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Dyck C, Isaac KV, Edelstein-Keshet L. Models for Implant-Induced Capsular Contracture Post Breast Cancer Surgery. Bull Math Biol 2023; 86:7. [PMID: 38091110 PMCID: PMC10719149 DOI: 10.1007/s11538-023-01236-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Accepted: 11/09/2023] [Indexed: 12/17/2023]
Abstract
Capsular contracture is a painful deformation of scar-tissue that may form around an implant in post-breast cancer reconstruction or cosmetic surgery. Inflammation due to surgical trauma or contamination in the tissue around the implant could account for recruitment of immune cells, and transdifferentiation of resident fibroblasts into cells that deposit abnormally thick collagen. Here we examine this hypothesis using a mathematical model for interacting macrophages, fibroblasts, myofibroblasts, and collagen. Our model demonstrates that cellular response can, together with inflammatory cell recruitment, account for prognoses.
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Affiliation(s)
- Cheryl Dyck
- Insight Math Unincorporated, Port Moody, BC, Canada
| | - Kathryn V Isaac
- Department of Surgery, Faculty of Medicine, University of British Columbia, Vancouver, BC, Canada
| | - Leah Edelstein-Keshet
- Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada.
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2
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Manjunatha K, Schaaps N, Behr M, Vogt F, Reese S. Computational modeling of in-stent restenosis: Pharmacokinetic and pharmacodynamic evaluation. Comput Biol Med 2023; 167:107686. [PMID: 37972534 DOI: 10.1016/j.compbiomed.2023.107686] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Revised: 10/11/2023] [Accepted: 11/06/2023] [Indexed: 11/19/2023]
Abstract
Persistence of the pathology of in-stent restenosis even with the advent of drug-eluting stents warrants the development of highly resolved in silico models. These computational models assist in gaining insights into the transient biochemical and cellular mechanisms involved and thereby optimize the stent implantation parameters. Within this work, an already established fully-coupled Lagrangian finite element framework for modeling the restenotic growth is enhanced with the incorporation of endothelium-mediated effects and pharmacological influences of rapamycin-based drugs embedded in the polymeric layers of the current generation drug-eluting stents. The continuum mechanical description of growth is further justified in the context of thermodynamic consistency. Qualitative inferences are drawn from the model developed herein regarding the efficacy of the level of drug embedment within the struts as well as the release profiles adopted. The framework is then intended to serve as a tool for clinicians to tune the interventional procedures patient-specifically.
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Affiliation(s)
- Kiran Manjunatha
- Institute of Applied Mechanics, RWTH Aachen University, Germany.
| | - Nicole Schaaps
- Department of Cardiology, Vascular Medicine and Intensive Care, RWTH Aachen University, Germany
| | - Marek Behr
- Chair for Computational Analysis of Technical Systems, RWTH Aachen University, Germany
| | - Felix Vogt
- Department of Cardiology, Vascular Medicine and Intensive Care, RWTH Aachen University, Germany
| | - Stefanie Reese
- Institute of Applied Mechanics, RWTH Aachen University, Germany
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3
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Sesa M, Holthusen H, Lamm L, Böhm C, Brepols T, Jockenhövel S, Reese S. Mechanical modeling of the maturation process for tissue-engineered implants: Application to biohybrid heart valves. Comput Biol Med 2023; 167:107623. [PMID: 37922603 DOI: 10.1016/j.compbiomed.2023.107623] [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: 07/09/2023] [Revised: 09/18/2023] [Accepted: 10/23/2023] [Indexed: 11/07/2023]
Abstract
The development of tissue-engineered cardiovascular implants can improve the lives of large segments of our society who suffer from cardiovascular diseases. Regenerative tissues are fabricated using a process called tissue maturation. Furthermore, it is highly challenging to produce cardiovascular regenerative implants with sufficient mechanical strength to withstand the loading conditions within the human body. Therefore, biohybrid implants for which the regenerative tissue is reinforced by standard reinforcement material (e.g. textile or 3d printed scaffold) can be an interesting solution. In silico models can significantly contribute to characterizing, designing, and optimizing biohybrid implants. The first step towards this goal is to develop a computational model for the maturation process of tissue-engineered implants. This paper focuses on the mechanical modeling of textile-reinforced tissue-engineered cardiovascular implants. First, an energy-based approach is proposed to compute the collagen evolution during the maturation process. Then, the concept of structural tensors is applied to model the anisotropic behavior of the extracellular matrix and the textile scaffold. Next, the newly developed material model is embedded into a special solid-shell finite element formulation with reduced integration. Finally, our framework is used to compute two structural problems: a pressurized shell construct and a tubular-shaped heart valve. The results show the ability of the model to predict collagen growth in response to the boundary conditions applied during the maturation process. Consequently, the model can predict the implant's mechanical response, such as the deformation and stresses of the implant.
