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Atashipour SR, Baqersad J. Noninvasive identification of directionally-dependent elastic properties of soft tissues using full-field optical data. J Mech Behav Biomed Mater 2024; 151:106266. [PMID: 38194784 DOI: 10.1016/j.jmbbm.2023.106266] [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: 09/07/2023] [Revised: 11/12/2023] [Accepted: 11/21/2023] [Indexed: 01/11/2024]
Abstract
This paper introduces an innovative approach for elastic property characterization of soft tissues, having directional-dependent material behavior, via their vibration response measurement and interpretation. The full-field time-dependent surface displacements as a result of externally excited soft tissues are collected through digital image correlation (DIC). A developed analytical model, capturing the low-amplitude vibration behavior of anisotropic layered human skin with the incorporation of the influence of subcutaneous elasticity and inertia, is employed to accurately predict its resonant frequencies and pertaining displacement field images. An efficient solution approach for the model is implemented into an inverse algorithm to rapidly characterize the anisotropic elastic properties based on importing the vibration characteristics. To show the merit of the approach, a 3-D finite element (FE) simulation model was used to generate full-field data, detected and matched with a set of specific vibration modes via modal assurance criterion (MAC). The validity of the model implemented into the inverse characterization algorithm is demonstrated through a comparison of predicted vibration frequencies and mode-shapes simulated via the 3-D FE model for different cases with anisotropic elastic properties in different layers of the skin. It is shown that modes are influenced differently when anisotropic properties are introduced to the model. Thus, the established inverse characterization algorithm is capable of rapidly predicting the elastic material properties of anisotropic soft sheets with adequate accuracy.
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Affiliation(s)
- Seyed Rasoul Atashipour
- Department of Mechanical Engineering, Kettering University, 1700 University Ave, Flint, MI, 48504, USA; Division of Dynamics, Department of Mechanics and Maritime Sciences (M2), Chalmers University of Technology, SE-412 96, Gothenburg, Sweden.
| | - Javad Baqersad
- Department of Mechanical Engineering, Kettering University, 1700 University Ave, Flint, MI, 48504, USA
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Mazier A, Bordas SPA. Breast simulation pipeline: From medical imaging to patient-specific simulations. Clin Biomech (Bristol, Avon) 2024; 111:106153. [PMID: 38061204 DOI: 10.1016/j.clinbiomech.2023.106153] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Revised: 11/17/2023] [Accepted: 11/20/2023] [Indexed: 01/16/2024]
Abstract
BACKGROUND Breast-conserving surgery is the most acceptable operation for breast cancer removal from an invasive and psychological point of view. Before the surgical procedure, a preoperative MRI is performed in the prone configuration, while the surgery is achieved in the supine position. This leads to a considerable movement of the breast, including the tumor, between the two poses, complicating the surgeon's task. METHODS In this work, a simulation pipeline allowing the computation of patient-specific geometry and the prediction of personalized breast material properties was put forward. Through image segmentation, a finite element model including the subject-specific geometry is established. By first computing an undeformed state of the breast, the geometrico-material model is calibrated by surface acquisition in the intra-operative stance. FINDINGS Using an elastic corotational formulation, the patient-specific mechanical properties of the breast and skin were identified to obtain the best estimates of the supine configuration. The final results are a shape-fitting closest point residual of 4.00 mm for the mechanical parameters Ebreast=0.32 kPa and Eskin=22.72 kPa, congruent with the current state-of-the-art. The Covariance Matrix Adaptation Evolution Strategy optimizer converges on average between 5 to 30 min depending on the initial parameters, reaching a simulation speed of 20 s. To our knowledge, our model offers one of the best compromises between accuracy and speed. INTERPRETATION Satisfactory results were obtained for the estimation of breast deformation from preoperative to intra-operative configuration. Furthermore, we have demonstrated the clinical feasibility of such applications using a simulation framework that aims at the smallest disturbance of the actual surgical pipeline.
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Affiliation(s)
- Arnaud Mazier
- Institute of Computational Engineering, Department of Engineering, Université du Luxembourg, Esch-sur-Alzette, Luxembourg
| | - Stéphane P A Bordas
- Institute of Computational Engineering, Department of Engineering, Université du Luxembourg, Esch-sur-Alzette, Luxembourg.
