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Modeling and simulation of 3D ultrasound imaging systems with
integrated μ-beamforming electronics
Dipartimento di Ingegneria Industriale e dell’InformazioneUniversità degli Studi di Pavia
Giulia Matrone 1
Giulia Matrone
07/06/2013
giulia.matrone@unipv.it
Università degli Studi di Pavia
Bioengineering Lab.
3D Ultrasound imaging
Giulia Matrone 2
Università degli Studi di Pavia
3D Ultrasound imaging
Giulia Matrone 3
Università degli Studi di Pavia
3D ultrasound technology: state of the art
• 2D phased-array probes
• The beam is electronically (no more mechanically)
steered and focused in 3D (azimuth + elevation directions)
• Digital beamforming
Open challenges :• transducers interconnection and arrangement
• front-end electronics integration inside the probe
• power constraints
• very low noise reception front-end
• high dynamic range and frame rate (e.g. for real-time applications)
• A fully-wired array would require many electronic leads connected to each element in the array (e.g. 64x64 array 4096 coaxial cables!). This could also reduce SNR!
CMUT
μ-beamforming
Objective
Giulia Matrone 4
Ultrasound System Simulator• Complete system analysis (US field & transducer & front-end electronics) in a
single versatile environment (Matlab)
• Quick system-level feedback for improved electronics design
• Simulated signals and images ↔ System performances ↔ Design parameters
• (micro-)Beamforming algorithms development and test
Ultrasound System
Probe
Propagation Medium(Human body / water tank / ...)
simulations!
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5
RECEIVER
1TRANSMITTER
TRANSDUCER
2
4
3US FIELD
Ultrasound system model
Giulia Matrone 5
TX digital Beamformer
RX digitalBeamformer
T/R
switch
HV
pulser
LNA VGA
CW Beamformer
ADC
ADC
DAC
Processingunit
BeamformerControl
display
Università degli Studi di Pavia
1TRANSMITTER
Ultrasound system model
Giulia Matrone 6
TX digital Beamformer
RX digitalBeamformer
T/R
switch
HV
pulser
LNA VGA
CW analogBeamformer
ADC
ADC
DAC
Processingunit
BeamformerControl
display
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focus
1- Transmission model
Giulia Matrone 7
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Model inputs = real/synthetic waveforms
Input Parameters:
• PW (n° of cycles) / CW
• Frequency
• Rise/fall times
• Amplitude (e.g. ±100V)
• Pulse Repetition Frequency (PRF)
(e.g. 1-10 kHz, 1/depth)
• Focusing delays
TX Beamforming
Giulia Matrone 8
RX
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TX
TRANSMIT
BEAMFORMER
Maximum delay channel
Minimum delay channel
PulserHV
transmitter
Every beam
reach the
point in the
same time
Transducers
RECIEVE
BEAMFORMER
Maximum delay channel
Minimum delay channel
ADCLNA
Every beam reach the
receiver in the same
time
Transducers
Transmission chain Reception chain
TX Beamforming
Giulia Matrone 9
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TRANSDUCER
2
4
Ultrasound system model
Giulia Matrone 10
TX digital Beamformer
RX digitalBeamformer
T/R
switch
HV
pulser
LNA VGA
CW analogBeamformer
ADC
ADC
DAC
Processingunit
BeamformerControl
display
Università degli Studi di Pavia
2
4
2
2/4- Transducer
Giulia Matrone 11
The piezoelectric transducers in the US probe operate signals electro-acoustic (TX) and acousto-electric (RX) conversion
Equivalent electric models
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Mason’s Model
Redwood’s Model
KLM Model
v
F
DC
BA
I
V
CMUT
Giulia Matrone 12
A 16x16 2D CMUT array
with integrated front-end
electronics
Architecture of an endoscopic 3D
ultrasound imaging probe
Università degli Studi di Pavia
Capacitive Micromachined Ultrasonic Transducers (CMUT)
Advantages: • microfabrication• wide bandwidth • high sensitivity• CMOS compatibility • batch fabrication → low cost
CMUT
Giulia Matrone 13
MOVINGMEMBRANE
SUBSTRATE
Top electrode
Bottom electrode
VDC
CMUT CELLParallel plate capacitor
Voltage → electrostatic force → membrane deformation (non-linear relation)
System linearization → Bias voltage (VDC)
An AC voltage is superimposed to VDC during TX operation
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CMUT electro-mechanical model
Giulia Matrone 14
CMUT mechanical model: lumped element approach
))1(12/(
/192
84.1
23
20
2
EtD
rDk
trm
m
m
)27/(8 3
00 epi AgkV
2
/0
0
mkf
Resonance frequency (@VDC=0)
Parameters
re/Ae electrode radius/area
rm/Am membrane radius/area
g gap (electrodes distance)
t membrane thickness
E Young’s modulus
v Poisson’s ratio
ρ density
m membrane mass
k0 spring elastic constant
D membrane flexural stiffness
ε dielectric coefficientPull-in/collapse voltage
membrane (rigid plate)restoring vs electrostatic force
substrate
Usually VDC < Vpi
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Staticanalysis
CMUT electro-mechanical model
Giulia Matrone 15
CMUT equivalent electric model (small signals): Mason’s model
gNAC
gVA
VV
e
pie
piDC
/
/
/
2
Parameters
VS/IS
VL/IL
Voltage/current at the electricside during tx and rx
v vibration velocity
