Dual-energy x-ray approach for object/energy-specific attenuation coefficient correction in single-photon emission computed tomography: effects of contrast agent

Abstract.

Purpose: To investigate the influence of radiographic contrast agent on the accuracy of the photon counts arising from the emission of gamma rays of radionuclides in single-photon emission computed tomography (SPECT), when dual-energy x-ray CT (DXCT) is employed for providing object/energy-specific attenuation coefficient correction in SPECT.

Approach: Computer simulation was performed for three transmission CT approaches, namely, the conventional (single kVp, unimodal spectrum) x-ray CT, DXCT (single kVp, bimodal spectrum) with basis material decomposition (BMD), and DXCT with BMD followed by basis material coefficients transformation (BMT), to study the effects of these approaches on the accuracy of the photon counts from the SPECT image of a thorax-like phantom.

Results: All three CT approaches revealed that the error in the counts was both photon energy and iodine concentration-dependent. Differences in the trending increase/decrease in the errors with the respective increase in iodine concentration and photon energy were observed among the three CT approaches. Of the three, the BMT/SPECT approach resulted in the smallest error in the concentration of radionuclides measured, especially in the contrast agent-filled region, and the optimal level depended on the iodine concentration and photon energy.

Conclusion: With a judicious choice of the basis materials and photon energy, it may be possible to take advantage of the benefits of the BMT method to mitigate the accuracy problem in DXCT for quantitative SPECT imaging.

1. Introduction

Single-photon emission computed tomography (SPECT) is a functional medical imaging technique for mapping the distribution of the radiopharmaceutical drug administered into the body.¹ This involves detecting the gamma-ray photons emitted from the decay of the radioactive isotopes during the imaging process.¹ By taking the image at different times for the same cross section, this enables the functional state of an organ to be determined from the images.¹

Non-uniform gamma-ray photon attenuation by the surrounding tissues could contribute to inaccuracy in quantitative SPECT imaging of the distribution of the radiopharmaceutical drug in the body.¹ Object-specific (i.e., patient-specific) images containing a map of linear attenuation coefficients derived from a traditional transmission x-ray CT (XCT) system using a single polychromatic x-ray source can be used to correct photon attenuation² and other artifacts, e.g., cupping.³ However, these images suffer from beam hardening effects owing to the polychromatism of the x-rays.¹

An alternative approach to using XCT for providing object/energy-specific attenuation coefficient correction in SPECT is the dual-energy x-ray CT (DXCT) system. The fundamentals underpinning the DXCT approach were first proposed by Stonestrom et al.⁴ In this method, imaging may be performed at two different sets of polychromatic spectra, which may be obtained from two different kVp sources or from one kVp source with a filter to split the spectrum into two.⁵ Alternatively, one may also obtained two sets of data corresponding to the low and high energy spectra by applying energy-discriminating detectors, such as the ME100 linear array pixel detector based on semiconductor sensors (CdTe) which can detect x-ray photons from the respective low and high energy spectra.⁶ Patented in 2009,⁷ the DXCT method has been proposed to be used in place of the traditional XCT to mitigate the beam hardening artefacts.⁸ Since then, DXCT continues to lend itself to medical anatomical imaging application in the upper body regions such as brain,⁹ head/neck,¹⁰ and in the main body such as lungs,¹¹ heart,¹² and abdomen,¹³ to general structural examination such as musculoskeletal system¹⁴ and vascular system,¹⁵ and to oncology,¹⁶ including for attenuation correction in positron emission tomography (PET).^2,17

The practical implementation of DXCT incorporates a basis material decomposition (BMD) argument which is equivalent to the photoelectric-Compton decomposition argument that underpins the theory for dual-energy x-rays.¹⁸ Before the reconstruction of the attenuation map is carried out, which is the final stage of the DXCT approach,^8,19,20 a calibration process (hereafter known as the BMD calibration stage) is performed according to the BMD argument. This is an intermediate stage to relate the photon energy information to known engineering materials that mimic soft and hard tissue materials in the body. Materials such as acrylic and aluminum are commonly used for the BMD stage.^8,19,20 Details of the BMD calibration process have been reported elsewhere.²¹

One of the early proponents for the use of attenuation maps from DXCT for attenuation correction to enhance the accuracy of quantitative SPECT imaging was led by Hasegawa et al.³ Hasegawa et al. reported that SPECT images, in the absence of attenuation correction, or with minimal correction such as the use of a uniform water-equivalent map, resulted in erroneous count levels in some parts of the phantom, such the lung region (increased count level) and cardiac region (decreased count levels). Introducing DXCT imaging for an object-specific attenuation correction could result in an overall improvement in the accuracy of the reconstruction map but erroneous count levels persisted in some parts of the phantom, e.g., cardiac chamber (10% error).³ Motivated by the study performed by Gingold and Hasegawa, on the systematic bias in the BMD method for quantitative dual-energy x-ray absorptiometry (DXA), where the findings had implicated that dual-energy methods could result in energy-dependent errors, Goh et al.⁸ investigated the BMD method in DXCT and identified energy-dependent systematic errors present in the DXCT attenuation maps. Additionally, findings from computer simulation had led Goh et al.⁸ to speculate that the presence of energy-dependent systematic errors could be more problematic when high-atomic number element were present in the body, such as the use of iodine as a radiographic contrast agent in the body. Consequently, Goh et al.⁸ found that for a given attenuation map derived from a predetermined set of dual-energy spectra, the errors could be drastically reduced by a judicious selection of a set of basis materials for the basis material calibration process that could radiographically mimic the high atomic number element material present in the body. Clearly, without a good knowledge of the more appropriate set of basis materials, performing the calibration process by trial and error would incur much inconvenient. To overcome this, Goh et al.¹⁹ developed a facile and novel approach for identifying and applying the most appropriate set of basis materials without the need to perform a calibration process. This is known as the basis material coefficients transformation (BMT) method. In the BMT method, Goh et al. proposed that one may establish a more desired set of basis materials that is BMD-equivalent to the starting set of basis materials used in the calibration process. This involved a mathematical model to determine the matrix for transforming the basis material coefficients of the starting basis materials to a new set of basis material coefficients of the desired basis materials. Using computer simulation, Goh et al.¹⁹ reported that accuracy of better than 2% could be achieved when iodine was present in the body (at concentrations such as 10% by mass) when the BMT method was applied to establish acrylic and an iodine-water mixture as the desired basis set (even if the calibration basis materials such as acrylic and aluminum were used as the starting set of basis materials). Thus, while the DXCT/BMD method suffers from drawbacks, namely, the occurrence of energy-dependent systematic errors in the attenuation map arising from the presence of radiographic contrast agents,² or radioisotopes, containing high atomic number element in the body, findings from the simulation study suggest that the errors may be reduced by applying the BMT method.

