Topics covered in this article include:

• Introduction
• CT or Hounsfield Numbers
• Sensitometry Targets
  •  
    • Nominal Material Formulation and Specific Gravity
    • Electron Density and Relative Electron Density
• Linearity Plot
• Sensitometry Header Information
• Measured CT Numbers
• Contrast Scale
• Residual Plot
• Sensitometry Plot
• Effective Energy
• Mass Attenuation Coefficient Table

Introduction

Sensitometry information is given for the following Catphan® models: 500, 503, 504, 600, 604, 700.

CT or Hounsfield Numbers

Users of CT systems are often surprised when the CT number of a given tissue or substance is different from what they expect from previous experience. These differences do not usually indicate problems of a given CT scanner, but more likely arise from the fact that CT numbers are not universal. They vary depending on the particular energy, filtration, object size and calibration schemes used in a given scanner.

One of the problems is that we are all taught that the CT number is given by the equation: CT# = k(µ - µ_w)/µ_w, where k is the weighting constant (1000 is for Hounsfield Scale), µ is the linear attenuation coefficient of the substance of interest, and µ_w is the linear attenuation coefficient of water. Close review of the physics reveals that although the above equation is true to first order, it is not totally correct for a practical CT scanner. In practice, µ and µ_w are functions of energy, typical x-ray spectra are not monoenergetic but polychromatic, and a given spectrum emitted by the tube is “hardened” as it is transmitted (passes) through filter(s) and the object, finally reaching the detector. More accurately, µ=µ(E), a function of energy. Therefore: CT#(E) = k(µ(E) - µ_w(E))/µ_w(E)

Because the spectrum is polychromatic we can at best assign some “effective energy” Ê to the beam (typically some 50% to 60% of the peak kV or kVp). Additionally, the CT detector will have some energy dependence, and the scatter contribution (dependent on beam width and scanned object size, shape, and composition) may further complicate matters. Although the CT scanner has a built in calibration scheme that tries to correct for beam hardening and other factors, this is based on models and calibration phantoms that are usually round and uniformly filled with water, and will not generally match the body “habitus” (size, shape, etc.). The situation is really so complicated that it is remarkable that tissue CT numbers are in some first order ways “portable”!

In light of the above we can examine a parameter of CT performance, the “linearity scale”, as required by the FDA for CT manufacturer’s performance specifications. The linearity scale is the best fit relationship between the CT numbers and the corresponding µ values at the effective energy Ê of the x-ray beam. Linear attenuation coefficients increase as more energy is attenuated through the medium. Thus, it is expected that the linear attenuation coefficients have a directly proportional relationship with measured CT numbers. The effective energy Ê is determined by minimizing the residuals in a best-fit straight line relationship between CT numbers and the corresponding µ values.

In review, we will encounter considerable inter and intra scanner CT number variability. CT numbers can easily vary by 10 or more based on kVp, slice thickness, and object size, shape, and composition. There is some possibility of the use of iterative techniques and/or dual energy approaches that might lessen these effects, but certainly CT numbers are not strictly portable and vary according to the factors listed above. 

Please note: The CT number measurements for the individual materials are the median of the measurements from the input slices.

Sensitometry Targets

CTP401 (Catphan® 500) contains: LDPE (low density polyethylene), Acrylic, Teflon®, Air

CTP404 (Catphan® 503, 504, 600) contains: Polystyrene, LDPE, PMP (polymethylpentene), Air, Teflon®, Delrin®, Acrylic, and a vial for Water

CTP682 (Catphan® 605, 700) contains: Teflon®, Bone (Hydroxyapatite) 50%, Delrin®, Bone (Hydroxyapatite) 20%, Acrylic, Polystyrene, LDPE, PMP, Lung Foam #7112, Air, and a vial for Water

CTP732 (Catphan® 604) contains: Teflon®, Bone (Hydroxyapatite) 50%, Delrin®, Bone (Hydroxyapatite) 20%, Acrylic, Polystyrene, LDPE, PMP, and two Air targets.

The targets range from approximately +1000HU to -1000HU.

The monitoring of sensitometry target values over time can provide valuable information, indicating changes in scanner performance.

