Ultrasound physics - Module 2

Pulsed ultrasound emits discrete bursts to determine depth; continuous wave (CW) is mainly used in cardiac ultrasound and transmits continuously.

A-mode (amplitude mode): one-dimensional, height of peak equals signal strength; largely obsolete except in ophthalmoscopy and some cardiology.
- Equation cues: peak height proportional to echo amplitude.
B-mode (brightness mode): image built from successive scan lines; brightness reflects echo strength.
M-mode (motion mode): time-based display of motion, used for cardiac or fetal heart tracing.

Types: Power Doppler, Color Doppler, Pulsed-Wave Doppler (PW), Continuous-Wave Doppler (CW).
PW and CW measure velocity; CW provides higher velocity accuracy but cannot give depth information by itself.
CW is predominant in cardiac applications; many probes allow CW Doppler with a concurrent B-mode image; some CW-only probes exist.

Pulsed emission: short pulses typically about 2–3 cycles long.
Pulse duration (PD) ≈ 3 × period; period T = 1/f; so $PD \,\approx\, \frac{3}{f}$ and $T = \frac{1}{f}$ .
Transducers rely on the piezoelectric effect: apply voltage -> crystal expands/contracts to generate sound; reverse effect converts echoes to electrical signal.
In B-mode, short pulses are used; analogy: ringing a bell with a hammer.
Matching layer and gel reduce impedance mismatch and air gaps to improve transmission.

The operating frequency is set by the crystal thickness: $t = \frac{\lambda}{2}$ ; thinner crystals yield higher frequencies.
Wavelength: $\lambda = \frac{c}{f}$ ; speed of sound in tissue denoted by $c$ .
Behind the crystal is damping (backing) material to shorten pulses, improving axial resolution but broadening the beam’s frequency content.
Backing yields a wider bandwidth; CW transducers typically have no backing and produce a narrow, single frequency beam.

Bandwidth is the range of frequencies in the transmitted beam.
Q factor: $Q = \frac{f_{\text{center}}}{\text{Bandwidth}}$
- Low Q with wide bandwidth is desirable for short pulses and better resolution; CW has high Q (narrow bandwidth).
Bandwidth is inversely related to pulse duration: $\text{Bandwidth} \approx \frac{1}{\text{PD}}$
Spatial Pulse Length (SPL): $\text{SPL} = c \ times \ PD = n \ times \ \lambda$
- Higher PD -> longer SPL -> worse axial resolution; shorter PD -> better axial resolution.
Axial resolution ≈ (\frac{\text{SPL}}{2}).
Higher frequency gives shorter wavelengths and better resolution but reduced penetration due to tissue attenuation.

Axial resolution: determined by SPL; better with short PD and wide bandwidth.
Lateral resolution: determined by beam width; best at focus; degrades outside focal zone.
Contrast resolution: ability to differentiate subtle echogenic differences; influenced by dynamic range and compression.
Temporal resolution: ability to visualize motion over time; improved by higher frame rates.
Harmonic imaging relies on broadband (high bandwidth) transducers.

PRF: number of emitted pulses per second; limited by the need to receive echoes from the deepest region before the next pulse.
PRF max: $\text{PRF}<em>{\max} = \frac{c}{2d</em>{\max}}$ where $d_{\max}$ is the maximum imaging depth.
Deeper imaging reduces PRF and frame rate; shallow imaging allows higher PRF/frame rate.
PRP: time from the start of one pulse to the start of the next pulse; $\text{PRP} = \frac{1}{\text{PRF}}$ (inverse relationship).
Frame rate: number of frames displayed per second; related to PRF and lines per frame.
Time to acquire one line: $\frac{2d}{c}$ ; for multiple lines (n lines per frame): frame rate limit is roughly $\text{Frame Rate}_{\max} = \frac{c}{2 d n}$ .
Relationship: increasing depth or lines reduces the achievable frame rate, lowering temporal resolution.
Duty factor (DF): $\text{DF} = \frac{\text{PD}}{\text{PRP}}$ ; typical ultrasound spends most time listening, i.e., low DF during emission (often ~0.1% emission).

Linear array: many elements (≈256–512) forming multiple scan lines; high-frequency; good for superficial structures (musculoskeletal, thyroid, breast, testes).
Convex/Curved array: curved head; trapezoidal field; wider view with depth; reduced lateral resolution with depth.
Phased array: small footprint; good for imaging through ribs; steering and focusing capabilities.
Matrix arrays: advanced 2D arrays for multi-planar imaging; future/improving technology.
Other probes: Pediatric/probes (e.g., Pedof), continuous-wave Doppler non-imaging probes, intracardiac probes, intravascular ultrasound probes.

Resolution trade-offs: higher frequency improves resolution but reduces penetration; damping reduces pulse duration but broadens bandwidth.
Frame rate and temporal resolution improve with shallower depth and fewer lines; essential for real-time motion.
Compression and dynamic range alter contrast resolution; choices depend on clinical task.
Continuity of CW and PW imaging: many systems run CW Doppler alongside PW/B-mode imaging on the same or separate probes.
Always recall Nyquist considerations (to be discussed later).