# Wall shear stress and pressure patterns in aortic stenosis patients with and
without aortic dilation captured by high-performance image-based computational
fluid dynamics

Hadi Zolfaghari<EMAIL_ADDRESS>Mervyn Andiapen  Andreas Baumbach
Anthony Mathur  Rich R. Kerswell  Department of Applied Mathematics and
Theoretical Physics, University of Cambridge, Cambridge, UK  Barts Heart
Centre, Barts Health NHS Trust, London, UK  Centre for Cardiovascular Medicine
and Devices, William Harvey Research Institute, Queen Mary University of
London, London, UK

###### Abstract

Spatial patterns of elevated wall shear stress and pressure due to blood flow
past aortic stenosis (AS) are studied using GPU-accelerated patient-specific
computational fluid dynamics. Three cases of moderate AS, one with a dilated
ascending aorta and two within the normal range (root diameter less than 4cm)
are simulated for physiological beat cycle waveforms obtained from
echocardiography data. The computational framework is built based on sharp-
interface Immersed Boundary Method, where aortic geometries segmented from CT
angiograms are integrated into a high-order incompressible Navier–Stokes
solver. We show that even though the wall shear stress is elevated and
oscillatory due to turbulence in the ascending aorta for all the cases, its
spatial distribution is significantly more focused for the case with dilation
than those without dilation. This focal area is linked to aortic valve jet
impingement on the outer curvature of the ascending aorta, and has been shown
$in~{}vivo$ using 4D flow MRI of aortic stenosis patients with aortic dilation
(van Ooij et al., J. Am. Heart Assoc., 6(9), 2017). We show that this focal
area also accommodates a persistent pocket of high pressure, which is likely
to have contributed to the dilation process through an increased wall-normal
forcing. The cases without dilation, on the contrary, showed a rather
oscillatory pressure behaviour, with no persistent pressure “buildup” effect.
We further argue that a more proximal branching of the aortic arch could
explain the lack of a focal area of elevated wall shear stress and pressure,
because it interferes with the impingement process due to fluid suction
effects. These phenomena are further illustrated using an idealized aortic
geometry. We finally show that a restored inflow condition eliminates the
focal area of elevated wall shear stress and pressure zone from the ascending
aorta.

###### keywords:

Cardiovascular flow, image-based simulations, patient-specific modelling,
turbulent flows, hybrid supercomputing

.tifpng.pngconvert #1 .tif

##  1 Author summary

Dilation of the aorta can be a precursor to fatal events such as aortic
dissection. Aortic dilation is an involved process which depends on the
biological properties of the aorta as well as on the aortic blood flow
features. Recent flow imaging studies suggest that a stenotic (i.e., narrowed)
aortic valve leads to a turbulent flow character which elevates the fluid
stresses applied onto the aortic wall. These excessive stresses are then
linked to dilation of the aorta through weakening of the vessel wall tissue.
Not all patients with stenotic aortic valves develop aortic dilation, however.
Aortic geometry may be a key factor in whether or not a stenotic valve leads
to dilation, as it affects the way the restricted aortic flow jet interacts
with the vessel wall. We investigate the role of this factor by studying three
aortic stenosis patients with and without aortic dilation. To this end, we set
up and use a high-fidelity image-based computational framework for detailed
simulation of the turbulent flow states and show that certain geometrical
layouts of the aorta may be more likely to lead to dilation, because they
create persisting and focused areas of excessive blood flow stress on the
aortic wall.

##  2 Introduction

###  2.1 Background: chaotic character of the aortic stenosis flow

Blood flow through a stenotic or narrowed aortic valve is characterized by a
pulsatile and moderately high velocity jet inside a relatively small and
curved tube. The resulting flow is unsteady, irregular and chaotic [1] which
comprises a wide range of time and length scales. Therefore, the aortic
stenosis (AS) flow can be said to be turbulent [2]. This turbulent character
impacts the aortic wall as well as the blood components downstream of the
valve as we lay out next. It also acts to enhance itself through increasing
the thrombosis potential around the narrowed valve, which results in an even
more severe stenosis, and thereby stronger turbulence.

Turbulence has been shown to deteriorate the vascular wall and thereby trigger
aortic dilation or aneurysms. Davies et al. [3] by means of an in vitro study
showed that turbulent shear stresses as low as 1.5
$\mathrm{d}\mathrm{y}\mathrm{n}\mathrm{e}\mathrm{/}\mathrm{c}\mathrm{m}^{2}$
can trigger substantial endothelial cell DNA release, misalignment and loss,
while laminar shear stresses of magnitude 8.5
$\mathrm{d}\mathrm{y}\mathrm{n}\mathrm{e}\mathrm{/}\mathrm{c}\mathrm{m}^{2}$
did not initiate any cell cycle even at much longer exposure times. Other
works have highlighted the role of an oscillatory or turbulent wall shear
stress character in increasing the risk of atherosclerotic lesions [4, 5]. The
elevated wall shear stress in a turbulent flow environment has since been used
as an important risk stratification parameter in numerous studies involving an
impaired aortic flow [6, 7, 8, 9] or other diseased arterial flow scenarios
such as for intracranial aneurysms and stenoses [10, 11, 12, 13]. Of
particular importance is the large $in~{}vivo$ 4D flow MRI study of van Ooij
et al. [6], where a focal zone of high wall shear stress on the distal outer
curvature of ascending aorta (denoted by AAo hereinafter) was shown to be a
hallmark of AS in patients with present aortic dilation, which over-rides the
role of valve phenotype (i.e., whether the diseased valve was bicuspid or
tricuspid). They further argued that the apparent AAo dilation could be due to
this focal area, which has been reported in several studies of the bicupid
valve hemodynamics, where the dilation of AAo is more common than the aortic
stenosis patients with a tricuspid valve [14]. This zone, although more
extended towards the proximal AAo, has also been captured in recent numerical
simulations of aortic valve stenosis [15], which addressed a case with present
dilation. The hemodynamic evidence on aortic stenosis cases without dilation
is more scarce. Understanding the hemodynamics differences between aortic
stenosis cases with and without dilation can help quantify the role of flow
next to other relevant factors (such as mechanobiology of the arterial wall
tissue) in terms of future risk of developing aortic dilation.

###  2.2 Scope of this work

The present study resorts to high-order and high resolution image-based CFD
simulations to investigate the effect of aortic geometry on the hemodynamics
features of the aortic stenosis flow. Three patients who were candidates for
transcatheter aortic valve implantation (TAVI) are studied. One patient with
ascending aortic dilation is compared against two cases of minimal dilation.
Dilation is defined based on the aortic root diameter, where root diameters
above 4cm are considered to be dilated [16] (note that criticality of dilation
is not addressed here). For this present study, we particularly note the focal
area of high wall shear stress on the outer surface of the ascending aorta for
the mild to severe AS patients as shown in the large 4D flow MRI study of Van
Ooij et al. [6]. This zone which was linked to dilation of the ascending aorta
(aortopathy), has been shown in several studies concerning aortic stenosis of
the bicuspid valves (see in vivo study of [17] and in silico study of [18] as
examples). In the case of tricuspid valve with stenosis, this, to our
knowledge, has been shown only in CFD study of [15] (who studied a patient
with tricuspid valve stenosis and aortic dilation). Little has been reported
about hemodynamics of tricuspid aortic valve stenosis patients who do not
develop aortic dilation. In particular, it is unclear why the elevated wall
shear stress due to a turbulent flow character in the AAo for these cases does
not lead to aortic dilation. It is therefore useful to investigate the
hemodynamics for these patients next to cases with aortic dilation, to
understand the underlying flow-mediated factors behind the dilation.

We first present an image-based multi-GPU-accelerated blood flow simulation
tool based on the incompressible Navier-Stokes equations, aiming at high
resolution simulations of chaotic flow in patient-specific aortic geometries.
The GPU-accelerated incompressible Navier–Stokes solver with immersed boundary
method was presented previously in [19]. Here, the solver is upgraded with an
image-based module, which works out complex arterial geometries obtained from
CT or MRI scans. The code is also refurbished for integration of velocity and
pressure waveform data within the computational domain. As a result, the
presented simulation code takes 3D texture model of the aortic geometries
extracted from CT images, together with velocity and pressure waveforms
(obtained from echocardiography and Windkessel models respectively) as inputs,
and returns detailed flow field outputs including, velocity, pressure, and
Lagrangian coherent structures. Second-order quantities such as wall shear
stress are supported using the computational geometry toolkits and the Python
interface of the open source software Paraview (www.paraview.org). The
simulation data are resolved both in space (the grid resolution matches the CT
scan resolution, or goes beyond it depending on flow characteristics) and time
(numerous flow outputs, targeting a maximum frequency of 1400 Hz are generated
which amount to roughly 7TBs of data per simulation of a single heart-beat).
The sharp-interface Immersed Boundary technique is used for integration of the
complex geometry into a Cartesian simulation domain [20, 21, 22]. One key
advantage of this current implementation compared to more classical Immersed
Boundary implementations is that, no surface mesh for the solid is required
here. Instead the computational geometric features such as unit normals and
boundary cells are directly obtained from a level-set-like map that is
obtained from the segmentation output. This offers a superiority in terms of
computational performance (no load balancing issues stemming from a local
Lagrangian mesh, as the level-set map is defined globally and decomposed
equally across parallel processes) and geometrical pre-processing (it no
longer requires a meshing step after a computer-aided design file is produced
from the segmentation step). Although the current implementation only deals
with rigid wall models, it can be further extended to include moving walls
inferred from MRI images in a direction prescribed motion fashion [23], or
through an extension to fluid-structure interactions [24, 25]. The rigid body
assumption which is used in various studies in the literature [15, 26, 27, 28,
29, 30], provides a good approximation for a wide range of patients with
valvular and aortic diseases, as this cohort usually corresponds to a large
degree of atherosclerotic plaques is associated with higher stiffness of the
aortic wall [31, 32]. Further, as illustrated in [33] aortic flow models based
on rigid walls provide a good approximation of wall shear stress when the wall
deformation is below 10-15%.

Our simulations reveal a focal area of elevated wall shear stress on the outer
curvature of the AAo for the AS patient with aortic dilation, which is in
agreement with findings of [6]. However, for the cases without dilation, even
though the wall shear stress was elevated in the AAo, it was distributed more
evenly in the circumferential as well as streamwise directions. In line with
the hypothesis that this area develops due to aortic valve jet impingement on
the aortic wall for the dilated case, we showed that a temporally persistent
and focal zone of high pressure accompanies the elevated shear stress area. On
the other hand, the cases with root diameters within the normal range showed
no persistent high pressure zones. This focal area appeared to be spatially
more oscillatory with respect to the wall shear stress values, but less so
with regard to pressure. It could therefore be hypothesized that this coherent
high pressure zone might as well contribute to the dilation of the vessel by
supplying the normal force for the deformation, while high wall shear stress
and its oscillatory nature, weaken the aortic wall matrix to ease such
deformation. The difference in spatial distribution of wall shear stress and
pressure patterns is then investigated through volume rendering of the
instantaneous flow fields. It became apparent that the dilated aorta allows
for aortic valve jet impingement on the aortic wall which results in a
turbulent zone with elevated shear stresses, and a high pressure zone due to
adjacent flow deceleration. However, the aortic jet impingement location for
the cases with no dilation seems to coincide with the brachiocephalic artery
inlet. The suction effect by this artery further disrupts the otherwise focal
jet impingement process, leading to more severe turbulent flow with a farther
extended impact on the aortic wall. This stronger turbulence character is
verified using pressure signals taken within the AAo. We tested this latter
hypothesis using a mock model, where we created a simplified aortic geometry
with a more distal brachiocephalic artery inlet, and showed that the focal
zone of high wall shear stress and pressure was present due to undisturbed
aortic jet impingement. Further case studies and comparison to in vivo data
should be conducted to validate this observation.

