iv modeling and analysis of heart murmurs -...
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![Page 1: IV Modeling and Analysis of Heart Murmurs - uniroma2.itpeople.uniroma2.it/roberto.verzicco/publication/seminars/Mittal4.pdf · IV Modeling and Analysis of Heart Murmurs. Rajat Mittal,](https://reader030.vdocuments.mx/reader030/viewer/2022040612/5edd1f02ad6a402d6668184d/html5/thumbnails/1.jpg)
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
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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”
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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)?
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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
∂ ∂∂ ∂+ + + = ∂ ∂ ∂ ∂
∂ ∂∂ ∂∂+ = + + ∂ ∂ ∂ ∂ ∂
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Murmur Associated with Aortic Stenosis
LV AO
Aortic Valve Stenosis
Aortic Stenosis Murmur
Simplified Hemodynamic Modeling
LV AO
75% Aortic valve stenosis
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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
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Acoustic Sensors
7
Biopac sensor attached to the Micromanipulator
HP sensor attached to the Micromanipulator
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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
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Murmur Generating
9
3D printed Casts
U
Stenosis
Flow fluctuation
D
Wave propagatio
n
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Fluid Flow Circuit
10
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Biopac sensor attached to the Micromanipulator
HP sensor attached to the Micromanipulator
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Cardiothoracic Phantom-2nd generation
12
• Adding lung to the phantom • Foam is used to model the lung • Non-axisymmetric model
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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
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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
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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
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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
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3D Elastic Wave Simulation Radial velocity fluctuation contours
• 200x200x320 (12.8 M), about 60 hrs with 1024 cores for real time 0.8 sec
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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
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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)
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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!
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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
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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
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Computational Modeling
Aortic stenosis Patient specific geometry Model
U=0.25 m/s
Re=UD/ν=4000
D=1.5875 cm
Epidermal surface
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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
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Hemodynamic Simulation Results
25
x component of vorticity
75% 90%
Same contour level
50%
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Hemodynamic Simulation Results
26
Contour of surface pressure
75% 90%
5 times larger contour level
50%
Baseline 5 times smaller contour level
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Source Location
27
75%
90% 100 times larger contour level
Surface Signal
50%
1000 times smaller contour level
Baseline
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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
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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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