# High-Sensitivity Iodine Imaging by Combining Spectral CT Technologies

Matthew Tivnan1, Grace Gang1, Wenchao Cao2, Nadav Shapira2, Peter B. Noël2, J.
Webster Stayman1
1 Johns Hopkins University Department of Biomedical Engineering
2 Hospital of the University of Pennsylvania Department of Radiology

###### Abstract

Spectral CT offers enhanced material discrimination over single-energy systems
and enables quantitative estimation of basis material density images.
Water/iodine decomposition in contrast-enhanced CT is one of the most
widespread applications of this technology in the clinic. However, low
concentrations of iodine can be difficult to estimate accurately, limiting
potential clinical applications and/or raising injected contrast agent
requirements. We seek high-sensitivity spectral CT system designs which
minimize noise in water/iodine density estimates. In this work, we present a
model-driven framework for spectral CT system design optimization to maximize
material separability. We apply this tool to optimize the sensitivity spectra
on a spectral CT test bench using a hybrid design which combines source kVp
control and k-edge filtration. Following design optimization, we scanned a
water/iodine phantom with the hybrid spectral CT system and performed dose-
normalized comparisons to two single-technique designs which use only kVp
control or only k-edge filtration. The material decomposition results show
that the hybrid system reduces both standard deviation and cross-material
noise correlations compared to the designs where the constituent technologies
are used individually.

##  I Introduction

Spectral CT systems use data acquisition schemes involving varied spectral
sensitivities across photon energies. Thus, compared to single-energy CT
systems, spectral CT systems can provide more information about the energy-
dependent attenuation of the subject being scanned. In particular, spectral CT
enables estimation of basis material densities which has many benefits in
quantitative clinical imaging.

Contrast-enhanced imaging of iodine is one of the most widespread clinical
applications of spectral CT. Iodine density estimates show contrast-agent
concentration, and water density estimates provide virtual non-contrast
enhanced images for characterizing patient anatomy [1]. However, the
similarity of the attenuation spectra of water and iodine make accurate
material decomposition and density estimation challenging. As compared to
standard estimation of overall attenuation (as provided by single-energy CT
systems), the relative noise is much higher in the individual basis material
density estimates provided by spectral CT [2]. For some clinical applications,
such as imaging pancreatic cancer, very low levels of differential contrast-
enhancement can have a meaningful impact on diagnosis [3]. Therefore,
development of spectral CT systems which are capable of high-sensitivity
water/iodine decomposition is an important goal with direct clinical
implications.

One way to improve sensitivity is with advanced data processing. For example,
model-based approaches have been widely adopted in single-energy CT for their
improved dose-image quality tradeoffs. In this work, we use a direct one-step
model-based material decomposition (MBMD) algorithm rather than a two-step
reconstruction-decomposition approach, allowing for incorporation of
measurement statistics as well as advanced regularization approaches to help
reduce noise.

Another strategy for improving sensitivity, and the focus of this work, is to
optimize the spectral CT system design. There are several technologies which
can modulate the spectral sensitivity of a CT system: rapid kVp switching [4],
multiple x-ray sources [5], source filtration (e.g. k-edge filters) [6], dual-
layer/multi-layer detectors [7], photon counting detectors [8]. Each of these
spectral modulation technologies have potentially tuneable design parameters
such as kVp separation or k-edge filter thickness. There is evidence that
combining these methods can improve sensitivity [9]. In previous work, we
demonstrated that combining spectral modulation technologies into a hybrid
system offers greater control over designed spectral sensitivities [10] [11].
Our previous simulation results showed that joint optimization of these design
parameters in a hybrid system can result in higher sensitivity than systems
using the constituent spectral modulators individually.

Recently, we have also proposed a mathematical formula for _material
separability index_ which models the performance of a spectral CT system and
its advantage over single-energy CT. The metric takes into account
polyenergetic models of x-ray sources, attenuation, and detector sensitivity,
as well as noise and correlations [12].

In this work, we apply these theoretical models to the system design
optimization of a prototype spectral CT test bench which incorporates both kVp
control as well as k-edge filtration. We describe the specific spectral CT
model that includes polyenergetic x-ray physics as well as a quantitative
metric of water/iodine separability for the modeled system. We describe a
spectral CT system design optimization process for a physical prototype
including parameters of the design space and optimization methods. Finally, we
present the results of a water/iodine imaging study which compares the
optimized hybrid kVp control/k-edge filtration design with kVp control
individually and k-edge filtration individually.

##  II Methods

Figure 1: Comparison between two spectral CT system designs. Design B results
in a greater separability index than design A. As shown by the basis material
densiity estimates, the noise correlation is lower in design B and therefore
it is easier to detect a positive impulse of idoine plus a negative impulse of
water.

