Download Perfusion Assessment Using Intravoxel Incoherent Motion

ORIGINAL ARTICLE
Perfusion Assessment Using Intravoxel Incoherent Motion-Based
Analysis of Diffusion-Weighted Magnetic Resonance Imaging
Validation Through Phantom Experiments
Ju Hee Lee, MD,* Hyunhee Cheong, BA,† Seung Soo Lee, MD, PhD,† Chang Kyung Lee, PhD,†
Yu Sub Sung, PhD,† Jae-Wan Huh, PhD,‡ Jung-A Song, MD, PhD,§ and Han Choe, MD, PhD§
Objectives: The aims of this study were to demonstrate the theoretical meaning
of intravoxel incoherent motion (IVIM) parameters and to compare the robustness of 2 biexponential fitting methods through magnetic resonance experiments
using IVIM phantoms.
Materials and Methods: Intravoxel incoherent motion imaging was performed
on a 3 T magnetic resonance imaging scanner using 15 b values (0–800 s/mm2)
for 4 phantoms with different area fractions of the flowing water compartment
(FWC%), at the infusion flow rates of 0, 1, 2, and 3 mL/min. Images were
quantitatively analyzed using monoexponential free biexponential, and segmented biexponential fitting models.
Results: There were some inconsistent variations in Dslow with changing flow
rates. The perfusion fraction, f, showed a significant positive correlation with
the flow rate for both the free and segmented fitting methods (ρ = 0.838 to
0.969; P < 0.001). The fast diffusion coefficient, Dfast, had a significant positive
correlation with the flow rate for segmented fitting (ρ = 0.745 to 0.969;
P < 0.001), although it showed an inverse correlation with the flow rate for free
fitting (ρ = −0.527 to −0.791; P ≤ 0.017). Significant positive correlations with
the FWC% of the phantoms were noted for f (P = 0.510 for free fitting and P =
0.545 for segmented fitting, P < 0.001).
Conclusions: The IVIM model allows for an approximate segmentation of molecular diffusion and perfusion, with a minor contribution of the perfusion effect
on Dslow. The f and Dfast can provide a rough estimation of the flow fraction and
flow velocity. Segmented fitting may be a more robust method than free fitting
for calculating the IVIM parameters, especially for Dfast.
Key Words: intravoxel incoherent motion, perfusion,
diffusion-weighted imaging, phantom experiment, fitting algorithm
According to the IVIM theory, each IVIM parameter has a specific biologic meaning; in biologic tissue, the slow diffusion coefficient
(Dslow) stands for the degree of brownian motion of water molecule or
pure molecular diffusion, perfusion fraction (f) for the fraction of water
flowing in capillaries, and fast diffusion coefficient (Dfast) for flow velocity.1,2 Although a few phantom and animal experiments suggested
the flow dependency of f and Dfast,17–20 these studies did not separately
evaluate the effect of the flowing water fraction and flow velocity on the
IVIM parameters and thus provided only limited proof regarding the biologic meaning of IVIM parameters.
The IVIM-based analysis of DW imaging data has been usually
performed using either free, unconstrained, nonlinear, least square
fitting (hereafter referred to as free fitting), or segmented, partially
constrained fitting (hereafter referred to as segmented fitting).12,21–24
Although previous computer simulation studies claimed the superiority
of segmented fitting to that of free fitting in terms of its accuracy and
reliability, this result has not been completely proven with actual DW
imaging data. For successful clinical application of IVIM imaging, it
is crucial to analyze image data using the robust postprocessing method
as well as to adequately interpret the results with a correct understanding of the meaning of each IVIM parameter.
To this end, we conducted IVIM imaging experiments using the
phantoms that consist of static and flowing water compartments, in simulated conditions with various flowing water fractions and flow velocities. The purpose of our phantom experiments was to prove the
theoretical meaning of IVIM parameters and to compare the robustness
of the free and segmented fitting methods.
(Invest Radiol 2016;00: 00–00)
I
ntravoxel incoherent motion (IVIM) imaging is a method based on
diffusion-weighted (DW) imaging with multiple b values. It allows for
the separate analysis of 2 components of random water motion in biologic
tissue, that is, pure molecular diffusion and perfusion.1–4 The clinical usefulness of IVIM imaging has been widely investigated in the assessment of
various disease processes in many anatomical organs.5–16
Received for publication November 25, 2015; and accepted for publication, after revision, January 6, 2016.
From the *Department of Radiology, Center for Liver Cancer, National Cancer Center,
Goyang; †Department of Radiology and Research Institute of Radiology, Asan
Medical Center, Departments of ‡Biochemistry and Molecular Biology, and
§Physiology and Biomedical Institute of Technology, University of Ulsan College
of Medicine, Seoul, South Korea.
