Simulation of buffered advection diffusion of calcium in a hepatocyte cell

The calcium signaling is the basic and vital component of cell communication in almost all types of human and animal cells. All the vital functions of parenchymal cell of liver known as hepatocyte cell are regulated by this calcium signaling. The calcium concentration at specific levels are responsible for each of the various functions of the cell. The deeper understanding of the mechanisms and the factors affecting the calcium dynamics in a hepatocyte cell is vital for various clinical applications related to diseases of the liver. In this paper, mathematical model is proposed to study intracellular calcium dynamics in hepatocyte cell by incorporating the processes like diffusion, advection, buffering etc. The reaction advection diffusion equation has been employed for a two dimensional unsteady state case, to form an initial and boundary value problem. The initial and boundary conditions are formulated based on the physical conditions of cell. Finite volume method and Crank Nicolson scheme have been employed along spatial and temporal dimension respectively to obtain numerical solution. The impact of endogenous and exogenous buffers, advection and diffusion on calcium dynamics in hepatocyte cell has been studied with the help of numerical results. The rise and fall in spatio-temporal calcium concentration in hepatocyte cell in response to specific conditions of advection, diffusion and buffer concentrations is observed. These variations in spatio-temporal calcium concentrations are regulated in narrow range due to fine coordination among these processes of cell under normal environmental and physiological conditions. The proposed model gives better understanding of interrelationship and interdependence of these physical processes for fine coordination among them to maintain structure and functions of cell.