Flow Simulation & Analysis Group

IV Modeling and Analysis of Heart Murmurs

Rajat Mittal, Jung Hee Seo, Hani Bakhshae, Chi Zhu

Department of Mechanical Engineering & Division of Cardiology

Andreas Androu, Guillaume Garreau

Electrical Engineering

Johns Hopkins University

Cardiac Auscultation

2

Digital Stethoscope

BioSignetic Corporation

But… • Low specificity (high false positives) • Diagnosis is based on the empirical/statistical correlation • Source mechanism of murmurs is poorly understood • No modality provides simultaneous assessment of source and measurement

• 3000 year old technique • Cheap • Non-invasive, high sensitivity • Good as a screening tool

60% of all pediatric murmurs leading to referral are “innocent”

Computational Hemo-acoustics

3

Computational Hemo-acoustics (CHA) directly simulate the above procedure: • Prediction of murmur generation/propagation • Source mechanism of murmurs • Better Disease - Hemodynamics - Sound (Auscultation) relation Present Approach: -Immersed Boundary Method based Hybrid Approach • Blood Flow - IBM Incompressible Navier-Stokes solver • Flow induced sound - Linearized Perturbed Compressible Equations (LPCE) • Sound Propagation in tissue – Linear wave equation

Pressure Fluctuation in the Heart

Structural wave Propagation

Surface fluctuation on the chest

Can computational modeling provide the missing link between cause (pathology) and effect (sound)?

Computational Hemoacoustics

4

νρ

∇⋅ = + ∇ = ∇

20

0

10, DUU P UDt

Incompressible N-S Eqns.

Structural wave Eqns.

Hemodynamics Wave Propagation

( , )P x t

Hemodynamic Sound Source

Sound Signal

,1

ij jk iij p

k j i

ij ji iu i

j j j i

p uu u St x x x

p uu u St x x x x

λ δ µ

ηρ ρ

∂ ∂∂ ∂+ + + = ∂ ∂ ∂ ∂

∂ ∂∂ ∂∂+ = + + ∂ ∂ ∂ ∂ ∂

Murmur Associated with Aortic Stenosis

LV AO

Aortic Valve Stenosis

Aortic Stenosis Murmur

Simplified Hemodynamic Modeling

LV AO

75% Aortic valve stenosis

Cardio-Thoracic Phantom Studies

6

U

Stenosis

Flow fluctuation

Thoracic phantom (silicone gel)

D

Wave propagation

U=0.25 m/s D=1.5875 cm DT=9.84 cm Re=UD/ν=4000 St=fD/U

Material: EcoFlex-10 ρ=1040 kg/m3

E=55.16 kPa K=91.3 Mpa (cb=297.3 m/s) G=18.39 kPa (cs=4.2 m/s) µ=14 Pa s

DT

Acoustic Sensors

7

Biopac sensor attached to the Micromanipulator

HP sensor attached to the Micromanipulator

Silicone Rubber- Tissue Mimicking Material

• Silicone rubber, Ecoflex 010 (Smooth-on) – Easy to produce – Extremely stable – Non-toxic and – Negligible shrinkage

• Procedure to make

– Mixing Part A part B, – Adding Silicon thinner, – Degassing for 3-4 min in (-29 in Hg) to

remove air bubbles

Murmur Generating

9

3D printed Casts

U

Stenosis

Flow fluctuation

D

Wave propagatio

n

Fluid Flow Circuit

10

11

Biopac sensor attached to the Micromanipulator

HP sensor attached to the Micromanipulator

Cardiothoracic Phantom-2nd generation

12

• Adding lung to the phantom • Foam is used to model the lung • Non-axisymmetric model

z/DEn

ergy

0 1 2 3 40

5

10

15

20

25

30-6060-120120-480

×10-10

Experimental Measurements

Frequency spectrum

Outer-surface radial accelerations

Energy mapping

Frequency [Hz]

Rad

iala

ccel

erat

ion

100 101 102 10310-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

HPBIOPAC

Computational/Experimental Studies

U

Stenosis

Flow fluctuation

Thoracic phantom (silicone gel)

D

Wave propagation

Re=UD/ν=4000

Simple model for the aortic stenosis murmur

Material properties: Tissue mimicking, viscoelastic gel (EcoFlex-10) ρ=1040 kg/m3