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Affiliation(s)
- Mahmoud Sesa
- Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany.
| | - Hagen Holthusen
- Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany
| | - Lukas Lamm
- Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany
| | - Christian Böhm
- Biohybrid & Medical Textiles, Institute of Applied Medical Engineering, RWTH Aachen University, Forckenbeckstr. 55, 52074 Aachen, Germany
| | - Tim Brepols
- Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany
| | - Stefan Jockenhövel
- Biohybrid & Medical Textiles, Institute of Applied Medical Engineering, RWTH Aachen University, Forckenbeckstr. 55, 52074 Aachen, Germany
| | - Stefanie Reese
- Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany
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4
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Tilahun HG, Mullagura HN, Humphrey JD, Baek S. A biochemomechanical model of collagen turnover in arterial adaptations to hemodynamic loading. Biomech Model Mechanobiol 2023; 22:2063-2082. [PMID: 37505299 DOI: 10.1007/s10237-023-01750-1] [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: 01/31/2023] [Accepted: 07/06/2023] [Indexed: 07/29/2023]
Abstract
The production, removal, and remodeling of fibrillar collagen is fundamental to mechanical homeostasis in arteries, including dynamic morphological and microstructural changes that occur in response to sustained changes in blood flow and pressure under physiological conditions. These dynamic processes involve complex, coupled biological, chemical, and mechanical mechanisms that are not completely understood. Nevertheless, recent simulations using constrained mixture models with phenomenologically motivated constitutive relations have proven able to predict salient features of the progression of certain vascular adaptations as well as disease processes. Collagen turnover is modeled, in part, via stress-dependent changes in collagen half-life, typically within the range of 10-70 days. By contrast, in this work we introduce a biochemomechanical approach to model the cellular synthesis of procollagen as well as its transition from an intermediate state of assembled microfibrils to mature cross-linked fibers, with mechano-regulated removal. The resulting model can simulate temporal changes in geometry, composition, and stress during early vascular adaptation (weeks to months) for modest changes in blood flow or pressure. It is shown that these simulations capture salient features from data presented in the literature from different animal models.
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Affiliation(s)
- Hailu G Tilahun
- Department of Mechanical Engineering, Michigan State University, 3259 Engineering Building, East Lansing, MI, 48824, USA
| | - Haritha N Mullagura
- Department of Mechanical Engineering, Michigan State University, 3259 Engineering Building, East Lansing, MI, 48824, USA
| | - Jay D Humphrey
- Department of Biomedical Engineering, Yale University, New Haven, CT, 06520, USA
| | - Seungik Baek
- Department of Mechanical Engineering, Michigan State University, 3259 Engineering Building, East Lansing, MI, 48824, USA.
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5
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Manjunatha K, Behr M, Vogt F, Reese S. A multiphysics modeling approach for in-stent restenosis: Theoretical aspects and finite element implementation. Comput Biol Med 2022; 150:106166. [PMID: 36252366 DOI: 10.1016/j.compbiomed.2022.106166] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Revised: 09/19/2022] [Accepted: 10/01/2022] [Indexed: 11/21/2022]
Abstract
Development of in silico models that capture progression of diseases in soft biological tissues are intrinsic in the validation of the hypothesized cellular and molecular mechanisms involved in the respective pathologies. In addition, they also aid in patient-specific adaptation of interventional procedures. In this regard, a fully-coupled high-fidelity Lagrangian finite element framework is proposed within this work which replicates the pathology of in-stent restenosis observed post stent implantation in a coronary artery. Advection-reaction-diffusion equations are set up to track the concentrations of the platelet-derived growth factor, the transforming growth factor-β, the extracellular matrix, and the density of the smooth muscle cells. A continuum mechanical description of volumetric growth involved in the restenotic process, coupled to the evolution of the previously defined vessel wall constituents, is presented. Further, the finite element implementation of the model is discussed, and the behavior of the computational model is investigated via suitable numerical examples. Qualitative validation of the computational model is presented by emulating a stented artery. Patient-specific data are intended to be integrated into the model to predict the risk of in-stent restenosis, and thereby assist in the tuning of stent implantation parameters to mitigate the risk.
