IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO. 8, AUGUST 2011 1493
Contrast-Ultrasound Diffusion Imaging
for Localization of Prostate Cancer
Maarten P. J. Kuenen*, Massimo Mischi, and Hessel Wijkstra
Abstract—Prostate cancer is the most prevalent form of cancer
in western men. An accurate early localization of prostate cancer,
permitting efﬁcient use of modern focal therapies, is currently
hampered by a lack of imaging methods. Several methods have
aimed at detecting microvascular changes associated with prostate
cancer with limited success by quantitative imaging of blood
perfusion. Differently, we propose contrast-ultrasound diffu-
sion imaging, based on the hypothesis that the complexity of
microvascular changes is better reﬂected by diffusion than by
perfusion characteristics. Quantiﬁcation of local, intravascular
diffusion is performed after transrectal ultrasound imaging of an
intravenously injected ultrasound contrast agent bolus. Indicator
dilution curves are measured with the ultrasound scanner reso-
lution and ﬁtted by a modiﬁed local density random walk model,
which, being a solution of the convective diffusion equation,
enables the estimation of a local, diffusion-related parameter.
Diffusion parametric images obtained from ﬁve datasets of four
patients were compared with histology data on a pixel basis. The
resulting receiver operating characteristic (curve area )
was superior to that of any perfusion-related parameter proposed
in the literature. Contrast-ultrasound diffusion imaging seems
sing method for prostate cancer localiza-
tion, encouraging further research to assess the clinical reliability.
Index Terms—Biomedical imaging, blood vessels, cancer, pa-
rameter estimation, ultrasonography.
PROSTATE cancer is the most prevalent form of cancer
in men in western countries. It accounts for 25% and
10% of all cancer diagnoses and deaths, respectively , .
Nowadays, a variety of focal therapies such as cryoablation,
brachytherapy, and high-intensity focused ultrasound, are avail-
able to efﬁciently treat early detected and localized prostate
cancer . This may prevent a radical treatment as for example
radical prostatectomy, with the associated risks of the patient
Manuscript received January 12, 2011; revised February 24, 2011; accepted
February 27, 2011. Date of publication March 10, 2011; date of current ver-
sion August 03, 2011. This work was supported by the Dutch Organization for
Scientiﬁc Research (NWO) and the Technology Foundation (STW). Asterisk
indicates corresponding author.
*M. P. J. Kuenen is with the Department of Electrical Engineering, Eind-
hoven University of Technology, 5600 MB Eindhoven, The Netherlands and
also with the Department of Urology, AMC University Hospital, 1100 DD Am-
sterdam, The Netherlands (e-mail: email@example.com).
M. Mischi is with the Department of Electrical Engineering, Eindhoven Uni-
versity of Technology, 5600 MB Eindhoven, The Netherlands.
H. Wijkstra is with the Department of Urology, AMC University Hospital,
1100 DD Amsterdam, The Netherlands, and also with the Department of Elec-
trical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven,
Color versions of one or more of the ﬁgures in this paper are available online
Digital Object Identiﬁer 10.1109/TMI.2011.2125981
becoming incontinent or impotent . However, the limited
reliability of the available noninvasive diagnostic methods
hampers an efﬁcient use of focal therapies.
The main noninvasive diagnostic method, assessingthe
serum prostate-speciﬁc antigen (PSA) levelinblood,hasa
high false-positive rate (about 76%) . Therefore, PSA does
not enable an efﬁcient mass screening  andisonlyusedfor
patient stratiﬁcation prior to biopsy investigation . This inva-
sive and painful investigation commonly involves taking 6–12
spatially distributed samples of the prostatewithacoreneedle.
Although the biopsy investigation is currently the most reliable
diagnostic method, it is often repeated to achieve sufﬁcient
sensitivity , . The limited cancer localization is another
drawback. Furthermore, a considerable fraction of all detected
carcinomas will not develop into a life-threatening disease .
Therefore, the risk of overdiagnosis and overtreatment, with a
related loss in quality of life, represents a major issue in current
prostate cancer care ,.
These problems motivate the search for better noninvasive
methods for an early detection and localization of life-threat-
ening forms of prostate cancer. In particular, imaging methods
may reduce the number of biopsies by accurate targeting and
permit an efﬁcient application of focal treatments.
Several imaging modalities are being evaluated for early
prostate cancer detection. While computerized tomography
(CT) seems unsuitable for diagnostic prostate imaging ,
cancer detection sensitivity (on a patient basis) with mag-
netic resonance imaging (MRI) techniques such as diffusion
weighted imaging (73%–89%), contrast-enhanced MRI
(69%–95%), and MR spectroscopy (59%–94%) is promising
. Transrectal ultrasound (TRUS) techniques are however
equally promising, and they are more suitable than MRI in
terms of cost, time, resolution, and guidance of biopsies and
focal therapies , . Therefore, TRUS improvements could
be of great value for early prostate cancer localization.
