CT Physics: Beam Hardening and Dual-Energy CT

See the section on Reconstruction for simulated virtual non-contrast, iodine overlay, bone subtraction, and lung perfusion scans.

X-Ray Energy and Attenuation

Tissue: Iodine Concentration:

At 80 kV: Transmission % μ /cm CT Number HU
At 140 kV: Transmission % μ /cm CT Number HU

X-Ray Spectra

CT Numbers

Simulated attenuation of different energy x-ray beams by various materials. Left, x-ray beam spectra from a tungsten target with 2.5 mm Al filtration at 80 kV (blue) and 140 kV (orange); the spectra are normalized to have the same x-ray output. Gray line shows the attenuation curve of the selected material at each x-ray energy (log scale). Right, plot of attenuation (CT numbers) at the different x-ray energies. The black line represents where the CT numbers are equal at both energies.

You may wish to review the mechanisms of X-Ray interaction with Matter in fuller detail before reading this section.

X-Ray Production. Briefly, x-rays in diagnostic imaging are typically produced by bombarding a metal target with electrons. The tube potential, measured in kilovolts (kV) is the voltage from the electron source to the target. The kV setting determines the energy of the electrons that strike the target and thus the maximum energy of the resulting x-rays. Targets also often produce characteristic x-rays (see the spikes in the plot above), which have minimum energies depending on the material. Note that while the maximum energy is set by the kV (for 100 kV potential, the maximum energy is 100 keV), most of the x-rays produced by the target are at much lower energies. The average energy usually lies around 1/3 of the maximum energy (again, see the plots above).

X-Ray Attenuation. There are two important physical processes responsible for the attenuation of x-rays passing through a material (at diagnostic energies): the photo-electric effect and Compton (incoherent) scattering. Compton scattering is relatively similar across most materials, but the likelihood of photoelectric absorption varies considerably. Specifically, the likelihood of a photoelectric event is proportional to (Z/E)³, where Z is the atomic number and E is the x-ray photon energy. This means that it depends strongly on the material but also - importantly - on the x-ray energy.

The k-edge is the minimum energy required for the photoelectric event to occur with a k-shell electron - below this level, no photoelectric events can occur with k electrons. K-shell electrons are important because the energy to dislodge them (produce photo-elecric absorption) is right in the middle of the diagnostic range. Higher shells can also participate in the photoelectric effect, but they require much lower energies that are typically below the diagnostic range (basically, those energies are filtered out and/or absorbed by the body). The energy to dislodge a k-shell electron is referred to as the k-edge because, while below this energy the photoelectric event cannot occur, just above this energy, photoelectric events are most likely to occur. As noted above, they then drop off rapidly as x-ray energy increases.

Soft tissues. Solid organs, muscles, and fat are primarily composed of C, H, N, and O - all low-atomic number elements. These do not have relevant k-edge energies. Thus, while they do exhibit photo-electric absorption, the absorption is relatively similar across x-ray energies since we're operating in the tail of the energy drop-off (see the plot above).

Bone. Bone contains calcium, which has a somewhat higher Z and a k-edge at 4 keV. While this k-edge is below relevant diagnostic energies, the 'tail' does reach into diagnostic energies - thus, bone absorbs much more of the lower energy x-rays than soft tissues do.

Iodine. Iodine - typically used as CT or fluoroscopy contrast - has a much higher Z than soft tissues and has an important k-edge at 33 keV, smack in the middle of diagnostic x-ray energies. Because the photoelectric effect trails off rapidly, however, the absorption is much higher at lower energy x-ray beams than higher-energy beams (see the plots above).

Attenuation coefficient. X-rays are attenuated by material according to an exponential decay - in other words, for each given thickness of material, the same fraction of x-rays disappear. If 50% of the x-rays are absorbed by 1 cm, then 2 cm absorbs 75% (leaving only 25% of the original number of x-rays). The linear attenuation coefficient, designated μ, represents the degree of attenuation for a given material at a given x-ray energy (this is the exponent in the exponential decay formula). Note that for x-ray beams with many x-ray energies, we have to take into account the attenuation coefficients at each energy. This also means that the decay rate changes as the x-rays are attenuated, since the lower energies are lost first. This is referred to as beam hardening and is discussed more below.

