Medical Imaging

US, X-ray, CT, MRI, PET

Ultrasound, least expensive

Most common imaging modality and why?

Brightness mode

B-mode ultrasound

2D: ~50 fps up to ~1000 fps; 3D: ~20 fps

Common ultrasound frame rates (2D and 3D)

Applies Doppler directly to red blood cells, no contrast needed

Benefit of ultrasound for blood flow measurement?

High frame rate; Functional imaging; Inexpensive; Portable; Good for image-guided interventional procedures

Strengths of ultrasound (5)

Limited FOV (hard to orient w surrounding anatomy); Operator dependent (via probe placement & angle) and hard to interpret; Inappropriate for bone (e.g. brain surrounded by skull) and air (e.g. lung)

Limitations of ultrasound (3)

Echo magnitude mapped to pixel brightness and arrival time mapped to distance along the scan line

How is ultrasound brightness calculated?

Changes in acoustic impedance (i.e. density and compressibility)

What does ultrasound brightness represent?

By rasterizing A-scans (information in one position wrt distance from probe)

How is a 3D ultrasound image produced?

Longitudinal, mechanical pressure wave

What kind of wave does ultrasound produce?

> 20 kHz

What is the frequency range to qualify as “ultrasound “?

2 to 15 MHz

What is the diagnostic frequency range of ultrasound?

mm, MHz, us

Reasonable ultrasound wavelength, frequency, period units?

1500 m/s

Approximate speed of sound in soft tissue

330 m/s

Approximate speed of sound in air

4080 m/s

Approximate speed of sound in bone

Specular (mirror-like) from large surfaces; Scattering from small targets

Types of ultrasound reflection (2)

Absorption by reactions converting mechanical energy to heat (most); Redirection of sound energy outside beam

Types of ultrasound attenuation (2)

Particle displacement and velocity (pressure remains upright)

What is inverted after ultrasound reflections from closed boundary?

Pressure (particle displacement and velocity remain upright)

What is inverted after ultrasound reflections from open boundary?

Z measured in Rayl (SI = kg/m²/s)

Symbol and units of acoustic impedance

impedance = density * speed of sound

= sqrt( density / compressibility )

Definition of acoustic impedance

R: Amplitude of reflected pressure wave relative to incident wave

Ultrasound pressure reflection coefficient symbol and meaning

R = (Z₂ - Z₁) / (Z₂ + Z₁)

Ultrasound pressure reflection coefficient equation wrt acoustic impedance

T: Amplitude of transmitted pressure wave relative to incident wave

Ultrasound pressure transmission coefficient symbol and meaning

T = 1 + R

Relationship between ultrasound pressure reflection and transmission coefficients?

1.5 MRayl

Approximate acoustic impedance of soft tissue

0.0004 MRayl

Approximate acoustic impedance of air

7.8 MRayl

Approximate acoustic impedance of bone

When a material with high impedance causes a shadow at further depth when transmitted sound cannot reflect backwards through the impeding material to the probe

What is the ultrasound shadowing artifact?

The sound moves from a material with higher impedance to lower impedance, meaning the reflected pressure wave has inverted (i.e. the transition behaves as an open boundary)

When is the ultrasound pressure reflection coefficient negative and what does that represent?

Linear intensity measured in mW/cm^2 is squared power divided by double the acoustic impedance

Sound intensity symbol, units, and equation from physical constants

Intensity in decibels is 10 log base 10 of linear intensity divided by the linear intensity reference

Transformation between linear and log sound intensity

Intensity in decibels is 10 log base 10 of the multiplicative factor with respect to the reference intensity

Transformation between linear sound intensity times a constant to log intensity

Alpha with units dB/cm/MHz

Acoustic attentuation symbol and units

0.5 to 1 dB/cm/MHz

Acoustic attentuation range in soft tissue

0.5 dB/cm/MHz

Default acoustic attentuation value?

Intensity in dB is negative alpha * f * r where frequency is in MHz and r is the one way distance in cm

Log sound intensity as a function of acoustic attenuation

If there is a region with little attenuation (e.g. a homogenous cyst with no reflection), then an enhancement artifact deep to that the region appears brighter, due to the lack of relative attenuation

What is the ultrasound enhancement artifact?