Finally, we show that a healthy inflow condition (i.e., with no AS) leads to
no focal zone of elevated WSS and pressure in the dilated case. To this end,
we simulated a “restored” flow scenario, where the aortic inflow (i.e., after
aortic valve replacement) was modelled by tripling the aortic jet area while
maintaining the peak flow rate. It is shown that a restored flow eliminates
the focal area of excessive wall shear stress and pressure from the AAo. This
result is verified even under extreme stress, where we doubled the peak aortic
valve jet velocity.

##  3 Clinical data acquisition for the study group

Three patients with aortic valve stenosis were recruited from St Bartholomew’s
Hospital (London, UK) and CT scan were performed on a third-generation dual-
source system (SOMATOM Force, Siemens, Forchheim, Germany). The study received
ethical approval from the Health Research Authority and Westminster Research
Ethics Committee (18/LO/1583) and was sponsored by the Queen Mary University
of London with Joint Research and management Office, as defined under the
sponsorship requirements of the UK Policy framework for Health and Social Care
Research (2017) and ICH GCP.

##  4 Simulation procedure

###  4.1 Governing equations

We solve the dimensionless incompressible Navier–Stokes equations

$\frac{\partial{}}{\partial{t}}\begin{bmatrix}\textbf{\text@underline{u}}\\\
0\end{bmatrix}+\begin{bmatrix}\mathscr{-L}&\mathscr{G}\\\
\mathscr{D}&0\end{bmatrix}\begin{bmatrix}\textbf{{\text@underline{u}}}\\\
p\end{bmatrix}=\begin{bmatrix}\mathscr{N}\textbf{{\text@underline{u}}}\\\
0\end{bmatrix},$ (1)

where u=[$u_{x}$,$u_{y}$,$u_{z}$] and p denote dimensionless velocity and
pressure, respectively. Operators $\mathscr{G}$, $\mathscr{D}$, $\mathscr{L}$,
and $\mathscr{N}$, represent the differential operators $\nabla$,
$\nabla\cdot$, $Re^{-1}{\nabla}^{2}$ and
$-{\textbf{\text@underline{u}}}\cdot{\nabla}$, respectively. The Reynolds
number ($Re$) is defined as:

$Re=\frac{{\mathscr{U}_{0}\mathscr{L}_{0}}}{\nu},$ (2)

where $\mathscr{U}_{0}$, $\mathscr{L}_{0}$ and $\nu$ are the reference
velocity, length scale and blood kinematic viscosity. The flow equations (1)
are discretized using explicit 6th-order finite-differences in space and a
low-storage 3rd-order Runge-Kutta scheme [34] in time. The solver has been
optimized for task parallelism on multicore distributed memory supercomputers
[35] as well as for combined data- and task-parallelism on multicore-manycore
GPU-based hybrid-node supercomputers [36, 19]. It has been utilized for a
range of challenging laminar-turbulent transition flow scenarios [35, 37, 38,
39, 40]. The GPU-accelerated version of the solver which is up to two orders
of magnitude faster than the CPU-based paralllel solver, is particularly
favourable for ultimate usage in a clinical setting, as it reduces a single-
beat simulation time from months to 1-3 days at the resolution levels used in
this work, using only 8 GPUs.

###  4.2 Computer model of the aorta: geometry and boundary conditions

####  4.2.1 Aortic geometry

A geometrical model of the aorta is generated through two steps: i) medical
image processing, mainly the segmentation of CT angiography scans of the
patient’s chests and ii) creation of the 3D texture file , i.e. converting the
segmentation result into a geometrical format, such as a visualization toolkit
vtk (www.vtk.org) or stereolithography (stl) file, which is suitable for
integration into the flow solver (see Figure 1 under ”geometric model
reconstruction”). CT angiograms of three patients with severe aortic stenosis
who were selected for transcatheter aortic valve implantation (TAVI) in Barts
Heart Centre (Barts Health NHS Thrust) are used in this study. CT datasets in
DICOM format are then processed in 3D Slicer software (www.slicer.org), where
a region of interest (ROI) including the thoracic aorta is segmented to yield
an isolated geometrical model of the aorta. Second, the segmentation outputs
are reorganized as a standard geometry file which are suitable for integration
in a Cartesian grid Immersed Boundary flow solver. The spatial resolution of
the data could be adjusted via a standard upsampling or downsampling
procedure. A summary of the patient CT data and geometrical model outputs is
given in Table 1.

Figure 1: Workflow of creating the digital input model (shown inside the
dashed panel) for the patient-specific blood flow simulations. Geometric Model
Reconstruction: this block (on the left) shows how CT angiogram data (in DICOM
format) are segmented in 3D slicer software (where the region of interest is
marked up) and then converted in to a 3D volumetric model of the aorta.
Velocity Support: the velocity waveform is extracted from echocardiography
data and is used directly at aortic inflow boundary. It is then converted,
using a reference cardiac output, to a flow-rate waveform which is required
for construction of a pressure waveform. Pressure Support: the numerical
solver is capable of assimilation of $in~{}vivo$ pressure data, if available,
into the solution (this is done rigorously by modifying the Poisson equation
for pressure). In absence of this data, a surrogate model of the outflow
pressure is constructed based on the Windkessel model (WKM). In this study, a
pure velocity waveform is used at the inlet, a pure pressure waveform (based a
two-element WKM) is used at the descending aorta outlet, and adaptive zero-
stress boundary conditions are applied in the neck artery outflows. Figure 2:
Simulation domain $\Omega_{\text{sim}}$ and the embedded subset of interest
$\Omega_{\text{CT}}$. The $\Omega_{\text{CT}}$ includes the segmented model
geometry, all velocity and pressure support data are applied over fringe zones
outside of $\Omega_{\text{CT}}$, as volumetric patches attached to the inlet
and outlets of the model. The flow equations are then solved for the whole
$\Omega_{\text{sim}}$. The blue window which is magnified on to the right side
of the simulation domain shows the spatial resolution represented by thin mesh
lines on the surface.

####  4.2.2 Inflow boundary conditions based on spectral echocardiography data

For each patient, a cardiac waveform was extracted from the Continuous Wave
(CW) spectral echocardiography data (see Figure 1 under ”Velocity Support”),
and a heart rate of 60 beats per minute (bpm) is considered. The blood flow
velocity past the aortic valve (AV) is then converted to a discrete waveform
in CSV format to be read as an input for the numerical simulations.

The aortic jet issuing from the healthy or diseased aortic valve may take
complex geometrical shapes depending on a variety of factors including the
anatomy of the aortic root and the aortic valve. For calcified valves this
becomes even more complex, where one or more valve cusps might become
partially or fully immobile which leads to irregular cross-sectional jet
profiles. This leads to a diverse set of incoming jet profiles, ranging from
almost circular shapes to triangular, hexagonal or three-point-star profiles,
as well as more eccentric combinations of these in presence of calcification.
4D flow MRI imaging of the flow profiles behind an aortic valve with stenosis
indicates a peak flow velocity region roughly at the centre of the vessel’s
cross section [15, 41]. It also shows that the forward flow part of the
profile sustains its shape while accelerating and then decelerating in
amplitude during the systolic phase, and loses its shape only when the valve
is closed. Given these observations, and because the majority of turbulent
flow events occur during the systolic phase, we define the inflow profile
$\Omega_{in}(x,y)$ to include two parts: the core circular area $\Omega_{jet}$
with radius $r_{jet}$ indicates the jet issuing from the valve and an outer
part $\Omega_{cusp}$ which fills the region between the $\Omega_{jet}$ and the
aortic lumen ($\Omega_{in}=\Omega_{jet}\cup\Omega_{cusp}$). Note that here the
inflow cross-section is a subset of $x-y$ plane, as the $z-$ axis has been
locally aligned with the vessel walls at the inlet. We assume the flow profile
at the inlet to be uni-directional, therefore the inflow velocity field at the
inlet is purely in the $z-$direction. A plug velocity profile is then imposed
in $\Omega_{in}$ with the $z$-component $w$ of

$\centering w(x,y,t)=\begin{cases}U_{echo}(t)&\text{if }x\in\Omega_{jet},\\\
0&\text{if}~{}x\in\Omega_{cusp}.\end{cases}\@add@centering$ (3)

The radius of the core area is obtained based on a standard peak flow rate of
$Q_{peak}=0.0004${m}^{3}\mathrm{/}\mathrm{s}$$ for all cases in the paper.
With the peak velocity $U_{peak}$ obtained from the echocardiography data, the
radius of the aortic jet is defined as

$\centering r_{jet}=\sqrt{\frac{Q_{peak}}{4\pi
U_{peak}}}={\frac{1}{100\sqrt{\pi U_{peak}}}}.\@add@centering$ (4)

Finally, note that peripheral part ($\Omega_{cusp}$) of the inlet is not
annular, because the lumen shape is not circular. Therefore, we have to also
define a center for $\Omega_{in}$ to complete our definition. We define this
point $\mathbf{C}=(x_{C},y_{C})$ based on the first moment of area of
$\Omega_{in}$, that is

$\centering\mathbf{C}=(x_{C},y_{C})=\frac{1}{\Omega_{in}}\int_{\Omega_{in}}(x,y)~{}d\Omega.\@add@centering$
(5)

The inflow profile model described above has been fabricated based on a series
of assumptions, because the phase-contrast flow MRI information at the inflow
was not present. Such date can help achieve a better model of the aortic
inflow profile, and will be a subject for our future work.

####  4.2.3 Outflow boundary conditions

Boundary conditions (BC) applied on the outflow boundaries include Dirichlet-
type homogeneous boundary conditions at the descending aorta outflow boundary
and zero-stress compatibility-type pressure boundary conditions at the outflow
boundaries of the neck arteries. The Dirichlet type BC values for pressure at
the descending aorta outflow are calculated dynamically based on a two-element
Windkessel model (2EWKM) [42]. These values construct a waveform which is
obtained from a flow rate waveform input which has a peak value that is a
fraction of that for the inflow waveform (a standard value for this fraction
is 0.85 which assumes that roughly 5% of the aortic flow is supplied to each
of the neck arteries [43]). Note that the these fractions have only been used
to obtain the outflow pressure waveform for the descending aorta. The zero
stress BCs that are applied to the neck arteries merely ensure that a sum of
flow fraction supplied to these arteries amounts to 15% of the incoming flow
(while the flow fraction to each artery can be different than 5%). Based on
this flow waveform, a pressure waveform is generated by time-integration of
the flow rate-pressure equation arising in the 2EWKM:

$\centering Q(t)=\frac{P(t)}{R_{out}}+C_{out}\frac{dP(t)}{dt},\@add@centering$
(6)

where $Q$ is the descending aorta flow rate in
$\mathrm{m}^{3}\mathrm{/}\mathrm{s}$, $P$ is the pressure in
$\mathrm{m}\mathrm{m}\mathrm{H}\mathrm{g}$, $R_{out}$ is the distal resistance
and $C_{out}$ is the capacitance accounting for the vessel compliance.

