CTDI Measurement and Phantom References

Physics of CT Dose Distribution: Rotational Symmetry vs. Planar Geometry

Radiation dose distribution in computed tomography differs fundamentally from conventional projection radiography. In planar radiography, a stationary, unidirectional x-ray beam enters the patient from one side and is attenuated exponentially through the anatomical tissues, producing an entrance-to-exit dose gradient that depends on beam energy, object thickness and scatter. In computed tomography, however, the x-ray tube rotates $360^\circ$ around the patient's longitudinal z-axis, creating a circumferential exposure pattern; actual symmetry depends on the object and modulation.

Cross-Sectional Dose Gradients Across Phantom Geometries

The radial dose distribution within the scan plane is heavily influenced by the cross-sectional diameter of the absorbing medium:

1. Standard $32\text{ cm}$ Body Phantom (Adult Torso):
   • In an adult body phantom, x-ray photons traversing toward the center experience significant Compton scattering and photoelectric attenuation through thick layers of polymethyl methacrylate (PMMA).
   • Consequently, the peripheral dose can be approximately $2\text{ to }3\text{ times the central value}$ under typical measurement conditions ($D_{\text{periphery}} \approx 2\text{--}3 \times D_{\text{center}}$).
   • The radial dose profile forms a distinct "U-shaped" or cupped curve with high peaks at the periphery and a deep nadir at the central axis.
2. Standard $16\text{ cm}$ Head Phantom (Adult Head & Pediatric Body):
   • In a $16\text{ cm}$ cylindrical phantom, the distance from the outer surface to the central axis is only $8\text{ cm}$.
   • Due to the smaller radius, beam attenuation is far less pronounced, and the beam hardening from rotational exposure balances internal scatter.
   • As a result, the dose distribution is relatively uniform across the entire cross-section, with central and peripheral values often much closer than in the body phantom.

Longitudinal z-Axis Scatter Profiles

Along the patient longitudinal axis ($z$-axis), the dose profile from a single axial rotation ($D(z)$) is not a perfect geometric rectangle corresponding to the nominal collimated slice thickness. Instead, pre-patient collimation penumbra, focal spot blooming, and internal Compton scatter generate extended radiation tails that spread several centimeters beyond the planned imaging section.

---

The Historical Precursor: Multiple Scan Average Dose (MSAD)

In early sequential (axial or "step-and-shoot") scanning, acquiring multiple contiguous or overlapping slices caused the scattered radiation tails from adjacent scans to accumulate in the central slice plane. Medical physicists developed the Multiple Scan Average Dose (MSAD) to describe the equilibrium dose at the center of an extended multi-slice examination series.

Mathematical Formulation of MSAD

MSAD is the average equilibrium dose over a table increment in a sufficiently long series of identical axial scans. It includes overlapping dose-profile tails. For constant technique and increment I, MSAD is related to the full dose-profile integral divided by I, or to a full-integral CTDI multiplied by nominal collimation divided by I. It is not the peak dose of a single rotation divided by pitch. Increasing overlap raises dose when other factors are fixed. CTDI100 samples only a finite integration length and may underestimate long scatter tails, especially with wide beams; specialized measurements are needed for those geometries.

Standard PMMA Phantoms & The 100 mm Pencil Ionization Chamber

To standardize CT dosimetry worldwide, the Food and Drug Administration (FDA) and the International Electrotechnical Commission (IEC) established the Computed Tomography Dose Index (CTDI) methodology, utilizing specialized phantoms and ionization instrumentation:

1. Polymethyl Methacrylate (PMMA) Phantoms

• Material: Cast acrylic (PMMA, Lucite), used as the standardized measurement material rather than an exact model of every tissue ($1.19\text{ g/cm}^3$ density).
• Head / Pediatric Body Phantom: $16\text{ cm}$ outer diameter cylinder, $14\text{ to }15\text{ cm}$ in length.
• Adult Body Phantom: $32\text{ cm}$ outer diameter cylinder, $14\text{ to }15\text{ cm}$ in length.
• Bore Hole Configuration: Each phantom contains five cylindrical holes parallel to the z-axis: one central hole along the rotational axis, and four peripheral holes located $90^\circ$ apart, centered exactly $1.0\text{ cm}$ below the outer acrylic surface. Unused holes are filled with matching PMMA acrylic rods.

2. The $100\text{ mm}$ Pencil Ionization Chamber

• Physical Dimensions: A slender cylindrical ionization chamber with an active measurement length of exactly $100\text{ mm}$ ($10\text{ cm}$) and a nominal active volume of approximately $3\text{ cm}^3$.
• Function: Connected to a calibrated electrometer, the chamber integrates the total electrical charge liberated by ionizing scatter and primary photons over its entire $100\text{ mm}$ active length during a single axial rotation of the gantry.

---

Match the displayed index to its reference phantom

The dose report must identify whether a displayed CTDIvol refers to a 16 cm or 32 cm phantom. Pediatric body protocols may use either reference under the manufacturer's implementation; age alone does not identify the phantom. Two displayed values calculated with different reference phantoms cannot be compared directly as though they measure the same patient exposure. Verify the reference before calculating size-specific dose or interpreting a dose alert.

Reference: AAPM CT dosimetry report.