Introduction
Recent multicenter oncology trials have evaluated quantitative diffusionweighted imaging (DWI) as a radiological marker of tumor malignancy and response to therapy (1–3). The underlying physical principle for this technology is that oncogenic processes and therapeutic interventions induce regional changes in cellularity of the imaged tissue that can be detected and quantified by mean (isotropic) diffusivity (4, 5). In clinical applications outside of the brain, tissues with low fractional anisotropy are typically assessed by combining 3 orthogonal DWI acquisitions as a function of diffusion gradient weighting, quantified by a bvalue to provide a mean diffusivity measure of the tissue. The optimal number of acquired bvalues depends on the diffusion model utilized to appropriately characterize tissue diffusivity (6–8).
The default measure of mean diffusivity in current clinical trials is the apparent diffusion coefficient (ADC), which assumes monoexponential signal decay with increasing bvalues (4, 9–11). Advanced body oncology trials are designed to allow for multiexponential DWI signal decay, either because of true multicomponent diffusion or perfusion effects, such as intravoxel incoherent motion (IVIM) (7, 8, 12, 13). For IVIM, the typically derived metrics include perfusionsuppressed ADC values and perfusion fraction. Characterization and minimization of technical errors in diffusion metrics is imperative for standardizing DWI measurements so that meaningful and consistent clinical trial results can be obtained to further establish the diagnostic and clinical response value of DWIderived biomarkers (14, 15).
Recent multisite DWI phantom studies (16–18) have revealed the major sources of technical errors that confounded ADC metrics originating from diffusion weighting (DW) bias caused by spatially dependent deviations from the nominal bvalue for offcenter anatomic locations. In contrast, excellent reproducibility was demonstrated for ADC measurements acquired at the magnet isocenter (16–18) using a temperaturecontrolled (icewater) phantom (variability <3%). Multiinstitutional phantom studies conducted across the National Institute of Healthfounded Quantitative Imaging Network (19) confirmed that gradient nonlinearity (GNL) is a main contributor to spatial DW bias and variability in offcenter ADC measurements across clinical magnetic resonance imaging (MRI) platforms (17). This platformdependent bias was shown to stem from nonuniform DW that resulted from GNL (20–22) and ranged from −55% to +25% depending on the anatomic location and gradient system design (17). In fact, detected GNL bias accounted for ∼95% of the observed absolute ADC error on a single MRI platform and resulted in an average 20% variation across MRI scanners.
Our previous work has shown that the bulk of the ADC error resulting from spatial GNL bias could be effectively removed for monoexponential diffusion medium of arbitrary anisotropy using 3 orthogonal DWI measurements (21, 23). The proposed ADC correction framework was based on the rotation of the system nonlinearity tensor into the acquired DWI frame, where system GNL tensor characteristics were obtained empirically. In this work, the DW bias correction was tested for IVIM diffusion in (nearly isotropic) renal tissue on a clinical scanner with GNL characteristics provided by the vendor (24, 25). The theoretically predicted DW bias contribution resulting from GNL was validated by the ADC measurements on an isotropic flood phantom. The effect of GNL bias correction via the elimination of error from either DWI intensities or bvalues was compared for the perfusionsuppressed ADC and perfusion fraction.
Methodology
The experimental design for this study was tailored to illustrate the feasibility of GNL correction in the presence of IVIM. The renal tissue was chosen as a model IVIM medium (24, 25) for its known high (∼20%) perfusion fraction, relatively low anisotropy (fractional anisotropy <0.3), and because we could select substantial tissue regions of interest (ROIs) with reasonably uniform parametric maps. A large isotropic gel phantom was prepared to empirically confirm spatial GNL characteristics of the scanner within the imaged (torsosized) volume. The DWI acquisition was optimized to improve the signaltonoise ratio such that the random measurement errors (DWI SD) in the studied bvalue range were lower than the predicted systematic GNL bias at a chosen spatial location. All acquired data were stored in Digital Image Communication in Medicine (DICOM) format (26), and data analysis was automated using routines developed in MATLAB 7 (MathWorks, Natick, MA).
