity of GroningenGroningenThe Netherlands
- Center for Mathematical ModelingUniversidad de ChileSantiagoChile
- Department of Fluid DynamicsTechnische Universität BerlinBerlinGermany
| | | |
Collapse
|
7
|
How does prestrain in the tympanic membrane affect middle-ear function? A finite-element model study in rabbit. J Mech Behav Biomed Mater 2022; 131:105261. [DOI: 10.1016/j.jmbbm.2022.105261] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Revised: 04/27/2022] [Accepted: 04/30/2022] [Indexed: 11/20/2022]
|
8
|
He Y, Northrup H, Le H, Cheung AK, Berceli SA, Shiu YT. Medical Image-Based Computational Fluid Dynamics and Fluid-Structure Interaction Analysis in Vascular Diseases. Front Bioeng Biotechnol 2022; 10:855791. [PMID: 35573253 PMCID: PMC9091352 DOI: 10.3389/fbioe.2022.855791] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2022] [Accepted: 04/08/2022] [Indexed: 01/17/2023] Open
Abstract
Hemodynamic factors, induced by pulsatile blood flow, play a crucial role in vascular health and diseases, such as the initiation and progression of atherosclerosis. Computational fluid dynamics, finite element analysis, and fluid-structure interaction simulations have been widely used to quantify detailed hemodynamic forces based on vascular images commonly obtained from computed tomography angiography, magnetic resonance imaging, ultrasound, and optical coherence tomography. In this review, we focus on methods for obtaining accurate hemodynamic factors that regulate the structure and function of vascular endothelial and smooth muscle cells. We describe the multiple steps and recent advances in a typical patient-specific simulation pipeline, including medical imaging, image processing, spatial discretization to generate computational mesh, setting up boundary conditions and solver parameters, visualization and extraction of hemodynamic factors, and statistical analysis. These steps have not been standardized and thus have unavoidable uncertainties that should be thoroughly evaluated. We also discuss the recent development of combining patient-specific models with machine-learning methods to obtain hemodynamic factors faster and cheaper than conventional methods. These critical advances widen the use of biomechanical simulation tools in the research and potential personalized care of vascular diseases.
Collapse
Affiliation(s)
- Yong He
- Division of Vascular Surgery and Endovascular Therapy, University of Florida, Gainesville, FL, United States
| | - Hannah Northrup
- Department of Biomedical Engineering, University of Utah, Salt Lake City, UT, United States
- Division of Nephrology and Hypertension, Department of Internal Medicine, University of Utah, Salt Lake City, UT, United States
| | - Ha Le
- Division of Nephrology and Hypertension, Department of Internal Medicine, University of Utah, Salt Lake City, UT, United States
| | - Alfred K. Cheung
- Division of Nephrology and Hypertension, Department of Internal Medicine, University of Utah, Salt Lake City, UT, United States
- Veterans Affairs Salt Lake City Healthcare System, Salt Lake City, UT, United States
| | - Scott A. Berceli
- Division of Vascular Surgery and Endovascular Therapy, University of Florida, Gainesville, FL, United States
- Vascular Surgery Section, Malcom Randall Veterans Affairs Medical Center, Gainesville, FL, United States
| | - Yan Tin Shiu
- Division of Nephrology and Hypertension, Department of Internal Medicine, University of Utah, Salt Lake City, UT, United States
- Veterans Affairs Salt Lake City Healthcare System, Salt Lake City, UT, United States
- *Correspondence: Yan Tin Shiu,
| |
Collapse
|
9
|
Philip NT, Patnaik BSV, Sudhir BJ. Hemodynamic simulation of abdominal aortic aneurysm on idealised models: Investigation of stress parameters during disease progression. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2022; 213:106508. [PMID: 34800807 DOI: 10.1016/j.cmpb.2021.106508] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Accepted: 10/25/2021] [Indexed: 06/13/2023]
Abstract
BACKGROUND AND OBJECTIVE Analysis and prediction of rupture risk of abdominal aortic aneurysms (AAA) facilitates planning for surgical interventions and assessment of plausible treatment modalities. Present approach of using maximum diameter criterion, is giving way to hemodynamic and bio-mechanical based predictors in conjunction with Computational fluid dynamic (CFD) simulations. Detailed studies on hemodynamic and bio-mechanical parameters at the stage of maximum growth/rupture is of practical importance to the clinical community. However, understanding the changes in these parameters at different stages of growth, will be useful for clinicians, in planning routine monitoring to reduce the risk of sudden rupture. This is particularly useful in medical resource starved nations. Present study investigates the hemodynamic and bio-mechanical changes occurring during the growth stages of aortic aneurysms using fluid structure interaction (FSI) studies. METHOD Six idealized fusiform aneurysm models spanning high (shorter) and low (longer) values of the shape index (DHr), have been analysed at three different stages of growth viz, a Dmax of 3.5cm, 4.25cm, 5cm. Pulsatile Newtonian blood flow, passing through an elastic arterial vessel wall with uniform thickness is assumed. Two-way coupled fluid structure interaction have been employed for the numerical simulation of blood flow dynamics and arterial wall mechanics. RESULTS Wall shear stress (WSS) parameters and vonmises stress indicators, co-relating rupture and thrombus formation, have been extracted and reported, at each growth stage. When the aneurysm progresses in diameter, the areas recording abnormally low TAWSS, as well as areas of high/low OSI were found to increase at different rates for shorter and longer aneurysms. Moreover, drastic increase in the maximum wall stresses (MWS) and wall displacement were observed as the aneurysm approached the critical diameter. CONCLUSION Hemodynamic predictors were found to be highly dependent on the shape index (DHr), when the aneurysm was small, whereas significant influence of DHr on the wall stresses happens, as the aneurysm approaches the critical diameter. Inconsistent variation of these indicators exhibited by shorter aneurysms (high DHr) at different growth stages, demands routine monitoring (using scans), of such aneurysms, to prevent unexpected rupture.
