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• Ultrasound Imaging

Ho Kyung Kim

Pusan National University

Introduction to Medical Engineering (Medical Imaging)

Suetens 6

Sound

Sonic: 20 Hz20 kHz (audible frequency)

Subsonic ()

Ultrasound

Acoustic wave

Reflects, diffracts, refracts, attenuates, disperses, and scatters when it propagates through matter

Ultrasound imaging

Estimates the tissue position by measuring the travel time of ultrasound that reflects at the

interface between different tissues (with the known acoustic wave velocity)

Noninvasive, inexpensive, portable

Excellent temporal resolution

Being applied to nondestructive testing (NDT) and sound navigation ranging (SONAR)

Not only to visualize morphology or anatomy but also to visualize function by means of blood and

myocardial velocities (velocity imaging Doppler imaging)

2

• Ultrasonic waves

Progressive longitudinal compression waves (opp. transverse waves)

Generated and detected by a piezoelectric crystal (which deforms under the influence of an

electric field and, vice versa, induces an electric field over the crystal after deformation)

3

Acoustic impedance

Substance (m/s) (106 kg/m2 s)

Air (25C)Fat

Water (25C)Soft tissue

Liver

Blood (37C)Bone

Aluminum

346

1450

1493

1540

1550

1570

4000

6320

0.000410

1.38

1.48

1.63

1.64

1.67

3.87.4

17.0

4

=

=

(acoustic pressure/particle velocity or mass density wave velocity)

• Wave equation

= 0 (linear wave eq.)

General solution: , = + ( + )

e.g., , = sin

= sin

( )

Any waveform propagates through a medium without changing its shape

Acoustic intensity (in units W/m2): ! =

" d

e.g., ! =

\$ " d

=

%

\$

The above is only valid when is only an infinitesimal disturbance of the static pressure. If not, wave propagation is associated with distortion of the waveform

5

Interference

Constructive or destructive interference between waves

Depending on the difference in traveled distance w.r.t. the wavelength

Diffraction: a complex interference pattern resulted from an infinite number of coherent

sources (i.e., sources with the same frequency and a constant phase shift)

6

• Attenuation

Loss of acoustic energy of the ultrasonic wave during propagation (e.g., conversion into

heat in tissues because of viscosity)

&(, ') = ()*+ ()*%-.+

/ = ln + per cm or nepers (Np) per cm

attenuation coefficient

/ in units of dB/cm when //20 log ( or //8.6859 ( 20 log + in dB)

/ in Np/(cm MHz) or dB/(cm MHz)

typically < = 1

7

Substance / (dB/(cm MHz)) Nonlinearity (>/)

Lung

Bone

Kidney

Liver

Brain

Fat

Blood

Water

Spleen

Muscle

41

20

1.0

0.94

0.85

0.63

0.18

0.0022

7.2

7.5

11.0

6.2

5.0

7.8

6.5

Reflection and refraction

Not only does the direction of propagation at the interface between two media change, but

also the amplitude of the waves

Snell's law for direction: ?@A BCD

=?@A BED

=?@A BF

Note that transmitted wave is refracted wave

cos H = 1 IIDsin HJ

Complex number if > & HJ > sin)

(incident & reflected waves are out of phase)

Amplitudes: L = M 1

Transmission coefficient: M NFNC=

\$ OP? BC\$ OP? BCQ\$D OP? BF

Reflection coefficient: L NENC=

\$ OP? BC)\$D OP? BF\$ OP? BCQ\$D OP? BF

Reflection is large if and differ strongly (e.g., tissue/bone, air/tissue)

8

• 9

Scattering

10

• Doppler effect

If an acoustic source moves relative to an observer, the frequencies of the observed and

transmitted waves are different the Doppler effect

Doppler frequency: R = S = TUQTU

W OP? B

e.g., If a scatterer moves away from the transducer with a velocity of 0.5 m/s and the pulse

frequency 2.5 MHz, the Doppler shift is approximately -1.6 kHz.