Given a value for diastolic blood pressure (typically
$80$\mathrm{m}\mathrm{m}\mathrm{H}\mathrm{g}$$), the equation above becomes a
well-posed initial value problem, where values of $R_{out}$ and $C_{out}$
could be found such that the time integration of the Eq. (6) results in a
periodic pressure waveform. For the idealized case, a flow waveform with a
sinosuidal systolic part and a null diastolic part is used, which allows an
analytical solution for pressure can be obtained [44].

###  4.3 High-performance computing with GPUs

Detailed numerical simulations of turbulent flows are costly in nature due to
the required large grid resolutions [2]. For instance, using a resolution of
$512\times 512\times 512$ grid points integrated in time for an average of
$2.7\times 10^{4}$ time-steps, our massively parallel CPU-based solver [35]
would require approximately two months to complete a single-beat aortic
simulation using only CPU cores of 8 hybrid nodes (8$\times$12 Intel Xeon
E5-2690 v3 cores, $8\times 64$GB RAM) of a Tier 0 supercomputer
($Piz~{}Daint$, Swiss National Supercomputing Centre). Resorting to our GPU-
based implementation brings down this simulation time to 3 days, which is more
practical in a clinical environment. Resorting to a higher number of GPUs,
even though may be accessible only through cloud based clusters, would lead to
even better solver throughput. For instance resorting to 256 P100 GPUs would
bring down the simulation time to 1-2hrs. The reduction of computational time
at the same rate as the increasing of computational resources is not the case
for majority of parallel implementations due communication overhead and data
transfer latency, nevertheless, it is achieved here thanks to strong scaling
capability of current GPU implementation [19].

Parallelism is achieved in a two-step process. First the computational domain
is decomposed into blocks of equal sizes, which are then processed in parallel
using the message passing interface (MPI) [35, 36], and then each MPI block is
decomposed into its grid points, and each grid point is then processed using a
CUDA (compute unified device architecture) thread [19, 36]. The solver uses a
novel high-throughput Poisson solver for pressure which significantly reduces
the time-to-solution, resulting in speedups of factor 10-300 compared to a
parallel CPU-based solver [19]. Even though the original solver was designed
based on periodic boundary conditions, it has been modified here for
incorporation of Dirichlet type pressure outflow boundary conditions.

All cases presented in the paper have been run using a simulation box
resolution of $512\times 512\times 512$. The simulation runs for a physical
time of one heart beat have been performed for roughly three days using 8
NVIDIA P100 GPUs, each seeded by 8 CPU cores. The average time-step for the
simulations was $dt=0.000037$\mathrm{s}$$. A CFL number of 0.5 was set. All
runs were performed on Haswell nodes of Cray XC40/50 $Piz~{}Daint$
supercomputer.

##  5 Results and Discussion

###  5.1 Hemodynamics of the AS and virtually restored scenarios

####  5.1.1 Overview of the patient specific and idealized cases

The reconstructed geometrical models for AS cases, labelled as TAVI0, TAVI1,
TAVI2 (see Table 1) and an idealized case are shown in figure 3. The TAVI0
case has marked dilation (AAo diameter of 4cm), while cases TAVI1 and TAVI2 do
not present dilation. The figure shows the geometries sorted in terms of out-
of-plane bending of the aortic arch, where TAVI0 has the highest bending,
followed by TAVI1, TAVI2 and Idealized (which has no out-of-plane bending)
cases. In addition to diseased cases TAVI0-2, we also investigate the
hemodynamics in a restored (i.e. after the narrowed valve is replaced with a
valve prosthesis) condition for the TAVI0 case. We model the restored flow by
increasing the aortic jet area three times as that in the diseased case, while
maintaining the flow rate waveform. This simplified model corresponds to a
reduction in peak flow velocity from 2.7$\mathrm{m}\mathrm{/}\mathrm{s}$ to
$0.9$\mathrm{m}\mathrm{/}\mathrm{s}$$, which is in the healthy range. Further
to a baseline restored case which we label as “TAVI0-Restored”, we also
investigate a case of restored flow under extreme stress (labelled as
“TAVI0-Restored+S”), which has the same aortic valve jet area as the
“Restored” case, but a peak velocity twice that case (i.e.
$1.8$\mathrm{m}\mathrm{/}\mathrm{s}$$).

Table 1: Physical dimensions of the geometric and waveform input models. The “TAVI0 Restored” and “TAVI0-Restored+S” (which is the stressed version of restored case) cases are based on the geometry of TAVI0 case. The inflow and out flow cross sections are given under “D- Slice” (datum slice, which is the slice at lowest $z$ inside $\Omega_{CT}$ subdomain which is introduced in figure 2). Lower curve shows the inlet and the upper curve shows the outlet boundary) and are roughly of a egg-like oval shape. The sizes of these inflow and outflow boundaries given in a $a\times b$ format, where $a$ is the major axis and $b$ is the minor axis of the oval. Case |  CT Resolution $($\mathrm{m}\mathrm{m}$\times$\mathrm{m}\mathrm{m}$\times$\mathrm{m}\mathrm{m}$)$ |  Inflow Size $($\mathrm{m}\mathrm{m}$\times$\mathrm{m}\mathrm{m}$)$ |  Outflow Size $($\mathrm{m}\mathrm{m}$\times$\mathrm{m}\mathrm{m}$)$ |  AV jet radius $($\mathrm{m}\mathrm{m}$)$ |  D- Slice
---|---|---|---|---|---
TAVI0 | $0.4\times 0.4\times 0.5$ | $40\times 36$ | $28\times 28$ | $7.0$ |
TAVI1 | $0.746\times 0.746\times 0.75$ | $30\times 28$ | $26\times 24$ | $7.7$ |
TAVI2 | $0.779\times 0.779\times 0.75$ | $35\times 31$ | $26\times 26$ | $7.5$ |
Idealized | NA | $29\times 29$ | $29\times 29$ | $6.8$ |
TAVI0 Restored | $0.4\times 0.4\times 0.5$ | $40\times 36$ | $28\times 28$ | $10.2$ |
TAVI0-Restored+S | $0.4\times 0.4\times 0.5$ | $40\times 36$ | $28\times 28$ | $10.2$ |
Figure 3: Geometric models for patients “TAVI0”, “TAVI1” and “TAVI2”, as well
as the Idealized model “Idealized”.

####  5.1.2 Wall shear stress: from waves to a chaotic character

The magnitude of instantaneous wall shear stress (WSS) is calculated as

${\sigma}_{w}=|{(\boldsymbol{\sigma}\cdot\mathbf{n})-(\boldsymbol{\sigma}\cdot\mathbf{n}\cdot\mathbf{n})\mathbf{n}}|$
(7)

where $\boldsymbol{\sigma}$ is the fluid’s Cauchy stress tensor and
$\mathbf{n}$ is the outward normal to the aortic wall. Figure 4 shows
instantaneous maps of WSS for cases TAVI0, TAVI1, TAVI2 and Idealized which
are demonstrated for six time instances, namely, MA (mid-acceleration), 3QA
(three-quarters acceleration), PF (peak flow), QD (quarter deceleration), MD
(mid-deceleration) and ES (end systole). These time instances within a
standard velocity waveform are indicated in figure 5. It is seen that a focal
area of spatially oscillatory and elevated WSS exists on the outer curvature
of the AAo for the TAVI0 cases. Cases TAVI1 and TAVI2, on the other hand, show
elevated WSS values more dispersed in space, i.e., more extended both in the
circumferential direction and also towards the distal aortic arch. The focal
zone of high WSS, which emerges around PF and persists through the beat cycle
roughly until MD, is suspected to form due to the turbulent impingement of the
strong stenotic jet on the outer wall of the ascending aorta (a similar case
for a tricuspid AS patient with dilation has been shown in [15]). This focal
area has been shown for patients with bicuspic aortic valve (BAV), and
extensively addressed in the context of regional aortic remodelling in the
recent literature [7, 45, 46] (see especially [45], where the regional zone of
elevated WSS was illustrated to be linked to regional aortic remodelling).

The absence of such focal zone for the cases TAVI1-2 despite aortic jet
velocities on par with the TAVI0 case is likely to be due to the secondary
disturbing effect of the Brachiocephalic artery inlet through coincidence with
the impingement zone. As the middle row (yz view) of figure 3 suggests, the
Brachiocephalic inlet is slightly more downstream for TAVI0 than TAVI1 and
TAVI2; this leaves more available space for the incoming jet to impinge
without further disturbance. However, presence of the brachiocephalic artery
inlet at the jet impingement site mimics wall suction mechanism which could
disrupt its localized impact (see figure 6), while it could enhance or weaken
the background turbulent flow.

The hypothesis that the focal zone of high WSS occurs when brachiocephalic
artery inlet is sufficiently distal to the impingement zone is tested using
the Idealized model presented in figure 3. The wall shear stress snapshots for
this case are shown next to patient cases in figure 4. It is shown that the
focal zone is present throughout the systolic phase which is in agreement with
our hypothesis.

Figure 4: Wall shear stress magnitude maps for instances MA, 3QA, PF, QD, MD
and ES are shown for patient-specific cases TAVI0, TAVI1 and TAVI2 as well as
the Idealized case. A persistent focal area of elevated and oscillatory wall
shear stress is observed on the outer curvature of the ascending aorta for
TAVI0 and the Idealized cases, whereas elevated values of WSS are more
dispersed in space for cases TAVI1 and TAVI2. This could be due to more
downstream branching location of the Brachiocephalic artery for the TAVI0 and
Idealized cases, compared to TAVI1 and TAVI2. The former cases allow jet
impingement on the vessel wall without further disturbance due to cross-flow
caused by this neck artery, while the latter cases include further disturbing
of this zone by this cross-flow effect (which acts as a source of
blowing/suction of fluid).  Figure 5: Time instance references used in the
paper for the in-beat snapshot presentations: peak flow (PF) denotes when flow
rate reaches its maximum. End systole (ES), denotes the state of flow at the
end of systolic deceleration. Other instances are then defined accordingly as
follows: mid-acceleration (MA) is temporally halfway between the start of the
pulse ($t=0$) and PF, three-quarters acceleration (3QA) is halfway between MA
and PF, mid-deceleration (MD) is halfway between PF and ES, quarter-
deceleration (QD) is halfway between PF and MD.  Figure 6: Volume rendering of
the undisturbed (left, TAVI0 case) and disturbed (right, TAVI2) aortic jet
impingement on the aortic wall at time QD. The undisturbed impingement case
shows that the aortic jet changes direction without breakdown while the
disturbed impingement case shows the jet undergoing large disturbances while
impinging (the destabilizing effect of blowing/suction by Brachiocephalic
artery).

