# Three-Dimensional Voxel-Wise Quantitative Assessment of Imaging Features in Hepatocellular Carcinoma

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## Abstract

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## 1. Introduction

#### Contributions and Organization

- Piece-wise smooth nonlinear registration: an iterative reweighted local cross-correlation (IRLCC) method was used to overcome the deformation caused by various reasons, and it assumes that the entire deformation is piece-wise smooth.
- Three-dimensional calculation: imaging features were quantified voxel-wise, based on registered images.
- Consistency: all 3D information of the whole lesion was used for quantitative analysis and visualization.

## 2. Materials and Methods

#### 2.1. Dataset

#### 2.2. Image Registration Framework

#### 2.2.1. Image Preprocessing

#### 2.2.2. Nonlinear Registration: The IRLCC Method

**Discretization and Optimization**—First, we discretized the domain $\Omega $ into a grid, used the grid directly to obtain discretized images, and then constructed a coarse-to-fine pyramid with Gaussian filtering of each discretized image. Let ${I}_{1}^{1}\left(\mathbf{x}\right)\cdots {I}_{1}^{L}\left(\mathbf{x}\right)$ be the L-level coarse-to-fine pyramidal representation of the fixed image ${I}_{1}\left(\mathbf{x}\right)$ from the coarsest resolution ${I}_{1}^{1}\left(\mathbf{x}\right)$ to the finest resolution ${I}_{1}^{L}\left(\mathbf{x}\right)={I}_{1}\left(\mathbf{x}\right)$ and ${I}_{2}^{1}\left(\mathbf{x}\right)\cdots {I}_{2}^{L}\left(x\right)$ be the L-level coarse-to-fine pyramidal representation of the moving image ${I}_{2}\left(\mathbf{x}\right)$. At each level $l(=1,\cdots ,L)$, let the deformation field ${u}^{l-1}\left(\mathbf{x}\right)$ estimated from the previous level be the initial value. The deformation field ${u}^{l}\left(\mathbf{x}\right)$ between two given images can be replaced by ${u}^{l}\left(\mathbf{x}\right)={u}^{l-1}\left(\mathbf{x}\right)+h\left(\mathbf{x}\right)$, where $h\left(\mathbf{x}\right)=({h}_{1}\left(\mathbf{x}\right),{h}_{2}\left(\mathbf{x}\right),{h}_{3}\left(\mathbf{x}\right))$ is the incremental deformation. Therefore, the optimum deformation ${u}^{l}\left(\mathbf{x}\right)$ was calculated via estimating the optimum incremental deformation. For the coarsest level, i.e., $l=1$. The initial previous-level deformation was set to

**0**.

Algorithm 1: Fixed-Point Iteration Algorithm |

Input: ${I}_{1}^{l},{I}_{2}^{l},{U}^{l-1}$, l is the current level.Output: ${U}^{l}$.Initialization: Upsample ${U}^{l-1}$ to the size in level l, then deform the moving image: ${I}_{2}^{l}\left(x\right)={I}_{2}^{l}(x+{U}^{l-1}\left(x\right))$; |

#### 2.3. The 3D Voxel-Wise Quantitative Assessment of Imaging Features

#### 2.3.1. Locations Extraction

**Operations of extracting APHE location: Equations (7) and (8)**—According to the definition of APHE in LI-RADS v2018, the area must meet two conditions: (1) its enhancement in AP must be unequivocally greater in whole or in part than the liver, and (2) the enhanced part must be brighter than the liver in AP. In this section, we use two subtraction operations to describe these conditions:

**Operations of extracting WO location: Equations (9)–(11)**—According to its definition in LI-RADS v2018, which is the visually assessed temporal reduction of enhancement of the area in whole or in part relative to the composite liver tissue from earlier to later phase, resulting in hypoenhancement in the post-AP, we divided the position extraction into two steps. One step is to check that the area is at least slightly enhanced in the AP (not necessarily APHE) by Equation (9).

