Utilizing artificial intelligence methods for blood flow pressure estimation can significantly enhance the computational speed of blood flow pressure. However, current related research can only calculate the blood flow pressure parameters of vessels with different geometric shapes under fixed boundary conditions, thus fail to achieve transient flow field calculation and consider the hemodynamic differences formed by patients' varying physiological and pathological conditions. In view of this, this study proposes a method for relative pressure estimation based on four-dimensional flow magnetic resonance imaging (4D flow MRI) of patient blood flow and deep learning. 4D flow MRI was used to obtain the patient's blood flow velocity gradient data, and feature engineering processing is performed on the sampled data. Then, a novel neural network was proposed to acquire the characteristic relationship between velocity gradient and pressure gradient in the vicinity of the point to be measured and within adjacent sampling time periods, thereby achieving the calculation of the relative pressure in the vicinity of the point to be measured. Statistical analysis was performed to evaluate the efficacy of the method, comparing it with computational fluid dynamics methods and catheter pressure measurement techniques. The accuracy of the proposed method exceeded 96%, while computational efficiency was improved by several tens of times, and no manual setting of physiological parameters was required. Furthermore, the results were compared with clinical catheter-measured pressure results, r2 = 0.9053, indicating a significant consistency between the two methods. Compared to previous research, the method proposed in this study can take the blood flow velocity conditions of different patients at different times as input features via 4D flow MRI, thus enabling the calculation of pressure in transient flow fields, which significantly improved computational efficiency and reduced costs while maintaining a high level of calculation accuracy. This provides new direction for future research on machine learning prediction of blood flow pressure.

1.
N. A.
ElSayed
,
G.
Aleppo
,
V. R.
Aroda
,
R. R.
Bannuru
,
F. M.
Brown
,
D.
Bruemmer
,
B. S.
Collins
,
S. R.
Das
,
M. E.
Hilliard
,
D.
Isaacs
et al, “
10. Cardiovascular disease and risk management: Standards of care in diabetes—2023
,”
Diabetes care
46
,
S158
S190
(
2023
).
2.
J.
Krizman
and
N.
Kraus
, “
Analyzing the FFR: A tutorial for decoding the richness of auditory function
,”
Hear. Res.
382
,
107779
(
2019
).
3.
Y.
Han
,
J.
Xia
,
L.
Jin
,
A.
Qiao
,
T.
Su
,
Z.
Li
,
J.
Xiong
,
H.
Wang
, and
Z.
Zhang
, “
Computational fluid dynamics study of the effect of transverse sinus stenosis on the blood flow pattern in the ipsilateral superior curve of the sigmoid sinus
,”
Eur. Radiol.
31
,
6286
6294
(
2021
).
4.
P.
Zhao
,
H.
Ding
,
H.
Lv
,
X.
Li
,
X.
Qiu
,
R.
Zeng
,
G.
Wang
,
J.
Wei
,
L.
Jin
,
Z.
Yang
et al, “
Ct venography correlate of transverse sinus stenosis and venous transstenotic pressure gradient in unilateral pulsatile tinnitus patients with sigmoid sinus wall anomalies
,”
Eur. Radiol.
31
,
2896
2902
(
2021
).
5.
M.
Kostic
,
E.
Colvin
,
H.
Duy
,
S.
Ro
,
C.
Quinsey
,
I.
Shevtsova
, and
S.
Machineni
, “
Idiopathic intracranial hypertension
,” in
Neuropediatrics—Recent Advances and Novel Therapeutic Approaches
(
IntechOpen
,
2023
).
6.
N.
Pijls
and
B.
De Bruyne
, “
Coronary pressure measurement and fractional flow reserve
,”
Heart
80
,
539
542
(
1998
).
7.
A.
Arzani
,
J.-X.
Wang
,
M. S.
Sacks
, and
S. C.
Shadden
, “
Machine learning for cardiovascular biomechanics modeling: Challenges and beyond
,”
Ann. Biomed. Eng.
50
,
615
627
(
2022
).
8.
A.
Taebi
, “
Deep learning for computational hemodynamics: A brief review of recent advances
,”
Fluids
7
,
197
(
2022
).
9.
G.
Li
,
Y.
Zhu
,
Y.
Guo
,
T.
Mabuchi
,
D.
Li
,
S.
Huang
,
S.
Wang
,
H.
Sun
, and
T.
Tokumasu
, “
Deep learning to reveal the distribution and diffusion of water molecules in fuel cell catalyst layers
,”
ACS Appl. Mater. Interfaces
15
,
5099
5108
(
2023
).
10.
G.
Li
,
K.
Watanabe
,
H.
Anzai
,
X.
Song
,
A.
Qiao
, and
M.
Ohta
, “
Pulse-wave-pattern classification with a convolutional neural network
,”
Sci. Rep.
9
,
14930
(
2019
).
11.
A. V.
Varadarajan
,
P.
Bavishi
,
P.
Ruamviboonsuk
,
P.
Chotcomwongse
,
S.