Collapse
Affiliation(s)
- Nimmy Thankom Philip
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, 600036, India
| | - B S V Patnaik
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, 600036, India
| | - B J Sudhir
- Sree Chitra Tirunal Institute for Medical Sciences and Technology, Trivandrum, 695011, Kerala.
| |
Collapse
|
10
|
Huang Y, Wang S, Luo T, Du MHF, Sun C, Sadat U, Schönlieb CB, Gillard JH, Zhang J, Teng Z. Estimation of the zero-pressure computational start shape of atherosclerotic plaques: Improving the backward displacement method with deformation gradient tensor. J Biomech 2022; 131:110910. [PMID: 34954525 DOI: 10.1016/j.jbiomech.2021.110910] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Revised: 10/16/2021] [Accepted: 12/10/2021] [Indexed: 01/06/2023]
Abstract
Advances in medical imaging have enabled patient-specific biomechanical modelling of arterial lesions such as atherosclerosis and aneurysm. Geometry acquired from in-vivo imaging is already pressurized and a zero-pressure computational start shape needs to be identified. The backward displacement algorithm was proposed to solve this inverse problem, utilizing fixed-point iterations to gradually approach the start shape. However, classical fixed-point implementations were reported with suboptimal convergence properties under large deformations. In this paper, a dynamic learning rate guided by the deformation gradient tensor was introduced to control the geometry update. The effectiveness of this new algorithm was demonstrated for both idealized and patient-specific models. The proposed algorithm led to faster convergence by accelerating the initial steps and helped to avoid the non-convergence in large-deformation problems.
Collapse
Affiliation(s)
- Yuan Huang
- EPSRC Cambridge Mathematics of Information in Healthcare, University of Cambridge, Cambridge, UK; Department of Radiology, University of Cambridge, Cambridge, UK
| | - Shuo Wang
- Department of Radiology, University of Cambridge, Cambridge, UK; Shanghai Key Laboratory of Medical Imaging Computing and Computer Assisted Intervention, Fudan University, Shanghai, China; Digital Medical Research Center, School of Basic Medical Sciences, Fudan University, Shanghai, China
| | - Tao Luo
- Department of Engineering, University of Cambridge, Cambridge, UK
| | - Michael Hong-Fei Du
- Department of Radiology, University of Cambridge, Cambridge, UK; John Farman Intensive Care Unit, Cambridge University Hospitals NHS Foundation Trust, Cambridge, UK
| | - Chang Sun
- Department of Radiology, University of Cambridge, Cambridge, UK
| | - Umar Sadat
- Cambridge Vascular Unit, Cambridge University Hospitals NHS Foundation Trust, Cambridge, UK
| | - Carola-Bibiane Schönlieb
- EPSRC Cambridge Mathematics of Information in Healthcare, University of Cambridge, Cambridge, UK; Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK
| | | | - Jianjun Zhang
- Department of Radiology, Zhejiang Hospital, Zhejiang University School of Medicine, Hangzhou, China
| | - Zhongzhao Teng
- Department of Radiology, University of Cambridge, Cambridge, UK; Nanjing Jingsan Medical Science and Technology, Ltd, Jiangsu, China.
| |
Collapse
|
11
|
Liu M, Liang L, Ismail Y, Dong H, Lou X, Iannucci G, Chen EP, Leshnower BG, Elefteriades JA, Sun W. Computation of a probabilistic and anisotropic failure metric on the aortic wall using a machine learning-based surrogate model. Comput Biol Med 2021; 137:104794. [PMID: 34482196 DOI: 10.1016/j.compbiomed.2021.104794] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2021] [Revised: 08/20/2021] [Accepted: 08/21/2021] [Indexed: 01/15/2023]
Abstract
Scalar-valued failure metrics are commonly used to assess the risk of aortic aneurysm rupture and dissection, which occurs under hypertensive blood pressures brought on by extreme emotional or physical stress. To compute failure metrics under an elevated blood pressure, a classical patient-specific computer model consists of multiple computation steps involving inverse and forward analyses. These classical procedures may be impractical for time-sensitive clinical applications that require prompt feedback to clinicians. In this study, we developed a machine learning-based surrogate model to directly predict a probabilistic and anisotropic failure metric, namely failure probability (FP), on the aortic wall using aorta geometries at the systolic and diastolic phases. Ascending thoracic aortic aneurysm (ATAA) geometries of 60 patients were obtained from their CT scans, and biaxial mechanical testing data of ATAA tissues from 79 patients were collected. Finite element simulations were used to generate datasets for training, validation, and testing of the ML-surrogate model. The testing results demonstrated that the ML-surrogate can compute the maximum FP failure metric, with 0.42% normalized mean absolute error, in 1 s. To compare the performance of the ML-predicted probabilistic FP metric with other isotropic or deterministic metrics, a numerical case study was performed using synthetic "baseline" data. Our results showed that the probabilistic FP metric had more discriminative power than the deterministic Tsai-Hill metric, isotropic maximum principal stress, and aortic diameter criterion.
Collapse
Affiliation(s)
- Minliang Liu
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Liang Liang
- Department of Computer Science, University of Miami, Coral Gables, FL, USA
| | - Yasmeen Ismail
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Hai Dong
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Xiaoying Lou
- Emory University School of Medicine, Atlanta, GA, USA
| | - Glen Iannucci
- Emory University School of Medicine, Atlanta, GA, USA
| | - Edward P Chen
- Emory University School of Medicine, Atlanta, GA, USA
| | | | | | - Wei Sun
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA.
| |
Collapse
|
12
|
Teixeira FS, Neufeld E, Kuster N, Watton PN. Modeling intracranial aneurysm stability and growth: an integrative mechanobiological framework for clinical cases. Biomech Model Mechanobiol 2020; 19:2413-2431. [PMID: 32533497 PMCID: PMC7603456 DOI: 10.1007/s10237-020-01351-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2019] [Accepted: 05/12/2020] [Indexed: 11/03/2022]
Abstract
We present a novel patient-specific fluid-solid-growth framework to model the mechanobiological state of clinically detected intracranial aneurysms (IAs) and their evolution. The artery and IA sac are modeled as thick-walled, non-linear elastic fiber-reinforced composites. We represent the undulation distribution of collagen fibers: the adventitia of the healthy artery is modeled as a protective sheath whereas the aneurysm sac is modeled to bear load within physiological range of pressures. Initially, we assume the detected IA is stable and then consider two flow-related mechanisms to drive enlargement: (1) low wall shear stress; (2) dysfunctional endothelium which is associated with regions of high oscillatory flow. Localized collagen degradation and remodelling gives rise to formation of secondary blebs on the aneurysm dome. Restabilization of blebs is achieved by remodelling of the homeostatic collagen fiber stretch distribution. This integrative mechanobiological modelling workflow provides a step towards a personalized risk-assessment and treatment of clinically detected IAs.
