Sains Malaysiana 42(5)(2013): 661–666

Simulations of Hirschsprung’s Disease Using Fractional Differential Equations

(Simulasi Penyakit Hirschsprung Menggunakan Persamaan Pembezaan Pecahan)

F.A. Abdullah*

School of Mathematical Sciences, Universiti Sains Malaysia

11800 USM, Pulau Pinang, Malaysia

Received: 20 July 2011/Accepted: 20 October 2012

ABSTRACT

In this paper, we examined a model of cell invasion focusing on the wavefront of the neural crest (NC) cells in the case of Hirschsprung’s disease (HSCR). Hirschsprung’s disease (HSCR) is a congenital defect of intestinal ganglion cells and causes patients to have disorders in peristalsis. This simulation model was performed using the fractional differential equations (FDEs) based upon two basic cell functions. Here, we simulated the mathematical model in a one-dimensional setting, based on the fractional trapezoidal numerical scheme and the results showed an interesting outcome for the mobility of the cellular processes under crowded environments.

Keywords: Fractional differential equation; Hirschsprung disease; simulation

ABSTRAK

Dalam penyelidikan ini, kami mengkaji model berkaitan penyerangan sel dan fokus kajian adalah pada gelombang penyerangan sel neural dalam penyakit Hirschsprung (HSCR). Penyakit Hirschsprung (HSCR) adalah penyakit yang berkaitan dengan kecacatan semasa lahir atau sebelum lahir dan berpunca daripada sel ganglion sehingga menyebabkan proses periltalsis menjadi tidak normal. Model simulasi adalah berdasarkan persamaan pembezaan pecahan (FDES) ke atas dua sel asas. Kajian ini mensimulasikan model matematik dalam satu dimensi berpandukan kepada kaedah berangka trapezoid pecahan. Hasil keputusan daripada simulasi ini menunjukkan wujud hasil yang menarik daripada pergerakan sel dalam keadaan bersesak.

Kata kunci: Penyakit Hirschsprung; persamaan pembezaan pecahan; simulasi

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*Corresponding author; email: farahaini@usm.my