For imaging purposes, a key indicator for prostate cancer is
angiogenesis, i.e., the formation of a dense microvascular net-
work characterized by an increased microvessel density (MVD)
–. Angiogenesis, which is required for cancer growth
beyond 1 mm,correlates with prostate cancer aggressiveness
(i.e., risks of extracapsular growth and development of metas-
tases) –. Therefore, imaging methods based on angio-
genesis detection may help to identify life-threatening forms of
prostate cancer at an early stage.
Hypothesizing a correlation between MVD and perfusion,
i.e., blood ﬂow per tissue volume, the use of ultrasound contrast
agents (UCAs) for quantitative TRUS imaging of microvascular
perfusion has gained interest , , . UCAs are dis-
persions of coated gas microbubbles that backscatter acoustic
0278-0062/$26.00 © 2011 IEEE
1494 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO. 8, AUGUST 2011
energy when hit by ultrasound waves , . Despite an
improvement in biopsy targeting, contrast-enhanced TRUS
methods based on intermittent imaging and destruction-re-
plenishment techniques have however not proven sufﬁciently
reliable to replace systematic biopsies –.
An alternative method involves dynamic TRUS imaging of
the passage of an intravenously injected UCA bolus , ,
. Up until now, only few quantitative studies have been car-
ried out. These studies quantify perfusion by extraction of time
and intensity features from the measured acoustic time-inten-
sity curves –. However, time features do not represent
the local hemodynamic characteristics since they generally de-
pend on the entire bolus history , whereas intensity features
are affected by scanner settings and nonlinear ultrasound prop-
The reasons that the developments in quantitative perfusion
imaginghavenotresultedinreliable prostate cancer localization
may be various. In addition to limitations in the ﬂow sensitivity,
important reasons may be linked to the complex and contradic-
tory effects of angiogenesis on perfusion , , , .
A lack of vasomotor control and the presence of arteriovenous
shunts cause a low ﬂow resistance , , but this can be
counterbalanced by the small microvessel diameter and an in-
creased interstitial pressure, due to extravascular leakage ,
. MVD characterization by quantiﬁcation of perfusion may
therefore be unreliable.
In this paper we propose contrast-ultrasound diffusion
imaging (CUDI) as an alternative noninvasive prostate cancer
localization method. CUDI is based on the hypothesis that
angiogenesis-induced changes in the microvascular architec-
ture correlate better with diffusion than with perfusion. In this
context, diffusion refers to the intravascular UCA spreading by
apparent diffusion, due to concentration gradient and ﬂow pro-
ﬁle, and by convective dispersion, due to multipath trajectories
through the microvasculature –. The microvascular
architecture of a solid tumor can be viewed as a distributed
network , in which ﬂow can be modeled as ﬂow through
a porous medium . Structural characteristics of porous
media determine the diffusion , . Therefore, we hy-
pothesize intravascular UCA diffusion to be correlated with the
microvascular structure and, therefore, with angiogenesis.
Based on the UCA bolus injection technique, CUDI is a new
method for quantiﬁcation of diffusion from time-density curves
(TDCs). These curves measure the image gray level versus time
at all pixels covering the prostate. By modeling the local in-
travascular UCA transport by the local density random walk
model, we provide a novel, theoretical framework to extract a
local, diffusion-related parameter from measured TDCs. CUDI
was evaluated in vivo by comparing ﬁve diffusion parametric
images from four patients, obtained by TDC ﬁtting at each pixel,
with histology data.
A. Data Acquisition
The data acquisition was performed at the AMC University
Hospital (Amsterdam, The Netherlands), after approval was
Fig. 1. TRUS power modulation imaging of the prostate after intravenous in-
jection of a UCA bolus. The displayed frames are recorded before UCA appear-
ance (top left), at initial wash-in (top right), at peak concentration (bottom left),
and at wash-out (bottom right).
granted by the local ethics committee. Written informed con-
sent was obtained from all patients prior to their participating
in this study.
A 2.4 mL SonoVue (Bracco, Milan, Italy) UCA bolus was
injected intravenously in the patient arm. SonoVue is a dis-
persion of microbubbles coated by a phospholipid shell,
whose mean diameter is 2.5 . TRUS imaging was per-
formed using an iU22 ultrasound scanner (Philips Healthcare,
Bothell, WA) equipped with a C8-4v probe. The adopted con-
trast-speciﬁc imaging mode was power modulation, at a fre-
quency of 3.5 MHz. The effective pulse length of two cycles
provided an axial resolution of 0.43 mm, while a low mechan-
ical index (MI) of 0.06 minimized microbubble disruption ,
. The compression was set to C38 and the gain was adjusted
to prevent truncation or saturation of the 8-bit gray level. All ac-
quired B-mode videos were stored in DICOM (Digital Imaging
and Communication in Medicine) format, which can be directly
input to the analysis software that we implemented in Matlab
(The MathWorks, Natick, MA). Four B-mode frames recorded
in power modulation mode are shown in Fig. 1.
