Pulsed Waves
Topics
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PW Defined
PRF
PRP
Distance Equation
Roundtrip Effect
PD
Duty Factor
Intensity
• Spatial Intensity
• Temporal Intensity
• Intensity Instruments
Pulsed Wave Ultrasound
The transducer used to produce continuous
wave (CW) US is busy transmitting sound
and has no time to “listen” for a returning
echo. Therefore it cannot produce an image.
The transducer used to produced pulsed
wave (PW) US is designed to transmit sound
pulses & then pauses to “listen” for a
returning echo.
Imaging requires a transmitter & a receiver
Pulsed Wave Ultrasound
 a few cycles of US followed by a gap of
time with no US
The gap (pause) is used by the transducer
to listen for returning echoes (receiving time)
Pulses generate scan lines
Each sound “pulse” represents one scan line.
Multiple scan lines create a single frame or image.
Pulse 1
Pulse 2
Pulse 3
Time
RECALL!
• Frequency
• Wavelength
• Period
PW uses these + more
Pulse Repetition Frequency (PRF)
 # of pulses in 1 sec.
 Dx. US has a few thousand pulses per
second; PRF is expressed in kHz.
1000 s
What is the PRF of this pulsed wave?
2 kHz
Pulse Repetition Period (PRP)
Time from the beginning of one pulse to the
beginning of the next pulse; expressed in s
Determined by the system
time
If PRF , then PRP 
time
1
PRP - 500 s
2
PRP - 250 s
time
PRF & PRP are reciprocals
PRF (kHz) X PRP (ms) = 1

PRF = 1/PRP
and
PRP = 1/PRF
Determine the PRF in the previous slide
Just a little diversion
How long does it take you to travel 150
miles if you drive at 50 mph?
Distance = speed X time
or
Distance ÷ speed = time
How long does it take sound to travel 1 cm.
into the body?
Distance Equation
Distance ÷ speed = time
1 cm ÷ 1540 m/sec. =
1 cm *
1 sec. =
1540 m
1 m * 1 sec. = 1/154000 sec.
100
1540 m
.0000065 sec.
= 6.5 μsec.
Let’s KICK IT UP A NOTCH!
How long in time does it take for the sound
echo to travel 1 cm. up through the body to
return to the transducer?
How long does it take a pulse of sound to
complete a round trip through 1 cm. of ST?
This is called the Roundtrip Effect
Don’t you think the US system may get
confused where an echo should show up on
your monitor if it sends another pulse before
the deep echo returns???
So what can a sonographer do to help?
Tell the machine how long to wait to listen
for the deep echo to return by adjusting
the depth control to the deepest level you
want to ‘hear’ the echo from.
Adjusting the depth is actually adjusting
the pulse repetition period.
Pulse Duration (PD)
 Time for 1 pulse to occur
 AKA – transmit time
 Dx US: 2 or 3 cycles/pulse
 Units - s
 PD range: .5 - 3 s
 Doppler US: 5-20 cycles/pulse
 Shorter pulses  the quality of the images
Pulse Duration - PD
time
PULSE DURATION (2 ms)
Pulse duration (ms) = # cycles/pulse x period (ms)
Pulse duration (ms) = # cycles/pulse  ƒ (kHz)
If PRF , then PRP  & Pulse Duration 
PD
time
PRP - 500s
PD
time
PRP - 250s
Duty Factor (Duty Cycle)
 Fraction (or %) of time that pulsed US is
transmitting (on); always between 0 and 1
(0-100%)
 0 indicates that no pulse occurring
 1 indicates that the pulse is on all
of the time, meaning that it is not
PW US but rather CW US
Duty Factor Ranges
2D (B-mode)
.01 - 1.0 %
Doppler US
.05 - 5.0 %
What implications do you think this might have?
Duty factor =
pulse duration (s)
pulse repetition period (s)
PRP 1000 s
time
PD 500 s
DF = 500/1000
= .5 or the pulse is on 50%
What is the PRF?
PRP 1000 s
time
PD 500 s
1 kHz
What is the PD if the DF is .25 ?
PRP 2000 s
500 s
time
What is the PRF?
.5 kHZ
Spatial Pulse Length (SPL)
 Length of space a pulse occupies;
is measured in mm.
 Shorter SPL improves image resolution
SPL
length
SPL = # cycles in pulse X  (mm)

SPL  with:  wavelength
 # cycles/pulse
 frequency
SPL
X
3
X
SPL
 = 2.5 mm
X X
SPL
X X
 = 4 mm
2
 = 2.5 mm
For all of you who have ever told me that
you like A&P better than Physics . . .
We have just completed the anatomy
of a wave; next will be its physiology
Up another notch
Let’s add some
Intensity!