**Operation of calculating adjacent liver value: Equation (12)**—Given that the extraction of APHE and WO location depends on comparison with the surrounding liver value, their value must be obtained. In particular, we first determined the liver area using the liver mask containing lesion and normal liver. Then, we removed the lesion area and calculated the mean ($\mu $) and variance ($\sigma $) of the intensity corresponding to the remaining part. Finally, we gave the adjacent liver value as follows:

**Add Operation: Equation (13)**—To show the APHE and WO features simultaneously, we logically combined $mas{k}_{APHE}$ and $mas{k}_{WO}$:

#### 2.3.2. Estimation

## 3. Results

#### 3.1. Setting of Registration Parameters

#### 3.2. Registration Results

#### 3.3. Voxel-Wise Quantitative Assessment Results and Visualization

#### 3.4. Quantitative Analysis

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

APHE | Arterial phase hyperenhancement |

WO | Subsequent Washout |

HCC | Hepatocellular carcinoma |

AUC | Area under the curve |

CT | Computed tomography |

CM | Contrast media |

MRI | Magnetic resonance imaging |

Pre | Pre-contrast Phase |

PAE | Percentage of arterial enhancement |

AP | Arterial Phase |

LI-RADS | Liver Imaging Reporting and Data System |

PV | Portal Venous Phase |

LLCR | Lesion-to-liver contrast ratio |

DP | Delayed Phase |

ROC | Receiver operating characteristics |

ROIs | Regions of interests |

## References

- Forner, A.; Llovet, J.M.; Bruix, J. Hepatocellular carcinoma. Lancet
**2012**, 379, 1245–1255. [Google Scholar] [CrossRef] [PubMed] - Bray, F.; Ferlay, J.; Soerjomataram, I.; Siegel, R.L.; Torre, L.A.; Jemal, A. Global cancer statistics 2018: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA Cancer J. Clin.
**2018**, 68, 394–424. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hennedige, T.; Venkatesh, S.K. Imaging of hepatocellular carcinoma: Diagnosis, staging and treatment monitoring. Cancer Imaging
**2013**, 12, 530–547. [Google Scholar] [CrossRef] [PubMed][Green Version] - Bano, J.; Nicolau, S.A.E.A. Multiphase Liver Registration from Geodesic Distance Maps and Biomechanical Modelling. In Abdominal Imaging. Computation and Clinical Applications, Proceedings of the 6th International Workshop, ABDI 2014, Held in Conjunction with MICCAI, Cambridge, MA, USA, 14 September 2014; Springer: Berlin/Heidelberg, Germany, 2013; pp. 165–174. [Google Scholar]
- Hwang, G. Nodular hepatocellular cacinomas (Detection with arterial-, portal-, and delayed-phase images at spiral CT). Radiology
**1997**, 202, 383–388. [Google Scholar] [CrossRef] - Kim, T.; Murakami, T.; Takahashi, S.; Tsuda, K.; Tomoda, K.; Narumi, Y.; Sakon, M.; Nakamura, H. Optimal phases of dynamic CT for detecting hepatocellular carcinoma: Evaluation of unenhanced and triple-phase images. Abdom. Imaging
**1999**, 24, 473–480. [Google Scholar] [CrossRef] - Laghi, A.; Iannaccone, R.E.A. Hepatocellular carcinoma: Detection with triple-phase multi-detector row helical CT in patients with chronic hepatitis. Radiology
**2003**, 226, 543–549. [Google Scholar] [CrossRef] - Kitao, A.; Zen, Y.; Matsui, O.; Gabata, T.; Nakanuma, Y. Hepatocarcinogenesis: Multistep changes of drainage vessels at CT during arterial portography and hepatic arteriography–radiologic-pathologic correlation. Radiology
**2009**, 252, 605–614. [Google Scholar] [CrossRef] - Lee, Y.J.; Lee, J.M.; Lee, J.S.; Lee, H.Y.; Park, B.H.; Kim, Y.H.; Han, J.K.; Choi, B.I. Hepatocellular carcinoma: Diagnostic performance of multidetector CT and MR imaging-a systematic review and meta-analysis. Radiology
**2015**, 75, 97–109. [Google Scholar] [CrossRef][Green Version] - American College of Radiology. Liver Imaging Reporting and Data System. 