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TMI-2014-0579.R1

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Stratification of Patients with Liver Fibrosis Using Dual-Energy CT Peter Lamb*, Dushyant V. Sahani, Jorge M. Fuentes-Orrego, Manuel Patino, Asish Ghosh, and Paulo R. S. Mendonça  Abstract—Quantifying the amount and characterizing the severity of liver fibrosis has direct clinical implications for patient diagnosis and treatment. Although this task is often accomplished through liver biopsy, the clinical utility of this procedure is disputed. Several imaging-based techniques for staging liver fibrosis have emerged, such as magnetic resonance elastography (MRE) and ultrasound elastography (USE), but they face challenges that include limited availability, high cost, poor patient compliance, low repeatability, and inaccuracy. Computed tomography (CT) can address many of these limitations, but is still hampered by inaccuracy in the presence of confounding factors associated with fibrosis, such as liver fat. Dual-energy CT (DECT), with its proven ability to discriminate between different tissue types, may offer a viable alternative for imaging-based characterization and quantification of liver fibrosis. In particular, the multi-material decomposition (MMD) method has been demonstrated in clinical practice to extend DECT’s core two-material decomposition capability to handle the complex composition of materials in the human body. By combining MMD with a biologically driven hypothesis we developed an algorithm for characterizing and quantifying liver fibrosis from DECT images. The algorithm was applied to images from a cohort of 12 patients, yielding quantitative maps showing the spatial distribution of liver fibrosis, as well as a fibrosis score for each patient with statistically significant correlation with the severity of fibrosis across a wide range of disease severities. A preliminary comparison of the proposed algorithm against MRE in a patient with severe fibrosis showed good agreement between the two methods. Finally, the application of the algorithm to longitudinal DECT scans of the cohort produced highly repeatable results. We conclude that our algorithm can successfully stratify patients with liver fibrosis and can serve to supplement and augment current clinical practice and the role of DECT imaging in staging liver fibrosis. Index Terms—Computed tomography, dual-energy CT, medical imaging, liver fibrosis, material decomposition. Copyright (c) 2014 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]. Manuscript received July 03, 2014; revised August 20, 2014; accepted August 25, 2014. Asterisk indicates corresponding author. *P. Lamb is with GE Global Research, 1 Research Circle, Niskayuna, NY 12309, USA (e-mail: [email protected]). P. R. S. Mendonça was with GE Global Research, Niskayuna, NY 12309, USA. He is now with Qualcomm Research, San Diego, CA 92121, USA (email: [email protected]). D. V. Sahani, J. M. Fuentes-Orrego, and M. Patino are with Massachusetts General Hospital, 55 Fruit Street, Boston, MA 02114, USA (e-mail: {dsahani,jmfuentes,mpatino}@partners.org). A. Ghosh is with GE Healthcare, 39 Staffords Crossing, Slingerlands, NY 12159, USA (e-mail: [email protected]).

I. INTRODUCTION

C

hronic liver disease (CLD) is a growing public health concern and the management of patients with CLD requires periodic assessment for the presence of inflammationinduced complications such as liver fibrosis. Under current clinical practice fibrosis staging is accomplished through liver biopsy; however, given the continually evolving nature of CLD it is desirable to assess the disease frequently, which is challenging for an invasive procedure. Moreover the utility of biopsies is often disputed due to concerns about sampling error, high complication rates, and lack of repeatability [1–6]. Over the last decade, tomographic imaging has assumed a fundamental role in decision making for patients with CLD for hepatocellular carcinoma (HCC), which is the most common primary malignant tumor of the liver and is the second and fifth leading cause of cancer deaths in the world and in the United States, respectively [7, 8]. Concurrent to its use in HCC screening, imaging is also being explored for its application to noninvasive staging of liver fibrosis [9–13]. Ultrasound (US) is a readily available, low-cost, and simple imaging modality, and one technique, US elastography (USE), has shown particular promise [14], especially to distinguishing severe fibrosis from mild or no fibrosis [15]. However, interpretation of its results is difficult, which, together with concerns about inter-equipment reproducibility, leads to poor inter-observer agreement [13]. Additional confounding factors to USE include large body sizes, field-of-view limitations, obscured visualization of organs, and confounding pathologies such as ascites [16, 17]. Advanced magnetic resonance (MR) techniques, such as diffusion weighted imaging, perfusion MR, and MR elastography (MRE), have also shown promise. Among these approaches, MRE has been found to be the most accurate for diagnosing and staging liver fibrosis. The performance of MRE has been validated in diverse patient cohorts [18–24], and is a reliable imaging-based biomarker for differentiating moderate- from severe-stage liver fibrosis. However, MRE has shown reduced accuracy in differentiating early- from mildstage and mild- from moderate-stage liver fibrosis [17, 23], which are key divisions for intervention with antiviral and antifibrotic therapies [25]. Additional limitations to the use of MRE include cost, accessibility, patient compliance, and reduced accuracy in the presence of confounding liver

