Quantitative lung perfusion blood volume using dual energy CT–based effective atomic number (Z_eff) imaging

Abstract

Background:

Iodine material images (aka iodine basis images) generated from dual energy computed tomography (DECT) have been used to assess potential perfusion defects in the pulmonary parenchyma. However, iodine material images do not provide the needed absolute quantification of the pulmonary blood pool, as materials with effective atomic numbers (Z_eff) different from those of basis materials may also contribute to iodine material images, thus confounding the quantification of perfusion defects.

Purpose:

(i) To demonstrate the limitations of iodine material images in pulmonary perfusion defect quantification and (ii) to develop and validate a new quantitative biomarker using effective atomic numbers derived from DECT images.

Methods:

The quantitative relationship between the perfusion blood volume (PBV) in pulmonary parenchyma and the effective atomic number (Z_eff) spatial distribution was studied to show that the desired quantitative PBV maps are determined by the spatial maps of Z_eff as ${\text{PBV}}_{Z_{\text{eff}}}(x)=a{Z}_{\text{eff}}^{\beta }(x)+b$, where a, b, and β are three constants. Namely, quantitative ${\text{PBV}}_{Z_{\text{eff}}}$ is determined by Z_eff images instead of the iodine basis images. Perfusion maps were generated for four human subjects to demonstrate the differences between conventional iodine material image-based PBV (PBV_iodine) derived from two-material decompositions and the proposed ${\text{PBV}}_{Z_{\text{eff}}}$ method.

Results:

Among patients with pulmonary emboli, the proposed ${\text{PBV}}_{Z_{\text{eff}}}$ maps clearly show the perfusion defects while the PBV_iodine maps do not. Additionally, when there are no perfusion defects present in the derived PBV maps, no pulmonary emboli were diagnosed by an experienced thoracic radiologist.

Conclusion:

Effective atomic number–based quantitative PBV maps provide the needed sensitive and specific biomarker to quantify pulmonary perfusion defects.

1 |. INTRODUCTION

Venous thromboembolism is a major global health concern and an economic burden with approximately 10 million cases occurring each year and a high lifetime risk of 8% after 45 years of age.⁵ Pulmonary embolism (PE) is a venous thromboembolic event associated with high morbidity and mortality.⁵ Currently, pulmonary CT angiography (CTA) is the preferred imaging modality for evaluating patients with clinically suspected acute PE.^6–17 Pulmonary CTA can also be used for the evaluation of other pulmonary thromboembolic diseases, such as chronic PE and chronic thromboembolic pulmonary hypertension (CTEPH).Pulmonary emboli often manifest as partial or complete intraluminal pulmonary vessel filling defects on pulmonary CTA images and each defect usually presents a sharp interface with the iodinated contrast. However, these radiological features are not specific to pulmonary emboli and can also result from a number of other pathological factors (e.g., the presence of a mucus plug or perivascular edema) and anatomical factors (e.g., vascular bifurcations and misidentification of pulmonary veins), all of which can generate PE-mimicking filling defects on pulmonary CTA images.⁸ In addition, the success rate and diagnostic accuracy of anatomic imaging with pulmonary CTA drop as the vessel size decreases to the subsegmental level.¹⁷ Furthermore, pulmonary CTA only provides anatomic imaging of pulmonary vessels and does not provide a direct assessment of the impact of PE on lung parenchymal perfusion. Also pulmonary CTA neither directly provide prognostic biomarkers of hemodynamic compromise nor identify patients at risk for fatal or other adverse events. The incapability to demonstrate parenchymal perfusion abnormalities remains an important limitation of CTA-based evaluation of pulmonary thromboembolic diseases.

As an alternative to pulmonary CTA, lung ventilation/perfusion (V/Q) scintigraphy and single photon emission computed tomography (SPECT) are used to evaluate pulmonary thromboembolic diseases. For patients with suspected CTEPH or chronic PE, the selection between CTA and nuclear medicine imaging often creates a diagnostic dilemma: CTA provides direct imaging of the embolus itself without parenchymal perfusion information, while nuclear medicine imaging provides functional information without direct proof of emboli. To extricate physicians from this dilemma, patients with suspected CTEPH may need to receive both CTA and nuclear medicine lung imaging, which increases both the overall healthcare cost and the ionizing radiation dose to patients. As a result, there is a compelling unmet clinical need to develop a method for simultaneous pulmonary vessel morphological assessment and parenchymal perfusion assessment without applying separate CT and nuclear medicine scans to the same patient.

Towards providing a “one-stop-shop” solution to morphological and functional lung imaging, prior studies have investigated the use of dynamic CT imaging to extract pulmonary perfusion information. However, this approach has not been clinically accepted resulting from concerns regarding radiation dose:^18–20 the effective dose of dynamic chest CT is approximately 7 mSv, compared to 2 mSv for a typical static pulmonary CTA scan.²¹ Another strategy employed is to use static dual energy CT (DECT) or multienergy CT (MECT) which do not require a prolonged breath-hold or a significant increase in radiation dose.^22–29 A DECT scan generates the so-called iodine material images (from iodine–water or iodine–soft tissue–air material decompositions) that can be used as a corollary for pulmonary perfusion blood volume (PBV) maps to depict the location and pattern of pulmonary perfusion defects. For a given pulmonary embolus identified on CTA images, the addition of those iodine material image-based PBV (PBV_iodine) maps can assist physicians in estimating the probability and severity of tissue damage while providing a prognosis and risk stratification in patients presenting with pulmonary thromboembolic diseases, including typical presentations and those associated with alternate diagnoses, such as COVID-19 pneumonia.^7,30–35

However, as shown by a recent survey conducted by the Society of Thoracic Radiology,³⁶ iodine material image-based pulmonary perfusion imaging remains underutilized in clinical practice due to several important limitations. The first important limitation of the iodine material image is that its signal does not necessarily reflect the magnitude of the pulmonary blood pool, as noniodine materials with Z_eff different from that of the counterpart basis material (e.g., water) can also contribute to the iodine image signal. This is particularly a problem for pulmonary consolidation and ground-glass opacity (GGO) that may not only have different Z_eff (relative to water), but also much higher densities than the normal lung tissue: as shown by the analysis in Section 2.2 and published literature,^37–39 those tissues can generate a relatively high signal in PBV_iodine images which can mislead the evaluation of regional perfusion conditions. The second limitation lies in the fact that DECT-based iodine material images can only provide a relative measurement of PBV. In fact, physicians heavily rely on comparing the iodine intensity across different lung lobes to identify regional perfusion defects. Due to this relative assessment nature, literature on DECT pulmonary perfusion imaging rarely reports the physical units of the pulmonary perfusion maps. This limitation poses a challenge in diagnosing systematic pulmonary defects.

