Computed Tomography (CT) Physics and Dose Metrics

Computed Tomography (CT) revolutionized diagnostic medicine by providing three-dimensional cross-sectional imaging of the human body. By rotating a highly collimated X-ray tube and an opposing detector array around a patient, CT scanners measure projection data at multiple angles. Specialized mathematical reconstruction algorithms convert these raw attenuation projections into quantitative gray-scale maps of anatomical tissue density.

This article outlines the physics of CT imaging, Hounsfield Unit scaling, scan acquisition parameters, and standard clinical CT dose metrics.

1. Hounsfield Units (CT Numbers)

Each pixel in a reconstructed CT image is assigned a value in Hounsfield Units (HU), also known as the CT Number. The HU is a normalized measurement of the linear attenuation coefficient (μ) of the tissue within that voxel relative to the attenuation coefficient of water (μ_w):

Because the attenuation coefficient varies with X-ray energy (beam spectrum), referencing the attenuation to water ensures that the CT numbers remain relatively stable across different scanner voltages (kVp).

By definition: * Water: HU = 0 * Air: HU = -1000 (since μ_{air} ≈ 0) * Fat: HU ≈ -120 to -80 * Soft Tissue (muscle, organs): HU ≈ +30 to +80 * Bone: HU ≈ +300 to +3000 (highly dense cortical bone)

2. Helical Scanning and Pitch

In modern multidetector CT (MDCT) scanners, the patient couch moves continuously through the rotating gantry. This results in a helical (spiral) acquisition path.

The primary geometric parameter of helical scanning is the Pitch:

Where: * I: The table travel distance in one 360^\circ rotation of the gantry. * N: The number of detector rows. * T: The width of a single detector row.

Clinical Impact of Pitch: * **Pitch = 1.0**: The table feed matches the beam width. There is no overlap or gap in the helical path. * **Pitch < 1.0**: The table feed is slower than the beam width. The scan path overlaps, resulting in higher image quality (lower noise) but a higher radiation dose to the patient. * **Pitch > 1.0**: The table feed is faster than the beam width. The scan path has gaps (interpolated by software), resulting in faster scan times and lower dose, but higher noise and potential helical artifacts.

3. Image Reconstruction Algorithms

The projections collected by the detector are reconstructed using: * Filtered Backprojection (FBP): A fast, analytical method that backprojects the filtered attenuation data onto a grid. It is computationally efficient but suffers from noise and streak artifacts in low-dose scans. * Iterative Reconstruction (IR): Reconstructs images through an optimization loop that compares actual projections with simulated projections from a mathematical model. IR reduces noise and artifacts, allowing diagnostic images to be acquired at up to 50\% lower dose compared to FBP.

4. CT Radiation Dose Metrics

CT scans deliver higher radiation doses compared to projection radiography. To monitor and optimize patient safety, standardized dose indices have been defined:

Computed Tomography Dose Index (CTDI) CTDI represents the average dose in a single slice. It is measured using a $100\text{ mm}$ long pencil ionization chamber inserted into standard cylindrical PMMA (acrylic) phantoms (head phantom: $16\text{ cm}$ diameter; body phantom: $32\text{ cm}$ diameter). * **$\text{CTDI}_{100}$**: The raw measurement in the phantom. * **Weighted CTDI ($\text{CTDI}_w$)**: Combines center ($\text{CTDI}_{100}^{\text{center}}$) and peripheral ($\text{CTDI}_{100}^{\text{periph}}$) readings to account for the dose gradient across the patient: $$\text{CTDI}_w = \frac{1}{3}\text{CTDI}_{100}^{\text{center}} + \frac{2}{3}\text{CTDI}_{100}^{\text{periph}}$$

Volume CTDI ($\text{CTDI}_{\text{vol}}$) $\text{CTDI}_{\text{vol}}$ accounts for the helical pitch. It is the primary indicator of scanner output:

If the pitch is < 1.0 (overlapping scans), the CTDI_{vol} increases.

Dose Length Product (DLP) DLP represents the total energy deposited in the patient during the scan and is proportional to overall stochastic risk (cancer risk):

DLP is measured in units of mGy·cm. The effective dose (E in mSv) can be estimated using tissue-specific conversion factors (k):

Size-Specific Dose Estimate (SSDE) $\text{CTDI}_{\text{vol}}$ is a scanner output metric measured in standard acrylic phantoms; it does not represent the actual absorbed dose to an individual patient. * A small patient scanned with a given $\text{CTDI}_{\text{vol}}$ absorbs a higher dose than the phantom indicates. * A large patient absorbs a lower dose. * **SSDE** (detailed in AAPM Report 204/220) applies size-dependent correction factors based on the patient's effective diameter (measured on the CT localizer image) to estimate the true absorbed dose.

Conclusion

Computed Tomography physics requires a balance of geometric design, mathematical reconstruction, and dose optimization. By understanding Hounsfield scaling, optimizing scan pitch, and monitoring dose indices like CTDI_{vol} and DLP, medical physicists ensure that diagnostic scans are performed with high clinical efficacy at minimal radiation hazard, adhering to the core tenets of radiation safety.