F=APR force (pressure)
C CMUT capacitance
φ electro-mechanical turns ratio
Zm mechanical impedance
ZR radiation impedance
ZL load impedance during rx
Transmission and Reception impulse responses (P/V, v/V, P/I, v/I and V/P, V/v, I/P, I/v )
ZIN T/R Switch + LNA
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P ↔Vv ↔ I
CMUT operating point
TX
RX
ACOUSTIC SIDEELECTRIC SIDE
3US FIELD
Ultrasound system model
Giulia Matrone 16
TX digital Beamformer
RX digitalBeamformer
T/R
switch
HV
pulser
LNA VGA
CW analogBeamformer
ADC
ADC
DAC
Processingunit
BeamformerControl
display
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ar
Pr
3- US field linear model
Giulia Matrone 17
Hypotheses:• isotropic, homogeneous, non-dissipative medium
• transducer: infinite rigid baffle, flat surface, no re-radiations
• LINEAR SYSTEM
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rp = observation point ra = active aperture (transducer)
Spatial Impulse Response
Giulia Matrone 18
The impulse response depends on the relative position of the transducer and the observation point
Spatial Impulse Response (SIR) in rp:
S
P dSr
crttrh
2
/),(
Università degli Studi di Pavia
ar
Prr
c
rt
Huygen’s principle
Acoustic impulse response
The SIR is found by observing the
pressure waves at a fixed point rp
over time. All the spherical waves
pass the point rp and are summed.
Pressure field
Giulia Matrone 19
The pressure at point rp is given by the Rayleigh integral:
where vn is the normal surface vibration velocity and S is the aperture surface and ρ is medium density.
S
anP dS
t
crtrv
rtrP
/,1
2),(
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ar
Prr
S T
aaaan
P
PS
an
P
dSdtr
crtttrvtr
t
tr
t
dSr
crtrv
trP
2
/,),(
),(
/,
2),(
Pressure field
Giulia Matrone 20
If we assume that vn is uniform over the aperture, then:
Università degli Studi di Pavia
ar
Prr
S
nP dSr
crttvtr
2
/*),(
h(rP,t)
Pressure field in rp:
),(*)(
),( trht
tvtrP P
nP
t
trtrP P
P
),(),(
Discrete representation
Giulia Matrone 21
Discrete representation:• The probe consists of N transducers (phisical elements)• Each transducer is divided into M mathematical elements
• Apodization weights and focusing delays can be included in the SIR:
N
i
PiP trhtrh1
),(),(
Ni S
rr
crrttrh
M
j
ij
ijP
ijP
Pi ...12
/),(
1
M
j
ij
ijP
iijP
iPi Srr
dcrrtwtrh
1 2
/),(
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Apodization
Received signal
Giulia Matrone 22
Received signal: ),(*)(*)(),( trhrftvtrV per
mt
perx
3
3
2
)(*)(
2)(
t
tvtE
ctv n
tmpe
Pulse-echo impulse (transducer excitation + electro-mechanical impulse response during RX/TX)
c
rcrrfm
)(2)()(
Inhomogeneities in the tissue, which give rise to the scattered signal
),(*),(),( trhtrhtrh rxtxpe
Pulse-echo spatial impulse response
perturbations
electro-mechanical impulse response
Università degli Studi di Pavia
The received signal is the scattered pressure field integrated over the transducer surface and convolved with the transducer electromechanical response.
Scatterer
1x64 linear array
z
x
Example - TX
Giulia Matrone 23
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-50
0
50
excitation s
ignal [V
]
time [us]
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1.5
-1
-0.5
0
0.5
1
1.5x 10
13
time [us]
TX
im
pu
lse
re
sp
onse
V->
A [
(m/s
2)/
V]
TX Impulse response
HV input @3MHz (V)
55 55.5 56 56.5 57 57.5-1.5
-1
-0.5
0
0.5
1
1.5x 10
6
time [s]
Pre
ssure
@fo
cus [
MP
a]
),(*)(
),( trht
tvtrp P
nP
FOCUS
TX pressure
min
Focusing delays profile1 64
max min
Example - RX
Giulia Matrone 24
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Beamforming
Vout
Beamformed RX signal (V)
60 80 100 120 140 160 180-1.5
-1
-0.5
0
0.5
1
1.5x 10
-4
time [s]
RX
sig
na
l [V
]
5
RECEIVER
Ultrasound system model
Giulia Matrone 25
TX digital Beamformer
RX digitalBeamformer
T/R
switch
HV
pulser
LNA VGA
CW analogBeamformer
ADC
ADC
DAC
Processingunit
BeamformerControl
display
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5- Reception
Giulia Matrone 26
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1) Amplification with variable gain is used to compensate for attenuation effects (Time Gain Compensation)
Gain
Amplified signals
Echoes amplitude
Distance from the probe
Medium Attenuation coefficient (dB cm-1 MHz-1)
Water (20°C) 0.002
Fat 0.66
Blood 0.2
Muscle 1.5
Bone 20
Soft tissue (average) 0.7
Reception
Giulia Matrone 27
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RXTX
2) BeamformingAmplified signals are re-aligned and coherently summed
• analog BF or• digital BF
μ-Beamforming
Dynamic focusing
Giulia Matrone 28
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• During reception, the focusing delays profile can be continuosly adjusted to track the travelling wave-front
• Improved focusing and resolution but a more sophisticated beam-forming electronics is required
Receiver model
Giulia Matrone 29
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Variable-gain amplification
M-channel µ-beamforming architecture
ADC
LNA C-Matrix1MM
LNA C-Matrix1MM
LNA C-Matrix1MM
...
