A simple model of collagen remodeling

Dudziuk, Grzegorz; Lachowicz, Mirosław; Leszczyński, Henryk; Szymańska, Zuzanna

doi:10.3934/dcdsb.2019091

Cited by 4 publications

(13 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The phenomenon that cells are able to sense direction is known from many biological scenarios, including chemotaxis and haptotaxis. It is known from the clinical practice but also had some reflection in emerging tendon healing models, see [25], that for the healing process the proper surgical intervention is of the highest importance. "Proper" means the best possible reconstruction of the collagen fibre arrangement along the longitudinal axis.…”

Section: Biology Of the Tendonmentioning

confidence: 99%

“…Only recently a simple model for the dynamics of collagen remodelling occurring in the latter stage of the tendon healing process was proposed by Dudziuk et al [25]. The authors propose an integro-differential equation describing the dynamics of the probability density of collagen fibres in space and orientation.…”

mentioning

confidence: 99%

“…The particular structure of these kinetic models allows for the derivation of simplified models for the associated dynamics via the methodology of grazing collision limits, that is, the integro-differential operators is approximated by Fokker-Planck differential operators of second order. This powerful tool of kinetic theory, used in other applications [50,51,15], allows for a reduction in the complexity of the kinetic model for the dynamics of tendon healing compared to [25]. In summary, the main contribution of our work is to propose a reduced model for the dynamics of tendon healing compared to previous literature.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Mathematical modelling of collagen fibres rearrangement during the tendon healing process

Carrillo¹,

Parisot²,

Szymańska³

2021

KRM

Self Cite

View full text Add to dashboard Cite

Tendon injuries present a clinical challenge to modern medicine as they heal slowly and rarely is there full restoration to healthy tendon structure and mechanical strength. Moreover, the process of healing is not fully elucidated. To improve understanding of tendon function and the healing process, we propose a new model of collagen fibres rearrangement during tendon healing. The model consists of an integro-differential equation describing the dynamics of collagen fibres distribution. We further reduce the model in a suitable asymptotic regime leading to a nonlinear non-local Fokker-Planck type equation for the spatial and orientation distribution of collagen fibre bundles. Due to its simplicity, the reduced model allows for possible parameter estimation based on data. We showcase some of the qualitative properties of this model simulating its long time asymptotic behaviour and the total time for tendon fibres to align in terms of the model parameters. A possible biological interpretation of the numerical experiments performed leads us to the working hypothesis of the importance of tendon cell size in patient recovery.

show abstract

Section: Biology Of the Tendonmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Mathematical modelling of collagen fibres rearrangement during the tendon healing process

Carrillo¹,

Parisot²,

Szymańska³

2021

KRM

Self Cite

View full text Add to dashboard Cite

show abstract

“…We show that the class corresponds to the partially integral stochastic semigroups and under some more restrictive assumptions leads to the stability result. We discuss possible applica-tions of the general theory such as redistribution of individuals - [10], thermal denaturation of DNA [7], and tendon healing process - [11].…”

Section: Microscopic Scalementioning

confidence: 99%

“…In particular under some rather restrictive assumptions we observe that any, even non-factorized, initial probability density tends in the evolution to a factorized equilibrium probability density - [16]. We discuss possible applications of the general theory such as redistribution of individuals -[10], thermal denaturation of DNA [7], and tendon healing process - [11].…”

mentioning

confidence: 99%

A class of individual-based models

Lachowicz

2018

BIOMATH

View full text Add to dashboard Cite

We discuss a class of mathematical models of biological systems at microscopic level - i.e. at the level of interacting individuals of a population. The class leads to partially integral stochastic semigroups- [5]. We state general conditions guaranteeing the asymptotic stability. In particular under some rather restrictive assumptions we observe that any, even non-factorized, initial probability density tends in the evolution to a factorized equilibrium probability density - [4]. We discuss possible applications of the general theory such as redistribution of individuals - [2], thermal denaturation of DNA [1], and tendon healing process - [3]. [1] M. Debowski, M. Lachowicz, and Z. Szymanska, Microscopic description of DNA thermal denaturation, to appear. [2] M. Dolfin, M. Lachowicz, and A. Schadschneider, A microscopic model of redistribution of individuals inside an 'elevator', In Modern Problems in Applied Analysis, P. Drygas and S. Rogosin (Eds.), Bikhauser, Basel (2018), 77--86; DOI: 10.1007/978--3--319--72640-3.[3] G. Dudziuk, M. Lachowicz, H. Leszczynski, and Z. Szymanska, A simple model of collagen remodeling, to appear.[4] M. Lachowicz, A class of microscopic individual models corresponding to the macroscopic logistic growth, Math. Methods Appl. Sci., 2017, on--line, DOI: 10.1002/mma.4680[5] K. Pichor and R. Rudnicki, Continuous Markov semigroups and stability of transport equations, J. Math. Analysis Appl. 249, 2000, 668--685, DOI: 10.1006/jmaa.2000.6968