The purpose of this work is to develop a new framework to derive quantitative pulmonary PBV maps from the available DECT data to overcome the current limitations of iodine image-based perfusion assessment and also achieve simultaneous functional and anatomical lung imaging using DECT acquisitions. The method was developed based on the physiological meaning of PBV and the imaging physics of DECT. The main contribution of this work is to show that the quantitative and absolute PBV measurements are determined by the local effective atomic number (Z_eff) distribution and can become an intrinsic absolute quantification of the perfused blood pool.

2 |. MATERIALS AND METHODS

2.1 |. Pulmonary PBV from DECT imaging

By definition, as shown in the model presented in Figure 1, PBV is the blood volume perfused into a unit mass of lung tissue in a volume-of-interest (VOI) located at x:

$$\mathrm{PBV}(x)=\frac{V_{\text{cap}}(x)}{m_{\text{lung}}(x)},$$ (1)

where V_cap(x) denotes the volume of the capillary bed within the VOI and m_lung(x) denotes the mass of the lung tissue in the VOI (Figure 1).

FIGURE 1.

An illustration of the concept of pulmonary perfusion blood volume (PBV). For a given volume-of-interest (VOI) in the lung parenchyma, its PBV is given by the ratio between the volume occupied by the capillaries (V_cap) and the mass of the lung tissue in the VOI (m_lung). m_lung = V_lungρ_lung, where V_lung and ρ_lung are the VOI volume and the lung tissue density, respectively. By definition, PBV is independent of the injected iodine concentration

In practice, it is difficult to directly measure the volume of the capillary bed within a VOI due to the limited spatial resolution of CT relative to the capillary size. Therefore, PBV must be determined from other quantities measurable in CT images. Using the mass conservation principle, as shown by the derivations presented in Appendix I, Equation (1) can be recast into the following form:

$$\text{PBV}(x)=\frac{1}{{\rho }_{\text{lung}}(x)}\frac{{\rho }_{\text{I}}(x)}{{\rho }_{{\text{I}}_0}},$$ (2)

where ρ_lung(x) denotes the mass density of the lung tissue in the VOI at x, ${\rho }_{{\text{I}}_0}$ is the concentration of the injected iodine at the feeding pulmonary artery, and ρ_I(x) is the iodine concentration in the VOI. The key difference between Equations (1) and (2) is that the three quantities in Equation (2) are, in principle, measurable using DECT imaging technology. For example, ρ_I(x) and ${\rho }_{{\text{I}}_0}$ can be measured based on the signal values of the iodine material image, and ρ_lung(x) can be measured using the water material image. These measurements do not require the CT to have capillary-level spatial resolution. In reality, however, the signals of the iodine and water material images do not always provide quantitatively accurate iodine concentrations and lung tissue densities. To explain this reason, let’s review the so-called “material decomposition”, in which the linear attenuation coefficient of the VOI at x is decomposed into two material bases as

$$\mu (x,E)=a_{\mathrm{I}}(x){\left(\frac{\mu }{\rho }\right)}_{\mathrm{I}}(E)+a_{\text{w}}(x){\left(\frac{\mu }{\rho }\right)}_{\text{w}}(E),$$ (3)

or three material bases as

$$\begin{gathered} \mu (x,E)=a_l(x){\left(\frac{\mu }{\rho }\right)}_{\text{I}}(E)+a_{\text{w}}(x){\left(\frac{\mu }{\rho }\right)}_{\text{w}}(E) \\ +a_{\mathrm{air}}(x){\left(\frac{\mu }{\rho }\right)}_{\mathrm{air}}(E). \end{gathered}$$ (4)

Here, E denotes the X-ray energy, and (μ/ρ)_I, (μ/ρ)_w, and (μ/ρ)_air denote the mass attenuation coefficients of pure iodine, water, and air, respectively. The material “water” can also be replaced by a “standard soft tissue material” defined by the CT vendor or the end-user, but the overall working principle remains the same.

2.2 |. Conventional “relative PBV” measurements using iodine basis images

The iodine material image, a_I(x), which describes the concentration of “iodine-like” materials, was used in literature^24,33,34 as a surrogate for the PBV since it is assumed to be equivalent to ρ_I(x), the true iodine concentration in the VOI, namely

$${\text{PBV}}_{\text{iodine}}(x)=\kappa a_{\mathrm{I}}(x)$$ (5)

where κ is a numerical constant. In other words, the iodine material image is assumed to be linearly proportional to the PBV, and ρ_lung(x) in Equation (2) is assumed to be constant throughout the lungs. However, these assumptions are not well supported by imaging physics as discussed below.

First, the iodine material image, a_I(x), does not necessarily provide the accurate iodine concentration distribution, ρ_I(x), despite the fact that the physical units of a_I(x) and ρ_I(x) are the same (i.e., mg/ml). The actual physical meaning of a_I(x) and a_w(x) from water–iodine material decompositions are given by the following formulae^40,41:

$$a_{\text{I}}(x)=\frac{{\rho }_{\text{e}}(x)}{N_{\text{a}}{(z/A)}_{\text{I}}}\frac{Z_{\text{eff}}^{\beta }(x)-Z_{\text{w}}^{\beta }}{Z_{\text{l}}^{\beta }-Z_{\text{w}}^{\beta }}$$ (6)

$$a_{\text{w}}(x)=\frac{{\rho }_{\text{e}}(x)}{N_{\text{a}}{(z/A)}_{\text{w}}}\frac{Z_{\text{eff}}^{\beta }(x)-Z_{\text{l}}^{\beta }}{Z_{\text{w}}^{\beta }-Z_{\text{I}}^{\beta }}$$ (7)

where β is an energy- and material-independent numerical constant, N_a is the Avogadro constant, ρ_e denotes electron density, A denotes the atomic mass number, and Z denotes the atomic number. For example, Z_I (=53) and Z_w (=7.4) are the atomic numbers of pure iodine and water, respectively. As shown in Appendix II, a_I(x) is equal to ρ_I(x) only under the condition that the VOI is entirely composed of the basis materials. When a voxel contains a foreign material with a Z_eff different from those of the basis materials, its contribution to the X-ray attenuation will be assigned to both material basis images. In that case, the assumption that a_I(x) is same as ρ_I(x) inevitably leads to either over- or under-estimation of the PBV.

