Data-driven generation of 4D velocity profiles in the aneurysmal ascending aorta

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Data-driven generation of 4D velocity proﬁles in the

aneurysmal ascending aorta

Simone Saittaa, Ludovica Magaa,b, Chloe Armourb, Emiliano Vottaa,

Declan P. O’Reganc, M. Yousuf Salmasid, Thanos Athanasioud, Jonathan

W. Weinsafte, Xiao Yun Xub, Selene Pirolab,f, Alberto Redaellia

aDepartment of Information, Electronics and Bioengineering, Politecnico di

Milano, Milan, Italy

bDepartment of Chemical Engineering, Imperial College London, London, UK

cMRC London Institute of Medical Sciences, Imperial College London, London, United

Kingdom

dDepartment of Surgery and Cancer, Imperial College London, London, United Kingdom

eDepartment of Medicine (Cardiology), Weill Cornell College, New York, NY, USA

fDepartment of BioMechanical Engineering, 3mE Faculty, Delft University of

Technology, Delft, Netherlands

Abstract

Background and Objective: Numerical simulations of blood ﬂow are a valu-

able tool to investigate the pathophysiology of ascending thoratic aortic

aneurysms (ATAA). To accurately reproduce in vivo hemodynamics, compu-

tational ﬂuid dynamics (CFD) models must employ realistic inﬂow boundary

conditions (BCs). However, the limited availability of in vivo velocity mea-

surements, still makes researchers resort to idealized BCs. The aim of this

study was to generate and thoroughly characterize a large dataset of syn-

thetic 4D aortic velocity proﬁles with features similar to clinical cohorts of

patients with ATAA.

Methods: Time-resolved 3D phase contrast magnetic resonance (4D ﬂow

MRI) scans of 30 subjects with ATAA were processed through in-house code

to extract anatomically consistent cross-sectional planes along the ascending

aorta, ensuring spatial alignment among all planes and interpolating all veloc-

ity ﬁelds to a reference conﬁguration. Velocity proﬁles of the clinical cohort

were extensively characterized by computing ﬂow morphology descriptors of

both spatial and temporal features. By exploiting principal component anal-

Corresponding author: s.pirola@tudelft.nl (Selene Pirola)

Preprint will be submitted to Computer Methods and Programs in BiomedicineNovember 2, 2022

arXiv:2211.00551v1 [q-bio.TO] 1 Nov 2022

ysis (PCA), a statistical shape model (SSM) of 4D aortic velocity proﬁles

was built and a dataset of 437 synthetic cases with realistic properties was

generated.

Results: Comparison between clinical and synthetic datasets showed that the

synthetic data presented similar characteristics as the clinical population in

terms of key morphological parameters. The average velocity proﬁle quali-

tatively resembled a parabolic-shaped proﬁle, but was quantitatively char-

acterized by more complex ﬂow patterns which an idealized proﬁle would

not replicate. Statistically signiﬁcant correlations were found between PCA

principal modes of variation and ﬂow descriptors.

Conclusions: We built a data-driven generative model of 4D aortic velocity

proﬁles, suitable to be used in computational studies of blood ﬂow. The

proposed software system also allows to map any of the generated velocity

proﬁles to the inlet plane of any virtual subject given its coordinate set.

Keywords: aortic velocity proﬁle, ascending aortic aneurysm, 4D ﬂow

magnetic resonance imaging, statistical shape modeling, inﬂow boundary

conditions

1. Introduction

Thoracic aortic aneurysm (TAA) is a life-threatening condition involv-

ing an abnormal dilatation of the aortic wall [1]. An accurate assessment of

blood ﬂow plays an essential role in clinical diagnosis, risk stratiﬁcation and

treatment planning of TAA [2, 3, 4]. Computational ﬂuid dynamics (CFD)

is a well established tool to quantify hemodynamics [5, 6] through in silico

trials [7, 8]. To achieve a high level of ﬁdelity, CFD models need to account

for patient-speciﬁc boundary conditions (BCs). When choosing inﬂow BCs,

prescribing patient-speciﬁc data in the form of 3-directional velocity pro-

ﬁles allows to obtain signiﬁcantly more accurate results compared to using

idealized proﬁles, as amply shown by several recent studies that make use

of velocity information extracted from phase-contrast magnetic resonance

imaging (PC-MRI) [9, 10, 11, 12]. Nonetheless, the limited availability of in

vivo velocity measurements, still makes researchers resort to idealized BCs.