Conflicts of interest and sources of funding: Supported by the Basic Science Research
Program through the National Research Foundation of Korea funded by the Ministry of Science, ICT, and future planning (2014R1A2A1A11052085).
The authors report no conflicts of interest.
Supplemental digital contents are available for this article. Direct URL citations appear
in the printed text and are provided in the HTML and PDF versions of this article
on the journal's Web site (www.investigativeradiology.com).
Correspondence to: Seung Soo Lee, MD, PhD, Department of Radiology and Research
Institute of Radiology, University of Ulsan College of Medicine, Asan Medical
Center, Asanbyeongwon-gil 86, Songpa-Gu, Seoul 138-736, South Korea. E-mail:
[email protected].
Copyright © 2016 Wolters Kluwer Health, Inc. All rights reserved.
ISSN: 0020-9996/16/0000–0000
DOI: 10.1097/RLI.0000000000000262
MATERIALS AND METHODS
Principles of IVIM Phantoms
Based on the IVIM theory that explains the random motion of
water in biologic tissue as 2 components, that is, a slower diffusion component and a faster perfusion component, we devised 2 compartment
IVIM phantoms that simplistically reflect human tissue composed of
diffusion-dominant intracellular and interstitial space and perfusiondominant microvasculature (Fig. 1). The phantoms were produced
using vertical glass columns packed with cross-linked dextran gel beads
and water. When water is infused into the phantoms, water flows
through the spaces between the beads, which serve as the flowing water
compartment of the phantom, thus simulating perfusion-dominant microvasculature in biologic tissue. The gel beads contain many pores
on their surface, thus allowing water to diffuse in and out of the gel
beads similarly to the transcapillary fluid exchange in biologic tissue.
Despite this fluid exchange through the pores, the water within the
gel beads is relatively static and, therefore, the space within the gel
beads serves as a static water compartment, and thus simulating the
diffusion-dominant intracellular and interstitial space. To perform magnetic resonance (MR) experiments in simulated conditions with various
flowing water fractions and flow velocities, we produced 4 phantoms
with different area fraction of flowing water compartments by using
the gel beads with different particle size profiles, after which we
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Investigative Radiology • Volume 00, Number 00, Month 2016
Lee et al
FIGURE 1. Principle of the IVIM phantom. A, A schematic model of
biologic tissue modified from that of Le Bihan at al.1 In terms of the
random motion of water molecules, biologic tissue can be divided into
2 compartments, that is, diffusion-dominant intracellular and interstitial
space and perfusion-dominant microvasculature. In intracellular and
interstitial space, molecular diffusion of water within the intracellular
space (a) and the interstitial space (b) accounts for the movement of
water, whereas blood flow or perfusion within a capillary (f)
predominates in microvasculature. The IVIM theory assumes that water
exchange through capillary fenestrations (t) is negligible. B, A schematic
drawing of the IVIM phantom. The spaces within the gel beads (c) serve as
a static water compartment, and thus simulating diffusion-dominant
intracellular and interstitial space. After water infusion into the phantom,
the spaces between the gel beads (f ) serve as a flowing water
compartment, and thus simulating perfusion-dominant microvasculature.
Water can move through the pores on the surface of the gel beads (t),
similar to that of transcapillary fluid exchange in biologic tissue.
performed MR imaging of the phantoms at different infusion flow
rate settings.
Preparation of IVIM Phantoms for MR Imaging
We produced 4 sets of IVIM phantoms using the gel beads
(Sephadex G-25; GE Healthcare, Piscataway, NJ) with different particle
size profiles, that is, coarse (wet particle diameter, 100–300 μm), medium (wet particle diameter, 50-150 μm), fine (wet particle diameter,
20–80 μm), and superfine (wet particle diameter, 20–50 μm),25 and
chromatography columns (XK16/20; GE Healthcare, Piscataway, NJ)
with an internal diameter of 1.6 cm. Despite their differences in particle
size, all 4 types of gel beads have the same pore size, that is exclusion
limit of 5 kd corresponding to the diameter of approximately 1.1 nm
for globular protein,26 as this approximates the size of capillary fenestrations in the brain and is smaller than that in skeletal muscle (5 nm) and
renal glomerulus (15 nm).27 The gel beads were prepared and were then
packed in the chromatography columns according to the manufacturer's
instructions.24 The phantoms were then equilibrated with normal saline
doped with 0.8 mM/L gadoterate meglumine (Dotarem; Guerbet,
Aulnay-Sous-Bois, France) to adjust the T2 relaxation time of the solution
to that of the blood at 3.0 T, that is, approximately 190 milliseconds.28
MR Imaging of the Phantoms
Magnetic resonance imaging was performed on a 3 T MR imaging scanner (Magnetom Skyra; Siemens, Erlangen, Germany) and
using a 16-channel ankle coil. The maximum gradient specifications
were 45 mT/min for the amplitude and 200 T/m per seconds for the
slew rate.
