Data Assimilation in Brain Tumor Models - Mathematical Methods and Models in Biomedicine - page 246

Fig. 5 Contour plot for a subset of the ensemble tumors. See text for additional details

The right column, labeled “truth,” displays the truth. We see that each time the data
assimilation is performed, the resulting analysis has improved tracking of the truth.
Figure 5 displays the level curves for a five member subset of the ensemble.
Two level curves are shown for each ensemble tumor corresponding to 25 % and
80 % of truth carrying capacity. The left and right columns display the background
and analysis ensemble, respectively. The decrease in the spread of the level curves
following data assimilation illustrates a reduction in uncertainty in estimated size
and location of the truth tumor. In clinical practice this would be useful in assessing
the location of the tumor boundary and the overall size of the tumor.
For comparison we also conducted a free run of the experiment where data
assimilation is not performed and the ensemble is simply integrated for 180 days
under their respective models. Figure 6 displays the tumor mass every tenth day
of the experiment. The blue curve shows the ensemble mean tumor mass for the
simulation where data assimilation is performed. The error bars corresponding to
one standard deviation evaluated over the ensemble are also displayed. The red
curve displays the tumor mass for the truth. The green curve shows the ensemble
mean tumor mass for the free run. Note how data assimilation yields a forecast that
more accurately estimates the truth tumor mass. Every 30th day when the LETKF