show abstract

Peningkatan Ekspresi Matrix Metalloproteinase-9 Ligamentum Sacrouterina dan Otot Levator Ani Postpartum Rattus Norvegicus

Ariani

2021

j.kesehatan metro sai wawai

View full text Add to dashboard Cite

Background: Vaginal delivery is a risk factor for pelvic organ prolapse. The biomolecular mechanism that links it is still unclear, thought to be through Matrix Metalloproteinase 9 (MMP-9). Purpose: This study aims to determine the increase in MMP-9 in the supporting tissues of the pelvic organs, especially the sacrouterine ligament and levator ani muscles in the postpartum period. Methods: This study was an observational cohort study on 5 female rats of Rattus norvegicus Wistar strain. Which were divided into nulliparous groups, postpartum day 1, day 3, and day 7. MMP-9 expression was calculated and analyzed using ANOVA. Results: There was a significant difference (p=0.01) of MMP-9 expression in the sacrouterine ligament between nulliparous rats, postpartum day 1, day 3, and day 7. There was also a significant difference (p=0.00) levator ani muscle MMP-9 expression between nulliparous rats, postpartum day 1, day 3, and day 7. There was a trend of increasing MMP-9 expression on the 1st to 3rd day postpartum, then decreasing gradually on the 7th day. Conclusion: Delivery changes the expression of MMP-9 in pelvic floor tissues such as the sacrouterine ligament and levator ani muscle and these changes are time-dependent.Abstrak. Latar Belakang: Persalinan pervaginam merupakan faktor resiko prolaps organ panggul. Mekanisme biomolekuler yang menghubungkannya masih belum jelas, diduga melalui perantaraan Matriks Metalloproteinase 9 (MMP-9). Tujuan: Penelitian ini bertujuan untuk mengetahui peningkatan MMP-9 pada jaringan penyokong organ panggul, terutama ligamentum sacrouterina dan otot levator ani periode post partum. Metode: Penelitian ini adalah studi observational cohort pada 5 tikus betina Rattus norvegicus strain Wistar. Yang terbagi menjadi kelompok nullipara, postpartum hari ke-1, hari ke-3 dan hari ke-7.. Preparat jaringan ligamentum sacrouterina dan otot levator ani diwarnai dengan imunohistokimia. Ekspresi MMP-9 dihitung dan dianalisa dengan menggunakan ANOVA. Hasil: Terdapat perbedaan yang signifikan (p=0,01) ekspresi MMP-9 pada ligamentum sacrouterina antara tikus nullipara, postpartum hari ke-1, hari ke-3, dan hari ke-7. Terdapat pula perbedaan yang signifikan (p=0,00) ekspresi MMP-9 otot levator ani antara tikus nullipara , postpartum hari ke-1, hari ke-3, dan hari ke-7. Tampak tren peningkatan ekspresi MMP-9 pada hari ke-1 hingga ke-3 postpartum, selanjutnya menurun bertahap pada hari ke-7. Simpulan: Persalinan mengubah ekspresi MMP-9 pada jaringan dasar panggul seperti ligamentum sacrouterina dan otot levator ani dan perubahan ini bersifat time-dependently.

show abstract

A simple model of collagen remodeling

Cited by 4 publications

References 18 publications

Mathematical modelling of collagen fibres rearrangement during the tendon healing process

Mathematical modelling of collagen fibres rearrangement during the tendon healing process

A class of individual-based models

Peningkatan Ekspresi Matrix Metalloproteinase-9 Ligamentum Sacrouterina dan Otot Levator Ani Postpartum Rattus Norvegicus

Contact Info

Product

Resources

About