Table 7.

Summary of results for the real tumor with real velocity (RTRV) test case, ground truth (ρ N/A, k N/A, p N/A, v N/A); based on real clinical data (taken from [7]). We set the tumor parameters to ρ _f = 15, k _f = 0 (reaction-only). We use a parametrization of tumor initial conditions with n _p = 343 Gaussians. We report 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, 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.

Patient		βv	${\mu }_{B,L^2}$	DICEB	${\mu }_{T,L^2}$	DiceT	${\Vert g\Vert }_{\text{rel}}$	$T^{total}[\text{s}]$	$T_{inv}^{tu}[\text{s}]$	$T_{inv}^{reg}[\text{s}]$
AAMH	Initial	1	1.00	4.36E−1	1.00	0.00	1.00	–	–	–
	final	1E−4	3.45E−1	7.92E−1	1.95E−1	9.57E−1	3.92E−2	6.28E+2	1.95E+2	4.35E+2
AAAN	initial	1	1.00	4.37E−1	1.00	0.00	1.00	–	–	–
	final	1E−4	3.54E−1	8.35E−1	3.77E−1	8.91E−1	1.06E−1	6.34E+2	2.15E+2	4.17E+2
AAAC	initial	1	1.00	4.82E−1	1.00	0.00	1.00	–	–	–
	final	1E−4	3.36E−1	8.44E−1	2.45E−1	9.55E−1	4.38E−2	4.92E+2	1.59E+2	3.32E+2
AAMP	initial	1	1.00	4.74E−1	1.00	0.00	1.00	–		–
	final	1E−4	3.32E−1	8.05E−1	1.34E−1	9.75E−1	3.31E−2	6.48E+2	2.36E+2	4.13E+2
AAQD	initial	1.00	1.00	2.92E−1	1.00	0.00	1.00	–	–	–
	final	1E−4	3.24E−1	8.06E−1	2.55E−1	9.31E−1	9.88E−2	1.10E+3	2.19E+2	8.81E+2
AAWI	initial	1	1.00	4.53E−1	1.00	0.00	1.00	–	–	–
	final	1E−4	3.45E−1	7.87E−1	3.92E−1	8.74E−1	5.26E−2	6.84E+2	2.92E+2	3.90E+2