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Eftimie R, Rolin G, Adebayo OE, Urcun S, Chouly F, Bordas SPA. Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives. Bull Math Biol 2023; 85:117. [PMID: 37855947 DOI: 10.1007/s11538-023-01222-8] [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: 04/19/2023] [Accepted: 10/02/2023] [Indexed: 10/20/2023]
Abstract
Keloids are fibroproliferative disorders described by excessive growth of fibrotic tissue, which also invades adjacent areas (beyond the original wound borders). Since these disorders are specific to humans (no other animal species naturally develop keloid-like tissue), experimental in vivo/in vitro research has not led to significant advances in this field. One possible approach could be to combine in vitro human models with calibrated in silico mathematical approaches (i.e., models and simulations) to generate new testable biological hypotheses related to biological mechanisms and improved treatments. Because these combined approaches do not really exist for keloid disorders, in this brief review we start by summarising the biology of these disorders, then present various types of mathematical and computational approaches used for related disorders (i.e., wound healing and solid tumours), followed by a discussion of the very few mathematical and computational models published so far to study various inflammatory and mechanical aspects of keloids. We conclude this review by discussing some open problems and mathematical opportunities offered in the context of keloid disorders by such combined in vitro/in silico approaches, and the need for multi-disciplinary research to enable clinical progress.
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Affiliation(s)
- R Eftimie
- Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 25000, Besançon, France.
| | - G Rolin
- INSERM CIC-1431, CHU Besançon, F-25000, Besançon, France
- EFS, INSERM, UMR 1098 RIGHT, Université de Franche-Comté, F-25000, Besançon, France
| | - O E Adebayo
- Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 25000, Besançon, France
| | - S Urcun
- Institute for Computational Engineering, Faculty of Science, Technology and Communication, University of Luxembourg, Esch-sur-Alzette, Luxembourg
| | - F Chouly
- Institut de Mathématiques de Bourgogne, Université de Franche-Comté, 21078, Dijon, France
- Center for Mathematical Modelling and Department of Mathematical Engineering, University of Chile and IRL 2807 - CNRS, Santiago, Chile
- Departamento de Ingeniería Matemática, CI2MA, Universidad de Concepción, Casilla 160-C, Concepción, Chile
| | - S P A Bordas
- Institute for Computational Engineering, Faculty of Science, Technology and Communication, University of Luxembourg, Esch-sur-Alzette, Luxembourg
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Elouneg A, Chambert J, Lejeune A, Lucot Q, Jacquet E, Bordas SPA. Anisotropic mechanical characterization of human skin by in vivo multi-axial ring suction test. J Mech Behav Biomed Mater 2023; 141:105779. [PMID: 36940583 DOI: 10.1016/j.jmbbm.2023.105779] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Revised: 02/10/2023] [Accepted: 03/12/2023] [Indexed: 03/17/2023]
Abstract
Human skin is a soft tissue behaving as an anisotropic material. The anisotropy emerges from the alignment of collagen fibers in the dermis, which causes the skin to exhibit greater stiffness in a certain direction, known as Langer's line. The importance of determining this anisotropy axis lies in assisting surgeons in making incisions that do not produce undesirable scars. In this paper, we introduce an open-source numerical framework, MARSAC (Multi-Axial Ring Suction for Anisotropy Characterization: https://github.com/aflahelouneg/MARSAC), adapted to a commercial device CutiScan CS 100® that applies a suction load on an annular section, causing a multi-axial stretch in the central zone, where in-plane displacements are captured by a camera. The presented framework receives inputs from a video file and converts them into displacement fields through Digital Image Correlation (DIC) technique. From the latter and based on an analytical model, the method assesses the anisotropic material parameters of human skin: Langer's line ϕ, and the elastic moduli E1 and E2 along the principal axes, providing that the Poisson's ratio is fixed. The pipeline was applied to a public data repository, https://search-data.ubfc.fr/femto/FR-18008901306731-2021-08-25_In-vivo-skin-anisotropy-dataset-for-a-young-man.html, containing 30 test series performed on a forearm of a Caucasian subject. As a result, the identified parameter averages, ϕˆ=40.9±8.2∘ and the anisotropy ratio E1ˆ/E2ˆ=3.14±1.60, were in accordance with the literature. The intra-subject analysis showed a reliable assessment of ϕ and E2. As skin anisotropy varies from site to site and from subject to subject, the novelty of the method consists in (i) an optimal utilization of CutiScan CS 100® probe to measure the Langer's line accurately and rapidly on small areas with a minimum diameter of 14mm, (ii) validation of an analytical model based on deformation ellipticity.