With regard to the use of attenuation maps from DXCT for attenuation correction to enhance the accuracy of quantitative SPECT imaging as proposed by Hasegawa et al., to the authors’ knowledge, so far no report has been published on the possible influence of the presence of high-atomic number element material on the final accuracy of the quantitative measurement in the SPECT images. Additionally, if errors do occur, it is not clear if the incorporation of the BMT method into DXCT could enhance the accuracy when object-specific attenuation correction is applied in SPECT imaging.

In this report, we present a computer simulation study to investigate the use of DXCT images for object-specific attenuation correction in SPECT imaging, when iodine-based contrast agent was present. The research is novel and important and would be of great interest to the SPECT imaging community mainly because the combination of DXCT with SPECT is rarely studied. The novelty and importance of the study are about the approach to mitigate the effects of the presence of high-atomic number element in the body on quantitative results derived from the reconstructed SPECT image, using BMT/SPECT and/or BMD/SPECT. Although the idea was first mooted in 1998 in discussion with the late Professor Bruce Hasegawa (a co-author in our previous papers^8,19), it was surprising to note that to date there has been no study on the use of DXCT/BMT for attenuation correction in SPECT, even though there is progressive development on the SPECT with XCT^22–25 and DXCT^22,26 that benefits qualitative and quantitative applications. For further details, Table 3 in the Appendix presents a chronological sequence of the progress of quantitative SPECT/CT to justify our current work. This report described a comparative analysis of three different attenuation correction methods, namely, DXCT with BMD⁸ and DXCT/BMD followed by the BMT method,¹⁹ versus the traditional x-ray CT. Thereafter the three methods were referred to as X/SPECT, BMD/SPECT, and BMT/SPECT, respectively. No clinical protocols and clinical cases were considered here.

Table 3.

Quantitative SPECT/CT: key studies underpinning the motivation of current work.

Reference	Study	Findings
Elleaume et al.23	Quantitative analysis of CT images containing contrast agent (iodine) using monoenergetic x-rays from synchrotron source	Two methods were compared: K edge subtraction versus temporal subtraction. Both methods measured the iodine concentration and showed comparable results.
Lee and Chen24	Quantitative analysis of radioactivity in SPECT using CTMAC, a CT-based mean attenuation correction from attenuation map derived from an x-rays CT (80-kVp source)	The performance of the CTMAC was compared with six other methods. All resulted in comparable errors. But among these methods, the CTMAC has the shortest correction time.
Yamada et al.26	Explored the possibility of attenuation correction for SPECT reconstruction using attenuation map derived from DXCT (80/140-kVP sources)	The presence of dense substances, e.g., iodine led to artifacts in the attenuation map, and the corresponding errors in the attenuation values, and this propagated into the SPECT image, resulting in artifacts. Compared to XCT, the quantified attenuation errors and artifacts produced by DXCT method were less severe. There was no study to mitigate the errors.
Dickson25	A survey on the adoption and current practice of quantitative SPECT	The survey focussed on UK. It found that a quantitative measurement of kBq/cc and standardized value uptake is performed by a significant minority.
Ljungberg and Pretorius22	Following from the review on the technological advances undertaken by Hasegawa’s group in 2006,6 Ljungberg et al. reflected the technological development, such as improved hardware components, including some form of dual-energy methods, and clinical applications of SPECT/CT to-date	Photon attenuation and scatter, and collimator response, present the bottle neck to the quality of the reconstructed image. The effects from these factors result in artefacts which must be mitigated, so that quantitative measurements and qualitative examination can produce useful conclusion, and not be based on false positives.

2. Theoretical Background

The DXCT approach underpins the modeling of the linear attenuation coefficient ($\mu$) at any point $(x,y)$ in the slice of interest in the body by a linear combination of the photoelectric (${\mu }_P$) and Compton scattering (${\mu }_C$) coefficients contribution, giving

$$\mu (x,y,E)={\mu }_P(x,y,E)+{\mu }_C(x,y),$$ (1)

where

$$\begin{gathered} {\mu }_P(x,y,E)=a_P(x,y)g(E), \\ {\mu }_C(x,y,E)=a_C(x,y)f_{KN}(E), \end{gathered}$$ (2)

and $a_P$ and $a_C$ contain information about the material at point $(x,y)$ in the slice of interest, $g$ and $f_{KN}$ are the photoelectric and Compton scattering energy dependence functions, respectively, and $E$ is energy (keV).⁴ For a given energy $E$, these functions can be expressed as

$$g(E)=1/E^3,$$ (3)

and

$$f_{\mathrm{KN}}(\alpha )=\frac{1+\alpha }{{\alpha }^2}[\frac{2(1+\alpha )}{1+2\alpha }-\frac{\ln (1+2\alpha )}{\alpha }]+\frac{\ln (1+2\alpha )}{2\alpha }-\frac{1+3\alpha }{{(1+2\alpha )}^2},$$ (4)

where $\alpha =E/510.975$.⁴

Consider a transmission CT system (with a fan beam geometry) comprising of an array of detector elements lined along a sector of the circle around the body, where $x$ represents the relative position of each detector element. The number of photons detected at each detector element, known as projection data, $P(x_i,\varphi )$, as the detectors rotate about the phantom from angles $\varphi =0\mathrm{deg}$ to 360 deg, is given as

$$P(x_i,\varphi )=\int S_{\text{in}}(E)e^{-\int \mu (x,y,E)\mathrm{d}s}\mathrm{d}E,$$ (5)

where $\mathrm{d}s$ refers to an elemental length of the integration over the straight path of the photon in the body from the point of entry to the point of exit, $S_{\text{in}}(E)$ models the energy spectra of the x-ray source (defined as the incident photon number density function of photon energy, $E$), and $\mu (x,y,E)$ denotes the linear attenuation coefficient at a point $(x,y)$ at a given $E$.²⁷ For the traditional XCT simulation, the $p(x_i,\varphi )$, was used to determine the $\mu (x,y,E_{\mathrm{eff}})$, to produce the image by a convolution/back-projection algorithm, where $E_{\mathrm{eff}}$ represents the effective (transmission) energy of the incident x-ray spectrum.