For MR experiments, we constructed a polyoxymethylene fixation device that holds 2 sets of the phantoms stably fitted to the ankle
coil system used in our MR experiments. The flow inlet of the phantom
was connected to a peristaltic pump (Minipuls 3; GILSON, Villiers,
France) using a flow line (Tygon; Saint-Gobain, Akron, OH), for controlled flow infusion through the phantoms. The flow outlet of each
phantom was connected to a glass measuring beaker to measure the
amount of actual flow through the phantoms (Fig. 2). To maintain constant temperature of the phantom through the MR experiments, the thermostatic jacket of XK tubes were filled with 20°C water before
imaging. The phantoms were wrapped with a 0.5-mm-thick tissue
equivalent material (ROM Transparent Bolus; Radiation Oncology Material, Seoul, South Korea) to reduce the susceptibility artifacts from air.
After completing preparation of the phantoms for MR imaging,
structural imaging was performed for guidance of DW imaging using a
3-dimensional, coronal, spoiled gradient echo sequence (echo time
[TE], 3.25 milliseconds; repetition time [TR], 2200 milliseconds; flip
angle, 8 degrees; field of view [FOV], 100 100 mm; matrix, 256 256; slice thickness, 1 mm; and number of slices, 72). T1 and T2 measurement of the phantoms were performed using the Look-Locker sequence (TE = 1.32 milliseconds; TR = 3 milliseconds; number of
inversion time [TI], 16; range of TI, 170–4985 milliseconds; ΔTI, 321
milliseconds; flip angle, 8 degrees; parallel imaging factor, 2; FOV,
352 352 mm; matrix, 192 192; slice thickness, 5 mm; intersection
gap, 0; and number of slices, 3) and multiecho spin-echo sequence
(TE = 26 milliseconds; ΔTE = 26 milliseconds; number of echoes = 15;
TR = 5000 milliseconds; FOV, 103 103; matrix 128 128; section
thickness, 3 mm; intersection gap, 0.6 mm; and number of slice, 3), respectively. Diffusion-weighted imaging was then performed using a
single-shot, echo-planar imaging sequence with the following parameters: TE, 70 milliseconds; TR, 5000 milliseconds; receiver bandwidth,
1500 Hz per pixel; FOV, 288 141 mm; matrix, 196 69; slice thickness, 4 mm; intersection gap, 0.8 mm; and number of slices, 10. Bipolar
DW gradients, that is, 15 b values of 0, 10, 20, 30, 40, 50, 75, 100, 150,
200, 300, 400, 500, 600, and 800 s/mm2, were applied in 3 orthogonal
directions and were subsequently averaged. A k-space–based parallel
imaging technique (generalized autocalibrating partially parallel acquisition, GRAPPA, Siemens Medical Solutions) was used with an acceleration
factor of 2. Fat suppression was achieved using a chemical shift-selective
fat suppression technique.
Diffusion-weighted imaging of the phantoms was performed in a
static state without flow infusion and with flow infusion using the peristaltic pump at the flow rates of 1, 2, and 3 mL/min. The same DW imaging was repeated 5 times with increasing or decreasing orders of flow
rates alternatively every other repetition. As 2 phantoms could be imaged
simultaneously, MR experiments were performed first for the coarse and
the medium phantoms and then for the fine and the superfine phantoms.
Measurement of Area Fraction of the Flowing Water
Compartment of the Phantoms Using Micro-CT
After completion of the MR experiments, the fluid within the
phantoms was replaced with a 1:1 dilute solution of a blood-pool contrast agent (Fenestra VC; MediLumine Inc, Montreal, Quebec, Canada)
in normal saline. Fenestra VC is an iodinated triglyceride nanoemulsion
with a particle size of 10 to 300 nm.29 Because of its particle size far
larger than the pore size (1.1 nm) of the gel beads, Fenestra VC resides
in the area outside of the gel beads. Each phantom was scanned on a
micro-CT scanner (SkyScan 1176; Bruker micro-CT, Kontich, Belgium)
using the scan parameters of 8.94 μm resolution, 70 kVp, 357 μA,
360-degree rotation, 0.3-degree rotation step, 900 milliseconds exposure time, 5 frames averaging, and a 0.5-mm-thick aluminum filter.