Second, compared with the PBV formula in Equation (2), using a_I as a surrogate for the PBV ignores the dependence of the PBV on the lung tissue density ρ_lung(x), a quantity that varies spatially in the lung. Therefore, the lack of consideration of the spatially varying ρ_lung(x) in PBV_iodine is problematic.

To experimentally demonstrate the possible contribution of consolidation to the iodine material image signal, the Z_eff of pulmonary consolidation was experimentally measured using the DECT images (Gemstone Spectral Imaging (GSI), GE Healthcare) of a human subject. Information about the patient and the scan protocol is provided in Table 2 (Subject 1). Ideally, the measurement of the Z_eff of pulmonary consolidation should use non-contrast DECT data to avoid the impact of iodine to the Z_eff result. Since no non-contrast chest DECT exam is performed at the authors’ institutions, we had to use contrast-enhanced chest DECT: we carefully chose a subject that had both pulmonary consolidation and known acute PE and impaired blood perfusion to the consolidated regions to minimize the influence of the iodine. Measurement of consolidation Z_eff was performed in a carefully chosen VOI without perceivable contrast-enhanced vessels as corroborated by the pulmonary CTA images. As shown in Figure 2 and Table 1, Z_eff of the consolidated tissue (8.11 [7.91, 8.29]) is indeed higher than that of water (7.42). Therefore, even without any iodine uptake, the consolidation can contribute to the signal of iodine material images. Further, the electron density (ρ_e) of the consolidated tissue measured by DECT is approximately three times that of the normal lung tissue’s ρ_e. According to Equation (6), a larger ρ_e further increases the signal of consolidated tissue in the iodine material image.

TABLE 2.

Subject demographics and scan parameters

	Subject 1	Subject 2	Subject 3	Subject 4
Age	40	65	68	23
BMI	26.9	36.9	27.4	20.4
Gender	Male	Female	Male	Female
Scanner	750HD	Revolution	Revolution	Revolution
Contrast volume (ml)	100	100	100	100
Contrast type	Isovue370	Omnipaque300	Omnipaque300	Omnipaque300
Helical pitch	1.375	0.992	0.992	0.992
Beam collimation (mm)	40	80	80	80
Rotation time	0.5	0.5	0.5	0.5
mA	600	240	200	200
Slice thickness (mm)	2.5	1.25	1.25	1.25

FIGURE 2.

Experimental measurement of Z_eff and ρ_e using dual energy CT (DECT) data of an acute pulmonary embolism (PE) patient with extensive bilateral consolidations and clinically proven pulmonary perfusion deficits. The dotted circles indicate volume-of-interests (VOIs) where measurements were performed. These VOIs are located within the consolidations without perceivable iodine uptake as shown by the CT angiography (CTA) maximum intensity projection (MIP) image. The results confirmed that Z_eff of the consolidation (8.11 [7.91, 8.29]) is higher than that of water (7.42) and its ρ_e (0.55 [0.54, 0.56] mol/ml) is more than three times that of the ρ_e of the normally aerated lung tissue (0.16 [0.10, 0.23] mol/ml)

TABLE 1.

Values of effective atomic number (Z_eff), mass density (ρ), and electron density (ρ_e) of typical materials in the chest

Material	Air (dry)	Normal lung tissue	Adipose tissue	Water	Muscle	Iodine	Pulmonary consolidation
Z eff	7.66	7.44 [7.34, 7.46]	5.82 [5.69, 5.90]	7.42	7.52 [7.42, 7.52]	53	8.11 [7.91, 8.29]
ρ (g/ml)	1.2 × 10−3	0.29 [0.17, 0.41]	0.95	1.0	1.05	4.9	0.98 [0.96, 1.00]
ρe (mol/ml)	6.0 × 10−4	0.16 [0.10, 0.23]	0.53	0.56	0.58	2.05	0.55 [0.54, 0.56]

Note: Except for pulmonary consolidation, the values are taken from the NIST Standard Reference Database No. 126 and other published papers.1–4 The values for the pulmonary consolidation were experimentally measured from the human subject image data shown in Figure 2.

As another demonstration, Figure 3 plots low-kV μ values against high-kV μ values for consolidated and normal lung tissues of a human subject. A line connecting the consolidation and normal lung tissue data points has a slope of 1.19 (99% CI [1.17, 1.21]), which is larger than the slope of water (1.14). Because the slope is positively correlated to the effective atomic number,⁴² this figure implies that compared with normal lung tissues, consolidations contain additional materials with Z_eff larger than that of water. All these experimental data support the premise that consolidated lung tissue contributes to the iodine material image and thus PBV_iodine is not a robust and accurate metric of pulmonary perfusion, as a higher PBV_iodine value does not necessarily mean a higher blood volume, and a “normal” PBV_iodine value does not necessarily rule out perfusion defects.

FIGURE 3.