Collapse
Affiliation(s)
| | - Esra Neufeld
- IT’IS Foundation & ETH Zürich, Zürich, Switzerland
| | - Niels Kuster
- IT’IS Foundation & ETH Zürich, Zürich, Switzerland
| | - Paul N. Watton
- Department of Computer Science, Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield, UK
- Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, USA
| |
Collapse
|
13
|
Sajjadinia SS, Carpentieri B, Holzapfel GA. A backward pre-stressing algorithm for efficient finite element implementation of in vivo material and geometrical parameters into fibril-reinforced mixture models of articular cartilage. J Mech Behav Biomed Mater 2020; 114:104203. [PMID: 33234496 DOI: 10.1016/j.jmbbm.2020.104203] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2020] [Revised: 11/06/2020] [Accepted: 11/09/2020] [Indexed: 10/23/2022]
Abstract
Classical continuum mechanics has been widely used for implementation of the material models of articular cartilage (AC) mainly with the aid of the finite element (FE) method, which, in many cases, considers the stress-free configuration as the initial configuration. On the contrary, the AC experimental tests typically begin with the pre-stressed state of both material and geometrical properties. Indeed, imposing the initial pre-stress onto AC models with the in vivo values as the initial state would result in nonphysiologically expansion of the FE mesh due to the soft nature of AC. This change in the model configuration can also affect the material behavior kinematically in the mixture models of cartilage due to the intrinsic compressibility of the tissue. Although several different fixed-point backward algorithms, as the most straightforward pre-stressing methods, have already been developed to incorporate these initial conditions into FE models iteratively, such methods focused merely on the geometrical parameters, and they omitted the material variations of the anisotropic mixture models of AC. To address this issue, we propose an efficient algorithm generalizing the backward schemes to restore stress-free conditions by optimizing both the involving variables, and we hypothesize that it can affect the results considerably. To this end, a comparative simulation was implemented on an advanced and validated multiphasic model by the new and conventional algorithms. The results are in support of the hypothesis, as in our illustrative general AC model, the material parameters experienced a maximum error of 16% comparing to the initial in vivo data when the older algorithm was employed, and it led to a maximum variation of 44% in the recorded stresses comparing to the results of the new method. We conclude that our methodology enhanced the model fidelity, and it is applicable in most of the existing FE solvers for future mixture studies with accurate stress distributions.
Collapse
Affiliation(s)
| | - Bruno Carpentieri
- Faculty of Computer Science, Free University of Bozen-Bolzano, Bozen-Bolzano, 39100, Italy.
| | - Gerhard A Holzapfel
- Institute of Biomechanics, Graz University of Technology, Stremayrgasse 16/2, Graz, 8010, Austria; Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| |
Collapse
|
14
|
Nama N, Aguirre M, Humphrey JD, Figueroa CA. A nonlinear rotation-free shell formulation with prestressing for vascular biomechanics. Sci Rep 2020; 10:17528. [PMID: 33067508 PMCID: PMC7567841 DOI: 10.1038/s41598-020-74277-5] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2020] [Accepted: 09/28/2020] [Indexed: 02/01/2023] Open
Abstract
We implement a nonlinear rotation-free shell formulation capable of handling large deformations for applications in vascular biomechanics. The formulation employs a previously reported shell element that calculates both the membrane and bending behavior via displacement degrees of freedom for a triangular element. The thickness stretch is statically condensed to enforce vessel wall incompressibility via a plane stress condition. Consequently, the formulation allows incorporation of appropriate 3D constitutive material models. We also incorporate external tissue support conditions to model the effect of surrounding tissue. We present theoretical and variational details of the formulation and verify our implementation against axisymmetric results and literature data. We also adapt a previously reported prestress methodology to identify the unloaded configuration corresponding to the medically imaged in vivo vessel geometry. We verify the prestress methodology in an idealized bifurcation model and demonstrate the significance of including prestress. Lastly, we demonstrate the robustness of our formulation via its application to mouse-specific models of arterial mechanics using an experimentally informed four-fiber constitutive model.
Collapse
Affiliation(s)
- Nitesh Nama
- grid.214458.e0000000086837370Department of Surgery, University of Michigan, Ann Arbor, MI USA
| | - Miquel Aguirre
- grid.6279.a0000 0001 2158 1682Mines Saint-Étienne, Univ Lyon, Univ Jean Monnet, INSERM, U 1059 Sainbiose, Centre CIS, 42023 Saint-Étienne, France
| | - Jay D. Humphrey
- grid.47100.320000000419368710Department of Biomedical Engineering, Yale University, New Haven, CT USA
| | - C. Alberto Figueroa
- grid.214458.e0000000086837370Department of Surgery, University of Michigan, Ann Arbor, MI USA ,grid.214458.e0000000086837370Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI USA
| |
Collapse
|
15
|
Adouni M, Faisal TR, Dhaher YY. Computational frame of ligament in situ strain in a full knee model. Comput Biol Med 2020; 126:104012. [PMID: 33045650 DOI: 10.1016/j.compbiomed.2020.104012] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2020] [Revised: 09/14/2020] [Accepted: 09/17/2020] [Indexed: 01/12/2023]
Abstract
The biomechanical function of connective tissues in a knee joint is to stabilize the kinematics-kinetics of the joint by augmenting its stiffness and limiting excessive coupled motion. The connective tissues are characterized by an in vivo reference configuration (in situ strain) that would significantly contribute to the mechanical response of the knee joint. In this work, a novel iterative method for computing the in situ strain at reference configuration was presented. The framework used an in situ strain gradient approach (deformed reference configuration) and a detailed finite element (FE) model of the knee joint. The effect of the predicted initial configuration on the mechanical response of the joint was then investigated under joint axial compression, passive flexion, and coupled rotations (adduction and internal), and during the stance phase of gait. The inclusion of the reference configuration has a minimal effect on the knee joint mechanics under axial compression, passive flexion, and at two instances (0% and 50%) of the stance phase of gait. However, the presence of the ligaments in situ strains significantly increased the joint stiffness under passive adduction and internal rotations, as well as during the other simulated instances (25%, 75% and 100%) of the stance phase of gait. Also, these parameters substantially altered the local loading state of the ligaments and resulted in better agreement with the literature during joint flexion. Therefore, the proposed computational framework of ligament in situ strain will help to overcome the challenges in considering this crucial biological aspect during knee joint modeling. Besides, the current construct is advantageous for a better understanding of the mechanical behavior of knee ligaments under physiological and pathological states and provide relevant information in the design of reconstructive treatments and artificial grafts.
