CT Imaging with 3D X-Ray Stacks

CT rotates an X-ray source around the body and rebuilds a 3D stack where each voxel reports density in Hounsfield units.

Why Does This Exist?

X-ray overlaps organs onto one plane. Surgeons need exact 3D boundaries for organ segmentation. CT spins source plus detector, collects hundreds of projections, and inverts them into a volume $512 \times 512 \times 500$ at $1$ mm spacing. Input is a helical acquisition; output is Hounsfield units where air is $-1000$ , water $0$ , bone near $+1000$ .

Think of It Like This

Slicing a loaf after X-raying every angle

You photograph a loaf from $500$ angles, then compute what each crumb must hold to explain all photos. The result slices cleanly: crust bright, air holes dark, raisins mid-gray. One photo alone smears raisins across crumbs.

Projections are photos and Hounsfield units are crumb densities. The analogy stops at dose: more angles sharpen but irradiate.

How It Actually Works

Filtered back-projection or iterative solvers invert $p = A\mu$ for projections $p$ and volume $\mu$ . Helical pitch sets slice overlap; $1$ mm slices suit chests. Contrast timing matters: arterial phase near $30$ s lights arteries, venous near $70$ s lights liver lesions. Windowing picks tissue: lung $[-1000, 200]$ , soft tissue $[-160, 240]$ .

Worked example

A liver lesion of $40$ HU sits in $60$ HU liver on venous phase, contrast $20$ HU above noise $12$ HU. At $1$ mm slices the $2$ cm lesion spans $20$ slices with volume $4.2$ mL. Arterial phase shows only $8$ HU contrast and hides it. That timing gap is why protocols fix the clock, not just the dose.

Watch Out For

Metal streaks faking fractures

Dental fillings starve detectors, so back-projection draws bright streaks across the jaw. The symptom is false fracture lines on axial cuts. Flag slices near metal and confirm on coronal views before calling.

The Quick Version

CT inverts hundreds of projections into a calibrated 3D volume.
Hounsfield units anchor tissue: air $-1000$ , water $0$ , bone high.
Contrast phase decides which lesions appear; timing is clinical.
Do not read soft tissue on lung windows; re-window per organ.
Metal streaks mimic fractures near fillings and implants.