The images were reconstructed using NRecon v.1.6.9.18 software
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IVIM Phantom Experiments
FIGURE 2. IVIM phantom and phantom setting for MR experiments. A, A photograph of the 2 IVIM phantoms installed in the polyoxymethylene fixation
device for MR imaging. Asterisks indicate the part of the phantoms filled with gel beads and where the MR images were obtained. B, A diagram of the
phantom setting for the IVIM imaging experiment. Two phantoms were imaged simultaneously. Each phantom was connected to the peristaltic pump
and to a glass beaker using water flow lines. Figure 2 can be viewed online in color at www.investigativeradiology.com.
(Bruker micro-CT) with the modified Feldkamp cone-beam reconstruction algorithm, which resulted in 35 35-mm axial images in an 8-bit
gray scale format (Fig. 3). On micro-CT images of the coarse phantom,
individual gel beads and contrast-filled space outside of the gel beads
were clearly differentiated, which allowed for direct quantification of the
area fraction of the contrast-filled space. The area fraction of the flowing
water compartment (FWC%), that is, percentage of the contrast-filled area
to the entire cross-sectional area of the phantom, was quantified by a researcher (H.H.C) using the ImageJ software (v. 1.45i; National Institutes
of Health, Bethesda, MD). However, for the remaining phantoms, direct
quantification of FWC% was not reliable because of too small particle
sizes for image resolution. Therefore, assuming that the relative size of
the contrast-filled space was proportional to the Hounsfield unit (HU)
of the phantoms, the FWC% of medium, fine, and superfine phantoms
was estimated as FWC% of the coarse phantom (HU of the phantom
of interest/HU of the coarse phantom).
Data Analysis
The DW image data were quantitatively analyzed according to
monoexponential and biexponential models using 2 fitting methods, that
is, free fitting and segmented fitting. The apparent diffusion coefficient
(ADC) was calculated by least square monoexponential fitting of all b
value data on a pixel-by-pixel basis according to the following equation2:
S ¼ S0 e−b ADC ;
½1
where S is the signal intensity at a given b value and S0 is the signal intensity at b = 0 s/mm2.
For biexponential IVIM analysis, DW signal decay was fitted to
the following equation3:
½2
S ¼ S0 f e−b Dfast þ ð1 − f Þ e−b Dslow ;
where f is the perfusion fraction, Dfast is perfusion-related diffusion that
indicates the diffusion coefficient of microcirculation, and Dslow is pure
molecular diffusion. With the unconstrained, free fitting method, all 3
parameters in the Equation 2 were simultaneously determined to minimize the distance between the fitted curve and the measured signal intensities. With the segmented fitting method, the IVIM parameters were
sequentially determined as described in previous studies.13,21,30,31 First,
under the assumption of the negligible contribution of the perfusion
component at the range of high b values, Dslow was determined from
monoexponential data fitting of b ≥ 200 s/mm2 data according to the
following equation:
S ¼ Sint e−b Dslow ;
½3
where Sint is the b = 0 intercept of the monoexponential fit of high b
value data. Because the optimal b values separating perfusion and diffusion effects vary depending on the tissue type,32 the threshold b
value of 200 s/mm2 in our study was determined by the b value where
perfusion effect is negligible for most human organs based on
previous studies.12,13,24,33
Then f can be estimated according to the following equation:
f ¼ ðS 0 − Sint Þ = S0
½4
with the Dslow and f, Dfast being calculated using a partially constrained,
nonlinear regression of all data sets according to the Equation 2. For all
fitting methods, the normalized root mean square error (RMSE), that is,
RMSE/S0, was calculated as a parameter indicating the fitting accuracy.
The product f·Dfast was calculated by multiplying f and Dfast to represent
the overall amount of flow through the phantom.34
All fitting algorithms were written on ImageJ software as plug-in
functions. One radiologist (J.H.L) measured the parameter values
using 1.5-cm circular regions-of-interest located in the center of the
phantoms. The average measurement on 3 consecutive DW images
covering the midportion of the phantom was used as the representative
parametric value.
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Investigative Radiology • Volume 00, Number 00, Month 2016
FIGURE 3. Confocal microscopic images and micro-CT images of gel beads. A–D, Confocal microscopic images (100 magnification) of G-25 coarse (A),
G-25 medium (B), G-25 fine (C), and G-25 superfine (D) gel beads, which have different particle size profiles. E–H, Micro-CT images of the coarse (E),
medium (F), fine (G), and superfine (H) phantoms after an infusion of a blood-pool contrast agent. The individual gel beads are depicted as low-attenuating
spheres on the images of the coarse phantom (E), although they are not clearly delineated on the images of and the medium (F), fine (G), and superfine
(H) phantoms due to the limited spatial resolution of the CT images. Figure 3 can be viewed online in color at www.investigativeradiology.com.