Figure 7 shows the separation in WSS patterns for cases with focal elevation
(TAVI0 and Idealized) next to that with a dispersed elevation (TAVI1-2). Time
histories of WSS data taken at a closed band around the ascending aorta artery
inlet are plotted over the systolic acceleration phase. A focal but more
intense zone of WSS for TAVI0 and Idealized cases are observed, whereas, WSS
oscillations span the entire azimuthal extent of the closed band for cases
TAVI1 and TAVI2.

Figure 7: Evolution of wall shear stress values over time (top panels) for a
band (solid black line shown on the bottom panels) in the ascending aortic
region. For each point on the band, the angle $\theta$ is defined with respect
to an origin on the surface enclosed within the band, and is taken to be the
mean value of $x$, $y$ and $z$ coordinates of the surface. Red bullet mark
shows $\theta=0$ and the positive azimuthal direction is shown by arrows. Wall
shear stress data on the band are then collected in time and plotted over a
period from the start of the pulse $t=0$ until $t=0.225$\mathrm{s}$$, which is
slightly past the peak flow. It can be seen that wall shear stress peaks cover
the entire band for cases TAVI1 and TAVI2, but are concentrated on one side of
the band for cases TAVI0 and Idealized. The white dashed lines show
approximately the boundary of high wall shear stress zones and the quiet zone
on for the cases TAVI0 and Idealized.

The mere locality of the elevated WSS in the ascending aorta, and even its
slightly higher magnitude, do not justify the dilation of the TAVI0 case as
opposed to cases TAVI1-2, because the wall shear stress is elevated for all
cases in AAo anyway. The flow deceleration around the jet impingement zone
however is expected to develop a zone of high pressure, which could be a
driving force for dilation. We emphasize again that the above observations are
made under several assumptions and could be overruled by anatomical factors of
the wall tissue. Our goal is to present the hemodynamic differences over this
given spectrum of aortic geometries, which could help understand a possible
contribution of hemodynamic factors in the aortic dilation.In the next
section, we take advantage of geometrical symmetry of the Idealized case and
investigate the possibility of a high pressure pocket underneath the
impingement zone.

####  5.1.3 Pressure behaviour in disturbed vs undisturbed stenotic jet
impingement

Figure 8 shows the jet impingement on the aortic surface for the Idealized
case. Three snapshots of velocity magnitude are taken on a slice cutting
through the aortic geometry on its axis of symmetry normal to the $x$ axis.
They show the jet velocity changes due to impingement at outer AAo wall due to
deceleration. This flow deceleration corresponds to a high pressure pocket
forming at the impingement zone (cf. middle rows of figure 8). Continuous
pressure signals between this three snapshots and at four selected probes A,
B, C, and D (shown on the middle left panel of the figure) confirm that the
pressure at the centre of impingement (point A) remains consistently higher
than the other neighbouring probes B, C and D. A mean pressure difference of
approximately $1000$\mathrm{P}\mathrm{a}$$ focused on a single location can
have implications on local dilation of the vessel, which may have been
deteriorated by the high shear stress. This focal zone of high pressure acts
as the normal force required for the local dilation of the aorta. In this
sense, even though elevated and oscillatory wall shear stresses weaken the
arterial wall for all cases (maybe more locally for the dilated case), the
elevated pressure, if persistent in time, could drive the expansion process by
forcing the weakened wall matrix in the outward normal direction (i.e., it
acts as tensile stress acting to expand the aorta).

Figure 8: Realization of the jet impingement process through velocity
magnitude (top panels) and pressure (middle panels) visualizations in the
Idealized case. From left to right, time instances 3QA, PF and QD are shown.
The bottom plot shows the time history of pressure values taken on four probes
A, B, C and D (see the middle left panel) around the impingement zone. It is
shown that probe A which is located roughly close to the centre of impingement
zone, consistently marks a higher pressure (of 1000Pa approximately) than
other neighbouring probes.

Figure 9 shows systolic snapshots of wall pressure for TAVI0-2 and Idealized
cases. Consistent to the WSS interpretations made in the previous section,
cases TAVI0 and Idealized present regional focal zones of high wall pressure,
which persist until mid-deceleration (MD) instance of the beat cycle. Cases
TAVI1 and TAVI2 show no clear regional pressure peak but rather an oscillatory
pressure behaviour. A frequently sampled signal of wall pressure (sampling
rate of 1400Hz), measured on the exterior surface of the ascneding aorta
further confirms this observation (figure 10). Pressure signals for TAVI0 and
Idealized cases show a “pressure buildup” effect (marked in red) with only low
amplitude oscillations, while the pressure signals for TAVI1 and TAVI2 cases
show rather higher amplitude oscillations near peak flow without any apparent
pressure buildup. This stronger oscillations show that the suction effect of
the brachiocephalic artery has led to an even higher amplitude oscillations
for the TAVI1 and TAVI2 cases (in terms of WSS, this was seen as a more
extended wall footprint, yet with a lower magnitude than the impingement
case). A measure for the relative amplitude of oscillations with respect to
the background is given in figure 10 as $|\delta_{p}|_{\max}/p_{i}$, where
$|\delta p|$ is twice the amplitude of oscillations present in the buildup
part of the signal, and $p_{i}$ is the pressure at the onset of pressure
buildup. Large pressure values observed in cases TAVI1-2 could be alarming in
terms of enhancing the risk of a sudden aortic dissection, however, the
strongly oscillatory behaviour as opposed to a persistent buildup may explain
why these cases do not undergo dilation despite turbulence.

Figure 9: Wall pressure maps for instances 3QA, PF, QD, MD are shown for
patient-specific cases TAVI0, TAVI1 and TAVI2 as well as the Idealized case
Idealized. A persistent zone of high pressure, which corresponds to a high
wall shear stress zone (cf. figure 4), is observed on the ascending aorta for
cases TAVI0 and Idealized, but not for the cases TAVI1 and TAVI2.  Figure 10:
Pressure signal taken as a time series of pressure at a probe located on the
aortic wall slightly upstream of neck arteries (the probe is marked in magenta
on the left column of figure 9, and is located at centre of the HWSS zone) for
TAVI0, TAVI 1, TAVI 2, and Idealized cases. Cases TAVI 0 and Idealized show
distinct pressure build up. Cases TAVI 1 and TAVI 2 lack a pressure build up,
but show strong oscillations near peak flow which is shown by the
dimenstionless parameter $|\delta_{p}|_{\max}/p_{i}$, where $\delta_{p}$
denotes twice the maximum amplitude of the oscillations, and $p_{i}$ is the
initial pressure value taken at 3QA instance.

###  5.2 Hemodynamics of the restored flow in the dilated aorta

Treatment scenarios for AS patients with aortic dilation may include the
aortic root replacement next to the aortic valve replacement (AVR). This is
justified by the increased risk of future aortic dissection in presence of
dilation, which is a marker of arterial wall deterioration. Even though the
progression and rapture of a dilated aorta is a biologically involved process,
hemodynamics may also play a role in this phenomenon. To this end, we study
the changes in wall shear stress and pressure in case of a restored aortic
flow in the dilated case TAVI0. The restored cases labelled as TAVI0-Restored
(without stress) and TAVI0-Restored+S (with extreme stress) are simulated.
Detailed specifications of these cases can be found in section 5.1.1.

Figure 11 shows the wall shear stress distributions for the TAVI0-Restored and
TAVI0-Restored+S flow scenarios at time instances 3QA, PF and QD. It is seen
that the focal zone of elevated WSS has been removed from the restored and
unstressed cases. The wall shear stress levels are in general half that of the
corresponding diseased (TAVI0) case. The stressed case (bottom panels of the
figure) does not indicate any sign of the focal zone seen for the TAVI0 case,
nevertheless, this case exhibits elevated levels of WSS throughout the aortic
wall. Figure 12 shows the pressure maps of cases TAVI0-Restored and
TAVI0-Restored+S for times 3QA, PF and QD. Consistent with the wall shear
stress outcome (figure 11), the regional pressure peak has been removed for
the restored case at both stressed and unstressed conditions. The unstressed
case TAVI0-Restored shows a uniformly decaying pressure from ascending to the
descending aorta, while the stressed case shows an oscillatory behaviour,
although it does not demonstrate any persistent regional pressure peak.

Figure 11: Wall shear stress maps for the virtually restored case of TAVI0 at
times 3QA, PF and QD. Top row corresponds to restored flow with the same
cardiac output (no stress scenario) as the stenosis case, and the bottom row
corresponds to a stressed scenario where cardiac output is doubled. It is seen
that both scenarios do not mark a high wall shear stress zone on the ascending
aorta as opposed to the stenosis case. However, new zones of high wall shear
stress have emerged downstream of the aortic arch bend towards the descending
aorta. Signs of helical wall-shear stress waves can be also observed on the
ascending aorta for the stressed scenario (see bottom right panel).

These observations suggest that the dilated aorta does not in itself lead to a
disorganized flow in the ascending aorta (the restored flow without stress
does not exhibit any chaos in AAo). Finally, figure 11 also shows that the
maximum wall shear stresses of up to 6Pa are found in the distal arch area for
TAVI0-Restored case. This zone of high WSS did not appear prior to AVR (see
TAVI0 case in figure 4), and may be related to dilation or other anatomical
features of TAVI0 case. The latter mechanism is not addressed in this paper,
however, the velocity field underneath this emerging zone of elevated WSS post
AVR are discussed in the following.

Figure 12: Wall pressure maps for the virtually restored case of TAVI0 at
times 3QA, PF and QD. Top row corresponds to restored flow with the same
cardiac output (unstressed scenario) as the stenosis case, and the bottom row
corresponds to a stressed scenario where cardiac output is doubled. It is seen
that the regional zone of high wall pressure on the ascending aorta which was
observed in the stenosis case is no longer present. The unstressed scenario
shows an almost uniformly decaying pressure from ascending towards the
descending aorta, but the stressed scenario shows an oscillatory behaviour,
which is likely to be related to the helical wave footprints on wall shear
stress maps for this case (see figure 11).

Figure 13 shows four slices of the background velocity fields at peak flow for
the restored scenarios next to the stenosis case. It is seen that the TAVI0
case undergoes severe turbulence in the ascending aorta, whereas the flow in
the descending aorta remains largely laminar (only a tiny region of reverse
flow is observed). The laminar flow in this zone is consistent with the lower
wall shear stress observations in figure 4. For the TAVI0-Restored case
(middle row panels of figure 13 ), the flow throughout the AAo becomes
laminar, which also corresponds to lower wall shear stress levels than the
diseased case (see figures 4 and 11). However, this restored case indicates a
zone of elevated WSS in the distal arch area as discussed in the previous
part. As the velocity slices suggest, this new zone is due to a relatively
large separation bubble at the intersection of distal aortic arch and the
descending aorta. This unstable zone grows in size for the stressed model (cf.
TAVI0-Restored+S case) and produces stronger oscillations in the descending
aorta (see figure 11). Whether such separation bubble emerges post AVR due to
extreme out-of-plane bending of the aorta or dilation itself is the subject of
a separate study.

