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Liver contrast-enhanced sonography: Computer-assisted
dierentiation between focal nodular hyperplasia and
inammatory hepatocellular adenoma by reference to
microbubble transport patterns
Baudouin Denis de Senneville, Nora Frulio, Hervé Laumonier, Cécile Salut,
Luc Latte, Hervé Trillaud
To cite this version:
Baudouin Denis de Senneville, Nora Frulio, Hervé Laumonier, Cécile Salut, Luc Latte, et al.. Liver
contrast-enhanced sonography: Computer-assisted dierentiation between focal nodular hyperplasia
and inammatory hepatocellular adenoma by reference to microbubble transport patterns. European
Radiology, Springer Verlag, 2020, �10.1007/s00330-019-06566-1�. �hal-03006999�
Liver contrast-enhanced sonography: Computer-assisted
differentiation between focal nodular hyperplasia and
inflammatory hepatocellular adenoma by reference to
microbubble transport patterns
Baudouin Denis de Senneville1, PhD, firstname.lastname@example.org
Nora Frulio2, MD, email@example.com
Hervé Laumonier2, PhD, firstname.lastname@example.org
Cécile Salut2, MD, email@example.com
Luc Lafitte1, MD, firstname.lastname@example.org
Hervé Trillaud2,3, PhD, email@example.com
1Institut de Mathématiques de Bordeaux (IMB), UMR 5251 CNRS/Université de Bordeaux, 351
cours de la Libération, F-33405, Talence, France
2CHU de Bordeaux, Service d’imagerie diagnostique et Interventionnelle Magellan/Saint André, F-
33000 Bordeaux, France
3EA IMOTION (Imagerie moléculaire et thérapies innovantes en oncologie), Université de
Bordeaux, F-33000 Bordeaux, France
Baudouin Denis de Senneville
Address: Institut de Mathématiques de Bordeaux (IMB), UMR 5251 CNRS/Université de
Bordeaux, 351 cours de la Libération, F-33405, Talence, France
Phone: (+33) (0)5 40 00 25 92
Fax: (+33) (0)5 40 00 21 23
Objective: A new computer tool is proposed to distinguish between focal nodular hyperplasia
(FNH) and an inflammatory hepatocellular adenoma (I-HCA) using contrast-enhanced ultrasound
(CEUS). The new method was compared with the usual qualitative analysis.
Methods: The proposed tool embeds an "optical flow" algorithm, designed to mimic the
human visual perception of object transport in image series, to quantitatively analyse
apparent microbubble transport parameters visible on CEUS. Qualitative (visual) and
quantitative (computer-assisted) CEUS data were compared in a cohort of adult patients with either
FNH or I-HCA based on pathological and radiological results. For quantitative analysis, several
computer-assisted classification models were tested and subjected to cross-validation. The
accuracies, area under the receiver-operating characteristic curve (AUROC), sensitivity and
specificity, positive predictive values (PPVs), negative predictive values (NPVs), false predictive
rate (FPRs) and false negative rate (FNRs) were recorded.
Results: Forty-six patients with FNH (n = 29) or I-HCA (n = 17) with 47 tumors (one patient with 2
I-HCA) were analysed. The qualitative diagnostic parameters were: accuracy = 93.6%,
AUROC=0.94, sensitivity = 94.4%, specificity = 93.1%, PPV = 89.5% and NPV = 96.4%, FPR =
6.9%, FNR = 5.6%. The quantitative diagnostic parameters were: accuracy = 95.9%, AUROC =
0.97, sensitivity = 93.4%, specificity = 97.6%, PPV = 95.3%, and NPV = 96.7%, FPR = 2.4%, FNR
Conclusions: Microbubble transport patterns evident on CEUS are valuable diagnostic indicators.
Machine-learning algorithms analysing such data facilitate the diagnosis of FNH and I-HCA
- Distinguishing between focal nodular hyperplasia and an inflammatory hepatocellular
adenoma using dynamic contrast-enhanced ultrasound is sometimes difficult.
- Microbubble transport patterns evident on contrast-enhanced sonography are valuable
- Machine-learning algorithms analysing microbubble transport patterns facilitate the
diagnosis of FNH and I-HCA.
- The technique offers a potential future means for accurately characterizing other hepatic
lesions, potentially obviating the need for biopsy or surgical resection.