###  II-A Spectral CT Physical Models

A general forward model for spectral CT is given by:

$\mathbf{\bar{y}}(\mathbf{x})=\mathbf{G}\mathbf{S}\exp{\Big{(}-\mathbf{Q}\mathbf{A}\mathbf{x}\Big{)}},$
(1)

where $\mathbf{x}$ is a column vector containing basis material densities,
$\mathbf{A}$ is a forward projection operator, $\mathbf{Q}$ contains mass
attenuation coefficients of basis materials, $\mathbf{S}$ models the system
spectral sensitivity, and $\mathbf{G}$ is a gain. This work will focus on
modeling flat-panel energy-integrating detectors, for which we can expand
$\mathbf{S}$ as follows:

$\mathbf{\bar{y}}(\mathbf{x})=\mathbf{G}\mathbf{S_{2}}\mathbf{S_{1}}\mathbf{S_{0}}\exp{\Big{(}-\mathbf{Q}\mathbf{A}\mathbf{x}\Big{)}},$
(2)

where $\mathbf{S_{0}}$ models the spectrum of photons emitted by the source
(including filtration), $\mathbf{S_{1}}$ models the probability of interaction
with the scintillator, and $\mathbf{S_{2}}$ models the generation of secondary
quanta in the scintillator, as well as detection and integration by the
photodetector. With this spectral CT system model, we can simulate systems
with different designs and predict how they will respond to different multi-
material objects. For example, we can predict the energy attenuated by an
object, $\mathbf{x}$, using the following formula:

$\text{Dose}=\boldsymbol{\epsilon^{T}}\mathbf{S_{0}}\Big{(}\boldsymbol{1}-\exp{\big{(}-\mathbf{Q}\mathbf{A}\mathbf{x}\big{)}}\Big{)},$
(3)

where $\boldsymbol{\epsilon}$ is a vector containing the energy, in mJ.

We can also use this model to estimate material density images from spectral
CT measurements via MBMD. Assuming a multivariate gaussian noise model with
mean, $\mathbf{\bar{y}(x)}$, and covariance, $\boldsymbol{\Sigma_{y}}$, a
maximum-likelihood estimator of basis material densities,
$\mathbf{\hat{x}}(\mathbf{y})$, is given by the following formulae:

$\displaystyle\Phi(\mathbf{x},\mathbf{y})=\big{(}\mathbf{y}-\mathbf{\bar{y}}(\mathbf{x})\big{)}^{T}\boldsymbol{\Sigma_{y}^{-1}}\big{(}\mathbf{y}-\mathbf{\bar{y}}(\mathbf{x})\big{)}$
(4)
$\displaystyle\mathbf{\hat{x}}(\mathbf{y})=\underset{\mathbf{x}}{\text{argmin}}\enspace\Phi(\mathbf{x},\mathbf{y}).$
(5)

Note that the above formula does not include a regularization term. While we
focus on unbiased estimators in this work, further noise reduction is possible
using the cross-material regularization strategies described in [13] [14]. To
perform the numerical optimization, we use the separable parabolic surrogates
algorithm described in [15] and a cross material preconditioner defined in
[16] to improve convergence rates. We note that in following sections this
MBMD approach will be used for water/iodine decomposition. However, the same
estimator can be applied as single-material model-based iterative
reconstruction (MBIR) with built-in polyenergetic corrections by using water
as the sole basis material.

###  II-B Material Separability

In this section we present a quantitative metric for material separability
originally described in [12]. The metric applies to maximum-likelihood MBMD
and is based on the Fisher information matrix which is defined below:

$\displaystyle\mathbf{F}=\mathbf{A^{T}}\mathbf{Q^{T}}\mathbf{D^{T}}\mathbf{S^{T}}\mathbf{G^{T}}\boldsymbol{\Sigma_{y}^{-1}}\mathbf{G}\mathbf{S}\mathbf{D}\mathbf{Q}\mathbf{A}$
(6) $\displaystyle\mathbf{D}=D\\{\exp{(-\mathbf{QAx})}\\}.$ (7)

Note that this expression is object-dependent. That is, different objects, as
described by $\mathbf{x}$, will affect the weights in $\mathbf{D}$ and will
therefore have an impact on $\mathbf{F}$. This is not surprising since CT
image quality is known to be object-dependent. The detectability index of a
signal, $\mathbf{w}$, which is in the same multi-material image space as
$\mathbf{x}$, is defined below:

$d^{2}(\mathbf{w})=\mathbf{w^{T}}\boldsymbol{\Sigma_{x}^{-1}}\mathbf{w}=\mathbf{w^{T}}\mathbf{F}\mathbf{w}.$
(8)

For two signals, $\mathbf{w_{A}}$ and $\mathbf{w_{B}}$ which are normalized
such that $d(\mathbf{w_{A}})=d(\mathbf{w_{B}})$, the separability index is
defined by the ratio between the detectability of their difference to the
detectability of their sum as shown below:

