Modeling and simulation of 3D ultrasound imaging systems ... · Transducers RECIEVE B EAM F ORM ER...

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

[email protected]

Università degli Studi di Pavia

Bioengineering Lab.

3D Ultrasound imaging

Giulia Matrone 2


3D Ultrasound imaging

Giulia Matrone 3


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

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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!


5

RECEIVER

1TRANSMITTER

TRANSDUCER

2

4

3US FIELD

Ultrasound system model

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TX digital Beamformer

RX digitalBeamformer

T/R

switch

HV

pulser

LNA VGA

CW Beamformer

ADC

ADC

DAC

Processingunit

BeamformerControl

display


1TRANSMITTER


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T/R

switch

HV

pulser

LNA VGA

CW analogBeamformer

ADC

ADC

DAC

Processingunit

BeamformerControl

display


focus

1- Transmission model

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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

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RX


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

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TRANSDUCER

2

4


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T/R

switch

HV

pulser

LNA VGA

CW analogBeamformer

ADC

ADC

DAC

Processingunit

BeamformerControl

display


2

4

2

2/4- Transducer

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The piezoelectric transducers in the US probe operate signals electro-acoustic (TX) and acousto-electric (RX) conversion

Equivalent electric models


Mason’s Model

Redwood’s Model

KLM Model

v

F

DC

BA

I

V

CMUT

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A 16x16 2D CMUT array

with integrated front-end

electronics

Architecture of an endoscopic 3D

ultrasound imaging probe


Capacitive Micromachined Ultrasonic Transducers (CMUT)

Advantages: • microfabrication• wide bandwidth • high sensitivity• CMOS compatibility • batch fabrication → low cost

CMUT

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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


CMUT electro-mechanical model

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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


Staticanalysis

CMUT electro-mechanical model

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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


P ↔Vv ↔ I

CMUT operating point

TX

RX

ACOUSTIC SIDEELECTRIC SIDE

3US FIELD


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T/R

switch

HV

pulser

LNA VGA

CW analogBeamformer

ADC

ADC

DAC

Processingunit

BeamformerControl

display


ar

Pr

3- US field linear model

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Hypotheses:• isotropic, homogeneous, non-dissipative medium

• transducer: infinite rigid baffle, flat surface, no re-radiations

• LINEAR SYSTEM


rp = observation point ra = active aperture (transducer)

Spatial Impulse Response

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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

/),(


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

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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),(


ar

Prr

S T

aaaan

P

PS

an

P

dSdtr

crtttrvtr

t

tr

t

dSr

crtrv

trP

2

/,),(

),(

/,

2),(

Pressure field

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If we assume that vn is uniform over the aperture, then:


ar

Prr

S

nP dSr

crttvtr

2

/*),(

h(rP,t)

Pressure field in rp:

),(*)(

),( trht

tvtrP P

nP

t

trtrP P

P

),(),(

Discrete representation

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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

/),(


Apodization

Received signal

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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


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

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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]


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


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


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T/R

switch

HV

pulser

LNA VGA

CW analogBeamformer

ADC

ADC

DAC

Processingunit

BeamformerControl

display


5- Reception

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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

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RXTX

2) BeamformingAmplified signals are re-aligned and coherently summed

• analog BF or• digital BF

μ-Beamforming

Dynamic focusing

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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

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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

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)(0

))()(()()(0)('

tVG

tVtchtG tanhtVGtV

offsetiLNA

i


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

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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

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C-matrixLNA

Delays pattern

µ-BMF

BMF

Test 1 - Linear array

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• Validation of the receiver model: mixed simulations --> Matlab vs. Eldo

• Input = 16 2-cycle sinusoids @3MHz


MATLAB ELDO

Results - Linear array

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Image formation

Results - Linear array

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References

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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.

Modeling and simulation of 3D ultrasound imaging systems ... · Transducers RECIEVE B EAM F ORM ER...

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