Figure 13: Peak flow velocity magnitude (left) and $z-$component of the
velocity field (right) for the TAVI0 case at stenosis (bottom), restored and
unstressed (middle) and restored and stressed (top) cases. Even though the
flow is less chaotic after restoration in the ascending aorta, the descending
aortic flow marks a major instability (a separation bubble) which is linked to
elevated wall shear stress in that location (see figure 11). This bubble could
be due to the major out-of-plane bending of the aorta.

##  6 Conclusion

We report a pattern separation of turbulent flow hemodynamics based on aortic
stenosis patients with and without aortic dilation using GPU-accelerated
image-based aortic flow simulations. Three aortic stenosis cases, one with
aortic dilation and two within normal aortic size range were considered.
Vessel geometries were extracted from CT angiograms, and aortic inflow
waveforms were obtained from echocardiography data. All cases exhibited a
turbulent flow with an elevated and oscillatory wall shear stress footprint on
the ascending aorta. However, the dilated case showed a focal zone of elevated
and oscillatory wall shear stress on the outer curvature of the aortic wall,
unlike other cases which exhibited a more extended distribution (i.e.,
covering the whole circumference of the vessel and further towards and even
past the aortic arch). Because the wall shear stress was elevated and
oscillatory for both dilated and non-dilated cases, it is suspected that
another flow-mediated mechanism might be driving the dilation. Further
inspection showed that this mechanism could be a local pressure maximum
adjacent to the elevated wall shear stress zone, which is only present for the
dilated case. We argue that this persistent zone of elevated pressure is due
to low velocity zone forming behind the aortic jet impingement site on the
ascending aorta. This observation is quantified using pressure probes, where
the non-dilated cases showed significantly stronger pressure oscillations
without developing a focal zone of high pressure. Moreover, we show that if
this impingement zone is disturbed, e.g. via fluid suction from a more
proximal brachiocephalic artery inlet, it could lead to stronger turbulence
with a more extended (less focal) elevated wall shear stress footprint. This
is examined using an idealized model of the aorta (a candy-cane geometry with
uniform aortic radius), where a more distal brachicephalic artery inlet was
shown to lead to undisturbed jet impingement and thereby it developed focal
zones of elevated wall shear-stress and pressure. Therefore, it can be said
that for the dilation case, a focal zone of elevated pressure cooperates with
a coinciding zone of elevated and oscillatory wall shear stress: the excessive
and oscillatory wall shear stress weakens the arterial wall matrix, while
pressure buildup provides the driving normal force to dilate it.

For the dilated case, we further inspected the aortic hemodynamics after the
aortic valve replacement using a virtually restored inflow model. Simulation
outcomes showed a laminar flow with no wall shear stress or pressure maxima in
the ascending aorta, but instead revealed a zone of elevated wall shear stress
at the distal aortic arch region. Velocity slices at this area showed a
separation bubble, which could be a result of dilation or out-of-plane
remodelling of the aorta. We showed that even an extreme case of stress (in
which the peak velocity was doubled) does not lead to any focal area of
elevated wall shear stress or pressure, even though it led to elevated and
oscillatory wall shear stress and pressure in the ascending aorta.

The distinct separation in wall hemodynamics between aortic stenosis patients
with and without dilation that is presented here should be tested on a larger
cohort of patients for further validation. Moreover, as we showed here, a
stronger turbulent flow may remove the stress from focal areas in the aorta,
thereby preventing the dilation. However, the key remaining question is,
whether this prevention is a case of life-saving turbulence, or is it evil in
disguise which can lead to sudden dissection through strong pressure
oscillations? Lastly, it is important to establish a fluid mechanics criterion
on occurrence of focal wall shear stress and pressure maxima (or jet
impingement) in terms of peak velocity and jet radius (equivalent to effective
orifice area). We have seen that a larger jet, even with peak velocities
double than normal, leads to no impingement on the wall, as it undergoes
turbulent breakdown before arriving at the wall. This is contrary to the
disease case, which involved a narrower jet with slightly higher peak
velocity.

##  7 Limitations

The rigid wall assumption was used for all simulations presented here, and is
based on the correlation between present aortic atherosclerosis in the cases
studied and aortic stiffness given in the literature. However, supporting
kinematics data for the specific cases studied here was not available which
could be a source of over-estimated wall pressure, even though it is less
likely to affect its distribution. More accurate simulations can be performed
by inferring wall kinematics from cine MRI scans.

Further, the inflow jet profile was fabricated in this work based on a
circular shape jet and fully stagnant peripheral part. This could be improved
by using PC MRI flow slices at the domain inflow, which yields a better
estimation of jet shape.

The pressure waveforms applied to the descending aorta outflow boundary were
based on a simple two-element Windkessel model. This could be improved by
pressure data or more complex Windkessel models.

## Acknowledgements

HZ and RRK would like to thank the Swiss National Supercomputing Centre (CSCS)
for providing technical support and GPU-node resources on the Cray XC40/50
supercomputer Piz Daint. HZ would like to additionally acknowledge the
financial support from Swiss National Science Foundation (SNSF) through the
Early PostDoc Mobility Fellowship P2BEP2$\\_191786$ and from the European
Commission under the Marie Curie Individual Fellowship OPTAVI-895580.

Appendix A: Flow rate and pressure waveforms The velocity waveforms are taken
from continuous wave (CW) spectral echocardiography data (see figure 1). All
physiological waveforms are projected based on a heartbeat of 60bpm (beats per
minute). For the idealized geometry case, a heart rate of 72bpm is used to
fabricate the velocity and pressure waveform. All flow and pressure waveforms
are shown in figures 14 and 15 and, while their corresponding velocity
waveform can be obtained using the reference values given in Table2.

Table 2: Flow rate and pressure waveform reference values Case |  $U_{peak}$ ($\mathrm{m}\mathrm{/}\mathrm{s}$) |  $R_{\textit{out}}$ ($\mathrm{m}\mathrm{m}\mathrm{H}\mathrm{g}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{3}\mathrm{/}\mathrm{s}$) |  $C_{\textit{out}}$ ($\mathrm{c}\mathrm{m}\mathrm{3}\mathrm{/}\mathrm{m}\mathrm{m}\mathrm{H}\mathrm{g}$) |  $p_{systole}$ ($\mathrm{m}\mathrm{m}\mathrm{H}\mathrm{g}$) |  $p_{diastole}$ $\mathrm{m}\mathrm{m}\mathrm{H}\mathrm{g}$
---|---|---|---|---|---
TAVI 0 | $2.7$ | $0.898$ | $2.066$ | $113$ | $80$
TAVI 1 | $2.1$ | $1.210$ | $1.351$ | $118$ | $80$
TAVI 2 | $2.2$ | $1.083$ | $1.900$ | $109$ | $80$
Idealized | $2.7$ | $1.127$ | $1.153$ | $113$ | $80$
TAVI 0 Restored | $0.9$ | $0.898$ | $2.066$ | $123$ | $80$
TAVI 0 Restored+ | $1.8$ | $0.6737$ | $0.950$ | $113$ | $80$
Figure 14: Flow rate waveforms from left to right, for cases TAVI0, TAVI1,
TAVI2 and Idealized.  Figure 15: Pressure waveforms, from left to right, for
cases TAVI0, TAVI1, TAVI2 and Idealized. Black curves show the waveform for
the descending aorta outflow boundary, while the red curves show the
corresponding waveforms at the inflow boundary.

