1010 review

Basics of Image Production

Pulse-Echo Technique

US grayscale scans are pulse-echo images of tissue cross-sections & volumes

• Pulses of US sent into patient

• Echoes produced at organ boundaries and within tissues

• Echoes return to transducer

• Echoes displayed on screen

    Echoes are displayed as visible dots

Brightness = echo strength

    Location = anatomic location of echo-generating structure

Scan Format

One pulse of US = one scan line

• Sonographic images are composed of many scan lines

Linear Scan Format

• Different starting points for each pulse

• Each pulse travels in same direction

• Vertical parallel scan lines

  • Rectangular image

Sector Scan Format

• Each pulse originates from same starting point

• Each pulse goes in slightly different directions

  • slice of pie image

Modified Sector Scan Format

• Pulses originate from different starting points

• Each pulse goes in a slightly different direction

  • Top of image curved

Nature of Sound

                Infrasound <20 Hz: frequency too low to hear for humans

Audible sound 20-20,000 Hz: frequencies that humans can hear

         Ultrasound >20,000 Hz: frequency too high for normal human hearing range

Sound propagates in the form of mechanical longitudinal waves & needs a medium to travel 

Acoustic Variables

1. Pressure 

   1. Compressions or Condensations AKA high pressure/density

   2. Decompressions or Rarefactions AKA low pressure/density

2. Density 

3. Temperature

4. Particle Motion

Wave Interactions

Constructive wave interference

When two waves superimpose & are inphase, energies or amplitudes add

Destructive wave interference

When two wave superimpose out of phase, energies or amplitudes cancel out

Frequency f

# of complete cycles/sec

**frequency determined by crystal thickness

• Choice of frequency determined by attenuation & resolution

Units: Hz, KHz, MHz…

Period T

Time required to complete one full cycle

T =  1                     Units: s, ms, μs

       f

Wavelength λ

Distance over which one complete cycle occurs

λ =  c                              Units: m, mm

       F

Propagation Speed c 

Speed that a wave moves through a medium

** determined by characteristics of propagating medium

• ↑ density = ↓ propagation speed

• ↑ stiffness = ↑ propagation speed

z = ρ c         average soft tissue speed = 1540 m/s

Pulsed Ultrasound

Continuous Mode Transducer CW

Sound generated continuous (AKA DF=100%)

• Sound wave has single frequency & amplitude

2 crystals in transducer

     1 crystal for sound transmission

     2 crystal for echo reception

**used in some doppler flow instruments

Pulse Wave Mode Transducer PW

Sound generated in pulses

• Each pulse contains range of amplitude & range of frequencies

• 1 crystal for sound transmission & echo reception

Pulse Repetition Frequency PRF

# of pulses/secs Units: KHz

• AKA number of times piezoelectric crystal or element is shocked/second

  • ↑ depth = ↓ PRF

  • ↓ depth = ↑ PRF

Range of PRF: 4-15 KHz

Pulse Repetition Period PRP

Time from beginning of one pulse to beginning of next pulse

• ↑ depth = ↑ PRP PRP (ms) =    1              . 

• ↓ depth = ↓ PRP                     PRP (KHz)

Units: ms

Pulse Duration PD

Length of time required to complete one pulse   (μs)

• US pulses are usually 2-3 cycles long

• Doppler US pulses usually 5-30 cycles long

PD (μs) = n T 

Duty Factor DF

Fraction or percentage of time US is actually on

• CW DF = 1 DF =  PD       x 1000

• PW DF = <.01         PRP

Spatial Pulse Length SPL

Length of space over which pulse occurs (mm)

SPL = n  λ

Properties of US waves

Amplitude

Amplitude is measured as maximum value - normal value

Peak Amplitude: max variation in either direction from resting. Depends on…

• Driving voltage to crystal (output)

• Electro-mechanical efficiency of transducer

Power

Rate at which work is done

• Determined by driving voltage to crystal (output power)

Absolute: Watts

Relative: Bel (B); decibel (dB0

     ↑ output power = ↑ amplitude &  ↑ intensity

Intensity 

Intensity is total power in sound beam over cross-sectional area it is applied

Units: Absolute = mw/cm²  

          Relative = dB

     ** Intensity is proportional to amplitude squared

I (w/cm²) =  P          .                                 Ways to Measure Intensity

                  A               - SPTP (LARGEST)

   Spatial: refers to distance or space               - SPTA bioeffects

Temporal: refers to time                    below 100mW/cm for unfocused

       Peak: max value                   below 1 W/cm for focused 

 Average: mean value                                      - SATA (smallest)       

