A Proposal for a Novel Formulation Based on the Hyperbolic Cattaneo’s Equation to Describe the Mechano-Transduction Process Occurring in Bone Remodeling
In this paper, we propose a model for the mechanical stimulus involved in the process of bone remodeling together with its evolution over time. Accumulated evidence suggests that bone remodeling could be interpreted as a feedback control process in which the mechanical state of the bone tissue is mo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/11/2436 |
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| author | Daria Scerrato Ivan Giorgio Alberto Maria Bersani Daniele Andreucci |
| author_facet | Daria Scerrato Ivan Giorgio Alberto Maria Bersani Daniele Andreucci |
| author_sort | Daria Scerrato |
| collection | DOAJ |
| description | In this paper, we propose a model for the mechanical stimulus involved in the process of bone remodeling together with its evolution over time. Accumulated evidence suggests that bone remodeling could be interpreted as a feedback control process in which the mechanical state of the bone tissue is monitored, then appropriate signals are derived from the daily mechanical usage of the bone, these signals are transmitted into the surrounding region, and then they are detected by other agents whose purpose is to adapt the bone mass to the mechanical requirements of the environment. Therefore, we employ the diffusion equation for mass transport which is improved with Cattaneo’s correction to model the stimulus. This last improvement considers the effects of relaxation and non-locality, which we believe play essential roles in signaling messengers transport phenomena and are essential to match the evidence that suggests time-dependent excitations provide a more significant response at specific frequencies. To illustrate this particular behavior, numerical simulations have been performed in a 2D framework. The results fit the central aspect addressed, related to the dependency of the time of the adaptive process of bone, suggesting that our model is promising and deserves further investigation, both theoretical and experimental. |
| first_indexed | 2024-03-09T17:57:32Z |
| format | Article |
| id | doaj.art-d158e2a3e6a54dafb349d52f84271e0f |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T17:57:32Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-d158e2a3e6a54dafb349d52f84271e0f2023-11-24T10:14:01ZengMDPI AGSymmetry2073-89942022-11-011411243610.3390/sym14112436A Proposal for a Novel Formulation Based on the Hyperbolic Cattaneo’s Equation to Describe the Mechano-Transduction Process Occurring in Bone RemodelingDaria Scerrato0Ivan Giorgio1Alberto Maria Bersani2Daniele Andreucci3Dipartimento di Scienze di Base ed Applicate per l’Ingegneria (SBAI), University of Rome La Sapienza, 00161 Roma, ItalyInternational Research Center on Mathematics and Mechanics of Complex Systems (M&MoCS), University of L’Aquila, 67100 L’Aquila, ItalyInternational Research Center on Mathematics and Mechanics of Complex Systems (M&MoCS), University of L’Aquila, 67100 L’Aquila, ItalyDipartimento di Scienze di Base ed Applicate per l’Ingegneria (SBAI), University of Rome La Sapienza, 00161 Roma, ItalyIn this paper, we propose a model for the mechanical stimulus involved in the process of bone remodeling together with its evolution over time. Accumulated evidence suggests that bone remodeling could be interpreted as a feedback control process in which the mechanical state of the bone tissue is monitored, then appropriate signals are derived from the daily mechanical usage of the bone, these signals are transmitted into the surrounding region, and then they are detected by other agents whose purpose is to adapt the bone mass to the mechanical requirements of the environment. Therefore, we employ the diffusion equation for mass transport which is improved with Cattaneo’s correction to model the stimulus. This last improvement considers the effects of relaxation and non-locality, which we believe play essential roles in signaling messengers transport phenomena and are essential to match the evidence that suggests time-dependent excitations provide a more significant response at specific frequencies. To illustrate this particular behavior, numerical simulations have been performed in a 2D framework. The results fit the central aspect addressed, related to the dependency of the time of the adaptive process of bone, suggesting that our model is promising and deserves further investigation, both theoretical and experimental.https://www.mdpi.com/2073-8994/14/11/2436bone remodelingmechanical stimuluscyclic loadsCattaneo’s equationfunctional adaptation |
| spellingShingle | Daria Scerrato Ivan Giorgio Alberto Maria Bersani Daniele Andreucci A Proposal for a Novel Formulation Based on the Hyperbolic Cattaneo’s Equation to Describe the Mechano-Transduction Process Occurring in Bone Remodeling Symmetry bone remodeling mechanical stimulus cyclic loads Cattaneo’s equation functional adaptation |
| title | A Proposal for a Novel Formulation Based on the Hyperbolic Cattaneo’s Equation to Describe the Mechano-Transduction Process Occurring in Bone Remodeling |
| title_full | A Proposal for a Novel Formulation Based on the Hyperbolic Cattaneo’s Equation to Describe the Mechano-Transduction Process Occurring in Bone Remodeling |
| title_fullStr | A Proposal for a Novel Formulation Based on the Hyperbolic Cattaneo’s Equation to Describe the Mechano-Transduction Process Occurring in Bone Remodeling |
| title_full_unstemmed | A Proposal for a Novel Formulation Based on the Hyperbolic Cattaneo’s Equation to Describe the Mechano-Transduction Process Occurring in Bone Remodeling |
| title_short | A Proposal for a Novel Formulation Based on the Hyperbolic Cattaneo’s Equation to Describe the Mechano-Transduction Process Occurring in Bone Remodeling |
| title_sort | proposal for a novel formulation based on the hyperbolic cattaneo s equation to describe the mechano transduction process occurring in bone remodeling |
| topic | bone remodeling mechanical stimulus cyclic loads Cattaneo’s equation functional adaptation |
| url | https://www.mdpi.com/2073-8994/14/11/2436 |
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