Download Quantitative Non-Gaussian Diffusion and Intravoxel

ORIGINAL ARTICLE
Quantitative Non-Gaussian Diffusion and Intravoxel Incoherent
Motion Magnetic Resonance Imaging
Differentiation of Malignant and Benign Breast Lesions
Mami Iima, MD, PhD,* Kojiro Yano, MD, PhD, MA,*† Masako Kataoka, MD, PhD,* Masaki Umehana, BSc,‡
Katsutoshi Murata, BSc,§ Shotaro Kanao, MD,* Kaori Togashi, MD, PhD,* and Denis Le Bihan, MD, PhDk ¶
Objectives: The purpose of this study was to explore the potential of nonGaussian diffusion and perfusion magnetic resonance imaging (MRI) using
intravoxel incoherent motion (IVIM) MRI for the diagnosis of breast lesions.
Materials and Methods: This study included 26 women with breast lesions.
Diffusion-weighted images were acquired using 16 b values up to 2500 s/mm2
and analyzed using a kurtosis diffusion model (apparent diffusion coefficient
[ADC0] and kurtosis [K]) for the diffusion component and IVIM model (perfusion fraction [fIVIM] and pseudodiffusion coefficient [D*]) for the perfusion
component. Diagnostic performance of diffusion and perfusion parameters was
evaluated from receiver operating characteristic analyses.
Results: The ADC0 in malignant lesions was significantly lower than that in benign lesions and normal tissue (P < 0.001, P < 0.001), whereas K was significantly higher (P < 0.05, P < 0.001), as well as fIVIM (P < 0.05, P < 0.01). No
significant difference was found in D*. The receiver operating characteristic analysis gave high area under the curve values for ADC0, K, and fIVIM for
distinguishing malignant from benign lesions (0.99, 0.85, and 0.82, respectively).
The ADC0 allowed benign tumors to be identified with 100% negative predictive
value and malignant tumors with 100% sensitivity. The malignant/benign diagnosis thresholds were 1.4 10−3 mm2/s as well as 0.6 and 7%, respectively, for
ADC0, K, and fIVIM.
Conclusions: With a proper methodological framework, IVIM MRI can provide
valuable information on tissue structure and microvasculature beneficial for the
diagnosis of breast cancer lesions.
Key Words: diffusion-weighted MR imaging, intravoxel incoherent motion,
kurtosis, breast cancer, differential diagnosis, noise correction
(Invest Radiol 2015;50: 205–211)
he concept behind diffusion magnetic resonance imaging (MRI)1 is
to probe tissue microstructure through the measurement of water
molecular displacements powered by Brownian motion. As such, water
diffusion is becoming an important biomarker of cancer because it has
been observed that the water apparent diffusion coefficient (ADC) is
significantly reduced in many primary or secondary cancer tissues.2
A putative mechanism for this drop in ADC is the increase in the
T
Received for publication May 5, 2014; and accepted for publication, after revision,
July 31, 2014.
From the *Department of Diagnostic Imaging and Nuclear Medicine, Kyoto University Graduate School of Medicine, Kyoto; †Information Science and Technology,
Osaka Institute of Technology, Osaka; ‡Kyoto University Faculty of Medicine,
Kyoto; §Siemens Japan K.K., Tokyo; kHuman Brain Research Center, Kyoto
University Graduate School of Medicine, Kyoto, Japan; and ¶NeuroSpin, CEASaclay, Gif-sur-Yvette, France.
Supported by a Grant-in-Aid for Scientific Research from the Ministry of Education,
Culture, Sports, Science and Technology of Japan (No. 24591756); a Grand-inAid for Japan Society for the Promotion of Science Fellows from Japan Society
for the Promotion of Science (No. 25-2430); and the Louis D. Foundation of the
Institute of France.
Conflicts of interest and sources of funding: none declared.
Supplemental digital content is available for this article. Direct URL citation appears in
the printed text and is provided in the HTML and PDF versions of this article on
the journal’s Web site (www.investigativeradiology.com)
Reprints: Denis Le Bihan, MD, PhD, Bât 145, Point Courrier 156 F-91191 Gif/Yvette,
France. E-mail: [email protected].