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TMI-2014-0579.R1 pathologies [17, 16, 26]. Imaging artifacts and contraindications for the use of MR in patients with metallic stents, prostheses, and cardiac pacing devices are further restrictions. Computed tomography (CT) offers a viable alternative to US and MR in diagnosing and stratifying patients with liver fibrosis. Compared to MR, CT is a more accessible imaging modality: in 2011, there were 33% more CT scanners than MR scanners per million population in the United States, and 200% more CT exams were performed per 1,000 population than MR exams [26]. CT is also a more simple and costeffective modality, and compared to US, CT is much more reproducible. Augmenting the clinical utility of CT, dualenergy CT (DECT) has the added benefit of superior material discrimination [27]. This is vitally important in imaging liver fibrosis, which requires quantification of a number of different tissue types including healthy liver tissue, fibrotic liver tissue, blood, and contrast agent. Furthermore, DECT has been shown to be a quantitative method to analyze the cirrhotic liver with high sensitivity and specificity [28], demonstrating potential application to the fibrotic liver as well. Moreover, DECT does not bring additional dose to the patient, operating within the limits specified by the American College of Radiology guidelines for abdominal CT [27], and has even demonstrated performance at or above the standards set by conventional CT [29]. Furthermore, in patients with liver cirrhosis, the American Association for the Study of Liver Diseases has advocated for dynamic, multiphase, contrastenhanced CT to detect and characterize HCC [30]. A DECTbased approach would serve to supplement and augment clinical practice and the role of tomographic imaging in staging liver fibrosis. In previous research we developed the multi-material decomposition (MMD) technique, a flexible, model-based method that extends DECT’s core material discrimination capability — typically restricted to two materials — to allow for the disambiguation of a larger number of materials [31]. This has the potential for enhancing the use of DECT in clinical applications such as liver fibrosis, in which the liver and liver pathologies have complex compositions. In the present work the MMD technique was combined with the hypothesis that hemodynamic-based studies using contrast agents and multiphase scan acquisitions can serve as an imaging-based biomarker for assessing the severity of liver fibrosis [32–34, 28], and used to develop an image analysis algorithm for characterizing and quantifying liver fibrosis. A preliminary analysis of the method indicated that it achieves quantitative agreement with MRE in the assessment of severe fibrosis. In a larger test with DECT images collected from a cohort consisting of 12 patients the proposed algorithm yielded measures of fibrosis severity with statistically significant agreement with the Ishak fibrosis score [35, 36], which was assumed to be the gold standard. This result was observed across the full range of disease severities, and a longitudinal study showed that the method is highly repeatable. Albeit a small pilot study, these two features (accuracy across different disease severities and repeatability)

