{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T02:33:51Z","timestamp":1780626831123,"version":"3.54.1"},"reference-count":76,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,17]],"date-time":"2022-11-17T00:00:00Z","timestamp":1668643200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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\u2019s 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.<\/jats:p>","DOI":"10.3390\/sym14112436","type":"journal-article","created":{"date-parts":[[2022,11,18]],"date-time":"2022-11-18T03:35:23Z","timestamp":1668742523000},"page":"2436","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["A Proposal for a Novel Formulation Based on the Hyperbolic Cattaneo\u2019s Equation to Describe the Mechano-Transduction Process Occurring in Bone Remodeling"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8746-0856","authenticated-orcid":false,"given":"Daria","family":"Scerrato","sequence":"first","affiliation":[{"name":"Dipartimento di Scienze di Base ed Applicate per l\u2019Ingegneria (SBAI), University of Rome La Sapienza, 00161 Roma, Italy"},{"name":"International Research Center on Mathematics and Mechanics of Complex Systems (M&MoCS), University of L\u2019Aquila, 67100 L\u2019Aquila, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0044-9188","authenticated-orcid":false,"given":"Ivan","family":"Giorgio","sequence":"additional","affiliation":[{"name":"International Research Center on Mathematics and Mechanics of Complex Systems (M&MoCS), University of L\u2019Aquila, 67100 L\u2019Aquila, Italy"},{"name":"Dipartimento di Ingegneria Civile, Edile-Architettura e Ambientale (DICEAA), University of L\u2019Aquila, 67100 L\u2019Aquila, Italy"},{"name":"Gruppo Nazionale di Fisica Matematica (INdAM-GNFM), 00185 Roma, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8525-7363","authenticated-orcid":false,"given":"Alberto Maria","family":"Bersani","sequence":"additional","affiliation":[{"name":"International Research Center on Mathematics and Mechanics of Complex Systems (M&MoCS), University of L\u2019Aquila, 67100 L\u2019Aquila, Italy"},{"name":"Gruppo Nazionale di Fisica Matematica (INdAM-GNFM), 00185 Roma, Italy"},{"name":"Dipartimento di Ingegneria Meccanica e Aerospaziale (DIMA), University of Rome La Sapienza, 00184 Roma, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniele","family":"Andreucci","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze di Base ed Applicate per l\u2019Ingegneria (SBAI), University of Rome La Sapienza, 00161 Roma, Italy"},{"name":"Gruppo Nazionale di Fisica Matematica (INdAM-GNFM), 00185 Roma, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1002\/zamm.201100082","article-title":"A mixture model with evolving mass densities for describing synthesis and resorption phenomena in bones reconstructed with bio-resorbable materials","volume":"92","author":"Lekszycki","year":"2012","journal-title":"Z. 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