Utilizing Parallel Processing in Computational Biology Applications - High-Throughput Image Reconstruction and Analysis - page 95

Figure 4.1 Two-dimensional analogue depicting inter-processor communication for (a) moving
and (b) copying rows and columns of cells. In three dimensions these rows and columns correspond
to sheet-like, two-dimensional slices through a cube.

owned by the sending process must be moved, and therefore communicated. Fol-
lowing the communication, the rank of the received tumor cells is set to that of
the receiving process.

4.3.2 Copying of Tumor Cells
Computing the diffusion and lifecycle of tumor cells on the boundary of the sub-
domains requires knowledge of tumor cell occupancy in the subdomain's ghost
cells. This requires copying tumor cells along the edge of the domain to the ghost
cells of neighboring domains. This operation, as shown in Figure 4.1(b), can be
described by

C q,I / P x + 1 , j,k ← C r , 1 , j,k C q,I / P x , j,k → C r , 0 , j,k (4.26)

when r x = q x + 1;

C q,i,J / P y + 1 , k ← C r , i , 1 , k C q,i,J / P y , k → C r , j , 0 , k (4.27)

when r y = q y + 1; and

C q,i,j,K / P z + 1 ← C r,i,j, 1 C q,i,j,K / P z → C r,i,j, 0 (4.28)

when r z = 1. In contrast to moving tumor cells, because the sending process

owns all of the tumor cells inside its subdomain, all tumor cells must be copied,
and therefore communicated, and the receiving process does not set the rank of
the received tumor cells.

q z +

4.3.3 Copying of Continuous Variables
Values of the diffusive variables O and M along the edge of the domain must be
copied to the ghost cells of neighboring domains, similar to the copying of tumor
cells. This operation can therefore be described, using O as an example, by

O q,I / P x + 1 , j,k ← O r , 1 , j,k O q,I / P x , j,k → O r , 0 , j , k (4.29)