11

Generation & detection

Transducer

Transmitter (when generating)

Detector (when detecting)

Consists of

Piezoelectric crystal

Usually polymeric materials, such as PZT (lead zirconate titanate) and PVDF

(polyvinylidene fluoride)

The amplitude of the vibration, driven with a sinusoidal electric signal, is maximal when

the thickness of the crystal is exactly half the wavelength of the induced wave (called

resonance with the fundamental resonance frequency)

Backing layer

To reflect the reflected energy from the crystal back into the crystal

Matching layer

To reduce the impedance between the crystal and tissues

12

• Gray-scale imaging

A-mode (amplitude) imaging

Based on the pulse-echo principle

Measurements of the reflected waves as a function of time

X =

Detected signal ~ MHz range ( called RF signal)

M-mode (motion) imaging

Repeated A-mode measurements for a moving object

13

B-mode (brightness) imaging

Repeated A-mode measurements by translating or tilting the transducer

14

• Image reconstruction

For the acquired RF data, perform filtering, envelope detection, attenuation correction, log-

compression, and scan conversion

Filtering

To remove high-freq. noise

To remove the transmitted low-freq. band signal for the second harmonic imaging

15

Envelope detection

To remove high-freq. information by means of a quadrature filter of a Hilbert transformation

16

Attenuation correction

To compensate the attenuation of reflected waves with depth using attenuation models

Also called time gain compensation because of the linear relationship between time and depth

• Log-compression

To reduce the large dynamic range between the specular and scatter (appeared as speckle

patterns) reflections by using a gray level transformation (using a logarithmic function)

17

Scan conversion

To convert polar-grid data (obtained from the tilting method) into a rectangular-grid data

(obtained from the translating method)

Also called sector reconstruction

Ex) A typical echograph includes 120 image lines and each line in the image corresponds to

a depth of 20 cm. Assuming = 1540 m/s, what is the acquisition time of an image?

The travel distance to and from the transducer is 40 cm. Therefore, the acquisition time of each

line is 267 s, and then that of the image is about 32 ms.

Because the reconstruction time is negligible, the temporal resolution is 30 Hz (i.e., 30 images per

second)

18

• Doppler imaging

To visualize velocities of moving tissues

3 different data acquisition methods

1) Continuous wave (CW) Doppler

Two crystal for transmitting continuous sinusoidal wave and detecting in the same

transducer

Only exception to the pulse-echo principle

No spatial (i.e., depth) information

2) Pulsed wave (PW) Doppler

Transmitting pulsed waves at a constant pulse repetition frequency (PRF)

M-mode acquisition but only one sample per each line at a fixed time (i.e., range gate),

resulting in one specific spatial position

3) Color flow (CF) imaging

B-mode acquisition but, for each image line, several pulses (37) instead of one are

transmitted

2D anatomical gray scale image onto where the color velocity information is superimposed

19

CW Doppler

Calculate the velocity of a scattering object (e.g., cardiac and blood velocities) using the

relationship between R and ^ Encode the spectral amplitude obtained from the Fourier transform of the timely-

segmented received signal into a gray value spectrogram or sonogram

Trade-off between the velocity resolution and temporal resolution

20

• PW Doppler

Not make use of the Doppler principle

Instead, S = and take only one sample of each of the received pulses at a fixed range gate

Then, the received signals are becomes samples of a slowly time-varying sinusoidal

function with frequency R = TU

21

CF imaging

Similar to the PW Doppler, but CF imaging calculates the phase shift between two

subsequent received pulses instead of calculating ^ from samples of a signal with R Alternatively, the phase shift can be calculated by cross-correlation of the signals received

from two pulses

22

• Spatial resolution

Distinguished to be the axial, lateral, and elevation resolution according to the direction of

wave propagation

23

Axial resolution

Determined by the duration M of the transmitted pulse

=

e.g., = ~0.5 mm for a typical 2.5 MHz

Lateral and elevation resolution

Typically, a few mm in the focal region

10 worse than the axial resolution Determined by the width of the ultrasonic beam (roughly ~ the size & shape of the transducer)

e.g., planar vs. concave crystals

24

main lobeside lobe

• Noise & contrast

Noise

Due to scatter reflections, called speckle noise

However, the speckle pattern enables the user to distinguish different tissues from each other

25

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