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Stress-modulated remodeling of a non-homogeneous body
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Track 14. Cardiovascular Mechanics 14.12. Tissue Adaptation and Remodelling $315 and function of endothelial cells and smooth muscle cells are not well under- stood yet. Hence we studied the effect of hydrostatic pressure on proliferation of the cells of a hybrid vascular graft by seeding bovine aortic smooth muscle cells (SMCs) and endothelial cells (ECs) on the luminal surface of a 3.0- mm inner diameter expanded PTFE graft and co-culturing them under four different hydrostatic pressures. It was found that 7 days' exposure of the cells of a hybrid graft to hydrostatic pressures of 80, 100, and 120mmHg resulted in a remarkable increase in the thickness of the cell layer (an index of the proliferation of SMCs) as compared with a control co-cultured under a hydrostatic pressure of 0 mmHg. The difference in the thickness of the cell layer between pressurized and non-pressurized samples was not statistically significant at 80 mmHg, but it was significant at 100 and 120 mmHg where the thickness of the cell layer was respectively 116% and 74.5% greater than that of control. It was also found that synthesis of collagen increased by 24.3, 90.1, and 15.8% at 80, 100, and 120mmHg, respectively, indicating that the cell layer became thicker under the elevated hydrostatic pressures not only by the proliferation of SMCs, but also by the increase in the amount of extracellular matrices. 14.12. Tissue Adaptation and Remodelling 4290 Th, 11:00-11:30 (P42) Theoretical framework for vascular growth and remodeling J.D. Humphrey. Department of Biomedical Engineering, Texas A&M University, College Station, TX, USA Research over the last three decades has revealed a ubiquitous cell-mediated growth and remodeling in arterial development, adaptation, and response to disease/injury, and demonstrated that these processes are controlled in large part by mechanical stimuli. Although the response of an artery to disease/injury versus perturbed blood pressures, flows, and axial loads may be manifested differently (e.g., formation of an acellular neointima, hypertrophy versus atrophy of smooth muscle in the media, or increased deposition of collagen in the adventitia), the basic underlying processes appear to be the same. Arterial adaptation results from changes in cellular activity that include changes in the rates of mitosis (cell division) or apoptosis (programmed cell death), rates of cell migration and differentiation (change of phenotype), hypertrophy and atrophy, and rates of synthesis, degradation, or cross-linking of extracellular matrix. Overall, therefore, what appears to be most important mechanically are the separate rates of turnover of individual constituents and the evolving configurations in which such turnover occurs. The goal of this work is to formulate a simple theoretical framework to model basic features of the biomechanics of arterial growth and remodeling. The framework is motivated by the hypothesis that growth and remodeling occurs via the heightened replacement of previously existing constituents with new constituents that have new 'natural configurations' but otherwise similar me- chanical properties. Towards this end, the stress response of each structurally- dominant constituent is modeled using a constrained mixture approach and the turnover of each constituent is modeled using explicit kinetics. Given the current lack of sufficient data, competing hypotheses are explored via numeri- cal simulations. Although there is clearly a need to evolve more sophisticated models, it is hoped that the present basic concepts and associated constrained mixture framework will serve to motivate appropriate new experiments and to focus advances in the modeling. 6736 Th, 11:30-11:45 (P42) On a theory of growth and residual stress in soft tissue A. Guillou 1, R.W. Ogden 2 . 1Dipartimento di Matematica, Politecnico di Torino, Italy, 2Department of Mathematics, University of Glasgow, UK In this paper we summarize a general continuum mechanical theory that takes account of growth in materials capable of large deformations, with particular reference to soft biological tissues such as arterial walls. The material response is elastic at any stage of the growth and the stress depends on the growth, but equally the growth depends on the stress. Part of the objective is to relate the growth to the development of residual stress. The theory, unlike that developed by Rodriguez et al. [1] and adopted also by many subsequent researchers, does not require the introduction of a so-called 'growth tensor', which itself requires the notion of a locally (fictitious or virtual) stress-free configuration. The theory is illustrated by its application to a circular cylindrical tube subject to extension and internal pressure when the wall thickness changes as a result of persistent high pressure - an artery is modelled as a thick-walled residually- stressed mechanically incompressible tube. For a specific model the theory is used for the numerical calculation of the resulting evolution in wall thickness and residual stress. An initial outline of the theory together with a simple illustration was provided by Guillou and Ogden [2]; here this work is developed further by use of a model that facilitates interpretation of the results. References [1] E.K. Rodriguez, A. Hoger and A.D. McCulloch, Stress-dependent finite growth in soft elastic tissues. J. Biomech. 