For the DXCT approach, Eq. (5) gives rise to two sets of line integrals, namely, $A_{\mathrm{P}}(x_i,\varphi )$ and $A_{\mathrm{C}}(x_i,\varphi )$, corresponding to the photoelectric (attenuation at lower photon energies) and Compton (scattering at upper photon energies) contributions along each ray path, i.e.,

$$A_{\mathrm{P}}(x_i,\varphi )=\int a_{\mathrm{P}}(x,y)\mathrm{d}s,$$ (6)

and

$$A_{\mathrm{C}}(x_i,\varphi )=\int a_{\mathrm{C}}(x,y)\mathrm{d}s.$$ (7)

Thus, $A_{\mathrm{P}}(x_i,\varphi )$ and $A_{\mathrm{C}}(x_i,\varphi )$ are unknowns to be determined. In theory, if $A_{\mathrm{P}}(x_i,\varphi )$ and $A_{\mathrm{C}}(x_i,\varphi )$ could be determined for each ray, these could be used to derive the ${\mathrm{a}}_{\mathrm{P}}$ and ${\mathrm{a}}_{\mathrm{C}}$ at any $(x,y)$ in the slice. It follows that the $\mu$ can be determined at any point in the slice by substituting the $a_P$ and $a_C$ into Eq. (2). Essentially, one makes measurements at two independent energy spectra, $S_1$ and $S_2$, corresponding to a lower and upper energy range, respectively, to obtain the respective $P_1$ and $P_2$, i.e.,

$$\begin{gathered} P_1(x_i,\varphi )=\int S_1(E)e^{-\int \mu (x,y,E)\mathrm{d}s}\mathrm{d}E, \\ {P}_2(x_i,\varphi )=\int S_2(E)e^{-\int \mu (x,y,E)\mathrm{d}s}\mathrm{d}E. \end{gathered}$$ (8)

The two spectra $S_1$ and $S_2$ data may be obtained by (1) different anode voltages, (2) a single x-ray source with different x-ray filter material in the beam, (3) a single x-ray source with energy-selective detectors to discriminate the x-ray energies into $S_1$ and $S_2.$ It follows that $P_1$ and $P_2$ in Eq. (8) may be expressed in terms of $A_{\mathrm{P}}(x_i,\varphi )$ and $A_{\mathrm{C}}(x_i,\varphi )$ as follows:

$$\begin{gathered} \ln (P_1(x_i,\varphi ))=b_0+b_1{A}_P(x_i,\varphi )+b_2{A}_C(x_i,\varphi )+b_3{[A_P(x_i,\varphi )]}^2 \\ +b_4{[A_C(x_i,\varphi )]}^2+b_5[A_P(x_i,\varphi )][A_C(x_i,\varphi )]\dots , \\ \ln (P_2(x_i,\varphi ))=c_0+c_1{A}_P(x_i,\varphi )+c_2{A}_C(x_i,\varphi )+c_3{[A_P(x_i,\varphi )]}^2+c_4{[A_C(x_i,\varphi )]}^2+c_5[A_P(x_i,\varphi )][A_C(x_i,\varphi )]\dots \end{gathered}$$ (9)

where the set of $b$ and $c$ coefficients may be determined analytically. In practice, the $b$ and $c$ coefficients are determined from experiments on two known materials, which we shall refer to as BM1 and BM2. This is the BMD argument whereby the basis material line integrals, $A_{\mathrm{BM}1}(x_i,\varphi )$ and $A_{\mathrm{BM}2}(x_i,\varphi )$, replace the $A_{\mathrm{P}}(x_i,\varphi )$ and $A_{\mathrm{C}}(x_i,\varphi )$ line integrals, i.e.,

$$\begin{gathered} \ln (P_1(x_i,\varphi ))=b_0+b_1{A}_{BM1}(x_i,\varphi )+b_2{A}_{BM2}(x_i,\varphi )+b_3{[A_{BM1}(x_i,\varphi )]}^2 \\ +b_4{[A_{BM2}(x_i,\varphi )]}^2+b_5[A_{BM1}(x_i,\varphi )][A_{BM2}(x_i,\varphi )]\dots , \\ \ln (P_2(x_i,\varphi ))=c_0+c_1{A}_{BM1}(x_i,\varphi )+c_2{A}_{BM2}(x_i,\varphi )+c_3{[A_{BM1}(x_i,\varphi )]}^2 \\ +c_4{[A_{BM2}(x_i,\varphi )]}^2+c_5[A_{BM1}(x_i,\varphi )][A_{BM2}(x_i,\varphi )]\dots . \end{gathered}$$ (10)

This decomposition argument is equivalent to the photoelectric-Compton decomposition argument; the former may be transformed to the latter using a simple linear transformation.¹⁸ Thus, to determine the $b$ and $c$ coefficients, a separate step is needed to calibrate the DXCT system for relating $P_1$ and $P_2$ to a combination of $A_{BM1}(x_i,\varphi )$ and $A_{BM2}(x_i,\varphi )$ using the known materials, $BM1$ and $BM2$. Since the $A_{BM1}(x_i,\varphi )$ and $A_{BM2}(x_i,\varphi )$ parameterize the actual lengths of the materials used, these physical measurements may be achieved to a high precision. [NB: the evaluation of $P_1(x_i,\varphi )$ and $P_2(x_i,\varphi )$ projections to enable radiographic (projection) images to be acquired leads to a variant method known as DXA, see, e.g., Ref. 28]. Following the calibration process to obtain $P_1$ and $P_2$, and $A_{\mathrm{BM}1}(x_i,\varphi )$ and $A_{\mathrm{BM}2}(x_i,\varphi )$, instead of using Eq. (10) to obtain the values $b$ and $c$, one applies the inverse dual-energy equations [obtained by inverting the relationship between the $P\mathrm{s}$ and $A\mathrm{s}$ in Eq. (10)], i.e.,

$$\begin{gathered} A_{BM1}(x_i,\varphi ))={b^{\prime }}_0+{b^{\prime }}_1\ln (P_1(x_i,\varphi ))+{b^{\prime }}_2\ln (P_2(x_i,\varphi ))+{b^{\prime }}_3{[\ln (P_1(x_i,\varphi ))]}^2+{b^{\prime }}_4[\ln (P_2(x_i,\varphi )){]}^2+{b^{\prime }}_5\ln (P_1(x_i,\varphi ))\ln (P_2(x_i,\varphi ))\dots , \\ {A}_{BM2}(x_i,\varphi ))={c^{\prime }}_0+{c^{\prime }}_1\ln (P_1(x_i,\varphi ))+{c^{\prime }}_2\ln (P_2(x_i,\varphi ))+{c^{\prime }}_3{[\ln (P_1(x_i,\varphi ))]}^2 \\ +{c^{\prime }}_4{[\ln (P_2(x_i,\varphi ))]}^2+{c^{\prime }}_5\ln (P_1(x_i,\varphi ))\ln (P_2(x_i,\varphi ))\dots \end{gathered}$$ (11)

to obtain the $b^{\prime }$ and $c^{\prime }$ coefficients numerically. Thereafter, Eq. (11) is applied to solve for $A_{\mathrm{BM}1}$ and $A_{\mathrm{BM}2}$ from the $P_1$ and $P_2$ which are derived from the slice of interest in the body. Finally, one determines the basis material coefficients, $a_{\mathrm{BM}1}(x,y)$ and $a_{\mathrm{BM}2}(x,y)$, from $A_{\mathrm{BM}1}(x_i,\varphi )$ and $A_{\mathrm{BM}2}(x_i,\varphi )$ by a convolution/back-projection algorithm, and $\mu (x,y,E_{\mathrm{disp}})$ is predicted using

$$\mu (x,y,E_{\mathrm{disp}})=a_{BM1}(x,y){\mu }_{BM1}(E_{\mathrm{disp}})+a_{BM2}(x,y){\mu }_{BM2}(E_{\mathrm{disp}})$$ (12)

where ${\mu }_{\mathrm{BM}1}$ and ${\mu }_{\mathrm{BM}2}$ represent the attenuation coefficients of $BM1$ and $BM2$, respectively at any desired energy, $E_{\mathrm{disp}}$, of interest.