Moreover, such lack of clinical data represents an obstacle for setting up

population-based in silico trials and for building datasets for training ma-

chine learning (ML) models. Generative models can be used to overcome this

limitation by creating larger data-driven synthetic datasets [13]. In particu-

lar, statistical shape models (SSMs) have been adopted in the cardiovascular

ﬁeld [14, 15]. SSMs are data-driven approaches for assessing shape variabil-

ity and creating large virtual cohorts from clinical ones. An SSM is typically

based on principal component analysis (PCA) and describes the shape prob-

ability distribution of the input data by a mean shape and modes of shape

variations [16]. Several studies have eﬀectively applied SSMs to study TAA

geometry [17, 18, 19]. Nonetheless, aortic hemodynamics, which have been

shown to play a key role in pathophysiology of this disease [6, 20, 21], have

not received the same attention. An exception is the work of Catalano et

al., who exploited SSMs to build an atlas of aortic hemodynamics in sub-

jects with by bicuspid (BAV) and tricuspid (TAV) aortic valve [2]. However,

the authors imposed an idealized parabolic velocity proﬁle as inlet BC for

their CFD models. Despite revealing important insights on BAV vs. TAV

biomarkers, the study is hampered by the use of such simpliﬁed inlet BCs,

which signiﬁcantly aﬀect the computed aortic blood ﬂow, especially in re-

gions that are close to the inlet, namely the ascending aorta [11, 22, 12].

Motivated by the need for boosting the impact and the ﬁdelity of numerical

studies involving ascending TAA (ATAA) hemodynamics, the present work

leverages SSMs to pursue three speciﬁc aims. We provide: i) a quantitative

and detailed characterization of a representative 4D ATAA inlet velocity pro-

ﬁle as a valid alternative to idealized inlet BCs for numerical simulations; ii)

a synthetic virtual cohort of 4D ATAA inlet velocity proﬁles with features

that are consistent with those of real ATAA inlet proﬁles and potentially

large enough to allow for ML approaches to be used; iii) insights into both

spatial and temporal hemodynamic features of ATAA velocity ﬁelds in the

ascending aorta.

2. Methods

2.1. Image data

Thoracic 4D ﬂow MRI scans of 30 subjects with ATAA acquired between

2017 and 2019 were retrospectively retrieved. Our dataset included fully

deintentiﬁed images provided by Weill Cornell Medicine, (NY, USA) and

Hammersmith Hospital (London, United Kingdom). None of the subjects

in our cohort were BAV-aﬀected. Respiratory compensated 4D ﬂow acqui-

sitions were performed with the following settings: spatial resolution (voxel

size) 1.4 – 2.0 mm (range), ﬁeld of view = 360 mm, ﬂip angle = 15°, VENC =

150 – 200 cm/s (range), time resolution 20 – 28 frames/cardiac cycle (range).

Data usage was approved by the Weill Cornell Medicine Institutional Review

Board (New York, NY, USA) and by the Health Research Authority (HRA)

(17/NI/0160) in the UK and was sponsored by the Imperial College London

Joint Research and Compliance Oﬃce, as deﬁned under the sponsorship re-

quirements of the Research Governance Framework (2005). The participants

provided their written informed consent to participate in this study.

2.2. Data preprocessing

4D ﬂow MRI data were preprocessed using in-house Python code and fol-

lowing the workﬂow presented in ﬁgure 1: for each patient, a 3D binary mask

of the aorta was extracted from PC-MR angiography (PC-MRA) images us-

ing semi-automatic tools available in the open source software ITK-SNAP

[23]. To guarantee consistency of inlet plane location among all ATAA sub-

jects, inlet planes were deﬁned with respect to a commonly used anatomical

landmark represented by the bifurcation of the pulmonary artery (PA) [24].