DWI of GelFlood Phantom
An isotropic floodDWI phantom was prepared in a large 300 × 380 × 150mm^{3} container using 1.8% weight gelatin (Gelita USA, Sioux City, IA) with 12.5 L of tap water. Coronal DWI scans of the phantom were acquired on a 3T Philips (Best, the Netherlands) Ingenia MRI scanner with large field of view (FOV = 480 × 480 mm^{2}) using three b values (0, 500, 1000), with DWI directions along primary magnet axis (LAB) and 8 excitations per b value. Other relevant scan parameters were as follows: retention time/echo time (TR/TE) = 4.0/0.066 s; 21 slices; slice thickness/gap = 4/1 mm; inplane resolution = 5 × 5 mm; and pixel bandwidth = 2686 Hz. The acquired DWI had a signaltonoise ratio >20 for the highest b (1000).
DWI Acquisition and IVIM Analysis for Renal Tissue
Sagittal DWI scans of an IVIM renal tissue (volunteer consented according to local institutional review board guidelines) were performed on a 3T Philips Ingenia MRI scanner near the isocenter and offset superiorly by 120 mm using a 32channel torso phasearray coil. Five b values (0, 100, 200, 500, and 800) were acquired for 2 sets of orthogonal DWI directions: U(″LAB″)=[(1, 0, 0)T, (0, 1, 0)T, (0, 0, 1)T]; and U(″OVP″)=[(−13, −23,−23)T, (23, −23, 13)T, (23, 13, −23)T]. Two distinct gradient direction scenarios were used to empirically test for GNL bias dependence on DWI orientation both for individual directions and the trace. The offsets and angles for sagittal FOV = 375 × 375 mm^{2} were fixed to 0, whereas the table with the volunteer was physically moved from SI∼0 to SI∼120 mm, keeping the initial landmark and ignoring table position. Other acquisition parameters were as follows: TR = 4.0 s; TE (LAB/OVP) = 0.0937/0.08 s; 11 slices; slice thickness = 5.5 mm; inplane resolution = 1.67 mm; and pixel bandwidth = 2583 Hz. Eight freebreathing singleshot echoplanar imaging (SSEPI) dynamics were acquired and stored individually and then coregistered for each slice using homebuilt 2D fullaffine transformation (allowing inplane scale, shear, rotation, and translation) before averaging for each DWI direction and bvalue. Coregistration efficiency (for removing the breathing artifact) was visually evaluated from difference images with respect to b = 0 with and without coregistration.
The perfusionsuppressed ADC component in the presence of IVIM was obtained as a slope of monoexponential fit for b > 100 values (24, 25) of each pixel for logtraceDWI (directionaverage image) intensity ratios relative to the b = 0 image. The perfusion fraction was derived as an intercept of the linear fit. The original spatial ADC bias error offcenter (SI∼120 mm) was measured as the deviation from the “true” reference ADC at SI∼0 mm for the same anatomy. The anatomic slice with the most uniform parametric map close to RL∼0 mm was selected as a reference. The slice ROI was defined by manually tracing the kidney border on the T_{2}weighted (b = 0) image. The ROI edges were defined to exclude edge artifacts that resulted from susceptibility gradients near phantomcontainer walls or residual misregistration for kidney anatomy. The ADC histograms were binned with the step of 0.01 between 0.5 and 3.5 (×10^{−3} mm^{2}/s), while for perfusion fraction histograms, a bin size of 0.005 between 0.05 and 0.7 was used. All histograms were smoothed with a 3point movingaverage. The ROI histogram statistics were characterized by mean and SD.
Systematic Bias Prediction and Correction
System nonlinearity tensor L(r) (20) was constructed using gradient design (spherical harmonics) coefficients provided by the vendor. The Frobenius norm of the biased b′k=LbkLT matrix normalized to the nominal b value at the isocenter bn=‖b(r0)‖ was used to generate (static) bias corrector maps for each (uk) gradient direction Ck=1bn‖Lbk(r0)LT‖=‖LukukTLT‖ (21) on a Cartesian grid sampled every 5 mm within a 360mm FOV. As defined, the correction factors for each pixel were dimensionless and positive, with an allowed range between 0 and 1 for negative GNL and between 1 and 2 for positive GNL (Ck=1 at the isocenter, where GNL was absent). For experimental data, assuming a nearly isotropic medium, a single directionaverage corrector map Cav was constructed for each orthogonal DWI Uschema (LAB and OVP) and interpolated according to DICOM header information on imaged volume and resolution. Because of the cylindrical symmetry of the GNL model for the horizontalbore system, the predicted corrector maps were symmetric around the SI along the AP vs the RL direction (coronal vs sagittal slices).
