Computational fluid dynamics simulations of blood flow regularized by 3D phase contrast MRI

Table 2 Signal-to-error ratio (in dB) between noisy and original PC-MRI measurements; and between the MRI-guided CFD estimates and the original PC-MRI measurements

	Noisy	CFD	CFD+3D	CFD+3D	CFD+3D	CFD+3D
	PC-MRI	\({\lambda =0}\)	\({\lambda =5\times 10^{-9}}\)	\({\lambda =5\times 10^{-8}}\)	\({\lambda =5\times 10^{-7}}\)	\({\lambda =5\times 10^{-6}}\)
\({\mathrm {SER}}_{u}\)	0.80	2.66	2.87	3.22	2.34	1.75
\({\mathrm {SER}}_{v}\)	−2.46	−0.50	−0.41	−0.39	−1.18	−1.67
\({\mathrm {SER}}_{w}\)	4.64	5.03	5.82	7.20	5.88	5.06
\({\mathrm {SER}}_{\vec {\nu }}\)	5.71	6.39	6.94	8.18	7.85	6.94

Additive zero-mean Gaussian noise with standard deviation of \(\sigma =8\) cm/s was used. CFD estimates were obtained using the combined solver with different values of the weight parameter \(\lambda\), constrained by the noisy PC-MRI measurements. All three PC-MRI velocity components were used to guide the CFD calculations. SER values were calculated according to Eqs. (21)–(24)

ISSN: 1475-925X