## References

  * [1] Stein PD, Sabbah HN.  Turbulent blood flow in the ascending aorta of humans with normal and diseased aortic valves.  Circulation research. 1976;39(1):58–65.
  * [2] Pope SB, Pope SB.  Turbulent flows.  Cambridge university press; 2000.
  * [3] Davies PF, Remuzzi A, Gordon EJ, Dewey CF, Gimbrone MA.  Turbulent fluid shear stress induces vascular endothelial cell turnover in vitro.  Proceedings of the National Academy of Sciences. 1986;83(7):2114–2117.
  * [4] Traub O, Ishida T, Ishida M, Tupper JC, Berk BC.  Shear stress-mediated extracellular signal-regulated kinase activation is regulated by sodium in endothelial cells: potential role for a voltage-dependent sodium channel.  Journal of Biological Chemistry. 1999;274(29):20144–20150.
  * [5] Lehoux S, Tedgui A.  Cellular mechanics and gene expression in blood vessels.  Journal of biomechanics. 2003;36(5):631–643.
  * [6] van Ooij P, Markl M, Collins JD, Carr JC, Rigsby C, Bonow RO, et al.  Aortic valve stenosis alters expression of regional aortic wall shear stress: New insights from a 4-dimensional flow magnetic resonance imaging study of 571 subjects.  Journal of the American Heart Association. 2017;6(9):e005959.
  * [7] Pasta S, Gentile G, Raffa G, Bellavia D, Chiarello G, Liotta R, et al.  In silico shear and intramural stresses are linked to aortic valve morphology in dilated ascending aorta.  European Journal of Vascular and Endovascular Surgery. 2017;54(2):254–263.
  * [8] Jr LaDisa JF, Dholakia RJ, Figueroa CA, Vignon-Clementel IE, Chan FP, Samyn MM, et al.  Computational simulations demonstrate altered wall shear stress in aortic coarctation patients treated by resection with end-to-end anastomosis.  Congenital heart disease. 2011;6(5):432–443.
  * [9] Kauhanen SP, Hedman M, Kariniemi E, Jaakkola P, Vanninen R, Saari P, et al.  Aortic dilatation associates with flow displacement and increased circumferential wall shear stress in patients without aortic stenosis: a prospective clinical study.  Journal of Magnetic Resonance Imaging. 2019;50(1):136–145.
  * [10] Valen-Sendstad K, Bergersen AW, Shimogonya Y, Goubergrits L, Bruening J, Pallares J, et al.  Real-world variability in the prediction of intracranial aneurysm wall shear stress: the 2015 international aneurysm CFD challenge.  Cardiovascular engineering and technology. 2018;9(4):544–564.
  * [11] Morbiducci U, Mazzi V, Domanin M, De Nisco G, Vergara C, Steinman DA, et al.  Wall shear stress topological skeleton independently predicts long-term restenosis after carotid bifurcation endarterectomy.  Annals of biomedical engineering. 2020;48(12):2936–2949.
  * [12] Szajer J, Ho-Shon K.  A comparison of 4D flow MRI-derived wall shear stress with computational fluid dynamics methods for intracranial aneurysms and carotid bifurcations—a review.  Magnetic resonance imaging. 2018;48:62–69.
  * [13] Zhang B, Gu J, Qian M, Niu L, Ghista D.  Study of correlation between wall shear stress and elasticity in atherosclerotic carotid arteries.  Biomedical engineering online. 2018;17(1):1–11.
  * [14] Wilton E, Jahangiri M.  Post-stenotic aortic dilatation.  Journal of cardiothoracic surgery. 2006;1(1):1–11.
  * [15] Manchester EL, Pirola S, Salmasi MY, O’Regan DP, Athanasiou T, Xu XY.  Analysis of turbulence effects in a patient-specific aorta with aortic valve stenosis.  Cardiovascular engineering and technology. 2021;12(4):438–453.
  * [16] Zhu P, Zhou P, Ling X, Ohene BE, Bian XM, Jiang X.  Surgical treatment of mild to moderately dilated ascending aorta in bicuspid aortic valve aortopathy: the art of safety and simplicity.  Journal of Cardiothoracic Surgery. 2020;15(1):1–6.
  * [17] Garcia J, Barker AJ, Markl M.  The role of imaging of flow patterns by 4D flow MRI in aortic stenosis.  JACC: Cardiovascular Imaging. 2019;12(2):252–266.
  * [18] Youssefi P, Gomez A, He T, Anderson L, Bunce N, Sharma R, et al.  Patient-specific computational fluid dynamics—assessment of aortic hemodynamics in a spectrum of aortic valve pathologies.  The Journal of thoracic and cardiovascular surgery. 2017;153(1):8–20.
  * [19] Zolfaghari H, Obrist D.  A high-throughput hybrid task and data parallel Poisson solver for large-scale simulations of incompressible turbulent flows on distributed GPUs.  Journal of Computational Physics. 2021;437:110329.
  * [20] Mittal R, Dong H, Bozkurttas M, Najjar F, Vargas A, Von Loebbecke A.  A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries.  Journal of computational physics. 2008;227(10):4825–4852.
  * [21] Mittal R, Iaccarino G.  Immersed boundary methods.  Annuual Review of Fluid Mechanics. 2005;37:239–261.
  * [22] Zolfaghari H, Izbassarov D, Muradoglu M.  Simulations of viscoelastic two-phase flows in complex geometries.  Computers & Fluids. 2017;156:548–561.
  * [23] Jin S, Oshinski J, Giddens DP.  Effects of wall motion and compliance on flow patterns in the ascending aorta.  J Biomech Eng. 2003;125(3):347–354.
  * [24] Lin YL, Derr NJ, Rycroft CH.  Eulerian simulation of complex suspensions and biolocomotion in three dimensions.  Proceedings of the National Academy of Sciences. 2022;119(1).
  * [25] Rycroft CH, Wu CH, Yu Y, Kamrin K.  Reference map technique for incompressible fluid–structure interaction.  Journal of Fluid Mechanics. 2020;898.
  * [26] Lantz J, Ebbers T, Engvall J, Karlsson M.  Numerical and experimental assessment of turbulent kinetic energy in an aortic coarctation.  Journal of biomechanics. 2013;46(11):1851–1858.
  * [27] Cheng Z, Tan F, Riga C, Bicknell C, Hamady M, Gibbs R, et al.  Analysis of flow patterns in a patient-specific aortic dissection model. 2010;.
  * [28] Numata S, Itatani K, Kanda K, Doi K, Yamazaki S, Morimoto K, et al.  Blood flow analysis of the aortic arch using computational fluid dynamics.  European Journal of Cardio-Thoracic Surgery. 2016;49(6):1578–1585.
  * [29] Assemat P, Armitage JA, Siu KK, Contreras KG, Dart AM, Chin-Dusting JP, et al.  Three-dimensional numerical simulation of blood flow in mouse aortic arch around atherosclerotic plaques.  Applied Mathematical Modelling. 2014;38(17-18):4175–4185.
  * [30] Prahl Wittberg L, van Wyk S, Fuchs L, Gutmark E, Backeljauw P, Gutmark-Little I.  Effects of aortic irregularities on blood flow.  Biomechanics and modeling in mechanobiology. 2016;15(2):345–360.
  * [31] Van Popele NM, Grobbee DE, Bots ML, Asmar R, Topouchian J, Reneman RS, et al.  Association between arterial stiffness and atherosclerosis: the Rotterdam Study.  Stroke. 2001;32(2):454–460.
  * [32] Cecelja M, Chowienczyk P.  Role of arterial stiffness in cardiovascular disease.  JRSM cardiovascular disease. 2012;1(4):1–10.
  * [33] Reymond P, Crosetto P, Deparis S, Quarteroni A, Stergiopulos N.  Physiological simulation of blood flow in the aorta: comparison of hemodynamic indices as predicted by 3-D FSI, 3-D rigid wall and 1-D models.  Medical engineering & physics. 2013;35(6):784–791.
  * [34] Wray AA.  Very low storage time-advancement schemes.  Internal Rep NASA-Ames Research Center, Moffett Field, CA. 1986;.
  * [35] Henniger R, Obrist D, Kleiser L.  High-order accurate solution of the incompressible Navier–Stokes equations on massively parallel computers.  Journal of Computational Physics. 2010;229(10):3543–3572.
  * [36] Zolfaghari H, Becsek B, Nestola MG, Sawyer WB, Krause R, Obrist D.  High-order accurate simulation of incompressible turbulent flows on many parallel GPUs of a hybrid-node supercomputer.  Computer Physics Communications. 2019;244:132–142.
  * [37] John MO, Obrist D, Kleiser L.  Stabilisation of subcritical bypass transition in the leading-edge boundary layer by suction.  Journal of Turbulence. 2014;15(11):795–805.
  * [38] John MO, Obrist D, Kleiser L.  Secondary instability and subcritical transition of the leading-edge boundary layer.  Journal of Fluid Mechanics. 2016;792:682–711.
  * [39] Zolfaghari H, Obrist D.  Absolute instability of impinging leading edge vortices in a submodel of a bileaflet mechanical heart valve.  Physical Review Fluids. 2019;4(12):123901.
  * [40] Zolfaghari H, Kerswell RR, Obrist D, Schmid PJ.  Sensitivity and downstream influence of the impinging leading-edge vortex instability in a bileaflet mechanical heart valve.  Journal of Fluid Mechanics. 2022;936.
  * [41] Archer GT, Elhawaz A, Barker N, Fidock B, Rothman A, Van Der Geest R, et al.  Validation of four-dimensional flow cardiovascular magnetic resonance for aortic stenosis assessment.  Scientific reports. 2020;10(1):1–10.
  * [42] Westerhof N, Lankhaar JW, Westerhof BE.  The arterial windkessel.  Medical & biological engineering & computing. 2009;47(2):131–141.
  * [43] Tse KM, Chang R, Lee HP, Lim SP, Venkatesh SK, Ho P.  A computational fluid dynamics study on geometrical influence of the aorta on haemodynamics.  European Journal of Cardio-Thoracic Surgery. 2013;43(4):829–838.
  * [44] Catanho M, Sinha M, Vijayan V.  Model of aortic blood flow using the Windkessel effect.  University of California of San Diago, San Diago. 2012;.
  * [45] Guzzardi DG, Barker AJ, Van Ooij P, Malaisrie SC, Puthumana JJ, Belke DD, et al.  Valve-related hemodynamics mediate human bicuspid aortopathy: insights from wall shear stress mapping.  Journal of the American College of Cardiology. 2015;66(8):892–900.
  * [46] Soulat G, Scott MB, Allen BD, Avery R, Bonow RO, Malaisrie SC, et al.  Association of regional wall shear stress and progressive ascending aorta dilation in bicuspid aortic valve.  Cardiovascular Imaging. 2022;15(1):33–42.


# Improving Robustness of Neural Inverse Text Normalization via Data-
Augmentation, Semi-Supervised Learning, and Post-Aligning Method

###### Abstract

Inverse text normalization (ITN) is crucial for converting spoken-form into
written-form, especially in the context of automatic speech recognition (ASR).
While most downstream tasks of ASR rely on written-form, ASR systems often
output spoken-form, highlighting the necessity for robust ITN in product-level
ASR-based applications. Although neural ITN methods have shown promise, they
still encounter performance challenges, particularly when dealing with ASR-
generated spoken text. These challenges arise from the out-of-domain problem
between training data and ASR-generated text. To address this, we propose a
direct training approach that utilizes ASR-generated written or spoken text,
with pairs augmented through ASR linguistic context emulation and a semi-
supervised learning method enhanced by a large language model, respectively.
Additionally, we introduce a post-aligning method to manage unpredictable
errors, thereby enhancing the reliability of ITN. Our experiments show that
our proposed methods remarkably improved ITN performance in various ASR
scenarios.

Index Terms—  ASR, inverse text normalization

##  1 Introduction

Inverse text normalization (ITN) converts spoken-form text to its
corresponding written-form, which is used as post-processing for an automatic
speech recognition (ASR) system’s output since it typically provides spoken-
form text. While some ASR systems [1] can generate written-form text through
training with written-form text data, they may still occasionally produce
spoken-form text, resulting in unstable conversion performance compared to
applying ITN. Written-form text is preferred due to its user-friendliness, and
many downstream tasks of ASR rely on written-form text, such as date-based
scheduling and address-based search. Thus, ensuring robust ITN performance is
essential for a product-level ASR system [2].

Recently, neural ITN methods [2, 3, 4, 5, 6] have outperformed the previous
finite-state transducer (FST)-based ITN approaches [7, 8, 9]. This is because
leveraging the data-driven modeling capabilities of neural networks is more
advantageous for capturing numerous spoken-written form relationships than
FST, which incurs expensive scaling costs for transformation rules within the
FST graph.

Despite promising results in neural ITN, significant performance degradation
occurs when applying it to ASR-generated spoken text [2, 3]. Neural ITN is
trained on the general spoken text and its corresponding written text, which
may lead to differences in linguistic context compared to ASR-generated spoken
text due to irregular interjections and ASR errors, i.e., the performance
degradation stems from the out-of-domain problem, indicating that addressing
this issue solely through an ordinary text corpus has limited effectiveness.
To resolve the out-of-domain problem, the most direct approach is to utilize
ASR-generated spoken or written text and their corresponding pairs for
training neural ITN. However, constructing such a corpus with human resources
is costly, making it nearly impractical to scale up the amount of ASR spoken-
written text in this manner.

Furthermore, neural ITN methods based on sequence-to-sequence (seq2seq) models
[2, 10] can introduce unpredictable errors, which pose a critical challenge
for product-level solutions as these errors may distort the original meaning
of ASR-generated spoken text. To address this issue, [3, 4] proposed an
additional tagger network to specify the normalization region; however, since
the tagger network still relies on a neural network-based approach, there is
no guarantee to control unpredictable errors associated with neural networks.

In light of the aforementioned problems, this paper contributes the following:

  * •

To address the out-of-domain problem, we directly train neural ITN using ASR-
generated text data. We create spoken-written text pairs from ASR-generated
spoken or written text using a data augmentation (DA) and semi-supervised
learning (SSL) pipeline. DA emulates the linguistic context of ASR-generated
spoken text to enhance the robustness of neural ITN, while SSL employs a large
language model (LLM) for confidence scoring to prevent neural ITN from
learning inaccuracies from pseudo-written text.

  * •

To address neural ITN’s unpredictable errors, we introduce a post-aligning
(PA) algorithm that provides better control than neural network-based models
alone. PA detects discrepancies between spoken and neural ITN hypotheses,
making targeted replacements. It also utilizes all neural ITN hypotheses, not
just the top-ranked one, for enhanced performance.

Experiments exhibit that applying our proposed methods showed remarkable
robustness in various ASR scenarios. Although our experiments were done in
Korean language, most proposed methods can be extended to other languages.