The corrector was then applied pixelbypixel to yield corrected DWI intensities or b maps to derive an unbiased ADC (21, 23). A corrected ADC map was derived from pixelbypixel correction (21, 23) of traceDWI image intensities (Scorrection) Sbc=S0Cav(r)−1Cav(r)Sb′1Cav(r) or of bmaps (bcorrection) bc(r)=bnCav(r). (Here, image intensities acquired without DW were denoted as S_{0}, whereas S_{b′} referred to biased DWI intensities.) The effect of correction on logintensity dependence on the bvalue (utilized to derive ADC and perfusion fraction) was different for S versus b correction. Numerically, for each spatial location, Scorrection scaled biased logintensities by inverse correction factor (with unaltered bvalues) versus bcorrection resulting in a direct multiplication of nominal bvalues by correction factors (with preserved intensities). Note also that the bcorrection for the isotropic medium was equivalent to the direct correction of the “measured” ADC map by ADCc(r)=ADC(r)/Cav(r). The correction efficiency was assessed by comparing histogram statistics (mean and SD) before and after correction for the reference ROI. The effect of both correction scenarios on the slope and intercept of linear regression fit was directly visualized for the mean ROI intensities as a function of b > 100.
Results
Figure 1 illustrates how the nonuniformity in DW (bvalue) is directly reflected in the measured ADC map for a coronal slice through the isotropic gel phantom (Figure 1A). The apparent b value is symmetrically lower SI (negative GNL) and higher RL (positive GNL) than nominal (isocenter), leading to correspondingly under or overestimated ADC values (Figure 1A). The colorbar scale in Figure 1A (right) reports on the observed bvalue bias range between 0.8 and 1.2 with respect to the nominal value at the isocenter. Within a relatively large ROI (220 × 240 mm^{2}), such nonuniformity resulted in artificial broadening of the ADC histogram that was accompanied by a shift of the mean ADC value (Figure 1B). Knowledge of specific gradient design information allowed for the deterministic prediction of GNL bias and effective removal of nonuniformity in the ADC map (Figure 1C). Effective bias removal was demonstrated by narrowing the ADC histogram down to a measurement uncertainty of ±2.5% and shifting its mean to the isocenter reference value (Figure 1B). The observed ADC bias (Figure 1A), normalized to the isocenter reference value, agreed with the predicted by GNL model for the scanner (see Methodology), with ROI pixelbypixel difference falling within 3%. As expected for the cylindrically symmetric GNL model, the bias measured along the SI for coronal phantom orientation (Figure 1A) also agreed with that predicted for the sagittal orientation (Figure 2). Furthermore, the predicted average corrector maps (assuming isotropic medium) were identical for OVP versus LAB DWI orientations.
Figure 1.
(A) Measured ADC nonuniformity (left) for a coronal slice (AP offset of 70 mm) through a floodphantom is corrected (C) using the vendorprovided GNL model. (B) The wide (2SD∼20%) histogram bias is reduced by correction down to the measurement error (2SD∼5%) in (C). The DWbias color bar in (A) and topaxis scale in (B) reflect the relative deviation from the nominal bvalue at the isocenter (r_{0}). In the absence of GNL bias, this ratio is a unity (b(r)=b(r_{0})).
Figure 2.
(A) Predicted directionaverage (LAB or OVP) DWbias maps across kidney ROIs at scanned SI offsets (z = 0 and 120 mm). The same bias is predicted for LAB and OVP DWI orientations. The gray scale bar shows the range of predicted DW bias with respect to the nominal bvalue. Scale value of 1 corresponds to absent GNL bias (uniform DW) predicted for the z = 0 mm reference. (B) Predicted width of DWbias histogram, colorcoded as their corresponding ROIs in (A), changes depending on scan position consistent with the phantom measurements in Figure 1.