Venugopalan
,
A.
Narayanaswamy
,
J.
Cuadros
,
K.
Kanai
,
G.
Bresnick
,
M.
Tadarati
et al, “
Predicting optical coherence tomography-derived diabetic macular edema grades from fundus photographs using deep learning
,”
Nat. Commun.
11
,
130
(
2020
).
12.
G.
Li
,
H.
Wang
,
M.
Zhang
,
S.
Tupin
,
A.
Qiao
,
Y.
Liu
,
M.
Ohta
, and
H.
Anzai
, “
Prediction of 3D cardiovascular hemodynamics before and after coronary artery bypass surgery via deep learning
,”
Commun. Biol.
4
,
99
(
2021
).
13.
P.
Du
,
X.
Zhu
, and
J.-X.
Wang
, “
Deep learning-based surrogate model for three-dimensional patient-specific computational fluid dynamics
,”
Phys. Fluids
34
,
081906
(
2022
).
14.
X.
Guo
,
W.
Li
, and
F.
Iorio
, “
Convolutional neural networks for steady flow approximation
,” in
Proceedings of
the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
(
Association for Computing Machinery
,
2016
), pp.
481
490
.
15.
M. R.
Pinsky
and
D.
Payen
, “
Functional hemodynamic monitoring
,”
Crit. Care
9
,
1
7
(
2005
).
16.
A.
Pashaei Kalajahi
,
H.
Csala
,
F.
Naderi
,
Z.
Mamun
,
S.
Yadav
,
O.
Amili
,
A.
Arzani
, and
R.
D'Souza
,
Input Parameterized Physics Informed Neural Network for Advanced 4D Flow MRI Processing
(
Elsevier
,
2024
). Available at SSRN 4700974.
17.
M.
Markl
,
A.
Frydrychowicz
,
S.
Kozerke
,
M.
Hope
, and
O.
Wieben
, “
4D flow MRI
,”
Magn. Reson. Imaging
36
,
1015
1036
(
2012
).
18.
M. J.
Ramaekers
,
J. J.
Westenberg
,
M. F.
Venner
,
J. F.
Juffermans
,
H. C.
van Assen
,
B. J.
Te Kiefte
,
B. P.
Adriaans
,
H. J.
Lamb
,
J. E.
Wildberger
, and
S.
Schalla
, “
Evaluating a phase-specific approach to aortic flow: A 4D flow MRI study
,”
Magn. Reson. Imaging
59
,
1056
1067
(
2024
).
19.
K.
Han
,
Y.
Wang
,
H.
Chen
,
X.
Chen
,
J.
Guo
,
Z.
Liu
,
Y.
Tang
,
A.
Xiao
,
C.
Xu
,
Y.
Xu
et al, “
A survey on vision transformer
,”
IEEE Trans. Pattern Anal. Mach. Intell.
45
,
87
110
(
2023
).
20.
J.
Xu
,
Z.
Li
,
B.
Du
,
M.
Zhang
, and
J.
Liu
, “
Reluplex made more practical: Leaky ReLU
,” in
IEEE Symposium on Computers and Communications (ISCC)
(
IEEE
,
2020
), pp.
1
7
.
21.
C. A.
Taylor
and
J.
Humphrey
, “
Open problems in computational vascular biomechanics: Hemodynamics and arterial wall mechanics
,”
Comput. Methods Appl. Mech. Eng.
198
,
3514
3523
(
2009
).
22.
S. V.
Ershkov
,
E. Y.
Prosviryakov
,
N. V.
Burmasheva
, and
V.
Christianto
, “
Towards understanding the algorithms for solving the Navier–Stokes equations
,”
Fluid Dyn. Res.
53
,
044501
(
2021
).
23.
Y.
Han
,
Q.
Yang
,
Z.
Yang
,
J.
Xia
,
T.
Su
,
J.
Yu
,
L.
Jin
, and
A.
Qiao
, “
Computational fluid dynamics simulation of hemodynamic alterations in sigmoid sinus diverticulum and ipsilateral upstream sinus stenosis after stent implantation in patients with pulsatile tinnitus
,”
World Neurosurg.
106
,
308
314
(
2017
).
24.
E.
Stolz
,
M.
Kaps
,
A.
Kern
,
S. S.
Babacan
, and
W.
Dorndorf
, “
Transcranial color-coded duplex sonography of intracranial veins and sinuses in adults. reference data from 130 volunteers
,”
Stroke
30
,
1070
(
1999
).
25.
S.
Huang
,
X.
Li
,
X.
Xue
,
X.
Qiu
, and
Z.
Wang
, “
Hemodynamic study of the therapeutic effects of the different degrees of sigmoid sinus diverticulum reconstruction on patients
,”
Med. Eng. Phys.
86
,
8
15
(
2020
).
26.
X.
Xue
,
M.
Fu
,
D.
Zhao
,
B.
Gao
, and
Y.
Chang
, “
The hemodynamic study on the effects of entry tear and coverage in aortic dissection
,”
Comput. Model. Eng. Sci.