$\displaystyle
s^{2}(\mathbf{w_{A}},\mathbf{w_{B}})=\frac{\mathbf{(\mathbf{w_{A}}-\mathbf{w_{B}})^{T}}\mathbf{F}(\mathbf{w_{A}}-\mathbf{w_{B}})}{\mathbf{(\mathbf{w_{A}}+\mathbf{w_{B}})^{T}}\mathbf{F}(\mathbf{w_{A}}+\mathbf{w_{B}})}.$
(9)

In theory this formula can characterize the separability of any two signals,
but for the purposes of characterizing water/iodine separability, we may
assume that $\mathbf{w_{A}}$ is a voxel impulse of iodine only at a certain
position and $\mathbf{w_{B}}$ is a voxel impulse of water at the same
position. Note that a single-energy CT system would be capable of detecting
$(\mathbf{w_{A}}+\mathbf{w_{B}})$ but it would be effectively impossible to
detect $(\mathbf{w_{A}}-\mathbf{w_{B}})$ leading to a material separability
index near 0.0%. In contrast, a spectral CT system with two or more distinct
spectral channels should be capable of detecting the differential signal.

###  II-C Spectral CT Prototype System Design Optimization

Our goal in this section is to apply the theoretical models above to maximize
water/iodine separability in a prototype spectral CT test bench using a
combination of kVp control and k-edge filtration. The spectral sensitivity
design consists of two channels. Each channel was parameterized by three
quantities: kVp setting, filtration material, and exposure. We explored six
possible kVp settings: 70, 80, 90, 100, 110, and 120 kVp. Eight possible
filter materials and thicknesses were 250 $\mu$m praseodymium, 250 $\mu$m
erbium, 127 $\mu$m lutetium, 250 $\mu$m hafnium, 100 $\mu$m tungsten, 100
$\mu$m gold, 250 $\mu$m lead, and no filter. For each spectrum there are 48
unique combinations of filter material and kVp settings. Therefore, there are
1128 unique spectral profiles. Exposure settings were optimized in a nested
optimization for each possible shape.

Figure 2: Hybrid method spectral CT test bench and water/iodine phantom.

For each possible design, we established a physical model, and computed the
separability index for a 0.5 mm voxel impulse of iodine and water at the
center of an 80 mm cylinder of water. The final design was chosen as the one
which maximized the water/iodine separability metric. The process above was
also repeated for the two spectral modulation technologies acting
individually. That is, the design space was constrained to cases with no
filtration for kVp control design. For the k-edge filtration design, the space
was constrained to designs with static kVp settings. For the hybrid design, we
used the full parameter space which includes combinations of kVp settings and
filtration materials.

The three optimized designs were implemented physically on the x-ray CT test
bench as shown in Figure 2. We constructed a water/iodine phantom using
cylindrical targets designed for CT calibration. Each cylinder is
approximately 27 mm in diameter and the composition of each cylinder has been
designed to match the attenuation spectra of water plus some concentration of
iodine. The nominal iodine concentrations are 0.0, 2.5, 5.0, 7.5, 10.0, 15.0,
and 20.0 mg/mL and they are arranged as shown in Figure 2. We used a
2-dimensional fan-beam system geometry with a source-to-axis distance of
831.58 mm and a source-to-detector distance of 1766.54 mm. The detector pixel
size is 0.278 $\times$ 0.278 mm and the central 60 detector rows were binned
to produce the one-dimensional projection measurements for each view.

Exposure settings were calibrated using preliminary scans for each design and
approximating photon counts according to the variance in the gain
measurements. A voxelized approximation of the water/iodine phantom was used
to approximate the dose attenuated by the phantom as defined by (3). The
target exposure was then established in such a way that the predicted dose
attenuated by the phantom was normalized to 1 mJ and the ratio of exposures
was matched to the design optimization results. The source mAs was scaled in
proportion to the ratio between the target exposure and initial exposure
estimates. The system spectral sensitivity was calibrated by scanning a
phantom containing known concentrations of water and iodine and fitting a
parameterized spectral model.

After calibration was complete, we scanned the water/iodine phantom using each
of the three optimized designs. Two-dimensional material density images with
200 $\times$ 200 voxels of size 0.5 mm were reconstructed via MBMD using 1000
iterations of the separable quadratic surrogates algorithm described in [15].
We also ran a standard model-based iterative reconstruction to estimate
attenuation. This was accomplished using the same polyenergetic model used for
MBMD but with a single-material (water) basis. To evaluate image quality, we
computed means and cross-material covariances in 7 ROIs centered on each
cylinder for the water and iodine basis material density images resulting from
MBMD. We also computed variance in the same ROIs for the MBIR reconstructed
image results.