2 are significant, since they are key challenges for both MRE and USE-based methods for assessment of liver fibrosis. The remainder of this paper is organized as follows: A brief discussion of related work is given in the next subsection. The fundamentals of DECT are described in Section II, followed by a review of the MMD method originally introduced in [31]. The proposed algorithm for quantification of liver fibrosis is presented in Section III. Experimental results and comparison with other techniques are shown in Section IV. Conclusions and directions for future work are discussed in Sections V and VI. A. Related Work Related work in DECT material discrimination. Multiple solutions have been proposed for augmenting the material decomposition capabilities of DECT. The MMD technique used in this paper is described in full detail in [31]. Other methods [37] seek to take advantage of the K-edge effect, which is a discontinuity in the mass attenuation curve of certain materials. It should be noted, however, that available tomographic methods based on the K-edge effect require energy-discriminating detectors and are still in the experimental phase. Post-reconstruction techniques include methods that use mass conservation [38] and voxel-by-voxel segmentation [39]. Several techniques perform material decomposition prior to image reconstruction, such as those in [40] and [41]. While pre-reconstruction methods lack the flexibility and computational efficiency of the MMD technique, they are potentially more accurate, but full verification on clinical (rather than phantom) data is needed to support this claim. Related work in hemodynamic-based imaging of liver fibrosis. Recent research has suggested that developing an imaging-based biomarker for assessing the severity of liver fibrosis is possible using hemodynamic-based contrastenhanced studies combined with a multiphase scan acquisition. The work in [32], for instance, reported that a linear/reticular pattern of contrast agent uptake in the liver was highly correlated with histologically proven areas of fibrosis on 5-min. delayed phase MR images. Correlation between the drop in hepatic venous outflow on perfusion MR and the severity of liver fibrosis was shown in [33]. Similar observations were described [34], which demonstrated the feasibility of discriminating between mild- and moderatedegree liver fibrosis using perfusion CT. Multiphase DECT was used to characterize the cirrhotic liver in [28], which suggests application to the fibrotic liver as well. Since the work described in this paper involves measuring hepatic hemodynamic changes, understanding the pathophysiology of blood flow through liver is paramount to distinguishing the signal from the noise occurring in hepatic diseases such as liver fibrosis. Excellent reviews on this topic are provided in [42–48]. II. BACKGROUND Dual-energy CT systems offer a fundamental advantage over single-energy CT through their superior ability to carry

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out material discrimination, or material decomposition. Such ability is the key enabler of the applications of DECT to clinical problems beyond the reach of single-energy CT systems. A. Fundamentals of Dual-Energy CT Dual-energy CT explores the dependency between the extent to which a medium can attenuate X-rays, expressed through the medium’s linear attenuation coefficient, , and the energy of the incident X-rays. The linear attenuation coefficient, in turn, depends on two physical properties of the medium: its (energy-independent) density , and its (densityindependent but energy-dependent) mass attenuation coefficient, . This relationship is expressed through the ( ). It has been shown [49] that for expression ( ) a medium consisting of the typical materials found in the human body as well as iodine-based contrast agents can be accurately expressed as a linear combination, with appropriate adimensional weights, of the linear attenuations of an arbitrary pair of materials, denoted a material basis [50]. Using ( ) ( ), this result yields ( )

( )

( ) for

(1)

where is the mass attenuation coefficient of material , and is its effective density in the material mix, i.e., the mass of material divided by the total volume of the mixture. The simple expression in (1) is the foundation for all clinical DECT systems. An important observation is that, in the absence of K-edge effects and within the energy limits of clinical X-rays, (1) cannot be extended through the inclusion of linear attenuation measurements at more energies, since the additional equations would be linearly dependent of the previous two. In particular, (1) does not allow for decomposition into three or more materials through extra measurements of at more X-ray energies. B. Multi-Material Decomposition of Dual-Energy CT Images This section presents a brief review of the MMD algorithm. A thorough description and analysis of the method can be found in [31]. The mass attenuation of a mixture of materials can be expressed as the weighted average of the mass attenuation of its constituents: ( ) subject to ∑ The weights ∑

∑

( )

in the expression are given by , where is the mass fraction of material

in the mixture, and therefore each corresponds to the mass fraction of its corresponding material. The constraint ∑ is interesting, as it is independent of the measurements in (1), and could in principle be used to

augment DECT’s ability and allow for decomposition into three materials. This process was carried out in [51], where the ∑ ( ) relation ( ) ( ) was explored to produce ( ) where

∑

( )

(2)

are the volume fractions of the

∑

constituent materials in the mix. A solution for (2) is possible with only two measurements of ( ) (at two distinct X-ray energies) due to the constraint ∑ . The work in [51] was further extended in the MMD algorithm [31] by including other physical constraints into the material decomposition expression in (2). Specifically, the volume fractions of a physically plausible material mix must satisfy the constraints

Violation of such constraints indicates that specific material triplet chosen to solve (2) is inadequate, and a different triplet should be selected. By sequentially choosing different triplets the MMD algorithm was shown to produce decompositions into as many as five materials [31]. It was also shown in [31] that the solution of (2) when is equivalent to the computation of the barycentric ( ( ) ( )) with coordinates [52] of the point ( ) with vertices respect to the triangle (

