PHYS C1

Amplitude

A, m

Maximum displacement of any point in medium from its rest position

Peak-to-peak amplitude

maximum displacement of rarefaction to maximum displacement of compression

= 2A

Period

T, s

time taken for a particle in medium to complete one cycle

Wavelength

λ, m

distance between points that are in phase

Frequency

(f, Hz)

number of cycles that each particle undergoes per unit time

directly proportional to viscosity (internal friction) and thus absorption

low f has higher penetrating power

Wave Equations

f = 1 / T

v = fλ

Ultrasound frequency

above human hearing (>20 kHz)

1 to 50 MHz

MI Typical frequency

1 MHz to 40 MHz

Low f purpose

greater penetration for large/deep structures as longer wavelength reduces attenuation

High f purpose

better resolution for superficial tissues (skin, eyes) as smaller structures detected without scattering

Bulk Modulus

K, Pa

Medium’s resistance to compression (stiffness)

High Bulk Modulus Explanation

High K (bones):

doesn’t deform easily under pressure

strengthens the elastic restoring force

propagating the wave

increase velocity of sound

Low Bulk Modulus Features

Low K (soft tissue):

• loosely packed particles

• overshoot and oscillate

• less efficient energy transfer

Velocity of Sound Formula

K = bulk modulus

ρ = density of medium (kg/m³)

Velocity of sound in fat, tissue, and muscle

Fat - 1459m/s

Tissue - 1540m/s

Muscle - 1580m/s

dB formula + def

dB: intensity of sound

dB = 10 log10 (I2 / I1)

where I1 = initial intensity

dB/I + A link

I = A²

So bringing power to front of log: dB= 10 log10 ((A2/A1)²) = 20 log10 (A2 / A1)

Absorption Def

wave’s energy being lost as heat due to viscosity (internal friction) of medium’s particles (directly proportional to frequency)

most prevalent in bone

reduces penetration power

Snell’s law

Specular reflection

angle i = angle r

produces brightest echo

Diffuse Reflection

sound beam hits interface at different incidence angles due to an uneven surface, causing numerous angles of reflection

Rayleigh Scattering

multi-directional reflection

scatter intensity dependent on frequency

darkest/weakest echo

Stochastic/probabilistic scattering

describes randomness of scatter directions

scatter pattern depends on orientation of areas of boundary relative to incident beam

speckled pattern created by constructive and destructive interference of scattered waves

Reflection def + Rules

Allows for visualisation of soft tissue structures in ultrasounds

If area of boundary is:

>λ (organ) - Specular reflection

<λ (red blood cells) - Rayleigh Scattering

=λ (internal regions of organ) - Stochastic/probabilistic scattering

Attenuation Def + Causes

Decrease in intensity/amplitude of wave with distance, reduces wave’s penetration power

Result of:

Spreading wavefronts over an increasingly large area

Absorption

Redirection of wave via reflection, refraction, diffraction, scattering

Refraction Def + Rules

Change in direction of a transmitted wave at a boundary interface caused by the change in wave’s velocity

If beam strikes interface at 90°, beam is partially reflected with rest transmitted and no refraction

V increases bends away normal

Artefacts

caused by refraction and creates:

distortion of object in monitor

appearance of object at wrong location

shadowing

Acoustic Impedance

(Z, kg/m²s = rayl)

measure of a medium’s resistance to the propagation of ultrasound wave

Z = ρc

difference in acoustic impedance at boundary interface causes reflection (echo) thus visualization of soft tissue structures

Link between Z and echo strength

larger the diff in Z, the more sound will be reflected (stronger echo)

Which spaces does sonography not produce good images of and why?

Since bone’s Z is much higher than soft tissue’s, nearly all sound is reflected at bone’s surface with little penetrating, making it unable to visualize deeper structures

Same for air (so lungs) as Z much lower than soft tissue

Coupling Jel

Applied over skin on area to be scanned, creating a more homogeneous medium by filling the air gap between transducer and skin

Because gel has a more similar acoustic impedance to skin than air, it reduces the number of sound waves reflected back to transducer without entering body

Also reduces friction

Pulse Echo Technique

A fraction of the incident beam reflected back to transducer at each interface before next pulse is applied

Echo Ranging

Measure of time taken for reflected beam (echo) to return to transducer

Used to determine depth of interface

d=vt/2

Piezoelectric Effect

pressure electric effect

used by transducer to convert between electrical signals and ultrasonic energy

Piezoelectric Crystals

Commonly lead zirconate titanate (PZT)

Each molecule has dipole, restricting their ability to move in the crystalline structure unless heated above Curie temp

Alignment Plates

Pair of charged plates across a material

-ve dipole region points to positive plate and vice versa

Ensure molecules in crystals remain parallel and correctly spaced for beam steering and focusing

Conducting Plates

placed on opposite faces of crystal and voltage spike is applied

AC current causes molecules to twist in opposite direction when polarity is reversed (electric field changes direction)

Movement causes contraction and expansion of crystals

Mechanical Vibration

Contraction and expansion of crystals provides mechanical vibration of molecules, creating compressions (high density areas) and rarefactions (low density areas) of pressure wave

Dampening/Backing Block

Shortens the time the crystal vibrates (thus pulse length) after the current input is gone, allowing transducer to effectively detect echoes to provide better axial resolution

Also decreases ultrasound energy sent backwards and laterally, reducing waste

Matching Layer

material with an intermediate acoustic impedance to reduce reflection at skin-crystal interface

Located between crystals and coupling gel

Increased efficiency

A(amplitude)-Mode

Simplest

Ophthalmology applications

Uses echo-ranging principle (time indicates depth)

Signal amplitude shown as peak on horizontal timeline

Spike height proportional to echo intensity

Time Gain Compensation Def

User controlled to increase amplitude of deeper echoes (which underwent more attenuation) so series of pulses from equally reflective interfaces have similar amplitude

How do users control Time Gain Compensation?

Inital/delay/slope - for a set time (delay), all echoes amplified by same amount (initial gain). After delay, gain increases with respect to time (slope) as deeper echoes return, until some maximum fixed gain is reached for the deepest echoes.

Segmented - sliding bar used to control gain for each depth range

B-Mode (brightness modulation, 2D)

Converts spikes to brightness-modulated dots

Real-time 2D imaging of body cross sections

Dot location depends on time for echo to return and direction its returned from

High intensity echoes = High peaks = Bright dot

Real-Time Imaging

Series of still shots viewed rapidly one after another to depict motion

Freeze frame - ability to pause on one shot

Transducer beam points in one direction (line of sight) at a time, all echoes assumed to originate from centre of this to collect a single line, line of sight then slightly moved to collect another line, gaps between lines are filled electronically

Doppler Ultrasound

Echoes frequency fluctuates depending on whether they are moving towards or away from transducer

Red = blood flowing towards, Blue = blood flowing away

Density of colour shows speed of flow