Synopsis
Majority of current clinical
MRI protocols continue to use DWI qualitatively, as an indicator of impeded
diffusion evident from sustained signal at high b-values. Quantitative microenvironment description relying on
multi-exponential diffusion models is precluded by required prolonged multi-b acquisition and high resolution/SNR
not routinely achievable in clinical setting. This study presents a model based
on multi-compartment formalism to quantify impeded diffusion fraction (IDF, of
water coordinated by macromolecules) from conventional clinical DWI
acquisition. The physical origin for IDF is verified using two-compartment diffusion
kurtosis phantom, and application example is demonstrated for prostate cancer.
INTRODUCTION
Multi-exponential
diffusion observed for complex tumor microenvironment is typically modelled by non-Gaussian DWI signal decay1,2 and/or multiple
diffusion compartments2,3.
Wide clinical adoption of quantitative diffusion metrics derived from these
advanced diffusion models is hindered by necessity of prolonged multi-b acquisitions, as well as, intrinsic
dependence of derived parameters on acquired b-range2,4
and corresponding model constraints1-4. Here we present multi-compartment diffusion formalism
applicable to conventional clinical DWI acquisition to quantify impeded
diffusion fraction (IDF, for water coordinated around macromolecules) of
potential interest for wide range of clinical cancer imaging applications2,5,6.METHODS
IDF
model: The IDF formalism (Figure 1) assumes sub-mm
partial-volume contributions to signal intensity, Sb, in a typical clinical DWI voxel (~10mm3) from
free water, Ff, capillary
pseudo-diffusion, Fp, and extra/intra-cellular
water, Fc. Fixed diffusion rates in
free and perfused sub-volumes are determined, respectively, by water
temperature (Df = 3μm2/ms @37˚C)7 and ~5μm-capillary pressure gradient (Dp>30μm2/ms>>Df ).4 Sub-cellular Dc is approximated by a population average of water
self-diffusion (Dcf=FfcDf)
and collective-diffusion impeded/coordinated by macromolecules (Dci=IDF·Di, Di<.03μm2/ms<<Df)8. When Ef-->0 (b>1.5ms/μm2, Ffc<0.5),
Fig.1 DWI model can
be “linearized” to derive IDFL as (Eq.[1]): log(Sb/S0)=C1+C2·b;
Ffc=-C2/Df; Fc=exp(C1); IDFL=exp(C1)+C2/Df .
Phantom
and in vivo DWI: The previously
described kurtosis phantom9,
included materials (Figure 3)with restricted diffusion in micro-vesicles (V1:2.8μm, V2:1.6μm), as well as, mono-exponential (ME) diffusion polyvinylpirrolidone
(PVP) media (V3:20%PVP, V5:40%PVP).10 V1 and V2 provided model system with bulk, Ff, and vesicular, Ffc,
from nanoscale lamella water
compartments proportional to vesicle sizes V1:V2~1.8. V3 and V5
provided single nanoscale hydration-coordination compartment (<10nm, Ff=0)11, ME diffusion-rate scaling with solute
concentration (Dc(V3):Dc(V5)=1.3:0.6~2).
The phantom DWI were acquired using b=0,.05,.1,.2,.5,.8,1,1.5,2,2.5,3ms/μm2,
echo-time (TE) = 105ms, repetition-time (TR)=10s, voxel-size (VS)=1.7x1.7x5mm3. Phantom
Df=2.15μm2/s was
measured at room temperature for V4 (0%PVP) with bmax=1.5ms/μm2. The example
in vivo multi-b DWI data set for prostate cancer (PCa)12 was shared through The Cancer Imaging Archive
(TCIA) for as de-identified
DICOM. The PCa DWI were acquired12 using 15 b-values (b = 0,.05,.1,.2,.5,.8,1,1.5,2,2.5,3ms/mm2) with TE=68ms;
TR=4s; VS=1.5x1.5x4mm3. The PCa
tumor lesion labels were assigned from histopathology.12
Data
analysis: The IDF performance was compared to
conventional apparent diffusion coefficient (ADC) and isotropic kurtosis model
parameters: apparent diffusion, Da, and kurtosis, Ka.