An accurate quantiﬁcation of the UCA diffusion dynamics
based on TRUS B-mode video data requires knowledge about
how the measured gray level relates to the UCA concentra-
tion. To this end, we investigated the relation between UCA
concentration and the backscattered acoustic intensity .We
also studied the measurement and conversion of into a gray
For low concentrations and MI, a linear relation between
and has been reported . We performed new measurements
at the Catharina hospital (Eindhoven, The Netherlands) to verify
this relationship for the current equipment, settings, and UCA.
The setup was similar to the static calibration setup reported
in . The UCA dispersions were contained in polyurethane
bags that were submerged into a water-ﬁlled basin. The basin
walls were covered by acoustic absorbers to minimize the
KUENEN et al.: CONTRAST-ULTRASOUND DIFFUSION IMAGING FOR LOCALIZATION OF PROSTATE CANCER 1495
Fig. 2. In vitro measurement results. The gray error bars depict the acoustic
intensity measured in a ﬁxed ROI by their mean and standard deviation, whereas
the black line shows the linear approximation for SonoVue concentrations up to
acoustic reﬂections from the wall. To reproduce the clinical
conditions, the ultrasound probe was positioned about 1 cm
away from the UCA dispersion. For each concentration, three
measurements were performed, from three different SonoVue
vials. The mean acoustic intensity was evaluated in a ﬁxed
region of interest (ROI) of the recorded B-mode images, with
QLAB (Philips Healthcare) acoustic quantiﬁcation software.
The results are shown in Fig. 2. For SonoVue concentrations
up to 1.0 mg/L, and are linearly related ( )as
where deﬁnes the sensitivity and is the background inten-
sity due to backscatter from tissue and blood. The exact pa-
rameter values are not relevant for this study, since a linearly
related measure of is sufﬁcient for a complete description
of the UCA diffusion dynamics. With the injected dose, the in
vivo measurements are performed within the linear calibration
range that was estimated in vitro ( Fig. 2). In fact, by consid-
ering a simple system of two mixing chambers representing the
right and left ventricles (100 and 110 mL), the concentration
would not overtake 0.84% of the injected concentration (5.0
g/mL) . Taking into account a blood volume fraction in the
prostate of 2% , the concentration in the prostate would re-
main below 0.84 mg/L, i.e., within the linear range.
The ultrasound transducer converts the backscattered ultra-
sound waves into an electrical voltage, proportional to .After
ampliﬁcation and demodulation, a compression of the signal dy-
namic range yields the quantization level ,andthe
gray mapping renders the displayed gray level .
This mapping is displayed on the B-mode image and can be
easily extracted and compensated for. The compression func-
tion, typically a logarithmic-like function , , is estimated
by comparing QLAB acoustic quantiﬁcation results to the quan-
tization level in single-pixel ROIs. The results
show a linear relationship ( ) between and
( Fig. 3). This implies a logarithmic compression function
,inwhich is determined by the dy-
namic range of the compression function as
Fig. 3. Quantization level versus QLAB normalized acoustic intensity ,
obtained from single-pixel ROIs. The black line represents the ﬁtted logarithmic
For the estimated dynamic range (45.73 dB), equals 24.22.
This dynamic range is sufﬁciently large to enable an accurate
TDC quantiﬁcation .
Combining all relations, the function that maps UCA concen-
tration to gray level can be written as
In (3), the baseline equals the quantization level
for , i.e., before the UCA appearance in the prostate.
C. Diffusion Modeling
Physical modeling of the intravascular UCA transport is re-
quired to analyze diffusion. Our analysis is based on the local
density random walk (LDRW) model –. This model can
provide a physical interpretation of the diffusion process, and it
accurately ﬁts UCA indicator dilution curves (IDCs) , .
IDCs measure the UCA concentration in a ﬁxed sample volume
as function of time and can thus be obtained from TDCs via (3).
After a general introduction to the LDRW model, the local as-
pects of the diffusion process by this model are discussed.