(

)

(

))

This

geometric

interpretation naturally leads to the representation of DECT data as points in a two-dimensional space of linear attenuation coefficients. III. QUANTIFICATION OF LIVER FIBROSIS VIA DUALENERGY CT The ability of the MMD algorithm to quantify the amount of different materials through DECT would suggest a simple technique for fibrosis quantification based on the direct measurement of the volume fraction of fibrotic tissue. However, current biological models consider fibrosis as a “wound-healing response to chronic liver injury” [53], or in other words, a scar. Therefore, fibrosis, particularly in the early stages of the disease, is not characterized by differences in the composition of the liver tissue, but rather by differences in its structure, which cannot directly be discriminated from healthy liver tissue by the MMD algorithm or by any other direct CT measurement. Therefore, we propose a surrogate measurement of fibrosis that is amenable to CT imaging. Recent research has suggested that an imaging-based biomarker for assessing the severity of liver fibrosis is possible using hemodynamic-based contrast-enhanced studies combined with a multiphase scan acquisition [32–34, 28]. This research is based on perfusion imaging, a technique that uses contrast-enhanced scanning to detect changes in organ blood flow [54]. The idea is simple: inject a patient with contrast

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TMI-2014-0579.R1 agent and acquire scans periodically as the contrast agent travels through the vasculature. The temporal element added by the periodic scanning provides the means for an imagingbased biomarker of blood flow, and quantitative information about blood volume, contrast agent volume, and blood flow rate can be ascertained. In the case of liver fibrosis, it is wellestablished that changes in liver blood flow are known to be associated with the evolution of disease [55, 56]. Therefore, a naïve approach to the problem would be simply to measure CT values in Hounsfield units as a surrogate indicator of the severity of the disease, since an increase in the concentration of contrast agent results in a corresponding increase in CT values. However, this method suffers from a significant drawback: chronic liver disease is often accompanied by other liver pathologies, in particular fatty liver disease [57]. Fat has a lower linear attenuation coefficient than normal liver tissue, and therefore observed CT values in the liver of a fibrotic patient are often the result of an averaging of CT values of fat and contrast, and the extent of their individual contributions cannot be discriminated. This problem cannot be addressed by direct DECT measurements either, because the presence of healthy liver tissue implies that there are three material types whose concentrations should be independently quantified. However, while the MMD algorithm cannot directly be used to measure fibrotic tissue, it can certainly be used to estimate the contributions of contrast agent, fat, and healthy liver tissue from DECT data. The visualization and quantification of contrast agent in the liver by MMD thus serves as the basis of our algorithm. A. Algorithm The quantification of the concentration of liver contrast agent in the presence of fat using the MMD algorithm could be carried out using a material triplet consisting of fat, contrast, and blood or, alternatively, fat, contrast, and healthy liver tissue. However, it has been experimentally established in [31] that the linear attenuation of healthy liver tissue occupies a point in linear attenuation coefficient space discussed in Section II-B which lies on the line joining the linear attenuation coefficients of fat and blood. Therefore, a simple geometric argument (see Figure 1) demonstrates that these two choices of material triplets will lead to the same estimated concentration of contrast agent. Since blood is a standard material in tables of linear attenuation coefficients [58, 59], whereas liver is not, we proceed with the choice of fat, contrast, and blood as our basic material triplet for the quantification of liver fibrosis. The first step of the algorithm is therefore the computation of the volume fractions of contrast agent at each voxel in the liver using (2). These volume fractions will, of course, be dependent on the timing of the image acquisition with respect to the time of the injection of contrast, according to a standard perfusion model [60]. Two approaches are possible to address this issue: the use of multiphase acquisitions, which would allow for the computation of phase-independent perfusion parameters, or normalization against a reference tissue. Since

4

Fig. 1. Graphical representation of quantification of contrast agent. The work in [31] established a relationship between the coefficients in (2) and ( ( ) ( )). Specifically, the barycentric coordinates of the point the solution of (2) corresponds to the barycentric coordinates of with ( ), and therefore the respect to the triangle volume fraction of contrast agent for the input will be given by the ratio of the areas of the triangles and , i.e., , as indicated in the top figure. An elementary geometric argument shows that the same value of would be obtained if instead of and one considered the triangles and shown in the bottom figure.