CT Numbers. We will discuss dual-energy CT systems in more detail below, but it is important to understand what the CT scanner reports for attenuation values. The value of a pixel in CT is described as a CT number and is measured in Hounsfield units (HU), named after Sir Godfrey Hounsfield, the inventor of the CT scanner. The CT number is directly related to the linear attenuation coefficient μ but is normalized so that water and air always yield the same values. Water is defined to be 0 HU, and air is defined to be -1000 HU. The formula for the HU scale is

HU = 1000 * (μ - μ_water) / (μ_water - μ_air)

Note that because x-ray attenuation changes at different x-ray energies, the HU can change with changing kV - except for that of water and air. This is the principle of dual-energy CT and is discussed below.

Beam Hardening

X-Ray Spectra

Illustration of beam hardening. The light blue curve represents the x-ray beam from the tube (tungsten target at 120 kV with 2.5 mm Al filtration); the x-axis represents x-ray energy, with the y-axis showing the relative number of photons at each energy. The dark blue curve shows the energy distribution of the beam after it passes through 5 mm of titanium, as one might see from an internal fixation rod. Note that the spectra have been normalized to have the same scale; only 20% of the incident beam actually passes through.

While this topic is not exactly related to dual-energy CT, the underlying principles are related, so we will discuss it here. Notably, dual energy CT can actually help reduce artifacts caused by this phenomenon.

As we have discussed above, an x-ray beam passing through a material is attenuated - its intensity reduced. The amount of attenuation is related to the linear attenuation coefficient, which we have shown above depends on the energy of the photon. X-ray beams contain a continuous spectrum of energies because of the way they are produced, which is discussed in full detail on the section about X-Ray Attenuation. Since we know that low energy x-rays are attenuated more than higher energy x-rays, it is pretty intuitive that the beam emerging from the material has much fewer low energy x-rays than high energy x-rays. Thus, the average energy of this beam is higher - and we call this phenomenon beam hardening. You can see an example in the figure above, which shows the incident beam energy spectrum versus the spectrum after passing through 5 mm of titanium.

Filtration. Beam hardening can be very helpful. For example, we use it in beam filtration - we need to remove the very low energy x-rays that would just add dose to the patient but not contribute to the image (because they can't get all the way through the patient). Putting a small amount of metal (e.g. 2.5 mm aluminum) in front of the tube gets rid of these low energy photons without impeding the higher energy photons too much.

Streak Artifacts. There are several phenomena that contribute to streak artifacts on CT, but beam hardening is one of them. As the x-ray beam passes through a metal rod, for example, it becomes harder. The beam then passes through soft tissues - but is attenuated much less by them because it is already harder. X-ray beams that pass through other soft tissues but not through the metal (or even through the metal afterwards) are attenuated much more (since their average energy is lower). In effect, the soft tissue looks much 'darker' ("less dense") and washed out on the CT image from the perspective of a beam that has passed through metal.

X-Ray Beam at 120 kV

X-Ray Beam at 120 kV
after Titanium

Effects of beam hardening on CT brightness and contrast. Left, simulated CT image of the abdomen obtained from using a standard CT x-ray beam (tungsten target at 120 kV with 2.5 mm Al filtration); right, simulated CT image using the same beam after passing through 5 mm titanium. Note how the structures all appear washed out and darker. (The bone has lower HU as well but is still brighter than the top of our window level.)

In the presence of an object that causes beam hardening, the CT reconstruction software is confused because it gets different attenuation values for the same pixel, depending on the direction of the beam (i.e. traveling through the metal versus not). Thus, it's not sure which attenuation is correct. This effect is much more noticeable if there are two attenuating objects near each other, such as the posterior fossa between the petrous temporal bones, and it creates dark bands. This artifact can be mitigated by using dual-energy CT and reconstructing the image as a 'virtual monochromatic' scan. A monochromatic scan would be an x-ray beam with only one energy - thus no possibility of beam hardening. Dual energy CT can simulate a monochromatic x-ray beam.