1994; 27: 455-467. [2] A. Guillou and R.W. Ogden, Growth in soft biological tissue and residual stress development. Proceedings of the IUTAM Symposium on Mechanics of Biological Tissue (G.A. Holzapfel and R.W. Ogden, eds), Graz, Austria, June/July 2004, 2006; pp.47-62, Springer. 4983 Th, 11:45-12:00 (P42) Stress-modulated remodeling of a non-homogeneous body D. Ambrosi 1, A. Guillou 1, E.S. Di Martino 2. 1Dipartimento di Matematica, Politecnico di Torino, Torino, Italy, 2Institute for Complex Engineered Systems, Cardiovascular Biomechanics Lab, Carnegie Mellon University, Pittsburgh, PA, USA Many soft tissues, and arteries in primis, exhibit residual stresses after un- loading, a mechanical characteristic related to the self-organization ability of the cellular matter under load. This behaviour can be theoretically predicted in a continuum mechanics framework by assuming that the biological body remodels toward a homeostatic stress state, that is, a state of tension that the cells tend to achieve by internal reorganization. In the last years much attention has been devoted to the investigation of the kinematics of growth. Most recent contributions are currently devoted to the dynamics of growth, Le. to the prediction of the remodeling process of material reorganization. This issue is strictly related to open questions concerning the stability of a stationary grown state, as dictated by a growth law, by the mechanical characteristics of the material and by the specific external loads. The aim of this contribution is to investigate by numerical simulation the role of the remodeling process in a non-homogeneous aortic vessel under some geometrical simplifications. The body is considered to be axis-symmetric and made of non-linear orthotropic hyperelastic material. The numerical results obtained suggest that a stress-modulated remodeling of the wall of the vessel can have a stabilizing effect versus possible local variations in the mechanical properties of the material. These preliminary results seem to suggest that stress mediates wall remodel- ing until a new, homeostatic, configuration is reached and that the latter may subsist until mechanical and biochemical factors in the wall call for a new remodeling stage. 6894 Th, 12:00-12:15 (P42) Dynamics of arterial remodeling in response to hypertension using a structural-based model A. Tsamis, N. Stergiopulos. Laboratory of Hemodynamics and Cardiovascular Technology, EPFL, Lausanne, Switzerland Arterial remodeling under sustained hypertension has been modeled earlier by means of stress-driven remodeling rate equations [1] and was extended to include adaptation of elastic properties [2]. The models, however, used Chuong & Fung's phenomenological strain energy function (SEF), in which elastic constants do not bear a clear physiological meaning. We here extend the work of Rachev et al. [2] by applying similar remodeling rate equations to the constituent-based SEF proposed by Zulliger et al. [3]. The wall is modeled as an elastic, incompressible, isotropic-transotropic ma- terial described by the SEF of Zulliger et al. [3], which accounts for the con- stituents and structural properties of the wall, including a statistical description for collagen engagement. The remodeling rate equations are similar to those of Rachev et al. [2], with the exception that compliance affects the properties of the collagen engagement probability density function. Geometric remodeling precedes adaptation of elastic properties by an appropriate choice of time constants. Wall remodeling alters the mass of collagen and elastin maintaining the relative percent composition of each constituent constant. The model predicts asymptotic wall thickening and unchanged deformed inner radius as to conserve hoop stress and intimal shear stress, respectively, at the final adapted hypertensive state. Compliance is also restored to control levels. Stress-strain curves remain relatively unchanged, showing that the incremental elastic modulus is not modified during the remodeling process. Pressure-diameter curves are in good agreement with experimental findings. References [1] Rachev A, Stergiopulos N, Meister JJ. Theoretical study of dynamics of arterial wall remodeling in response to changes in blood pressure. J Biomech 1996; 29: 635~42. [2] Rachev A, Stergiopulos N, Meister JJ. A model for geometric and mechanical adaptation of arteries to sustained hypertension. J Biomech Eng 1998; 120: 9-17. [3] Zulliger MA, Fridez P, Hayashi K, Stergiopulos N. A strain energy function for arteries accounting for wall composition and structure. J Biomech 2004; 37: 989-1000.