(a) 140 kV contrast-enhanced CT image of a patient showing consolidation in the right lung. Two region-of-interests (ROIs) were drawn on the consolidation and the contralateral normal lung tissue. (b) For each ROI, its mean attenuation coefficient measured in the 80 kV image (μ_low) was plotted against the attenuation coefficient measured in the 140 kV image (μ_high). In part (b), the “+” markers indicate individual data points in each ROI while each solid disk marker represents the ROI mean. The black line connecting the data of ROI 1 and ROI 2 has a slope of 1.19 (99% CI [1.17, 1.21]), which is larger than the slope of water (1.14). This implies that compared with the normal lung tissue, the consolidation contains materials with Z_eff slightly higher than that of water

2.3 |. Absolute quantification of pulmonary PBV from DECT-based Z_eff imaging

Instead of using the iodine material image-based PBV_iodine, a new metric was developed in this work to quantitatively measure PBV.As shown in Appendix II, the PBV defined in Equation (2) is quantitatively related to the effective atomic number Z_eff as follows:

$${\text{PBV}}_{Z_{\text{eff}}}(x)=k{Z}_{\text{eff}}^{\beta }(x)+b,$$ (8)

where constants k and b are determined as follows:

$$k=\frac{1}{{\rho }_{{\text{I}}_0}\left(Z_{\text{I}}^{\beta }-Z_{\text{w}}^{\beta }\right)},b=-\frac{Z_{\text{w}}^{\beta }}{{\rho }_{{\text{I}}_0}\left(Z_{\text{I}}^{\beta }-Z_{\text{w}}^{\beta }\right)}.$$ (9)

A value of 2.94 is widely used in literature for the exponent β.^43,44 For the term ${\rho }_{{\text{I}}_0}$ (iodine concentration in a feeding pulmonary artery), it can be reliability measured from the iodine material image due to the absence of consolidations within the large artery. Equation (8) provides an absolute (rather than relative) measurement of PBV with a physical unit of (ml/g) or (ml/100 g) depending on the user’s preference.

2.4 |. Proof-of-concept human subject evaluation studies

As an initial proof-of-concept evaluation of the proposed quantitative $PB{V}_{Z_{\text{eff}}}$ measurement method, pulmonary DECT angiography data of four human subjects were retrospectively collected and processed under IRB approval. Among these subjects, three received DECT on a 256-slice MDCT scanner (Revolution CT,GE Healthcare) equipped with the GSI DECT technology; one subject received DECT on a 64-slice MDCT scanner (Discovery CT750 HD, GE Healthcare) equipped with GSI. The age, gender, BMI, and other relevant information about the DECT exams are listed in Table 2.

2.4.1 |. DECT scan protocol

For scans performed on the 256-slice CT system, the intravenous contrast injection used 100 ml of Iohexol 300 mg I/ml (Omnipaque 300; GE Healthcare) with a 10 ml saline flush, both at a rate of 5 ml/s. A bolus tracking scan (SmartPrep, GE Healthcare) was used to determine the scan timing: once the enhancement in the left atrium exceeded 60 HU, the actual DECT angiography scan was triggered and performed under the helical mode with a helical pitch of 0.992. The scan range extended from the apices of the lung to just below the diaphragm. The X-ray tube potential rapidly switched between 80 and 140 kV while the gantry rotated at a speed of 0.5 s per revolution. The tube current (mA) was adjusted for each subject based on their body size under the guidance of the GSI-assist technology. The beam collimation was 80 mm and the reconstruction slice thickness was 1.25 mm. For the subject who received the DECT on the 64-slice scanner, the beam collimation was 40 mm and the reconstruction slice thickness was 2.5 mm. The contrast injection was 100 ml of Iopamidol 370 mg I/ml (Isovue 370; Bracco Diagnostics Inc.) at a rate of 4 ml/s, followed by 45 ml of saline at 2 ml/s. The bolus tracking scan used a region-of-interest (ROI) placed on the pulmonary artery at the level of carina, and the trigger threshold was 110 HU. Other scan parameters are listed in Table 2.

2.4.2 |. Image processing and data analysis

For the DECT acquisition of each subject, iodine (water) and water (iodine) material images were directly generated by the CT scanner. According to the CT manufacturer, these material images were generated via a two-material (water–iodine) decomposition process without requiring any knowledge of each material’s volume fraction or the volume-conservation assumption. GE DECT systems also provide Z_eff maps. If Z_eff is not directly available, it can be computed from the water and iodine material images as follows:

$$Z_{\text{eff}}(x)={\left[\frac{a_{\text{w}}(x){(z/A)}_{\text{w}}{Z}_{\text{w}}^{\beta }-a_{\text{I}}(x){(z/A)}_{\text{I}}{Z}_{\text{I}}^{\beta }}{a_{\text{w}}(x){(z/A)}_{\text{w}}-a_{\text{I}}(x){(z/A)}_{\text{I}}}\right]}^{1/\beta },$$

where Z_w = 7.42, Z_I = 53, (z/A)_w = 0.555, (z/A)_I = 0.418, and β = 2.94.

The iodine concentration of the feeding artery, ${\rho }_{{\text{I}}_0}$, was measured by placing an ROI on the pulmonary trunk in the iodine material image. Since the ROI is completely within the iodinated blood, its a_I signal can be safely used to estimate the input iodine concentration, ${\rho }_{{\text{I}}_0}$. Next, Equation (8) and the measured Z_eff and ${\rho }_{{\text{I}}_0}$ were used to calculate ${\text{PBV}}_{Z_{\text{eff}}}$ of each pixel within the lungs. The measured ${\rho }_{{\text{I}}_0}$ was applied to the whole lung regions of a given patient. The calculation of ${\text{PBV}}_{Z_{\text{eff}}}$ was performed off the CT console on a computer using the Matlab software (version R2020b; Mathworks, Inc.) and the results were saved as RGB DICOM images for radiologist review. For comparison purposes, conventional PBV_iodine maps were also generated from iodine material images. The lung region of each PBV map was color-coded using the “hot” color map and overlaid on the corresponding grayscale 140 kV equivalent CT image.

A radiologist with 35 years of clinical experience evaluated both ${\text{PBV}}_{Z_{\text{eff}}}$ and PBV_iodine maps. For each patient and each type of PBV map, the reader evaluated whether the images demonstrated evidence of perfusion defects, GGOs, consolidations, atelectasis, lung tumors, or other pulmonary abnormalities; the gold-standard diagnosis was established based on clinical and laboratory records, CT and nuclear medicine images (if available), and other relevant imaging results. The diagnostic performance of ${\text{PBV}}_{Z_{\text{eff}}}$ and PBV_iodine were compared qualitatively by the experienced radiologist.