There are other causes of streaks and dark bands on CT images. In the context of metal implants, the actual CT number of the implant may be higher than the CT number scale used to store the data (this is called overranging). Thus, the numbers are 'clipped', and the reconstruction is inaccurate. This problem can be lessened by reconstructing the image with an "extended scale" - which allows the scanner to store and use much higher CT numbers. An additional problem is photon starvation. This is exactly what it sounds like: there are not enough x-ray photons to fully penetrate the highly attenuating structure. Without enough photons, your signal-to-noise (SNR) goes down, and you see noise and streaks in the image. (For more about how the number of photons relates to noise, see the section on SNR in X-ray Imaging.)

Dual-Energy Radiography

We will discuss the reconstruction techniques for dual-energy imaging below, but realize that dual-energy imaging has been around for a long time in plain radiography.

DEXA. Probably the first use of the dual-energy principle was in evaluating bone mineral density (BMD) - using dual-energy x-ray absorptiometry (DEXA) scans. These are basically (nowadays) digital radiography systems with images taken at two different energies. Since the thickness of soft tissue varies widely across patients, we cannot just use the absolute x-ray beam attenuation to find out how much calcium is present. However, by using known attenuation coefficients of soft tissue and mineralized bone (i.e. with calcium), we can calculate the fraction of bone mineral present by comparing how many x-rays get through at low versus high energies.

Dual-energy Radiography. Dual-energy systems are also utilized in some centers for chest radiography. By taking images with two different energies and performing the same calculations as for DEXA, we can find out how much calcium is present at each point - and then subtract it. This lets us create chest radiographs without bones present - in principle making nodules easier to find. This technique may gain more popularity in the future.

Dual-Energy CT Systems

kV: Contrast
Acquired CT	Composite

Simulation of acquired dual-energy images (left) and the composite image created by averaging both (right). In reality, the low-energy (80 kV) image would be noisier than the high-energy image.

Dual-energy scanners. There are several different systems currently that are able to create dual-energy CT acquisitions. Some scanners will do two separate scans at different energies. Newer dual-source scanners are able to scan at both energies simultaneously - one x-ray tube scans at the higher energy while the other scans at the lower energy. Thus, the scan is completed at the same time, without any possibility of patient motion between the two scans. Typically, scans are done at 80 kV and 140 kV (or 120 kV for pediatric patients). The 'conventional' CT images that are produced are generated by averaging the two scans - but additional images can be reconstructed, as discussed below.

Low kV scan. The lower kV scan (typically 80 kV) is noisier than the higher kV scan because fewer of the low energy x-rays are able to penetrate the body. However, the contrast, especially with iodine present, is much better at the low kV. This is because the average energy of the 80 kV beam is around the 30 keV k-edge of iodine - thus, structures with iodine appear much brighter at the lower kV. The higher kV scan is less noisy but also less contrasty - see the simulation above for examples. Indeed, some advocate using the low energy scan to look for subtle liver lesions, since they will be more apparent because of the greater contrast. Use of iodine overlay reconstruction would be an alternative way to increase the visibility of lesions, see below.

Dose. Given that two separate acquisitions are being performed, one would expect that the dose might double. However, the eventual image being used uses information from both acquisitions - so each individual scan does not need to be as high a dose. Overall, it seems that dual-energy scans can be completed with doses similar or slightly higher than traditional, single-energy CT.