The LDRW model characterizes the UCA transport in a
straight, inﬁnitely long tube of constant section ,inwhich
a carrier ﬂuid ﬂows with a constant velocity ,asshownin
Fig. 4. The model assumes a Brownian motion of microbub-
bles. The concentration dynamics is then given by the
mono-dimensional convective diffusion equation as
in which and represent the distance along the tube’s main axis
and the time variable, respectively. The diffusion coefﬁcient
is assumed constant. The boundary conditions, representing a
rapid bolus injection and the UCA mass conservation, are given
In (5), is the total injected UCA mass dose, and and
are the bolus injection time and site, respectively. The solution
is a normal distribution in space that translates at the
1496 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO. 8, AUGUST 2011
Fig. 4. UCA concentration dynamics by the LDRW model in an inﬁnitely-long
straight tube, with the lower curves describing the UCA concentration proﬁle
in space for increasing time.
carrier velocity and has a variance that increases linearly with
time, as shown in Fig. 4. The LDRW formulation for the IDC
is obtained by sampling at an arbitrary detection
The parameters ,and are deﬁned as
where is the distance between the injection and
detection sites. The parameter equals the IDC integral, and
is the mean transit time (MTT), i.e., the average time a mi-
crobubble takes to travel the distance , . The param-
eter is proportional to the Péclet number, which equals the
ratio of the diffusive time and the convective time .
In the appendix, we provide an analytical relation between and
the statistical skewness of the IDC.
By its relation to , the parameter is interesting for the char-
acterization of diffusion. However, also depends on the length
, which cannot be measured in our clinical application. As
a consequence, does not characterize diffusion locally. This
would require the deﬁnition of a local diffusion-related param-
eter that is independent of .
To describe local aspects of the UCA diffusion process, we
consider a short segment of the inﬁnitely-long tube without
making assumptions about the bolus injection. The boundary
condition (5a) representing the bolus injection is replaced by a
local boundary condition describing the spatial UCA concen-
tration proﬁle at time , just before the bolus passage at the
detection site . In line with the LDRW model, we assume a
normally distributed initial spatial concentration proﬁle given as
Fig. 5. Assumed UCA concentration proﬁle in space at , i.e., just before
the bolus passage at the detection site .
with mean and variance . By adopting
the boundary condition of (8) instead of (5a), we can obtain an
analytical solution for if we assume locally con-
stant hemodynamic parameters, i.e., and
for . This interval covers the tube segment
containing the bulk of the UCA bolus at (see Fig. 5). For
,and are not relevant and may have any value.
In particular, if for , the bolus injection
time can be estimated as
The estimate is a theoretical estimate that cannot be interpreted
as the true injection time, since only holds for
. However, (9) can be used to represent the IDC as
in (6), although with a different parametrization
Using the parametrization in (10), we deﬁne a new parameter ,
dependent on and only
After combining (11) and (6), the IDC can be expressed as
Being dependent on and only, is the local, diffusion-re-
lated parameter that we have adopted for characterization of the
microvascular structure. The parameter can be interpreted as
the local ratio between the diffusive time and the squared convec-
tive time. For low values of , the UCA concentration proﬁle
hardly spreads while passing . This leads to a symmetric IDC,
characterized by high values of . On the other hand, high values
KUENEN et al.: CONTRAST-ULTRASOUND DIFFUSION IMAGING FOR LOCALIZATION OF PROSTATE CANCER 1497
Fig. 6. IDC shape for various values of with .
Fig. 7. Signal conditioning and ﬁtting of a single-pixel TDC in the logarithmic
of lead to a skewed IDC, represented by small values of .
D. Parameter Estimation
Local diffusion can be estimated from measured TDCs using
the modiﬁed LDRW IDC formalization in (12) and the relation
between UCA concentration and gray level in (3).
The accuracy of the parameter estimation is determined
by the temporal characteristics of IDC noise, i.e., all signals
that the model function (6) cannot explain. Typical ultrasound
noise sources such as speckle are less signiﬁcant here: sta-
tionary noise affects only the IDC baseline and signals from
moving linear scatterers (e.g., red blood cells) are effectively
suppressed by contrast-speciﬁc imaging techniques . IDC
noise is therefore mainly related to microbubbles and might
be caused by random microbubble movement into and out of
the sample volume, represented by a pixel. Such movement
produces a noise component whose variance relates directly
to the microbubble concentration, satisfying the multiplicative
character of IDC noise that was previously measured .
We evaluated the multiplicative character of IDC noise by
analyzing over 50 000 curves measured in vivo. Signals at fre-
quencies above 0.5 Hz were considered as noise, because the
spectrum of (6) is restricted to frequencies lower than 0.5 Hz for
a realistic range of (0.1–1.5 )and (10–50 s). We com-
pared the high-frequency noise power with the low-frequency
signal magnitude using a short-time Fourier transform with a
Hamming window of 3.2 s. For IDCs in the real domain, the
average correlation coefﬁcient was , compared with
for log-domain TDCs. The relatively strong corre-
lation in the real domain indicates multiplicative noise. More-
over, frequencies above 0.5 Hz contained 54% of the total signal
power in the real domain, compared with 6% in the logarithmic
domain. For these reasons, parameter estimation is performed
in the logarithmic domain . Although the logarithmic com-
pression affects the error metrics for TDC ﬁtting, the effects on
the estimation of and are negligible .