Keywords: Ultrasound Imaging ; Adenoma ; Perfusion imaging ; Computer-Assisted Diagnosis ;
Abbreviations and acronyms:
CEUS: contrast-enhanced ultrasound
FNH: Focal nodular hyperplasias
HCA: Hepatocellular adenomas
I-HCA: Inflammatory hepatocellular adenoma
CT: Computed tomography
MRI: Magnetic resonance imaging
CNIL: National Commission on Informatics and Liberty
RF: Random forest
KNN: k-nearest neighbour
SVM: Support vector machine
LR: Logistic regression
PPV: Positive predictive value
NPV: Negative predictive value
AUC: Area under the curve
RAM: Random access memory
Benign hepatocellular tumours are rare, constituting 10% of all hepatic tumours (1). Two large
groups of benign hepatocellular tumours can be distinguished: reactive regenerative lesions (focal
nodular hyperplasias [FNHs]), and tumoural lesions (hepatocellular adenomas [HCAs]). Both
lesions are most common in young females (1). Diagnostic imaging is essential to guide treatment
decisions, which range from no treatment to surgical resection or confirmatory biopsy.
Traditionally, multiphase computed tomography (CT) or magnetic resonance imaging (MRI) has
been used for detailed evaluation of hepatic lesions. However, the high-level radiation associated
with multiphase CT and the limited accessibility of MRI have rendered dynamic contrast
agent-enhanced ultrasound (CEUS) an attractive, safe, non-invasive, accurate, and economic tool
for evaluating hepatic lesions (2)–(6). Although the appearance is not always typical in some cases,
both FNH and HCA demonstrate typical, reproducible, arterial phase enhancement patterns on
CEUS in most cases. The diagnostic criteria for FNH are a hyper-enhancing lesion in the arterial
phase with rapid centrifugal filling from a central vessel, and radial vascular branches (the “spoke
and wheel” sign) (2)(5) and also sustained enhancement in portal and late phase (7). HCAs
constitute a heterogeneous group of tumours exhibiting multiple histological subtypes
(inflammatory, with FNH1A or catenin gene mutations, or unclassified) (8). On CEUS, HCAs are
hyper-enhancing in the arterial phase; the enhancement pattern commences peripherally and
exhibits rapid centripetal filling; this pattern is characteristic of 86–90% of all inflammatory HCAs
(I-HCAs). Other HCA subtypes exhibit iso-vascularity or moderate hyper-vascularity, with mixed
filling patterns in the arterial phase (2)(9). In clinical practice, it is essential to distinguish FNH
from adenoma to ensure appropriate management. Confirmed FNHs are managed conservatively
(with regular follow-up); HCAs require cessation of oral contraceptive use, (commonly) biopsy, and
either surgery or (at least) follow-up imaging. I-HCA show the most important hypervascularity and
10-15% of I-HCA are also found to be β-catenin activated with a risk for malignant transformation.
Distinguishing between FNH and I-HCA using CEUS is sometimes difficult because both lesions
evidence hyper-enhancement during the arterial phase and it can be challenging to qualitatively
differentiate centrifugal from centripetal tumour filling, particularly for larger nodules. Computer-
assisted methods are thus required for quantitative spatiotemporal assessment of organ perfusion.
Such techniques must be faster and more reproducible than visual analysis, and must lack learning
curves. Efforts have been made to quantify enhancement parameters in vascular compartments as
indicators of several pathological conditions (10–14). In particular, transport equations have been
recently derived to estimate microbubble velocity at the time of bolus contrast arrival (15). In
practice, a so-called "optical flow" algorithm is employed to mimic the human visual perception of
microbubble transport in CEUS (16-18). Here, we use this approach to quantitatively distinguish
between FNH and I-HCA. We quantify divergence (sources and sinks), curling (shearing),
amplitudes, and convergence towards the centre of tumour (centrifugal/centripetal nature) in dense
transport fields (16); these are very simple indicators of displacement vector directions, orientations,
and magnitudes. In turn, these serve as inputs to a binary FNH/I-HCA classifier.
The purpose was to compare, as a preliminary study, the original concept of computer-assisted
method with the usual qualitative analysis for the diagnosis of two benign hepatocellular tumours
(FNH and I-HCA) with hypervascularity during the arterial phase of the CEUS.
