Ansys Left Ventricle Mechanics

Original Article

Fluid Mechanics of Fetal Left Ventricle During Aortic Stenosis

Hospital, Linz, Austria

(Received 19 January 2022; accepted 5 June 2022; published online 22 June 2022) Associate Editor Lakshmi Prasad Dasi oversaw the review of this article. Abstract—In cases of fetal aortic stenosis and evolving Hypoplastic Left Heart Syndrome (feHLHS), aortic stenosis is associated with specific abnormalities such as retrograde or bidirectional systolic transverse arch flow. Many cases progressed to hypoplastic left heart syndrome (HLHS) malformation at birth, but fetal aortic valvuloplasty can prevent the progression in many cases. Since both disease and intervention involve drastic changes to the biomechan- ical environment, in-vivo biomechanics likely play a role in inducing and preventing disease progression. However, the fluid mechanics of feHLHS is not well-characterized. Here, we conduct patient-specific echocardiography-based flow simulations of normal and feHLHS left ventricles (LV), to understand the essential fluid dynamics distinction between the two cohorts. We found high variability across feHLHS cases, but also the following unifying features. Firstly, feHLHS diastole mitral inflow was in the form of a narrowed and fast jet that impinged onto the apical region, rather than a wide and gentle inflow in normal LVs. This was likely due to a malformed mitral valve with impaired opening dynam- ics. This altered inflow caused elevated vorticity dynamics and wall shear stresses (WSS) and reduced oscillatory shear index at the apical zone rather than mid-ventricle. Secondly, feHLHS LV also featured elevated systolic and diastolic energy losses, intraventricular pressure gradients, and vortex formation numbers, suggesting energy inefficiency of flow and additional burden on the LV. Thirdly, feHLHS LV had poor blood turnover, suggesting a hypoxic environment, which could be associated with endocardial fibroelastosis that is often observed in these patients.

Keywords—Fluid mechanics, Fetal heart, Aortic stenosis,

Fluid

dynamics.

Hypoplastic Left Heart Syndrome (Hlhs) Is A Com-

plex critical congenital heart disease that can have

Severe Outcomes.27 In A Subset Of Hlhs Patients,

pathogenesis is associated with aortic stenosis during mid-gestation with a normal-sized or dilated heart,

Which Progresses To Hlhs By Birth.4,15 The Aortic

stenosis causes depressed left ventricular (LV) function and is accompanied by abnormalities such as bidirec-

Tional Or Retrograde Transverse Aortic Arch Flow,

monophasic mitral valve inflow, left-to-right foramen

Pulmonary

veins.15,17 Natural history studies showed that only 19.4–36% of such patients will be biventricular at birth, and the remaining will have HLHS single ven- tricular malformation.11,15,20 For this reason, these patients are known to have fetal aortic stenosis with evolving HLHS (feHLHS).

In such patients, fetal aortic valvuloplasty (FAV)

Has Shown Much Promise In Reversing The Original

prognosis and increasing biventricular birth outcomes.

Fav Involves Introducing A Needle Through The Mo-

ther’s abdomen into the fetal LV and inflating a bal- loon catheter at the stenotic aortic valve to relieve the stenosis.16,32 Two single-centre studies have reported 66–68% biventricular postnatal outcomes in cases with technically successful FAV.23,30 Procedural success and Hong Shen Wong and Hadi Wiputra have contributed equally to this work.

Bioengineering, Imperial College London, London, UK. Electronic

1158

biventricular outcome rates have also shown signs of improvement in the later years, suggesting that expe-

The

heart.

During

feHLHS, outflow obstruction caused high pressures in

Instantaneous Peak Gradient From The Aortic Valve

(AV) or mitral regurgitation (MR) velocities, estimated by the simplified Bernoulli equation.17,18 Elevated LV pressure often leads to severe MR, which can cause left atrial pressurization and dilation, and consequently,

Foramen

ovale.31 Further, LV ejection fraction and myocardial strains are severely depressed.9 After the intervention, de-pressurization of the LV can be achieved, decreased

Lv End-Diastolic Volume And Acute Improvements In

diastolic function and ventricular strains.5,9,24,38 Fur-

Hemodynamics After Fav, Such As That Seen Aortic

arch and foramen ovale, allowed for increased growth of the AV and mitral valves (MV).11,17,25 Unfortu- nately, there is currently little data on the biome- chanical environment of feHLHS hearts before or after the intervention.