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Affiliation(s)
- Kiran Manjunatha
- Institute of Applied Mechanics, RWTH Aachen University, Germany.
| | - Marek Behr
- Chair for Computational Analysis of Technical Systems, RWTH Aachen University, Germany
| | - Felix Vogt
- Department of Cardiology, Pulmonology, Intensive Care and Vascular Medicine, RWTH Aachen University, Germany
| | - Stefanie Reese
- Institute of Applied Mechanics, RWTH Aachen University, Germany
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6
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Hernández-López P, Cilla M, Martínez M, Peña E. Effects of the Haemodynamic Stimulus on the Location of Carotid Plaques Based on a Patient-Specific Mechanobiological Plaque Atheroma Formation Model. Front Bioeng Biotechnol 2021; 9:690685. [PMID: 34195181 PMCID: PMC8236601 DOI: 10.3389/fbioe.2021.690685] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2021] [Accepted: 05/10/2021] [Indexed: 11/17/2022] Open
Abstract
In this work, we propose a mechanobiological atheroma growth model modulated by a new haemodynamic stimulus. To test this model, we analyse the development of atheroma plaques in patient-specific bifurcations of carotid arteries for a total time of 30 years. In particular, eight geometries (left or right carotid arteries) were segmented from clinical images and compared with the solutions obtained computationally to validate the model. The influence of some haemodynamical stimuli on the location and size of plaques is also studied. Plaques predicted by the mechanobiological models using the time average wall shear stress (TAWSS), the oscillatory shear index (OSI) and a new index proposed in this work are compared. The new index predicts the shape index of the endothelial cells as a combination of TAWSS and OSI values and was fitted using data from the literature. The mechanobiological model represents an evolution of the one previously proposed by the authors. This model uses Navier-Stokes equations to simulate blood flow along the lumen in the transient mode. It also employs Darcy's law and Kedem-Katchalsky equations for plasma and substance flow across the endothelium using the three-pore model. The mass balances of all the substances that have been considered in the model are implemented by convection-diffusion-reaction equations, and finally the growth of the plaques has been computed. The results show that by using the new mechanical stimulus proposed in this study, prediction of plaques is, in most cases, better than only using TAWSS or OSI with a minimal and maximal errors on stenosis ratio of 2.77 and 32.89 %, respectively. However, there are a few geometries in which haemodynamics cannot predict the location of plaques, and other biological or genetic factors would be more relevant than haemodynamics. In particular, the model predicts correctly eleven of the fourteen plaques presented in all the geometries considered. Additionally, a healthy geometry has been computed to check that plaque is not developed with the model in this case.