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ISSN: 0020-9996/15/5004–0205
Investigative Radiology • Volume 50, Number 4, April 2015
density of cell membranes (caused by cell proliferation), which act as
obstacles for water diffusion.3 Such interactions of diffusing water with
tissue components are responsible for a non-Gaussian diffusion behavior (as opposed to free diffusion), which has been readily observable
when using a high degree of diffusion weighting (the so-called high b
values) now achievable on clinical MRI scanners.4,5 Another aspect of
diffusion MRI is its sensitivity to perfusion because the flow of blood
water in randomly oriented capillaries mimics a diffusion process
through the “intravoxel incoherent motion” (IVIM) effect.6 Recently,
IVIM MRI has undergone a striking revival, especially for body organ
studies.4 Intravoxel incoherent motion MRI might be especially useful
to investigate cancer tissues for which vascularity is a key parameter,
to characterize tumors and predict or monitor therapeutic responses.
A key feature of IVIM diffusion MRI is that it does not involve contrast
agents and can therefore be an alternative for perfusion MRI in patients
exposed to the risk for nephrogenic systemic fibrosis.
Indeed, a significant progress has been made since the early introduction of the IVIM and ADC concepts4,5 and important methodological issues must now be revisited to exploit the full potential of
quantitative diffusion and IVIM MRI in clinical practice. Hence, our
aim was to explore the potential of non-Gaussian diffusion and perfusion MRI using IVIM MRI using an updated quantitative imaging
framework to simultaneously take into account IVIM effects (low b
values) and non-Gaussian diffusion effects (high b values) as well as issues related to effects of noise. This framework is introduced in the context of breast cancer. The choice of breast cancer, one of the most
common cancers in women worldwide, was motivated by the high potential of diffusion MRI to differentiate benign and malignant breast lesions, to evaluate tumor extension,7–9 and to predict the response to
neoadjuvant chemotherapy in patients with breast cancer.10
MATERIALS AND METHODS
Patient Population
This retrospective study was approved by an institutional review
board, and informed consent was waived. Between April and December
of 2011, a total of 26 consecutive patients were enrolled in this study, with
the following inclusion criteria: breast lesions with a long diameter larger
than 8 mm at the time of MRI examination. Four patients were excluded
because of poor signal quality caused by either motion artifacts or noise.
Thus, 22 patients (31–74 years; mean, 52.4 years) were consequently selected for the study, with 23 lesions: 15 malignant (9 invasive ductal carcinomas, 4 invasive lobular carcinomas, 1 mucinous carcinoma, and 1
phyllodes tumor) and 8 benign tumors (2 fibroadenomas, 4 fibrocystic
changes, 1 pseudoangiomatous stromal hyperplasia, and 1 inflammation). One patient had bilateral lesions: an invasive ductal carcinoma in
1 breast and a fibrocystic lesion in the other breast.
Standard of Reference
Malignant tumors were histopathologically diagnosed through
biopsy first and confirmed after surgery. Benign lesions were diagnosed
through biopsy first and the absence of tumor growth during
their follow-up period for at least 18 months by ultrasonographic or
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Iima et al
radiological findings.11 Breasts without abnormal findings were
regarded as negative for cancer on the basis of clinical and/or radiological follow-up for at least 8 months. All pathologic results were defined
according to the World Health Organization classification of breast
tumors.12
MRI Acquisitions
Breast MRI was performed at 3 T (Trio B17; Siemens Medical
Solutions) using a dedicated 16-channel breast array coil (6 channels covering each breast13). The following images were obtained after localizers
were acquired: (1) bilateral fat-suppressed T2-weighted images (repetition time/echo time, 5500/77 milliseconds; flip angle, 140 degrees; field
of view, 330 330 mm2; matrix, 448 448; slice thickness, 1 mm; acquisition time, 1 minute and 30 second); (2) trace-weighted diffusion images (single-shot echo planar imaging) with spectral attenuated inversion
recovery for fat suppression with the following parameters: b values
(3, 5, 10, 20, 30, 50, 70, 100, 200, 400, 600, 800, 1000, 1500, 2000,
2500 s/mm2) (the minimum b value was 3 s/mm2 owing to the presence
of crusher pulses); repetition time/echo time, 4,600/86 milliseconds; flip
angle, 90 degrees; field of view, 160 300 mm2; matrix, 80 166; slice
thickness, 3.0 mm; 25 slices without gap; bandwidth, 1585 Hz; acquisition
time, 3 minutes 55 seconds; generalized autocalibrating partially parallel
acquisitions with acceleration factor of 2; (3) T1-weighted images were
obtained using a 3-dimensional fat-suppressed gradient-echo sequence
(repetition time/echo time, 3.7/1.36 milliseconds; flip angle, 15 degrees;
field of view, 330 330 mm2; matrix, 346 384; slice thickness,
1 mm; acquisition time, 60 seconds). Fat-suppressed T1-weighted dynamic contrast-enhanced images were also acquired before and after injection (0–1, 1–2, and 5–6 minutes) of a gadolinium-based contrast agent
(ProHance; Eisai, Tokyo, Japan) but were not considered for this study.
