Dariya Malyarenko^{1}, Scott D Swanson^{1}, Amaresha S Konar^{2}, Eve LoCastro^{2}, Ramesh Paudyal^{2}, Michael Z Liu^{3}, Sachin R Jambawalikar^{3}, Lawrence H Schwartz^{3}, Amita Shukla-Dave^{4}, and Thomas L Chenevert^{1}

Multi-center clinical trials utilizing quantitative diffusion kurtosis imaging (DKI) protocols require accurate, precise, and stable phantoms for validation of derived imaging metrics. This study examines the precision and reproducibility of isotropic (i)DKI parameters obtained from a phantom based on nanostructured vesicles that restrict diffusion and mimic tissue cellularity. Ten test-retest iDKI studies were performed on four scanners at three imaging centers over a six-month period. The tested prototype phantoms exhibited physiologically-relevant and highly-repeatable apparent diffusion and kurtosis parameters. Achieved precision was sufficient to characterize thermal and temporal stability trends to guide robust quantitative iDKI phantom production.

**Introduction**

**Methods**

The developed prototype iDKI phantom consisted of seven
sample vials immersed in water bath. Four restricted diffusion materials were tested
based on water solutions of cetyltrimethylammonium
bromide (CTAB) or behentriammonium chloride (BTAC) and cetearyl (CA) or decyl (DEC) alcohols, as well as
prolipid 161 (PL161). Three negative control, mono-exponential diffusion
samples included polyvinylpirrolidone
(PVP) solutions in water at 0, 20% and 40%. The constructed iDKI phantoms were scanned at three imaging centers on four MRI
scanners (two at 1.5T and 3T each) at ambient temperature over a period of six
months. Shared multi-*b* DKI scan protocol included 11 *b*-values (*b* = 0,
50, 100, 200, 500, 800, 1000, 1500, 2000, 2500, 3000s/mm^{2}), repeated
two times. All image and statistical analysis was
automated using MATLAB R2015b (Mathworks, Natick MA).

Seven circular ROIs (12mm diameter, 155 pixels) were
defined separately for the test-retest runs on DWI(*b*=0) for phantom tubes (Figure 1A) avoiding air-bubble susceptibility
artifacts. The parametric maps of apparent diffusion, *D*_{app} ,
and kurtosis, *K*_{app}, coefficients (Fig.1B) were derived using
linear-least-squares fit of voxel DWI log-signal to quadratic dependence on *b*-value^{4} (Fig.1C). To satisfy iDKI model^{4}
convergence and ensure SNR_{bmax}>2, maximum fit *b*-values were constrained to *b*_{max}=1500 s/mm^{2}
for CA-BTAC (V2), and *b*_{max}=2000
s/mm^{2} for water (V4) and PL-161 (V6) vials (Fig.1C, D). The
apparent scan temperature (*T*_{a}) was self-calibrated using
water (V4) ADC(*b*_{max}=1000 s/mm^{2}) based on Speedy-Angell
relation^{8}, and ranged between 19.5 and 25.5 (±1^{o}C).

Bland-Altman (BA) repeatability analysis was performed
for *D*_{app} and *K*_{app} across all
test-retest sample scans (pool of 70), excluding outliers outside 1.5 interquartile ranges above/below the upper/lower
quartiles. Sample-specific coefficient of variance (wCV) and
corresponding 95% confidence interval (CI) were assessed^{1} (including BA-outliers) for all test-retest
parameter values. Thermal and temporal phantom
stability was evaluated by inter-scan Pearson correlation, *R*, for the derived kurtosis parameters versus *T*_{a} and days from phantom manufacturing (using *R*-significance threshold of *p*_{R}<0.05). Temperature and scan date were independent covariates (*R*=0.13, *p*_{R}=0.66).

**Results and Discussion**

Four different chemical
designs tested for iDKI phantom materials in V1, V2, V6, and V7 (Figure 1) exhibited
restricted diffusion at high *b*-values
(>1000 s/mm^{2}), with DWI signals sustained above 20% of S_{0}
(Fig.1C) and *K*_{app} exceeding negative control noise-induced bias
(Fig.1B, *K*_{app}<0.1). All four tested iDKI materials allowed physiologically-relevant *K*_{app}
ranges 0.4-1.7(Table 1). Except for V7 (*K*_{app}) outlier, the achieved intra-scan iDKI parameter
precision (95% CI) was 1%-3.5% (Figure 2, Table 1) and independent of magnetic field
(SNR).

The inter-scan variability of *D*_{app} for the negative
control samples (not shown) was fully
explained by dependence on scanner ambient temperature (*R*>0.96, *p*_{R}<1e-7).
Observed kurtosis phantom *D*_{app} sensitivity to temperature
(2-3%/ ^{o}C) was higher than that of *K*_{app}
(Figure 3A,B). All iDKI phantom materials underwent initial parameter
stabilization period of 3-4 weeks following preparation (Fig.3C,D), coincidental
with evident sample degassing, when
parameters changed by 6-22%. The
parameter values for vesicular phase materials remained temporally stable post
initial stabilization period (Fig.3C,D).

The candidate materials
based on more-viscous multi-lamellar vesicle phase, exhibited either poor
temporal stability (V6:PL161) or notable dependence
on site storage and thermal equilibrium conditions (V1:DEC-CTAB). The kurtosis parameter values of CA-CTAB
vesicular material had limited *K*_{app}
precision (9%, Table 1) and large (22%) initial *D*_{app} stabilization change (Fig.3C(V7),
due to apparent formation of in-volume gas micro-bubbles), but provided good
thermal stability (no significant *T*_{a} dependence). CA-BTAC (V2) phantom has shown best
intra-scan repeatability and inter-scan stability with the lowest 6% change in
*D*_{app} during stabilization stage and moderate thermal dependence (2%/
^{o}C; *R*=0.87, *p*_{R}=1.2e-4).

This research was funded by National Institutes of Health Grants: U01CA166104, U01 CA211205, R01CA190299, P01CA085878 and P30 CA008748

**Disclosure: ** S.D.Swanson, D.I.Malyarenko and T.L.Chenevert are co-inventors on intellectual property assigned
to and managed by the University of Michigan for the technology underlying the manufacturing of the quantitative
diffusion kurtosis phantoms utilized in this manuscript.

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