The modiﬁed LDRW TDC formalization is obtained by com-
bining (12) and (3). After compensating for the gray mapping,
and estimating and subtracting the baseline , this expression is
In (13), the factor is included in , since only a relative
measure of the UCA concentration is required.
The accuracy of the parameter estimation is improved by
low-pass ﬁltering the TDCs both in space and time (see Fig. 7).
The spatial ﬁlter design is based on the size of the smallest
microvascular networks for which local diffusion must be es-
timated. As angiogenesis is required for cancer to grow beyond
1mm , a reliable analysis of image regions with a radius
as small as 0.62 mm is necessary. To maintain sufﬁcient res-
olution for accurate characterization at this scale, we adopted
a Gaussian ﬁlter with mm, whose 3-dB value is at
0.59 mm. The loss of information due to spatial ﬁltering is lim-
ited, because the axial scanner resolution (0.43 mm) is inferior
to the B-mode pixel resolution (0.15 mm). The nonuniform spa-
tial TRUS statistics, generally due to a lower lateral resolution
at larger depths, are compensated by spatial ﬁltering; after ﬁl-
tering, the average correlation coefﬁcient between neighboring
pixel IDCs is independent of the scanning depth, suggesting a
uniform spatial resolution. After spatial ﬁltering, downsampling
in both spatial dimensions by a factor three permits reducing the
computation time by 89%.
Low-pass ﬁltering may also be performed in time, given the
scanning frame rate (about 10 Hz) as compared to the maximum
TDC frequency of 0.5 Hz. We adopted a ﬁnite impulse response
ﬁlter of 100 coefﬁcients and a cutoff frequency of 0.5 Hz. A zero
phase shift is obtained by ﬁltering in both forward and backward
1498 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO. 8, AUGUST 2011
Fig. 8. In vivo CUDI parametric image obtained from the same data as shown in Fig. 1 with histology. On the left, the diffusion parametric image is overlaid on
the ultrasound power modulation image. The parameter is displayed as a color coding; uncolored pixels are associated with ﬁt failure. The manually selected
white contour represents the prostate boundary. The corresponding fundamental ultrasound image (middle) is also shown, in which the red and green polygons
represent the adopted ROIs for cancerous and healthy tissue, respectively. Three corresponding histology slices, all showing cancer in the right peripheral zone,
are shown on the right.
A well-known issue in IDC analysis is recirculation, i.e., the
subsequent bolus passages through a selected ROI that mask
the last segment of the ﬁrst-pass IDC tail , , . In
cardiovascular applications, IDC parameter estimation is often
restricted to the interval where recirculation does not
occur. The recirculation time is commonly deﬁned as the time
when the IDC decays to 30% of its peak value , . An ef-
fect similar to recirculation occurs also in the prostate, where
additional UCA passages may also be due to multiple feeding
arteries . The effects on measured curves are, however, less
evident than in cardiovascular applications (see Fig. 7). There-
fore,weadoptamorespeciﬁc approach to deﬁne .TheIDC
decay during an interval is given as
where is assumed without loss of generality. For large
, the IDC decays approximately exponentially, which corre-
sponds to a linear TDC decay in the logarithmic domain. There-
fore, is determined such that the linear TDC approximation
has the highest on the interval between the peak time and
. The choice of is restricted to the interval where the IDC
amplitude, in the real domain, decays to between 20% and 50%
of the peak amplitude. The inﬂuence of TDC noise on the deter-
mination of is reduced by additional low-pass ﬁltering with
cutoff frequency at 0.1 Hz.
LDRW model ﬁtting can be performed with a linear regres-
sion algorithm as described in . However, the computational
complexity of this algorithm is high as both the parameter
and the regression interval are iteratively determined. Given the
large number of TDCs (about for each dataset, after down-
sampling), we have adopted a different method, based on the
statistical IDC moments . We have extended this method by
inclusion of the estimation of (see Appendix), which makes
the method non-iterative. However, the computation of the sta-
tistical IDC moments requires the complete ﬁrst-pass IDC. For
the interval , the IDC is approximated by an exponen-
tial decay, corresponding to the linear TDC approximation. As
aﬁnal step, the obtained parameter estimates are used as ini-
tialization to ﬁt (13) to the TDC for using the Leven-
berg–Marquardt iteration , to increase the ﬁtting accuracy.