Collapse
Affiliation(s)
- Malek Adouni
- Northwestern University, Physical Medicine and Rehabilitation Department, 345 East Superior Street, Chicago, IL, 60611, United States; Australian College of Kuwait, Mechanical Engineering Department, East Meshrif, P.O. Box 1411, Kuwait.
| | - Tanvir R Faisal
- Department of Mechanical Engineering, University of Louisiana at Lafayette, LA, 70508, USA
| | - Yasin Y Dhaher
- Northwestern University, Physical Medicine and Rehabilitation Department, 345 East Superior Street, Chicago, IL, 60611, United States; Department of Physical Medicine and Rehabilitation, University of Texas Southwest, Dallas, TX, United States; Department of Orthopedic Surgery, University of Texas Southwest, Dallas, TX, United States; Bioengineering, University of Texas Southwest, Dallas, TX, United States
| |
Collapse
|
16
|
Liu M, Liang L, Sulejmani F, Lou X, Iannucci G, Chen E, Leshnower B, Sun W. Identification of in vivo nonlinear anisotropic mechanical properties of ascending thoracic aortic aneurysm from patient-specific CT scans. Sci Rep 2019; 9:12983. [PMID: 31506507 PMCID: PMC6737100 DOI: 10.1038/s41598-019-49438-w] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2019] [Accepted: 08/24/2019] [Indexed: 12/15/2022] Open
Abstract
Accurate identification of in vivo nonlinear, anisotropic mechanical properties of the aortic wall of individual patients remains to be one of the critical challenges in the field of cardiovascular biomechanics. Since only the physiologically loaded states of the aorta are given from in vivo clinical images, inverse approaches, which take into account of the unloaded configuration, are needed for in vivo material parameter identification. Existing inverse methods are computationally expensive, which take days to weeks to complete for a single patient, inhibiting fast feedback for clinicians. Moreover, the current inverse methods have only been evaluated using synthetic data. In this study, we improved our recently developed multi-resolution direct search (MRDS) approach and the computation time cost was reduced to 1~2 hours. Using the improved MRDS approach, we estimated in vivo aortic tissue elastic properties of two ascending thoracic aortic aneurysm (ATAA) patients from pre-operative gated CT scans. For comparison, corresponding surgically-resected aortic wall tissue samples were obtained and subjected to planar biaxial tests. Relatively close matches were achieved for the in vivo-identified and ex vivo-fitted stress-stretch responses. It is hoped that further development of this inverse approach can enable an accurate identification of the in vivo material parameters from in vivo image data.
Collapse
Affiliation(s)
- Minliang Liu
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Liang Liang
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA.,Department of Computer Science, University of Miami, Coral Gables, FL, USA
| | - Fatiesa Sulejmani
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Xiaoying Lou
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA.,Emory University School of Medicine, Atlanta, GA, USA
| | - Glen Iannucci
- Emory University School of Medicine, Atlanta, GA, USA
| | - Edward Chen
- Emory University School of Medicine, Atlanta, GA, USA
| | | | - Wei Sun
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA.
| |
Collapse
|
17
|
Maes L, Fehervary H, Vastmans J, Mousavi SJ, Avril S, Famaey N. Constrained mixture modeling affects material parameter identification from planar biaxial tests. J Mech Behav Biomed Mater 2019; 95:124-135. [DOI: 10.1016/j.jmbbm.2019.03.029] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2019] [Revised: 03/07/2019] [Accepted: 03/29/2019] [Indexed: 12/11/2022]
|
18
|
Misiulis E, Džiugys A, Navakas R, Petkus V. A comparative study of methods used to generate the arterial fiber structure in a clinically relevant numerical analysis. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2019; 35:e3194. [PMID: 30817080 DOI: 10.1002/cnm.3194] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2018] [Revised: 02/13/2019] [Accepted: 02/16/2019] [Indexed: 06/09/2023]
Abstract
The advanced constitutive material models of artery wall require the definition of the mean collagen fiber directions in the material configuration. There are several proposed methods; however, it is unclear how much does the fiber structures obtained by these methods differ one from the other and how much this difference may affect the results of the structural analysis of a clinically relevant scenario. Therefore, in this paper, we address this issue by presenting the results of the comparative study of our developed and currently state-of-the-art fiber definition methods. In addition, we present the verification of our developed numerical model that incorporates the extended Holzapfel-Gasser-Ogden (HGO) constitutive material model and the generalized prestressing algorithm (GPA). In the case of the patient-specific internal carotid artery (ICA), the percentage error of the mean fiber directions defined by different methods does not exceed 17.73% (at least 0.05%, at most 81.82%) and has negligible effect on the stress levels, as the percentage error of the mean circumferential Cauchy stress does not exceed 0.1%. Both fiber definition methods produce comparable fiber structure, but our proposed method has an advantage, as it does not depend on method and software used to model the arterial wall mechanics.