The above clinical evidence for feHLHS progression to HLHS, and for interventions to reduce risks of this progression, has led to the prevailing thought that the biomechanical stimuli of the heart exert influence on

Determine Morphological Outcomes. Large And Small

animal experiments have corroborated this notion, the occlusion of lamb fetal foramen ovale was shown to

Lead To The Underdevelopment Of Lv Chamber And

aortic and mitral valves,39 while left atrial ligation in chick embryo has led to hypoplastic LV29 and evidence

Understanding Of Lv Biomechanics During Fehlhs

may help develop future strategies for better prognosis or to improve intervention outcomes.

Dynamics (Cfd) Simulations Based On 4D Echocar-

diography images and characterized essential differ- ences against those in normal human fetal LVs.

(Dsrb Protocol Number 2014/00056 At The Former,

and IRB protocol number 1009/2017 at the latter), and

Written Consent From All Participants. All Fehlhs

cases were within the selection criteria for aortic valvuloplasty intervention1 and underwent the inter- vention later, and their characteristics are listed in Table 1. Data for an additional 7 healthy fetal subjects from our previous publication were also analysed.36

Imaging And Image Processing Methods Were As

established in our previous studies.13,37 Briefly, 4D B- mode ultrasound images were acquired using the Vi-

Vid-7, Vivid E9, Or Vivid E95 (Ge Healthcare,

Chicago, IL, USA) ultrasound system via the Spatio-

Temporal Image Correlation (Stic) Mode. The Stic

sweep took 10–15 s, with an image capture rate of 70– 90 frames per second, thus giving 40 volumes for 1 cardiac cycle. Subsequently, images were exported as a stack of 2D cine images with 0.5mm spacing between consecutive planes. The lumen cavity of the left and right ventricle (LV, RV), and left and right atrium (LA, RA) were segmented with a custom-written semi- automatic lazy-snapping algorithm,14 reconstructed via Vascular Modeling Toolkit (VMTK, www.vmtk.

Org), And Smoothed With Geomagic Studio (Geomagic

Inc., Morrisville, NC, USA).

A Validated Cardiac Motion Estimation Algorithm

was used to track the motion of the patient-specific

Reconstructed Lv, Rv And La Endocardial Wall Over

the cardiac cycle.35 This algorithm fits a global motion model of spatial b-splines of temporal Fourier onto results of a set of pair-wise image registrations between different time frames, thus enforcing the cyclic nature of motions. Segmentation was performed at a partic- ular time point, as it could be animated with the mo- tion model to all other time points. The stroke volume of cardiac chambers could then be calculated based on their re-animated motions.

Methods For Image-Based Cfd Simulation Were

adapted from our previous studies,13,37 and utilized

Burg, Pa, Usa). Lv Luminal Blood Space Was Meshed

into at least 1–1.5 million tetrahedral elements, which

Was Shown To Exceed Mesh Convergence Require-

ments.36 A user-defined function was used to control the wall motions according to the motion model from motion tracking. Blood viscosity was modelled with

Society

Fluid Mechanics of Fetal Left Ventricle During Aortic Stenosis

1159

reported,13 while density, q, was prescribed as 1060 kg/

M3. Dynamic Mesh Cfd Simulations Were Conducted

to solve the 3D Navier Stokes equation with 400 time steps per cardiac cycle for at least three cycles, and only the last cycle was used for analysis to minimize artefacts of the stagnant initial condition. Convergence criteria were set to be less than 1024 for all scaled residuals.

Inlet and outlet boundary conditions were idealized

As Instantaneous Opening Or Closing Of Valves, By

converting surfaces between openings and walls. When opened, inlets and outlets were prescribed with pres-

Fehlhs Cohort, Mitral Valve Insufficiency Was Mod-

elled by having a regurgitation orifice that was mod- elled as a permanently open orifice, located within the mitral orifice zone on the model’s surface. The sizes of all the aortic outlet, mitral inlet, and mitral regurgi- tation orifice were iteratively adjusted until CFD sim- ulations produced valve velocities that matched clinical patient-specific Doppler scans satisfactorily, including

Aortic Outflow Velocity, Peak E- And A-Wave Inflow

velocities and peak mitral regurgitation velocity. Due to the low resolution of echo images, the valve mor-

Phology And Orifice Shapes And Sizes Could Not Be

discerned. Orifices were thus approximated to be at the centre of their likely location, for example, the aortic orifice was assumed to be at the centre of the aortic

Was

assumed to be at the centre of the mitral valve.

A Windkessel Lumped Parameter Model Was Used

for ventricular-vascular coupling in our flow simula- tions. During the coupling of the model to the CFD boundary conditions, the model was run for 10 cardiac

Achieved. The Lumped Parameter Model Was Adapted

from Pennati et al.21 who proposed a methodology for allometric scaling of the lumped parameter from 38

Weeks Gestational Age (Ga) To Other Ga, As Briefly

explained in supplementary section S1 (which includes Table S1). However, we recalibrated it to fit more re- cent human fetal clinical measurements,10,34 in contrast to some of its original fit to fetal lamb measurements.