Up to ﬁve iterations were used; a higher number of iterations
did not signiﬁcantly improve the results. On a Windows-based
workstation with an Intel Core2 Duo processor running at 3.16
A parametric image is produced by displaying the estimates
of for all pixels covering the prostate, as a color coding over-
laid on the B-mode image, see Fig. 8. The parametric image is
ﬁltered with the same Gaussian ﬁlter ( mm) as the one
adopted for spatial ﬁltering, to emphasize local diffusion at the
scale where microvascular networks can be associated with the
presence of cancer.
In some cases, shadowing effects or a lack of perfusion may
result in ﬁt failure. Then, the estimated parameters do not rep-
resent the UCA transport dynamics. If the determination coefﬁ-
cient of the TDC ﬁt in the logarithmic domain is lower than
0.75, the ﬁt is not accepted and no color is displayed.
E. Method Validation
To validate whether the diffusion-related parameter can be
estimated independently of the bolus history, the convective dif-
fusion (4) was simulated by a ﬁnite difference approximation.
The adopted boundary conditions were (5b) and (8). For various
, a large number of IDCs were obtained for increasing .We
analyzed the dependency of the diffusion-related parameters
and on both and ,byﬁtting the IDCs with the pro-
The performance of the parameter estimation algorithm was
then evaluated by ﬁtting simulated TDCs, for
and , with additive white noise sequences. By
adding these noise sequences to the TDCs, we reproduced the
multiplicative noise character in the real domain . The noise
level was 12 dB was lower than the signal power, representing
the noise level encountered in vivo.
A preliminary clinical validation of the method was also per-
formed by analysis of ﬁve datasets registered from four pa-
tients referred for radical prostatectomy at the AMC University
Hospital (Amsterdam, the Netherlands). After radical prostate-
ctomy, the prostate was cut in slices of 4 mm thickness and a
pathologist marked the presence of cancer by histology anal-
ysis based on the level of cell differentiation . We selected
KUENEN et al.: CONTRAST-ULTRASOUND DIFFUSION IMAGING FOR LOCALIZATION OF PROSTATE CANCER 1499
the histology slice(s) corresponding to the ultrasound imaging
plane and compared them with theCUDIresults.Fig.8shows
an example parametric diffusion image with the corresponding
histology. A quantitative comparison was performed for each
dataset by selecting two ROIs containing healthy and cancerous
tissue, based on the histology. Because the histology analysis
was not speciﬁcally aimed at a high-resolution validation, we
limited the ROI selection to areas larger than 50 mm that did
not show signiﬁcant variation across subsequent slices. We con-
sidered only the peripheral zone of the prostate , since about
70% to 80% of all cancers are found in this anatomical zone ,
. From the histogram of in each ROI, the mean value and
standard deviation of each speciﬁc class (healthy and cancerous
tissue) were used to determine the optimal tissue-classiﬁcation
threshold by Bayes inference . This threshold (based on all
datasets) was used to derive the optimal sensitivity and speci-
ﬁcity for pixel classiﬁcation. In addition, we evaluated the re-
ceiver operating characteristic (ROC) curve on a pixel basis.
A comparison was performed with different IDC parameters
proposed in the literature , –, by repeating the
same tissue classiﬁcation procedure. We extracted the peak
value (PV), the peak time (PT), the appearance time (AT, the
time at which the IDC achieves 5% of PV), the full-width
at half-maximum (FWHM, the time duration while the IDC
exceeds , ), the wash-in time (WIT, the time
it takes for the IDC to rise from 5% to 95% of its peak value
), the area under the IDC (AUC, the LDRW parameter ),
the MTT (the LDRW parameter ) and the LDRW parameter
. The parameters PT and AT were computed with respect to
the estimated theoretical injection time . All parameters were
extracted from linearized ﬁts to ensure that the comparison is
not affected by differences in preprocessing.
The parameters and , estimated from IDCs obtained by
simulations of the convective diffusion (4), conﬁrmed the theo-
1%. This result conﬁrms that ,incontrastto , is independent
of and , i.e., independent of the detection site and the his-
tory of the bolus, respectively.
The parameter estimation algorithm ﬁtted simulated TDCs
with an average and in the logarithmic
and real domains, respectively. If the complete TDC could be
used for ﬁtting, the mean relative error for was 4.33%. When
the IDC tail was excluded from the ﬁtting, as required for ﬁtting
of TDCs obtained in vivo , the mean relative error was 10.15%.
On the obtained B-mode image sequences that were com-
pared with histology, the algorithm showed an average
after ﬁltering in space and time, which was by 18% higher
than without ﬁltering. In these data, 89% of the pixel IDC ﬁts
were considered sufﬁciently accurate ( in the loga-
rithmic domain) and pixel TDC ﬁts were included in the
comparison with histology.