Data Processing
Traditionally, magnetic resonance images have been quantitatively processed using fitting algorithms that provide estimate of parameters according to a given nonlinear signal model.14 Intravoxel
incoherent motion/diffusion MRI has been no exception. Although
the original IVIM model6 remains somewhat unchallenged, several
models have been successfully introduced to take into account the
non-Gaussian (not free) water diffusion behavior observed at high b
values in biological tissues (see Supplemental Digital Content 1,
http://links.lww.com/RLI/A169). Here, we have chosen the kurtosis
model because it seems more robust when using medium-range b values
(lower than 3000 s/mm2).15 The overall measured signal, M(b), can
then be modeled as follows (see Supplemental Digital Content 1,
http://links.lww.com/RLI/A169):
h
i1=2
MðbÞ ¼ S ðbÞ2 þNCF
(½1)
n
h
io
with S ðbÞ ¼ So f IVIM expðbDÞþ ð1f IVIM Þ exp bADC 0 þ ðbADC 0 Þ2 K=6
(½2)
where S0 is the theoretical signal acquired at b = 0; fIVIM, the (T1-,T2weighted) volume fraction of incoherently flowing blood in the tissue;
D*, the pseudodiffusion coefficient associated to the IVIM effect; and
ADC0, the virtual ADC that would be obtained when b approaches 0.
The dimensionless coefficient K (kurtosis) characterizes the degree of
deviation of the signal behavior from a monoexponential decay (K =
0 when the diffusion-driven molecular displacements obey the Gaussian law), a marker of the heterogeneity of the diffusion environment.
The noise correction factor (NCF) is a parameter that characterizes
the “intrinsic” noise contribution from the image acquisition setup (depending on the coils, the MRI sequence parameters, etc) (see Supplemental Digital Content 1, http://links.lww.com/RLI/A169).
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To overcome some pitfalls often encountered with the usual
data-fitting algorithms (see Discussion), we have introduced a completely new approach. Instead of fitting the signal data to the IVIM/
diffusion model using the standard iterative (fitting) search approach,
we directly derive the parameters by comparing the raw signal data with
those of a database of simulated signals built once for all for the entire
study using an exhaustive set of discretized and bounded parameter
combinations with Eq. [2]. In other words, a distance, di, is calculated
between the measured signal attenuation profile, M(b), and each simulated signal, Sdb(i), of the database. The parameter combination, Pi,
giving the shortest distance, dmin, is deemed to represent the searched
parameter estimates. In our study, the distance, di , was defined as
follows:
di ¼ S b ðMðbÞ Sn2dbðiÞ ðbÞ S 2 ðb ¼ 0Þ þ NCF 1=2 ÞwðbÞ
½
2
(½3)
where Sndb(i)(b) is the (normalized) simulated signal from the database
for the parameter combination P i(S i0, f iIVIM, D*i, ADC i0, Ki) obtained
from Eq. [2], scaled with S(b = 0), which was estimated as [M2(b = 3)
– NCF]1/2. W(b) is a weighting factor introduced to compensate the acquisition sampling bias, at the disadvantage of the diffusion parameters,
when the number of data points with high b values, nbhigh, is lower than
those with low b values, nblow, (as in our study). This bias can be seen as
a trend (slope) in the error residuals plotted against b values between the
simulated and raw signals (good fitting should lead to a random distribution of the error residuals). W(b) was set to 1/nblow (1/9) for signals
acquired with b < 400 mm2/s and 1/nbhigh (1/7) for signals acquired
with b ≥ 400 mm2/s. Above b = 400 mm2/s, the IVIM contribution to
the signal becomes negligible16 (as a worst-case scenario, maximizing
IVIM contribution with fIVIM = 20% and D* = 8.0 10−3 mm2/s,
the IVIM contribution at b = 400 s/mm2 is 0.8%, well within noise).