The nonlinear IDF fit (Fig.1) was performed for b≥.1μs/mm2 of kurtosis phantom and PCa. All fit fractions were constrained between 0
and 1 (0 & .9 in vivo ). Unconstrained linear fits were performed for log(Sb/S0)of ME: log(FADC)-ADC·b; kurtosis: -Dab+Ka(Dab)2/6), and IDFL (Eq.[1].) Linear IDFL fit utilized subset of b-values typical of clinical DWI protocols2,5,6 (ms/μm2): 1 and
2 (PCa) and 1,1.5, and 2 (phantom). Conventional ME ADC fit used all .1<b<2ms/μm2 with
subsequent generation of eADC=exp(-bmaxADC)map. Data analysis utilized MATLAB R2015b curve-fitting toolboxes
(Mathworks, Natick MA).RESULTS AND DISCUSSION
Figure 2 illustrates good fidelity
of voxel-based IDF DWI model fit both for single (V3) and multi-compartment (V1,V2) phantom (Fig.2a) and wide-range of
PCa histology (Fig.2b). The relative fit
fractions (Fig.2, Table 1)
reflect physical phantom properties. Total fit free water Ff+Ffc ratios (V2:V1~1.8;
V3:V5~2) and IDF ratios (V1:V2~1.6; V5:V3~1.8) scale with vesicle size (volume/surface) and PVP
concentration reflecting coordinated water fraction. PCa fit fractions (Fig.2, Table 1) are decreasing with increasing malignancy,
consistent with increasing tissue density and macromolecule crowding. Among fit-fractions, IDF provides highest contrast between G3 and G4
cancers (11%), as well as,
cancer versus normal (40%).
Figure 3 IDF map effectively eliminates
free water (Ff+Ffc~1) and linear IDFL≈IDF, with
finite positive bias for Ff+Ffc>.5 (e.g., V2). Da of ME
diffusion materials (V3,V5) scales with Ffc (inverse PVP
concentration), while multi-exponential (V1,V2) show relative Da and Ka values scaling with Ff and inverse
Ffc (and IDF).
Relative Da contrast (V2:V1~1.7)
is closer reflection of physical characteristics for phantom compartments (V1:V2
size) than Ka (V2:V1~1.2). IDF
contrast is qualitatively similar to eADC, but b-independent and on linear-scale (Fig.3, color-bars).
Similar to phantom results, prostate IDFL(Figure 4) effectively filters-off free (luminal) water contribution
from large (sub-mm) secretory ducts and blood vessels confounding Da map in transition
zone (TZ) and prostate base. It also
shows better contrast between peripheral zone (PZ) atrophy (low IDF) and nTZ
tissue compared to Da, Ka, or eADC. For the G3/G4 lesion (bright on
eADC), IDFL evidently captures complementary5,13 Ka~1/Da contrast information, visually most similar to eADC, but on a linear scale.
In practice, the two b-values between 1<b<2
ms/μm2 would be optimal for IDFL
evaluation in tissue with Ffc<.5 (Dc<1.5μm2/ms, typical of dense tumor6,12). In this range,
conventional ME model ADC~DC=Ffc·Df,
is consistent with reported ADC correlation to histopathology fractions3,12,13. IDF contrast
could be particularly useful for characterization of glandular malignancies
(e.g., prostate, breast, pancreas) obstructing secretory duct lumen (reducing Ff)3,14 and increasing macromolecular crowding (reducing
Ffc)6,12. The
linearized IDF solution is directly applicable for current clinical oncology DWI
protocols, allowing for retrospective evaluation of previously acquired multi-b DWI
data.CONCLUSION
Phantom IDF scales linearly with increasing size of restricted microscale
compartment and concentration of nanoscale macromolecular aggregates. Prostate
IDF contrast eliminates capillary
and luminal water background and scales with tissue density. Measured
as counterpart of free water diffusion, IDF allows organ-independent b-range optimization for cancer DWI.Acknowledgements
Funding support from National Institutes of Health
Grants: U01CA166104, U24CA237683, P01CA085878 and P30 CA008748.
We thank our Quantitative Imaging Network (QIN) collaborator, Dr. Peter
LaViolette (Medical College of Wisconsin) for providing access to multi-b DWI DICOM for histology-confirmed prostate cancer through The Cancer Imaging Archive (TCIA).References
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