Table 1.

The bending energy and change of tumor volumes are calculated using the constrained (ABA_CON) and unconstrained ABA algorithms (ABA), respectively

Patient number	Dataset	Bending energy		Change of tumor volumes
		ABA	ABA_CON	ABA (%)	ABA_CON (%)
1	t1 → t3	0.052	0.002	63.21	0.00
	t2 → t3	0.036	0.000	78.99	7.59
2	t1 → t3	0.079	0.000	63.13	9.28
	t2 → t3	0.051	0.001	61.07	0.09
3	t1 → t3	0.021	0.000	51.01	0.00
	t2 → t3	0.036	0.000	48.84	0.48
4	t1 → t3	0.057	0.001	16.38	1.43
	t2 → t3	0.004	0.001	−6.95	−6.66
5	t1 → t3	0.011	0.007	40.15	36.50
	t2 → t3	0.012	0.009	−1.30	5.41
6	t1 → t3	0.051	0.035	17.27	−19.97
	t2 → t3	0.020	0.024	9.89	9.16
7	t1 → t3	0.019	0.020	33.33	32.85
	t2 → t3	0.006	0.005	12.34	19.23
8	t1 → t3	0.015	0.015	16.29	12.45
	t2 → t3	0.012	0.020	4.96	0.39
9	t1 → t3	0.004	0.003	−5.62	−6.80
	t2 → t3	0.001	0.001	16.58	14.32
10	t1 → t3	0.001	0.000	26.55	14.55
	t2 → t3	0.002	0.001	8.52	−4.92
Median		0.017	0.0015	16.93	3.42
p values		0.005		0.002

The Wilcoxon signed rank test was applied to the data to determine if the results are significantly different (p values are listed in the final row). The results demonstrate that the constrained ABA causes smoother deformation fields and preserves tumor volumes significantly.