K=1.04 GPa (cb=1000.0 m/s) G=18.39 kPa (cs=4.2 m/s) µ=14 Pa s Other parameters: U=0.25 m/s D=1.5875 cm DT=9.84 cm (gelA), 16.51 cm (gelB) c.f. Biological soft tissue: K=2.25 GPa (cb=1500 m/s) G=0.1 MPa (cs=10 m/s) µ=0.5 Pa s

DT

L=7D

Computational Modeling

15

Hemodynamics IBM, Incompressible N-S

Elastic wave eq. for viscoelastic material Generalized Hooke’s law Kelvin-Voigt model

0

1

λ δ µ

ηρ ρ

′ ′∂ ∂′ ′∂ ∂+ + + = ∂ ∂ ∂ ∂

′ ′∂ ∂′ ′∂ ∂∂+ = + ∂ ∂ ∂ ∂ ∂

ij jk iij

k j i

ij ji i

j j j i

p uu ut x x x

p uu ut x x x x

High-order IBM, 6th order Compact Finite Difference Scheme, 4 stage Runge-Kutta method

i ij jP n p n′ ′=

4~ (10 )iu O −′

0iu′ =

0iu′ =

210, ( ) νρ

∂∇ ⋅ = + ⋅∇ + ∇ = ∇

∂

UU U U P Ut

Freq [Hz]PS

D100 101 102 10310-7

10-6

10-5

10-4

10-3

10-2

10-1

100

-1.0D-0.5D00.5D1.0D1.5D2.0D2.5D3.0D3.5D4.0D

Flow Simulation

Axial velocity

Vorticity

Pressure

ReD=4000 Wall pressure spectrum

2D 0

3D Elastic Wave Simulation Radial velocity fluctuation contours

• 200x200x320 (12.8 M), about 60 hrs with 1024 cores for real time 0.8 sec

Comparison with Experimental Measurements

Frequency [Hz]

Rad

iala

ccel

erat

ion

[m/s

ec2 ]

Exp

100 101 102 10310-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

-1D01D2D3D4DExp-HPExp-BIOPAC

Frequency spectrum

Outer-surface radial accelerations

z/D

Sim

ulat

ion

Exp

0 1 2 3 40

1

2

3

0

5

10

15

20

25

30-6060-120120-480

×10-10×10-7

Energy mapping

Solid: simulation Dashed: measurement

Free-Space Green’s Tensor

d

( , ) ( , ) ( )i ij jU r G r Fω ω ω=

1( ) ( )21( ) ( )

2

i ti i

i ti i

u t U e d

f t F e d

ω

ω

ω ωπ

ω ωπ

−

−

=

=

∫

∫

( )2 2

2 ( ) ( ) ( )i lij kl ik jl il jk i

j k

u u f t rt x x

ρ λδ δ µ δ δ δ δ δ∂ ∂− + + =

∂ ∂ ∂

(1) (1)0 22

(1) (1)0 22

( , ) ( ) ( 3 ) ( )12 ( 2 )

2 ( ) ( 3 ) ( )12

p i jij ij p ij p

i jsij s ij s

ik x xG r h k r h k r

r

x xik h k r h k rr

ω δ δπ λ µ

δ δπµ

= + − +

− − + −

Green’s tensor (Ben-Menahem & Singh,1981)

/ , ( 2 ) /

/ , /p p p

s s s

k c c

k c c

ω λ µ ρ

ω µ ρ

= = +

= =

r

θ

Analytical estimation of elastic wave solution (no geometrical effects)

Evaluation of Radial Acceleration

d r

θ

2, , 2,( , ) ( ) ( , ) ( ), ( ) ( )ω ω ω ω ω ω= = ∆∑

m mn k k n k k kk

a r i G r F F P A

( )ωkP

2 ( )ωa

1x2x

Frequency [Hz]R

adia

lacc

eler

ati o

n[ m

/sec

2 ]100 101 102 10310-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

3D SimulationGreen-CompGreen-ShearGreen-Total

Oblique shear waves contribute significantly to the stethoscopic signal!

