Multiscale mathematical modeling in dental tissue engineering: towards computer-aided design of a regenerative system based on hydroxyapatite granules, focusing on early and mid-term stiffness recovery
We here explore for the very first time how an advanced multiscale mathematical modeling approach may support the design of a provenly successful tissue engineering concept for mandibular bone. The latter employs double-porous, potentially cracked, single millimeter-sized granules packed into an ove...
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doaj-876d987eb99a4886b33ef3b15af605d92020-11-24T22:25:48ZengFrontiers Media S.A.Frontiers in Physiology1664-042X2016-09-01710.3389/fphys.2016.00383209685Multiscale mathematical modeling in dental tissue engineering: towards computer-aided design of a regenerative system based on hydroxyapatite granules, focusing on early and mid-term stiffness recoveryStefan Scheiner0Vladimir S. Komlev1Vladimir S. Komlev2Alexey N. Gurin3Christian Hellmich4TU Wien - Vienna University of TechnologyRussian Academy of SciencesRussian Academy of SciencesCentral Scientific Research Institute of Dentistry and Maxillofacial SurgeryTU Wien - Vienna University of TechnologyWe here explore for the very first time how an advanced multiscale mathematical modeling approach may support the design of a provenly successful tissue engineering concept for mandibular bone. The latter employs double-porous, potentially cracked, single millimeter-sized granules packed into an overall scaffold material, which is then gradually penetrated and partially replaced by newly grown bone tissue. During this process, the newly developing scaffold-bone compound needs to attain the stiffness of mandibular bone under normal physiological conditions; and the question arises how the compound stiffness is driven by the key design parameters of the tissue engineering system: macroporosity, crack density, as well as scaffold resorption/bone formation rates. We here tackle this question by combining the latest state-of-the-art mathematical modeling techniques in the field of multiscale micromechanics, into an unprecedented suite of highly efficient, semi-analytically defined computation steps resolving several levels of hierarchical organization, from the millimeter down to the nanometer scale. This includes several types of homogenization schemes, namely such for porous polycrystals with elongated solid elements, for cracked matrix-inclusion composites, as well as for assemblies of coated spherical compounds. Together with the experimentally known stiffnesses of hydroxyapatite crystals and mandibular bone tissue, the new mathematical model suggests that early stiffness recovery (i.e within several weeks) requires total avoidance of microcracks in the hydroxyapatite scaffolds, while mid-term stiffness recovery (i.e. within several months) can also be achieved through provision of small granule sizes, in combination with high bone formation and low scaffold resorption rates.http://journal.frontiersin.org/Journal/10.3389/fphys.2016.00383/fullMultiscalehomogenizationhydroxyapatiteMaterial optimizationBone ingrowth |
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language |
English |
format |
Article |
sources |
DOAJ |
author |
Stefan Scheiner Vladimir S. Komlev Vladimir S. Komlev Alexey N. Gurin Christian Hellmich |
spellingShingle |
Stefan Scheiner Vladimir S. Komlev Vladimir S. Komlev Alexey N. Gurin Christian Hellmich Multiscale mathematical modeling in dental tissue engineering: towards computer-aided design of a regenerative system based on hydroxyapatite granules, focusing on early and mid-term stiffness recovery Frontiers in Physiology Multiscale homogenization hydroxyapatite Material optimization Bone ingrowth |
author_facet |
Stefan Scheiner Vladimir S. Komlev Vladimir S. Komlev Alexey N. Gurin Christian Hellmich |
author_sort |
Stefan Scheiner |
title |
Multiscale mathematical modeling in dental tissue engineering: towards computer-aided design of a regenerative system based on hydroxyapatite granules, focusing on early and mid-term stiffness recovery |
title_short |
Multiscale mathematical modeling in dental tissue engineering: towards computer-aided design of a regenerative system based on hydroxyapatite granules, focusing on early and mid-term stiffness recovery |
title_full |
Multiscale mathematical modeling in dental tissue engineering: towards computer-aided design of a regenerative system based on hydroxyapatite granules, focusing on early and mid-term stiffness recovery |
title_fullStr |
Multiscale mathematical modeling in dental tissue engineering: towards computer-aided design of a regenerative system based on hydroxyapatite granules, focusing on early and mid-term stiffness recovery |
title_full_unstemmed |
Multiscale mathematical modeling in dental tissue engineering: towards computer-aided design of a regenerative system based on hydroxyapatite granules, focusing on early and mid-term stiffness recovery |
title_sort |
multiscale mathematical modeling in dental tissue engineering: towards computer-aided design of a regenerative system based on hydroxyapatite granules, focusing on early and mid-term stiffness recovery |
publisher |
Frontiers Media S.A. |
series |
Frontiers in Physiology |
issn |
1664-042X |
publishDate |
2016-09-01 |
description |
We here explore for the very first time how an advanced multiscale mathematical modeling approach may support the design of a provenly successful tissue engineering concept for mandibular bone. The latter employs double-porous, potentially cracked, single millimeter-sized granules packed into an overall scaffold material, which is then gradually penetrated and partially replaced by newly grown bone tissue. During this process, the newly developing scaffold-bone compound needs to attain the stiffness of mandibular bone under normal physiological conditions; and the question arises how the compound stiffness is driven by the key design parameters of the tissue engineering system: macroporosity, crack density, as well as scaffold resorption/bone formation rates. We here tackle this question by combining the latest state-of-the-art mathematical modeling techniques in the field of multiscale micromechanics, into an unprecedented suite of highly efficient, semi-analytically defined computation steps resolving several levels of hierarchical organization, from the millimeter down to the nanometer scale. This includes several types of homogenization schemes, namely such for porous polycrystals with elongated solid elements, for cracked matrix-inclusion composites, as well as for assemblies of coated spherical compounds. Together with the experimentally known stiffnesses of hydroxyapatite crystals and mandibular bone tissue, the new mathematical model suggests that early stiffness recovery (i.e within several weeks) requires total avoidance of microcracks in the hydroxyapatite scaffolds, while mid-term stiffness recovery (i.e. within several months) can also be achieved through provision of small granule sizes, in combination with high bone formation and low scaffold resorption rates. |
topic |
Multiscale homogenization hydroxyapatite Material optimization Bone ingrowth |
url |
http://journal.frontiersin.org/Journal/10.3389/fphys.2016.00383/full |
work_keys_str_mv |
AT stefanscheiner multiscalemathematicalmodelingindentaltissueengineeringtowardscomputeraideddesignofaregenerativesystembasedonhydroxyapatitegranulesfocusingonearlyandmidtermstiffnessrecovery AT vladimirskomlev multiscalemathematicalmodelingindentaltissueengineeringtowardscomputeraideddesignofaregenerativesystembasedonhydroxyapatitegranulesfocusingonearlyandmidtermstiffnessrecovery AT vladimirskomlev multiscalemathematicalmodelingindentaltissueengineeringtowardscomputeraideddesignofaregenerativesystembasedonhydroxyapatitegranulesfocusingonearlyandmidtermstiffnessrecovery AT alexeyngurin multiscalemathematicalmodelingindentaltissueengineeringtowardscomputeraideddesignofaregenerativesystembasedonhydroxyapatitegranulesfocusingonearlyandmidtermstiffnessrecovery AT christianhellmich multiscalemathematicalmodelingindentaltissueengineeringtowardscomputeraideddesignofaregenerativesystembasedonhydroxyapatitegranulesfocusingonearlyandmidtermstiffnessrecovery |
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