By extending the equivalent argument to a different set of basis materials, Goh et al. developed the BMT method. This involves determining the $a_{\mathrm{BM}3}(x,y)$ and $a_{\mathrm{BM}4}(x,y)$ of a more compatible basis material set, using a transformation matrix that relates $a_{\mathrm{BM}3}(x,y)$ and $a_{\mathrm{BM}4}(x,y)$ to $a_{\mathrm{BM}1}(x,y)$ and $a_{\mathrm{BM}2}(x,y)$ as follows:

$$\left(\begin{array}{c}{a}_{BM3}\\ a_{BM4}\end{array}\right)=\left[\begin{array}{cc}{m}_{11}& m_{12}\\ m_{21}& m_{22}\end{array}\right]\left(\begin{array}{c}{a}_{BM1}\\ a_{BM2}\end{array}\right),$$ (13)

where the values of the matrix entries, $m_{11}$, $m_{12}$, $m_{21}$, and $m_{22}$ depend on the linear attention of the basis materials 1, 2, 3, and 4.^8,19 Thereafter, $\mu (x,y,E_{\mathrm{disp}})$ is evaluated using

$$\mu (x,y,E_{\mathrm{disp}})=a_{BM3}(x,y){\mu }_{BM3}(E_{\mathrm{disp}})+a_{BM4}(x,y){\mu }_{BM4}(E_{\mathrm{disp}}),$$ (14)

where ${\mu }_{BM3}$ and ${\mu }_{BM4}$ represented the attenuation coefficients of the new set of basis materials.

3. Materials and Methods

3.1. In Silico Study of Transmission and Emission CT

A schematic of the simulation flow of the respective BMD/SPECT, BMT/SPECT, and X/SPECT is shown in Fig. 1. The simple thorax-like phantom [Fig. 2(a)], containing varying concentrations of iodine/water mixture in the heart region (Table 1),^8,19 was employed in both the transmission imaging and SPECT simulations.

Fig. 1.

Schematic diagram showing the simulation flow for non-uniform attenuation correction in the SPECT imaging.

Fig. 2.

Schematics of the in silico study of transmission CT for x-ray sources and emission CT from radionuclide sources. (a) Schematic of the simple thorax-like phantom. (b) Overview of the x-ray transmission process. (c) Evaluating the line integrals for the x-ray transmission. (d) Evaluating the line integrals for the gamma-ray emission. Each panel shows a 2D thorax-like phantom [described by a function $f(x,y)$], with predetermined distributed attenuation constants. The global $xy$ coordinate system (the initial position) is indicated in (b) and (c); the center of the phantom defined the origin of the coordinate system. Each line integral is parameterized by $(\varphi ,t)$; the line is described by an equation $t=x\cos \varphi +y\sin \varphi$; the corresponding project data collected at the detector is represented by $P_{\varphi }(t)$ or $P(x_i,\varphi )$. Line C-C’ indicates the transformed $x$ axis when the $x$ ray source-detector rotates to $\varphi$; $(t,s)$ represents the coordinates of the rotated coordinate system. Symbols s and d represent distances.

Table 1.

The organs and their compositions in the simple thorax-like phantom.

Region of interest	Composition	Density ($\mathrm{g}/{\mathrm{cm}}^3$)
Heart	Water and iodine mixture, at 0%, 1%, 5%, and 10% (with respect to the mass of iodine)	1.00 (0%)
		1.01 (1%)
		1.04 (5%)
		1.08 (10%)
Main body	Water	1.00
Spine	Bone mineral	3.06
Sternum	Compact bone	1.85
Lung	Void space	0.00

With regard to the transmission CT simulations, the polychromatic x-ray source for the traditional XCT simulation involved a bremsstrahlung 80-kVp spectrum.²⁹ For the DXCT simulations, a 120-kVp spectrum²⁹ filtered with 1-mm gadolinium to produce a bimodal profile with peak photon energies of 47 and 99 keV, was used for the DXCT/BMD and DXCT/BMT approaches.

For the SPECT simulation, radiopharmaceuticals associated with two types of radionuclides, ${}^{201}\mathrm{Tl}$ and ${}^{99\mathrm{m}}\mathrm{Tc}$, were employed; these radionuclides emit the respective gamma-ray energies of 75 and 140 keV, respectively. In each case, the radionuclide was modeled as uniformly distributed in the heart and main body with the respective concentrations of $1.5\times {10}^6$ and $0.3\times {10}^6\text{disintegration}/\mathrm{s}$, giving a ratio 5:1, to consistency with previous studies^3,30–32 and with clinical practices reported elsewhere.³³

Figures 2(b)–2(d) shows schematics of the in silico study of transmission CT for x-ray sources and emission CT from radionuclide sources. Both transmission (with a fan beam geometry) CT and SPECT in silico studies employed a ray-tracing algorithm. The detector was modeled as an array of detector elements lined along a sector of the circle around the phantom [Fig. 2(b)]. In the transmission CT, a ray-tracing algorithm was employed to simulate the emission of x-ray from a point source outside the patient and the propagation of the ray in a straight line spread over a fan-beam geometry [Fig. 2(c)]. The rays terminated on the other side of the patient over an array of detectors. We assumed that the collimator coupled to the detector (an infinite collimation) could only detect photons that were travelling in parallel directions within a bundle of ray. In addition, the total number of photons collected by the detector in a given time interval was proportional to the total concentration of the x-ray source along the line defined by $t$ [Fig. 2(c)]. Projection data, $P(x_i,\varphi )$, from angles $\varphi =0\mathrm{deg}$ to 360 deg, was determined. Following each exposure (generating one projection), the detector-collimator system was rotated to $\varphi$ to generate the next projection and so on. During the reconstruction stage (Sec. 3.2), Eq. (5) was evaluated by a convolution/back-projection method to determine $\mu (x,y,E)$ at any point $(x,y)$ in the body for a given $E$.