3 |. RESULTS

Figures 4–7 show color-coded ${\text{PBV}}_{Z_{\text{eff}}}$ and PBV_iodine maps of the patients’ lung regions overlaid on top of the corresponding grayscale CT images. Quantitative measurement results of PBV, material image signals, Z_eff, and electron density (ρ_e) values are summarized in Table 3. In addition, the Supporting Information provides the original water and iodine material images, Z_eff maps, and ρ_e maps without using the color overlay display method.

FIGURE 4.

Images of Subject 1 with clinically proven pneumonia and acute pulmonary embolism. The CT angiography source images in Row 1 show multiple segmental and subsegmental pulmonary emboli (pointed by the arrows) in the vessels that supply the posterior regions of the left and right lungs. The CT images in Row 2 with a wider display range show extensive ground-glass opacity and consolidation in both lungs. ${\text{PBV}}_{Z_{\text{eff}}}$ maps (color overlay on the grayscale CT image) in Row 3 demonstrated regional perfusion defects in the posterior area of both lungs. In contrast, PBV_iodine maps (color overlay on the grayscale CT image) in Row 4 do not clearly show the perfusion abnormalities because the consolidated tissue contributed to the iodine material image signal such that the reduction of iodine concentration in the consolidated area was counteracted in PBV_iodine

FIGURE 7.

Images of a “control case” (Subject 4) without pulmonary embolism and without pulmonary hypertension. The lung regions of PBV_iodine and ${\text{PBV}}_{Z_{\text{eff}}}$ maps are color-coded and overlaid on the grayscale CT images

TABLE 3.

Results of quantitative measurements (mean value [first quantile, third quantile]) of the four subjects’ DECT image data

Subject 1
	Normally aerated		Consolidation		p
HU	−769	[−856, −760]	37	[15, 69]	<0.001
aI (mg/ml)	1.2	[0.2, 1.5]	1.2	[1.0, 1.6]	0.626
aw (g/ml)	0.183	[0.122, 0.202]	1.015	[0.998, 1.035]	<0.001
ρe (mol/ml)	0.108	[0.072, 0.114]	0.552	[0.544, 0.561]	<0.001
Z eff	9.25	[8.63, 9.85]	8.11	[7.91, 8.29]	<0.001
PBVZeff (mg/100 g)	29.29	[17.10, 40.22]	9.42	[6.37, 11.98]	0.001
Subject 2
	Normally aerated		Ground-glass opacity		p
HU	−885	[−926, −8.76]	−610	[−640, −568]	<0.001
aI (mg/ml)	0.9	[0.4, 1.1]	1.6	[1.1, 2.2]	<0.001
aw (g/ml)	0.091	[0.065, 0.091]	0.349	[0.334, 0.377]	<0.001
ρe (mol/ml)	0.050	[0.036, 0.051]	0.194	[0.186, 0.210]	<0.001
Z eff	10.46	[9.93, 11.11]	8.83	[8.79, 9.74]	<0.001
PBVZeff (mg/100 g)	32.70	[24.37, 41.46]	8.78	[7.66, 14.56]	<0.001
Subject 3
	Right lung		Left lung with atelectasis		P
HU	−517	[−652, −428]	197	[164, 227]	<0.001
aI (mg/ml)	3.0	[1.8, 4.2]	6.7	[5.8, 7.6]	<0.001
aw (g/ml)	0.405	[0.302, 0.457]	1.022	[1.013, 1.030]	<0.001
ρe (mol/ml)	0.226	[0.168, 0.256]	0.570	[0.565, 0.575]	<0.001
Z eff	10.09	[9.71, 10.34]	10.10	[9.71, 10.34]	0.096
PBVZeff (mg/100 g)	32.24	[19.40, 45.73]	32.82	[26.66, 36.51]	0.566
Subject 4
	Right lung		Left lung		P
HU	−725	[−778, −713]	−723	[−767, −699]	0.840
aI (mg/ml)	2.7	[1.9, 3.0]	2.6	[1.8, 3.0]	0.437
aw (g/ml)	0.206	[0.174, 0.206]	0.209	[0.186, 0.218]	0.407
ρe (mol/ml)	0.115	[0.098, 0.116]	0.117	[0.104, 0.122]	0.389
Z eff	11.21	[10.09, 11.67]	11.13	[10.04, 11.86]	0.220
PBVZeff (mg/100 g)	44.47	[26.70, 51.02]	43.13	[26,00, 54.25]	0.212

Note: The p values were given by two-sample t-tests with the unequal variance assumption.

Figure 4 shows images of Subject 1 with clinically confirmed acute PE and pneumonia. Extensive GGO and consolidation were found in the posterior regions of both the lungs. As shown by this subject’s pulmonary CTA source images in the first row of Figure 4, multiple emboli exist in the pulmonary vessels supplying the posterior lung regions. ${\text{PBV}}_{Z_{\text{eff}}}$ maps demonstrate regional perfusion defects in the lungs. In comparison, PBV_iodine maps do not clearly show the perfusion defects. This is because the consolidation and GGO contributed to the iodine material images and counteracted the reduction of iodine uptake in those areas.

Figure 5 shows images of Subject 2 with clinically confirmed PE. The subject has a history of lung infection and consolidations and GGOs within the bilateral upper and right middle lobes. The bilateral lobar, segmental and subsegmental pulmonary emboli can be seen on the pulmonary CTA images in the first row in Figure 5. The PBV maps show a global reduction in blood volume; some regions such as the bilateral upper lobes show severe perfusion defects. Although the PBV_iodine maps also show regional defects in the upper lobes, they failed to show the systematic reduction in blood perfusion because their values do not provide the quantitative blood volume level and are dependent on extrinsic factors such as the injected iodinated contrast level. The GGOs contributed to the iodine material image signal and reduced the sensitivity of PBV_iodine maps to perfusion defects.

FIGURE 5.

