Spectral imaging (radiography)

Spectral imaging is an umbrella term for energy-resolved

An energy-resolved imaging system probes the object at two or more photon energy levels. In a generic imaging system, the projected signal in a detector element at energy level ${\textstyle \Omega \in \{E_{1},E_{2},E_{3},\ldots \}}$ is[1]

$${\displaystyle n_{\Omega }=q_{\Omega }\int \Phi _{\Omega }(E)\times \exp[-\mu _{1}(E)t_{1}-\mu _{2}(E)t_{2}-\mu _{3}(E)t_{3}\ldots ]\times \Gamma _{\Omega }(E)\,dE,}$$

(1)

where ${\textstyle q}$ is the number of incident photons, ${\textstyle \Phi }$ is the normalized incident energy spectrum, and ${\textstyle \Gamma }$ is the detector response function.

${\textstyle \mu }$

${\textstyle t}$

${\textstyle q\times \Phi }$

${\textstyle \Omega }$

${\textstyle \Omega }$

${\textstyle \Gamma }$

Most elements appearing naturally in human bodies are of low atomic number and lack absorption edges in the diagnostic X-ray energy range. The two dominating X-ray interaction effects are then Compton scattering and the photo-electric effect, which can be assumed to be smooth and with separable and independent material and energy dependences. The linear attenuation coefficients can hence be expanded as^[6]

$${\displaystyle \mu (E)=a_{PE}\times f_{PE}(E)+a_{C}\times f_{C}(E).}$$

(2)

In contrast-enhanced imaging, high-atomic-number contrast agents with K absorption edges in the diagnostic energy range may be present in the body. K-edge energies are material specific, which means that the energy dependence of the photo-electric effect is no longer separable from the material properties, and an additional term can be added to Eq. (2) according to^[12]

$${\displaystyle \mu (E)=a_{PE}\times f_{PE}(E)+a_{C}\times f_{C}(E)+\sum a_{K}\times f_{K}(E),}$$

(3)

where ${\textstyle a_{K}}$ and ${\textstyle f_{K}}$ are the material coefficient and energy dependency of contrast-agent material ${\textstyle K}$.

Energy weighting

Summing the energy bins in Eq. (1) (${\textstyle n=\sum n_{\Omega }}$) yields a conventional non-energy-resolved image, but because X-ray contrast varies with energy, a weighted sum (${\textstyle n=\sum w_{\Omega }\times n_{\Omega }}$) optimizes the contrast-to-noise-ratio (CNR) and enables a higher CNR at a constant patient dose or a lower dose at a constant CNR.^[13] The benefit of energy weighting is highest where the photo-electric effect dominates and lower in high-energy regions dominated by Compton scattering (with weaker energy dependence).

Energy weighting was pioneered by Tapiovaara and Wagner^[13] and has subsequently been refined for projection imaging^[14][15] and CT^[16] with CNR improvements ranging from a few percent up to tenth of percent for heavier elements and an ideal CT detector.^[17] An example with a realistic detector was presented by Berglund et al. who modified a photon-counting mammography system and raised the CNR of clinical images by 2.2–5.2%.^[18]

Material decomposition

Equation (1) can be treated as a system of equations with material thicknesses as unknowns, a technique broadly referred to as material decomposition. System properties and linear attenuation coefficients need to be known, either explicitly (by modelling) or implicitly (by calibration). In CT, implementing material decomposition post reconstruction (image-based decomposition) does not require coinciding projection data, but the decomposed images may suffer from beam-hardening artefacts because the reconstruction algorithm is generally non-reversible.^[19] Applying material decomposition directly in projection space instead (projection-based decomposition),^[6] can in principle eliminate beam-hardening artefacts because the decomposed projections are quantitative, but the technique requires coinciding projection data such as from a detection-based method.

In the absence of K-edge contrast agents and any other information about the object (e.g. thickness), the limited number of independent energy dependences according to Eq. (2) means that the system of equations can only be solved for two unknowns, and measurements at two energies (${\textstyle |\Omega |=2}$) are necessary and sufficient for a unique solution of ${\textstyle t_{1}}$ and ${\textstyle t_{2}}$.^[7] Materials 1 and 2 are referred to as basis materials and are assumed to make up the object; any other material present in the object will be represented by a linear combination of the two basis materials.

Material-decomposed images can be used to differentiate between healthy and malignant tissue, such as

The basis-material representation can be readily converted to images showing the amounts of photoelectric and Compton interactions by invoking Eq. (2), and to images of effective-atomic-number and electron density distributions.^[6] As the basis-material representation is sufficient to describe the linear attenuation of the object, it is possible to calculate virtual monochromatic images, which is useful for optimizing the CNR to a certain imaging task, analogous to energy weighting. For instance, the CNR between grey and white brain matter is maximized at medium energies, whereas artefacts caused by photon starvation are minimized at higher virtual energies.^[31]

K-edge imaging

In

) if one or several K absorption edges are present in the imaged energy range, a technique often referred to as K-edge imaging. With one K-edge contrast agent, measurements at three energies (${\textstyle |\Omega |=3}$) are necessary and sufficient for a unique solution, two contrast agents can be differentiated with four energy bins (${\textstyle |\Omega |=4}$), etc. K-edge imaging can be used to either enhance and quantify, or to suppress a contrast agent.

Enhancement of contrast agents can be used for improved detection and diagnosis of tumors,

Most studies of contrast-enhanced spectral imaging have used iodine, which is a well-established contrast agent, but the K edge of iodine at 33.2 keV is not optimal for all applications and some patients are hypersensitive to iodine. Other contrast agents have therefore been proposed, such as gadolinium (K edge at 50.2 keV),^[39] nanoparticle silver (K edge at 25.5 keV),^[40] zirconium (K edge at 18.0 keV),^[41] and gold (K edge at 80.7 keV).^[42] Some contrast agents can be targeted,^[43] which opens up possibilities for molecular imaging, and using several contrast agents with different K-edge energies in combination with photon-counting detectors with a corresponding number of energy thresholds enable multi-agent imaging.^[44]

Technologies and methods

Incidence-based methods obtain spectral information by acquiring several images at different

Detection-based methods instead obtain spectral information by splitting the spectrum after interaction in the object. So-called sandwich detectors consist of two (or more) detector layers, where the top layer preferentially detects low-energy photons and the bottom layer detects a harder spectrum.[47]^[48] Detection-based methods enable projection-based material decomposition because the two energy levels measured by the detector represent identical ray paths. Further, spectral information is available from every scan, which has work-flow advantages.^[49]

The currently most advanced detection-based method is based on

The main intrinsic challenge of photon-counting detectors for medical imaging is pulse pileup,[62] which results in lost counts and reduced energy resolution because several pulses are counted as one. Pileup will always be present in photon-counting detectors because of the Poisson distribution of incident photons, but detector speeds are now so high that acceptable pileup levels at CT count rates begin to come within reach.^[67]

See also

• Photon-counting mammography
• Photon-counting computed tomography

References