121
,
929
945
(
2019
).
27.
K.
Xu
,
X.
Qiu
,
C.
Dai
,
K.
He
,
G.
Wang
,
Z.
Mu
,
B.
Gao
,
S.
Gong
,
Z.
Wang
, and
P.
Zhao
, “
Fluid-structure interaction study on the causes of mending material damage after sigmoid sinus wall reconstruction
,”
Comput. Methods Programs Biomed.
245
,
108040
(
2024
).
28.
S.
Tian
,
L.
Wang
,
J.
Yang
,
R.
Mao
,
Z.
Liu
, and
Y.
Fan
, “
Sigmoid sinus cortical plate dehiscence induces pulsatile tinnitus through amplifying sigmoid sinus venous sound
,”
J. Biomech.
52
,
68
73
(
2017
).
29.
P.
Zhao
,
H.
Ding
,
H.
Lv
,
X.
Li
,
X.
Qiu
,
R.
Zeng
,
G.
Wang
,
J.
Wei
,
L.
Jin
,
Z.
Yang
et al, “
Ct venography correlate of transverse sinus stenosis and venous transstenotic pressure gradient in unilateral pulsatile tinnitus patients with sigmoid sinus wall anomalies
,”
Eur. Radiol.
31
,
2896
2902
(
2021
).
30.
Z.
Stankovic
,
B. D.
Allen
,
J.
Garcia
,
K. B.
Jarvis
, and
M.
Markl
, “
4D flow imaging with MRI
,”
Cardiovasc. Diagn. Ther.
4
,
173
(
2014
).
31.
B.
Su
,
J.-M.
Zhang
,
H.
Zou
,
D.
Ghista
,
T. T.
Le
, and
C.
Chin
, “
Generating wall shear stress for coronary artery in real-time using neural networks: Feasibility and initial results based on idealized models
,”
Comput. Biol. Med.
126
,
104038
(
2020
).
32.
M.
Movahhedi
,
X.-Y.
Liu
,
B.
Geng
,
C.
Elemans
,
Q.
Xue
,
J.-X.
Wang
, and
X.
Zheng
, “
Predicting 3D soft tissue dynamics from 2D imaging using physics informed neural networks
,”
Commun. Biol.
6
,
541
(
2023
).
33.
S.
Wang
,
D.
Wu
,
G.
Li
,
Z.
Zhang
,
W.
Xiao
,
R.
Li
,
A.
Qiao
,
L.
Lin
, and
H.
Liu
, “
Deep learning-based hemodynamic prediction of carotid artery stenosis before and after stent intervention
,”
Front. Physiol.
13
,
1094743
(
2023
). Available at SSRN 4214496.
34.
L.
Liang
,
W.
Mao
, and
W.
Sun
, “
A feasibility study of deep learning for predicting hemodynamics of human thoracic aorta
,”
J. Biomech.
99
,
109544
(
2020
).
35.
L. H.
Nguyen
and
S.
Holmes
, “
Ten quick tips for effective dimensionality reduction
,”
PLoS Comput. Biol.
15
,
e1006907
(
2019
).
36.
N. R.
Mehta
,
L.
Jones
,
M. A.
Kraut
, and
E. R.
Melhem
, “
Physiologic variations in dural venous sinus flow on phase-contrast MR imaging
,”
Am. J. Roentgenol.
175
,
221
225
(
2000
).
37.
H.
Taud
and
J.
Mas
, “
Multilayer perceptron (MLP)
,” in
Geomatic Approaches for Modeling Land Change Scenarios
, Lecture Notes in Geoinformation and Cartography (
Springer
,
2018
), pp.
451
455
.
38.
X.
Zhao
,
Y.
Liu
,
J.
Ding
,
F.
Bai
,
X.
Ren
,
L.
Ma
,
J.
Xie
, and
H.
Zhang
, “
Numerical study of bidirectional Glenn with unilateral pulmonary artery stenosis
,”
J. Mech. Med. Biol.
14
,
1450056
(
2014
).
39.
W.
Ladd
,
C.
Jensen
,
M.
Vardhan
,
J.
Ames
,
J. R.
Hammond
,
E. W.
Draeger
, and
A.
Randles
, “
Optimizing cloud computing resource usage for hemodynamic simulation
,” in
IEEE International Parallel and Distributed Processing Symposium (IPDPS)
(
IEEE
,
2023
), pp.
568
578
.
40.
M.
Zhou
,
Y.
Yu
,
R.
Chen
,
X.
Liu
,
Y.
Hu
,
Z.
Ma
,
L.
Gao
,
W.
Jian
, and
L.
Wang
, “
Wall shear stress and its role in atherosclerosis
,”
Front. Cardiovasc. Med.
10
,
1083547
(
2023
).
41.
T. R.
Meling
and
T. R.
Meling
, “
The impact of surgical simulation on patient outcomes: A systematic review and meta-analysis
,”
Neurosurg. Rev.
44
,
843
854
(
2021
).
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