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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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