2018. Available online: https://www.acr.org/Clinical-Resources/Reporting-and-Data-Systems/LI-RADS (accessed on 2 February 2023).
- Chernyak, V.; Fowler, K.J.; Kamaya, A.; Kielar, A.Z.; Elsayes, K.M.; Bashir, M.R.; Kono, Y.; Do, R.K.; Mitchell, D.G.; Singal, A.M.; et al. Liver Imaging Reporting and Data System (LI-RADS) Version 2018: Imaging of Hepatocellular Carcinoma in At-Risk Patients. Radiology
**2018**, 289, 816–830. [Google Scholar] [CrossRef] - Elsayes, K.M.; Hooker, J.C.; Agrons, M.M.; Kielar, A.Z.; Tang, A.; Fowler, K.J.; Chernyak, V.; Bashir, M.R.; Kono, Y.; Do, R.K.; et al. 2017 Version of LI-RADS for CT and MR Imaging: An Update. Radiographics
**2017**, 37, 1994–2017. [Google Scholar] [CrossRef] - Kyung Won Kim, M.; Jeong Min Lee, M.; Ernst Klotz, P.; Hee Sun Park, M.; Dong Ho Lee, M.; Ji Young Kim, M.; Soo Jin Kim, M.; Se Hyung Kim, M.; Jae Young Lee, M.; Joon Koo Han, M. Quantitative CT Color Mapping of the Arterial Enhancement Fraction of the Liver to Detect Hepatocellular Carcinoma. Radiology
**2009**, 250, 425–434. [Google Scholar] - Liu, Y.I.; Shin, L.K.; Jeffrey, R.B.; Kamaya, A. Quantitatively defining washout in hepatocellular carcinoma. Am. J. Roentgenol.
**2013**, 200, 84–89. [Google Scholar] [CrossRef] [PubMed] - Agarwal, S.; Grajo, J.R.; Fuentes-Orrego, J.M.; Abtahi, S.M.; Harisinghani, M.G.; Saini, S.; Hahn, P.F. Distinguishing hemangiomas from metastases on liver MRI performed with gadoxetate disodium: Value of the extended washout sign. Eur. J. Radiol.
**2016**, 85, 635–640. [Google Scholar] [CrossRef] - Kloeckner, R.; dos Santos, D.P.; Kreitner, K.F.; Leicher-Duber, A.; Weinmann, A.; Mittler, J.; Duber, C. Quantitative assessment of washout in hepatocellular carcinoma using MRI. BMC Cancer
**2016**, 16, 758. [Google Scholar] [CrossRef][Green Version] - Stocker, D.; Becker, A.S.; Barth, B.K.; Skawran, S.; Kaniewska, M.; Fischer, M.A.; Donati, O.; Reiner, C.S. Does quantitative assessment of arterial phase hyperenhancement and washout improve LI-RADS v2018–based classification of liver lesions? Eur. Radiol.
**2020**, 30, 2922–2933. [Google Scholar] [CrossRef] - Zhao, H.C.; Wu, R.L.; Liu, F.B.; Zhao, Y.J.; Wang, G.B.; Zhang, Z.G.; Huang, F.; Xie, K.; Geng, X.-P. A retrospective analysis of long term outcomes in patients undergoing hepatic resection for large (>5 cm) hepatocellular carcinoma. HPB
**2016**, 18, 943–949. [Google Scholar] [CrossRef][Green Version] - Jialin Peng, J.W.; Kong, D. A new convex variational model for liver segmentation. In Proceedings of the 21st International Conference on Pattern Recognition (ICPR2012), Tsukuba, Japan, 11–15 November 2012; pp. 3754–3757. [Google Scholar]
- Beare, R.; Lowekamp, B.; Yaniv, Z. Image Segmentation, Registration and Characterization in R with SimpleITK. J. Stat. Softw.
**2018**, 86. [Google Scholar] [CrossRef] [PubMed][Green Version] - Yaniv, Z.; Lowekamp, B.C.; Johnson, H.J.; Beare, R. SimpleITK Image-Analysis Notebooks: A Collaborative Environment for Education and Reproducible Research. J. Digit. Imaging
**2017**, 31, 290–303. [Google Scholar] [CrossRef][Green Version] - Lowekamp, B.C.; Chen, D.T.; Ibanez, L.; Blezek, D. The Design of SimpleITK. Front. Neuroinform.
**2013**, 7, 45. [Google Scholar] [CrossRef][Green Version] - Huang, C.; Qiu, C.; Peng, Z.; Yuan, J.; Kong, D. Iterative Reweighted Local Cross Correlation Method for Nonlinear Registration of Multiphase Liver CT Images. In Proceedings of the 2021 IEEE International Conference on Image Processing (ICIP), Anchorage, Alaska, 19–22 September 2021; pp. 136–140. [Google Scholar]
- Cachier, P.; Bardinet, E.; Dormont, D.; Pennec, X.; Ayache, N. Iconic Feature Based Nonrigid Registration: The PASHA Algorithm. Comput. Vis. Image Underst.