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Investigative Radiology • Volume 00, Number 00, Month 2016
ADC Measurement of the Ice Water Phantom
To confirm the performance of our MR system in the acquisition
of DW imaging, the ADC of the ice water phantom was measured 5
times using the same DW imaging sequence for the IVIM phantoms.
The ice water phantom was prepared by immersing a sealed 15 mL tube
of tap water into a 0.6-L plastic container filled with ice cubes according to the protocol reported previously.35 The mean ± standard deviation ADC value of the ice water phantom was 1.978 ± 0.005 10−3
mm2/s, which closely approximated the known diffusion coefficient
of water at 0°C (1.1 10−3 mm2/s),36 indicating the adequacy of our
MR system for DW imaging.
Statistical Analysis
The Spearman correlation coefficient was used to evaluate the
correlation of the ADC and IVIM parameters with flow rates for each
phantom and to analyze the correlation of the ADC and IVIM parametric values obtained at a flow rate of 1 to 3 mL/min with FWC% of the
phantoms. The normalized RMSE values for monoexponential, free
biexponential, and segmented biexponential fitting methods were summarized as the mean and standard deviation at each flow rate and were
compared among the 3 fitting methods using the Friedman test and the
post hoc Dunn multiple comparisons test. The measurement repeatability of the ADC or IVIM parameters across 5 repeated scans was evaluated using the within-subject coefficient of variation (CV) for the 3
fitting methods. A P value less than 0.05 was considered to indicate a
statistically significant difference. Statistical analyses were performed
using commercial software (IBM SPSS statistics version 21 software;
IBM, Armonk, NY, and GraphPad InStat version 3.0; GraphPad Software, San Diego, CA).
RESULTS
Phantom Characteristics
The T1 and T2 of the gadoterate meglumine solution were 192.8
milliseconds and 191.1 milliseconds, respectively; the T2 of the
gadoterate meglumine solution was nearly the same as that of whole
blood (ie, 190 milliseconds). The T1 and T2 of the phantoms were as
follows: T1 = 182.3 milliseconds, T2 = 102.3 milliseconds for the
coarse phantom; T1 = 181.1 milliseconds, T2 = 77.1 milliseconds for
the medium phantom; T1 = 180.9 milliseconds, T2 = 73.4 milliseconds
for the fine phantom; and T1 = 180.1 milliseconds, T2 = 62.7 milliseconds for the superfine phantom. The estimated FWC% were 31.4% for
the coarse phantom, 27.8% for the medium phantom, 24.7% for the fine
phantom, and 24.3% for the superfine phantom.
IVIM Phantom Experiments
ADC and IVIM Parameters of the Phantoms at Various
Flow Rates
Figure 4 shows examples of the signal decay curve of the coarse
phantom seen on DW images; at no flow, the logarithm of the phantom
signal decays linearly as a function of the b value, and thus indicating
monoexponential decay. However, at a flow rate of 3 mL/min, the phantom signal curve shows an obvious biexponential decay, with a steeper
slope at a range of lower b values than that at a range of higher b values.
The ADC and IVIM parametric values of the phantoms are summarized in Table 1 and are displayed according to the various flow rates
in Figure 5. The ADC values gradually increased as increasing flow
rates and with statistically significant positive correlations (ρ = 0.659
to 0.969; P ≤ 0.002). There were some variations in Dslow with changing flow rates, although the correlation between the Dslow and the flow
rates was not consistent across different phantoms and fitting methods.
Interestingly, there was a tendency toward the highest Dslow value noted
at the flow rate of 1 mL/min among the various flow rates. The f values
consistently showed significant positive correlations with the flow rates
in all of the phantoms for both free fitting (ρ = 0.838 to 0.969;
P < 0.001) and segmented fitting (ρ = 0.938 to 0.969; P < 0.001). However, conflicting results were noted for Dfast between the 2 biexponential
fitting methods. The Dfast values obtained with segmented fitting have a
significantly positive correlation with the flow rate in all of the phantoms (ρ = 0.745 to 0.969; P < 0.001), whereas those obtained with free
fitting showed opposite results, that is, a significantly inverse correlation with the flow rate (ρ = −0.527 to −0.791; P ≤ 0.017). Of note, high
Dfast values (60.554 to 142.013 10−3 mm2/s) with large variations
were obtained with free fitting at no flow state. As a result, the product
f·Dfast for segmented fitting also had a strong positive correlation with
the flow rates in all of the phantoms (ρ = 0.931 to 0.969; P < 0.001),
while inconsistent results were noted for the flow rates for free fitting
across different phantoms.