In all patients, we observed that the presence of cancer was
associated with higher values of . For each parameter, the mean
value and standard deviation in healthy and cancerous tissue
are reported in Table I. We used this information to derive the
sensitivity and speciﬁcity for pixel classiﬁcation, as well as the
TAB L E I
MEAN AND STANDARD DEVIATION OF IDC PARAMETERS
MEASURED IN HEALTHY AND CANCEROUS TISSUE
TAB L E I I
SENSITIVITY,SPECIFICITY,AND ROC CURVE AREA ON PIXEL BASIS OF
SEVERAL HEMODYNAMIC PARAMETERS EXTRACTED FROM FITTED IDCS
ROC curve area. For all the considered parameters, the results
are reported in Table II.
IV. DISCUSSION AND CONCLUSION
Contrast-ultrasound diffusion imaging (CUDI) is an inno-
vative noninvasive imaging method for prostate cancer local-
ization. The passage of an intravenously injected UCA bolus
through the prostate is measured by dynamic TRUS imaging.
The TDCs obtained from all pixels covering the prostate are an-
alyzed and a parametric image, based on intravascular diffusion,
In a preliminary clinical validation, we have compared
the cancer localization accuracy of the proposed method,
CUDI, with several quantitative indicators of perfusion. More
precisely, we compared the correspondence between several
methods for MVD characterization and the level of cell differ-
entiation, evaluated by a histology analysis.
The results show that the diffusion-related parameter has a
ROC curve that is superior to that of any other IDC parameter.
Although the sensitivity of some other parameters is higher,
is the only parameter whose sensitivity and speciﬁcity both ex-
ceed 80%. While these results are obtained on a pixel basis, the
clinical diagnosis would be based on a larger scale; currently,
carcinomas are considered clinically signiﬁcant if their size is at
least 0.5 cm . Lesion classiﬁcation is then based on large
amounts of pixels. A perfect pixel-based sensitivity is therefore
not strictly necessary. On the other hand, a high speciﬁcity is
essential to exclude healthy areas.
Although they are less speciﬁcthan , all IDC time parame-
ters are smaller in the cancerous areas than in healthy areas. This
1500 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 30, NO. 8, AUGUST 2011
is consistent with previous qualitative observations , .
Perhaps, the lower speciﬁcity of the time parameters compared
to is related to the difﬁculty of interpreting these time parame-
ters locally at the measurement site . The amplitude-related
parameters PV and AUC show relatively large variations, in
both healthy and cancerous tissue. This may be due to their de-
pendency on the amount of UCA entering the prostate or to non-
linear ultrasound propagation through UCA dispersions .
Imaging of intravascular diffusion is a new concept, based
on modeling the intravascular UCA transport by the convec-
tive diffusion equation. Whereas other researchers have taken
a bottom-up approach, by analyzing ﬂow through individual
vessels and deducing the effects on vascular networks , we
have pursued a top-down approach, aimed at macroscopic mod-
eling of the microvascular network, similarly to . In fact, we
characterize the microvascular network as similar to a porous
medium , whose structural characteristics are reﬂected in
The parameter measures the ratio between diffusion and
convection. High values of , with a relatively low diffusion
with respect to convection, seem to be associated with the
presence of cancer. This relative decrease in diffusion may be
caused by an increased microvessel tortuosity. This is however
the ﬁrst study that investigates the effects of changes in the
microvascular architecture on intravascular diffusion; a better
understanding requires additional research.
The presented method for estimation of diffusion has the ad-
vantage that a local diffusion-related parameter can be es-
timated independently for each pixel. This parameter depends
only on the local, hemodynamic parameters and and does
not depend on the entire dilution history between the injection
and detection site. This novel approach is based on the assump-
tion of a Normal UCA concentration distribution in space; an
assumption that is also included in the LDRW model . The
width of this distribution before the bolus passage through the
detection site, given by , determines the resolution by which
we can estimate (see Fig. 5). We have not been able to verify
the use of this assumption in an experimental in vitro setup.
However, the spatial UCA distribution in the systemic arteries is
mainly determined by the transpulmonary circulation and can be
well described by the LDRW model . Moreover, the LDRW
model is reported to be the most suitable for ﬁtting IDCs mea-
sured in the microcirculation of animal models . These re-
sults support the validity of the LDRW model assumptions.