Figure 2A illustrates DW bias expected across kidney ROIs at 2 locations measured in this work. The corresponding bias histograms in Figure 2B show how steep GNL along the SI near z = 120 mm results in the broad and shifted ROI histogram compared to the reference at z = 0 mm. Figure 3, A and D, illustrate that the observed bias for the perfusionsuppressed ADC maps at z = 120 mm was consistent with the one predicted from the system GNL model (Figure 2) and virtually independent of DWI direction schema U(″LAB″ or ″OVP″) as expected for the nearly isotropic medium. The strong nonuniform bias gradient along the SI was evident across the kidney parametric map at the z = 120mm superior offset location (Figure 3, A and D). Similar to the phantom data in Figure 1C, the uniformity of the kidney ADC map was nominally restored after GNL bcorrection (Figure 3, C and F), closely reproducing the ADC of the reference parametric maps acquired near the isocenter (RL∼0 mm) (Figure 3, B and E).
Figure 3.
Observation (A and D) and bcorrection (C and F) of GNL bias in perfusionsuppressed ADC for the parametric maps of the uniform sagittal slice (RL∼0 mm) through the kidney at the 120mm superior offset (A, D, C, and F) versus isocenter references (B and E) for U(″LAB″) (A–C) and U(″OVP″) (D–F) DWI. The common scale of the quantitative parametric ADC maps is given by the color bar.
The efficiency of bias correction is further quantified by the changes observed for ADC histograms of kidney ROIs in Figure 4A. ADC histograms for all ROI pixels of a uniform renal tissue slice were narrower in the vicinity of the isocenter (green) compared with the superior offset for both LAB and OVP DWI orientations (solid and dotted magenta). The steep DW nonuniformity bias across kidney ROIs observed in Figure 3, A and D, resulted in additional (nonbiological) broadening of the corresponding ADC histograms (Figure 4A, solid and dotted magenta). The mean ADC value for the reference histogram (Figure 4A, green) was ∼20% higher than mean ADCs at z = 120 mm either for OVP (dotted magenta) or LAB (solid magenta) DWI schema. With a similar initial bias resulting from GNL and identical corrector maps (Figure 2A), the effect of correction was similar independent of DWI orientation. The example of corrected ROI histograms for LAB DWI is shown in Figure 4A. The original mean bias of 20% (Figure 4, solid magenta) for ADC (z = 120 mm) was reduced to <2.5% after correcting the GNL bias either in DWI intensities (Scorrection; Figure 4A, orange) or in bvalues (bcorrection; Figure 4A, blue), nearly matching the unbiased reference histogram (green) for ADC (z = 0 mm). The bias correction by DWI intensity route apparently slightly overcorrected the ADC histogram, shifting it to somewhat higher values (orange trace) relative to the reference (green trace).
Figure 4.
(A) Perfusionsuppressed ADC histograms are shown for kidney ROIs corresponding to Figure 3A (solid magenta, LAB DWI) and D (dotted magenta, OVP DWI) before correction, and to Figure 3B (green histogram) and C (blue histogram) for the reference (isocenter) map and bvaluecorrected map of LAB DWI, respectively. The orange trace in (A) corresponds to a histogram of the corrected ADC map (not shown) achieved via Scorrection for LAB DWI intensity. (B) Mean ROI logintensity signal (symbols) and fit (lines) are plotted as a function of the bvalue for LAB DWI at the isocenter (green), before (magenta) and after bias correction via b values (blue pluses), and DWI intensities (orange crosses). Note the horizontal shift of data points with respect to measured (biased, magenta) signal after bcorrection vs vertical shift after Scorrection. The error bar of the mean reference signal at the highest bvalue (green) reflects the 2SD of the corresponding logintensity within the kidney slice ROI. The figure labels are colorcoded to mark correspondence between the histogram ROIs in (A) and mean data values shown in (B).