Spectral CT. An even newer technology just becoming available is so-called spectral CT, which relies on a totally different mechanism to differentiate materials by x-ray energy absorption. These scanners utilize a single tube energy but have a special detector. The detector is able to count individual photons (thus, it is called a photon-counting detector); by detecting individual photons, these detectors can measure their exact energy, as well. Photon-counting detectors behave similarly to photomultiplier tubes (PMTs) used in nuclear medicine imaging (e.g. SPECT), which utilize energy filtration to discard scatter events. By measuring photon energy, the CT scanner can determine how many x-rays of each energy penetrate a region, thus how many x-rays of each energy are blocked by any particular tissue. In principle, spectral CT offers huge advantages over traditional dual-energy systems since energies can be separated much more finely. For example, if you saw a sharp drop-off of energies above 33 keV, you would know that iodine is present in that voxel - you would be able to detect the k-edge itself. Thus, a spectral CT scanner should be able to distinguish many more material types than a simple dual-energy CT system. Another advantage of spectral CT is that only one scan needs to be done, so radiation dose should be the same as a single energy CT.

Spectral CT is very new, and there is not much clinical experience with these systems. The remainder of the article will discuss dual-energy systems.

Dual-Energy Reconstruction

kV: Contrast
Acquired CT	Tissue Decomposition	DE Reconstruction

Simulation of dual-energy CT decomposition and reconstruction in the abdomen. Left, acquired CT images at each kV; middle, material decomposition into soft tissue, iodine, and bone (white = 100% of that material, black = 0%); right, reconstructions. For reconstruction, you can choose a virtual non-contrast image, a non-contrast with iodine overlay (in green), or a bone subtraction image. Note that the liver cyst does not enhance.

As alluded to above, the biggest advantage of using dual energy systems is the ability to decompose images into the underlying materials. By detecting the different attenuation at different x-ray energies, we can detect how much of each material is present in any voxel. This allows us to do a number of interesting and useful things, such as creating virtual noncontrast, bone subtraction, and iodine only images. We can also perform stone composition analysis.

Material Decomposition. (This sub-section discusses the mathematics of the decomposition calculation, which can be skipped.) Since different materials have differential x-ray attenuation at different x-ray energies, we can calculate the composition of a given voxel. The attenuation by each material removes a certain fraction of the incoming x-rays - i.e. the total attenuation is the product of the individual attenuations. As noted earlier and discussed in more detail in the section on x-ray interaction with matter, x-ray attenuation is an exponential process. Multiplying exponentials is the same as adding the exponents - in other words the sum of attenuation coefficients from each component (multiplied by the amount of each material) gives the total attenuation. Let's say we want to separate the contributions from soft tissue (ST), iodine contrast (I), and bone (B) - in equations,

μ_{80 kV, total} = f_ST * μ_{ST, 80} + f_I * μ_{I, 80} + f_B * μ_{B, 80}

and

μ_{140 kV, total} = f_ST * μ_{ST, 140} + f_I * μ_{I, 140} + f_B * μ_{B, 140}

where f_ST is the fraction made up by soft tissue, etc. We can find the attenuation coefficients for each component by scanning pure samples of each and programming those values into the software. Additionally, since we assume that each voxel is composed of only ST, I, and B, we know that the fractions must add up to 100%, or f_ST + f_I + f_B = 1. Thus, we have 3 (linear) equations with 3 unknowns, easy to solve for each fraction.

Virtual Non-contrast. By decomposing a contrast-enhanced CT of the abdomen into soft tissue, iodine, and bone components, we can create some useful new images. For example, we can create an image composed of only the soft tissue and bone components of each voxel - a virtual noncontrast image. This could be useful to evaluate the aorta for intramural hematoma (IMH), the kidneys for small stones, or a hyperdense cyst for true enhancement.

Bone Subtraction. Similarly to removing iodine, we can remove the calcium component of the image. This is useful in CT angiography - instead of tediously removing the bone to create an angiogram maximum intensity projection (MIP) or 3-D volume-rendered image, we can automatically remove the bone by a simple calculation. Additionally, we can remove the calcified atherosclerotic plaque, making it easier to assess for stenosis with somewhat less blooming artifact.

Iodine Overlay. On top of the virtual non-contrast image, we can overlay the iodine-only image in a different color. This will make a contrast-enhanced CT look more like a fused PET/CT image - enhancing structures will be brightly colored (e.g. green in the simulation above). The overlay can be useful for looking at the liver for enhancing lesions or hyperdense renal cysts for superimposed enhancement (e.g. a small papillary renal carcinoma).

