The One-Dimensional (1D) Numerical Model: An Application to Oxygen Diffusion in Mitochondria Cell - Gandhi Napitupulu; Achmad Nagi; Mutiara Rachmat Putri; Ivonne Milichristi Radjawane (Bina Nusantara University, 2023)
The first model of oxygen transport was formulated by August Krogh. However, the investigations conducted have yet to yield a complete analytical model and a widely applicable solution for One-Dimensional (1D) network construction. The research sought to provide numerical and analytical solutions for the oxygen transfer model in mitochondrial cells to enable researchers to estimate the molecular dynamics and diffusion characteristics in mitochondrial cells. The oxygen diffusion process in mitochondria was modeled with ID numerical models. The numerical models used to solve the equations were explicit and implicit. The explicit model consisted of Forward Time Center Space (FTCS) and DuFort-Frankel. Meanwhile, the implicit model had Crank-Nicholson and Laasonen. The numerical solutions of the explicit and implicit were divided into four scenarios with a variation of Δt and compared with the analytical solutions. The results show that the Laasonen method is the best in describing the diffusion process. The best scenario with the lowest slope value and small Root Mean Square Error (RMSE) value is scenario 2 (Δt = 3,33E-4 s and Δx = 2,00E-5 cm). The numerical model and analytical solution show that the time required to reach a steady state is 0,7 s. It indicates oxygen exchange in two sides of the mitochondrial cell after 0,7 s.