To do this, all resistances were scaled by an age-de- pendent factor, while all compliances were scaled by

Another. The Original Value Of The Inertances And

valvular dissipative coefficients were retained from

The Age-Dependent Scaling Factors At Specific Ages

between 22 and 38 weeks gestation were first deter- mined by fitting literature values of LV and RV vol-

Sinusoidal Volume Over Time Waveform),8 The Fetal

abdominal aortic pulse pressures,34 and fetal LV sys- tolic and diastolic pressures10 at the matching GA. Subsequently, a 5th order and 6th order polynomial fit were calculated for the resistance scaling factor and the capacitance scaling factor, respectively. We interpreted Johnson et al.’s data as indicating that the minimum diastolic LV pressure was 5 mmHg regardless of age, rather than diastolic pressure increasing with age, as the latter would lead to excessively high diastolic pressure when extrapolated to the near-term fetus.

Figure 1 Showed That A Satisfactory Match Was

obtained. Further details of the scaling factors are gi- ven in S1 of the supplementary text.

The Above Lumped Parameter Model For Healthy

fetuses was directly adopted in an age-matched way for feHLHS cases, but with the following modification. Firstly, patient-specific volumes over time data were adopted for all cardiac chambers except the right at- rium (RA), which was approximated using the atrial length, width and the ellipsoid method.28 Secondly, aortic stenosis was modelled by iteratively adjusting

Doppler Measurements. Third, Mitral Regurgitation

was modelled in the CFD simulation for feHLHS cases if present. Fourthly, to emulate elevated LA pressures

Table 1.

Characteristics of aortic stenosis with evolving hypoplastic left heart syndrome (feHLHS) fetal subjects before aortic valvuloplasty, postnatal outcomes of the same subjects and postnatal procedures undertaken.

Surg. Valv., Ross

GA gestational age, LV left ventricle, BV biventricular, UV univentricular, RK Ross-Konno procedure, BV-UV conv. biventricular to

Society

WONG et al.

1160

observed in many fetal aortic stenosis cases, we mod- elled LA pressure (PLA) as a linear function of VLA and LA compliance (CLA), as below, and assigned it as an additional pressure source of the LA in the lumped parameter model.

Figure 1.

Outputs from our Windkessel lumped parameter model showed physiologic A pressure-volume loop and B abdominal aortic pulse pressure across gestational age and C systolic and diastolic pressures of the left ventricle across gestational age. Literature values of clinically measured abdominal aortic pulse pressure by Versmold et al.34 and LV pressures by Johnson et al.10 are plotted in B and C as well, demonstrating that our model had a good match with these literature values.

Society

Fluid Mechanics of Fetal Left Ventricle During Aortic Stenosis

Ð5Þ

where Wd tð Þ was the rate of work done by the ventricle wall, KEbulk was the rate of change in kinetic energy of

The Fluid Within The Ventricle And Kemv, Keav, And

KEregurg were the kinetic energy flux through the mitral valve, aortic valve, and mitral regurgitation orifice, respectively, CS was the control surface, CV was the control volume, A was the surface area, t was time, and T was the cardiac cycle duration. Lastly, the oscillatory

*

is the wall shear stress vector.

We Performed Simulations With Two Different Fluids,

existing blood in the chamber and fresh blood from inflow, using an arbitrary but low diffusivity coefficient 1029 m2/s which minimized mixing and enabled better differentiation of the two fluids.

Diastolic Vortex Formation Time

To further characterize diastolic vorticity, we cal- culated the formation time (s) of the mitral inflow

Ð7Þ

where U was the mitral inflow velocity, D was the jet diameter, t was the duration of either the E or A wave, whichever was higher, or the entire diastolic duration

All Continuous Variables Were Checked For Normal

distribution using the Anderson-Darling test. A com- parison of continuous variables between the two sub- groups (Healthy vs feHLHS) was performed using a t- test for independent samples if they had normal dis- tribution or using the Mann-Whitney U test if not.

Statistical significance was determined at P < 0.05.