Figure 2(d) shows the ray tracing schematic for the emission CT. The specific regions of the phantom were designated with the following $\rho (x,y)$, namely, $0.3\times {10}^6$ (main body) and $1.5\times {10}^6$ (heart region) count/pixel, with a 1:5 ratio. An element of the respective sources was assumed to be an isotropic source of gamma rays. The number of gamma-ray photons emitted per second by such an element was proportional to the concentration of the source at that point. Simulated radionuclide projection data were acquired using a ray-tracing algorithm with the following considerations. First, the gamma ray from the emitting source would be subjected to attenuation in the phantom; the degree of attenuation was regulated by the photon energy and the attenuation coefficient property of the tissue encountered by the photon in the path of travel, as described in Eq. (19). The attenuation maps from the respective XCT, DXCT/BMD, and DXCT/BMT were used in the SPECT simulation to account for this effect. In addition, the noise from the radionuclide source was assumed to be regulated by Poisson process, i.e., the noise is correlated with the intensity of each pixel, to consistency with studies reported else.^2,34 Thus, Poisson noise was applied to the respective main body and heart region of the phantom.

3.2. Reconstruction of Energy-Specific CT Images

To perform object/energy-specific attenuation correction for the SPECT images, the attenuation maps from the traditional XCT and DXCT simulation were converted to display the attenuation coefficients at the energy $E_{\mathrm{disp}}=75$ and 140 keV, where were associated with the radionuclides ${}^{201}\mathrm{Tl}$ and ${}^{99\mathrm{m}}\mathrm{Tc}$, respectively, used in the SPECT imaging.² For simplicity, the respective operation on XCT and DXCT involved simple scaling or linear combination of the attenuation information acquired to the linear attenuation map of the desired energy. In this study, no attempt was made to model the effects from a predetermined energy window around the desired energy.

For the traditional XCT simulation, the $\mu (x,y,E_{\mathrm{eff}})$ was used to predict the $\mu (x,y,E_{\mathrm{disp}})$ using

$$\mu (x,y,E_{\mathrm{disp}})=\mu {(x,y,E_{\mathrm{eff}})}^{\prime }[{\mu }_{\text{water}}(E_{\mathrm{disp}})/{\mu }_{\text{water}}(E_{\mathrm{eff}})],$$ (15)

where ${\mu }_{\text{water}}$ represented the $\mu$ of water. The ${\mu }_{\text{water}}(E_{\mathrm{eff}})$ was identified with the average values within a reconstructed XCT image of a uniform water phantom; the ${\mu }_{\text{water}}(E_{\mathrm{disp}})$ was obtained from a table of attenuation coefficients.³⁵

For the DXCT simulation, after obtaining the $P_1(x_i,\varphi )$ and $P_2(x_i,\varphi )$ for the slice of interest in the body, the basis material line integrals, $A_{\mathrm{AC}}(x_i,\varphi )$ and $A_{\mathrm{AL}}(x_i,\varphi )$, corresponding to acrylic and aluminum materials (to radiographically mimic soft and hard tissues respectively) were determined from Eq. (11), where coefficients $b_{\mathrm{AC}}\mathrm{s}$ and $b_{\mathrm{AL}}\mathrm{s}$ were determined from a basis material calibration algorithm. To execute the BMD method, we evaluated the basis material coefficients, $a_{\mathrm{AC}}(x,y)$ and $a_{\mathrm{AL}}(x,y)$, from $A_{\mathrm{AC}}(x_i,\varphi )$ and $A_{\mathrm{AL}}(x_i,\varphi )$ by a convolution/back-projection algorithm, from which $\mu (x,y,E_{\mathrm{disp}})$ was predicted using Eq. (12), giving

$$\mu (x,y,E_{\mathrm{disp}})=a_{AC}(x,y){\mu }_{AC}(E_{\mathrm{disp}})+a_{AL}(x,y){\mu }_{AL}(E_{\mathrm{disp}}),$$ (16)

where ${\mu }_{\mathrm{AC}}$ and ${\mu }_{\mathrm{AL}}$ represented the attenuation coefficients of acrylic and aluminum, respectively. To execute the BMT method, i.e., to obtain the basis material coefficients of a more compatible basis material set, namely, acrylic ($a_{\mathrm{AC}}(x,y)$) and iodine at 20% by weight in a mixture of iodine and water ($a_{\mathrm{I}20}(x,y)$), with regard to the iodinated heart region, we evaluated the transformation matrix relating $a_{\mathrm{AC}}(x,y)$ and $a_{\mathrm{I}20}(x,y)$ to $a_{\mathrm{AC}}(x,y)$ and $a_{\mathrm{AL}}(x,y)$ using Eq. (13), giving

$$\left(\begin{array}{c}{a}_{\mathrm{AC}}\\ a_{\mathrm{I}20}\end{array}\right)=\left[\begin{array}{cc}{m}_{11}& m_{12}\\ m_{21}& m_{22}\end{array}\right]\left(\begin{array}{c}{a}_{\mathrm{AC}}\\ a_{\mathrm{AL}}\end{array}\right).$$ (17)

Thereafter, $\mu (x,y,E_{\mathrm{disp}})$ was evaluated using Eq. (14), giving

$$\mu (x,y,E_{\mathrm{disp}})=a_{AC}(x,y){\mu }_{AC}(E_{\mathrm{disp}})+a_{I20}(x,y){\mu }_{I20}(E_{\mathrm{disp}}),$$ (18)

where ${\mu }_{\mathrm{AC}}$ and ${\mu }_{\mathrm{I}20}$ represented the attenuation coefficients of acrylic and iodine at 20% by weight, respectively. Figure 3 shows a typical final reconstructed image of the phantom containing the attenuation coefficient values, ready for use in the SPECT reconstruction stage.

Fig. 3.

Intermediate results. (a) A reconstructed image (i.e., attenuation map) of the thorax-like phantom, by the DXCT/BMT protocol, using acrylic and iodine (20%) as the basis materials. The image was reconstructed at photon energy of 75 keV. (b) Graph of the linear attenuation coefficient versus pixel number derived from the region in the image indicated by line bb’. (c) Graph of the linear attenuation coefficient versus pixel number derived from the region in the image indicated by line cc’.

3.3. Reconstruction of Attenuation-Corrected SPECT Images

A SPECT image ($128\times 128\text{pixels}$) reconstruction technique involving the iterative maximum likelihood expectation maximization (ML-EM)^3,30—which considered the respective $\mu (x,y,E_{\mathrm{disp}})$ from Eqs. (15)–(18)—was used to evaluate the number of photon counts ($\rho (x,y)$) from $P(x_i,\varphi )$ as follows:

$$P(x_i,\varphi )=\iint \rho (x,y)e^{(-[d-s]\mu )}\delta (x\cos \varphi +y\sin \varphi -t)\mathrm{d}x\mathrm{d}y,$$ (19)

where $[d-s]$ represented the relative distance between the radionuclide point source in the body and the exit point of the gamma-ray photon, $t$ the relative distance between the radionuclide point source and the origin of the coordinate system fixed to the body, and $\delta$ the Dirac delta function.²⁷ Of note, the $\rho (x,y)$ is proportional to the concentration of the radionuclide at each point in the heart and main body.

