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Impeded diffusion fraction model for multi-exponential DWI:  demonstration in kurtosis phantom and prostate cancer
Dariya Malyarenko1, Scott D Swanson1, and Thomas L Chenevert1
1University of Michigan, Ann Arbor, MI, United States

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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9. Swanson S, Malyarenko D, Chenevert T. Tunable diffusion kurtosis in lamellar vesicle suspensions toward development of quantitative phantom surrogate of tumor microenvironment. Proc. Intl Soc Mag Reson Med 2019, TP3632, Montreal CA.

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14. Carlin D, Orton MR, Collins D, Nandita M. deSouza NM. Probing Structure of Normal and Malignant Prostate Tissue Before and After Radiation Therapy With Luminal Water Fraction and Diffusion-Weighted MRI. J. Magn. Reson. Imaging 2019; 50:619–627

Figures

Figure 1: Water DWI scales from nanometer to millimeter: IDF model constraints. Left: nanoscale water coordination, IDF (Di<.03μm2/ms), near cell membrane (or macromolecules) effecting cellular diffusion, Dc. Middle: free diffusion, Df =3μm2/ms, in luminal space (blue) or large-cell (e.g., stromal fibroblast), and pseudo-diffusion in randomly oriented capillary (Dp>30μm2/ms). Right: partial volume contributions of cellular, Fc, bulk free, Ff, and perfused, Fp, tissue for typical clinical DWI pixel (2x2mm2). Equations summarize IDF formalism for measured DWI signal, Sb.

Figure 2: Example nonlinear curve-fit (dashed) for a single voxel DWI (asterisks) of three phantom vials (a) and PCa lesions (b). The corresponding vial and ROI labels are shown in the legends. The PCa label assignments for Gleason scores (G3 and G4) and zone locations (nTZ: normal transitional zone) are from Hurrel, et al.(JMI 2017)12. The fit DWI voxel fractions are summarized in Table 1.

Figure 3: Parametric maps for nonlinear fit fractions (Fig.1) of quantitative kurtosis phantom are shown in top row (left-to-right): Ffc, Ff, Fp, and IDF. Bottom row shows parametric maps derived from linear fits for Da(μm2/ms), Ka, eADC(b=2ms/μm2) and IDFL. Phantom material-vial labels are marked on Fp map. Common scale for all fraction-maps is shown on the right color-bar, while metric-specific color-bars accompany Da, Ka and eADC parametric maps. Except Da (units of μm2/ms), all map scales are dimensionless.

Figure 4: Linear fit parametric maps for example PCa DWI (using typical clinical b-value subset) are arranged in columns for (left-to-right): Da (μm2/ms), Ka, eADC and IDFL. Metric-specific color-bars show parameter scales. PCa maps show single slice image with right-left atrophy, normal transition zone (TZ, middle), and mixed G3/G4 tumor in lower peripheral zone (PZ), corresponding to histopathology labeling from Hurrel, et al.(JMI 2017).12

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)
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