Spatial Intensity Conversion

Spatial peak intensity (SP) & spatial average intensity (SA) can be related by Beam Uniformity Ratio (BUR)

**BUR is unitless with minimum value of 1

SA x BUR = SP       or       SP    =  SA

      BUR            

Temporal Intensity

         Temporal Peak Intensity TP - peak intensity with each pulse

          Pulse Average Intensity PA - average intensity during sound transmission (PD)

    Temporal Average Intensity TA - average intensity over entire pulse cycle (PD & PRP)

PA & TA related by duty factor

PA x DF = TA             or            TA   = PA

    DF

Attenuation (A)

Measure of reduction in power (amplitude) & intensity as sound traverses a medium (dB)

Processes of attenuation…

1. Absorption

2. Reflection

3. Refraction

4. Scattering

            a = Aᶜ L       or       a = ½  f  L   only soft tissue

Unit:    Bel (B) = log                 for intensity or power… decibel (dB) = 10 log (I/Io)

  Decibel (dB) = 10 log         for amplitude or voltage… decibel (dB) = 10 log (A/Ao)

Attenuation Coefficient Ac

Attenuation per unit length of path travel  (dB/cm)

• Influencing factors on Ac…

  • Tissue characteristics

  • Frequency

   Aᶜ = ½ f     only for soft tissue

Important Numbers

    Log 1/10 = -1 3 dB = ½ 

  Log 1/100 = -2 6 dB = ¼ 

Log 1/1000 = -3 9 dB = ⅛ 

       Log 10 =  1 10 dB = 1/16 

     Log 100 =  2 100 dB = 

   Log 1000 =  3 1000 dB = 

Half Intensity Depth HD

Distance which will reduce initial intensity by 50% of its original value (cm)

HD =  3   or HD =    6     for soft tissue   

         Ac f

Attenuation Related artifacts 

Acoustic Shadow

Reduction in echo amplitude from reflectors

behind strongly reflecting/attenuating structure

Acoustic Enhancement

Increase in echo amplitude from reflectors 

behind weakly attenuating structure

Reflection, Refraction & Scattering

Acoustic Impedance

Measure of resistance of medium to propagation of sound (rayls)

• Determines magnitude (size/strength) of reflection at specular interfaces

Z  =  ρ  c 

Acoustic Reflection

Incident Intensity (I_I): intensity that strikes interface (W/cm²)

• Reflected Intensity (I_R): intensity after striking interface

  • Changes direction & returns to original direction

• Transmitted Intensity (I_T): intensity after striking interface

  • Continues in same direction it was traveling 

           I_I  =  I_R  +  I_T

Specular Reflection

Occurs at interfaces which are large compared to wavelength of incident sound

Magnitude of reflection depends on 

• Angle of incidence

• Acoustic impedance mismatch

     Normal incidence is… 90° 

Øi  =  Ør  =  Øt      Magnitude controlled ONLY by acoustic impedance

Oblique Incidence AKA not 90°

Change in direction of transmitted sound wave at specular interface (refraction) may occur 

Transmission angle Øt depends on…

• Angle of incidence Øi

• Propagation speeds (c) of a media

Calculating Intensity Coefficients

     Intensity Reflection Coefficients

IRC = I_r or IRC = ( Z₂  -  Z₁ )2

          I_i                       ( Z₂  +  Z₁ )

     Intensity Transmission Coefficients

ITC = 1 - IRC  or ITC =  I_t                .

          I_i

Refraction 

NO refraction if propagation speeds are equal or if the Øi is perpendicular

• Or if  c₁  >>  c₂ = total internal reflection TIR (no transmission)

sinØi  =  c₁              c₁  > c₂ = smaller Øt

sinØt  =  c₂                         c₁ < c₂ = larger Øt

Scattering 

AKA non-specular reflection. Random redirection of waves in multiple directions

Occurs at…

• Interfaces with equal or smaller wavelengths than incident of sound

  • Ex. heterogeneous tissue & suspensions

• Rough boundaries

Rayleigh Scattering

Form of scatter when sound scatters systemically in all directions

• Occurs at interfaces with dimensions which are significantly smaller than wavelength of incident sound

Back Scatter

Scatter returning in general direction of transducer

Contrast Agents 

Use microbubble that contain perfluorochemicals (perfluorocarbons) or gas which is surrounded by protective shell

• Produce echoes from impedance difference of gas & suspending liquid (AKA blood)

• Enhance echogenicity of perfused tissues improving contrast resolution

Range Equation

Also known as Distance Equation. Determines position (depth) of echoes/reflectors