MATERIALS AND METHODS
Study design and population
In this retrospective single-centre study conducted from July 2005 to July 2018, we identified
images from patients who underwent CEUS and were (otherwise) definitively diagnosed with FNH
or I-HCA. We included I-HCA patients who had been histologically diagnosed (6) and FNH
patients diagnosed based on commonly accepted MRI criteria (3), imaging follow-up, or
histologically. All MRIs were performed using a 1.5-T machine running a published imaging
protocol (19)(20). The study adhered to all local regulations and data protection agency
recommendations (the National Commission on Informatics and Liberty (CNIL) dictates). Patients
have been informed for the use of their data anonymously.
We enrolled 46 patients (Table 1) with the inclusion criteria, 29 had FNH and 17 I-HCA (18 I-HCA
tumours were analysed because one patient had two tumours). Of 29 FNH patients, 23 (79%) were
female and the median age was 44 (21–61) years; of 17 I-HCA patients, 16 (94%) were female and
the median age was 40.5 (21–66) years. The median diameters of FNH and I-HCA lesions were
respectively 2.9 (3–10) and 6.9 (3.4–12) cm. Histological data of the 18 I-HCA tumours were
available for 15 surgical specimens and 3 percutaneous biopsies Histological data on 7/29 FNH
tumours (24%) were available (percutaneous biopsy, six samples; one surgical sample); imaging
follow-up data were available for 15/22 patients without histological diagnosis (68%) with a median
follow-up of 12 (4–84) months ; CEUS was performed using Sequoia (n = 37), S2000 (n = 4), and
S3000 (n = 5) instruments.
Histological samples were obtained by biopsy or during surgical resection; for ethical reasons, no
samples were taken purely for the purpose of this study; clinical indications were required. All
analyses were performed as previously described (8)(9)(19), in the same laboratory.
CEUS was performed by abdominal radiologists who had 5-10 years of experience. Each patient
received a bolus injection of ultrasound contrast agent (SonoVue, Bracco). Contrast-enhanced
sequences were obtained using dedicated, low mechanical index (MI) contrast-imaging software
(MI < 0.2) employing one of three US machines (Sequoia, S2000 and S3000; a Siemens Medical
Solution instrument featuring Cadence Contrast Pulse Sequencing [CPS]; and a Convex Array 4C1-
S probe). Standard pre-settings were used, but it was possible to adjust settings for individual
patients. SonoVue was injected intravenously as a bolus of 2.4 mL via a 20-gauge cannula into the
antecubital vein, followed by flushing with 5 mL normal saline. Digital cine clips showing dynamic
contrast enhancement within the lesion and surrounding liver tissue were continuously recorded,
commencing 5 s before SonoVue injection and covering the arterial (10–45 s post-injection), portal
(60–90 s), and late (120–150 s) phases. Injection was repeated using the same dose (2.4 mL
SonoVue) if the data were of poor quality. All sequences were digitally stored. Intra-tumoural
vascular geometry and lesional enhancement patterns were evaluated.
CEUS analysis of lesional type
Qualitative visual analysis
Data were reviewed in consensus by two abdominal radiologists blinded to pathological and MRI
diagnoses. Each lesion was classified using pre-defined criteria for FNH and I-HCA. For FNH,
these were hyper-enhancement in the arterial phase, with rapid centrifugal filling; (usually) an
obvious central vessel and radial vascular branches (especially in larger lesions; the “spoke and
wheel” sign); and iso- or hyper-enhancement in the portal and venous phases, without washout. For
I-HCA, the criteria were hyper-enhancement in the arterial phase, frequently accompanied by rapid
centripetal filling; no radial vascular structure; and iso- or hyper-enhancement in the portal and
venous phases, without washout (3) (9) (21).
Computer-assisted quantitative analysis using a transport equation model
Microbubble transport fields in lesions were estimated (using a transport equation) on a pixel-by-
pixel basis employing the so-called “optical flow” process (15). The “optical flow” problem has
long been studied by vision scientists in efforts to analyse general visual motion in images of a
moving target (16)(17). For each lesion, the absolute changes in four image-based displacement
indicators were calculated: (i) the divergence δ (reflecting the presence of sources and sinks); (ii)
the curl ρ (reflecting local vortices); (iii) the amplitude γ (reflecting the magnitude of apparent
displacement); and, (iv) the centripetal nature τ (reflecting the flow field convergence towards the
centre of tumour). The analysis was restricted to a region of interest, manually drawn on a high
contrast CEUS image, encompassing the tumour. The analytical window size was fixed at 2 s
commencing at the bolus arrival time, and thus covered the filling phase. The reader is referred to
Appendix A for additional information on numerical resolution and implementation. All computer-
assisted analyses were blinded to pathological data.