Intensity
 Important when considering bioeffects
 Changed by the operator using the output
power control to change the wave amplitude
 Directly related to power;
if power is doubled, the intensity doubles
 Proportional to wave amplitude squared
(I  A2)
Sound beams are not uniform…
They vary in intensity depending on
the location & time where the
measurement is taken in the beam
 Intensity: usually highest in the center;
weakest in the periphery
 Intensity varies with time in pulsed US
 Intensity is not constant within the pulse
Intensity is usually highest in the
center & weakest in the periphery
Intensity varies with time in PW US
Intensity is not constant within the pulse
Because Intensity varies:
Specific terms are used to describe
variation in intensities associated with
clinical ultrasound:
Spatial - refers to a location or space
Temporal - refers to time
Peak - maximum value
Average - mean value
Spatial Intensities
Center of the sound beam is more intense than the edges
Spatial peak intensity Isp
- Maximum beam’s intensity
Spatial average intensity Isa
- Ave of beam’s intensity
Spatial Intensities
 Spatial Peak (SP) –greatest intensity in
the sound field; usually at the center
 Spatial Average (SA) –average intensity in
the sound beam field
 SP/SA Factor (BUC - Beam Uniformity Coefficient)
– describes the distribution of a beam in space
 Must be  1
 Relates to space (distance) as
duty factor relates to time
Temporal Intensities
Temporal Peak (TP) - greatest intensity in the
pulse as it passes by. Since it doesn’t include
the pulse’s ‘off’ time, it is always  the average.
Only in CW (w/ constant amplitudes) is the
TP =TA.
Temporal Average (TA) - average intensity
across the PRP (includes when the pulse is
‘on’ and ‘off’). Only in CW is TP =TA because
there is no ‘off’ time.
Pulse Average (PA)
- average intensity over the PD (time when the
pulse is ‘on’). Only describes a PW US; CW US
doesn’t have pulses to average.
I
n
t
e
n
s
i
t
y
Pulse Average
Temporal Peak
Temporal Average
Time
Why is the TA lower than the PA?
TA averages the intensity over the entire
PRP; so when the transducer is receiving
(listening for the returning echo) the
intensity is minimal thus lowering the
average (liken this to a low test score that
brings down your grade average)
PA & TA are related to the duty factor
TA = PA X DF
Recall: DF = PD X PRF
If the duty factor is “1” (100%), then we
are describing a continuous wave.
What are we describing when the duty
factor is “0” ?
HOWEVER,
Physicists like to measure the beam
over a certain area & over a certain
amount of time.
SO….
By combining the spatial & temporal
values, 6 intensities can be measured
Intensities can be converted…
to another intensity by using
the duty factor or the SP/SA factor.
SPTP
SPTA
SPPA
SATP
SATA
SAPA
Example
A wave’s SPPA intensity was measured
at 400 mW/cm2 & a duty factor of 25%.
What is its SPTA?
Recall that:
SPTA = SPPA x Duty Factor
SPTA = 400 mW/Cm2 x .25
SPTA = 100 mW/cm2
Example
A wave’s SPPA intensity was measured at
400 mW/cm2, a DF of 25% & SP/SA of 5.
What is its SATA?
Recall that:
SATA = SPTA (SP/SA)
SATA = 100 mW/cm2  5
SATA = 20 mW/cm2
Ranking the 7 ways to measure intensity
in order from largest to smallest:
1. SPTP – highest intensity measurement used
in Dx. US
2. Im
– ave. intensity measured in most intense
half cycle (similar in value to SPTP)
3. SPPA (used only for PW US)
4. SPTA – used to measure biological effects
5. SATP
6. SAPA (used only for PW US)
7. SATA – lowest intensity measurement used
in Dx. US
Determining the Sound Beam Intensity
Various methods are performed by
the manufacturer or a physicist to
determine the intensity of the US
beam (requires special equipment)
Equipment to Determine the
Intensity of a Sound Beam
Radiation force balance
or scale determines the
intensity or power
of the sound beam by
measuring the force the
sound beam exerts on
the balance or scale.
Equipment to Determine the
Intensity of a Sound Beam
Hydrophone system: a hydrophone
and probe; are placed in a water bath
in the field of the emitted sound beam.
The output is calibrated to indicate
pressure or intensity.
What ways can a sonographer decrease a
patient’s chance for bioeffects from US?
Formulas to remember!
c=x
 x t (period) = 1
DF = PD/PRP
ƒ = # cycles/sec
T = time for 1 cycle
ƒxT=1
ƒ = 1/T
T = 1/ƒ
c=ƒxλ
λ = distance of 1 cycle
PRF = # pulses/sec
PRP = 1 pulse + dead time (s)
PRF (kHz) x PRP (s) = 1
PRF = 1/PRP
PRP = 1/PRF
PRP = PD/DF
PD = time for 1 pulse [on] (s)
PD = # cycles in pulse (n) x T
PD = n / ƒ (kHz)
PD = DF x PRP
DF = PD/PRP = on  (on + off)
DF = PD x PRF
SPL = n x λ