Medical Imaging Physics — X-rays, Ultrasound and MRI

Introductory College⏱ 11 min readApplied Physics

Medical imaging physics: how X-rays, CT, ultrasound and MRI work — photons, sound echoes, and magnetic resonance.

Quick answer

Medical imaging turns physics into pictures: X-rays cast photon shadows through tissue, ultrasound maps echo times of sound pulses, and MRI reads radio signals from hydrogen protons nudged by giant magnets.

$I = I_0 e^{-\mu x}\quad\text{(X-ray attenuation)}$

Unit: radiation dose: sievert (Sv); ultrasound: MHz frequencies

Example: A 120 kVp X-ray beam is attenuated ~10× more by bone than soft tissue — that contrast difference is the entire image.

What you will learn

Explain X-ray contrast via differential absorption
Describe CT as multi-angle X-ray reconstruction
Explain ultrasound echo timing and Doppler blood flow
Describe MRI via proton magnetic resonance (no ionizing radiation)

X-rays: shadows of dense tissue

X-rays are photons with wavelengths around $10^{-10}\ \mathrm{m}$ — thousands of times shorter than visible light, and energetic enough to knock electrons out of atoms (ionizing radiation). Fired through the body, they are absorbed more by dense, high-atomic-number material (bone, teeth) and less by soft tissue:

$I = I_0 e^{-\mu x}$

where $\mu$ is the attenuation coefficient and $x$ the thickness. The detector records the surviving photons: bone casts a dark shadow on film (white on modern displays), tissue a faint one. Contrast is everything — radiologists sometimes add contrast agents (iodine, barium) to make soft structures absorb differently.

CT: X-rays from every angle, computed into 3D

A CT scanner rotates an X-ray source and detectors around the patient, collecting hundreds of 1D shadow profiles from every angle. Mathematics (tomographic reconstruction, essentially the inverse Radon transform) then computes the 2D slice that could have cast all those shadows.

Stack the slices and you get a 3D volume — bone, organs, vessels — viewable from any angle. The price: many X-ray exposures, so CT doses exceed plain X-rays by 100× or more. Used when the diagnostic payoff justifies it: trauma, cancer staging, surgical planning.

Ultrasound: sonar for the body

Ultrasound skips radiation entirely. A transducer emits sound pulses at 2–15 MHz and listens for echoes — exactly like sonar. Echo time gives depth ( $d = v\Delta t/2$ , with $v \approx 1540\ \mathrm{m/s}$ in tissue); echo strength maps tissue boundaries.

Moving blood adds the Doppler shift: echoes from approaching red cells return at higher frequency. The shift measures flow velocity — cardiologists watch it live to find narrowed valves and blocked arteries. No ionizing radiation, real-time, portable: the obstetrician's and emergency physician's workhorse.

MRI: magnets, protons and radio echoes

MRI's magnet — typically 1.5 to 3 tesla, ~30,000–60,000× Earth's field — aligns the magnetic moments of hydrogen protons throughout the body (you are mostly water, so protons are everywhere). A radio-frequency pulse tips them out of alignment; as they relax back, they broadcast faint radio signals.

Gradient coils make the field vary slightly across the body, so each location broadcasts at a slightly different frequency — position encoded in frequency. Different tissues relax at different rates (T1, T2), giving exquisite soft-tissue contrast: brain, cartilage, tumors.

Crucially: no ionizing radiation. The tradeoffs are cost, time (minutes per scan), noise, and the magnet's absolute ban on ferromagnetic objects near it.

Key idea

Each modality is a different physics question: X-ray asks 'what absorbs photons?', ultrasound asks 'what echoes sound?', MRI asks 'where are the protons and how fast do they relax?'. No single image answers everything.

Variables and units

Symbol	Name	Unit	Meaning
$I$	Attenuated intensity	W/m²	X-ray beam intensity after tissue
$μ$	Attenuation coefficient	1/m	Tissue absorption strength
$f$	Sound frequency	MHz	Ultrasound frequency
$B₀$	MRI field	tesla (T)	Magnetic field strength

Common mistakes

✗ MRI uses radiation like X-rays do.

MRI uses strong magnetic fields and radio waves — no ionizing radiation at all. That is why it is preferred for repeated soft-tissue imaging, though the magnet makes it incompatible with some implants.

✗ Ultrasound can see through anything, including bone.

Bone reflects ultrasound strongly, which is why sonographers work around it. Ultrasound excels at soft tissue, fluids, and blood flow — each modality has its window.

✗ A clearer image always justifies more radiation.

Radiology follows ALARA — as low as reasonably achievable. Dose is minimized while keeping diagnostic quality, especially for children and repeated scans.

Real-world applications

X-ray imaging diagnoses fractures and dental problems in seconds.
CT scans build 3D images from hundreds of X-ray slices for detailed diagnosis.
Ultrasound safely images fetuses and measures blood flow with Doppler shifts.
MRI maps soft tissues like the brain and joints with no ionizing radiation.

Frequently asked questions

How does an X-ray image work?

X-rays are high-energy photons that pass through soft tissue but are absorbed by dense bone and teeth. A detector (or film) records the shadows: dense structures appear white, soft tissue gray, air black.

How does ultrasound see inside the body?

Ultrasound sends high-frequency sound pulses into the body and listens for echoes. Timing the echoes gives depth; the Doppler shift of moving blood reveals flow speed and direction.

How does an MRI work?

MRI uses powerful magnets to align the magnetic moments of hydrogen protons in your body, then radio pulses tip them; as they relax back, they emit signals that encode position and tissue type. No ionizing radiation involved.

Is medical imaging radiation dangerous?

X-ray/CT use ionizing radiation (real, but doses are kept minimal — ALARA: as low as reasonably achievable). Ultrasound and MRI use sound and magnetic fields with no ionizing radiation.