**2003**, 89, 272–298. [Google Scholar] [CrossRef] - Cachier, P.; Pennec, X. 3D Non-Rigid Registration by Gradient Descent on a Gaussian-Windowed Similarity Measure using Convolutions. In Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis, Burnaby, BC, Canada, 12–15 December 2011. [Google Scholar]
- Avants, B.B.; Epstein, C.L.; Grossman, M.; Gee, J.C. Symmetric diffeomorphic image registration with cross-correlation: Evaluating automated labeling of elderly and neurodegenerative brain. Med. Image Anal.
**2008**, 12, 26–41. [Google Scholar] [CrossRef] [PubMed][Green Version] - Black, M.J.; Anandan, P. The Robust Estimation of Multiple Motions: Parametric and Piecewise-Smooth Flow Fields. Comput. Vis. Image Underst.
**1996**, 63, 75–104. [Google Scholar] [CrossRef] - Brox, T.; Bruhn, A.; Papenberg, N.; Weickert, J. High Accuracy Optical Flow Estimation Based on a Theory for Warping. In Proceedings of the Computer Vision-ECCV 2004: 8th European Conference on Computer Vision, Prague, Czech Republic, 11–14 May 2004; Volume 4, pp. 25–36. [Google Scholar]
- Ce, L. Beyond Pixels: Exploring New Representationsand Applications for Motion Analysis. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, USA, 2009. [Google Scholar]
- Sun, Y.; Yuan, J.; Rajchl, M.; Qiu, W.; Romagnoli, C.; Fenster, A. Efficient convex optimization approach to 3D non-rigid MR-TRUS registration. In Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, Nagoya, Japan, 22–26 September 2013. [Google Scholar]
- Qiu, W.; Yuan, J.; Fenster, A. 3D prostate MR-TRUS non-rigid registration using dual optimization with volume-preserving constraint. In Medical Imaging 2016: Image Processing; Styner, M.A., Angelini, E.D., Eds.; International Society for Optics and Photonics, SPIE: Bellingham, WA, USA, 2016; Volume 9784, pp. 458–463. [Google Scholar]
- Dice, L.R. Measures of the Amount of Ecologic Association Between Species. Ecology
**1945**, 26, 297–302. [Google Scholar] [CrossRef] - Heimann, T.; Van Ginneken, B.; Styner, M.A.; Arzhaeva, Y.; Aurich, V.; Bauer, C.; Beck, A.; Becker, C.; Beichel, R.; Bekes, G.; et al. Comparison and Evaluation of Methods for Liver Segmentation From CT Datasets. IEEE Trans. Med. Imaging
**2009**, 28, 1251–1265. [Google Scholar] [CrossRef] - Huttenlocher, D.P.; Klanderman, G.A.; Rucklidge, W.J. Comparing Images Using the Hausdorff Distance. IEEE Trans. Pattern Anal. Mach. Intell.
**1993**, 15, 850–863. [Google Scholar] [CrossRef][Green Version] - Zhu, W. Segmentation and Registration of CT Multi-Phase Images for Abdominal Surgical Planning. Ph.D. Thesis, University of Strasbourg, Strasbourg, Germany, 2015. [Google Scholar]
- Hecht, E.M.; Israel, G.M.; Krinsky, G.A.; Hahn, W.Y.; Kim, D.C.; Belitskaya-Levy, I.; Lee, V.S. Renal masses: Quantitative analysis of enhancement with signal intensity measurements versus qualitative analysis of enhancement with image subtraction for diagnosing malignancy at MR imaging. Radiology
**2004**, 232, 373–378. [Google Scholar] [CrossRef] [PubMed] - Ho, V.B.; Allen, S.F.; Hood, M.N.; Choyke, P.L. Renal Masses: Quantitative Assessment of Enhancement with Dynamic MR Imaging. Radiology
**2002**, 224, 695–700. [Google Scholar] [CrossRef]