Figure 3: Spectral sensitives for each design, MBIR and MBMD reconstruction
results, and covariance metrics by ROI.

##  III Results

The optimized kVp control design was found to be 48.47% of photons at 70 kVp
and 51.53% of photons at 120kVp. This design results in a water/iodine
separability index of 2.54%. This result in not particularly surprising, since
this is the largest possible kVp separation, matching intuition that spectra
which are very different from one another enable greater material
separability. The optimized k-edge filtration design was found to be 58.16% of
photons at 70 kVp with a 250 $\mu$m praseodymium filter and 41.84% of photons
at 70 kVp with a 250 $\mu$m lead filter. This design results in a water/iodine
separability index of 7.32%. The optimized hybrid design was found to be
34.88% of photons at 70 kVp with a 250$\mu$m lead filter and 65.12% of photons
at 120 kVp with a 250 $\mu$m praseodymium filter. This design results in a
water/iodine separability index of 12.52%.

The sample mean of estimated density for all ROIs was within 10% of the
nominal value for both water and iodine for all three designs. As shown in
Figure 3 sample variance in the attenuation image estimated via MBIR is
comparable for all three designs. This is expected because the total dose
absorbed by the phantom was normalized for each design. The sample covariance
in the water and iodine density images estimated with MBMD shows that the
noise is much lower for the hybrid design than for either of the spectral
modulation technologies acting individually. The correlation coefficient is
also closer to zero for the hybrid design than either of the individual
designs.

##  IV Conclusion

In this work we apply a previously developed quantitative metric of material
separability based on the Fisher information matrix. We have shown that this
metric can be used to optimize spectral CT system design for higher
sensitivity and demonstrated efficacy in a physical system. Furthermore, the
results of the imaging study show that spectral CT systems which use a
combination of multiple spectral modulation technologies have the potential
for improved performance with respect to designs using the constituent
individual technologies.

There are several limitations in this preliminary work which should be
acknowledged. First, we used a relatively small phantom compared to the size
of a human patient. Material decomposition will be a more poorly conditioned
problem for larger objects. Additionally, we did not incorporate a scatter
model. For low-contrast applications, scatter and other systemic biases are a
concern and must be addressed. These topics are the subject of ongoing
studies.

Despite these limitations, the results suggest that hybrid design is a
promising strategy for spectral CT with the potential to overcome low-
concentration limits of more traditional single-technology spectral methods.
While this work has concentrated on two more traditional spectral
technologies, other combinations including other source-side modulation
schemes or energy-sensitive detectors (such as dual-layer or photon counting
detectors) could provide additional advantages. Jointly optimizing such hybrid
systems for material separability may potentially have a significant benefit
for clinical applications involving high sensitivity to low contrast
concentrations, and will be investigated in future work.

## Acknowledgements

This work was supported, in part, by NIH grant R21EB026849.

## References

  * [1] Sauter, A. P _et al._ , _European journal of radiology_ , vol. 104, 2018\.
  * [2] Faby, S _et al._ , _Medical physics_ , vol. 42, no. 7, pp. 4349–4366, 2015\.
  * [3] Kawamoto, S _et al._ , _Abdominal Radiology_ , vol. 43, no. 2, 2018.
  * [4] Xu, D _et al._ , in _Medical Imaging 2009: Physics of Medical Imaging_ , vol. 7258. Int. Soc. for Optics and Photonics, 2009.
  * [5] Gang, G. J _et al._ , _Medical Physics_ , vol. 45, no. 1, pp. 144–155, 2018\.
  * [6] Tivnan, M _et al._ , in _SPIE Medical Imaging, 2019_ , 2019.
  * [7] Ma, Y. Q _et al._ , in _Conference proceedings. International Conference on Image Formation in X-Ray Computed Tomography_ , vol. 2020, 2020.
  * [8] Taguchi, K and Iwanczyk, J. S, _Medical physics_ , vol. 40, no. 10, 2013.
  * [9] Primak, A _et al._ , _Medical physics_ , vol. 36, no. 4, pp. 1359–1369, 2009.
  * [10] Tivnan, M _et al._ , in _Medical Imaging 2020: Physics of Medical Imaging_ , vol. 11312. International Society for Optics and Photonics, 2020.
  * [11] Tivnan, M and Stayman, J. W, in _Fully 3D_ , vol. 11072, 2019, p. 1107211.
  * [12] Tivnan, M _et al._ , _arXiv preprint arXiv:2010.07483_ , 2020.
  * [13] Wang, W _et al._ , in _Medical Physics_ , 2019, pp. E257–E257.
  * [14] Wang, W and Webster, J, in _Fully3D_. SPIE, 2019, p. 110720Z.
  * [15] Tilley II, S. W _et al._ , _Physics in medicine and biology_ , 2018.
  * [16] Tivnan, M _et al._ , 2020.