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Affiliation(s)
| | - Myriam Cilla
- Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain
- Centro Universitario de la Defensa, Academia General Militar, Zaragoza, Spain
- Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicina (CIBER-BBN), Zaragoza, Spain
| | - Miguel Martínez
- Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain
- Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicina (CIBER-BBN), Zaragoza, Spain
| | - Estefanía Peña
- Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain
- Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicina (CIBER-BBN), Zaragoza, Spain
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7
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Computational model of damage-induced growth in soft biological tissues considering the mechanobiology of healing. Biomech Model Mechanobiol 2021; 20:1297-1315. [PMID: 33768359 PMCID: PMC8298377 DOI: 10.1007/s10237-021-01445-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2020] [Accepted: 03/04/2021] [Indexed: 11/01/2022]
Abstract
Healing in soft biological tissues is a chain of events on different time and length scales. This work presents a computational framework to capture and couple important mechanical, chemical and biological aspects of healing. A molecular-level damage in collagen, i.e., the interstrand delamination, is addressed as source of plastic deformation in tissues. This mechanism initiates a biochemical response and starts the chain of healing. In particular, damage is considered to be the stimulus for the production of matrix metalloproteinases and growth factors which in turn, respectively, degrade and produce collagen. Due to collagen turnover, the volume of the tissue changes, which can result either in normal or pathological healing. To capture the mechanisms on continuum scale, the deformation gradient is multiplicatively decomposed in inelastic and elastic deformation gradients. A recently proposed elasto-plastic formulation is, through a biochemical model, coupled with a growth and remodeling description based on homogenized constrained mixtures. After the discussion of the biological species response to the damage stimulus, the framework is implemented in a mixed nonlinear finite element formulation and a biaxial tension and an indentation tests are conducted on a prestretched flat tissue sample. The results illustrate that the model is able to describe the evolutions of growth factors and matrix metalloproteinases following damage and the subsequent growth and remodeling in the respect of equilibrium. The interplay between mechanical and chemo-biological events occurring during healing is captured, proving that the framework is a suitable basis for more detailed simulations of damage-induced tissue response.
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8
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Escuer J, Martínez MA, McGinty S, Peña E. Mathematical modelling of the restenosis process after stent implantation. J R Soc Interface 2019; 16:20190313. [PMID: 31409233 DOI: 10.1098/rsif.2019.0313] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
The stenting procedure has evolved to become a highly successful technique for the clinical treatment of advanced atherosclerotic lesions in arteries. However, the development of in-stent restenosis remains a key problem. In this work, a novel two-dimensional continuum mathematical model is proposed to describe the complex restenosis process following the insertion of a stent into a coronary artery. The biological species considered to play a key role in restenosis development are growth factors, matrix metalloproteinases, extracellular matrix, smooth muscle cells and endothelial cells. Diffusion-reaction equations are used for modelling the mass balance between species in the arterial wall. Experimental data from the literature have been used in order to estimate model parameters. Moreover, a sensitivity analysis has been performed to study the impact of varying the parameters of the model on the evolution of the biological species. The results demonstrate that this computational model qualitatively captures the key characteristics of the lesion growth and the healing process within an artery subjected to non-physiological mechanical forces. Our results suggest that the arterial wall response is driven by the damage area, smooth muscle cell proliferation and the collagen turnover among other factors.
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Affiliation(s)
- Javier Escuer
- Applied Mechanics and Bioengineering Group (AMB), Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain
| | - Miguel A Martínez
- Applied Mechanics and Bioengineering Group (AMB), Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain.,Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Spain
| | - Sean McGinty
- Division of Biomedical Engineering, University of Glasgow, Glasgow, UK
| | - Estefanía Peña
- Applied Mechanics and Bioengineering Group (AMB), Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain.,Biomedical Research Networking Center in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Spain
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9
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Comellas E, Gasser TC, Bellomo FJ, Oller S. A homeostatic-driven turnover remodelling constitutive model for healing in soft tissues. J R Soc Interface 2016; 13:rsif.2015.1081. [PMID: 27009177 DOI: 10.1098/rsif.2015.1081] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2015] [Accepted: 03/01/2016] [Indexed: 01/08/2023] Open
Abstract
Remodelling of soft biological tissue is characterized by interacting biochemical and biomechanical events, which change the tissue's microstructure, and, consequently, its macroscopic mechanical properties. Remodelling is a well-defined stage of the healing process, and aims at recovering or repairing the injured extracellular matrix. Like other physiological processes, remodelling is thought to be driven by homeostasis, i.e. it tends to re-establish the properties of the uninjured tissue. However, homeostasis may never be reached, such that remodelling may also appear as a continuous pathological transformation of diseased tissues during aneurysm expansion, for example. A simple constitutive model for soft biological tissues that regards remodelling as homeostatic-driven turnover is developed. Specifically, the recoverable effective tissue damage, whose rate is the sum of a mechanical damage rate and a healing rate, serves as a scalar internal thermodynamic variable. In order to integrate the biochemical and biomechanical aspects of remodelling, the healing rate is, on the one hand, driven by mechanical stimuli, but, on the other hand, subjected to simple metabolic constraints. The proposed model is formulated in accordance with continuum damage mechanics within an open-system thermodynamics framework. The numerical implementation in an in-house finite-element code is described, particularized for Ogden hyperelasticity. Numerical examples illustrate the basic constitutive characteristics of the model and demonstrate its potential in representing aspects of remodelling of soft tissues. Simulation results are verified for their plausibility, but also validated against reported experimental data.