**Figure 1.**Four-phase image of CT images. Lesion area is labeled by the red box: (

**a**) shows the pre-contrast phase image without injecting intravenous contrast media; (

**b**) shows the lesion areas tend to enhance more strongly than background liver during late arterial phase imaging (APHE); (

**c**) shows the liver continues to enhance, and the lack of portal venous blood supply to HCCs results in the characteristic washout in the portal venous phase (WO); (

**d**) shows the hypodense appearance of HCC in the delayed phases (WO).

**Figure 2.**Summary of CT and MRI diagnostic Liver Imaging Reporting and Data System (LI-RADS) categories. APHE = arterial phase hyperenhancement; HBP = hepatobiliary phase; HCC = hepatocellular carcinoma; TIV = tumor in vein; TP = transitional phase [11].

**Figure 3.**Illustration of 3D quantitative estimation model. Circle denotes a composition where the warped image is reconstructed by the deformation field computed from nonlinear registration, resulting in the warped image.

**Figure 4.**The parameterization results: (

**a**) shows two slices of APHE results and (

**b**) shows two slices of WO results. The green contour is the lesion contour in the AP image.

**Figure 5.**Registration illustration: RGB image shows AP, Pre, and DP image together without or with deformation. Contours image shows three mask contours on AP image without or with deformation.

**Figure 6.**Three-dimensional view: (

**a**–

**c**) are fused together to show in (

**d**); (

**f**) shows deformed Pre liver, (

**g**) shows deformed DP liver; and (

**e**–

**g**) are fused together to show in (

**h**).

**Figure 7.**Locations of three different view: (

**a**,

**d**,

**g**) show the APHE location (green), (

**b**,

**e**,

**h**) show WO location (red), and (

**c**,

**f**,

**i**) show the locations together. The purple area is the lesion delineated by experts.

**Figure 8.**Images (

**a**–

**c**) are the same slice and (

**d**–

**f**) are the other same slice. The locations are shown on the AP liver image, and the heat map displays the corresponding quantitative estimation results, where the green contour is the lesion contour.