...
ADC
1
1
1
MAIN BEAMFORMER
ADC
The N-element transducer array is divided in M-element subapertures. Signals received by each sub-aperture are processed by a M-channel μ-beamformer
Receiver model: VGLNA
Giulia Matrone 30
)(0
))()(()()(0)('
tVG
tVtchtG tanhtVGtV
offsetiLNA
i
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The Variable-Gain Low-Noise Amplifier model includes:
• a white gaussian noise source (LNA noise)• an amplification stage
−non-linear gain & saturation → tanh function−variable gain
• a signal derivative limiter (Slew-Rate)• a BP filter → LNA finite bandwidth
LNA C-Matrix11616
VIN
VOUT
0 10 20 30 40 50 60 70 80 90
14
16
18
20
22
24
26
Time (µs)G
ain
(dB
)O
utp
ut sig
na
l
Receiver model: C-matrix
Giulia Matrone 31
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• 16-channels µ–beamforming unit (delay and sum)
• Matrix of digitally controlled capacitors that sample and store the received signals
• A series of shift registers and switches activate the write/read/clear phase
Signal distorsions may be due to:
• delays quantization • parasitic capacitances
• capacitances non-linearity• bandwidth limitations
LNA C-Matrix11616
Delays pattern
µ-BMF
BMF
Test 1 - Linear array
Giulia Matrone 32
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C-matrixLNA
Delays pattern
µ-BMF
BMF
Test 1 - Linear array
Giulia Matrone 33
• Validation of the receiver model: mixed simulations --> Matlab vs. Eldo
• Input = 16 2-cycle sinusoids @3MHz
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MATLAB ELDO
Results - Linear array
Giulia Matrone 34
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Image formation
Results - Linear array
Giulia Matrone 35
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References
Giulia Matrone 36
Università degli Studi di Pavia INTRODUCTION
•T. Szabo, “Diagnostic Ultrasound Imaging: Inside Out”, Elsevier Academic Press, 2004.•J. Powers, F. Kremkau, “Medical Ultrasound Systems,” Interface Focus, 2011.•A. Thrush, T.Hartshorne, “Peripheral Vascular Ultrasound: How, Why and When,” Elsevier Academic Press, 2005.•P. Rako, “Diagnostic ultrasound gets smaller, faster, and more useful”, Electronics Design, Strategy, News (EDN), pp. 20-28, June 2009. http://www.edn.com/article/CA6666227.html
CMUT•I. O. Wygant et al., "Analytically Calculating Membrane Displacement and the Equivalent Circuit Model of a Circular CMUT Cell,“ Proc. IEEE Intl. Ultrason. Symp. 2008.•http://www-kyg.stanford.edu/khuriyakub/opencms/en/research/ultrasonic/3D_Imaging/index.html•A. Savoia, G. Caliano and M. Pappalardo, “A CMUT Probe for Medical Ultrasonograpy: from Microfabrication to System Integration,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., 2012.
SPATIAL IMPULSE RESPONSE•J. A. Jensen, "FIELD a program for simulating ultrasound systems”, Proc. Nordic-Baltic Conf. on Biomedical Imaging, 1996.•J. A. Jensen, “A model for the propagation and scattering of ultrasound in tissue", J. Acoust. Soc. Amer., 1991. •J. A. Jensen, “Linear description of ultrasound imaging systems”, Notes for the Intl. Summer School on Advanced Ultrasound Imaging, Technical University of Denmark, 2001.
PUBLISHED WORKS•G. Matrone, M. Terenzi, A. S. Savoia, G. Caliano, G. Magenes, D. Ronchi, and F. Quaglia, "An Ultrasound System Simulation Tool for Advanced Front-End Electronics Design," Proc. IEEE Intl. Ultrason. Symp., 2012.•G. Matrone, F. Quaglia, G. Magenes, “Simulating Ultrasound Fields for 2D Phased-Array Probes Design Optimization,” Proc. IEEE Intl. Conf. Eng. Med. Biol. Soc., 2011.•G. Matrone, F. Quaglia, G. Magenes, "Modeling and Simulation of Ultrasound Fields Generated by 2D Phased Array Transducers for Medical Applications," Proc. IEEE Intl. Conf. Eng. Med. Biol. Soc., 2010.
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