Collapse
Affiliation(s)
- Edgaras Misiulis
- Laboratory of Combustion Processes, Lithuanian Energy Institute, Kaunas, Lithuania
- Kaunas University of Technology, K. Donelaičio St. 73, 44249, Kaunas, Lithuania
| | - Algis Džiugys
- Laboratory of Combustion Processes, Lithuanian Energy Institute, Kaunas, Lithuania
- Kaunas University of Technology, K. Donelaičio St. 73, 44249, Kaunas, Lithuania
| | - Robertas Navakas
- Laboratory of Combustion Processes, Lithuanian Energy Institute, Kaunas, Lithuania
| | - Vytautas Petkus
- Health Telematics Science Institute, Kaunas University of Technology, Kaunas, Lithuania
| |
Collapse
|
19
|
Liu M, Liang L, Sun W. Estimation of in vivo constitutive parameters of the aortic wall using a machine learning approach. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2019; 347:201-217. [PMID: 31160830 PMCID: PMC6544444 DOI: 10.1016/j.cma.2018.12.030] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
The patient-specific biomechanical analysis of the aorta requires the quantification of the in vivo mechanical properties of individual patients. Current inverse approaches have attempted to estimate the nonlinear, anisotropic material parameters from in vivo image data using certain optimization schemes. However, since such inverse methods are dependent on iterative nonlinear optimization, these methods are highly computation-intensive. A potential paradigm-changing solution to the bottleneck associated with patient-specific computational modeling is to incorporate machine learning (ML) algorithms to expedite the procedure of in vivo material parameter identification. In this paper, we developed an ML-based approach to estimate the material parameters from three-dimensional aorta geometries obtained at two different blood pressure (i.e., systolic and diastolic) levels. The nonlinear relationship between the two loaded shapes and the constitutive parameters are established by an ML-model, which was trained and tested using finite element (FE) simulation datasets. Cross-validations were used to adjust the ML-model structure on a training/validation dataset. The accuracy of the ML-model was examined using a testing dataset.
Collapse
Affiliation(s)
- Minliang Liu
- Tissue Mechanics Laboratory The Wallace H. Coulter Department of Biomedical Engineering Georgia Institute of Technology and Emory University, Atlanta, GA
| | - Liang Liang
- Tissue Mechanics Laboratory The Wallace H. Coulter Department of Biomedical Engineering Georgia Institute of Technology and Emory University, Atlanta, GA
| | - Wei Sun
- Tissue Mechanics Laboratory The Wallace H. Coulter Department of Biomedical Engineering Georgia Institute of Technology and Emory University, Atlanta, GA
| |
Collapse
|
20
|
Qiu TY, Zhao LG, Song M. A Computational Study of Mechanical Performance of Bioresorbable Polymeric Stents with Design Variations. Cardiovasc Eng Technol 2018; 10:46-60. [DOI: 10.1007/s13239-018-00397-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/04/2018] [Accepted: 11/30/2018] [Indexed: 10/27/2022]
|
21
|
Liu M, Liang L, Liu H, Zhang M, Martin C, Sun W. On the computation of in vivo transmural mean stress of patient-specific aortic wall. Biomech Model Mechanobiol 2018; 18:387-398. [PMID: 30413984 DOI: 10.1007/s10237-018-1089-5] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2018] [Accepted: 10/24/2018] [Indexed: 11/29/2022]
Abstract
It is well known that residual deformations/stresses alter the mechanical behavior of arteries, e.g., the pressure-diameter curves. In an effort to enable personalized analysis of the aortic wall stress, approaches have been developed to incorporate experimentally derived residual deformations into in vivo loaded geometries in finite element simulations using thick-walled models. Solid elements are typically used to account for "bending-like" residual deformations. Yet, the difficulty in obtaining patient-specific residual deformations and material properties has become one of the biggest challenges of these thick-walled models. In thin-walled models, fortunately, static determinacy offers an appealing prospect that allows for the calculation of the thin-walled membrane stress without patient-specific material properties. The membrane stress can be computed using forward analysis by enforcing an extremely stiff material property as penalty treatment, which is referred to as the forward penalty approach. However, thin-walled membrane elements, which have zero bending stiffness, are incompatible with the residual deformations, and therefore, it is often stated as a limitation of thin-walled models. In this paper, by comparing the predicted stresses from thin-walled models and thick-walled models, we demonstrate that the transmural mean stress is approximately the same for the two models and can be readily obtained from in vivo clinical images without knowing the patient-specific material properties and residual deformations. Computation of patient-specific mean stress can be greatly simplified by using the forward penalty approach, which may be clinically valuable.
Collapse
Affiliation(s)
- Minliang Liu
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Technology Enterprise Park, Room 206, 387 Technology Circle, Atlanta, GA, 30313-2412, USA
| | - Liang Liang
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Technology Enterprise Park, Room 206, 387 Technology Circle, Atlanta, GA, 30313-2412, USA
| | - Haofei Liu
- Department of Mechanics, Tianjin University, 92 Weijin Road, Tianjin, 300072, China
| | - Ming Zhang
- Department of Mechanics, Tianjin University, 92 Weijin Road, Tianjin, 300072, China
| | - Caitlin Martin
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Technology Enterprise Park, Room 206, 387 Technology Circle, Atlanta, GA, 30313-2412, USA
| | - Wei Sun
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Technology Enterprise Park, Room 206, 387 Technology Circle, Atlanta, GA, 30313-2412, USA.