R_I: Linear intensity of reflected pressure wave relative to incident wave

Ultrasound intensity reflection coefficient symbol and meaning

R = (Z2 - Z1) / (Z2 + Z1)

Ultrasound intensity reflection coefficient equation wrt acoustic impedance

T_I: Linear intensity of transmitted pressure wave relative to incident wave

Ultrasound intensity transmission coefficient symbol and meaning

T_I = 1 - R_I

Relationship between ultrasound intensity reflection and transmission coefficients?

Scattered echoes (speckle) have significantly lower amplitudes than reflected echoes, so log scaling reveals the texture within the images which is helpful medically

Motivation for presenting B-mode ultrasound images in dB?

Via piezoelectric transduction, where applied AC current produces cyclic expansion and contraction which propogate a sound wave, and received sound waves cause deformation which produces an electric signal

How are ultrasound pulses produced and received?

Lead zirconate titanate (PZT) ceramic in the 1980s, modern transducers use a composite of PZT with epoxy

Material of clinical ultrasound transducers

A cosine wave in a short envelope

What shape of ultrasound is transmitted?

Time gain compensation where gain refers to amplification and time refers to increased effect after longer time since production. This corrects for attenuation axially

Ultrasound TGC meaning

The operator sets the TGC slope in dB/cm along different regions of depth (i.e. TGC is constant along the lateral direction)

How is TGC applied to ultrasound images?

Regions that should appear uniformly bright have varying brightness with depth due to incorrect choice of TGC slopes by the operator. That, a region can be too dark because there is not enough TGC, or too bright if too much

What is an ultrasound incorrect TGC artifact?

Full wave rectification (i.e. absolute value) is applied to the radio frequency signal then low pass filtering to smooth

How are ultrasound envelopes detected (oversimplified)?

The radio frequency images has extra bands from the switching signs that make the shape and brightness of lesions for example harder to interpret

Why perform ultrasound envelope detection?

The time for the pulse to leave and return to the transducer is recorded and the scanner assumes a speed of sound of 1540 m/s. The depth may be calculated directly as half the round trip time * speed

How are depths of ultrasound echoes estimated?

1540 m/s = 1.54 mm/us

Average speed of sound in soft tissue over the length of a typical ultrasound scan?

Each cm of (one way) depth takes 13 us (of round trip time)

Rule of thumb for estimating ultrasound depths from time between pulse and echo?

How close together two point-like objects can be and still appear distinct in the image

What does spatial resolution measure?

Axial and lateral as in OCT, elevation desrcibes distance in or out of page

Ultrasound descriptions of the cardinal directions

Half of the pulse length (i.e. the FWHM of the pulse envelope). The pulse length can be given as N sub c times lambda where N sub c is the number of cycles of the cosine carrier

Ultrasound axial resolution

Linear (rectangular image), curvilinear (fulstrum image or sector with point cut off), phased (sector image)

Types of ultrasound arrays and geomtry of their image

Linear array to image objects close to surface (e.g. breast), curvilinear array to image objects far from surface (e.g. abdominal), phased array to image if object is in the way (e.g. ribs for cardiac imaging)

When to use each type of ultrasound array

Subset of elements used to form each scan line, with N elements turning on and off to translate the scan lines

Linear array ultrasound image generation

L is the length of the array of elements in the transducer

Ultrasound aperture length symbol and meaning

All elements are used to form each scan line, and the beam is steered electronically

Phased array ultrasound image generation

Near field is the Fresnel zone, with lateral FWHM approxiamtely equal to the aperture length until the transition distance, when the beams spreads out in the far field Fraunhofer zone

Zones of unfocused ultrasound beam

The squared aperture length divided by 4 times the wavelength, gives the distance at which the (near field) Fresnel zone transitions to the (far field) Fraunhofer zone in an unfocused beam

Transition distance of ultrasound beam meaning and defintion

Distance to the focal zone in an focused beam (i.e. where the beam is most laterally focused)

Focal distance of ultrasound beam meaning and defintion

The ratio of focal distance to aperture length

F number of ultrasound beam meaning

Focused always, it gives the best lateral resolution at the focus, but lateral resolution is worse far from the focus. The solution is to image multiple times with different focal distances

Are clinical ultrasound images focused or unfocused? What is the trade off and how is it managed?