The accuracies, area under the ROC curve (AUROC), sensitivity, specificity, positive predictive
values (PPVs), negative predictive values (NPVs), false predictive rate (FPRs) and false negative
rate (FNRs) of qualitative and quantitative analyses were recorded (we considered the diagnostic of
an adenoma as a “positive case” in the scope of this study).
For quantitative analyses, using one of the four microbubble displacement indicators (δ, ρ, γ or τ) as
an input feature, we developed machine learning models to differentiate between FNH and I-HCA.
For this binary classification task, the following four machine learning algorithms were applied
using the commercial software Matlab (©1994-2019 The MathWorks, Inc.)/“Statistics and Machine
Learning” toolbox: random forest (RF), k-nearest neighbour (KNN), support vector machine
(SVM), and logistic regression (LR). Default hyperparameters in Matlab implementations were
employed. We refer the interested reader to (22) (23) for additional information about above-
mentioned computer-assisted classification algorithms. We evaluated the diagnostic performances
through self-validation (the complete 47-tumours set was used for both train and test samples) and
through 10-fold-stratified cross-validation (the 47-tumours set was randomly partitioned into
complementary 90%-training and 10%-test subsets). The cross-validation steps were repeated 100
times with shuffling of the folds and test metric averages calculated. We also compared the medians
and interquartile ranges of all four indicators using the unpaired Mann–Whitney U-test. A p-value <
0.025 was considered to reflect statistical significance.
Qualitative CEUS analysis
FNH and I-HCA were correctly identified via qualitative CEUS in 27/29 and 17/18 tumours,
respectively (accuracy = 93.6%, AUROC=0.94, sensitivity = 94.4%, specificity = 93.1%, PPV =
89.5%, NPV = 96.4%, FPR = 6.9%, FNR = 5.6%; Table 2, first row).
Quantitative CEUS analysis
Figures 1 and 2 show typical microbubble transport fields as revealed by dynamic contrast imaging;
one clip (Fig. 1) is from an FNH patient and the other (Fig. 2) from an I-HCA patient. Of the four
tested transport indicators, divergence and centripetal indicators differed most significantly between
the two populations (Mann–Whitney test, p-value = 2 × 10−4 for divergence, and 1 × 10−7 for
centripetal indicator) (Figs. 3 and 4). The centripetal indicator served as a valuable binary classifier
in all tested machine learning systems (Table 2). In particular, using the naïve Bayes classifier
applied on the centripetal indicator, the diagnostic parameters were: accuracy = 95.9%, AUROC =
0.97, sensitivity = 93.4%, specificity = 97.6%, PPV = 95.3%, NPV = 96.7%, FPR = 2.4%, FNR =
6.6% (in average over the 100 cross-validation steps, FNH and I-HCA were thus correctly identified
in 28.3/29 and 16.8/18 tumours, respectively).
We show that the dense transport fields provide valuable kinetic information in CEUS time series;
the results are more accurate than those of qualitative visual analysis. Using the qualitative analysis,
one false negative case and two false positive cases were to deplore. Concerning the false negative
case, the filling direction was difficult to determine visually. Concerning the two false positive
cases, one tumour (44 mm) presented two feeding pedicles, and one (22 mm) underwent a too fast
filling. For both FNH tumours it was also difficult to appreciate visually the centrifugal filling. A
quantitative approach delivers reproducible results and minimises operator dependency, as visual
interpretation of CEUS images lacks a learning curve when the process is automated. Our method
deals with the intrinsic variations in spatio-temporal greys that are inevitable during dynamic
imaging. This allows numerical access to visual perceptions of microbubble trajectories. We used
four simple indicators (δ, ρ, γ, and τ) of transport field direction/orientation and amplitude. The
amplitude and curl indicators were not useful (Figs. 4b, c), whereas the divergence and centripetal
indicators were (Fig. 4a, d). Best results were obtained using the indicator τ which best fits the
initial centrifugal/centripetal tumour filling hypothesis (Figs. 4d). For its part, the divergence
operator gave decent results. In theory, the divergence of any vector field is positive for sources
(centrifugal trajectories) and negative for sinks (centripetal trajectories). The divergence operators
were positive for both FNH and I-HCA data; bolus arrival manifested as one or several sources of
microbubbles. However, for I-HCA lesions, the divergence operator was modulated by centripetal
filling, whereas the divergence operator was enhanced by centrifugal filling in FNH patients.