the former approach comes with an increase in patient dose, a significant concern in CT imaging, we have adopted the second approach, using blood in the aorta as the reference tissue. The normalized, unitless metric, referred to as normalized iodine concentration (NIC), is the final measure of the severity of liver fibrosis, and it is computed as the ratio between the volume concentration of contrast agent in the liver and in the aorta: (3) 1) Sensitivity Analysis: A detailed analysis of the MMD algorithm is presented in [31]. Here, we present a more focused analysis of the algorithm’s sensitivity to noise as it pertains to the quantification of contrast agent in the liver. In particular, the full MMD algorithm has to account for the possibility of noisy data “jumping” triangles, whereas here we contend with a single triangle with the linear attenuation coefficients of fat, blood (or liver), and contrast agent at its vertices, as depicted in Figure 1. It was shown in [31] that the

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jumping of triangles was the most pronounced source of bias and variance to the MMD algorithm; when a single triangle is considered this effect can be disregarded and an expression for the observed volume fraction corresponding to a noisy observation of pair of linear attenuation ( ( ) ( )) was derived: coefficients (4) where is the volume concentration of material for the noise-free input ; is the two-dimensional random vector of the additive noise perturbing ; and are the length of and the unity normal vector to the edge opposite to in the triangle , respectively; and is the area of . In [31] the expression in (4) is only an approximation (albeit a good one) for the effect of noise on the algorithm, whereas here the expression is exact, since is the only triangle that is considered. To validate this result we conducted an experiment in which each value of within was perturbed with 1000 realizations of additive Gaussian noise. Volume fractions of contrast agent, as well as of fat and blood, were computed using the MMD algorithm. It is important to note that, as in [31], the shape of the covariance of the added noise (depicted as the red

ellipse in the plots in Figure 2) was estimated from real image data, but with standard deviation of each marginal distribution artificially increased to over 7 HU and 9 HU, which is significantly more than the ±7 HU max error ( HU) recommended by the American College of Radiology for CT-phantom accreditation [61]. Figure 2 shows the results of this experiment, demonstrating that for zero-mean noise the algorithm produces unbiased results, and that the standard deviation of the error in the estimated volume fractions is consistently low. IV. EXPERIMENTS AND RESULTS We conducted a retrospective, HIPPA-compliant study with approval from the Institutional Review Board of MGH. DECT imaging was performed on 12 patients (58 ± 8 years; 6 male, 6 female) using a GE Discovery CT750 HD scanner (GE Healthcare, Milwaukee, WI), a single-source 64-channel multidetector CT with fast kVp switching (80/140 kVp), and bow-tie filtering set to large. Effective patient diameter [62] was 53.2 ± 6 cm. Of these patients, 7 had a histologically confirmed diagnosis of fibrosis. The remaining 5 patients comprised the control group, and had various conditions including: colon cancer ( ), pancreatic cancer ( ), cholangiocarcinoma ( ), and hemangiomas ( ).

Fig. 2. Sensitivity analysis of the algorithm. Each point in the triangle with vertices given by the linear attenuation coefficients of fat, blood, and contrast agent at energies and was perturbed with zero-mean Gaussian noise with covariance represented by the red ellipse shown in each plot. Volume fractions for the three materials were computed for 1000 realizations of . Bias and standard deviation for corresponding to each material are shown on the left and right columns, respectively.