When the parametric values obtained at a flow rate of 1 to 3 mL/min
were compared with FWC% of the phantoms, statistically significant
positive correlations with FWC% were noted for ADC (P = 0.695;
P < 0.001), f for both free fitting (ρ = 0.510; P < 0.001) and segmented
fitting (ρ = 0.545; P < 0.001), and f·Dfast for both free fitting (ρ = 0.481;
P < 0.001) and segmented fitting (ρ = 0.532; P < 0.001).
For ADC and all IVIM parameters for the coarse and medium
phantoms, a large standard deviation of the parameter values was noted
at the flow rate of 1 mL/min. When the biexponential fitting curves and
the fitted parametric values for each repeated scan of 4 IVIM phantoms
at the flow rate of 1 mL/min (Supplementary Figure 1, Supplemental
Digital Content 1, http://links.lww.com/RLI/A255 and Supplementary
Table 1, Supplemental Digital Content 2, http://links.lww.com/RLI/A256)
were reviewed, in contrast to the fine and superfine phantoms, signal
FIGURE 4. Diffusion-weighted, signal decay curves of the G-25 coarse phantom at no flow (A) and at a flow rate of 3 mL/min (B).
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TABLE 1. Summary of the ADC and the IVIM Parameters
Monoexponential
Phantoms
Coarse
Medium
Fine
Superfine
Free Biexponential
Segmented Biexponential
Flow rate
ADC
Dslow
f (%)
Dfast
Dslow
f (%)
Dfast
0
1
2
3
0
1
2
3
0
1
2
3
0
1
2
3
1.670 ± 0.103
2.018 ± 0.266
2.317 ± 0.039
2.439 ± 0.019
1.491 ± 0.013
1.771 ± 0.187
1.801 ± 0.010
1.777 ± 0.005
1.499 ± 0.010
1.732 ± 0.009
1.879 ± 0.005
1.905 ± 0.003
1.429 ± 0.012
1.607 ± 0.088
1.809 ± 0.048
1.885 ± 0.034
1.632 ± 0.098
1.841 ± 0.216
1.313 ± 0.012
1.323 ± 0.006
1.464 ± 0.011
1.629 ± 0.112
1.402 ± 0.013
1.302 ± 0.009
1.476 ± 0.011
1.630 ± 0.010
1.543 ± 0.003
1.396 ± 0.003
1.435 ± 0.010
1.565 ± 0.059
1.537 ± 0.029
1.409 ± 0.023
2.0 ± 0.3
8.2 ± 2.0
40.6 ± 0.8
40.1 ± 0.3
1.6 ± 0.1
7.0 ± 3.3
19.5 ± 0.3
22.4 ± 0.4
1.5 ± 0.1
5.3 ± 0.1
16.1 ± 0.1
23.4 ± 0.2
1.2 ± 0.2
3.1 ± 0.9
13.4 ± 1.6
22.2 ± 0.3
75.960 ± 22.654
16.462 ± 16.082
6.713 ± 0.059
9.895 ± 0.074
60.554 ± 29.561
13.560 ± 11.249
7.018 ± 0.061
8.157 ± 0.111
86.053 ± 59.923
13.155 ± 9.277
7.715 ± 0.017
7.785 ± 0.039
142.013 ± 121.750
59.461 ± 43.242
7.706 ± 0.121
7.774 ± 0.129
1.618 ± 0.094
1.804 ± 0.208
1.635 ± 0.021
1.478 ± 0.005
1.458 ± 0.011
1.622 ± 0.123
1.498 ± 0.009
1.407 ± 0.005
1.467 ± 0.011
1.617 ± 0.008
1.591 ± 0.003
1.516 ± 0.003
1.432 ± 0.014
1.556 ± 0.059
1.577 ± 0.024
1.521 ± 0.022
2.2 ± 0.4
8.5 ± 2.2
25.0 ± 0.4
33.4 ± 0.4
1.5 ± 0.1
6.3 ± 2.7
13.1 ± 0.1
16.5 ± 0.1
1.4 ± 0.1
5.1 ± 0.1
12.3 ± 0.1
16.8 ± 0.1
0.9 ± 0.1
2.5 ± 0.9
10.2 ± 1.2
15.7 ± 0.4
8.073 ± 0.540
8.623 ± 1.062
10.153 ± 0.048
12.014 ± 0.043
8.382 ± 0.487
8.665 ± 1.773
9.435 ± 0.036
10.801 ± 0.084
7.353 ± 0.183
8.043 ± 0.097
9.237 ± 0.054
10.556 ± 0.038
7.162 ± 0.848
7.641 ± 0.432
9.307 ± 0.090
10.561 ± 0.077
Data are presented as mean ± standard deviation.