The noise correction factor has been added to the simulated signals
and not subtracted from the measured signals (inverting Eq. [1]) to circumvent potential problems that could arise with negative squared
values when signals are close to the noise floor (high b values).
The database was built with the following parameter ranges:
S0: [0.975–1.025] step 0.002
fIVIM: [0–20] step 1 (%)
D*: [3.5–25] step 0.5 (10−3 mm2/s)
ADC0: [0.8–2.1] step 0.1 (10−3 mm2/s)
K: [0.0–1.3] step 0.1
To limit its size, we excluded from the database unrealistic parameter combinations leading to Sdb(i)(b = 2500) > Sdb(i)(b = 2000)
(which may arise when both ADC0 and K are high, a known pitfall of
the kurtosis model), or D* < 3ADC0 (lower limit to allow a meaningful
separation of 2 exponentials in Eq. [2]6). Furthermore, the steps within
each parameter range were set to provide a reasonable accuracy on the
estimated parameters while restricting the size of the data bank. The
method was implemented with MATLAB code (Mathworks, Naticks,
MA) to run the analysis at the region of interest (ROI) level and at the
pixel level so as to generate parametric maps of the diffusion and
perfusion parameters.
To show pitfalls that may result from using a standard
(monoexponential) ADC diffusion model and compare our results with
those in the literature, we also performed a 2-step process at the ROI
level using the nonlinear subspace trust region fitting algorithm built
into MATLAB (Mathworks, Natick, MA). The ADC and fIVIM values
(referred thereafter as ADCmono and fIVIMmono to distinguish them from
the ADCo and fIVIM values obtained with the full approach described
previously) were also estimated by fitting the diffusion signal decay,
S/S0, for 200 s/mm2 ≤ b ≤ 1000 s/mm2 with a monoexponential function, then by fitting the residual of the signal at b < 200 s/mm2 with
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Investigative Radiology • Volume 50, Number 4, April 2015
Quantitative Diffusion/IVIM MRI in Breast Cancer
TABLE 1. Diffusion Parameters in Malignant lesions, Benign Lesions, and Normal Tissue
P*
Parameter
ADC0 (10−3 mm2/s)
K
ADCmono (10−3 mm2/s)
Malignant
Benign
Normal
1.05 (0.94–1.17)
0.82 (0.70–0.94)
1.00 (0.88–1.11)
1.73 (1.51–1.94)
0.55 (0.42–0.68)
1.50 (1.35–1.66)
1.97 (1.87–2.07)
0.25 (0.16–0.34)
1.78 (1.67–1.90)
Malignant Versus
Benign Tumor
Malignant Versus
Normal Tissue
Benign Versus
Normal Tissue
<0.001
<0.05
<0.001
<0.001
<0.001
<0.001
<0.05
<0.01
<0.05
Values are presented as mean (95% confidence interval).
*Bonferroni corrected.
ADC0 indicates apparent diffusion coefficient; K, kurtosis.
the IVIM model (equations A1, A2, A3; supplemental information,
Supplementary Digital Content 1, http://links.lww.com/RLI/A169), as
also done by other groups17–19:
Regions of Interest
Two readers (M.I., radiologist A, and M.K., radiologist B, with
6 years and 10 years of experience in breast MRI, respectively, blinded
to the final pathologic results) manually drew ROIs on the slice with the
largest tumor area using the b = 0 and b = 1000 s/mm2 diffusionweighted images, avoiding T2-shine through areas usually found in necrotic or cystic parts under guidance of the T2-weighted images. The
ROIs were defined as slightly smaller than the actual lesions to reduce
partial volume effects. The ROIs were also drawn in the normal homogeneous breast parenchyma for all patients as controls (avoiding contamination by fatty tissue) except in 2 patients who had bilateral
lesions or surgical history in the controlateral breast. The median and
range of ROI size were 97.6 (63.4–196.0) mm2, 75.9 (42.2–263.3)
mm2, and 171.7 (119.3–271.6) mm2 for the malignant tumors, benign
tumors, and normal tissue, respectively.
Statistical Analysis
All the parameters in malignant and benign lesions as well as
normal tissue were compared with the Mann-Whitney test. Bonferroni
correction was used to account for multiple comparisons. Receiver operating characteristic curve analyses were conducted to assess ADC0, K,
and fIVIM in terms of their utility for discrimination of malignant and
benign lesions. An optimal threshold was established for those parameters, giving the best sensitivity and specificity balance. For all tests, a
P < 0.05 was considered statistically significant. All statistical analyses
were conducted using statistical software MedCalc (version 11.3.2.0,
Mariakerke, Belgium).