• Range = distance (mm)

• For soft tissue, pulse round-trip travel time (PRTTT) is 13 μs/cm

R  =  ½ (c PRTTT)

Ultrasound Transducers

Convert electrical energy to mechanical energy & vice versa

Piezoelectric Crystals

• Natural

  • Quartz, rochelle salts, tourmaline

• Synthetic

  • Barium titanate, lead titanate, lead zirconate titanate (PZT)

Polarization Process

Process of geometrically aligning dipoles of crystal to induce PZT properties

Curie Temperature

Temperature where polarization is lost 

Frequency Bandwidth 

All transducers operated in pulse-echo mode generate a wide range of US frequencies known as frequency bandwidth (BW)

• All frequencies in frequency envelope contribute to resultant sound beam energy & imaging characteristics

Bandwidth is inversely related to SPL

• Long pulse = narrow BW

• Short pulse = wide BW

Quality Factor Q

Quality factor is operating frequency divided by BW, unitless

Q  =   Fo                         ** Low Q factor is better for imaging 

        BW

• BW & GF are inversely related 

  • Narrow BW = high QF

↑ d = ↓ n = ↓ PD = wide BW = low QF

Diffraction

Small source = rapid divergence, ↓ intensity & ↑ attenuation

Large source = multiple sources, ↓ divergence, ↑ intensity & ↓ attenuation

Huygens Principle

• Large sound source can be considered collection of multiple small sources, creates complex pattern for beam

Transducer Construction (unfocused)

1. PZT element/crystal

• Transducing component

• **thickness determines transducer frequency (fo)

  • Ideal crystal thickness = ½ λ

  • fo =  c_t  2(th)

• Determining factors

  • Propagation speed of transducer c_t

  • Thickness of transducer element th

2. Dampening material 

• Attached to inner face of PZT element

• Absorbs sound & dec. #cyles/pulse (n)

  • ↓ PD & SPL

    • Improves axial resolution & wider BW

    • ↓ amplitude, sensitivity, & efficiency

3. Insulation Ring

• Same material as damping to absorb radial mode vibrations

4. Tuning Coil

• Offsets capacitive effect of crystal & improve transmission & reception

5. Electric Shield

• Picks up stray signals (noise) & grounds them

6. Electric Connectors

• Electrical link between transducer & instrumentation

7. Housing

• Protects transducer components & patient + operator

  • Crack can be electrical hazard

8. Matching Layer

• Material placed infront of transducer element to reduce reflections

• Acoustic impedance has intermediate value between crystal & soft tissue

  • match layer = ¼ λ  for best transmission

Transducer Zones (unfocused)

Focal Zone

distance between equal beam widths that are a multiple of minimum value (at focus)

• Region where sound beam is equal or less than x2 BW at focal length

Beam Diameter

Depends on…                                           Narrow beam benefits….

• Transducer diameter                        -  ↑  intensity

• Frequency           -  improved lateral resolution

• Distance from sound source            -  ↓  BW artifacts

Focusing

Any mechanical or electronic process that reduces BW resulting in…

• ↑  intensity

•  improved lateral resolution

• ↓  BW

Mechanical Focusing

• External

  • acoustic lens, system of acoustic lens & mirrors

• Internal

  • shaping or curving of the crystal

Electronic Focusing

• Involves array transducers & accomplished by phasing

  • Voltage applied to all elements as complete group but with time differences

Mechanical transducers

Moves PZT element with a motor drive

Oscillating

Has a pivot point that produces a sector scan

Rotating

Crystals arranged on wheel & rotate in circular housing

• Each crystal activated as they pass through arc shaped sector field

Reflecting

Transducer is stationary while beam is scanned by moving mirror

Automatic scanning

Electronic scanning performed with array transducers

Types of construction:

• Linear

• Convex

• Annular 

  • Element rings arranged concentrically

  • Scanning performed mechanically & focusing is electronic

Operation of electronic transducer

Sequence/Switched

• Applying voltage pulses to groups of elements sequentially

Phased

• Voltage applied to all elements as complete group, but small time differences

  • Resulting sound pulse sent out in specific path direction

• Used for scanning & focusing

Damage of a Crystal

• Mechanical Transducer

If one crystal malfunctions, ENTIRE image lost

• Linear Switched & Convex Switched

1 crystal damaged = drop-out of single scan line from crystal & extending deeper

• Linear & Convex Phased, Vector Arrays

1 crystal damaged = erratic steering & focusing

• Annular phased Arrays

1 crystal damaged = drop out in horizontal section of image at particular depth

• Each crystal has own unique focal depth & contributes info only for that depth

Detail Resolution

Ability of US system to separately display reflectors or interfaces which are spatially apart

• Axial Resolution

• Lateral Resolution

• Elevational Resolution

Axial Resolution

BEST resolution

Also called… Range, Depth, or Longitudinal Resoltuion

Minimum reflector spacing along axis of sound beam that results in separate echoes displayed

Length determined by… Ax Res =  SPL        .

