UT 200 - Day 2 - Attenuation, Reflection, and Refraction

definition of impedance

resistance to the propagation of a sound through a medium

why does reflection occur?

there’s a difference in impedance in the two mediums

relationship between impedance and reflection

linear relationship - as impedance goes up, reflection goes up

what determines the amount of reflection?

acoustic impedance mismatch

minimal difference acoustic impedance =

minimal reflection and high transmission

significant difference in acoustic impedance =

significant reflection and minimal transmission

formula for % reflection

criteria for specular reflection

1. difference in acoustic impedance

2. sound beam strikes boundary at 90 degrees

Luez’s law

angle of incidence = angle of reflection

θr = θi

• specifically in relation to specular reflection

different names for 90 degree angle

right angle, normal incidence, perpendicular, orthogonal incidence

size of the reflector is larger than wavelength of incident beam

specular reflection

is scattering angle dependent

no

relationship between frequency and scattering

proportional: higher frequency = more scattering

scattering occurs because of

rough textured tissue, ie. liver, thyroid, pancreas

the reflector is smaller than the sound wavelength, such as red blood cells

Rayleigh’s scattering

relationship between rayleigh scattering and frequency

Rayleigh Scattering = frequency⁴

surface type of specular vs. non-specular

• specular: smooth, large

• non-specular: rough

border size of specular vs. non-specular

• specular: border larger than incident angle

• non-specular: border smaller than incident angle

angle dependency of specular vs. non-specular

• specular: angle dependent

• non-specular: not angle dependent

artifacts in specular vs. non-specular

• specular: more artifacts, more noise

• non-specular: less artifacts, less noise

acoustic impedance (z) is dependent on

density and propagation speed

what happens when the impedance difference is small

inability to visualize structure

what happens when there’s an oblique incidence

sound doesn’t return to the transducer → no image produced on display

equation for incident intensity

incident intensity = reflected intensity + transmitted intensity

intensity reflection coefficient (IRC) + intensity transmitted coefficient (ITC) = ?

100%

if tissue impedance is the same, then there is —% transmission

100

% reflection of soft tissue/ air boundary

99%

% reflection of soft-tissue/ bone boundary

90%

% reflection of soft tissue/soft tissue boundary

<1%

refraction definition

bending or change of sound wave as it passes through tissue interface

criteria for refraction

1. difference in propagation speed between tissues

2. sound beam MUST strike at an oblique incidence

refraction equation, also known as

Snell’s Law

what equation is this?

Snell’s Law

if c2 > c1, what happens to the transmitted beam?

beam bends away from the normal; transmitted beam has bigger angle than incident angle

(low → high → high)

if c2 < c1, what happens to the transmitted beam?

beam bends toward the normal; transmitted beam has smaller angle than incident beam

(high → low → low)

degree of refraction

absolute difference between incident and transmitted angle

critical angle, also known as

grazing incidence

what happens during critical angle

enormous refraction resulting in no incident transmission energy, all incident energy internally reflected

what causes “edge shadows”

critical angle or “total internal reflection”

attenuation definition

decrease in the amplitude and intensity of sound beam as it travels through tissue

sources of attenuation

• reflection

• absorption

• refraction

• destructive interference

biggest cause of attenuation in ultrasound?

absorption

attenuation unit of measumrent

dB

relationship between attenuation and frequency

exponential; higher frequency = more attenuation

relationship between scan depth and attenuation

proportional; deeper image = more attenuation

absorption converts sound energy into?

heat

bone has a — rate of absorption than soft tissue

higher

3 dB increase

2x

6 dB increase

4x

9 dB increase

8x

3 dB attenuation

1/2x

6 dB attenuation

1/4x

9 dB attenuation

1/8x

equation for attenuation coefficient (qc)

qc = 1/2f

total attenuation equation

total attenuation = attenuation coefficient x path length

attenuation coefficient unit of measurement

dB/cm

half-intensity depth

depth where sound has lost half (50%/ 3dB) of its intensity

equation for half value layer

HVL = 6dB/frequency