期刊
KINETIC AND RELATED MODELS
卷 14, 期 2, 页码 283-301出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/krm.2021005
关键词
Collagen remodelling; Kinetic model; Tendon healing; Integrodifferential equations; Alignment
资金
- Advanced Grant Nonlocal-CPD (Nonlocal PDEs for Complex Particle Dynamics: Phase Transitions, Patterns and Synchronization) of the European Research Council Executive Agency (ERC) under the European Union's Horizon 2020 research and innovation programme [883363]
- EPSRC [EP/P031587/1]
- Institute of Mathematics, Polish Academy of Sciences
- National Science Centre, Poland [2017/26/M/ST1/00783]
- National Centre for Research and Development [STRATEGMED1/233224/10/NCBR/2014]
This study introduces a new model for tendon healing, describing the rearrangement of collagen fibers during the healing process. The simplified model allows for parameter estimation and showcases the qualitative properties as well as the time for tendon fibers to align. The research suggests the potential importance of tendon cell size in patient recovery based on numerical experiments.
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.
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