By digitally delaying outgoing (incoming) signals such that the signals arrive at (from) the focus simultaneously

How does ultrasound create a focused beam?

Point spread function: this is the signal produced in an image of a single point-like object

PSF meaning

Squared sinc of distance from focus divided by the F number and lambda. Square is due to product of transmitted and received waves

Shape of lateral ultrasound PSF

Two point-like objects are barely resolved when the maximum of one PSF overlaps the first zero of the other PSF

Rayleigh resolution criterion

lambda times the F number

Ultrasound lateral resolution

Mechanically, so it is determined physically by the scanner and cannot be adjusted

How are clinical ultrasound images focused elevationally?

lambda time F divded by H where H is the elevational length of the probe

Ultrasound elevational resolution

Axial: a few hundred microns, lateral: 1-2 mm, elevational: 5-10 mm

Common ultrasound resolutions in each direction

Increasing frequency improves resolution (since lambda decreases) but causes more attentuation and thus reduces penetration depth

How does changing the ultrasound frequency impact the image?

Lateral focusing since elevational focusing is physical so cannot be adjusted, and multiple images can be taken at different lateral focii to help mitigate the effects

Which is generally more aggressive in ultrasound imaging: lateral or elevational focusing? Why?

2 times lambda times the squared F number

Ultrasound depth of field

Continuous adjustment of the receive focus to track transmitted pulses as they propagate away from the probe

Meaning of ultrasound dynamic receive focusing

Time for echoes to return from the maximum depth: in soft tissues, this takes 13 us per cm

Ultrasound listening time

half the lateral resolution

Ultrasound max line spacing

Lateral FOV divided by the max line spacing (always round up!)

Ultrasound min number of scan lines

Min number of scan lines times listening time times number of transmit focal zones

Ultrasound min time per frame

30 fps or more

Condition for real time frame rates

X-ray imaging with ~0.05 mm (only optical methods are better)

Imaging modality with highest resolution?

Photons from a (almost) point source pass through the patient and transmitted photons are measured to create a "shadow" of the patient

X-ray imaging mechanism

The transmission and detection of photons are random events, which give rise to small variations in image intensity

What is noise in an x-ray image?

Linearly proportional

How does x-ray image intensity vary with the number of photons detected at each pixel in the image?

Proportional to the square root

How does x-ray image noise vary with the number of photons detected at each pixel in the image?

Proportional to the intensity over the noise, which means proportional to the square root. This is because these are Poisson processes

How does x-ray image SNR vary with the number of photons detected at each pixel in the image? Why?

Transmission through ~25 cm soft tissue is only feasible with radiowaves and x-rays (between has too little transmission and outside that range has too much transmission, no contrast). However, resolution is diffraction limited, and the large lambda of radiowaves means small features cannot be resolved

Why are x-rays used for imaging rather than another wavelength?

With inverted log scale (i.e. bright = attenuation, dark = transmission)

How are x-ray images scaled for display?

To avoid exposing unnecessary structures to radiation

Why use a point source for x-ray imaging?

Through bremsstrahlung by slowing electrons down in a high Z material. While EM waves can be generated by accelerating charged particles, the high frequency of x-rays is unattainable

How are x-rays generated for imaging? Why not another method?

Electrons are boiled off a heated filament then accelerated toward a rotating anode by an applied current. At the anode, the electrons interact with a high Z material (e.g. tungsten) and generate photons but also generates lots of heat

How does a modern x-ray tube work?

~95%

How much energy from the electrons goes to heating the target during x-ray generation?

Electrons moving through target produce Bremsstrahlung, by slowing down near nuclei, or head on collision of electron with nuclei where all energy of electron goes to photon. Characteristic radiation is also created when K shell electrons are ejected

Sources of photons in x-ray generation?

~80 KeV

Energy of characteristic radiation from tungsten?

The rotation of the target distributes heat which allows higher energies to be used

Why use a rotating anode to generate x-rays?