RESULTS
The diffusion parameters across malignant and benign tumors as
well as normal breast tissue are summarized in Table 1. The ADC0
in malignant lesions was significantly lower than that in benign lesions
(P < 0.001) and normal breast tissue (P < 0.001). The K in malignant
lesions was significantly higher than that in benign lesions (P < 0.05)
and normal breast tissue (P < 0.001). Benign tumors had significantly
lower mean values of ADC0 and higher mean values of K than normal
breast tissue did (P < 0.05 and P < 0.01, respectively). Although
ADCmono values obtained with a monoexponential model also showed
significant difference between malignant and benign tumors or normal
tissue (P < 0.001, P < 0.001) or that between benign tumors and normal
tissue (P < 0.05), they were always found smaller than ADC0 values,
reflecting improper handling of non-Gaussian diffusion. In malignant
tumors, fIVIM was significantly higher than that in benign tumors and
normal breast (P < 0.05 and P < 0.01, respectively) (Table 2). The
fIVIMmono values obtained using the 2-step process ADC model were
underestimated in malignant lesions and overestimated in benign lesions and normal tissue, underlining the fact that the bias in fIVIM estimates using a simple ADC model for diffusion depends on the degree
of non-Gaussian diffusion effects. There was no significant difference
in fIVIMmono or D* across malignant and benign tumors and normal
breast tissue.
Examples of parametric diffusion and perfusion maps obtained in
the patients with invasive ductal carcinoma and pseudoangiomatous stromal hyperplasia (PASH) are shown in Figures 1 and 2. The pattern differences observable between the fIVIM, ADC0, and K maps are striking,
showing tumor heterogeneity not detectable at the ROI level. Locations
presenting a high fIVIM/low ADC0/high K combination are potentially
the most active parts, suggesting spots where biopsy should be made.
The receiver operating characteristic analysis gave high AUC
values for AUC of ADC0, K and fIVIM for distinguishing malignant
TABLE 2. IVIM Parameters in Malignant and Benign Lesions and Normal Tissue
P*
Parameter
fIVIM, %
D* (+) (10−3 mm2/s)
fIVIMmono, %
Malignant
Benign
Normal
Malignant Versus
Benign Tumor
Malignant Versus
Normal Tissue
Benign Versus
Normal Tissue
12.3 (8.86–15.7)
10.9 (5.95–15.9)
8.63 (7.39–9.86)
5.00 (0.60–9.40)
13.9 (5.96–21.9)
8.66 (6.97–10.4)
4.45 (2.63–6.27)
12.6 (8.78–16.3)
6.64 (4.97–8.31)
<0.05
0.52
1.00
<0.01
0.36
0.20
1.00
1.00
0.44
Values are presented as mean (95% confidence interval).
*Bonferroni corrected.
fIVIM indicates perfusion fraction; D*, pseudodiffusion coefficient.
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Iima et al
FIGURE 1. Invasive ductal carcinoma in a 61-year-old woman. A, Anatomical contrast-enhanced image. B, The fIVIM map. C, The ADC0 map. D,
The K map. The white rectangle in A shows the area covered by the parametric maps. The high fIVIM fraction area at the periphery of the tumor in B
matches the enhancing lesion very well in A. The lesion center has low perfusion (suggesting necrosis). An area on the left part of the tumor exhibits
a low ADC0 with high K value, suggesting high cellularity (viable malignant component), whereas the central part has a high ADC0 and low K, suggesting
lower cellularity (possible necrosis).
from benign lesions. Although those AUC values were not tested for
statistical significance between them given the small size of the patient
population, the AUC of ADC0 (0.99) was found higher than that of K
and fIVIM (0.85 and 0.82, respectively) (Table 3). The ADC0 allowed
benign tumors to be identified with 100% negative predictive value
and malignant tumors with 100% sensitivity. The malignant/benign diagnosis thresholds were 1.4 10−3 mm2/s as well as 0.6 and 7%, respectively, for ADC0, K, and fIVIM.
