The role of structural viscoelasticity in deformable porous media with incompressibleconstituents: Applications in biomechanics
The main goal of this work is to clarify and quantify, by means of mathematical analysis, the role of structural viscoelasticity in the biomechanical response of deformable porous media with incompressible constituents to sudden changes in external applied loads. Models of deformable porous media wi...
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| Language: | English |
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AIMS Press
2018-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018042 |
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| author | Maurizio Verri Giovanna Guidoboni Lorena Bociu Riccardo Sacco |
| author_facet | Maurizio Verri Giovanna Guidoboni Lorena Bociu Riccardo Sacco |
| author_sort | Maurizio Verri |
| collection | DOAJ |
| description | The main goal of this work is to clarify and quantify, by means of mathematical analysis, the role of structural viscoelasticity in the biomechanical response of deformable porous media with incompressible constituents to sudden changes in external applied loads. Models of deformable porous media with incompressible constituents are often utilized to describe the behavior of biological tissues, such as cartilages, bones and engineered tissue scaffolds, where viscoelastic properties may change with age, disease or by design. Here, for the first time, we show that the fluid velocity within the medium could increase tremendously, even up to infinity, should the external applied load experience sudden changes in time and the structural viscoelasticity be too small. In particular, we consider a one-dimensional poro-visco-elastic model for which we derive explicit solutions in the cases where the external applied load is characterized by a step pulse or a trapezoidal pulse in time. By means of dimensional analysis, we identify some dimensionless parameters that can aid the design of structural properties and/or experimental conditions as to ensure that the fluid velocity within the medium remains bounded below a certain given threshold, thereby preventing potential tissue damage. The application to confined compression tests for biological tissues is discussed in detail. Interestingly, the loss of viscoelastic tissue properties has been associated with various disease conditions, such as atherosclerosis, Alzheimer’s disease and glaucoma. Thus, the findings of this work may be relevant to many applications in biology and medicine. |
| format | Article |
| id | doaj-art-655a3a47980d40308048f471a336bf1b |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-07-01 |
| publisher | AIMS Press |
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| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-655a3a47980d40308048f471a336bf1b2025-01-24T02:40:56ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-07-0115493395910.3934/mbe.2018042The role of structural viscoelasticity in deformable porous media with incompressibleconstituents: Applications in biomechanicsMaurizio Verri0Giovanna Guidoboni1Lorena Bociu2Riccardo Sacco3Politecnico di Milano, Dipartimento di Matematica, ItalyUniversity of Missouri, Department of Electrical Engineering and Computer Science, USANC State University, Department of Mathematics, USAPolitecnico di Milano, Dipartimento di Matematica, ItalyThe main goal of this work is to clarify and quantify, by means of mathematical analysis, the role of structural viscoelasticity in the biomechanical response of deformable porous media with incompressible constituents to sudden changes in external applied loads. Models of deformable porous media with incompressible constituents are often utilized to describe the behavior of biological tissues, such as cartilages, bones and engineered tissue scaffolds, where viscoelastic properties may change with age, disease or by design. Here, for the first time, we show that the fluid velocity within the medium could increase tremendously, even up to infinity, should the external applied load experience sudden changes in time and the structural viscoelasticity be too small. In particular, we consider a one-dimensional poro-visco-elastic model for which we derive explicit solutions in the cases where the external applied load is characterized by a step pulse or a trapezoidal pulse in time. By means of dimensional analysis, we identify some dimensionless parameters that can aid the design of structural properties and/or experimental conditions as to ensure that the fluid velocity within the medium remains bounded below a certain given threshold, thereby preventing potential tissue damage. The application to confined compression tests for biological tissues is discussed in detail. Interestingly, the loss of viscoelastic tissue properties has been associated with various disease conditions, such as atherosclerosis, Alzheimer’s disease and glaucoma. Thus, the findings of this work may be relevant to many applications in biology and medicine.https://www.aimspress.com/article/doi/10.3934/mbe.2018042deformable porous media flowincompressible constituentsviscoelasticityexplicit solutionvelocity blow-upconfined compression |
| spellingShingle | Maurizio Verri Giovanna Guidoboni Lorena Bociu Riccardo Sacco The role of structural viscoelasticity in deformable porous media with incompressibleconstituents: Applications in biomechanics Mathematical Biosciences and Engineering deformable porous media flow incompressible constituents viscoelasticity explicit solution velocity blow-up confined compression |
| title | The role of structural viscoelasticity in deformable porous media with incompressibleconstituents: Applications in biomechanics |
| title_full | The role of structural viscoelasticity in deformable porous media with incompressibleconstituents: Applications in biomechanics |
| title_fullStr | The role of structural viscoelasticity in deformable porous media with incompressibleconstituents: Applications in biomechanics |
| title_full_unstemmed | The role of structural viscoelasticity in deformable porous media with incompressibleconstituents: Applications in biomechanics |
| title_short | The role of structural viscoelasticity in deformable porous media with incompressibleconstituents: Applications in biomechanics |
| title_sort | role of structural viscoelasticity in deformable porous media with incompressibleconstituents applications in biomechanics |
| topic | deformable porous media flow incompressible constituents viscoelasticity explicit solution velocity blow-up confined compression |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018042 |
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