Using our quantitative method, diagnosis is near-instantaneous once the region of interest
(encompassing the tumour) is delineated. Although the duration of the temporal window for the
analysis must be sufficient to cover the filling phase, 2 s was adequate; this is a great advantage,
eliminating all long-term bias imparted by probe motion, and respiratory and other motion artefacts
Several limitations of our work must be mentioned, particularly the small sample size. This was a
single-centre retrospective study lacking an external validation cohort. Considering that only two
categories of focal liver lesions were examined (FNH and I-HCA), an inherent overestimation of
both qualitative and quantitative analysis has to be taken into account. Also, mean tumour diameter
was significantly smaller in the FNH group, associated with recruitment bias: only patients with
histological diagnoses obtained after surgical resection or via percutaneous biopsy were included in
the I-HCA group. However, in our centre, when an I-HCA tumour is identified using MRI (26) or
CEUS, a pathological analysis is performed only when the tumour diameter is > 3 cm. Thus, the I-
HCA group featured only tumours that met this criterion, unlike the FNH group, for which tumours
of all diameters (including small tumours) were evaluated. Also, the fact that any US artefacts can
intrinsically be interpreted as “false” motions by the transport equation constitutes a major source of
uncertainty. This may bias the microbubble estimations in transport fields, in turn affecting all four
image-based indicators. This is also of concern when brief US “shadow” artefacts develop in obese
patients (one of our cohort was obese and was constantly miss-classified by our quantitative
approach due to poor image quality). Similarly, in-plane and/or out-of-plane organ motion within
the image field-of-view must be no more than moderate. Please note that when organ motions are
large or complex, it is possible to “pop” microbubbles on-line to virtually repeat the imaging
session. Alternatively, image post-processing strategies may be valuable (24)(28) (Appendix A).
Finally, manually drawn masks encompassing lesions must exclude adjacent feeding arterials;
otherwise, the estimated displacement is likely to be calculated from the border to the centre of the
tumour, compromising FNH diagnosis.
In conclusion, this proof-of-concept study indicates that microbubble displacements evident on
CEUS can be used to efficiently diagnose FNH/I-HCA lesions. Machine learning allows for
computer-assisted diagnoses. In the future, we will optimise the model (28), enrol larger patient
cohorts, include other lesional features, and study other pathologies.
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44 ± 11
40.5 ± 11
42 ± 11
29 ± 16
60.5 ± 29
36 ± 28
Table 1. Demographic characteristics. Median values of age and tumor size are shown with
standard deviations and minimum-maximum intervals in parentheses. Statistical comparison of age
and tumor size between FNH and I-HCA groups were performed using an unpaired Mann–Whitney
U-test (last column), a p-value < 0.025 was considered to reflect statistical significance.
86.6 ± 14.9
0.82 ± 0.23
74.1 ± 35.1
94.3 ± 16.5
81.7 ± 34.7
87.9 ± 16.5
86.9 ± 14.6
0.82 ± 0.21
75.5 ± 33.8
94.1 ± 16.4
83.1 ± 33.0
88.6 ± 15.7
86.6 ± 14.8
0.81 ± 0.23
74.9 ± 34.6
94.1 ± 16.2
82.0 ± 34.0
88.1 ± 16.5
85.4 ± 14.5
0.75 ± 0.25
67.5 ± 33.9
96.6 ± 15.0
84.5 ± 34.1
83.9 ± 17.4
77.2 ± 16.0
0.68 ± 0.25
60.1 ± 40.3
87.9 ± 24.5
64.4 ± 41.7
80.1 ± 20.8
67.4 ± 15.0
0.52 ± 0.28
42.0 ± 43.9
84.3 ± 31.0
39.6 ± 42.7
68.0 ± 25.2
76.7 ± 16.3
0.69 ± 0.25
60.2 ± 41.5
87.0 ± 24.8
61.7 ± 41.9
80.4 ± 21.0
64.6 ± 12.9
0.40 ± 0.26
33.9 ± 41.6
84.2 ± 31.5
31.8 ± 40.0
64.3 ± 23.8
72.2 ± 15.9
0.56 ± 0.28
48.8 ± 42.4