The ML-EM algorithm²² was employed to reconstruct the attenuation-corrected radionuclide images (the objective function) based on a square ($128\times 128$) grid covering the circular outline of the phantom. Before a reconstruction began, uniform values of $\rho (x,y)$ were assigned to all regions as an “initial” estimate of the unknown $\rho (x,y)$. When the reconstruction started, the algorithm determined all the SPECT projections (as described in Sec. 3.1), with the help of the respective XCT, DXCT/BMD, and DXCT/BMT reconstructed attenuation maps for attenuation correction. This evaluated the difference between the calculated projections (ML-EM) and the in silico-derived projections (Sec. 3.1). Should the difference be large, it implied that the estimated activity distribution did not adequately predict the actual distribution (from the in silico simulation). Therefore, the initial estimate would be updated based on the difference between the calculated projections of the estimate and the in silico-derived projections by back-projecting the deviations between these two projection sets. The result of the back-projection yielded an error image containing pixel values that were used as weighting factors to update the initial image estimate. The entire process up to this point was repeated (iteratively) until the deviation converged to a sufficiently small value.

The error in the attenuation-corrected $\rho (x,y)$ map, arising from the systematic errors in the attenuation map, was defined as

$$\text{Error}=100\times (C_{\mathrm{nom}}-C_{\text{sim}})/C_{\mathrm{nom}},$$ (20)

where $C_{\mathrm{nom}}$ and $C_{\text{sim}}$ represented the values of the normalized count in the region of interest (ROI), obtained from the nominal (${\rho }_{\mathrm{nom}}(x,y)$, a reference/nominal image reconstructed using in silico-derived reconstructed images (Sec. 3.1), i.e., corresponding to ${\rho }_{X/\mathrm{SPECT}}(x,y)$, ${\rho }_{\mathrm{BMD}/\mathrm{SPECT}}(x,y)$ and ${\rho }_{\mathrm{BMT}/\mathrm{SPECT}}(x,y)$, respectively. The normalized counts referred to the counts per pixel within a selected region-of-interest of the respective nominal and simulated maps, normalized by the total number of counts over the whole image. A circular region with a diameter of six pixels wide at the center of the radionuclide distribution was defined as the ROI. The mean count and standard deviation of the mean in the ROI were computed at the end of the run.

4. Results

4.1. Overview

Figure 4 shows the graph of the error versus iodine concentration in the two regions of interest, namely, heart and main body. In general, the magnitudes of the error increased non-linearly with increasing iodine concentration. The specific trending variation depended on the method used in the attenuation correction and the energy used in generating the attenuation coefficient image.

Fig. 4.

Graphs of error (counts) versus iodine concentration for the (a), (c), (e) heart and (b), (d), (f) main body regions of the thorax-like phantom at 75 and 140 keV derived from SPECT imaging with attenuation correction using images derived from the respective transmission x-rays methods, namely XCT, DXCT/BMD, and DXCT/BMT.

Overall, it was concluded that the BMT/SPECT approach was most effective in reducing the magnitude of the errors of the counts in the iodine-filled heart region. From Fig. 4, for informational purpose, we present a summary of the results obtained with X/SPECT, BMD/SPECT, and BMT/SPECT, in Table 2, highlighting the largest magnitude of the error observed in each of the three cases. For further details, Table 4 in the Appendix lists the largest (magnitude) errors (%) found within each region of the heart and main body, and corresponding radionuclide activity (count/pixel), at the respective energies, 75 and 140 keV.

Table 2.

Summary of the largest (magnitude) errors (%) in the predicted radionuclide activity (count/pixel), associated with the respective $E=75$ and 140 keV, derived from Fig. 4.

		When iodine was absent in the heart			When iodine was present in the heart
Region	E, keV	X/SPECT (%)	BMD/SPECT (%)	BMT/SPECT (%)	X/SPECT (%)	BMD/SPECT (%)	BMT/SPECT (%)
Heart	75	−3.0	1.2	0.8	−35.0	5.5	0.8
	140	−5.0	−0.3	0.4	−95.0	−5.0	0.9
Main body	75	−3.4	1.2	0.9	−3.7	1.1	0.8
	140	−2.9	0.1	0.4	−3.3	0.1	0.4

Table 4.

Summary of the largest (magnitude) errors (%) found within each region of the heart and main body, and corresponding radionuclide activity (count/pixel), at the respective energies, 75 and 140 keV.

			X/SPECT		BMD/SPECT		BMT/SPECT
Region	E, keV	Iodine conc (%)	Largest error (%)	Count/pixel	Largest error (%)	Count/pixel	Largest error (%)	Count/pixel
Heart	75	0	−1.13	1516956	3.47	1448014	2.84	1457432
		1	2.56	1461648	3.63	1445606	2.56	1461648
		5	−26.72	1900818	4.21	1436858	1.41	1478839
		10	−35.08	2026260	4.83	1427541	−0.09	1501413
	140	0	−2.75	1541298	1.18	1482267	1.80	1472927
		1	1.76	1473557	0.59	1491199	1.76	1473557
		5	−52.15	2282252	−1.73	1525913	1.71	1474361
		10	−93.18	2897708	−4.52	1567803	1.82	1472723
Main body	75	0	−11.68	335029	−6.82	320460	−7.03	321075
		1	−6.74	320216	−6.50	319489	−6.74	320216
		5	−11.56	334685	−5.42	316246	−5.80	317404
		10	−11.65	334947	−4.50	313494	−4.80	314409
	140	0	−11.00	332989	−7.79	323364	−7.59	322758
		1	−7.51	322535	−7.72	323168	−7.51	322535
		5	−11.65	334943	−7.45	322348	−7.21	321635
		10	−12.57	337707	−7.11	321342	−6.83	320491

4.2. X/SPECT

With regard to the X/SPECT simulation, in the absence of iodine, the errors associated with 75 and 140 keV yielded $-3\%$ and $-5\%$, respectively, in the heart [Fig. 4(a)]. In the main body, the errors were $-3.4\%$ (75 keV) and $-2.9\%$ (140 keV) [Fig. 4(b)]. The errors increased in magnitude (negatively) in both regions with increasing iodine concentration in the heart. In particular, at the respective 75 and 140 keV, the errors in the heart (up to $-100\%$) were dramatically larger than those in the main body region (up to $-5\%$), for the range of iodine concentration studied.

Overall, in the heart, the errors at 75 keV were smaller than those at 140 keV. On the other hand, in the main body, the errors at 75 keV were larger than those at 140 keV.

Overall, both the low- and high-energy attenuation maps yielded errors that were more insensitive to variation in iodine concentration in the main body as compared errors in the heart region. Thus, high iodine concentration could result in an overestimation of the counts and, consequently, large errors were observed from the counts data.

4.3. BMD/SPECT

With regard to the BMD/SPECT simulation, attenuation correction using DXCT/BMD images resulted in underestimating (75 keV) and overestimating (140 keV) the counts in the heart [Fig. 4(c)]. In the absence of iodine, the errors were $\sim 1.2\%$ (75 keV) and $-0.3\%$ (140 keV). These errors increased positively (75 keV) and negatively (140 keV) with increasing iodine concentration.