DISCUSSION
The diffusion and perfusion parameters obtained from the kurtosis diffusion/IVIM model could well differentiate malignant from benign breast tumors with high sensitivity and specificity. The ADC0
values in malignant lesions were significantly lower than those in benign lesions and normal tissues, consistent with the ADC values reported from other studies,17,19–21 but our ADC0 values (obtained with
a larger range of b values and using a non-Gaussian diffusion model)
were lower than ADCmono values and ADC values reported in the literature. Indeed, with state-of-the-art MRI scanners, it is now becoming
possible to extract further useful information from IVIM MRI, acquiring data beyond the usual range of b values used in clinical practice
(600–1000 s/mm2).16,19 The ADC values, as obtained from only 2 b
values or a monoexponential diffusion model, are significantly lower
than the ADC0 value estimated when higher b values are taken into
account using non-Gaussian diffusion model such as the kurtosis
model, depending on tissue types, which points out that some important
information may be missed when using a simple ADC.5 Indeed,
significant differences for K between malignant, benign, and normal
breast tissue were found, as also observed in prostate cancer.22,23 The
failure to take into account non-Gaussian diffusion effects furthermore
results in ADC values that are highly dependent on the choice of b
values,19,21 making it difficult to compare studies across centers. In contrast, an important feature of ADC0 and K is that their intrinsic values do
not depend on the b values used for image acquisition (only the accuracy on their estimates will still depend on the number and ranges of
b values). Other non-Gaussian models, such as the biexponential
model, were also explored in this study, according to Iima et al.18 However, the results were not as robust compared with the kurtosis model
(not shown) when dealing with noisy clinical data. Indeed, because
there are only 2 unknown parameters to estimate, the kurtosis model
is gaining momentum in clinical studies.22–24 Whereas ADC0 represents
diffusion at low b values, K comes mainly from the curvature of the diffusion signal decay observed at high b values. The ADC0 is considered
to reflect more diffusion in the extracellular space, which also reflects
the amount of cell filling (shape and size) in tissues and cell proliferation. Large K values point out to enhanced diffusion hindrance effects in malignant tissues, likely related to cell proliferation and
membrane interactions with diffusing water. Another important point
is that using a simple ADC (calculated from 2 b values or using a
monoexponential fit) to remove diffusion effects from the overall signal
to extract IVIM parameters, as often performed,16,17,19 may not be sufficient. The curvature from non-Gaussian diffusion not taken into account with a simple ADC model propagates at low b values and
results in a pseudo-IVIM effect, leading to an overestimation of fIVIM
and D* values (see supplemental information, Supplemental Digital
FIGURE 2. Pseudoangiomatous stromal hyperplasia in a 46-year-old woman. A, Anatomical contrast-enhanced image. B, The fIVIM map. C, The ADC0
map. D, The K map. The white rectangle in A shows the area covered by the parametric maps. The left-center lesion with a high ADC0 (C) and a
very low K (D) corresponds to the nonenhancing lesion in A. The corresponding lesion in B has heterogeneous fIVIM fraction. Such parameter
combination highly suggests the presence of a tissue structure containing parts with a quasi-free diffusion component (fluid-filled lobules or cystic
component, although a detailed correlation between pathologic and radiologic images was not performed for this retrospective study) coexisting with
more cell-filled parts with higher and more heterogeneous fIVIM values.
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Investigative Radiology • Volume 50, Number 4, April 2015
Quantitative Diffusion/IVIM MRI in Breast Cancer
TABLE 3. Diagnostic Abilities of Diffusion and Perfusion MRI Parameters
Parameter
AUC
Threshold
Sensitivity, %
Specificity, %
PPV, %
NPV, %
Accuracy, %
ADC0 (10−3 mm2/s)
K
fIVIM
0.99
0.85
0.82
≦1.40
>0.60
>7.0
100 (15/15)
80 (12/15)
80 (12/15)
88 (7/8)
88 (7/8)
88 (7/8)
94 (15/16)
92 (12/13)
92 (12/13)
100 (7/7)
70 (7/10)
70 (7/10)
96 (22/23)
83 (19/23)
83 (19/23)
ADC0 indicates apparent diffusion coefficient; AUC, area under the curve; fIVIM, perfusion fraction; K, kurtosis; MRI, magnetic resonance imaging; NPV, negative
predictive value; PPV, positive predictive value.