86.9 ± 27.4
52.5 ± 44.4
74.1 ± 22.7
67.2 ± 14.7
0.52 ± 0.27
40.6 ± 44.1
83.9 ± 31.0
37.8 ± 41.9
68.5 ± 25.0
70.3 ± 15.4
0.54 ± 0.28
48.6 ± 43.3
83.8 ± 29.8
49.0 ± 43.3
73.5 ± 23.9
80.2 ± 16.2
0.70 ± 0.28
61.6 ± 38.6
91.9 ± 20.9
71.4 ± 40.7
80.8 ± 20.0
Centripetal indicator (γ)
95.7 ± 10.1
0.97 ± 0.09
93.5 ± 19.6
97.1 ± 11.2
94.9 ± 17.7
96.8 ± 10.3
95.8 ± 10.0
0.97 ± 0.09
92.8 ± 21.3
97.5 ± 9.4
94.6 ± 19.1
96.7 ± 9.9
95.9 ± 9.8
0.97 ± 0.08
93.4 ± 19.8
97.6 ± 10.0
95.3 ± 17.5
96.7 ± 10.4
91.8 ± 11.9
0.92 ± 0.13
83.4 ± 28.0
97.0 ± 10.5
91.5 ± 24.3
92.4 ± 12.6
Table 2. Diagnostic performances of the various classifiers. Qualitative (i.e., visual) and
quantitative scores are given; the latter were derived via evaluation of divergence δ, curl ρ,
amplitude γ, and centripetal indicator τ (after 10-fold cross-validation) by various machine-learning
algorithms. AUROC: area under the ROC curve; PPV: positive predictive value; NPV: negative
predictive value. Accuracies, sensitivities, specificities, PPVs, and NPVs are shown in percentages.
Quantitative indicators are shown with standard deviations and 95% confidence intervals in
Fig. 1. Typical results obtained when evaluating an FNH lesion. Data obtained at different CEUS
timepoints are shown: 0.5 s (left column), 1 s (middle column), and 1.5 s (right column) after bolus
arrival. The manually drawn mask encompassing the lesion is shown in (a). Contrast images (top
row) and estimated, apparent transport vector fields (bottom row). The flow field exhibits fast
centrifugal filling of the lesion from a central vessel and radial vascular branches. The pixel-wise
centripetal indicator is shown in the insets of the bottom row (note the large negative values,
attributable to centrifugal filling of the lesion, and the small positive values attributable to the
tumour feeding arterial).
Fig. 2. Typical results from a patient with an I-HCA lesion. The manually drawn mask
encompassing the lesion is shown in (a). Data obtained at different times during CEUS are shown:
0.5 s (left column), 1 s (middle column), and 1.5 s (right column) after bolus arrival. Contrast
images (top row) and estimated, apparent vector transport fields (bottom row). The flow field is
hyper-enhanced in the arterial phase (enhancement commences peripherally) and exhibits rapid
centripetal filling. The pixel-wise centripetal indicator is shown as insets in the bottom row (note
the large positive values, attributable to centripetal filling of the lesion).
Fig. 3. Boxplots of indicators of the four dense transport fields (divergence δ [a], curl ρ [b],
amplitude γ [c], and centripetal indicator τ [d]) for both patient populations (FNH vs. I-HCA self-
validations). The medians are shown by the central marks, the first and third quartiles are the edges
of the boxes, the whiskers extend to the most extreme timepoints not considered to be outliers, and
the outliers are individually marked in red.
Fig. 4. ROC curves obtained using the four quantitative indicators (divergence δ [a], curl ρ [b],
amplitude γ [c], and centripetal indicator τ [d]) as binary classifiers (naive Bayes) for the two
populations (i.e., FNH vs. I-HCA) after 10-fold cross-validation.
APPENDIX 1: Estimation of apparent microbubble displacement during CEUS
This appendix deals with numerical implementation of the algorithm estimating microbubble
displacement during CEUS. For each CEUS clip, the lesion was first manually delineated on a
hyper-enhanced image. A binary mask was then constructed (this is termed Γ below). We then
proceeded as follows:
Estimation of CEUS dense transport fields
We used the transport equation to estimate the apparent microbubble transport field (
suggested in (15):
where I denotes the grey level intensity on CEUS images and It the partial temporal derivative of I.