Nominal Material Formulation and Specific Gravity

Table 5.1: Table of material and properties information for Sensitometry inserts

• Lung #7112: a material used to simulate lung density.
• Polymethylpentene (PMP): a plastic material known for its tissue-like and relatively lower attenuation properties.
• Low-density polyethylene (LDPE): a plastic material that mimics the attenuation properties of soft tissues like adipose tissue
• Polystyrene: a plastic material that has an electron density similar to that of water and is used to simulate the dosimetric behavior of water over a wide range of energies.
• Acrylic (polymethylmethacrylate or PMMA): a plastic material used to mimic the photon properties of soft tissue. 
• Bone 20% and Bone 50% (Hydroxyapatite 20% or 50%): both are used for bone density calibration. Bone 20% is softer than Bone 50%, so it is expected to have weaker attenuation properties and therefore, a lower CT number [HU]. 
• Delrin® (polyoxymethylene or POM): a plastic material that has similar attenuation properties to that of cancellous bone.
• Teflon®: a synthetic fluoropolymer used to mimic human bone that is harder than Bone 50%, has stronger attenuation properties, and therefore has a larger CT number [HU] than Bone 50%.

Electron Density and Relative Electron Density
 

 Table 5.2: Table of electron density and relative electron density for the Sensitometry inserts.

¹Z_eff, the effective atomic number, is calculated using a power law approximation.

² For standard material sensitometry inserts, The Phantom Laboratory purchases a multiple year supply of each material in a single batch. Samples of the purchased material are then measured to determine the actual specific gravity. The specific gravity of air is taken to be .0013. For custom cast materials the specific gravity of each cast batch is noted and supplied with the phantom. The Lung #7112 is a foam, and while it is purchased in large batches, its density varies through the batch. For this reason the lung numbers may have a greater variation.

³ These are minimum and maximum measured values from a sample of 94 scans using different scanners and protocols. The Bone 20% limits are not taken from actual measurements but are scaled from measurements taken using an insert with a slightly different composition from an actual Catphan®700 Bone 20% insert. HU can vary dramatically between scanners and imaging protocols. Numbers outside this range are not unusual. Water was not measured so nominal values of +/- 7 HU are given.

⁴ Relative Electron Density is the electron density of the material in e/cm³ divided by the electron density of water (H₂O) in e/cm³.

Linearity Plot

The CT linearity measurements come from a representative slice. The representative slice is the slice closest to the median of the estimated effective energy. The CT measurements from this representative slice are then used for the plotted points in the graph below. This plot is the optimal linear fit of measured CT numbers vs. attenuation coefficient from the linear attenuation coefficient table values. 

The "Table Values" come from multiplying the density of the material and its mass attenuation coefficient. These values are provided in a sensitometry data spreadsheet linked in the Mass Attenuation Coefficient Table section below.

Figure 5.1: The Linearity Plot of measured CT number [HU] vs corresponding known Attenuation Coefficient [cm^-1] (calculated by multiplying the mass attenuation coefficient by the material's density) for each sensitometry insert. A higher attenuation coefficient means that the material absorbs (attenuates) more x-rays, and corresponds to higher CT numbers. The R² value for the best fit line is not shown above, but it is included in the report.

Sensitometry Header Information

The data displayed from the DICOM header is information significant to sensitometry analysis. 

Measured CT Numbers

The CT number measurements for the individual materials are from the representative slice closest to the median of the estimated effective energy. The approximate range of expected CT numbers for each target material can be found in Table 5.1 above.

Contrast Scale

The linearity plot exhibits the relationship between the measured signal, or measured CT numbers, and the expected linear attenuation coefficients. By analyzing this plot, we can assess how effectively the imaging system distinguishes between materials with varying densities based on their known attenuation coefficients. The plot shows a directly proportional relationship, thus the contrast scale is the slope of the linearity plot.

Residual Plot

The residuals are calculated from linearity plots for each tabular energy value. The residuals are the distances of the measured values from the line in the linearity plot. From this residual plot the estimated effective energy is derived as the minimum point on the plot. 

Sensitometry Plot

The sensitometry plot displays the theoretical (solid line in plot) and measured CT numbers (dotted line in plot) vs energy (keV) for each material. The estimated effective energy value shown is obtained from the minimum residual from the linear fit of measured CT values vs. attenuation coefficient. 

Effective Energy

The effective energy is obtained from the minimum point, or best fit, on the residual plot. The effective energy is the energy used when measuring the CT numbers that best correlate with the expected attenuation coefficients, as described by the maximum linear correlation coefficient. These measured CT numbers would deviate the least from the line of best fit, or have the lowest residual, and thus the corresponding effective energy used to produce these results would be known.

Mass Attenuation Coefficient Table

On the worksheet found at the link below are mass attenuation coefficients for sensitometry materials used in Catphan® phantoms. Linear attenuation coefficients are calculated by multiplying the mass attenuation coefficient by its corresponding density.

sensitometrydata.xlsx

Data is provided for selected energies from 20 keV to 20 MeV. Contributions from different interactions are given as well as totals both with and without coherent scattering effects. The values were obtained from the NIST XCOM database using our best knowledge of material compositions. The data is subject to change pending new information.