A simple model of collagen remodeling

Grzegorz Dudziuk , Mirosław Lachowicz , Henryk Leszczyński , Zuzanna Szymańska


In the present paper we propose and study a simple model of collagen remodeling occurring in latter stage of tendon healing process. The model is an integro-differential equation describing the possibility of an alignment of collagen fibers in a finite time. We show that the solutions may either exist globally in time or blow-up in a finite time depending on initial data. The latter behavior can be related to the healing of injury without the scar formation in a finite time: a full alignment of collagen fibers. We believe that the present model is an essential ingredient of the full description of collagen remodeling.
Author Grzegorz Dudziuk
Grzegorz Dudziuk,,
, Mirosław Lachowicz
Mirosław Lachowicz,,
, Henryk Leszczyński (FMPI / IM)
Henryk Leszczyński,,
- Institute of Mathematics
, Zuzanna Szymańska
Zuzanna Szymańska,,
Journal seriesDiscrete and Continuous Dynamical Systems-Series B, ISSN 1531-3492, (N/A 100 pkt)
Issue year2019
Publication size in sheets0.6
Keywords in Englishcollagen remodeling, blow-ups, integro-differential equations, alignment, mathematical model, tendon healing
ASJC Classification2604 Applied Mathematics; 2607 Discrete Mathematics and Combinatorics
URL http://aimsciences.org/article/doi/10.3934/dcdsb.2019091
Languageen angielski
Score (nominal)100
Score sourcejournalList
ScoreMinisterial score = 100.0, 28-01-2020, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2018 = 0.782; WoS Impact Factor: 2018 = 1.008 (2) - 2018=1.283 (5)
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