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TMI-2014-0579.R1 All patients received positive oral contrast media, 900 ml (Readi CAT, containing 1–2% w/v of barium sulfate; Bracco Diagnostics, Princeton, NJ), taken 60–90 minutes prior to the scan. Based on each patient’s body weight, 80–120 ml (1.5 cc/kg) of a nonionic contrast agent (Isovue, 370 mg of iodine per ml; Bracco Diagnostics, Princeton, NJ) was bolus-injected intravenously using a mechanical power injector (Empower; ACIST Medical Systems, Eden Prairie, MN) at a rate of 3.0– 3.5 ml/sec, via a 20-gauge catheter placed in the antecubital vein. Each patient was placed supine on the CT table and the liver was scanned craniocaudally during the arterial and delayed phases. DECT scanning was performed using rapid (< 0.5 msec) switching of tube voltages (80/140 kVp, matched with 630 mAs), 0.6 second rotation time, 64 x 0.625 mm slice collimation, and 1.375 mm pitch. The arterial phase was acquired using automated bolus tracking (Smartprep; GE Healthcare, Milwaukee, WI), beginning 12–15 seconds after the attenuation threshold (125 HU) was reached at the supraceliac abdominal aorta. A fixed time delay of 180 seconds following the injection of contrast agent was used to trigger scanning during the delayed phase. One patient also had 2- and 5-minute delayed phase DECT scans, and MRE was acquired for another patient for comparison. DECT images were reconstructed from the scan acquisitions at 70 keV using a 5 mm slice thickness in the axial plane, and a 3 mm slice thickness in the coronal and sagittal planes. The MMD algorithm was used to compute the concentration of contrast agent at each voxel in the DECT volume, in particular at the liver and the aorta, as required by (3). On the contrast agent maps of the delayed phase, three two-dimensional regions of interest (ROI) (mean: 359 pixels; range: 200–582) were placed in the liver parenchyma in areas corresponding to the same biopsy sites used for fibrosis grading, with careful attention to avoid liver vasculature, lesions, and other regions of potential attenuation difference. In order to carry out the computation of required by the (unitless) NIC measurement in (3), three ROIs (mean: 129 pixels; range: 100–220) were also

Fig. 3. Correlation of contrast agent concentration and severity of liver fibrosis. (A)–(C) depict DECT images at the delayed phase for patients with varying degrees of liver fibrosis. Corresponding pathology images are provided as insets. Note that it is difficult to directly determine the severity of liver fibrosis from the DECT images alone. (D)–(F) are the corresponding contrast agent maps of the liver, overlaid on top of the original DECT images. These contrast agent maps allow for easily visualization of the severity of liver fibrosis, and furthermore demonstrate strong correlation of contrast agent trapping and severity of liver fibrosis.

6 TABLE I STRATIFICATION OF PATIENTS WITH LIVER FIBROSIS USING THE PROPOSED DECT BIOMARKER Number of subjects 5 4 3

Diagnosis (Ishak score) No fibrosis (0) Mild fibrosis (1-2) Severe fibrosis (5-6)

NIC 0.3741 ± 0.02 0.4598 ± 0.02 0.7712 ± 0.03

p-value < 0.0001 < 0.0001 0.0452

A preliminary study involving 12 patients and the NIC metric shows statistically significant stratification of patients by degree of fibrosis.

placed at the origins of the celiac axis, superior mesenteric artery, and renal arteries, with similar attention given to avoid vessel walls. NIC measurements were made for all 12 patients, and statistical significance regarding correlation with degree of fibrosis was obtained using ANOVA and Student’s t-test. A p-value < 0.05 was considered statistically significant. These patients underwent a subsequent contrast-enhanced scan during the same phase to provide two separate time points, with a time interval between scans of 63.9 ± 35.1 days. NIC repeatability was investigated using the images from these two scans in a linear regression model. A. Results Visualization of the spatial distribution of contrast agent within the liver and comparison against biopsy images are shown Figure 3. Quantitative results of characterizing liver fibrosis using our DECT-based technique are presented in Table I. NIC values for the patients in this study correlate with severity of liver fibrosis (as measured by histology), and allow for statistically significant stratification of patients by severity of fibrosis ( for each group). NIC repeatability is shown in Figure 4, which depicts a strong and positive linear correlation between NIC measurements at different time points for the same patient, with a coefficient of determination ( ) of 0.927. As many other imaging-based biomarkers for assessing liver fibrosis suffer in repeatability, this is a promising result for our DECT-based approach. Despite reports of low accuracy in the assessment of earlyto mild-stage liver fibrosis, the usefulness of MRE to discriminate between moderate- to severe-stage liver fibrosis

Fig. 4. Repeatability of the DECT biomarker for liver fibrosis. Two contrastenhanced DECT scans of the same phase were acquired for 12 patients, with a time interval between scans of 63.9 ± 35.1 days. NIC measurements were made using images from both scans and compared for repeatability. A strong and positive linear correlation was found between NIC measurements, with a value of 0.927.