Transcript of Stress-modulated remodeling of a non-homogeneous body
Track 14. Cardiovascular Mechanics 14.12. Tissue Adaptation and Remodelling $315
and function of endothelial cells and smooth muscle cells are not well under- stood yet. Hence we studied the effect of hydrostatic pressure on proliferation of the cells of a hybrid vascular graft by seeding bovine aortic smooth muscle cells (SMCs) and endothelial cells (ECs) on the luminal surface of a 3.0- mm inner diameter expanded PTFE graft and co-culturing them under four different hydrostatic pressures. It was found that 7 days' exposure of the cells of a hybrid graft to hydrostatic pressures of 80, 100, and 120mmHg resulted in a remarkable increase in the thickness of the cell layer (an index of the proliferation of SMCs) as compared with a control co-cultured under a hydrostatic pressure of 0 mmHg. The difference in the thickness of the cell layer between pressurized and non-pressurized samples was not statistically significant at 80 mmHg, but it was significant at 100 and 120 mmHg where the thickness of the cell layer was respectively 116% and 74.5% greater than that of control. It was also found that synthesis of collagen increased by 24.3, 90.1, and 15.8% at 80, 100, and 120mmHg, respectively, indicating that the cell layer became thicker under the elevated hydrostatic pressures not only by the proliferation of SMCs, but also by the increase in the amount of extracellular matrices.
14.12. Tissue Adaptation and Remodelling 4290 Th, 11:00-11:30 (P42) Theoret ical framework for vascular growth and remodel ing J.D. Humphrey. Department of Biomedical Engineering, Texas A&M University, College Station, TX, USA
Research over the last three decades has revealed a ubiquitous cell-mediated growth and remodeling in arterial development, adaptation, and response to disease/injury, and demonstrated that these processes are controlled in large part by mechanical stimuli. Although the response of an artery to disease/injury versus perturbed blood pressures, flows, and axial loads may be manifested differently (e.g., formation of an acellular neointima, hypertrophy versus atrophy of smooth muscle in the media, or increased deposition of collagen in the adventitia), the basic underlying processes appear to be the same. Arterial adaptation results from changes in cellular activity that include changes in the rates of mitosis (cell division) or apoptosis (programmed cell death), rates of cell migration and differentiation (change of phenotype), hypertrophy and atrophy, and rates of synthesis, degradation, or cross-linking of extracellular matrix. Overall, therefore, what appears to be most important mechanically are the separate rates of turnover of individual constituents and the evolving configurations in which such turnover occurs. The goal of this work is to formulate a simple theoretical framework to model basic features of the biomechanics of arterial growth and remodeling. The framework is motivated by the hypothesis that growth and remodeling occurs via the heightened replacement of previously existing constituents with new constituents that have new 'natural configurations' but otherwise similar me- chanical properties. Towards this end, the stress response of each structurally- dominant constituent is modeled using a constrained mixture approach and the turnover of each constituent is modeled using explicit kinetics. Given the current lack of sufficient data, competing hypotheses are explored via numeri- cal simulations. Although there is clearly a need to evolve more sophisticated models, it is hoped that the present basic concepts and associated constrained mixture framework will serve to motivate appropriate new experiments and to focus advances in the modeling.
6736 Th, 11:30-11:45 (P42) On a theory o f growth and residual s t ress in sof t t issue
A. Guillou 1 , R.W. Ogden 2 . 1Dipartimento di Matematica, Politecnico di Torino, Italy, 2Department of Mathematics, University of Glasgow, UK
In this paper we summarize a general continuum mechanical theory that takes account of growth in materials capable of large deformations, with particular reference to soft biological tissues such as arterial walls. The material response is elastic at any stage of the growth and the stress depends on the growth, but equally the growth depends on the stress. Part of the objective is to relate the growth to the development of residual stress. The theory, unlike that developed by Rodriguez et al. [1] and adopted also by many subsequent researchers, does not require the introduction of a so-called 'growth tensor', which itself requires the notion of a locally (fictitious or virtual) stress-free configuration. The theory is illustrated by its application to a circular cylindrical tube subject to extension and internal pressure when the wall thickness changes as a result of persistent high pressure - an artery is modelled as a thick-walled residually- stressed mechanically incompressible tube. For a specific model the theory is used for the numerical calculation of the resulting evolution in wall thickness and residual stress. An initial outline of the theory together with a simple illustration was provided by Guillou and Ogden [2]; here this work is developed further by use of a model that facilitates interpretation of the results.
