Figure 10.

The degree of nanoparticle normalization fold increase over diffusion alone as a function of two dynamic magnetic shift parameters (pull left duration and pull right duration). For each tissue slice, the average over time for slow-acting therapies (left panel) or maximum over time for fast-acting therapies (right panel) was considered. Then, the degree of nanoparticle normalization, J^time-avg and J^time-max, was calculated using the formulae of Equation (3). The fold increase of the degree of normalization versus diffusion alone was plotted. High J values corresponded to high average concentrations and low spatial variances in the particle concentrations. Hence, the highest J value would be for a uniform high concentration. Low J values corresponded to low concentrations or high spatial variances that would correspond to hot and cold spots in the tissue and are the opposite of what dynamic magnetic shift is trying to achieve. The shift parameters are shown with the first pull duration and direction on the horizontal axis, and the second pull duration on the vertical axis. The first pull was either to the west (W) or east (E) for a fraction of the total time (hence, it is shown from −1 to 1). The second pull was always in the opposite direction to the first and was similarly a fraction of the total time. Thus, the location (+0.6, −0.2) corresponded to 20% (18 minutes) initial waiting time, followed by a 60% (54 minutes) pull to the east, then a final 20% (18 minutes) pull to the west. In this representation, pure diffusion (no pulling) corresponded to the vertical axis centered at “D” for diffusion only. For any pair where magnetic actuation was not applied for the full duration (anywhere within the interior of the triangles), diffusion occurs first during the initial waiting period. The optimal shift parameters are marked by the four blue stars. The found optima are different for phase-specific (time-averaged metric) and phase-nonspecific (time-maximum metric) therapies.