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Fig. 5. Qualitative comparison of MRE and DECT for assessment of liver fibrosis. (A) 58 year-old male cirrhotic patient with severe liver fibrosis evidenced on conventional contrast-enhanced MR during the portal venous phase. Corresponding MRE (B) and DECT maps of liver fibrosis (C). The image in (C) is a color overlay of the contrast agent map on the original DECT scan. Note that regions of high contrast agent trapping (red) correlate with areas of high tissue stiffness on MRE (also red).

has been validated in multiple patient cohorts. A preliminary qualitative comparison of MRE and DECT was performed for one patient with severe liver fibrosis and is presented in Figure 5. In this figure, it can be seen that regions of high contrast agent trapping in the liver depicted on the DECT image correlate with the areas of higher tissue stiffness shown in the MRE image. V. DISCUSSION AND FUTURE WORK As mentioned in Section I, one advantage of the proposed method over biopsy is the specification of the spatial distribution of the disease, thereby overcoming sampling errors. This benefit is further compounded by DECT’s higher spatial resolution when compared against MR and US. However, there is no clinical consensus on how to make the best use of spatial information in the management and treatment of liver fibrosis, apart from the opportunity for improving biopsy guidance [63]. It should be noted that the hemodynamics of blood flow through the liver is intricate, especially since the liver has a dual blood supply from the portal vein and hepatic artery, and thus delayed outflux of contrast agent in fibrotic livers may not solely be due to fibrosis. Abnormal hepatic blood flow can be affected by certain conditions, including tumor or bland thrombus, arterioportal shunts, liver cirrhosis, Budd-Chiari syndrome, and inflammatory changes [42, 44]. Moreover, liver fibrosis is a reaction to inflammation of the liver and can elicit an angiogenic response which, if prolonged and untreated, leads to the abnormal angioarchitecture distinctive of liver cirrhosis [48]. The increased tortuousness of the liver’s microvascular bed could contribute to delayed outflux of contrast agent. Conversely, anti-angiogenic therapies might yield a false negative as these therapies may improve liver blood flow but may not treat the underlying fibrosis. Ultimately, the hemodynamics in such cases is very complex, and have yet to be fully investigated or understood [42]. Despite these unanswered questions, as mentioned earlier research has shown that hemodynamic changes in the liver correlates with severity of liver fibrosis. The main purpose of the present work was to perform a small pilot study to assess if measurement of contrast agent in the liver by DECT correlates with severity of fibrosis. Future work will involve parsing the role of confounding factors and their impact on the association between severity of fibrosis and excess retention of contrast agent. We plan to validate the

7 proposed method in larger patient cohorts so that robustness can be investigated in the presence of the aforementioned conditions and other confounding factors such as hepatic steatosis, iron deposition, and steatohepatitis (inflammation). Additionally, we will investigate the optimal timing of image acquisition for characterizing and quantifying fibrosis. Preliminary data indicates potential advantages for acquiring delayed phases at a time greater than two minutes after injection of contrast agent, as shown in Figure 6. Thus far we adopted the simple approach of subsuming the spatial information through a voxel-wise averaging of contrast agent concentration. Techniques derived from the study of the geometry of random fields [64] have already been used to derive more effective hypothesis tests on the presence of abnormal blood flow in the brain by taking into account the topology and geometry of excursion sets [65] of positron emission tomography images. It is plausible that the application of these techniques to the spatial maps produced by our method would yield a more informative, image-based fibrosis score. VI. CONCLUSION This paper introduced an algorithm for the quantification and characterization of liver fibrosis from DECT images. The algorithm is based on a combination of the MMD technique with a biologically driven hypothesis about hemodynamic properties of fibrotic livers. Using image data collected from a cohort consisting of 12 patients, the proposed method yielded quantitative maps showing the spatial distribution of fibrosis in the liver, and statistically significant correlation with the severity of fibrosis established from a gold-standard score obtained through biopsy. Results also indicate DECT’s correlation to existing imaging-based methods for fibrosis characterization, such as MRE, as well as high degree of repeatability. We conclude that the algorithm can successfully form the basis of an imaging application for the assessment of liver fibrosis, with potential use in other clinical applications that require visualization and accurate quantification of contrast agents.

Fig. 6. Contrast-agent concentration at different scan times using the proposed algorithm. (A)–(C) show multiphase DECT images of a patient with cirrhosis, with an area of known liver fibrosis (red arrow). Visual assessment of the images shows significantly higher contrast retention in the fibrotic area when compared with non-fibrotic areas five minutes after injection.

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