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Affiliation(s)
- Ester Comellas
- International Center for Numerical Methods in Engineering (CIMNE), Campus Nord UPC, Building C1, c/Gran Capita s/n, 08034 Barcelona, Spain Department of Strength of Materials and Structural Engineering, ETSECCPB, Universitat Politcnica de Catalunya, Barcelona Tech (UPC), Campus Nord, Building C1, c/Jordi Girona 1-3, 08034 Barcelona, Spain
| | - T Christian Gasser
- Department of Solid Mechanics, School of Engineering Sciences, KTH Royal Institute of Technology, Teknikringen 8, 100 44 Stockholm, Sweden
| | - Facundo J Bellomo
- INIQUI (CONICET), Faculty of Engineering, National University of Salta, Av. Bolivia 5150, 4400 Salta, Argentina
| | - Sergio Oller
- International Center for Numerical Methods in Engineering (CIMNE), Campus Nord UPC, Building C1, c/Gran Capita s/n, 08034 Barcelona, Spain Department of Strength of Materials and Structural Engineering, ETSECCPB, Universitat Politcnica de Catalunya, Barcelona Tech (UPC), Campus Nord, Building C1, c/Jordi Girona 1-3, 08034 Barcelona, Spain
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10
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Nicolás M, Peña E, Malvè M, Martínez M. Mathematical modeling of the fibrosis process in the implantation of inferior vena cava filters. J Theor Biol 2015; 387:228-40. [DOI: 10.1016/j.jtbi.2015.09.028] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2015] [Revised: 09/13/2015] [Accepted: 09/17/2015] [Indexed: 11/26/2022]
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11
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Abstract
Myocardial infarction, commonly known as heart attack, is caused by reduced blood supply and damages the heart muscle because of a lack of oxygen. Myocardial infarction initiates a cascade of biochemical and mechanical events. In the early stages, cardiomyocytes death, wall thinning, collagen degradation, and ventricular dilation are the immediate consequences of myocardial infarction. In the later stages, collagenous scar formation in the infarcted zone and hypertrophy of the non-infarcted zone are auto-regulatory mechanisms to partly correct for these events. Here we propose a computational model for the short-term adaptation after myocardial infarction using the continuum theory of multiplicative growth. Our model captures the effects of cell death initiating wall thinning, and collagen degradation initiating ventricular dilation. Our simulations agree well with clinical observations in early myocardial infarction. They represent a first step toward simulating the progression of myocardial infarction with the ultimate goal to predict the propensity toward heart failure as a function of infarct intensity, location, and size.
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Affiliation(s)
- P Sáez
- a Mathematical Institute, University of Oxford , Oxford , UK
| | - E Kuhl
- b Department of Mechanical Engineering , Stanford University , Stanford , CA , USA
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12
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Effect of Transmural Transport Properties on Atheroma Plaque Formation and Development. Ann Biomed Eng 2015; 43:1516-30. [PMID: 25814436 DOI: 10.1007/s10439-015-1299-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2014] [Accepted: 03/10/2015] [Indexed: 10/23/2022]
Abstract
We propose a mathematical model of atheroma plaque initiation and early development in coronary arteries using anisotropic transmural diffusion properties. Our current approach is on the process on plaque initiation and intimal thickening rather than in severe plaque progression and rupture phenomena. The effect of transport properties, in particular the anisotropy of diffusion properties of the artery, on plaque formation and development is investigated using the proposed mathematical model. There is not a strong influence of the anisotropic transmural properties on LDL, SMCs and collagen distribution and concentrations along the artery. On the contrary, foam cells distribution strongly depends on the value of the radial diffusion coefficient of the substances [Formula: see text] and the ratio [Formula: see text]. Decreasing [Formula: see text] or diffusion coefficients ratio means a higher concentration of the foam cells close to the intima. Due to the fact that foam cells concentration is associated to the necrotic core formation, the final distribution of foam cells is critical to evolve into a vulnerable or fibrotic plaque.