Content 1, http://links.lww.com/RLI/A169 and Fig. 3, especially when
large bvalues are used to calculate the ADC, as also reported by Bokacheva
et al.19 This bias might partially explain why the D* values reported in this
study are somewhat lower than the values reported by other groups.16,19
Note that caution should be advised because poor fat suppression
may also result in high K values owing to the fact that fat tissues have very
low diffusion coefficients.25 Furthermore, noise bias effects at high
b values, resulting from the non-Gaussian nature of the noise in
magnitude-reconstructed images26 must be addressed to avoid erroneous
K value estimates. The main effect of such noise is that it may mimic a
curvature in the diffusion signal attenuation plot because, at high b values,
the signal reaches a “noise floor” and does not get to 0 (see Supplemental Digital Content 1, http://links.lww.com/RLI/A169, Figs. 4 and 5.
The signal attenuation appears curved, even for monoexponential diffusion, and fitting signals with diffusion models will give erroneous
values (eg, underestimation of ADC0, overestimation of K). Many groups
have investigated the effect of non-Gaussian noise in diffusion MRI
and suggested methods to retrieve signal values from noise-corrupted
FIGURE 3. Simulated data without tissue perfusion. Even in the absence
of perfusion, owing to the curvature of the diffusion signal attenuation
(crosses), S/So, fitting the diffusion signal decay with a straight line
(ADC model, here from signal values at b = 200 and 1000 s/mm²)
automatically places data points at low b values above the ADC line
(dashed line), resulting in a false IVIM effect (non-0 value for fIVIM in
the absence of perfusion).
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data.27–31 In this study, we have used a simple procedure where a noise
correction factor is experimentally obtained through a phantom calibration process relying on the diffusion MRI signal property itself.
Another issue is that the usual fitting approaches (such as the
popular Marquardt-Levenberg algorithm) used to estimate diffusion
and perfusion parameters from measured signals suffer from several
drawbacks. Such algorithms are generally very sensitive to noise.14 This
sensitivity leads to instabilities in the estimated parameter values, especially when many parameters are set free, as with Eq. [2]. To mitigate
this issue, the IVIM/diffusion equation is often fitted in 2 steps: first, estimating the diffusion parameters (usually from a monoexponential diffusion model), then estimating the perfusion parameters from the
FIGURE 4. Noise correction modeling in 3 alkanes. The raw signal
attenuation (crosses) is well fitted by the diffusion/noise model
(Eq. [A7]) (dashed line). After noise removal, the corrected signal points
(circles) are perfectly aligned, as expected for free, Gaussian diffusion. The
differences between raw and corrected signal values are large for
nonane, which has a low signal at large b value (high diffusion), but very
small for undecane, which keeps a high signal level at high b values
(low diffusion). Error bars are smaller than the dot size and not shown.
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Iima et al
FIGURE 5. A, Left, Without noise correction, the raw signal (crosses) appears well fitted with the kurtosis diffusion model (circles), but the IVIM
component (residual signal after removal of the diffusion component) would be negative (inset). B, Right, The raw signal (crosses) is, however, very
much better fitted by the noise correction model (dashed line). The corrected signal attenuation (circles) becomes close to a straight line, which is
confirmed as K becomes close to 0, whereas ADC0 value decreases to 2.07 × 10−3 mm²/s. The IVIM effect (inset) is now positive, as expected
(fIVIM = 6.8%), and well fitted by an exponential decay (D* = 14.7 × 10−3 mm²/s).
residual signal.17–19 This 2-step process may increase robustness (because there are fewer parameters to estimate for each step) and is based
on the assumption that IVIM perfusion effects are not expected to contribute to the signal for b values above a cutoff value. However, it is
preferable to handle Eq. [2] as a whole because diffusion effects are obviously present at low b values. Another drawback is that local minima
may result in parameter estimates that are somewhat far from the true
values, so that the results are very sensitive to the set of initial parameter
values that are required to launch the fitting process. The exhaustive search
approach that we have introduced not only alleviates the issues of local
minima and sensitivity to initial values of the iterative approach but is
also much more efficient (hence, faster) in terms of computing requirements because only a simple distance needs to be calculated, whereas
the iterative method requires a bunch of more complex calculus elements
(such as those present in Eq. [2]) to be performed for each iteration
(or even twice if a 2-step approach is used to sequentially estimate diffusion and perfusion parameters). Interestingly, because the noise correction
factor may vary in space across the image (see Supplemental Digital Content 1, http://links.lww.com/RLI/A169), the noise correction factor may
also be included as 1 of the free parameters to estimate within the database.