References [1] E.K. Rodriguez, A. Hoger and A.D. McCulloch, Stress-dependent finite growth
in soft elastic tissues. J. Biomech. 1994; 27: 455-467. [2] A. Guillou and R.W. Ogden, Growth in soft biological tissue and residual stress
development. Proceedings of the IUTAM Symposium on Mechanics of Biological Tissue (G.A. Holzapfel and R.W. Ogden, eds), Graz, Austria, June/July 2004, 2006; pp.47-62, Springer.
4983 Th, 11:45-12:00 (P42) Stress-modulated remodel ing of a non-homogeneous body
D. Ambrosi 1 , A. Guillou 1 , E.S. Di Martino 2. 1Dipartimento di Matematica, Politecnico di Torino, Torino, Italy, 2Institute for Complex Engineered Systems, Cardiovascular Biomechanics Lab, Carnegie Mellon University, Pittsburgh, PA, USA
Many soft tissues, and arteries in primis, exhibit residual stresses after un- loading, a mechanical characteristic related to the self-organization ability of the cellular matter under load. This behaviour can be theoretically predicted in a continuum mechanics framework by assuming that the biological body remodels toward a homeostatic stress state, that is, a state of tension that the cells tend to achieve by internal reorganization. In the last years much attention has been devoted to the investigation of the kinematics of growth. Most recent contributions are currently devoted to the dynamics of growth, Le. to the prediction of the remodeling process of material reorganization. This issue is strictly related to open questions concerning the stability of a stationary grown state, as dictated by a growth law, by the mechanical characteristics of the material and by the specific external loads. The aim of this contribution is to investigate by numerical simulation the role of the remodeling process in a non-homogeneous aortic vessel under some geometrical simplifications. The body is considered to be axis-symmetric and made of non-linear orthotropic hyperelastic material. The numerical results obtained suggest that a stress-modulated remodeling of the wall of the vessel can have a stabilizing effect versus possible local variations in the mechanical properties of the material. These preliminary results seem to suggest that stress mediates wall remodel- ing until a new, homeostatic, configuration is reached and that the latter may subsist until mechanical and biochemical factors in the wall call for a new remodeling stage.
6894 Th, 12:00-12:15 (P42) Dynamics o f arterial remodel ing in response to hyper tens ion using a st ructural -based model A. Tsamis, N. Stergiopulos. Laboratory of Hemodynamics and Cardiovascular Technology, EPFL, Lausanne, Switzerland
Arterial remodeling under sustained hypertension has been modeled earlier by means of stress-driven remodeling rate equations [1] and was extended to include adaptation of elastic properties [2]. The models, however, used Chuong & Fung's phenomenological strain energy function (SEF), in which elastic constants do not bear a clear physiological meaning. We here extend the work of Rachev et al. [2] by applying similar remodeling rate equations to the constituent-based SEF proposed by Zulliger et al. [3]. The wall is modeled as an elastic, incompressible, isotropic-transotropic ma- terial described by the SEF of Zulliger et al. [3], which accounts for the con- stituents and structural properties of the wall, including a statistical description for collagen engagement. The remodeling rate equations are similar to those of Rachev et al. [2], with the exception that compliance affects the properties of the collagen engagement probability density function. Geometric remodeling precedes adaptation of elastic properties by an appropriate choice of time constants. Wall remodeling alters the mass of collagen and elastin maintaining the relative percent composition of each constituent constant. The model predicts asymptotic wall thickening and unchanged deformed inner radius as to conserve hoop stress and intimal shear stress, respectively, at the final adapted hypertensive state. Compliance is also restored to control levels. Stress-strain curves remain relatively unchanged, showing that the incremental elastic modulus is not modified during the remodeling process. Pressure-diameter curves are in good agreement with experimental findings.
References [1] Rachev A, Stergiopulos N, Meister JJ. Theoretical study of dynamics of arterial
wall remodeling in response to changes in blood pressure. J Biomech 1996; 29: 635~42.
[2] Rachev A, Stergiopulos N, Meister JJ. A model for geometric and mechanical adaptation of arteries to sustained hypertension. J Biomech Eng 1998; 120: 9-17.
[3] Zulliger MA, Fridez P, Hayashi K, Stergiopulos N. A strain energy function for arteries accounting for wall composition and structure. J Biomech 2004; 37: 989-1000.
