A Wound/Slough Model Accounting for Cellular Diffusion and Debridement

Yaprak R., Coşkun E.

6th International Conference on Computational Mathematics and Engineering Sciences, Ordu, Türkiye, 20 - 22 Mayıs 2022, ss.232

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Ordu
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.232
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

In this study, we consider the nondimensionalized wound/slough interaction model [1] and develop it to have impulsive effects which can be stated as

𝑈𝑡=Δ𝑈+𝑁1(𝑈,𝑉),𝒙∈[0,1]𝑛,𝑡>0𝑉𝑡 = 𝐷Δ𝑉 + 𝑁2(𝑈, 𝑉) + 𝐼𝑖(V(𝑡𝑖, 𝒙)), 𝑖 = 0,1,2, …

where Δ is the usual Laplace operator for 𝑛=1,2,3; 𝐷 is a nondimensional parameter accounting for cellular diffusion; 𝑁1 and 𝑁2 are the reaction terms; 𝑈,𝑉 are the cellular density of wound and slough respectively. The impulsive effects are used to simulate medical treatment technique known as debridement [2] which is implemented at 𝑡=𝑡1,𝑡2,… to speed up the healing process, the 𝐼𝑖(.)’s are control functions to be determined to achieve optimal healing.

Keywords: Wound healing; Impulsive differential equations; Debridement.

REFERENCES

1.Yaprak, R., Coşkun, E., “A Slough/Wound Interaction Model Accounting for Cellular Diffusion.”, International Conference on Mathematics and Mathematics Education(ICMME-2021), Gazi University-Ankara, 71-72, 2021.

2.Bradley, M., Nicky, C., Sheldon, T., “The debridement of chronic wounds: a systematic review.”, Health Technol Assess, 3(1999).