In the main body region [Fig. 4(d)], in the absence of iodine, the errors at 75 and 140 keV were $\sim 1.2\%$ (75 keV) and 0.1% (140 keV). The magnitudes in both cases decreased, albeit marginally, with increasing iodine concentration, and flattened out beyond 1% iodine concentration.

A comparison of the errors in the heart and main body revealed that the errors in the main body were appreciably smaller than those in the heart region, over the range of iodine concentration shown here. The counts were underestimated in the main body (for 75 and 140 keV). However, in the heart region, the counts were underestimated at 75 keV but overestimated at 140 keV.

Overall, in the main body region, both the low and high energy attenuation maps yielded errors that were more insensitive to variation in iodine concentration than in the heart region.

4.4. BMT/SPECT

With regard to the BMT/SPECT simulation, attenuation correction using DXCT/BMT images resulted in underestimating the counts in the heart in both 75 and 140 keV [Fig. 4(e)]. In the absence of iodine, the errors were $\sim 0.7\%$ (75 keV) and 0.4% (140 keV). The errors increased with increasing iodine concentration. While the magnitudes of the error from the 75 keV were larger than those of the 140 keV at low iodine concentration, the rate of increase of the former was greater than that of the latter. Thus, beyond 8% iodine concentration, the magnitude of the error at the 140 keV overtook the 75 keV; at 10% iodine concentration, the error at the 140 keV peaked at 0.9% while the error at the 75-keV peaked at 0.8%. Overall, the small errors in both cases (75 and 140 keV) suggested that the presence of iodine in the heart had no appreciable effect on the measurement accuracy of radionuclide distribution.

In the main body, the magnitudes of the error at 75 and 140 keV [Fig. 4(f)] revealed similar trending response to the results from the BMD/SPECT protocol [Fig. 4(d)]. Namely, (1) the magnitude of the errors in the absence of iodine were small, $\sim 0.9\%$ (75 keV) and 0.4% (140 keV); (2) the BMT/SPECT protocol underestimated the counts; (3) with increasing iodine concentration the errors decreased gradually; the decrease was more obvious at the lower energy (75 keV) as compared to the higher energy (140 keV); (4) the decrease in the magnitude of the error eventually plateaued out at higher iodine concentration; (5) over the range of iodine concentration studied here, the magnitude of the error at 75 keV was larger than that of 140 keV.

Considering that a ratio of 5:1 for the number of counts was used to model the heart and main body, one might expect that the errors in the former were larger than the latter. However, the results were not as straight-forward as we may think. The magnitude of the errors at the 75 keV in the iodinated heart was marginally smaller than in the main body; the magnitude of the errors at the 140 keV in the iodinated heart was larger than those in the main body.

Of note, we assumed that there was a high specificity of radiopharmaceutical uptake within the target organ, i.e., heart, by setting the target-to-background (otherwise known as tumour-to-background ratio) ratio of 5:1 which was also consistent with clinical practices reported elsewhere.³³ This also helps to achieve an adequate difference in activity concentration between the heart tissue and the surrounding soft tissue.³ Low retention rate in the target organ is problematic as it could result in the leakage into surrounding tissues (tissues external to the target organ). Thus one may find the radiopharmaceutical in the other areas such as main body.

Overall, the errors in the count derived from the BMT/SPECT approach were below 1%. In the heart, the low energy attenuation maps yielded errors that were more insensitive to variation in the iodine concentration as compared to the high energy attenuation maps.

5. Discussion

With X/SPECT simulation, the small errors in the counts obtained at 0% iodine were consistent with the findings reported elsewhere using the uniform scaling method ($\sim 9\%$ to 10% error in myocardial radioactivity concentration³⁶). However, the uniform scaling method led to appreciable errors in the presence of iodine in the heart. The large errors were attributed to (1) failure of the uniform scaling method to accurately account for possible non-uniformity within the region of interest, and (2) scaled attenuation coefficient values associated with materials that possess absorption edges within the current medical diagnostic energy range. The error increased from 10% to 30% (75 keV) and 20% to 95% (140 keV), with increasing iodine concentration. These findings were in good order-of-magnitude agreement with experimental findings from SPECT imaging of small animal-like phantom, in the presence of ${\mathrm{I}}^{125}$-NaI, using attenuation correction from micro-XCT data.³⁷

The greatly reduced errors in the counts (the non-iodinated heart) predicted by the BMD/SPECT simulation, as compared to X/SPECT, showed that attenuation correction using the DXCT approach was more effective than x-ray CT. The errors were much lower than those determined by experiment (overestimated the concentration in the cardiac region by $\sim 10\%$³), but the report from the experimental study did not provide a detailed explanation about how the DXCT experiment was carried out. Given that the study preceded the development of BMD/DXCT, it was speculated that the study was carried out using a “direct” approach that attempted to generate the attenuation map using the photoelectric and Compton coefficients (see Sec. 3.2). The BMD stage underpins assumptions about the basis materials and compatibility of the attenuation coefficients of these basis materials with those of the materials present in the slice of interest. While the direct approach could address the energy-specific problem by generating the attenuation at the desired energy,⁴ the absence of the basis materials stage means that the attenuation map would not be able to adequately reflect the attenuation coefficients associated with the materials present in the slice of interest. More importantly, the current study predicted that the errors in the count may be reduced further, especially in the iodinated heart, if the attenuation map derived from BMT/SPECT method was used. Thus, the BMT/SPECT method was most effective for correcting systematic errors arising from iodine present in the slice.

With regard to the BMD/SPECT and BMT/SPECT methods, the small errors in the counts associated with the main-body (non-iodinated region) suggested that the presence of iodine in the heart region had no appreciable effect on the measurement accuracy in the non-iodinated region. These were consistent with previous results^8,19 which had revealed that the regions with high errors were associated with those containing high atomic number elements.

While iodine concentrations of 1% and below were normally found in the body after the administration of iodinated contrast media, values at 1% and above were included in the simulation studies for the following reasons similar to those mentioned in previous studies.^8,19 First, systematic errors in the small iodine concentration range were usually not significant. However, as these errors could be higher at high iodine concentration, it was worthwhile to investigate the effectiveness of the BMT method for reducing the systematic errors introduced at high concentration range. Second, it would be desirable to generate results that would be applicable to a wide range of systems.

Current clinical SPECT/CT systems use a variety of techniques to convert the Hounsfield Unit (HU) to linear attenuation coefficients, and some are adaptable to patient and scan protocols. CT reconstructions are also relatively sophisticated and capable of mitigating some of the cited issues pointed out in Sec. 1. In principle, the DXCT would have advantages over conventional CT in eliminating the beam hardening artifacts by presenting an attenuation coefficient tomogram at any energy, free from beam hardening artifacts.⁴ In reality, clinical experience dictates that advances in the computer algorithms and clinical protocol could reduce the differences between, e.g., BMT/SPECT and X/SPECT. Thus, the advantage of the BMT/SPECT may be less clear.