Source Localization

Surface measurements 1, 2, .... Mu u u

Source mapping

1, 2, .... NF F F

1( ; )

N

m m n nn

u G x x F=

=∑

1 1

M N

u F

u F

=

G

[ ] [ ]F u+= G

G: M by N complex matrix

G+: Pseudo inverse of G

Source Localization

z/D

Nor

mal

ized

Sour

ceEn

ergy

-1 0 1 2 3 4

0.2

0.4

0.6

0.8

1

EstimatedMeasured

*30-120 Hz

Proceeding towards using a multi-sensor stethoscopic array (StethoVest) for automatic murmur localization

23

Computational Modeling

Aortic stenosis Patient specific geometry Model

U=0.25 m/s

Re=UD/ν=4000

D=1.5875 cm

Epidermal surface

24

Fluid Solver:

Acoustic Solver:

vi – structure velocity. λ, μ – 1st and 2nd Lame’s constants. ρs – density. K – bulk modulus, = 1.04 GPa. G – shear modulus, = 18.39 KPa. η – viscosity, = 14.0 Pa s.

Vicar Code, sharp interface IBM

See: Mittal, R., et al., JCP, 2008

Interior nodes: 6th –order compact scheme Immersed boundary: approximating polynomial method Time advancement: 4th –order Runge-Kutta method

See: Seo, J. H., & Mittal, R. ,JCP, 2011

Numerical methods:

Computational Modeling

Hemodynamic Simulation Results

25

x component of vorticity

75% 90%

Same contour level

50%

Hemodynamic Simulation Results

26

Contour of surface pressure

75% 90%

5 times larger contour level

50%

Baseline 5 times smaller contour level

Source Location

27

75%

90% 100 times larger contour level

Surface Signal

50%

1000 times smaller contour level

Baseline

Realistic Thorax Model

28

CT scan data (Visible Human)

Material property (density and speed of sound) mapping

3D model of the thorax (density iso-surfaces)

Need to account or thoracic structures on sound propagation

Cited Paper - Hemoacoustics • Jung Hee Seo, Vijay Vedula, Theodore Abraham, and Rajat Mittal, “Multiphysics computational models for cardiac

flow and virtual cardiography”, Int. J. Num. Meth. Biomed. Eng., doi: 10.1002/cnm.2556, 2013.680, DOI: 10.1007/s10439-014-1018-4.

• Jung Hee Seo and Rajat Mittal, “A Coupled Flow-Acoustic Computational Study of Bruits from a Modeled Stenosed Artery”, Medical & Biological Engineering & Computing, Vol 50(10) pp 1025-35, 2012.

• Andreou, A.G.; Abraham, T.; Thompson, W.R.; Jung Hee Seo; Mittal, R., “Mapping the cardiac acousteome: An overview of technologies, tools and methods,” Information Sciences and Systems (CISS), 2015 49th Annual Conference on , vol., no., pp.1,6, 18-20 March 2015, doi: 10.1109/CISS.2015.7086899

• Bakhshaee, H.; Garreau, G.; Tognetti, G.; Shoele, K.; Carrero, R.; Kilmar, T.; Chi Zhu; Thompson, W.R.; Jung Hee Seo; Mittal, R.; Andreou, A.G., “Mechanical design, instrumentation and measurements from a hemoacoustic cardiac phantom,” Information Sciences and Systems (CISS), 2015 49th Annual Conference on , vol., no., pp.1,5, 18-20 March 2015, doi: 10.1109/CISS.2015.7086901.

• Jung Hee Seo and Rajat Mittal, “A Coupled Flow-Acoustic Computational Study of Bruits from a Modeled Stenosed Artery”, Medical & Biological Engineering & Computing, Vol 50(10) pp 1025-35, 2012.

• J. H. Seo and R. Mittal, “A Higher-Order Immersed Boundary Method for acoustic wave scattering and low-Mach number flow-induced sound in complex geometries”, Journal of Computational Physics, 2011, Vol. 230, Issue 4, pp. 1000-1019 .

• Jung Hee Seo, Vijay Vedula, Theodore Abraham, and Rajat Mittal, “Multiphysics computational models for cardiac flow and virtual cardiography”, Int. J. Num. Meth. Biomed. Eng., doi: 10.1002/cnm.2556, 2013.680,

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