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Affiliation(s)
- A Elouneg
- Université de Franche-Comté, CNRS, institut FEMTO-ST, F-25000 Besançon, France; Institute of Computational Engineering and Sciences, Department of Engineering, Université du Luxembourg, Esch-sur-Alzette, Luxembourg
| | - J Chambert
- Université de Franche-Comté, CNRS, institut FEMTO-ST, F-25000 Besançon, France
| | - A Lejeune
- Université de Franche-Comté, CNRS, institut FEMTO-ST, F-25000 Besançon, France
| | - Q Lucot
- Université de Franche-Comté, CNRS, institut FEMTO-ST, F-25000 Besançon, France
| | - E Jacquet
- Université de Franche-Comté, CNRS, institut FEMTO-ST, F-25000 Besançon, France
| | - S P A Bordas
- Université de Franche-Comté, CNRS, institut FEMTO-ST, F-25000 Besançon, France; Institute of Computational Engineering and Sciences, Department of Engineering, Université du Luxembourg, Esch-sur-Alzette, Luxembourg.
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Aggarwal A, Jensen BS, Pant S, Lee CH. Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: application to planar soft tissues. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2023; 404:115812. [PMID: 37235184 PMCID: PMC10208436 DOI: 10.1016/j.cma.2022.115812] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Data-based approaches are promising alternatives to the traditional analytical constitutive models for solid mechanics. Herein, we propose a Gaussian process (GP) based constitutive modeling framework, specifically focusing on planar, hyperelastic and incompressible soft tissues. The strain energy density of soft tissues is modeled as a GP, which can be regressed to experimental stress-strain data obtained from biaxial experiments. Moreover, the GP model can be weakly constrained to be convex. A key advantage of a GP-based model is that, in addition to the mean value, it provides a probability density (i.e. associated uncertainty) for the strain energy density. To simulate the effect of this uncertainty, a non-intrusive stochastic finite element analysis (SFEA) framework is proposed. The proposed framework is verified against an artificial dataset based on the Gasser-Ogden-Holzapfel model and applied to a real experimental dataset of a porcine aortic valve leaflet tissue. Results show that the proposed framework can be trained with limited experimental data and fits the data better than several existing models. The SFEA framework provides a straightforward way of using the experimental data and quantifying the resulting uncertainty in simulation-based predictions.
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Affiliation(s)
- Ankush Aggarwal
- Glasgow Computational Engineering Centre, James Watt School of Engineering, University of Glasgow, Glasgow, G12 8LT, Scotland, United Kingdom
| | - Bjørn Sand Jensen
- School of Computing Science, University of Glasgow, Glasgow, G12 8LT, Scotland, United Kingdom
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark
| | - Sanjay Pant
- Zienkiewicz Centre for Computational Engineering, Swansea University, Swansea, SA18EP, Wales, United Kingdom
| | - Chung-Hao Lee
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, 73019, OK, United States of America
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Chetoui MA, Ambard D, Canãdas P, Kouyoumdjian P, Royer P, Le Floc'h S. Impact of extracellular matrix and collagen network properties on the cervical intervertebral disc response to physiological loads: A parametric study. Med Eng Phys 2022; 110:103908. [PMID: 36564135 DOI: 10.1016/j.medengphy.2022.103908] [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: 06/21/2022] [Revised: 10/03/2022] [Accepted: 10/13/2022] [Indexed: 11/05/2022]
Abstract
Current intervertebral disc finite element models are hard to validate since they describe multi-physical phenomena and contain a huge number of material properties. This work aims to simplify numerical validation/identification studies by prioritizing the sensitivity of intervertebral disc behavior to mechanical properties. A 3D fiber-reinforced hyperelastic model of a C6-C7 intervertebral disc is used to carry out the parametric study. 10 parameters describing the extracellular matrix and the collagen network behaviors are included in the parametric study. The influence of varying these parameters on the disc response is estimated during physiological movements of the head, including compression, lateral bending, flexion, and axial rotation. The obtained results highlight the high sensitivity of the disc behavior to the stiffness of the annulus fibrosus extracellular matrix for all the studied loads with a relative increase in the disc apparent stiffness by 67% for compression and by 57% for axial rotation when the annulus stiffness increases from 0.4 to 2 MPa. It is also shown that varying collagen network orientation, stiffness, and stiffening in the studied configuration range have a noticeable effect on rotational motions with a relative apparent stiffness difference reaching 6.8%, 10%, and 22%, respectively, in lateral bending. However, the collagen orientation does not affect disc response to axial load.
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Affiliation(s)
| | | | - Patrick Canãdas
- LMGC UMR5508, Univ. of Montpellier, CNRS, Montpellier, France
| | - Pascal Kouyoumdjian
- Orthopedic Surgery and Trauma Service, Spine Surgery, CHRU of Nîmes, Nîmes, France
| | - Pascale Royer
- LMGC UMR5508, Univ. of Montpellier, CNRS, Montpellier, France
| | - Simon Le Floc'h
- LMGC UMR5508, Univ. of Montpellier, CNRS, Montpellier, France
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