| |
Collapse
|
22
|
A modular inverse elastostatics approach to resolve the pressure-induced stress state for in vivo imaging based cardiovascular modeling. J Mech Behav Biomed Mater 2018; 85:124-133. [DOI: 10.1016/j.jmbbm.2018.05.032] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2018] [Revised: 03/28/2018] [Accepted: 05/22/2018] [Indexed: 01/18/2023]
|
23
|
Wang X, Eriksson TSE, Ricken T, Pierce DM. On incorporating osmotic prestretch/prestress in image-driven finite element simulations of cartilage. J Mech Behav Biomed Mater 2018; 86:409-422. [PMID: 30031245 DOI: 10.1016/j.jmbbm.2018.06.014] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2017] [Revised: 04/20/2018] [Accepted: 06/07/2018] [Indexed: 10/28/2022]
Abstract
Medical imaging performed in vivo captures geometries under Donnan osmotic loading, even when the articulating joint is otherwise mechanically unloaded. Hence patient-specific finite element (FE) models constructed from such medical images of cartilage represent osmotically induced prestretched/prestressed states. When applying classical modeling approaches to patient-specific simulations of cartilage a theoretical inconsistency arises: the in-vivo imaged geometry (used to construct the model) is not an unloaded, stress-free reference configuration. Furthermore when fitting nonlinear constitutive models that include osmotic swelling (to obtain material parameters), if one assumes that experimental data-generated from osmotically loaded cartilage-begin from a stress-free reference configuration the fitted stress-stretch relationship (parameters) obtained will actually describe a different behavior. In this study we: (1) establish a practical computational method to include osmotically induced prestretch/prestress in image-driven simulations of cartilage; and (2) investigate the influence of considering the prestretched/prestressed state both when fitting fiber-reinforced, biphasic constitutive models of cartilage that include osmotic swelling and when simulating cartilage responses. Our results highlight the importance of determining the prestretched/prestressed state within cartilage induced by osmotic loading in the imaged configuration prior to solving boundary value problems of interest. With our new constitutive model and modeling methods, we aim to improve the fidelity of FE-based, patient-specific biomechanical simulations of joints and cartilage. Improved simulations can provide medical researchers with new information often unavailable in a clinical setting, information that may contribute to better insight into the pathophysiology of cartilage diseases.
Collapse
Affiliation(s)
- Xiaogang Wang
- Department of Mechanical Engineering, University of Connecticut, Storrs, CT, USA
| | - Thomas S E Eriksson
- Department of Defense and Security, System and Technology, Weapons and Protection, FOI - Swedish Defense Research Agency, Stockholm, Sweden
| | - Tim Ricken
- Institute for Mechanics, Structural Analysis and Dynamics, Stuttgart University, Stuttgart, Germany
| | - David M Pierce
- Department of Mechanical Engineering, University of Connecticut, Storrs, CT, USA; Department of Biomedical Engineering, University of Connecticut, Storrs, CT, USA.
| |
Collapse
|
24
|
Liang L, Liu M, Martin C, Sun W. A machine learning approach as a surrogate of finite element analysis-based inverse method to estimate the zero-pressure geometry of human thoracic aorta. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2018; 34:e3103. [PMID: 29740974 DOI: 10.1002/cnm.3103] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2017] [Accepted: 04/19/2018] [Indexed: 06/08/2023]
Abstract
Advances in structural finite element analysis (FEA) and medical imaging have made it possible to investigate the in vivo biomechanics of human organs such as blood vessels, for which organ geometries at the zero-pressure level need to be recovered. Although FEA-based inverse methods are available for zero-pressure geometry estimation, these methods typically require iterative computation, which are time-consuming and may be not suitable for time-sensitive clinical applications. In this study, by using machine learning (ML) techniques, we developed an ML model to estimate the zero-pressure geometry of human thoracic aorta given 2 pressurized geometries of the same patient at 2 different blood pressure levels. For the ML model development, a FEA-based method was used to generate a dataset of aorta geometries of 3125 virtual patients. The ML model, which was trained and tested on the dataset, is capable of recovering zero-pressure geometries consistent with those generated by the FEA-based method. Thus, this study demonstrates the feasibility and great potential of using ML techniques as a fast surrogate of FEA-based inverse methods to recover zero-pressure geometries of human organs.
Collapse
Affiliation(s)
- Liang Liang
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Minliang Liu
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Caitlin Martin
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| | - Wei Sun
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA
| |
Collapse
|
25
|
Liang L, Liu M, Martin C, Elefteriades JA, Sun W. A machine learning approach to investigate the relationship between shape features and numerically predicted risk of ascending aortic aneurysm. Biomech Model Mechanobiol 2017; 16:1519-1533. [PMID: 28386685 PMCID: PMC5630492 DOI: 10.1007/s10237-017-0903-9] [Citation(s) in RCA: 79] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2016] [Accepted: 03/27/2017] [Indexed: 02/07/2023]
Abstract
Geometric features of the aorta are linked to patient risk of rupture in the clinical decision to electively repair an ascending aortic aneurysm (AsAA). Previous approaches have focused on relationship between intuitive geometric features (e.g., diameter and curvature) and wall stress. This work investigates the feasibility of a machine learning approach to establish the linkages between shape features and FEA-predicted AsAA rupture risk, and it may serve as a faster surrogate for FEA associated with long simulation time and numerical convergence issues. This method consists of four main steps: (1) constructing a statistical shape model (SSM) from clinical 3D CT images of AsAA patients; (2) generating a dataset of representative aneurysm shapes and obtaining FEA-predicted risk scores defined as systolic pressure divided by rupture pressure (rupture is determined by a threshold criterion); (3) establishing relationship between shape features and risk by using classifiers and regressors; and (4) evaluating such relationship in cross-validation. The results show that SSM parameters can be used as strong shape features to make predictions of risk scores consistent with FEA, which lead to an average risk classification accuracy of 95.58% by using support vector machine and an average regression error of 0.0332 by using support vector regression, while intuitive geometric features have relatively weak performance. Compared to FEA, this machine learning approach is magnitudes faster. In our future studies, material properties and inhomogeneous thickness will be incorporated into the models and learning algorithms, which may lead to a practical system for clinical applications.