##  2 Data Generation Pipeline

In Fig. 1, we illustrate the proposed training data generation pipeline. To
train the neural ITN, spoken-written form text pairs are essential. However,
we can obtain either spoken or written text from the ASR system. The objective
of our pipeline is to create pairs solely based on spoken or written text. To
accomplish this, in a high-level description, DA generates spoken text from
written text, and vice versa is achieved by SSL; thus, we achieve the training
of the neural ITN with ASR-generated text. Consequently, the pipeline is
applied to the three types of datasets: spoken-written text corpus (type I),
written text corpus (type II), and spoken text corpus (type III), where type I
is from text corpus for Korean text normalization publicly released by AI
Hub111https://www.aihub.or.kr; type II and type III are from our in-house ASR
system trained using both spoken and written ASR labels.

###  2.1 Data augmentation

Fig. 1: Training data generation pipeline with DA and SSL based on dataset
types.

As shown in Fig. 1, DA pipeline includes noise augmentation and multi-text
normalization (MTN). Given written text, DA generates the noise-augmented
written text ($\text{written text}^{*}$) and its corresponding spoken text
(pseudo-spoken text). The used noise types in Fig. 1 are chosen to compensate
for the weak points of the baseline neural ITN, when it is exposed to ASR
spoken text. The baseline neural ITN was trained using type I corpus alone
without any ASR-related datasets. Note that widely used noise types for DA in
the general natural language processing field [11] was not effective according
to our experiments.

To generate $\text{written text}^{*}$, repetition noise is added to written
text at first. The repetition is common in ASR spoken text because a speaker
can actually repeat the words or ASR system can cause the repetition error.
Regardless of where this error originated from, the baseline neural ITN showed
the vulnerability when it was exposed by the repetition error. For example,
baseline neural ITN repeats the words more than the spoken text actually did.
To mitigate this case by training, we randomly repeat the words in the given
written text. After that, the numbers in the written text are substituted into
other random numbers to expand the coverage of numbers.

To generate spoken text given $\text{written text}^{*}$, MTN is adopted. The
spoken-written form has a many-to-one relationship rather than one-to-one. For
example, if the written form is “2024”, people can say “two oh two four”,
“twenty twenty-four”, or “two thousand twenty-four”. However, the common text
normalization techniques only support the one-to-one relationship. To address
this problem, we expand the text normalization to MTN to support a many-to-one
relationship. MTN randomly outputs the spoken form among the candidates given
written form and we refer the output of MTN to pseudo-spoken text.

In Korean, spacing rules in writing are considered unstable, resulting in
inconsistent adherence by native speakers [12]. Consequently, the Korean ASR
corpus contains numerous spacing errors, indicating the frequent occurrence of
spacing errors caused by the Korean ASR system. For example, despite one of
the spoken forms of “2013” being “이천십삼”, the ASR system can produce variations
such as “이천 십삼”, “이 천십삼”, or “이천십 삼”. To replicate this effect, the DA
pipeline includes spacing noise augmentation applied to spoken-form text.
Spacing errors are introduced exclusively in regions that deviate from the
written form to prevent over-regularization.

To sum up, DA generates a pair of pseudo-spoken text and $\text{written
text}^{*}$ from written text. Note that the written text can come from type I
and III as well as type II as illustrated in Fig. 1, in order to effectively
expand the amount of training data. Also, spacing noise augmentation is
applied to all spoken text regardless of the type of the dataset.

###  2.2 Semi-Supervised learning

Our SSL pipeline in Fig. 1 comprises four primary steps [13]:

  1. 1.

Training a teacher ITN model on type I and II datasets with DA.

  2. 2.

Generating pseudo-written text using the teacher model on the type III
dataset.

  3. 3.

Filtering out some of the pseudo-written text based on confidence scoring.

  4. 4.

Training a student model on all spoken-written text pairs generated from the
data generation pipeline: (spoken text, written text), (pseudo-spoken text,
$\text{written text}^{*}$), and (spoken text (ASR), pseudo-written text).

Fig. 2: PA block diagram and examples of alignments between spoken-text
(column) and written-text (row). The bold blue numbers indicate the alignment
path, orange boxes represent boundary syllables, and green boxes highlight
normalization regions.

We iterate through this procedure over multiple epochs, wherein the trained
student at each epoch serves as a teacher to generate new pseudo-written text
from the spoken text and train a new student. Note that DA is also applied to
the pseudo-written text generated by the SSL pipeline. This process encourages
the student model to learn a more fluent context of ASR text than the teacher
model initially had from the type III dataset.

Confidence scoring plays a crucial role in SSL [14]. The traditional approach
to confidence scoring relies on the likelihood of the teacher model for
unlabeled data [15]. However, SSL using this approach did not demonstrate
improvement in our work because the likelihood measure fails to discern
unnaturally converted pseudo-written text. For instance, consider the
sentence: “응 응 오늘 아 할 일 많아” (“Yes, yes, today, there is a lot of work to do”);
neural ITN may erroneously convert it to “응 응 오늘 아 할 1 많아”, as the Korean word
“일” can mean both “work” and “one”. However, “응 응 오늘 아 할 1 많아” is
linguistically unnatural because “일” is intended to mean “work” in this
context. Unfortunately, likelihood-based scoring methods occasionally assign a
high score to such unnatural sentences.

The ideal confidence scoring method for ITN should assess the naturalness of
written text converted by neural ITN to obtain reliable pseudo-written text.
However, developing a model to evaluate naturalness for confidence scoring is
not a trivial task. Instead, we assume that recently proposed approaches based
on LLMs [16, 17, 18] have the potential to assess naturalness effectively.
Considering that LLMs are trained on a vast amount of natural language data,
and naturalness can be defined by expressions commonly used by people, LLMs
have the potential to discriminate linguistically unnatural sentences.

To verify this assumption, we adopt Chat-GPT222https://chat.openai.com, one of
the representative LLMs, with the following prompts:

  * •

Which of the two sentences, {spoken text} or {pseudo-written text} when the
numeric part of {spoken text} is converted to numbers, is more commonly used
by people? Do you think people would find it easier to recognize if the
altered sentence is quoted in a news article? Please respond with “yes” or
“no” only.

  * •

Tell me if {pseudo-written text} is the correct conversion for the numeric
part pronounced in Korean in {spoken text}. Please respond with only “yes” or
“no”.

At the first prompt, using the second sentence enhances Chat-GPT’s ability to
make decisions about whether the pseudo-written text closely resembles
standard written form, as news articles typically quote sentences in this
form. The second prompt is similar to the first one. Since Chat-GPT’s
responses can vary across trials, asking Chat-GPT a similar prompt again can
improve the reliability of the answer, especially if we consider the pseudo-
written text as valid only when Chat-GPT responds positively to both prompts.

For the rejected samples that received a negative response from Chat-GPT to
one of the prompts, we utilized them by directly copying the spoken-form text
to use it as pseudo-written text instead of discarding them. While this method
may not reduce quantitative errors, it can be beneficial from a qualitative
perspective, as incorrect conversions can distort the original meaning of the
spoken text.

##  3 Post-Aligning

As depicted in Fig. 2, certain hypotheses are firstly dropped from $N$-bests
when the difference in scores between them and the 1-best hypothesis exceeds
the threshold $\alpha$ because lower-scored hypotheses usually have erroneous
conversions. We assume that $M$ hypotheses are remained from this process.
After that, the alignment between spoken text and each ITN hypothesis is
conducted based on edit-distance. From the alignment, the set of $K$
normalization pairs,
$D_{m}=\left\\{\left(s_{i},w_{i}\right)\right\\}_{i=1}^{K}$ is obtained where
$m$ is the hypothesis number, $s_{i}$ and $w_{i}$ are the normalization region
and its target in spoken and written text, respectively. For intuitive
understanding, we provide an example in Fig. 2-(a) in which the normalization
regions correspond to green boxes of which the start point is found when the
current score in the path is higher than the previous score and the end-point
is found when the current score is the same with the previous score.

Although the written text can be recovered by replacing the $s_{i}$ to $w_{i}$
in spoken text, the baseline alignment has a limitation when a deletion error
occurs in written text. In Fig. 2-(b), if we allow the deletion normalizations
such as (“오”, “”), the erroneously deleted “사용” by neural ITN cannot be
recovered. The deletion normalization is mainly due to the existence of
numerous spacing in Korean spoken text because the spacing characters in
spoken text are matched with certain numbers in written text instead of Korean
syllables, leading to deletion normalization. To cope with this problem, we
proposed a blacklist passing scheme which does not allow the characters as an
end-point if the characters are in the blacklist. As described in Fig. 3-(c),
the proposed alignment detects actual erroneous deletion (“사용”, “”); thus, we
can restore “사용”, by not allowing the deletion normalization.

Given $D_{m}$, we identify the candidates of normalization pairs involving the
replacement. All pairs in $D_{0}$ are included in the candidates. The
repeatedly appeared pairs in $D_{1}$ to $D_{M}$ are counted and if the
counting number of a certain pair is greater than $\eta$, it is also included
in the candidates. Note that the spacing in $s_{i}$ and $w_{i}$ is not
considered for counting, e.g., (“사십”, “40”) and (“사 십”, “40”) is considered to
be the same. By doing so, we expected the boosting effect of neural ITN
because hypotheses more than 1-best are exploited via this process for written
text prediction.

From the candidates, we ignore the Korean deletion normalization to restore
the deletion errors caused by neural ITN. Although we only deal with deletion
errors, other error types also can be handled by providing some rules at this
stage. Finally, by substituting $s_{i}$ in the spoken text to $w_{i}$ in
candidates, we can obtain the written text.

Table 1: ITN performance comparison on AI-Hub, ASR-TEL, and ASR-BC considering
the application of methods (DA, SSL, and PA) and dataset utilization for
training (type I, type II, and type III). The numbers in bold indicate the
best result.
---
Method | Training Dataset | Test Dataset
DA |  SSL |  PA |  Type I |  Type II |  Type III | AI-Hub | ASR-TEL (ITN label) | ASR-BC (ASR label)
|  |  |  |  |  |  I-CER |  NI-CER |  CER |  I-CER |  NI-CER |  CER |  I-CER |  NI-CER |  CER
|  |  |  |  |  |  0.32 |  0.34 |  0.34 |  49.58 |  6.00 |  6.45 |  41.54 |  21.18 |  21.40
|  |  |  |  |  |  0.77 |  0.64 |  0.66 |  56.09 |  1.39 |  1.96 |  27.31 |  15.96 |  16.09
|  |  |  |  |  |  0.66 |  0.65 |  0.65 |  15.90 |  0.24 |  0.40 |  17.85 |  15.01 |  15.04
|  |  |  |  |  |  0.74 |  0.68 |  0.69 |  12.49 |  0.21 |  0.34 |  16.43 |  14.90 |  14.92
|  |  |  |  |  |  0.76 |  0.61 |  0.63 |  54.58 |  0.55 |  1.12 |  26.74 |  14.69 |  14.82
|  |  |  |  |  |  0.65 |  0.66 |  0.66 |  15.14 |  0.17 |  0.33 |  17.35 |  14.64 |  14.67
|  |  |  |  |  |  0.73 |  0.69 |  0.70 |  11.96 |  0.18 |  0.31 |  16.36 |  14.64 |  14.66

##  4 Experiments and Results

###  4.1 Experimental setup

Model: For neural ITN, we employed a conventional transformer-based seq2seq
model. The encoder and decoder networks consist of 12 and 1 layer(s),
respectively, with all layers having 1024 hidden units. For beam search, we
used a beam size of 5. For PA, $\alpha$ and $\eta$ were set to 5 and 1,
respectively, based on our validation set. For SSL, we initially trained our
neural ITN on type I and II datasets with DA until the validation loss no
longer decreased. Subsequently, we conducted additional training for 10
epochs, including the SSL. As the baseline, we employed the model trained
exclusively on the type I dataset without the application of DA, SSL, or PA.