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13
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Sáez P, Peña E, Tarbell JM, Martínez MA. Computational model of collagen turnover in carotid arteries during hypertension. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2015; 31:e02705. [PMID: 25643608 DOI: 10.1002/cnm.2705] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2014] [Revised: 01/15/2015] [Accepted: 01/15/2015] [Indexed: 06/04/2023]
Abstract
It is well known that biological tissues adapt their properties because of different mechanical and chemical stimuli. The goal of this work is to study the collagen turnover in the arterial tissue of hypertensive patients through a coupled computational mechano-chemical model. Although it has been widely studied experimentally, computational models dealing with the mechano-chemical approach are not. The present approach can be extended easily to study other aspects of bone remodeling or collagen degradation in heart diseases. The model can be divided into three different stages. First, we study the smooth muscle cell synthesis of different biological substances due to over-stretching during hypertension. Next, we study the mass-transport of these substances along the arterial wall. The last step is to compute the turnover of collagen based on the amount of these substances in the arterial wall which interact with each other to modify the turnover rate of collagen. We simulate this process in a finite element model of a real human carotid artery. The final results show the well-known stiffening of the arterial wall due to the increase in the collagen content.
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Affiliation(s)
- P Sáez
- Group of Applied Mechanics and Bioengineering. Aragón Institute of Engineering Research, University of Zaragoza, Zaragoza, Spain; Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Zaragoza, Spain; Mathematical Institute, University of Oxford, Oxford, UK
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14
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Buganza Tepole A, Kuhl E. Computational modeling of chemo-bio-mechanical coupling: a systems-biology approach toward wound healing. Comput Methods Biomech Biomed Engin 2014; 19:13-30. [DOI: 10.1080/10255842.2014.980821] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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15
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Weickenmeier J, Jabareen M. Elastic-viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative deformation gradient. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2014; 30:1238-62. [PMID: 24817477 DOI: 10.1002/cnm.2654] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Revised: 04/27/2014] [Accepted: 05/04/2014] [Indexed: 05/17/2023]
Abstract
The characteristic highly nonlinear, time-dependent, and often inelastic material response of soft biological tissues can be expressed in a set of elastic-viscoplastic constitutive equations. The specific elastic-viscoplastic model for soft tissues proposed by Rubin and Bodner (2002) is generalized with respect to the constitutive equations for the scalar quantity of the rate of inelasticity and the hardening parameter in order to represent a general framework for elastic-viscoplastic models. A strongly objective integration scheme and a new mixed finite element formulation were developed based on the introduction of the relative deformation gradient-the deformation mapping between the last converged and current configurations. The numerical implementation of both the generalized framework and the specific Rubin and Bodner model is presented. As an example of a challenging application of the new model equations, the mechanical response of facial skin tissue is characterized through an experimental campaign based on the suction method. The measurement data are used for the identification of a suitable set of model parameters that well represents the experimentally observed tissue behavior. Two different measurement protocols were defined to address specific tissue properties with respect to the instantaneous tissue response, inelasticity, and tissue recovery.
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Affiliation(s)
- J Weickenmeier
- Department of Mechanical and Process Engineering, ETH Zurich, Zurich, Switzerland
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16
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Use it or lose it: multiscale skeletal muscle adaptation to mechanical stimuli. Biomech Model Mechanobiol 2014; 14:195-215. [PMID: 25199941 DOI: 10.1007/s10237-014-0607-3] [Citation(s) in RCA: 77] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2014] [Accepted: 07/15/2014] [Indexed: 01/25/2023]
Abstract
Skeletal muscle undergoes continuous turnover to adapt to changes in its mechanical environment. Overload increases muscle mass, whereas underload decreases muscle mass. These changes are correlated with, and enabled by, structural alterations across the molecular, subcellular, cellular, tissue, and organ scales. Despite extensive research on muscle adaptation at the individual scales, the interaction of the underlying mechanisms across the scales remains poorly understood. Here, we present a thorough review and a broad classification of multiscale muscle adaptation in response to a variety of mechanical stimuli. From this classification, we suggest that a mathematical model for skeletal muscle adaptation should include the four major stimuli, overstretch, understretch, overload, and underload, and the five key players in skeletal muscle adaptation, myosin heavy chain isoform, serial sarcomere number, parallel sarcomere number, pennation angle, and extracellular matrix composition. Including this information in multiscale computational models of muscle will shape our understanding of the interacting mechanisms of skeletal muscle adaptation across the scales. Ultimately, this will allow us to rationalize the design of exercise and rehabilitation programs, and improve the long-term success of interventional treatment in musculoskeletal disease.