Images of Subject 2 with clinically confirmed pulmonary embolism. The CT angiography (CTA) source images in Row 1 show bilateral lobar, segmental, and subsegmental pulmonary emboli (arrows). The lung-window CT images in Row 2 show bilateral ground-glass opacities. The bilateral perfusion defects can be visualized more clearly in the ${\text{PBV}}_{Z_{\text{eff}}}$ maps (color overlay on the grayscale CT image) in Row 3 than the PBV_iodine maps (color overlay on the grayscale CT image) in Row 4

Figure 6 shows images of Subject 3 who has large left and medium right pleural effusions, loculations in the right oblique fissure, compressive collapse of the left lower lobe, and lung edema with atelectasis in the left lung. However, no PE or pulmonary hypertension was found in this patient. The ${\text{PBV}}_{Z_{\text{eff}}}$ maps show normal perfusion with an average PBV value of 33 [27, 37] ml/100 g in the left lung and 32 [19, 46] ml/100 g in the right lung. In comparison, the iodine material images of this subject show a much higher signal in the left lung (6.7 [5.8, 7.6] mg/ml) than the right lung (3.0 [1.8, 4.2] mg/ml, p < 0.001). Instead of a greater blood perfusion, the high iodine material image signal of the left lung was actually caused by the lung fluid that has a Z_eff different from that of water. If a sub-optimal display range is used for the iodine basis image (fourth column in Figure 6), the right lung may appear hypoperfused compared with the left lung. This example shows a limitation of the iodine image-based relative perfusion measurement and an advantage of the proposed quantitative PBV measurement.

FIGURE 6.

Images of Subject 3 without any pulmonary embolism or pulmonary hypertension. The patient has large pleural effusions and compressive collapse in the left lung. The atelectasis in the left lung significantly elevated the local signal in the iodine material images. Consequently, when an adaptive display range is selected for PBV_iodine maps, the right lung appears to be hypoperfused compared with the left lung. In contrast, the ${\text{PBV}}_{Z_{\text{eff}}}$ maps are robust against local density variation and shows a uniform pulmonary perfusion. The lung regions of PBV_iodine and ${\text{PBV}}_{Z_{\text{eff}}}$ maps are color-coded and overlaid on the grayscale CT images

Finally, Figure 7 shows images of a “control” case (Subject 4) whose gold-standard clinical diagnosis has ruled out PE, CTEPH, or other lung diseases. For this subject without any consolidation and GGO, both ${\text{PBV}}_{Z_{\text{eff}}}$ and PBV_iodine maps show normal pulmonary perfusion signals without any false positives or false negatives. Meanwhile, blood vessels in PBV_iodine show higher PBV_iodine signals than the normally aerated lung parenchyma because of the higher electron density of the vessels (see the Supporting Information for the electron density maps). In clinical practice, the much brighter vessels can be distracting for the evaluation of parenchymal perfusions and they are segmented and hidden on PBV_iodine maps in some products.^47,48 In comparison, the proposed ${\text{PBV}}_{Z_{\text{eff}}}$ map is more homogenous since the definition of PBV in Equation (2) requires a normalization of the local tissue density.

4 |. DISCUSSION

In the current DECT PBV_iodine method, pulmonary perfusion conditions are estimated using iodine material images generated by applying a two- or three-material decomposition to the acquired DECT data. There are two fundamental pitfalls of this approach. First, as shown in Equation (5), a material with an effective atomic number different from those of the basis materials can be partially assigned to the iodine basis images. Therefore, the iodine material images, a_I(x), do not necessarily provide quantitatively accurate iodine density distribution, ρ_I(x). The difference between a_I(x) and ρ_I(x) can be significant for consolidations and GGOs that have not only a higher Z_eff relative to water but also a higher density relative to the normal lung tissue. Second, by definition, PBV is the volume of blood perfused per unit mass of lung tissue (Equation (1)). The iodine material images do not reflect the mass of the lung tissue. One can argue that the signal of a_I(x) with a unit of (mg/ml) has a positive correlation with ρ_I(x) and thus has a positive correlation with PBV according to Equation (2). However, the existence of a positive correlation is not equivalent to quantitatively accurate PBV due to the fact that an important quantity, ρ_lung(x), in the PBV formula in Equation (2) is not characterized by a_I(x).

Due to the two pitfalls of PBV_iodine, the identification of perfusion defects in PBV_iodine maps would have to rely heavily on the choice of display window/level, the choice of display color map, the relative difference in color between different lung regions, and the reader’s experience. In addition, as shown by the human subject results in this work, lung regions with consolidations and GGOs can generate a higher PBV_iodine signal relative to the normally aerated lung regions. In fact, data published in multiple prior studies support the existence of this effect.^37–39 For example, in a fast kV switching DECT study of patients with COVID-19 pneumonia and suspected PE, two of the three showcases demonstrated higher iodine material image signal in the consolidation regions than the normally aerated parenchyma regions: one case shows a_I value of 6.053 mg/ml in the consolidation, compared to 0.723 mg/ml in the normally aerated region.³⁷ In another dual-source DECT-based study of patients with GGOs, two of the three showcases demonstrated higher a_I signals in the GGO regions than normally aerated regions.³⁸ The increased signal of consolidations and GGOs in PBV_iodine maps can be misleading, as both the reflex pulmonary artery vasoconstriction theory and nuclear medicine perfusion imaging can indicate a decreased (instead of increased) perfusion for consolidations and GGOs.^45,46 Due to this limitation of PBV_iodine, some DECT postprocessing tools exclude consolidation or GGO regions in the final PBV_iodine maps, despite the strong clinical needs to assess perfusion conditions of these regions, particularly for patients with COVID-19 pneumonia.^47,48

In contrast to PBV_iodine, this work shows that ${\text{PBV}}_{Z_{\text{eff}}}$ derived from DECT data is a quantitative biomarker of pulmonary perfused blood volume. As shown by the preliminary human subject results presented in Section 4, for patients with acute PE and pneumonia, the quantitative PBV maps clearly demonstrate regional perfusion defects in the area supplied by the embolized vessels, while the iodine material images failed to demonstrate the defects since pneumonia-induced consolidations add a positive signal to the iodine material image to counteract the reduced perfusion in the area. More interestingly, for a patient without PE, but with pleural effusion and atelectasis, the quantitative ${\text{PBV}}_{Z_{\text{eff}}}$ maps correctly demonstrate normal perfusion and are more specific than iodine image-based relative perfusion maps.