Collapse
Affiliation(s)
- Liang Liang
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Technology Enterprise Park, Room 206 387 Technology Circle, Atlanta, GA, 30313-2412, USA
| | - Minliang Liu
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Technology Enterprise Park, Room 206 387 Technology Circle, Atlanta, GA, 30313-2412, USA
| | - Caitlin Martin
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Technology Enterprise Park, Room 206 387 Technology Circle, Atlanta, GA, 30313-2412, USA
| | - John A Elefteriades
- Aortic Institute of Yale-New Haven Hospital, Yale University, New Haven, CT, USA
| | - Wei Sun
- Tissue Mechanics Laboratory, The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Technology Enterprise Park, Room 206 387 Technology Circle, Atlanta, GA, 30313-2412, USA.
| |
Collapse
|
26
|
Rausch MK, Genet M, Humphrey JD. An augmented iterative method for identifying a stress-free reference configuration in image-based biomechanical modeling. J Biomech 2017; 58:227-231. [PMID: 28549603 DOI: 10.1016/j.jbiomech.2017.04.021] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2016] [Revised: 02/22/2017] [Accepted: 04/24/2017] [Indexed: 10/19/2022]
Abstract
Continued advances in computational power and methods have enabled image-based biomechanical modeling to become an important tool in basic science, diagnostic and therapeutic medicine, and medical device design. One of the many challenges of this approach, however, is identification of a stress-free reference configuration based on in vivo images of loaded and often prestrained or residually stressed soft tissues and organs. Fortunately, iterative methods have been proposed to solve this inverse problem, among them Sellier's method. This method is particularly appealing because it is easy to implement, convergences reasonably fast, and can be coupled to nearly any finite element package. By means of several practical examples, however, we demonstrate that in its original formulation Sellier's method is not optimally fast and may not converge for problems with large deformations. Fortunately, we can also show that a simple, inexpensive augmentation of Sellier's method based on Aitken's delta-squared process can not only ensure convergence but also significantly accelerate the method.
Collapse
Affiliation(s)
- Manuel K Rausch
- Department of Biomedical Engineering, Yale University, United States; Department of Aerospace Engineering & Engineering Mechanics, University of Texas at Austin, United States.
| | - Martin Genet
- LMS, École Polytechnique, CNRS, Université Paris-Saclay, France; Inria, Université Paris-Saclay, France
| | - Jay D Humphrey
- Department of Biomedical Engineering, Yale University, United States
| |
Collapse
|
27
|
Strbac V, Pierce D, Rodriguez-Vila B, Vander Sloten J, Famaey N. Rupture risk in abdominal aortic aneurysms: A realistic assessment of the explicit GPU approach. J Biomech 2017; 56:1-9. [DOI: 10.1016/j.jbiomech.2017.02.019] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2016] [Revised: 02/13/2017] [Accepted: 02/16/2017] [Indexed: 10/20/2022]
|
28
|
Maas SA, Erdemir A, Halloran JP, Weiss JA. A general framework for application of prestrain to computational models of biological materials. J Mech Behav Biomed Mater 2016; 61:499-510. [PMID: 27131609 DOI: 10.1016/j.jmbbm.2016.04.012] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2015] [Revised: 03/28/2016] [Accepted: 04/06/2016] [Indexed: 11/15/2022]
Abstract
It is often important to include prestress in computational models of biological tissues. The prestress can represent residual stresses (stresses that exist after the tissue is excised from the body) or in situ stresses (stresses that exist in vivo, in the absence of loading). A prestressed reference configuration may also be needed when modeling the reference geometry of biological tissues in vivo. This research developed a general framework for representing prestress in finite element models of biological materials. It is assumed that the material is elastic, allowing the prestress to be represented via a prestrain. For prestrain fields that are not compatible with the reference geometry, the computational framework provides an iterative algorithm for updating the prestrain until equilibrium is satisfied. The iterative framework allows for enforcement of two different constraints: elimination of distortion in order to address the incompatibility issue, and enforcing a specified in situ fiber strain field while allowing for distortion. The framework was implemented as a plugin in FEBio (www.febio.org), making it easy to maintain the software and to extend the framework if needed. Several examples illustrate the application and effectiveness of the approach, including the application of in situ strains to ligaments in the Open Knee model (simtk.org/home/openknee). A novel method for recovering the stress-free configuration from the prestrain deformation gradient is also presented. This general purpose theoretical and computational framework for applying prestrain will allow analysts to overcome the challenges in modeling this important aspect of biological tissue mechanics.
Collapse
Affiliation(s)
- Steve A Maas
- Department of Bioengineering, and Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, USA
| | - Ahmet Erdemir
- Computational Biomodeling (CoBi) Core and Department of Biomedical Engineering, Lerner Research Institute, Cleveland Clinic, USA
| | - Jason P Halloran
- Mechanical Department Cleveland State University, Cleveland, Ohio, USA
| | - Jeffrey A Weiss
- Department of Bioengineering, and Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, USA.
| |
Collapse
|
29
|
Georg Y, Delay C, Schwein A, Lejay A, Thaveau F, Gaertner S, Stephan D, Heim F, Chakfe N. [Contribution of mathematical models and biomechanical properties in predicting the risk of abdominal aortic aneurysm rupture]. ACTA ACUST UNITED AC 2015; 41:63-8. [PMID: 26318549 DOI: 10.1016/j.jmv.2015.07.107] [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: 01/16/2015] [Accepted: 07/17/2015] [Indexed: 11/25/2022]
Abstract
INTRODUCTION Rupture is the worst outcome of abdominal aortic aneurysm (AAA). The decision to operate should include counterbalancing the risk of aneurysm rupture against the risk of aneurysm repair, within the context of a patient's overall life expectancy. Current surgical guidelines are based on population studies, and important variables are missed in predicting individual risk of rupture. METHODS In this literature review, we focused on the contribution of biomechanical and mathematical models in predicting risk of AAA rupture. RESULTS Anatomical features as diameter asymmetry and lack of tortuosity are shown to be anatomical risk factors of rupture. Wall stiffness (due to modifications of elastin and collagen composition) and increased inflammatory response are also factors that affect the structural integrity of the AAA wall. Biomechanical studies showed that wall strength is lower in ruptured than non-ruptured AAA. Intra-luminal thrombus also has a big role to play in the occurrence of rupture. Current mathematical models allow more variables to be included in predicting individual risk of rupture. CONCLUSION Moving away from using maximal transverse diameter of the AAA as a unique predictive factor and instead including biological, structural and biomechanical variables in predicting individual risk of rupture will be essential in the future and will help gain precision and accuracy in surgical indications.
