Contribution from ESI-Group - Cardioproof · 2019-10-23 · Aortic valve modelling: • valve shape (planar or 3D) • the valve maximum opening area (AVA) is characterized by the

Contribution from ESI-GroupNumerical simulation of patient-specific hemodynamics in the left ventricle and the aortic root.Overview and recent improvements & results

ESI activities

ESI contribution to WP4:Task 4.2 - Design and implementation of interface for providing input to CFD code; ESI effort 3 PM; deliverable D4.1: Implementation of mechanics-CFD interface (M4)

ESI contribution to WP5:Task 5.2 – SPH haemodynamic simulations and comparison with the flow data; ESI effort 64 PM; deliverables from ESI:• D5.1 - Implementation of software tools …. (M7)• D5.4 - SPH simulations of patient-specific ventricle/aortic valve (M24)• D5.5 - Influence of the valve replacements on the haemodynamics (M30)• D5.6 - Description of the clinically relevant output (M36)

Final Review 28/02/2017 P. Groenenboom/O. Amoignon

SPH in hemodynamicsBackground


SPH = Smoothed Particle Hydrodynamics• Meshless Lagrangian method: best for fluid dynamic with free-surface,

fluid-structure interaction with large deformations, gas explosion …• ESI’s SPH: part of the Virtual Performance Solution (VPS) software*, a

general Computational Structural Mechanics solver used for design in aerospace and automotive industry

Lubrication

*http://virtualperformance.esi-group.com/

Car driving into pool

Sketch showing the influence between

SPH particles

SPH in hemodynamicsComplementary to body-fitted mesh CFD

SPH for blood ejection from the left ventricle through the opening and closing aortic valve: gives inflow conditions to body-fitted mesh CFD Body-fitted mesh CFD for accurate hemodynamics away from large deformations.


SPH in hemodynamicsDecision tool


Patient systolic flow modelling4D boundaries transferred from MRI to SPH


In green: patient data

(1/2 speed)

0 ms 100 ms 200 ms 300 ms 400 ms 460ms

From MRI to 4D boundary in VPS:• MUG produced 4D mesh from the MRI of the patient’s left

ventricle and aorta: connectivities and coordinates at discrete times [t0, t1, t2 …]

• ESI:• Meshes from MUG are imported at discrete times in

VPS• Interpolation procedure to obtain continuous (in

time) boundary displacements.


CFD with SPH

Available patient data for the definition of a pressure response model (from the arterial network) at the outflow boundary:

• minimum and maximum values from the cuff pressures (corrected measures)• the arterial pressure response to the systolic flux q(t) is modelled by a

Windkessel model (electric circuit analogy)

q(t) computed

P(t) imposed

( ) ( ) ( )( ) ( ) ( )∫−

− ++−=t

RCuRCt

RCt duuqeC

etZqZqPetP0

00

Outflow pressure b.c. with Windkessel model

Patient systolic flow modellingOutflow: Arterial network response model


Final Review 28/02/2017 Author

Requirements on the arterial response model*:– initial outflow pressure as near as possible to

the low cuff pressure– maximum outflow pressure as near as possible

to the high cuff pressure + Constraints

– lower and upper bounds on the Windkessel parameters

– location (in time) of the peak outflow pressure near the location of the peak systolic flux.

( )( )[ ]

( ) ( )( )

≤≤≤≤≤≤≤≤

−+

−+−

∈

000

22

,0

2

,,,

:subject to

maxlogmin0

uPluZluCluRl

PtPPtPPtP

ZZ

CC

RR

cuffhighq

cuffhighTt

cufflowePZCR

*The systolic flux obtained from MRI data is used as an input (clinical data) to the optimization problem above.

( ) ( ) ( )( ) ( ) ( )∫−

− ++−=t

RCuRCt

RCt duuqeC

etZqZqPetP0

00 P(t)q(t)

Patient systolic flow modellingWindkessel model parameters identification


Final Review 28/02/2017 Author

P(t)

q(t)

P(t)qSPH(t)

Left: systolic flux from MRI.

