Table 8.

Results for the AAMH and the AAAN patient real tumor/ real velocity (RTRV) test case, ground truth (ρ N/A, k N/A, p N/A, v N/A) using real clinical input data. The table shows the (summed) mismatch for the brain tissue probability maps (${\mu }_{B,L^2}$) and tumor probability map (${\mu }_{T,L^2}$) in patient space, the mean Dice coefficient for the hard segmentation corresponding to the brain tissue (DICE_B ) and the tumor (DICE_T ), respectively for different values for reaction scaling parameter ρ _f and of the diffusion coefficient scaling parameter k _f ., as well as the relative norm of the gradient for the coupled problem (3) $\left({\Vert g\Vert }_{\text{rel}}\right)$. We also report the total run time in seconds (T _total ), and the run time of the individual components of our Picard scheme, respectively (also in seconds; tumor solver:$T_{inv}^{tu}$; image registration:$T_{inv}^{reg}$). Note that the latter sums up to less than the reported total run time as we do not explicitly measure time spent in additional coupling functionality and forward solvers. We execute our code in parallel on 11 nodes using 256 MPI tasks of HazelHen.

	ρf	kf	np	${\mu }_{B,L^2}$	DICEB	${\mu }_{T,L^2}$	DICET	${\Vert g\Vert }_{\text{rel}}$	$T^{total}\left[\text{s}\right]$	$T_{inv}^{tu}\left[\text{s}\right]$	$T_{inv}^{reg}\left[\text{s}\right]$
ID AAMH	initial canfig			1.00	4.36E−1	1.00	0.00	1.00	–	–	–
	0	0	343	3.40E−1	7.92E−1	l.47E−1	9.69E−1	l.19E−1	6.09E+2	2.13E+2	3.63E+2
	0	0	125	3.38E−1	7.95E−1	1.73E−1	9.62E−1	1.31E−1	5.09E+2	7.86E+l	4.04E+2
	15	0	343	3.45E−1	7.92E−1	1.95E−1	9.57E−1	3.92E−2	6.28E+2	l.95E+2	4.35E+2
	15	0	125	3.50E−1	7.91E−1	2.36E−1	9.53E−1	4.83E−2	4.47E+2	7.20E+l	3.48E+2
	5	lE−2	343	3.44E−1	7.92E−1	l.88E−1	9.64E−1	7.68E−2	l.23E+4	l.18E+4	3.41E+2
	10	lE−2	343	3.46E−1	7.92E−1	2.0 7E−1	9.62E−1	5.16E−2	l.33E+4	l.28E+4	3.44E+2
	15	lE−2	343	3.48E−1	7.93E−1	2.35E−1	9.59E−1	3.47E−2	1.18E+4	l.13E+4	3.63E+2
ID AAMN	initial canfig.			1.00	4.37E− 1	1.00	0.00	1.00	-	-	-
	0	0	343	3.42E−1	8.39E−1	2.56E−1	9.36E−1	2.19E−1	6.58E+2	2.02E+2	4.23E+2
	0	0	125	3.56E−1	8.33E−1	4.40E−1	6.68E−1	2.36E−1	4.54E+2	8.89E+l	3.38E+2
	15	0	343	3.54E−1	8.35E−1	3.77E−1	8.91E−1	l.06E−1	6.34E+2	2.15E+2	4.17E+2
	15	0	125	3.67E−1	8.30E−1	5.71E−1	3.44E− 1	1.28E−1	4.67E+2	8.38E+l	3.57E+2
	5	lE−2	343	3.50E−1	8.35E−1	3.17E−1	9.06E−1	1.79E−1	1.82E+4	1.77E+4	3.33E+2
	10	lE−2	343	3.52E−1	8.35E−1	3.60E−1	8.85E−1	l.41E−1	l.88E+4	l.82E+4	3.41E+2
	15	lE−2	343	3.S5E−1	8.34E−1	3.98E−1	8.62E−1	l.13E−1	1.85E+4	l.80E+4	3.28E+2