4 Pulsed Ultrasound: Doppler Concepts and Pulsed Parameters

CW Doppler vs PW Doppler

• CW Doppler uses continuous transmission and reception with two dedicated transducer elements: one solely sends, the other solely receives.
• CW Doppler can only create waveforms (no anatomical images).
• PW Doppler uses pulsed transmission with the same piezoelectric crystals that alternate rapidly between sending and receiving; pulses are emitted and echoed signals are analyzed to obtain depth information.
• In PW, the same crystals are used for sending and receiving, enabling range resolution (sensitive region limited to a specific depth range). CW has no range resolution and a sensitive region along the entire beam path.

Pulse Concepts and Structure

• A pulse is a collection of cycles that travel together and has a beginning and an end; the pulse moves as a single unit.
• A pulse consists of two components:
  • ON-TIME = transmit time = talking time
  • OFF-TIME = receive time = listening time
• Talking and listening relate to the pulse’s on-time and off-time.

Talking and Listening Parameters

• Pulse Duration (PD) is the actual time from the start of the pulse to the end of that pulse (excludes listening time).
• Listening Time is the duration the system is listening between pulses.
• Pulse Repetition Period (PRP) is the total time from the start of one pulse to the start of the next pulse; it includes both talking and listening times.

Five Key Pulsed-Sound Parameters

• PD (Pulse Duration)
• PRP (Pulse Repetition Period)
• PRF (Pulse Repetition Frequency)
• DF (Duty Factor)
• SPL (Spatial Pulse Length)
• Each parameter is described by a figure in the source material as describing pulsed sound.

Pulse Duration (PD)

• PD = time from the start of the pulse to its end; does not include listening time.
• Units: any unit of time (s, ms, μs).
• Determined by the SOURCE; cannot be changed by the Sonographer.
• PD is the talking time of the pulse.
• PD = (# of cycles in the pulse) × (period of each cycle).
• Formula representations:
  • $PD = N<em>{cycles} imes T</em>{cycle}$
  • Since T{cycle} = rac{1}{f}, also PD = rac{N{cycles}}{f}
• PD is directly proportional to the number of cycles in the pulse and to the cycle period, and inversely proportional to the frequency.
• Long-duration pulses come from many cycles or long-period cycles.
• Short-duration pulses come from few cycles or short-period cycles. High-frequency transducers have shorter PDs due to shallower depths of penetration (less need for deep travel).

Spatial Pulse Length (SPL)

• SPL is the distance (or length) of one pulse.
• Unit: any distance unit.
• Determined by the SOURCE and the MEDIUM.
• SPL = (#cycles in the pulse) × (wavelength).
• Since wavelength λ = c / f (c is the propagation speed in tissue), SPL is directly proportional to the number of cycles and wavelength, and inversely proportional to frequency: higher frequency → shorter SPL.

Pulse Repetition Period (PRP)

• PRP is the time from the start of one pulse to the start of the next one; it includes both talking and listening time.
• Unit: time (s, ms, μs).
• Determined by the sound source, not by the medium.
• PRP increases with imaging depth: deeper imaging requires more time for echoes to return.

Pulse Repetition Frequency (PRF)

• PRF is the number of pulses transmitted into the body each second.
• Unit: Hz.
• Typical values: $1{,}000 ext{ Hz} ext{ to } 10{,}000 ext{ Hz}$.
• Determined by the sound source, not the medium.
• PRF is inversely related to DEPTH: as depth increases, PRF decreases.
• High-frequency transducers (shorter depth) tend to support higher PRF; low-frequency transducers (deeper imaging) have lower PRF.

Depth and Imaging Depth Effects on PRF/PRP

• PRF ↑, DEPTH ↓ for deeper tissues; PRF ↓, DEPTH ↑ for shallower tissues (and higher frequency transducers have shallower penetration).
• PRP and PRF are reciprocal: $PRP imes PRF = 1$ (reciprocals).
• PRP ↑ → PRF ↓; PRP ↓ → PRF ↑.
• Imaging depth adjustments by the Sonographer directly change the OFF (listening) time, while the ON (talking) time is not typically changed.
• PRF can be changed by changing imaging depth and thus the corresponding off time.
• For this reason, deep imaging has longer PRP and lower PRF; shallow imaging has shorter PRP and higher PRF.