Although Equation (8) provides a formula to calculate ${\text{PBV}}_{Z_{\text{eff}}}$ from the βth power of Z_eff, it is not the only approach to calculate ${\text{PBV}}_{Z_{\text{eff}}}$: as shown by Equation (S18) in Appendix II, ${\text{PBV}}_{Z_{\text{eff}}}$ can also be obtained via a pixel-wise division of the iodine material image by the electron density image, albeit some commercial DECT systems do not directly provide electron density images. Fundamentally speaking, both of the two calculation methods are derived from the definition of PBV and are equivalent. In practice, one can choose either one based on the types of DECT images provided by a given clinical system.

This work has the following limitations. First, only four representative human subject cases were studied to demonstrate the pitfalls of the conventional PBV_iodine evaluation method and to show the effectiveness of the proposed quantitative ${\text{PBV}}_{Z_{\text{eff}}}$ metric based on the effective atomic number maps. To fully demonstrate the clinical value of ${\text{PBV}}_{Z_{\text{eff}}}$, a large cohort of human subject studies needs to be studied in the future. Second, it is worth emphasizing that ${\text{PBV}}_{Z_{\text{eff}}}$ derived from DECT data only represents a steady-state perfusion measurement. It does not provide other important hemodynamic information such as pulmonary blood flow. If one desires to obtain a complete set of perfusion measurements including pulmonary flow information, time-resolved CT scans are required for measuring the contrast dynamics of pulmonary vasculature and tissues. Third, the iodine material images and PBV_iodine maps in this work were generated by commercial CT scanners from a single vendor that uses two-material (water and iodine) decomposition. It is possible that by using three- or multi-material decompositions (especially with one basis material similar to consolidations and GGOs in terms of Z_eff), the issues of the iodine material image and PBV_iodine in quantifying the perfusion of consolidated and GGO regions can be mitigated. However, the selection of the proper basis material can be challenging, considering the Z_eff of consolidations and GGOs may vary across patients. How to further improve DECT material decomposition for more accurate pulmonary embolism detection and how PBV_iodine from improved multi-material decomposition compares to ${\text{PBV}}_{Z_{\text{eff}}}$ deserve further investigation in the future.

5 |. CONCLUSION

In conclusion, a new quantitative biomarker, ${\text{PBV}}_{Z_{\text{eff}}}$, from DECT imaging was developed to quantitatively assess pulmonary PBV. Compared with the relative pulmonary perfusion measurements using iodine images derived from two-material decomposition, the proposed ${\text{PBV}}_{Z_{\text{eff}}}$ provides a more accurate and robust imaging biomarker of potential pulmonary perfusion defects.

APPENDIX I: PULMONARY PERFUSED BLOOD VOLUME

Using the relationship between mass, mass density, and volume, the PBV formula in Equation (1) can be recast to

$$\mathrm{PBV}(x)=\frac{1}{{\rho }_{\text{lung}}(x)}\frac{V_{\text{cap}}(x)}{V_{\text{lung}}(x)},$$ (S1)

where V_cap(x)∕V_lung(x) denotes the volume fraction of the capillary bed in the VOI at x. When the iodinated contrast medium is injected into the blood stream and the pulmonary capillary bed is perfused with the iodinated blood, the mass of iodine that flows into the VOI in the lung is the same mass of iodine in the capillary bed, namely,

$$m_{\mathrm{I},\text{cap}}=m_{\mathrm{I},\text{VOI}}.$$ (S2)

However, the mass of iodine in the capillary bed is given by the product of iodine concentration in the input artery, ${\rho }_{{\text{I}}_0}$,and the volume of the capillary bed in the VOI, V_cap(x), i.e.,

$$m_{\text{I},\text{cap}}={\rho }_{{\text{I}}_0}{V}_{\text{cap}}(x)=m_{\text{I},\text{VOl}}$$ (S3)

Therefore, the averaged concentration of iodinated blood in the lung tissue VOI is given by

$${\rho }_{\text{I}}(x)=\frac{m_{\text{l},\text{VOl}}}{V_{\text{lung}}(x)}=\frac{{\rho }_{{\text{I}}_0}{V}_{\text{cap}}(x)}{V_{\text{lung}}(x)}\mathrm{..}$$ (S4)

This formula can be re-arranged to obtain the ratio of the capillary bed in the lung tissue VOI as the ratio between the iodine concentration in the VOI and the iodine concentration in the input artery as follows:

$$\frac{V_{\text{cap}}(x)}{V_{\text{lung}}(x)}=\frac{{\rho }_{\text{l}}(x)}{{\rho }_{{\text{l}}_0}}$$ (S5)

By combining Equations (S1) and (S5), the following equation is obtained for PBV:

$$\mathrm{PBV}(x)=\frac{1}{{\rho }_{\text{lung}}(x)}\frac{{\rho }_{\mathrm{I}}(x)}{{\rho }_{{\mathrm{I}}_0}}$$ (S6)

This is the primary result presented in Equation (2) in the main text.