Right: outflow pressure response given by the Windkessel model (different Windkessel parameters in MUG and ESI modelling)

Left: (red) systolic flux computed by the SPH.

Right: pressures computed by SPH in the left ventricle, aorta and in outflow (Windkessel pressure response)

Patient systolic flow modellingOutflow boundary conditions / Windkessel model


Background: morphology and kinematics of the patients’ valve (AV) are not available in CP (only one patient).Aortic valve modelling:

• valve shape (planar or 3D)• the valve maximum opening area (AVA) is characterized by the measured valve

pressure drop, i.e. by the simplified Bernoulli formula usual in clinical analysis

• the valve opening and closing speeds follow the opening and closing speeds correlations from Arsenault et al. *

mmHg)(),sm(),m( units thewith,2 132 PqAPqA ∆∆= −

*Arsenault M., Masani N., Magni G., Yao J., Deras L., and Pandian N., Variation of Anatomic Valve Area During Ejection in Patients With Valvular Aortic StenosisEvaluated by Two-dimensional Echocardiographic Planimetry: Comparison With Traditional Doppler Data, J Am Coll Cardiol 1998;32:1931–7.

Patient systolic flow modellingAortic valve / Patient valve modelling approach


Modelling the valve with rotating leaflets was tested (patient B2304-29) and comparison with the planar valve model does not show significant differences.



Echocardiographic data of the valve for patient OPBG010 were integrated in the SPH simulations. Too coarse (time-) resolution and difficulties to fit the segmented valve model to the mesh of the aorta limited the exploitation of the results.




Model of the SJM_Regent 19

(CAD)Finite element model of

the Medtronic Open pivot 21A

Patient systolic flow modellingAortic replacement valve / Mechanical valves

Background: kinematics of the mechanical valves (AV) are not available in CP.Integration of the FEM valve model in SPH/VPS

• orientation• aorta mesh adaption: deformation and smoothing

Improved initial particle distribution by a filling algorithm suitable for complex domain shapesGroenenboom, P., “Particle Filling and the Importance of the SPH Inertia Tensor”, in: Violeau, D., Hérault, A. and Joly, A, eds., Proceedings of 9th International SPHERIC Workshop, Paris, France, 2014


SPH software developmentPerformance / Initial particle distribution


SPH software developmentEnhanced capability / Pressure boundary condition

FE mesh model for the outflow opening in the aorta.

Issue: How to deal with pressure outlets since meshless methods (i.e. SPH) do not have any surface entities on which to apply a pressure.Solution: Define dummy (deformable) shell elements. The corresponding pressure force is distributed to the particles approaching the surface.

Example: Outflow from box with trajectories Example: Outflow mesh in aorta

Final Review 28/02/2017

AVA estimateValve opening

scheme

Shell elements(outflow bc)

Valve elements

Patient data:• delta P valve• P cuff (corrected)• LV 4D model from MRI

4D model from MRI

Outflow pressure b.c. fitted Windkessel model

q(t)

CLINICAL DATA MODELING PHASE SPH (VPS) SIMULATIONSCLINICALLY

RELEVANT OUPUT

Peak systolic pressure Detailed pressure gradient:

aortic root, valve, aorta

Maximum velocities

Comparison with clinical dataProcess from clinical data to exploitable output

P. Groenenboom/O. Amoignon


Left picture: the calibration phase. Right picture: replacement valves evaluation phase.The methodology to create an SPH software usable by non-experts in simulations, for systolic flow simulations, has been validated.