In the future, several improvements can be made to the approach.
We have observed (data not shown) that some parameter combinations,
although associated with the shortest distance with the measured signal,
could sometimes not properly reflect the signal model, as given by
Eq. [2], resulting in a trend (slope) for the error residual plotted against
b values. The reason for this bias is that biexponential fitting is sensitive
to the sampling acquisition scheme: if the number of data points at low
and high b values is not balanced (which could be justified, given that
IVIM effects are small) “blind” fitting may favor the IVIM component
of the signal. In this study, we have weighted the distance by the number
210
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of low/high b value signals to successfully overcome this problem.
Other distance definitions to minimize this bias will have to be investigated in the future, for instance, weighing the distance calculated for
each b value in Eq. [3] by the signal amplitude or by the interval between b values to homogenize acquisition sampling biases.
One of our limitations is the small number of the population size;
the IVIM and diffusion parameter thresholds for the best diagnostic performance will likely change a little bit when using a larger cohort of patients. Furthermore, the patients were referred for an MRI examination
because suspicious lesions had been found with mammography or ultrasound examinations. Hence, there is a prevalence bias toward patients
with high risk for breast cancer, which could impact our statistical results
for predictive values (underestimation of NPV and overestimation of
PPV). This pitfall is common to most MRI studies of breast cancer because MRI is far too expensive to be used as a screening modality at this
stage. Possible effects of anisotropy such as those in the canals32 were
also not investigated because only diffusion-trace–weighted images were
acquired. Motion correction and registration of images across b values
have been found beneficial for brain studies33 but are precluded for breast
studies because of the absence of fixed, visible anatomical landmarks,
which are necessary for image realignment, especially on the diffusionweighted images where contrast varies deeply across b values.
A point regarding the interpretation of the fIVIM parameter is
that it remains T1- and T2-weighted. Conversion of fIVIM to a flowing
blood volume34 would require the removal of relaxation effects, which
is not straightforward.35 Relaxation parameters depend on the field
strength, the tissue type, and, for the blood, the arterial/vein ratio.36–38
Further studies comparing IVIM data with results of quantitative dynamic contrast-enhanced perfusion MRI models39 or arterial spin labeling methods40 may be of great interest, as well as refining the IVIM
© 2014 Wolters Kluwer Health, Inc. All rights reserved.
Copyright © 2015 Wolters Kluwer Health, Inc. All rights reserved.
Investigative Radiology • Volume 50, Number 4, April 2015
exponential model used in Eq. [2], depending on the underlying vascular
functional architecture (see Appendix).6 No significant difference could
be found in D* between tissue type, as observed in some previous IVIM
study.17 Finally, morework is needed to precisely model the effects of blood
microcirculation on the IVIM signal and to establish a relationship between
IVIM parameters and tissue perfusion, such as blood volume and flow.34
In conclusion, we have shown that multiple diffusion and perfusion MRI parameters can be obtained in a clinical setting with IVIM
MRI, provided that an adequate methodological framework is used to
correct for noise effects to take into account the non-Gaussian diffusion
signal decay. Setting aside the usual data-fitting process with its known
sensibility to noise and initial parameter values due to the presence of
local minima also appears as an important methodological shift, not
only within the scope of diffusion and perfusion MRI. With the exhaustive search method, we have introduced that diffusion and perfusion parameters can be estimated at once (in 1 step) without worrying about
those limitations and in a much less computer-intensive manner. Processing speed may also be increased by limiting the size of the database,
choosing parameter value ranges according to organ and tissue types. In
the context of breast cancer, the diffusion and IVIM parameters, ADC0,
K, and fIVIM, may help improve diagnostic accuracy and guide biopsy
location. Although these preliminary results need to be validated at a
broader scale, they suggest that images of tissue structure and blood microvasculature can be obtained without contrast agents using IVIM
MRI, which is an interesting alternative to perfusion MRI. With further
study, these applications might play an important role in the screening,
diagnosis, or monitoring of the breast cancer as well as serve as a potential prognostic biomarker of breast.
ACKNOWLEDGMENTS
The authors thank Masakazu Toi, MD, PhD, for his excellent advice to this study; Takuma Imakita, BSc, for his exceptional contribution
to software development; as well as Masayuki Nakagawa, RT, and
Tosiaki Miyati, PhD, for their excellent contribution in data acquisition.
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