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Sáez P, Peña E, Martínez MA, Kuhl E. Computational modeling of hypertensive growth in the human carotid artery. COMPUTATIONAL MECHANICS 2014; 53:1183-1196. [PMID: 25342868 PMCID: PMC4203466 DOI: 10.1007/s00466-013-0959-z] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Arterial hypertension is a chronic medical condition associated with an elevated blood pressure. Chronic arterial hypertension initiates a series of events, which are known to collectively initiate arterial wall thickening. However, the correlation between macrostructural mechanical loading, microstructural cellular changes, and macrostructural adaptation remains unclear. Here, we present a microstructurally motivated computational model for chronic arterial hypertension through smooth muscle cell growth. To model growth, we adopt a classical concept based on the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. Motivated by clinical observations, we assume that the driving force for growth is the stretch sensed by the smooth muscle cells. We embed our model into a finite element framework, where growth is stored locally as an internal variable. First, to demonstrate the features of our model, we investigate the effects of hypertensive growth in a real human carotid artery. Our results agree nicely with experimental data reported in the literature both qualitatively and quantitatively.
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Affiliation(s)
- Pablo Sáez
- Group of Applied Mechanics and Bioengineering, Aragón Institute of Engineering Research, University of Zaragoza, Spain ; CIBER-BBN. Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina, Spain
| | - Estefania Peña
- Group of Applied Mechanics and Bioengineering, Aragón Institute of Engineering Research, University of Zaragoza, Spain ; CIBER-BBN. Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina, Spain
| | - Miguel Angel Martínez
- Group of Applied Mechanics and Bioengineering, Aragón Institute of Engineering Research, University of Zaragoza, Spain ; CIBER-BBN. Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina, Spain
| | - Ellen Kuhl
- Departments of Mechanical Engineering, Bioengineering, and Cardiothoracic Surgery, Stanford University, CA 94305, USA
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Cilla M, Peña E, Martínez MA. Mathematical modelling of atheroma plaque formation and development in coronary arteries. J R Soc Interface 2013; 11:20130866. [PMID: 24196695 DOI: 10.1098/rsif.2013.0866] [Citation(s) in RCA: 67] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
Atherosclerosis is a vascular disease caused by inflammation of the arterial wall, which results in the accumulation of low-density lipoprotein (LDL) cholesterol, monocytes, macrophages and fat-laden foam cells at the place of the inflammation. This process is commonly referred to as plaque formation. The evolution of the atherosclerosis disease, and in particular the influence of wall shear stress on the growth of atherosclerotic plaques, is still a poorly understood phenomenon. This work presents a mathematical model to reproduce atheroma plaque growth in coronary arteries. This model uses the Navier-Stokes equations and Darcy's law for fluid dynamics, convection-diffusion-reaction equations for modelling the mass balance in the lumen and intima, and the Kedem-Katchalsky equations for the interfacial coupling at membranes, i.e. endothelium. The volume flux and the solute flux across the interface between the fluid and the porous domains are governed by a three-pore model. The main species and substances which play a role in early atherosclerosis development have been considered in the model, i.e. LDL, oxidized LDL, monocytes, macrophages, foam cells, smooth muscle cells, cytokines and collagen. Furthermore, experimental data taken from the literature have been used in order to physiologically determine model parameters. The mathematical model has been implemented in a representative axisymmetric geometrical coronary artery model. The results show that the mathematical model is able to qualitatively capture the atheroma plaque development observed in the intima layer.
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Affiliation(s)
- Myriam Cilla
- Applied Mechanics and Bioengineering, Aragón Institute of Engineering Research (I3A), University of Zaragoza, , Zaragoza, Spain
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