A triangulated mesh of the selected plane within the aortic lumen was gener-

ated; 4D ﬂow velocity data were then probed at inlet plane nodal locations.

For the generic subject indexed by j, we deﬁned the inlet plane nodal co-

ordinates as ˜

Ξ(j)= [ ˜

ξ(j)

1, ..., ˜

ξ(j)

τ, ..., ˜

ξ(j)

T(j)]|, and the corresponding measured

velocity vector ﬁeld as ˜

V(j)= [˜

v(j)

1, ..., ˜

v(j)

τ, ..., ˜

v(j)

T(j)]|, with ˜

ξ(j)

τ,˜

v(j)

τ∈RN(j)×3

and where T(j)and N(j)are the number of frames in the cardiac cycle of

subject jand the number of probed nodal locations on the inlet plane, re-

spectively; therefore, in general, the dimensions of ˜

Ξ(j)and ˜

V(j)vary among

subjects.

2.3. Statistical shape modeling

Alignment. Consistent spatial orientation among the extracted inlet velocity

proﬁles was ensured through two steps: ﬁrst, each inlet plane was centered at

the origin by applying the translation T(j)to transform the nodal coordinates

ξ(j)

τinto ˜x(j)

τ=˜

ξ(j)

τ+T(j). Second, two consecutive rigid rotations were

applied to the translated coordinates ˜

x(j)

τand to the corresponding velocities

v(j)

τ. The ﬁrst rotation (R1∈R3×3) transformed ˜

x(j)

τand the corresponding

velocity proﬁle ˜

v(j)

τto ˆ

x(j)

τ=R(j)

1˜

x(j)

τand ˆ

v(j)

τ=R(j)

1˜

v(j)

τ, respectively, so

to make the inlet plane containing ˆ

x(j)

τnormal to the z-axis. The second

rigid rotation (R2∈R3×3) transformed ˆ

x(j)

τand ˆ

v(j)

τto x(j)

τ=R(j)

2ˆ

x(j)

τand

v(j)

τ=R(j)

2ˆ

v(j)

τ, and it ensured that the x-axis was aligned with the right-to-

left direction of the subject.

Figure 1: Schematic representation of the adopted workﬂow. All 4D ﬂow acquisitions go

through a preprocessing pipeline for the extraction of velocity proﬁles. The SSM process

consists in a common alignment and spatiotemporal resampling of the proﬁles and then

a combination of PCA modes to generate new ones. Only the proﬁles that meet speciﬁc

acceptance criteria are included in the ﬁnal dataset.

Resampling. After alignment, each velocity proﬁle v(j)

τwas mapped onto a

reference disk with unit radius using linear radial basis functions, eﬀectively

enabling the resampling of each velocity proﬁle at N= 1071 ﬁxed spatial

locations uniformly distributed over the reference disk (ﬁgure 2a and b).

Each velocity proﬁle time sequence was temporally interpolated to a refer-

ence temporal interval t∈[0,1] discretized in T= 20 frames, using cubic

polynomials. Finally, for the generic subject j, the spatiotemporally aligned

and resampled velocity proﬁles are deﬁned as: V(j)= [v(j)

1, ..., v(j)

t, ..., v(j)

T]|,

with v(j)

t∈RN×3.

Principal component analysis. The 30 aligned 4D velocity proﬁles were re-

arranged into column vectors and assembled into a matrix V= [V(1), ...,

V(j), ..., V(30)], with V∈RP×Jwhere Jis the number of subjects (30) and

P= 3 ×N×T. Matrix Vwas used as input for a PCA. Standard PCA

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Data-drivengenerationof4DvelocityprolesintheaneurysmalascendingaortaSimoneSaittaa,LudovicaMagaa,b,ChloeArmourb,EmilianoVottaa,DeclanP.O'Reganc,M.YousufSalmasid,ThanosAthanasioud,JonathanW.Weinsafte,XiaoYunXub,SelenePirolab,f,AlbertoRedaelliaaDepartmentofInformation,ElectronicsandBioengineering,Poli...

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Data-driven generation of 4D velocity profiles in the aneurysmal ascending aorta

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