Practically, the desired transport field V was estimated between two points in time (t and t + δt,
respectively) on a pixel-by-pixel basis using the so-called “optical flow” process (17). The
algorithm yields the displacement between two images when the following function is optimised
where is the image-coordinate domain, the estimated pixel-wise transport vector
components, and the spatial location. All slices were re-sampled via bi-cubic interpolation to
obtain a common isotropic, in-plane, 0.25 × 0.25-mm2 pixel representation. A spatial low-pass filter
was then applied (29) (the cut-off frequency was the proportional pixel fraction of the original
image, divided by 16, as suggested by (15)) to mitigate the impact of US speckles on the transport
equation. An in-house developed, freely available, software provided 2D transport fields using the
optical flow metric of Eq. (2) (http://bsenneville.free.fr/RealTITracker/). The reader is referred to
(15) for additional details on the numerical implementation of Eq. (2).
Note that possible periodic, spontaneous, and drift displacements of tissue must be initially
compensated for (24)(25), because they may change image intensities over time; Eq. 1 would
(erroneously) attribute such changes to microbubble transport. As proposed in (15), B-mode
images, which are not prone to contrast enhancement, are used to this end. We estimated
translational displacements restricted to the binary mask Γ. We used a gradient-driven descent
algorithm maximising the inter-correlation coefficients. This translation was used to compensate for
displacement of imaged tissues on CEUS images prior to microbubble transport estimation
employing Eq. (2).
Pixel-wise analysis of dense flow fields
We next calculated a pixel-wise understanding of flow directions/orientations and amplitude, as
Maps of sources and sinks: Sources and sinks in the transport were analysed using the divergence
operator. Mathematically, the divergence of a two-dimensional vector
is expressed as:
The final, discrete divergence operator employed in numerical implementation was:
where denotes the pixel coordinates and t the frame acquisition time. We emphasise that
positive and negative values are associated with pixels located near sources and sinks, respectively.
Vortex maps: Local vortices in the estimated transport vectors were analysed with the aid of the
curl operator. Mathematically, the curl of
is expressed as:
The resulting discrete curl operator is:
Amplitude maps: The amplitudes of estimated transport vectors were calculated as Euclidian
distances. Mathematically, the magnitude of
is expressed by:
Centripetal indicator maps: The convergence of estimated transport vectors towards the centre of
tumour were calculated with the aid of the scalar product. The cosine of the angle formed by two
is expressed by:
In our study,
is any vector of the estimated flow field, and
has the same origin as
, but the
extremity located at the gravity centre of tumour (i.e, the centre of mass of the binary mask Γ). That
way, the cosine of the angle
lies in intervals [-1,0] and [0,1] for centrifugal and centripetal
Quantitative analysis of dense flow fields
As described above, we created four sets of pixel-wise maps (of divergence, curl, amplitude and
convergence towards the centre of tumour). Each set was then simplified to a single parameter as
follows. The spatiotemporal averages of each map were individually computed under a mask
defining the imaged tissue (i.e., Γ) within the relevant time window. The duration spanned by that
window is termed ΔT below and commenced at the bolus arrival time t0. Spatiotemporal averaging
was weighted by the grey level intensity in CEUS image I; thus, the values for scenarios exhibiting
identical microbubble transport behaviours were identical irrespective of the numbers of pixels
evidencing microbubbles. The divergence and curl operators were termed δ and ρ, respectively. We
measured the absolute value of curl; thus, the direction of vortex rotation didn’t affected analysis.
The centripetal indicator was termed τ.
Determination of the temporal window
The temporal window of analysis was of duration ΔT and commenced at the bolus arrival time t0;
this was determined individually for each patient. To this end, we used a published time intensity
curve (TIC) widely employed to determine time constants (10). The average US image intensity
over Γ (termed ) was analysed as a function of time using a two-compartment model, as
where I∞ is the asymptotic US signal enhancement, and k the uptake rate. I∞, t0, and k were
computed using the Levenberg–Marquardt least-square fit (30) employing all images of the US
sequence. The use of a simple two-compartment model was motivated by the fact that only the rise
step was screened. The goodness-of-fit was considered acceptable when the Pearson correlation
coefficient (r2) was > 0.95. In such cases, the t0 values chosen earlier served as the start times for
the temporal windows.
Hardware and implementation
Our test platform was an Intel 2.5 GHz i7 workstation (eight cores) with 32 GB of RAM. The
implementation was performed in C++ and parallelised via multi-threading.
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