Page 17 - Artificial Intelligence for Computational Modeling of the Heart

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respect to the centerline position. 193
Fig. 6.7 Fitting the surface model ¯r(z,φ) to the points corresponding to
the patient-specific anatomical model. 195
Fig. 6.8 Examples of synthetically generated CoA anatomical models. 196
Fig. 6.9 Cascaded pressure drop model resulting from coupling the
optimized Young-Tsai model with a deep neural network. The
neural network is used as a correction to the Young-Tsai model
and it predicts the pressure based on both the Y-T model output
but also the input quantities. 199
Fig. 6.10 Evaluation of the pressure drop models. P CFD represents the
pressure drop extracted from the 3D CFD computations, while
P Estimated is the pressure drop determined analytically using
the pressure drop models: top – original Young-Tsai model
(Eq. (6.8)), middle – optimized pressure drop model and bottom –
coupled model. The line in the scatter plot is the y = x line. 201
Fig. 6.11 Lumped parameter closed loop model of the cardiovascular
system. Notations: Q LA−in : left atrial inflow; P LA :leftatrial
pressure; Q LA−LV : flow rate through the mitral valve; P LV :left
ventricular pressure; Q Ao : aortic flow rate; P Ao : aortic pressure;
Q RA−in : right atrial inflow; P RA : right atrial pressure; Q RA−RV :
flow rate through the tricuspid valve; P RV : right ventricular
pressure; Q PAo : pulmonary artery flow rate; P PAo : pulmonary
artery pressure; R s−LA : left atrial source resistance; E LA :left
atrial time-varying elastance; R MV : mitral valve resistance;
L MV : mitral valve inertance; R s−LV : left ventricular source
resistance; E LV : left ventricular time-varying elastance; R AV :
aortic valve resistance; L AV : aortic valve inertance; R sys−p :
proximal systemic resistance; C sys : systemic compliance;
R sys−d : distal systemic resistance; R sysV en : venous resistance;
C sysV en : venous compliance; Rs − LA: right atrial source
resistance; E RA : right atrial time-varying elastance; R TV :
tricuspid valve resistance; L TV : tricuspid valve inertance;
R s−RV : right ventricular source resistance; E RV : right
ventricular time-varying elastance; R PAV : pulmonary valve
resistance; L PAV : pulmonary valve inertance; R pulSys−p :
proximal pulmonary resistance; C pulSys : pulmonary compliance;
R pulSys−d : distal pulmonary resistance; R pulSysV en : pulmonary
venous resistance; C pulSysV en : pulmonary venous compliance. 204
Fig. 6.12 Overall workflow of the proposed deep learning based model. 207
Fig. 6.13 Correlation between predictions and ground-truth. (A) Predicted
vs. Ground-truth time at max. elastance; (B) Predicted vs.
Ground-truth resistance. 208
Fig. 6.14 Time series predictions (red (mid gray in print version)) vs.
ground-truth (blue (dark gray in print version)). (A) Pulmonary
artery pressure; (B) Aortic pressure; (C) Right ventricular
pressure; (D) Left ventricular pressure; (E) Right atrial pressure; (F)
Left atrial pressure; (G) Right ventricular volume; (H) Left
ventricular volume; (I) Pulmonary artery flow rate; (J) Aortic flow
rate; (K) Right ventricle PV loop; (L) Left ventricle PV loop. 209