The proposed method focuses on the temporal characteris-
tics of the UCA diffusion dynamics. Alternative methods can
be based also on spatial diffusion characteristics and will be in-
vestigated in the future. In this study, relatively simple linear
ﬁlters were used to improve the robustness of parameter esti-
mation. More advanced ﬁltering methods can possibly provide
additional improvements. In this context, coherence-enhancing
diffusion ﬁltering seems an interesting method to improve the
signal quality given the anisotropy caused by the TRUS resolu-
tion and the microvascular characteristics.
An important issue concerns the validation of CUDI, as de-
termining the position of the imaging plane with respect to the
histology planes is difﬁcult. In fact, the imaging plane often
crosses several histology planes. The presented validation was
therefore restricted to patients whose histology did not show sig-
niﬁcant variation across subsequent slices. We are currently in-
vestigating new strategies to improve the comparison between
imaging and histology. The validation could be improved by
comparing CUDI results directly with the MVD, rather than
with the level of cell differentiation. This approach, requiring
the use of immunohistology –, would be more accu-
rate as CUDI aims at characterizing the microvascular structure.
An additional step in the validation may also involve the zonal
anatomy of the prostate. Here, the validation was restricted to
the peripheral zone, where the majority of cancers are found
, . As the microvascular structure varies among different
anatomical zones of the prostate, it may also be interesting to
investigate the intravascular diffusion in different zones.
In the future, three-dimensional ultrasound imaging may
offer great advantages for the proposed method. From a clinical
perspective, the entire prostate could be studied with a single
UCA bolus injection. This would resolve an important current
issue, i.e., the selection of proper TRUS imaging planes such
that any signiﬁcant carcinoma is covered. From a technical
perspective, the UCA transport could be observed in all spa-
tial dimensions, which would open up new possibilities for
spatio-temporal analysis of intravascular UCA diffusion. More-
over, the in vivo validation would be simpliﬁed as imaging and
histology results could be compared more accurately.
In conclusion, also given the additional possibilities offered
by three-dimensional ultrasound, imaging of intravascular dif-
fusion may be a promising alternative to perfusion imaging for
the localization of prostate cancer. The intravascular nature of
UCA microbubbles makes contrast-enhanced ultrasound an at-
tractive imaging modality to assess intravascular diffusion. Fur-
thermore, the use of CUDI should not be limited to prostate
cancer; the same diffusion principles also apply to many other
forms of cancer, such as breast cancer. Further clinical studies
are however required to evaluate the clinical reliability of CUDI.
LDRW IDC MOMENTS AND SKEWNESS
For a random variable with probability density function
(PDF) , the moments for are given as
For , the central moments are given as
To interpret the LDRW IDC formalization in (6) as a PDF, we
deﬁne for and divide by its integral
. The moments are then given as
The LDRW IDC moments, which for are denoted by ,
have been derived in  and 
KUENEN et al.: CONTRAST-ULTRASOUND DIFFUSION IMAGING FOR LOCALIZATION OF PROSTATE CANCER 1501
In (18), equals the expectation of .If is known, the
moments and can be computed from measured IDCs.
Therefore, solving and from (18a) and (18b) provides a
noniterative method to estimate these parameters .
In the current study, is however unknown so we cannot
measure . We can only measure the moments , which de-
pend on . To estimate all LDRW parameters by measuring ,
we include in the moments analysis. The ﬁrst moment for
is by linearity of the expectation given as
This result can also be derived by substitution of in the
integrand of (17). Similarly, for can be derived. ,
and can then be solved from the obtained equations for ,
and . However, this system is very complicated and has
no analytical solution.
Alternatively, we can also measure the central moments
and derive expressions for in terms of ,and . By sub-
stituting , we observe that the central moments are
compensated for by the time shift by
In fact, the argument ensures that the resulting function
is independent of [see (6)]. Therefore, the moments
of are given by (18). By expanding ,the
central moments can be completely described in terms of
. In particular, and are given as
and can be solved from (21). To obtain the solution, we com-
pute the IDC skewness , i.e., the third standardized moment
of , which is a function of only
This result conﬁrms the relation between and the IDC skew-
ness , , . Solving from (22) provides an estimate
of that is independent of and . Subsequently, can be es-
timated from (21a) as
Finally, we use (19) to estimate from as
The fourth parameter is given directly by the IDC integral.
Since the IDC integral as well as the moments ,,and
can directly be computed from measured IDCs, all LDRW IDC
parameters can be estimated by (22)–(24).
In summary, we have obtained a method to estimate all
LDRW IDC parameters, including . Being noniterative,
this method has low computational requirements compared to
various iterative methods.
The authors would like to thank the Department of Pathology
of the AMC University Hospital in Amsterdam for the histology
data, and I. Herold (M.D.) and Prof. Dr. H. Korsten (M.D.) of
the Department of Anesthesiology of the Catharina Hospital in
Eindhoven for providing equipment and assistance during the
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