Medical Imaging

Physical foundations of radiography, tomography, ultrasound, and magnetic resonance imaging.

Conceptual context

Medical imaging converts invisible physical interactions into anatomical or functional maps. In radiography and tomography, a detector records how a beam changes after crossing tissue. Ultrasound records echoes generated at acoustic interfaces. Magnetic resonance detects signals from spins precessing in a field. Contrast is not merely a display effect: it begins because tissues alter energy, phase, amplitude, or travel time differently. The central task is therefore to connect a measured signal with traveled thickness and material properties without confusing signal, dose, brightness, and diagnosis.

🟢 Essential level

In radiography, thicker or more attenuating tissue leaves less $I$ than thinner or weakly attenuating tissue. The difference between signals creates contrast only when the detector can separate it from noise. $I0$ provides a reference, while $T$ states what fraction survives the path. In ultrasound, contrast mainly appears when $Z$ changes across an interface: a larger mismatch returns a stronger echo. In magnetic resonance, $B0$ sets $fL$, but final brightness also depends on sequence timing and relaxation. Each modality observes a different physical property. An image is therefore not a direct photograph of the interior. It is a reconstruction built from a physical model, instrument calibration, sampled signals, and acquisition choices.

The same anatomy can therefore look very different across modalities because each instrument asks a completely different physical question of the tissue, and reading an image well always means knowing exactly which question was actually asked and how the answer was turned into a picture.

🔵 Formal level

Basic formulas

For a narrow beam crossing homogeneous material, the basic relation among $I0$, $I$, $\mu$, and $x$ is:

Exponential attenuation

The normalized surviving signal is written with:

Relative transmission

This ratio is always dimensionless and stays between zero and one as long as the system remains passive, with no additional electronic amplification of the signal.

Real student questions

Does more attenuation always mean a better image? No. It may increase tissue separation but reduce signal and worsen noise or required dose.

Is display brightness equal to $I$? Not directly. Brightness depends on detector response, reconstruction, and windowing.

Does negative $HU$ mean negative attenuation? No. It means attenuation below the water reference.

Does large $Z$ always create a strong echo? No. Echo strength depends on the difference between two impedances.

Does MRI use ionizing radiation? No. It uses $B0$, radiofrequency, and gradients.

Why do modalities show different structures? They encode different physical properties such as attenuation, reflection, travel time, phase, frequency, and relaxation.

Final synthesis

Medical images arise when tissue properties modify measurable signals. Thickness and attenuation control $T$, acoustic mismatch controls echoes, and field strength controls resonance. Sound interpretation requires equations, limits, noise, graph shape, and reconstruction to be read together without turning one physical signal into a clinical conclusion.