6.5MedicalStretch

Ultrasound and MRI Imaging

A pregnancy scan uses nothing but reflected sound waves; an MRI scanner uses no radiation at all, only a powerful magnetic field and radio pulses aimed at your own hydrogen atoms. Two of medicine’s most valuable imaging tools, and neither one relies on anything as familiar as visible light or X-rays.

45 min Video by DrPhysicsA Module 6.5 Medical imaging

Ultrasound and Magnetic Resonance Imaging — A Level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Describe how a piezoelectric transducer generates and detects ultrasound
Define acoustic impedance and use $Z = ρ c$
Explain the pulse-echo technique for ultrasound imaging
Describe the basic principle of magnetic resonance imaging (MRI)

Producing and detecting ultrasound

$Ultrasound$ is sound of frequency above the range of human hearing, typically 1–15 MHz for medical imaging. A $piezoelectric transducer$ — a crystal that mechanically deforms when a p.d. is applied across it, and vice versa — both emits ultrasound pulses (driven by an alternating p.d.) and detects returning echoes (which generate a small p.d. as the crystal is deformed by the returning wave).

Tip — The same physical crystal does both jobs: converting electrical energy into a sound pulse, and converting a returning sound echo back into an electrical signal.

Acoustic impedance and reflection at boundaries

Every material has an $acoustic impedance$ , $Z$ , depending on its density and the speed of sound within it. At a boundary between two materials of different acoustic impedance, some of an ultrasound pulse reflects and some transmits — a bigger mismatch in $Z$ produces a stronger reflection.

Z = ρ c

Acoustic impedance; ρ = density, c = speed of sound in the medium.

1Use

Z = ρ c

Z = 1060 \times 1540

Answer

Z \approx 1.63 \times 1 0^{6}

kg m⁻² s⁻¹

Tip — Air has a vastly different acoustic impedance from human tissue, so without a coupling gel to eliminate the air gap between the transducer and skin, almost all the ultrasound would reflect straight back before ever entering the body.

The pulse-echo technique

A transducer emits a short ultrasound pulse, then listens for echoes reflected from boundaries between different tissues within the body. Knowing the speed of sound in tissue and the time delay before an echo returns lets the depth of each reflecting boundary be calculated, building up a full image from many such measurements.

1The pulse travels to the boundary AND back, so the one-way travel time is half the total:

t = \frac{26 \times 1 0 ^{- 6}}{2} = 13 \times 1 0^{- 6}

2Depth:

d = c t = 1540 \times 13 \times 1 0^{- 6}

Answer

d \approx 0.020

m (2.0 cm)

Tip — Always halve the total round-trip time before calculating depth — a very common mistake is using the full echo time as if it were a one-way journey.

Magnetic resonance imaging (MRI)

MRI exploits the fact that hydrogen nuclei (single protons), abundant throughout the body’s water and fat, behave like tiny magnets. A strong external magnetic field aligns these nuclei; a radio-frequency pulse then knocks them out of alignment, and as they relax back into alignment, they emit their own radio-frequency signal, which is detected and used to build a detailed image of soft tissue.

Crucially, MRI uses no ionising radiation at all — unlike X-ray imaging — making it particularly valuable for repeated scans and for imaging soft tissue, where it typically achieves better contrast than X-ray or ultrasound imaging.

Tip — The single biggest advantage of MRI over X-ray imaging is the complete absence of ionising radiation, though MRI scanners are typically far more expensive and scans take considerably longer.

Equation recap

Z = ρ c

Acoustic impedance.

d = \frac{c t}{2}

Depth from pulse-echo time (t = round-trip time).

Common mistakes to avoid

Using the full round-trip echo time as if it were the one-way travel time to the boundary.

Always halve the measured time first — the pulse travels to the boundary AND back before the echo is detected.

Believing ultrasound reflects strongly at every tissue boundary equally.

The strength of reflection depends on the DIFFERENCE in acoustic impedance between the two tissues — similar tissues reflect very little.

Assuming MRI uses ionising radiation, like X-rays.

MRI uses only magnetic fields and radio-frequency pulses — no ionising radiation is involved at all.

Key takeaways

A piezoelectric transducer both emits ultrasound pulses and detects returning echoes.
Acoustic impedance Z=ρc; reflection strength at a boundary depends on the impedance mismatch.
Pulse-echo timing (halving the round-trip time) gives the depth of internal boundaries.
MRI aligns hydrogen nuclei with a strong magnetic field, then detects radio-frequency signals emitted as they relax after a disturbing RF pulse — with no ionising radiation involved.

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Ultrasound and MRI Imaging

45 min Video by DrPhysicsA Module 6.5 Medical imaging