We can also create 'perfusion' maps of organs with the iodine overlay. For example, if we want to see if myocardium is enhancing, a dual-energy scan (images would have to be acquired simultaneously because of cardiac motion) could show defects from myocardial infarction. This should lend confidence to the diagnosis of occlusive coronary disease on a CT coronary angiogram. Similarly, we can evaluate the lungs for perfusion defects from pulmonary emboli (PE). This should be able to show smaller PEs or lend confidence to the diagnosis of a segmental or subsegmental PE.

kV: Contrast
Acquired CT	Tissue Decomposition	DE Reconstruction

Simulation of dual-energy chest CT with lung perfusion reconstruction. Left, acquired CT images at each kV; middle, material decomposition into soft tissue, iodine, and air (white = 100% of that material, black = 0%); right, reconstruction with virtual non-contrast and lung perfusion (iodine overlay) images. Note the right upper lobe sub-segmental pulmonary embolism / oligemia.

Stone composition. Similarly to iodine decomposition, we can also analyze renal stones for their composition. Uric acid stones are treated differently (with urine alkalization) than other stones (which are treated with lithotripsy). Note that uric acid only contains C, H, N, and O - most of the other stone types include calcium. The presence of calcium will substantially change the stone attenuation at lower x-ray energies; the other compositional differences will also have some impact. Dual-energy CT software can separate urate from other stones and help with treatment decisions.

Virtual Monochromatic Imaging. Dual-energy CT data can also be decomposed and then reconstructed to form a simulated ("virtual") monochromatic image. Monochromatic refers to the x-ray beam: a monochromatic beam has only a single x-ray energy, versus the real-life polychromatic beam, which has a wide spectrum of x-ray energies. This allows you to play around with the tissue contrast a bit (e.g. lower keV for greater contrast) or remove beam-hardening artifacts. In order to generate a virtual monochromatic image, the scanner software decomposes each voxel into water and iodine components, similarly to the 3-material decomposition done for virtual non-contrast images above. It then re-draws the image using known attenuation values at the desired keV - thus, it simulates what the scan would have looked like with the monochromatic beam. Obviously, this is only a virtual image, and thus it still suffers from some artifacts.

As mentioned, one principal use for virtual monochromatic images would be removing beam-hardening streak artifacts. Now, the way most software performs this correction, it does not directly account for the beam hardening - but by using the high-energy image, which has minimal beam hardening, it can tell the tissue composition with minimal artifacts. By using that information to reconstruct the image, the beam-hardening artifacts are lessened, though not completely gone. In the simulation below, as has been our clinical experience, the beam-hardening artifacts are still present on the lower keV images but not so at the higher keV images.

Acquired Image: kV		Virtual Monochromatic Image: keV

Simulation of Virtual Monochromatic image reconstruction to improve beam-hardening artifacts in the posterior fossa. Left, simulated transverse images of the posterior fossa, acquired at 80 kV or 140 kV (the latter with added tin filtration). Right, calculated virtual monoenergetic images at the given keV setting. Note how the higher keV images improve or eliminate beam hardening.

Take-Home Points

Different materials attenuate x-rays differently at low and high energies. Materials with high atomic numbers and high k-edges attenuate the low-energy x-rays much more than soft tissue does.
Low-energy scans have greater contrast, especially with iodine. However, the tend to be noisier because the x-rays penetrate less (though the actual noise depends on the mAs).
On CT images, the Hounsfield scale is always defined so that water is 0 and air is -1000. Numbers for other materials (e.g. iodine) can change depending on the x-ray energy.
Dual-energy CT systems exploit the different HU values for materials at different energies to decompose images into the components made up by different materials. For example, virtual non-contrast images can be created. Iodine overlays can show enhancing lesions or organ perfusion.

References

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Mass absorption spectra obtained from NIST here.