SPI FORMULAS

Power is proportional to

amplitude squared

Intensity is ___________________to power

directly related

Intensity is proportional to

amplitude squared2

Intensity (w/cm2)

power (w) divided by area

1MHz =

1.54 mm wavelength

2MHZ =

0.77mm wavelength

wavelength is equal to

1.54mm/microseconds divided by frequency

Propagation speed is determined by

medium only

what characteristics of a medium affect the speed of sound

stiffness (elasticity)

density (intertia)

Stiffness is ___________________to propagation speed

directly related

Density and speed are _____ related.

inversely related

wavelength is______________________to frequency

inversely related

Pulse duration is determined by

sound source

pulse duration is directly related to

the number of cycles in the pulse and directly related to period

Pulse Duration (PD)

The actual time from start of a pulse to the end of that pulse (not including the listening time)

Pulse duration is ____________________________to frequency

inversely related

Pulse duration is directly related to _____________and inversely related to frequency

number of cycles divided by frequency

PRP is unrelated to

period; it is related only to depth of view.

PRP and depth of view

Directly related

PRF is unrelated to

frequency

PRF and Depth of view are

inversely related

Shallow imaging

-Less listening

-Shorter PRP

-Higher PRF

-Higher duty factor

deep imaging

-More listening

-Longer PRP

-Lower PRF

-Lower duty factor

PRP and PRF are ______ related.

inversely related

duty factor

the percentage or fraction of time that the system transmits a pulse

Duty factor is determined by

Sound source only

Duty factor is _____ related to imaging depth.

Inversely

*When depth increases, DF decreases

When depth decreases, DF increases

The transmit time is called the _______.

pulse duration

transmit time and receive time

In ultrasound

transmit time is 0.2% and

receive time is 99.8%

The duty factor for continuous wave ultrasound is

1.0 or 100%

Spatial Pulse Length (SPL)

Length or distance that a pulse occupies in space; distance from start of a pulse to end of that pulse

spatial pulse length is determined by

Both the source and the medium

spatial pulse length is ______________________ to wavelength

directly related

spatial pulse length is ________________________to frequency

inversely related

Distance and attenuation are ______ related.

directly related

Frequency is _____________to attenuation

directly related

Scattering is ________________to scattering

directly related

Rayleigh scattering and frequency

directly related. when frequency doubles, Rayleigh scattering is 16 times greater

Rayleigh scattering is proportional to frequency 64

Absorption is __________________to frequency

directly related

Total attenuation increases with

higher frequency or longer path length

total attenuation

the total amount of sound (in dB) that has been attenuated at a given depth

total attenuation is equal to

attenuation coefficient (db/cm) x distance

attenuation coefficient

the rate at which sound is attenuated per unit depth

attenuation coefficient is _________________to frequency

directly related

attenuation coefficient is equal to

1/2 the frequency

0.5 db/cm divided by frequency (MHZ)

Impedance

the acoustic resistance to sound traveling in a medium

Impedance is determined by

medium only

Impedence is equal to

rayls = density (kg/m3) x propagation speed (m/s)

Impedance is calculated

by multiplying the density(kg/m3) of a medium by the propagation speed (m/s)of the medim

Incidence (starting) Intensity is equal to

reflected intensity + transmitted intensity

incidence angle

angle between incident sound direction and a line perpendicular to the boundary of a medium

intensity reflection coefficient (IRC)

the percentage % of the intensity that bounces back when a sound beam strikes the boundary between two media

Intensity Transmission Coefficient (ITC)

the percentage of intensity that passes in the forward direction when the beam strikes an interface between two media

IRC + ITC =

100%

Reflection with normal incidence

When a sound beam strikes a tissue boundary at a 90 DEGREE ANGLE (normal incidence), reflection occurs ONLY if the media on the other side of the boundary have DIFFERENT IMPEDANCES

transmission with normal incidence

these are simply reflection questions, whatever is not transmitted, must be reflected

transmission with normal incidence and media with same impedance

All of the sound is transmitted when the two media have the same impedance

Intensity Transmission Coefficient (ITC) is equal to

transmitted intensity divided by incident intensity x 100 = 1 - (IRC)

IRC (%) + ITC (%) =

100%

ITC (%)

(transmitted intensity/incident intensity) x 100

Normal incidence is also known as

Perpendicular incidence

Normal incidence is unrelated to

reflection and transmission with oblique incidence

REFLECTION ANGLE = INCIDENT ANGLE

When reflection occurs with oblique incidence, the sound beam is NOT redirected back to the transducer, but rather in a DIFFERENT DIRECTION.

The direction it goes in will be EQUAL and OPPOSITE to the incident angle:

ANGLE OF INCIDENCE = ANGLE OF REFLECTION

reflection coefficient

the reflective property of a boundary

Incident intensity =

reflected intensity + transmitted intensity

angle of incidence = angle of reflection

law of reflection

Snell's Law of Refraction

the relationship of the angle of incidence to the angle of refraction

Time of flight is directly related to

how deep a sound pulse travels

time of flight is equal to

depth (mm) =

1.54(mm/microsec) x goreturn time microsec

PRP (microseconds) equals to

Imaging depth(cm) x 13mcrosc/cm

PRF (Hz)=

77,000 cm/s / Imaging Depth (cm)

quality factor/Q factor

a measure of beam purity

the operating frequency of the transducer divided by the bandwidth

quality factor is inversely related to

Bandwidth

With cw transducer

electrical frequency is equal to acoustic frequency

The speed of sound in PZT and the frequency of sound are ____ related.

directly related

PZT thickness is ____________ to frequency

inversely related

diameter of PZT and focal length are

directly related

Thin PZT

higher frequency and shorter wavelength cycles

Thick pzt

Low frequency and longer wavelength cycles

Frequency is _________________ to focal depth

directly related

focal depth (mm) is equal to

diameter(mm)2 x frequency(MHZ)/6 and

diameter(mm)2 /wavelength

Crystal diameter and beam divergence are ______ related.

inversely related

small crystal diameter pzt produce beams that

spread out more

large crystal diameter pzt produce beams that

diverge less

large diameter crystals improve

lateral resolution because they diverge less

Frequency and beam divergence are ______ related.

inversely related

lower frequency more divergence

high frequency less divergence

Higher frequency sound beams improves

lateral resolution

Sin Divergence Angle

1.85/ diameter (mm) x frequency(MHz) and

1.2 x wavelength/ diameter

Axial resolution is determined by

spatial pulse length

Axial resolution can be improved by

reducing the spatial pulse length

reduced pulse duration

higher frequency transducers

Synonym for axial resolution

LARRD

longitudinal resolution

axial resolution

radial resolution

range resolution

depth resolution

Lower numerical values of axial resolution indicate

shorter pulses

Axial resolution is equal to

mm= spatial pulse length(mm)/2 and

mm = wavelength(mm) x number of cycles in pulse/ frequency

axial resolution in soft tissue

mm= 0.77 x number of cycles in pulse/frequency

Lateral resolution is determined by

Width of the sound beam (narrower beams have better resolution)

lateral resolution

the ability to accurately identify reflectors that are arranged perpendicular to the ultrasound beam

lateral resolution is best at the

focus and focal zone where the beam is narrowest

Lateral resolution is equal to

beam diameter

Frame rate is improved by

1. Decreased line density

2. Decreased depth

3. Decreased sector width

4. Decreased number of focal zones

5. Using write-zoom

6. Decreased persistence

7. Increased operating frequency

frame rate and tframe are

inversely related and reciprocals