In the case of ASR, we adopted the conformer-transducer model [19, 20], which
was trained on our in-house dataset comprising 13k hours of Korean utterances.
Note that our ASR labels encompass both spoken and written forms, enabling our
ASR system to generate both written and spoken outputs.

Datasets: For training, we utilize AI-Hub and ASR-generated datasets for
written and spoken text, corresponding to type I, type II, and type III
datasets, respectively. AI-Hub contains 300k spoken-written text pairs and
covers a wide range of entities, including floats, times, currencies, units,
addresses, and account numbers. We divided AI-Hub into subsets of 240k, 10k,
and 50k sentences for training, validation, and testing, respectively. To
obtain diverse ASR error distributions, we applied our ASR system to 4M
utterances from various domains, including smart speakers, broadcasts, and
conversational domains. Of these, 3M utterances were used to train the ASR
system, while the remaining 1M were not. Among the 4M utterances, we obtained
1M in written form (type II), and we randomly extracted 1M in spoken form from
the remaining 3M utterances (type III). Note that we distinguished the written
form by assessing whether the ASR-generated text includes non-Korean
characters.

For testing, we have adopted three test sets: the AI-Hub test set (50k
sentences), ASR-generated datasets from an additional 5k utterances recorded
in a phone-call scenario (ASR-TEL), and 5k utterances in a broadcasting
scenario (ASR-BCN). Since using ASR labels as the ground truth text cannot
measure the pure and potential performance of the neural ITN, we manually
labeled the ASR-TEL for ITN evaluation while we continued to use existing ASR
labels for ASR-BCN. The character error rates (CER) of our ASR system for ASR-
TEL and ASR-BCN were 7.0% and 15.89%, respectively.

Metrics: The ITN performance is measured by ITN CER (I-CER), and Non-ITN CER
(NI-CER), focusing on the quality of text normalization and measuring
undesirable perturbations to the original source text, respectively [2]. CER
is also utilized.

###  4.2 Experimental results and discussion

Table I summarizes the experimental results, demonstrating the significant
effectiveness of DA, SSL, and PA in ASR-TEL (CER: 0.31%) and ASR-BCN (CER:
14.66%), except for AI-Hub, where the baseline achieved the best results (CER:
0.34%). The degradation in AI-Hub is attributed to differences in written form
styles between AI-Hub and ASR-generated text datasets. For example, the spoken
form “십만원” (one hundred thousand won) can be represented in both written
forms: “10만원” or “100,000원”. Additionally, the noise augmentation methods in
DA primarily aim to simulate ASR-generated text with distinct linguistic
contexts compared to ordinary text. This implies that DA may have led to an
over-regularization effect on the AI-Hub test set. However, it’s worth noting
that the I-CER, NI-CER, and CER for all proposed methods in AI-Hub remain
below 1%, which is reasonable considering the performance improvements in ASR-
TEL and ASR-BCN.

Applying DA to type I resulted in a remarkable reduction in NI-CER in ASR-TEL
(6.00% $\to$ 1.39%) and ASR-BCN (21.18% $\to$ 15.96%) compared to the
baseline, while a reduction in I-CER was only evident in ASR-BCN (41.54% $\to$
27.31%). This suggests that noise augmentation in DA effectively mitigates the
distortion of the original text by the neural ITN. Furthermore, given that
ASR-BCN comprises broadcasts, including news content, the semantic context for
ITN in ASR-BCN can be closer to that of AI-Hub than ASR-TEL, which has a more
irregular semantic context due to its origin in a fully conversational domain.
This leads to different results regarding I-CER. This is supported by the
results when type II, including conversational domains, is involved for
training, which showed a dramatic reduction in I-CER: 15.90% and 17.85% in
ASR-TEL and ASR-BCN, while showing different results in NI-CER: 0.24% and
15.01% in ASR-TEL and ASR-BCN.

When applying SSL, we observed an improvement in CER in both ASR-TEL and ASR-
BCN, with marginal degradation in NI-CER. We found that this degradation
depends on the reliability of the confidence-scoring model, which restricts
erroneous pseudo-written text for training the student model. This is why we
used two similar prompts to improve reliability.

PA consistently improved performance in both I-CER and NI-CER in ASR-TEL and
ASR-BCN. PA selectively carries out ITN while conserving the original text not
involved in ITN, leading to NI-CER reduction. Also, PA utilizes $M$-best
hypotheses when building the ITN candidates, leading to I-CER reduction
because additional ITN conversions are achieved if some hypotheses have
correct predictions when the 1-best has failed.

Note that the relative performance improvements with proposed methods in CER
in ASR-TEL with ITN labels compared to the baseline was 95.18%, implying that
our proposed methods have outstanding potential power for ITN if the ASR
system provides correct outputs to the neural ITN.

##  5 Conclusion

In this work, we proposed novel methods to address the performance degradation
of neural ITN when it encounters ASR-generated text due to the out-of-domain
problem. To enable the direct utilization of ASR-generated text for neural ITN
training, DA and SSL effectively generated spoken-written text pairs from just
one of them, leading to a significant improvement in performance. PA provided
further enhancements through its selective and boosted ITN conversion
approach. Although our datasets also include foreign words, this work
primarily focuses on the conversion of numeric words. Our future work will
expand to effectively handle foreign words as well.

## References

  * [1] A. Radford, J. W. Kim, T. Xu, G. Brockman, C. McLeavey, and I. Sutskever, “Robust speech recognition via large-scale weak supervision,” in _International Conference on Machine Learning_. PMLR, 2023, pp. 28 492–28 518.
  * [2] M. Sunkara, C. Shivade, S. Bodapati, and K. Kirchhoff, “Neural inverse text normalization,” in _ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)_ , 2021, pp. 7573–7577.
  * [3] T.-B. Nguyen, L. D. M. Nhat, Q. M. Nguyen, Q. T. Do, C. M. Luong, and A. Waibel, “Adapitn: A fast, reliable, and dynamic adaptive inverse text normalization,” in _ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)_ , 2023, pp. 1–5.
  * [4] A. Antonova, E. Bakhturina, and B. Ginsburg, “Thutmose Tagger: Single-pass neural model for Inverse Text Normalization,” in _Proc. Interspeech 2022_ , 2022, pp. 550–554.
  * [5] S. Tan, P. Behre, N. Kibre, I. Alphonso, and S. Chang, “Four-in-one: a joint approach to inverse text normalization, punctuation, capitalization, and disfluency for automatic speech recognition,” in _2022 IEEE Spoken Language Technology Workshop (SLT)_ , 2023, pp. 677–684.
  * [6] D. Paul, Y. Pang, S.-J. Chen, and X. Zhang, “Improving data driven inverse text normalization using data augmentation and machine translation,” _Proc. Interspeech 2022_ , pp. 5221–5222, 2022.
  * [7] M. Shugrina, “Formatting time-aligned asr transcripts for readability,” in _Human Language Technologies: The 2010 Annual Conference of the North American Chapter of the Association for Computational Linguistics_ , 2010, pp. 198–206.
  * [8] Y. Zhang, E. Bakhturina, and B. Ginsburg, “NeMo (Inverse) Text Normalization: From Development to Production,” in _Proc. Interspeech 2021_ , 2021, pp. 4857–4859.
  * [9] P. Ebden and R. Sproat, “The kestrel tts text normalization system,” _Natural Language Engineering_ , vol. 21, no. 3, pp. 333–353, 2015.
  * [10] M. Ihori, A. Takashima, and R. Masumura, “Large-context pointer-generator networks for spoken-to-written style conversion,” in _ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)_. IEEE, 2020, pp. 8189–8193.
  * [11] J. Wei and K. Zou, “Eda: Easy data augmentation techniques for boosting performance on text classification tasks,” _arXiv preprint arXiv:1901.11196_ , 2019.
  * [12] S. Kim, “When keeping up means falling behind: The dear price of stressing “correct” orthography in teaching korean as a heritage language,” _Korean Language in America_ , vol. 18, no. 1, pp. 71–91, 2013.
  * [13] Q. Xie, M.-T. Luong, E. Hovy, and Q. V. Le, “Self-training with noisy student improves imagenet classification,” in _Proceedings of the IEEE/CVF conference on computer vision and pattern recognition_ , 2020, pp. 10 687–10 698.
  * [14] H. Yao, X. Hu, and X. Li, “Enhancing pseudo label quality for semi-supervised domain-generalized medical image segmentation,” in _Proceedings of the AAAI Conference on Artificial Intelligence_ , vol. 36, no. 3, 2022, pp. 3099–3107.
  * [15] D.-H. Lee _et al._ , “Pseudo-label: The simple and efficient semi-supervised learning method for deep neural networks,” in _Workshop on challenges in representation learning, ICML_ , vol. 3, no. 2. Atlanta, 2013, p. 896.
  * [16] L. Ouyang, J. Wu, X. Jiang, D. Almeida, C. Wainwright, P. Mishkin, C. Zhang, S. Agarwal, K. Slama, A. Ray _et al._ , “Training language models to follow instructions with human feedback,” _Advances in Neural Information Processing Systems_ , vol. 35, pp. 27 730–27 744, 2022.
  * [17] B. Min, H. Ross, E. Sulem, A. P. B. Veyseh, T. H. Nguyen, O. Sainz, E. Agirre, I. Heintz, and D. Roth, “Recent advances in natural language processing via large pre-trained language models: A survey,” _ACM Computing Surveys_ , 2021\.
  * [18] T. Brown, B. Mann, N. Ryder, M. Subbiah, J. D. Kaplan, P. Dhariwal, A. Neelakantan, P. Shyam, G. Sastry, A. Askell _et al._ , “Language models are few-shot learners,” _Advances in neural information processing systems_ , vol. 33, pp. 1877–1901, 2020.
  * [19] P. Guo, F. Boyer, X. Chang, T. Hayashi, Y. Higuchi, H. Inaguma, N. Kamo, C. Li, D. Garcia-Romero, J. Shi _et al._ , “Recent developments on espnet toolkit boosted by conformer,” in _ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)_. IEEE, 2021, pp. 5874–5878.
  * [20] J. Kim, Y. Lee, and E. Kim, “Accelerating rnn transducer inference via adaptive expansion search,” _IEEE Signal Processing Letters_ , vol. 27, pp. 2019–2023, 2020.