In clinical practice, one may exercise a decision to scan either SPECT or (contrast) CT first (or second), or low dose non contrast, and higher dose Contrast CT or vice versa. Alternatively one may wait and scan with the bolus, or until after the contrast has diffused, or reverse the order. In one case one could observe high HU values but spatially localized, with small impact on the path integral of the forward projector. In the other case, one could observe much lower HU but over a larger volume, and possible larger impact on the integration. The key issue is: how close is the image of the CT to the density distribution or the attenuation map during the radiopharmaceutical uptake and metabolism, excluding registration or temporal resolution issues (which in practice may predominate). Other factors that may also mask the actual results are related to scatter correction, energy window width, energy, and spatial resolution and collimator.

The SPECT reconstruction model used [Eq. (19)] is a simple approach that enables the question concerning the accuracy of the X/SPECT versus BMD/SPECT and BMT/SPECT to be answered. Of course, there are other methods of SPECT reconstruction as reported in studies such as the central ray approximation as reported by Liang et al.³⁸ and more recently by Kortelainen et al.³⁹ for the purpose of modeling not only object-specific attenuation but also distance-dependent detector response. Addressing all these are out the scope of this study but they have been identified as subjects for further investigation where our method is concerned.

What is the significance of the effects of iodine concentration on the radionuclide counts and the impact on clinical diagnosis? As revealed by the predictions from the in silico study, when iodine was present, due to the errors propagated from the reconstructed attenuation map, this caused the counts to be underestimated or overestimated. The severity of these errors depended on the photon energy used in the reconstruction of the attenuation map and the protocol adopted. Qualitatively, this could mask the actual radionuclide distribution within the structures in the image.²⁶ Of course, when the iodine solution was absent, the small errors observed could be attributed to the noise as well as errors propagated from the reconstructed attenuation map. Qualitatively, this would not mask the radionuclide distribution in the image.²⁶ We anticipate that these effects could have significance implication for myocardial perfusion imaging to assess the function of the heart muscle, in the context of the current study using the thorax-like phantom. Thus, when iodine is introduced to facilitate the delineation of the features of the heart in the attenuation map for attenuation correction of SPECT images, any errors arising from XCT and DXCT/BMD could compromise the attenuation correction process, and could affect the quantitative assessment of the counts from the radiopharmaceuticals carried by the blood through the arteries. Consequently, this may limit the radiologist’s ability to detect, e.g., clogged arteries and scar tissue arising from a heart attack or inefficient pumping of the blood. Further discussion is out of the scope of this project but this topic has been targeted for further study.

The simple scaling method was used because the XCT images derived from the single spectrum 80 kVp yields an effective mean photon energy of 44 keV and this would not be considered representative of the attenuation map at the photon energy of 75 and 140 keV. To this end, we adopted the uniform scaling method which is a commonly used approach for linearly scaling the attenuation values (at any point on the attenuation map) to any value at the desired photon energy, with respect to the attenuation values of water. Ideally, if the attenuation values versus photon energy over the range of energy of interest are linearly related, and the gradient of this line is similar for all materials, this would lend strong justifications to the simple scaling method. In reality, this is not the case. For materials, e.g. Iodine, present in the body which possess a K edge within the energy range, this could disrupt the linearity assumption. Thus, this may not reproduce exactly the attenuation maps at 75 and 140 keV.

The DXCT method proposed by Alvarez and Macovski involves a model that predicts that the attenuation value at any point in the image is a simple linear combination of two attenuation coefficients (related to the basis materials used), weighted by the respective basis material coefficients. This assumes that only the photoelectric attenuation and Compton scattering contribute predominantly to altering the behavior of the x-ray photon traversing through the body. This is valid within the range of diagnostic energy of interest here. However, contrast media present in the body containing high atomic number elements (e.g., Iodine) which possess a K edge within the energy range could be problematic where one of the basis materials does not possess similar characteristic K edge. To get around this would require a judicious choice of basis materials which could account for the abrupt increase in the attenuation value at the energy of the K edge. Such a basis material would need to have a similar K edge presence as that found in the element of the contrast medium. This simulation study has illustrated how such a case could be averted by performing the basis material transformation approach.

6. Conclusion

This report has presented the predictions from a computer simulation study of the influence of radiographic contrast agent on the accuracy of the concentration of radionuclides in SPECT imaging with object-specific attenuation correction using transmission CT. Attenuation maps of the thorax-like phantom derived from each of the three transmission CT approaches, namely the conventional x-ray CT, DXCT/BMD, and DXCT/BMT, were incorporated into the processing stage of the SPECT protocol to investigate for effects on the accuracy of counts in the emission image. Our findings are summarized as follows.

• •All the three transmission CT approaches for attenuation correction in SPECT imaging revealed that the error in the counts was photon energy and iodine concentration-dependent.
• •Differences in the trending increase/decrease in the errors with the respective increase in iodine concentration and photon energy existed among the three CT approaches.
• •Of the three approaches, the BMT/SPECT approach resulted in the smallest error in the concentration of radionuclides measured, especially in the contrast agent-filled region, and the optimal level depended on the iodine concentration and photon energy.

With a judicious choice of the basis materials and photon energy, it may be possible to take advantage of the benefits of the basis material transformation to mitigate the accuracy problem for quantitative SPECT imaging.

Overall, the conclusions hold for the findings derived from this simulation study. However, further investigation, involving experiments, would have to be carried out to validate these predictions.

7. Appendix

Table 3 presents a summary of the progress of quantitative SPECT/CT research conducted to date, in a chronological sequence, in order to justify our current work.

Table 4 presents the numerical results of the largest errors (%) found within the respective heart and main body regions in the phantom, and the corresponding radionuclide activity (count/pixel), at the respective energies, 75 and 140 keV.

Biographies

Kheng Lim Goh investigated the energy-dependent systematic errors in dual-energy x-ray CT for his MSc thesis (National University of Singapore), under the supervision of Dr Soo Chin Liew. In 1995, he visited the late Professor Bruce Hasegawa at his Medical Physics Laboratory (University of California, San Francisco) to learn about dual-energy systems before he went to Aberdeen University to do his PhD in biomedical physics and bioengineering. He is a reader at Newcastle University (Singapore).

Soo Chin Liew is a principal research scientist at the Centre for Remote Imaging, Sensing and Processing, with a joint faculty appointment at Physics Department, National University of Singapore. He obtained his PhD in physics from the University of Arizona and did postdoctoral research on emission–transmission CT at the University of California at San Francisco. His research involves the applications of physics and imaging science in medical imaging, nuclear microscopy, and satellite remote sensing.

Disclosures

The authors had no conflict of interest.