ADC indicates apparent diffusion coefficient; IVIM, intravoxel incoherent motion; Dslow, slow diffusion coefficient; f, perfusion fraction; Dfast, fast diffusion coefficient.
fitting curves of the coarse and the medium phantoms revealed the
fitting results, which deemed to be outlier. When these results were
excluded, the standard deviation of the parametric values decreased,
especially for the medium phantom. However, the overall trend in parametric values including the tendency toward the highest Dslow value
at the flow rate of 1 mL/min did not change after excluding the
outlier results.
Fitting Error and Measurement Repeatability of the
Fitting Algorithms
Figure 6 displays normalized RMSE representing the fitting error for the 3 fitting methods at various flow rates. The normalized
RMSE was least for free fitting, followed by segmented fitting and
monoexponential fitting, and with a statistically significant difference
among the 3 fitting methods at all of the flow rates (P < 0.001). This indicates that the model curves obtained with free fitting best represent
the actual data. Of note, the fitting error for monoexponential fitting increases with an increasing flow rate, and thus indicating the inaccuracy
of the monoexponential model for explaining the actual biexponential
signal decay in the presence of flow within the phantoms.
The CV values representing measurement repeatability over 5
repeated scans are summarized in Table 2. The CV values for ADC
and Dslow with free and segmented fittings were similar to each other.
Overall, the CV values for the flow-related parameters, that is, f, Dfast,
and f·Dfast, were larger than those for ADC and Dslow. The CV values
for Dfast and f·Dfast for free fitting were obviously larger than those for
segmented fitting, and thus indicating poorer measurement repeatability
for those parameters with free fitting that those with segmented fitting.
DISCUSSION
Through the MR experiment using IVIM phantoms with various fractions of flowing water compartments at various flow rates,
we evaluated the flow effects on the ADC and IVIM parameters. As
expected, the ADC increased in proportional to the flow rates, which
reconfirmed that the ADC reflects both the diffusion and the perfusion
components. Unlike the theoretic definition of Dslow, which is the
coefficient of brownian motion and is not related with microvascular
flow,1,2 our results showed some variations in Dslow with changing
flow rates, and thus indicating the existence of flow effects on the diffusion signal intensity even at higher b values (200 ≤ b ≤ 800 s/mm2).
Of note, there was a tendency toward a higher Dslow at the lowest infusion flow rate (1 mL/min) compared with the Dslow values at no flow
and at higher infusion flow rates (2 and 3 mL/min). One possible explanation for these observations would be the contribution of slowflow velocities to the signal decay at higher b values. After infusion
of the solution into the phantoms, a wide range of flow velocities
may have been generated within the phantoms, and with slow velocities being more dominant at a slower infusion flow rate. As the IVIM
model separates 2 components of water motion, that is, diffusion versus perfusion, based on the magnitude of movement at a given time, a
very sluggish flow may have resulted in signal decay at higher b
values, and thus leading to alteration in Dslow. A previous phantom experiment using sponge phantoms also reported a variation of Dslow
with change in flow rates.17
As the fast diffusion coefficient, that is, Dfast, is defined by
blood velocity and the mean capillary segment length according to
the IVIM theory,1 this parameter was expected to be correlated with
the flow rates in our phantom experiments. The findings obtained with
segmented fitting were consistent with our expectations and confirmed that Dfast reflects flow velocity. However, the results of Dfast
obtained with free fitting were completely opposite to those obtained
with segmented fitting. We hypothesized that these unexpected findings may have resulted from the mathematical instability of the free
fitting method. Because of the high degree of freedom, simultaneous
fit for all 3 parameters in the biexponential model may lead to inaccurate and unreliable fitting results. This hypothesis is further supported
by our finding showing a poorer measurement repeatability of Dfast
with free fitting than with segmented fitting.
The perfusion fraction, that is, f, is defined as the fraction of
flowing water.1,2 Our results demonstrating a positive correlation between the FWC% of the phantoms and f proved the dependency of f
on the fraction of flowing water. However, our results also demonstrated a correlation between f and the flow rate, and thus suggesting
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This paper can be cited using the date of access and the unique DOI number which can be found in the footnotes.