Collapse
Affiliation(s)
- Y Georg
- Groupe européen de recherche sur les prothèses appliquées à la chirurgie vasculaire (Geprovas), faculté de médecine, institut d'anatomie pathologique, 4, rue Kirschleger, 67085 Strasbourg cedex, France; Service de chirurgie vasculaire et transplantation rénale, hôpitaux universitaires de Strasbourg, 1, place de l'Hôpital, BP n(o) 426, 67091 Strasbourg cedex, France
| | - C Delay
- Groupe européen de recherche sur les prothèses appliquées à la chirurgie vasculaire (Geprovas), faculté de médecine, institut d'anatomie pathologique, 4, rue Kirschleger, 67085 Strasbourg cedex, France; Service de chirurgie vasculaire et transplantation rénale, hôpitaux universitaires de Strasbourg, 1, place de l'Hôpital, BP n(o) 426, 67091 Strasbourg cedex, France
| | - A Schwein
- Groupe européen de recherche sur les prothèses appliquées à la chirurgie vasculaire (Geprovas), faculté de médecine, institut d'anatomie pathologique, 4, rue Kirschleger, 67085 Strasbourg cedex, France; Service de chirurgie vasculaire et transplantation rénale, hôpitaux universitaires de Strasbourg, 1, place de l'Hôpital, BP n(o) 426, 67091 Strasbourg cedex, France
| | - A Lejay
- Groupe européen de recherche sur les prothèses appliquées à la chirurgie vasculaire (Geprovas), faculté de médecine, institut d'anatomie pathologique, 4, rue Kirschleger, 67085 Strasbourg cedex, France; Service de chirurgie vasculaire et transplantation rénale, hôpitaux universitaires de Strasbourg, 1, place de l'Hôpital, BP n(o) 426, 67091 Strasbourg cedex, France
| | - F Thaveau
- Groupe européen de recherche sur les prothèses appliquées à la chirurgie vasculaire (Geprovas), faculté de médecine, institut d'anatomie pathologique, 4, rue Kirschleger, 67085 Strasbourg cedex, France; Service de chirurgie vasculaire et transplantation rénale, hôpitaux universitaires de Strasbourg, 1, place de l'Hôpital, BP n(o) 426, 67091 Strasbourg cedex, France
| | - S Gaertner
- Service des maladies vasculaires, hypertension artérielle et pharmacologie clinique, hôpitaux universitaires de Strasbourg, 1, place de l'Hôpital, 67091 Strasbourg cedex, France
| | - D Stephan
- Service des maladies vasculaires, hypertension artérielle et pharmacologie clinique, hôpitaux universitaires de Strasbourg, 1, place de l'Hôpital, 67091 Strasbourg cedex, France
| | - F Heim
- Groupe européen de recherche sur les prothèses appliquées à la chirurgie vasculaire (Geprovas), faculté de médecine, institut d'anatomie pathologique, 4, rue Kirschleger, 67085 Strasbourg cedex, France; Laboratoire de physique et mécanique textile, ENSISA, 11, rue Alfred-Werner, 68093 Mulhouse cedex, France
| | - N Chakfe
- Groupe européen de recherche sur les prothèses appliquées à la chirurgie vasculaire (Geprovas), faculté de médecine, institut d'anatomie pathologique, 4, rue Kirschleger, 67085 Strasbourg cedex, France; Service de chirurgie vasculaire et transplantation rénale, hôpitaux universitaires de Strasbourg, 1, place de l'Hôpital, BP n(o) 426, 67091 Strasbourg cedex, France.
| |
Collapse
|
30
|
A method for incorporating three-dimensional residual stretches/stresses into patient-specific finite element simulations of arteries. J Mech Behav Biomed Mater 2015; 47:147-164. [PMID: 25931035 DOI: 10.1016/j.jmbbm.2015.03.024] [Citation(s) in RCA: 47] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2015] [Revised: 03/24/2015] [Accepted: 03/25/2015] [Indexed: 11/21/2022]
Abstract
The existence of residual stresses in human arteries has long been shown experimentally. Researchers have also demonstrated that residual stresses have a significant effect on the distribution of physiological stresses within arterial tissues, and hence on their development, e.g., stress-modulated remodeling. Through progress in medical imaging, image analysis and finite element (FE) meshing tools it is now possible to construct in vivo patient-specific geometries and thus to study specific, clinically relevant problems in arterial mechanics via FE simulations. Classical continuum mechanics and FE methods assume that constitutive models and the corresponding simulations start from unloaded, stress-free reference configurations while the boundary-value problem of interest represents a loaded geometry and includes residual stresses. We present a pragmatic methodology to simultaneously account for both (i) the three-dimensional (3-D) residual stress distributions in the arterial tissue layers, and (ii) the equilibrium of the in vivo patient-specific geometry with the known boundary conditions. We base our methodology on analytically determined residual stress distributions (Holzapfel and Ogden, 2010, J. R. Soc. Interface 7, 787-799) and calibrate it using data on residual deformations (Holzapfel et al., 2007, Ann. Biomed. Eng. 35, 530-545). We demonstrate our methodology on three patient-specific FE simulations calibrated using experimental data. All data employed here are generated from human tissues - both the aorta and thrombus, and their respective layers - including the geometries determined from magnetic resonance images, and material properties and 3-D residual stretches determined from mechanical experiments. We study the effect of 3-D residual stresses on the distribution of physiological stresses in the aortic layers (intima, media, adventitia) and the layers of the intraluminal thrombus (luminal, medial, abluminal) by comparing three types of FE simulations: (i) conventional calculations; (ii) calculations accounting only for prestresses; (iii) calculations including both 3-D residual stresses and prestresses. Our results show that including residual stresses in patient-specific simulations of arterial tissues significantly impacts both the global (organ-level) deformations and the stress distributions within the arterial tissue (and its layers). Our method produces circumferential Cauchy stress distributions that are more uniform through the tissue thickness (i.e., smaller stress gradients in the local radial directions) compared to both the conventional and prestressing calculations. Such methods, combined with appropriate experimental data, aim at increasing the accuracy of classical FE analyses for patient-specific studies in computational biomechanics and may lead to increased clinical application of simulation tools.
Collapse
|