APPENDIX II: PBV MEASUREMENT USING DECT IMAGING

In DECT-based lung perfusion assessment, the iodine basis image, a_I(x), is used as a surrogate for iodine concentration ρ_I(x). The problem with this approach is that the physical meaning of a_I(x) is not the same as ρ_I(x). Instead, its formula is given by^40,41

$$a_{\mathrm{I}}(x)=\frac{{\rho }_{\text{e}}(x)}{N_{\text{a}}{(z/A)}_{\mathrm{I}}}\frac{Z_{\text{eff}}^{\beta }(x)-Z_{\text{w}}^{\beta }}{Z_{\mathrm{I}}^{\beta }-Z_{\text{w}}^{\beta }}.$$ (S7)

In which, Z_eff is defined as

$$Z_{\text{eff}}={\left[\sum _{j=1}^n{f}_i{Z}_i^{\beta }\right]}^{1/\beta }$$ (S8)

Here Z_i is the atomic number of the i^th constituent material in the VOI at x, and f_i is the fraction of electrons associated with the ith material. As shown in Equation (S7), a_I(x) is not necessarily the same as ρ_I(x).They are equal only in the following special case:

Special case: The VOI is entirely composed of iodine and water. Under this special condition,

$$\begin{gathered} Z_{\text{eff}}^{\beta }(x)=f_{\text{I}}(x)Z_{\text{I}}^{\beta }+\left[1-f_{\text{I}}(x)\right]Z_{\text{w}}^{\beta } \\ =f_{\text{I}}(x)\left(Z_{\text{I}}^{\beta }-Z_w^{\beta }\right)+Z_w^{\beta }, \end{gathered}$$ (S9)

where f_I denotes the fraction of electrons coming from the iodine atoms. Under the condition in Equation (S9), the formula of a_I(x) in Equation (S7) can be written as:

$$\begin{array}{l}{a}_{\mathrm{I}}(x)=\frac{{\rho }_{\text{e}}(x)}{N_{\text{a}}{(z/A)}_{\mathrm{I}}}\frac{f_{\mathrm{I}}(x)\left(Z_{\mathrm{I}}^{\beta }-Z_{\text{w}}^{\beta }\right)+Z_{\text{w}}^{\beta }-Z_{\text{w}}^{\beta }}{Z_{\mathrm{I}}^{\beta }-Z_{\text{w}}^{\beta }}\\ =\frac{{\rho }_{\text{e}}(x)f_{\mathrm{I}}(x)}{N_{\text{a}}{(z/A)}_{\text{I}}}=\frac{{\rho }_{{\text{e}}_{\text{I}}}(x)}{N_{\text{a}}{(z/A)}_{\text{I}}}={\rho }_{\text{I}}(x)\end{array}.$$ (S10)

Aside from the above special case, a_I(x) is not the same as ρ_I(x).To find an alternative way to estimate PBV, the Z_eff formula in Equation (S8) can be recast into the following form:

$$Z_{\text{eff}}^{\beta }=f_{\text{I}}{Z}_{\text{I}}^{\beta }+\sum _{j=2}^n{f}_j{Z}_j^{\beta },$$ (S11)

where f_j (j = 2, … n) denotes the electron fraction for non-iodine materials in the VOI. As shown in Table 1, the atomic numbers of non-iodine materials in the lung are relatively similar to Z_w and are much smaller than Z_I. As a result, the following approximation can be justified:

$$Z_{\text{eff}}^{\beta }\approx f_{\text{I}}{Z}_{\text{I}}^{\beta }+Z_{\text{w}}^{\beta }\sum _{j=2}^n{f}_i=f_{\text{I}}{Z}_{\text{I}}^{\beta }+Z_{\text{w}}^{\beta }\left(1-f_{\text{I}}\right).$$ (S12)

Therefore,

$$f_{\text{I}}(x)\approx \frac{Z_{\text{eff}}^{\beta }(x)-Z_{\text{w}}^{\beta }}{Z_{\text{I}}^{\beta }-Z_{\text{w}}^{\beta }}.$$ (S13)

Per the definition of electron fraction, f_I(x) can be written as

$$f_{\text{I}}=\frac{{(z/A)}_{\text{I}}{f}_{m_{\text{I}}}}{\sum _j{(z/A)}_j{f}_{m_j}}\approx \frac{(1/2)f_{m_{\text{I}}}}{(1/2)\sum _j{f}_{m_j}}\approx \frac{m_{\text{I}}}{m_{\text{lung}}}=\frac{m_{\text{I}}}{{\rho }_{\text{lung}}{V}_{\text{lung}}},$$ (S14)

where we used the fact that for the majority of tissue materials, Z∕A ≈ 1∕2. Based on both Equations (S13) and (S14):

$$\frac{m_{\text{I}}(x)}{{\rho }_{\text{lung}}(x)V_{\text{lung}}(x)}\approx \frac{Z_{\text{eff}}^{\beta }(x)-Z_{\text{w}}^{\beta }}{Z_{\text{I}}^{\beta }-Z_{\text{w}}^{\beta }}.$$ (S15)

The mass of iodine in the VOI, m_I(x), is related to V_cap(x) and ${\rho }_{{\text{I}}_0}$ by

$$V_{\text{cap}}(x)=\frac{m_{\text{I}}(x)}{{\rho }_{{\text{I}}_0}}.$$ (S16)

According to Equations (S15) and (S16) and the PBV formula in Equation (S1),

$${\text{PBV}}_{Z_{\text{eff}}}(x)=\frac{m_{\text{I}}(x)/{\rho }_{{\text{I}}_0}}{{\rho }_{\text{lung}}{V}_{\text{lung}}}\approx \frac{1}{{\rho }_{{\text{I}}_0}}\frac{Z_{\text{eff}}^{\beta }(x)-Z_{\text{w}}^{\beta }}{Z_{\text{I}}^{\beta }-Z_{\text{w}}^{\beta }}.$$ (S17)

This is the desired result presented in Equations (8) and (9) in the main text.

By comparing the formula of ${\text{PBV}}_{Z_{\text{eff}}}(x)$ in Equation (S17) with the formula of a_I(x) in Equation (S7), one can observe that ${\text{PBV}}_{Z_{\text{eff}}}(x)$ and a_I(x) are related by

$${\text{PBV}}_{Z_{\text{eff}}}(x)=\frac{N_{\text{a}}{(z/A)}_{\text{I}}}{{\rho }_{{\text{I}}_0}}\frac{a_{\text{I}}(x)}{{\rho }_{\text{e}}(x)}.$$ (S18)

Therefore, an alternative method to calculate ${\text{PBV}}_{Z_{\text{eff}}}(x)$ is to normalize the iodine material image a_I(x) by the electron density image ρ_e(x) and then scale the result by $N_{\text{a}}{(z/A)}_{\text{I}}/{\rho }_{{\text{I}}_0}$.

DATA AVAILABILITY STATEMENT

The data supporting the results of this study are available upon reasonable request to the corresponding author.