Investigative Radiology • Volume 00, Number 00, Month 2016
IVIM Phantom Experiments
FIGURE 5. The ADC and IVIM parameters of the phantoms according to the various flow rates. The graphs display the ADC values (A), Dslow values
obtained with free fitting (B), Dslow values obtained with segmented fitting (C), f values obtained with free fitting (D), f values obtained with segmented
fitting (E), Dfast values obtained with free fitting (F), Dfast values obtained with segmented fitting (G), f·Dfast values obtained with free fitting (H),
and f·Dfast values obtained with segmented fitting (I) for the coarse, medium, fine, and superfine phantoms at various flow rates. Data are the mean
parameter values, and the error bars indicate the range of 1.96 standard deviation. For some data points, error bars were not expressed in graphs
due to the very small standard deviations of those data points. Figure 5 can be viewed online in color at www.investigativeradiology.com.
the influence of flow velocities on f in our phantoms. Though not yet
fully understood, there may be a few possible explanations for this
finding. First, IVIM-based analysis of DW imaging may not allow
for complete separation of the 2 components of perfusion, that is,
the fraction of flowing water and the flow velocity. As a result, both
of these components of perfusion may have influence on f. Another
possible explanation may be the contribution of fluid exchange between the static and flowing water compartments to f. Similarly to
transcapillary fluid exchange through capillary fenestrations in biologic tissue, water may have moved across the surface pores of gel
beads in our phantoms, and this water movement may be more
facilitated at a higher flow infusion rate. As transcapillary fluid exchange is not modeled as a specific parameter in the IVIM theory,
this intercompartmental fluid movement may have been incorporated
into f.
The product f·Dfast is a parameter reflecting the overall amount
of water flow or blood flow in biologic tissue.34 As expected, f·Dfast
obtained with segmented fitting was proportional to the flow rate.
However, f·Dfast obtained with free fitting showed inconsistent results across different phantoms, which is considered as a consequence of the aforementioned inaccurate estimation of Dfast using
free fitting.
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Investigative Radiology • Volume 00, Number 00, Month 2016
Lee et al
Regarding the 2 fitting methods for IVIM analysis, despite the
higher fitting accuracy, that is, smaller normalized RMSE value, of
free fitting compared with that of segmented fitting, segmented fitting
may be a stronger fitting method for IVIM analysis than free fitting in
terms of the accuracy and reliability, especially for estimating Dfast.
Our findings repeated the results of previous computer simulation
studies, which also demonstrated the higher accuracy and reliability
of the measurement of IVIM parameters using the segmented fitting
method than with the free fitting method.21,37,38
Our study does have some limitations. First, our 2-compartment
IVIM phantoms simplistically simulate biologic tissue, although they
do not completely account for the structural complexity of normal or
pathologic tissue. Therefore, our study did not evaluate other factors
such as cellularity,39,40 interstitial fluid pressure,34 and the various size
of capillary fenestration that potentially affect the ADC and IVIM parameters in biologic tissue. Unlike the gadoterate meglumine solution
that was used in our study to simulate blood perfusion, blood contains
blood cells and macromolecules such as albumin that may influence
water diffusion. Thus, our study results do not reflect the influence of
these blood contents on IVIM parameters. Second, considering the fact
that molecular diffusion is highly dependent on temperature,36 the difference in the temperature between our phantoms and human body may
have been a source of bias in our results. Finally, the results of our phantom experiment, which was performed in the ideal experimental condition, do not address the various sources of measurement error in in vivo
human imaging. Despite these limitations, our results obtained from the
phantom experiments of controllable perfusion-related factors can validate the IVIM theory and provide valuable information for the interpretation of each IVIM parameter.
In conclusion, the IVIM model allows for an approximate segmentation of molecular diffusion and perfusion, and with a minor contribution of the perfusion effect on Dslow. Perfusion parameters, that is, f
and Dfast, can provide a rough estimation of the flowing water fraction
FIGURE 6. A graph displaying the normalized root mean squared error
(RMSE) for monoexponential fitting, free biexponential fitting, and
segmented biexponential fitting at various flow rates. Data points
represent the mean normalized RMSE values, and the error bar indicates
the range of 1.96 standard deviation of normalized RMSE. For some
data points, error bars were not expressed in graphs due to the very
small standard deviations of those data points. Figure 6 can be viewed
online in color at www.investigativeradiology.com.
TABLE 2. CV Values Representing the Measurement Repeatability
of the ADC and the IVIM Parameters Over 5 Repeated Scans
Free Fitting
ADC
Dslow
f
Dfast
f·Dfast
Segmented Fitting
4.97%
4.57%
7.78%
112.31%
40.92%
4.36%
8.99%
6.59%
11.68%
CV indicates coefficient of variation; ADC, apparent diffusion coefficient;
IVIM, intravoxel incoherent motion; Dslow, slow diffusion coefficient; f, perfusion
fraction; Dfast, fast diffusion coefficient; f·Dfast, product of f and Dfast.
and flow velocity. For IVIM-based analysis of DW images, segmented
fitting may be a stronger method than free fitting.
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