Comparison with clinical dataDemonstration of conceptsFrom clinical data to evaluating replacement solutions



Id. Patient DiseaseAVA

estimate mm2

Aortasection

mm2

Valve (maximum opening =

factor*AVA)

”1” ”2” ”3”

B0305-28 CoA 391 581 0.7 1 1.3

B2804-29 CoA 709 0.7 1 1.3

B0504-44 CoA 313 719 0.7 1 1.3

B0399-47 CoA 400 873 0.7 1 1.3

B0205-84 CoA 349 681 0.7 1 1.3

B1036-85 AVD 35 524 2 3

B0147-86 AVD 57 716 1 2 3

B1162-87 AVD 38 1136 2 3

B0649-88 AVD 65 901 1 2 3

B0764-89 AVD 119 1950 0.7 1 2

B0553-90 AVD 60 932 1.5 2 2.5

OPBG010 AVD 50 1272 1 2 3

Bland-Altman plot comparing the computed pressuredrop between the left ventricle and the ascending aorta(dP) with clinical or estimated values of the patientpressure drop across the valve (Data)

Comparison with clinical dataList of simulated cases and valve pressure drop



Bland-Altman plot comparing the maximumpeak pressure in the ascending aorta (PAO)with the expected patient value (correctedhigh cuff pressure).

Bland-Altman plot comparing themaximum computed velocities through thevalve (SPH) with patients velocities (Echo).

Comparison with clinical dataVelocity and aortic pressure



Clinical data (deltaP valve, Peak systolic pressure, Pcuff, flux) vs SPH simulations (gauge pressures in LV, aora and Windkessel model imposed pressure at the outflow boundary).

A po

ster

iori

adju

stm

ent o

f the

art

eria

l res

pons

e m

odel

ling

(Win

dkes

sel)

Corrected Windkessel model including the pressure drop between valve and outflow boundary.

Windkessel nodel neglecting pressure gradients between valve and outflow boundary.

Comparison with clinical dataOutflow boundary conditions adapted to aorta



Adju

stm

ent o

f the

max

imum

aor

tic v

alve

ope

ning

are

a (A

VA) AVA=210mm2

AVA=150mm2

SPH simulations with different valve AVA: Clinical data (deltaP valve, Peak systolic pressure, Pcuff, flux) vs SPHsimulations (gauge pressures in LV, aora and Windkessel model imposed pressure at the outflow boundary).

AVA=210mm2

AVA=150mm2

Comparison with clinical dataAdaption of the patient’s valve modelling



Adju

stm

ent o

f the

max

imum

aor

tic v

alve

ope

ning

are

a (A

VA)

AVA=210mm2

AVA=150mm2

AVA=150mm2

AVA=210mm2

SPH simulations with with different valve AVA: Clinical data (deltaP valve, maximum velocity across valve) vs SPH simulations (pressure gradients and velocities computed at gauge points in the ventricle, at the opening of the valve and in the aorta).

Comparison with clinical dataAdaption of the patient’s valve modelling



Comparison with clinical dataPatient valve vs. mechanical valve

Patient valve modelled by a rotating leaflets valve (BV5).Mechanical valve (ONXA) opened during the simulation (kinematics not available)

Summary and outlook


• Progress in ESI implementation of SPH for cardiovascular simulations: – SPH coupling to body-fitted mesh CFD in VPS*– pressure-based outflow boundary conditions (forces equilibrium)– initialization scheme (filling algorithm)

• Validated integration of clinical data:– Parameters identification of the Windkessel model for the arterial response modelling used in the

outflow boundary condition– Adaption of the arterial response modelling to the pressure gradients created by the aorta.

• Integration of advanced biological or prosthetic valve models:– Degree of fidelity of patient valve model depends on available clinical data– Realistic adaption of the aorta wall (mesh) to the FEM of a prosthetic valve.– Coupled fluid-structure interaction between blood and prosthetic valve possible in VPS* if construction

details available


*ESI’s SPH is part of the software VPS (Virtual Performance System) http://virtualperformance.esi-group.com/

Documents

Contribution from ESI-Group - Cardioproof · 2019-10-23 · Aortic valve modelling: • valve shape (planar or 3D) • the valve maximum opening area (AVA) is characterized by the