Duty Factor (DF)

• DF = fraction of time the system is transmitting (talking).
• Unit: dimensionless (expressed as a percentage when multiplied by 100).
• Determined by the SOURCE; can be changed by the Sonographer.
• Typical clinical imaging range: $DF ext{(clinical)} <br /> ightarrow 0.002 ext{ to } 0.005 ext{ or } 0.2 ext{\% to } 0.5\%.$
• Interpretation: approximately 0.2% transmitting and 99.8% listening for anatomical imaging.
• The maximum DF for continuous wave (CW) is 1.0 (100%).
• CW uses two crystals (one always transmitting, one always receiving);
  minimum DF is 0% (no pulse; machine is off).
• For PW imaging, DF can be very small; typical anatomical imaging DF ~0.2% (listening ~500 times longer than transmitting).

Duty Factor Formula and Practical Implications

• DF = (PD) / (PRP) × 100% (i.e., as a percentage).
• Relationship indicators:
  • Shallow Imaging: shorter PRP, higher PRF, higher DF.
  • Deep Imaging: longer PRP, lower PRF, lower DF.
  • In practice, DF reflects the proportion of time spent transmitting vs listening; less listening implies higher DF; more listening implies a lower DF.

Summary of Key Practical Points

• CW Doppler vs PW Doppler:
  • CW: continuous transmission and reception, two separate transducers, cannot form images, used for Doppler waveform analysis only.
  • PW: pulsed transmission with same crystals; allows range-specific sampling (range cell) and Doppler waveform acquisition with depth resolution.
• Pulse structure fundamentals:
  • A pulse contains on-time (transmitting) and off-time (listening).
  • The duration and repetition of pulses determine PD, PRP, PRF, and DF.
• Core relationships:
  • PD = Ncycles × Tcycle = N_cycles / f.
  • SPL = Ncycles × λ = Ncycles × (c / f).
  • PRP = PD + Listening Time; PRF = 1 / PRP; PRP × PRF = 1.
  • DF = PD / PRP × 100%.
• Depth, frequency, and imaging quality:
  • Higher frequency → shallower depth, shorter PD and SPL per pulse, higher PRF and DF at shallow depths.
  • Deeper imaging → longer PRP, lower PRF, lower DF; more listening time relative to transmitting.
• Practical imaging notes:
  • DF values in clinical PW imaging are typically very small (0.2% – 0.5%), indicating that most of the cycle is spent listening.
  • In CW, DF can reach 100% because there is continuous transmission.
  • Adjusting imaging depth changes off-time (listening) and thus PRP, PRF, and DF, while on-time (transmit) remains constant for PW.

Quick Reference Formulas (LaTeX)

• Pulse Duration: $PD = N<em>{cycles} \times T</em>{cycle} = \frac{N_{cycles}}{f}$
• Spatial Pulse Length: $SPL = N<em>{cycles} \times \lambda = N</em>{cycles} \times \frac{c}{f}$
• Pulse Repetition Period: $PRP = PD + \text{Listening Time}$
• Pulse Repetition Frequency: $PRF = \frac{1}{PRP}$ (thus $PRP \times PRF = 1$)
• Duty Factor: $DF = \frac{PD}{PRP} = \text{(PD/PRP)} \times 100\%$
• Wavelength: $\lambda = \frac{c}{f}$
• Speed of sound in tissue: $c \approx 1540\ \text{m/s}$ (typical tissue value)

Reference Notes

• PRF values commonly range from $10^3 \text{ Hz}$ to $10^4 \text{ Hz}$ depending on depth and transducer.
• Typical anatomical imaging DF is around $0.2\%$ (≈ 0.002) to $0.5\%$ (≈ 0.005).
• Depth changes primarily affect OFF time; ON time is fixed by transducer pulse characteristics.