• Length of pulse SPL         2

  • ↑ SPL = ↑ Ax Res (mm)

    • Worsens resolution

**Axial Resolution improved by…

• Higher frequency transducers

• Highly dampened transducers

Lateral Resolution

Poor lateral resolution may result in imaging artifacts

Also called… Transverse, Azimuthal or Horizontal Resolution

Minimum reflector spacing required across beam that results in separate echoes displayed

• Limited by BW

  • Lat Res = BW/BD (mm)

  • To improve… ↓ Beam diameter BD

    • By focusing (**best resolution at focus)

• Two reflectors must be separated by distance larger than BW to be resolved

Elevational Resolution

Also called… Section Thickness

Resolution perpendicular to longitudinal direction & perpendicular to scan plane

• Determined by beam width in z axis

** improve with harmonic imaging to reduce noise or narrower BW

Components of Pulse-Echo Imaging System

Transducer ➡ Beam Former ➡ Signal Processor ➡ Image Processor ➡ Display

Beam Former

• Pulser (output)

  • Makes electric voltage pulses to excite PZT crystal & times PRF

• Pulse delays (focusing, steering)

  • Have transmission channels for complicated sequences/phasing operations

• Coded Excitation (multiple focusing, harmonics)

  • Coded pulses are multiple pulses that are used to form one scan line

• T/R switch (transmit & receive)

  • Protects amplifier from high voltages produced by pulser (hundred of volts)

    • Accepts only weaker returning volts from transducer 

• Amplification (gain)

  • Electronically boosts ALL received voltages to be further processed

• Compensation (TGC)

  • Electronically boosts received volts according to arrival time & equalizes differences in amplitudes due to reflector depth

• Analog-digital conversion

  • Analog volts of echoes are converted to digital for signal processing

Signal Processor

• Filtering

  • Removes electronic noise outside signal BW

• Harmonic imaging

  • Beam is much narrower & improves lateral resolution

  • Fundamental frequency Fo filtered out & harmonic frequencies produce image

  • With pulse inversion technique, ↓ FR

• Detection (demodulation)

  • Conversion of volts from radiofrequency form to video form

    • Consists of rectification & smoothing

  • NOT operator depend (system process)

• Compression

  • Reduces dynamic range DR with logarithmic compression (dB)

  • Ratio of largest-smallest power that system can handle

    • ↓ differences between largest & smallest echo amplitudes to usable range

Image Processor

• Scan conversion

  • Reformats echo data into image form for processing, storage, & display

• Preprocessing

  • Occurs before echo data is stored in image memory

    • Ex. gain, TGC, write magnification, interpolation

• Image memory

  • A number for each pixel is stored that corresponds to echo intensity received from specific location in the body

• Contrast resolution

  • Ability of gray-scale display to distinguish echoes of slight different intensities

    • ↑  bits/pixels = improved contrast resolution

• Post processing

  • Functions accessed after images are stored

    • AKA actions performed on freeze-framed image

Binary Numbers

Binary numbers are assigned to echoes and have a decimal equivalent

2⁵ = 32 different shades

• BUT the number stored in bit memory would be 31 since 0 counts as a number

Modes of US

A mode

AKA amplitude mode

Escalation of displayed spikes indicates the amplitude of echoes

• Depth vs. amplitude

B mode

AKA brightness mode

Dot brightness corresponds to amplitude or strength of signal

• Echoes displayed as brightened dots

M mode

AKA motion mode

Demonstration of movement of any interface

• Echoes displayed as a function of time

PACS - picture archiving & communications systems 

Computerized storage & transmission systems for digitized images

Temporal Resolution

Ability to distinguish closely spaced events in time

    **Improves with faster frame rate

• Each image or frame is made up of number of scan lines

• For each focus, on each scan line, in each frame, a pulse is required

• PRF determined by number of focuses, lines/frame, & frame rate

PRF = # focuses (lines/frame) (frame rate)

Time is required for echoes to return from one pulse before next pulse is emitted

As penetration increases… PRF must decrease

Penetration (cm) (#focuses) (lines/frame) (frame rate) ≤ 77,000