**Figure 9.**Classification results: (

**a**,

**b**) show the boxplot of APHE and WO volume ratio, respectively; (

**c**) shows the ROC curve of WO volume ratio.

**Figure 10.**Illustration of sliding and deformation by superimposing the PV image onto the AP in axial (

**a**); frontal (

**b**); and sagittal view (

**c**); respectively.

Category | Number of Patients | Ratio (%) | |
---|---|---|---|

Gender | Male | 29 | 83% |

Female | 6 | 17% | |

Age | ≥60 | 23 | 66% |

<60 | 12 | 34% | |

maximum diameter | ≥5 cm | 8 | 23% |

3∼5 cm | 21 | 60% | |

<3 cm | 6 | 17% | |

Thickness | 5 mm | ||

Slice Resolution | 512 × 512 | ||

Number of slice | 38∼53 slices |

$\mathit{\alpha}$ | $\mathit{\beta}$ | OutIter | InIter | SOR | Size of Coarsest Level Image |
---|---|---|---|---|---|

0.001 | 0.001 | 5 | 1 | 20 | 32 |

$\mathit{\alpha}$ | $\mathit{\beta}$ | OutIter | InIter | SOR | Size of Coarsest Level Image |
---|---|---|---|---|---|

0.00015 | 0.0001 | 3 | 1 | 20 | 32 |

**Table 4.**Registration accuracy evaluated by DSC, MSD, and HDD (mean ± sd). The N refers to no registration, R to the rigid registration in the image preprocessing, and $NR$ to the proposed nonlinear registration model with the volume preserving prior $P\left(u\right)$ in Equation (2).

Region | Phase | Method | DSC (%) | MSD (mm) | HDD (mm) |
---|---|---|---|---|---|

liver | Pre–AP | N | $89.2\pm 5.7$ | $2.64\pm 1.42$ | $11.80\pm 3.45$ |

R | $93.0\pm 2.2$ | $1.68\pm 0.39$ | $9.22\pm 2.04$ | ||

NR | $\mathbf{98.6}\pm \mathbf{0.3}$ | $\mathbf{0.38}\pm \mathbf{0.11}$ | 4.34 ± 1.04 | ||

DP–AP | N | $85.1\pm 10.5$ | $3.74\pm 2.73$ | $14.67\pm 6.88$ | |

R | $90.1\pm 6.0$ | $2.18\pm 1.27$ | $10.72\pm 4.37$ | ||

NR | 98.1 ± 1.2 | 0.54 ± 0.38 | 6.16 ± 2.92 | ||

lesion | Pre–AP | N | $67.5\pm 11.5$ | $3.04\pm 1.76$ | $10.13\pm 3.89$ |

R | $83.1\pm 4.1$ | $2.03\pm 0.67$ | $8.03\pm 2.52$ | ||

NR | 98.7 ± 0.5 | 0.31 ± 0.27 | 2.24 ± 0.58 | ||

DP–AP | N | $68.8\pm 17.0$ | $4.50\pm 3.26$ | $13.02\pm 7.14$ | |

R | $80.9\pm 8.6$ | $2.42\pm 1.32$ | $9.00\pm 3.61$ | ||

NR | 98.3 ± 0.8 | 0.64 ± 0.72 | 2.34 ± 0.82 |

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## Share and Cite

**MDPI and ACS Style**

Huang, C.; Ying, S.; Huang, M.; Qiu, C.; Lu, F.; Peng, Z.; Kong, D. Three-Dimensional Voxel-Wise Quantitative Assessment of Imaging Features in Hepatocellular Carcinoma. *Diagnostics* **2023**, *13*, 1170.
https://doi.org/10.3390/diagnostics13061170

**AMA Style**

Huang C, Ying S, Huang M, Qiu C, Lu F, Peng Z, Kong D. Three-Dimensional Voxel-Wise Quantitative Assessment of Imaging Features in Hepatocellular Carcinoma. *Diagnostics*. 2023; 13(6):1170.
https://doi.org/10.3390/diagnostics13061170

**Chicago/Turabian Style**

Huang, Chongfei, Shihong Ying, Meixiang Huang, Chenhui Qiu, Fang Lu, Zhiyi Peng, and Dexing Kong. 2023. "Three-Dimensional Voxel-Wise Quantitative Assessment of Imaging Features in Hepatocellular Carcinoma" *Diagnostics* 13, no. 6: 1170.
https://doi.org/10.3390/diagnostics13061170