Physiological Features

The peak local valve velocities of our simulations were successfully tuned to achieve a satisfactory match with Doppler velocity measurements at the valves, as demonstrated in Supplementary Table S2. We report a velocity error of 2 0.005 ± 0.049 m/s or a percentage error of 4.5% ± 4.3%. Table 2 compared the left heart

Parameters Of The Five Fehlhs Cases Used For Cfd

simulations to the healthy cohort. In the feHLHS co-

Hort, Av Velocities Were Much Higher Than That In

normal LVs, with all cases exceeding the 95th per- centile of normal LVs, and 2 cases exceeded twice of this the 95th percentile value. Diastolic E or A wave velocities were also elevated above the 95th percentile

Was Monophasic For 3 Cases, And Thus No E-Wave

velocities were recorded. Severe regurgitation was observed, with peak regurgitation velocity ranging from 2.60 to 4.69 m/s. These high velocities translated to a high transmitral pressure gradient of 27–88 mmHg via Bernoulli’s equation, indicating severely elevated pressures, which was likely the reason for the enlarged

Lv End-Diastolic Volume (Edv). Lv Stroke Volume

(SV) was depressed with varying severity, and given the usually enlarged LV, ejection fraction (EF) was low. In terms of the RV, all feHLHS cases except for feHLHS-

3 Were Moderately Enlarged And Had Higher Stroke

volumes. Generally, large variability in physiological features was observed amongst feHLHS cases, similar

Flow Patterns Within The Fetal Lvs From Cfd Sim-

ulations are shown in Figure 2, Supplementary Fig-

Ure S1, And Supplementary Videos S1–10. Vortex

dynamics in normal fetal LVs were similar to previous descriptions,13 where wide diastolic vortex rings, cor-

Propagate From The Mitral Towards The Apex. These

vortex rings occupied the entire width of the LV and propagated to various extents towards the LV apex.

The Rings Merged And Interacted With Endocardial

walls, bringing about elevated WSS along the way and creating complex secondary vorticity structures that did not dissipate completely but were ejected during the subsequent systole.

Society

WONG et al.

Table 2.

Comparison of cardiac parameters between healthy fetuses and case-specific feHLHS.

0.009*

Data are presented as mean ± SD and [5th percentile, 95th percentile]. For a healthy cohort, data from the current study were combined with those from Hadi et al. 36 NA – There was no clear subject specific image scan data. AV aortic valve, MV mitral valve, RV right ventricle, SV stroke volume, LV left ventricle, EDV end-diastolic volume, EF ejection fraction, Regurg regurgitation.

*P < 0.05 comparing all healthy cases to all diseased cases.

Society

Fluid Mechanics of Fetal Left Ventricle During Aortic Stenosis

1163

Flow patterns in feHLHS were drastically different. Here, MV inflow occurred as a narrow jet with typi- cally high velocity, generating a small-diameter vortex

Ring That Propagated Quickly Towards The Apex And

impinged on the apical endocardium. In our simula- tions, narrowed mitral inlet orifice was necessitated so that the simulation can yield inflow velocities that

Matched With High Doppler Measurements (Supple-

mentary Table S2). This suggested mild MV stenosis, which consequently resulted in the observed fast and narrow inflow jets. Table 3 quantifies the MV annulus and inflow jet dimensions, demonstrating that while

Inflow Was Narrowed In Fehlhs Cases, Their Mv

annulus was not small. This suggested that the MV was not hypoplastic, but rather, it was an impaired ability for MV to open that caused the stenosis. After aortic valvuloplasty intervention, although stroke volume increased, peak MV inflow velocities did not decrease consistently across cases and remained above the 95 percentile of those for normal hearts (Table 2). This

Suggested That The Mv Stenosis Was Due To A Mal-

formed valve, rather than congestion of fluid in the LV preventing proper MV opening motions.

Inflow Vortex Rings In Fehlhs Lvs Had Minimal

interaction with the endocardial walls before imping- ing at the apex. The jet impingement stirred up sec- ondary vortices and elevated wall shear stresses (WSS)

Wss Depended On The Mv Inflow Velocity. These

vortices were weak for feHLHS-1, 2 and 4, and mod-

Erate For Fehlhs-3, But In Fehlhs-5, Chaotic Flow

structures erupted from the high-speed impingement and spread throughout the LV, elevating WSS over a substantial surface area.

Mostly Demonstrated Monophasic Inflow, Which Was

frequently reported for this disease.15 Only feHLHS-1 and 5 demonstrated a discernible biphasic mitral in- flow profile, which was likely linked to better diastolic ventricular function.5 This further contributed to the

Figure 2.

WSS color contour and k2 iso-velocity surfaces in two representative healthy fetal LVs and five feHLHS LVs. These results are also shown in Supplementary Videos S1–10.

Society

WONG et al.

Related Journal Articles & DOI Links

Selected peer-reviewed publications relevant to 12 Lead ECG Acquisition. Click the DOI to access the full paper (may require institutional access).

Why Choose Us?

Bangalore guidance for robotics, Spectre and autonomous systems projects.