The slope error of linear fit for ROImean logintensity dependence on the bvalue shown in Figure 4B (magenta) is effectively corrected either for bvalues (blue pluses) or DWI signal Sintensities (orange crosses). As expected from the corresponding correction formalism, bcorrection scaled biased data points (magenta circles) horizontally along the baxis, whereas Scorrection scaled them vertically. Because bias is a multiplicative factor for bcorrection, the observed difference between the biased and corrected data location along the baxis was larger for higher bvalues. Both correction methods brought corrected data closer to the reference fit line (Figure 4B, green). The correction efficiency was similar by either method within measurement and fit uncertainty, as is evident from the proximity of the experimental and corrected data points to the fit lines. Although the original GNL bias and bias correction have a noticeable effect on the slope (ADC = 1.9 vs 1.5 × 10^{−3} mm^{2}/s) of the fit lines in Figure 4B, the effect on their intercept (∼0.23, perfusion fraction) was barely detectible. An insignificant change (<2%) resulting from the bias for the IVIM perfusion fraction (absolute intercept value ∼0.2) was likewise confirmed from observing the corresponding parametric maps and their histograms (without correction) in Figure 5. Both offset (Figure 5A) and reference (Figure 5C) parametric perfusion maps produce nominally overlapping histograms (Figure 5D, magenta and green) without GNL correction. For completeness, we confirmed that, like bcorrection (applied directly to ADC maps), Scorrection (Figure 5B) did not introduce significant sporadic bias into the perfusion maps and corresponding ROI histograms (Figure 5D).
Figure 5.
IVIM perfusion fraction maps for sagittal slice (RL∼0 mm) acquired with OVP DWI at a superior offset of 120 mm (A) and obtained after Scorrection (B) show negligible bias compared to the isocenter reference (C). Similar results are observed for their corresponding ROI histograms in (D). The figure labels are colorcoded to mark correspondence between the histogram ROIs in (A–C).
Discussion
The purpose of this study was to illustrate that GNL bias correction is feasible for quantitative diffusion metrics of the IVIM model. Although the current study design was tailored to emphasize the effect of GNL bias, similar effects may be observed routinely for large FOVs typical of body DWI applications. Consistent with previous findings (16–18), GNL causes nonuniform DW that follows a spatially static pattern for a given system independent of the nominal bvalue and is readily predictable from the deterministic gradient system design and applied DWI directions (20–22). For the isotropic medium, directionaverage bias is independent of the DWI schema. This further simplifies deriving spatial DW correction maps. In the multisite trial setting, the static GNL corrector maps would need to be calculated once for a specific system model and could then be applied to any acquired DWI scan according to its DICOM geometry.
In this study, DW bias observed across a sagittal slice through the kidney followed the trends predicted from the system gradient design for both LAB and OVP DWI orientations. The spatially dependent bias resulted in significant (∼20%) nonuniformity error for the perfusionsuppressed ADC map offcenter (z = 120 mm) compared to the same anatomy close to the isocenter. DW nonuniformity as a result of GNL shifted and broadened kidney ADC histograms. For multisite clinical trials, such system and location specific errors would likely lead to significant technical variability that would confound a populationwide analysis of predictive power for obtained ADC metrics if left uncorrected (14, 15). The observed bias was independent of the nominal bvalue and the DWI direction schema and mainly affected the ADC derived from the slope of the linear fit for the perfusionsuppressed component of the IVIM diffusion. As expected, the IVIM perfusion fraction derived from the fit intercept was immune to the bvalue bias. DW bias correctors reduced the ADC nonuniformity and mean error to <3% for diffusion in the presence of perfusion. Similar to anisotropic monoexponential medium (23), the same correction efficiency (within measurement and fit uncertainty) was achieved for ADC extracted using either corrected trace DWI intensities or corrected bvalues. These corrections did not introduce sporadic bias into the perfusion fraction maps.
Although the described correction removes the errors related to GNLinduced bias in DW, it does not address other sources of nonGNL bias error in quantitative diffusion metrics or geometric distortions. Although these bias sources are presumed to have a minor effect on bvalues for most horizontalbore systems (17, 18, 22), including the scanner in this study, they may need to be treated differently depending on severity when observed for a specific scanner model. To reduce the variability of quantitative IVIM diffusion metrics derived in a multisite clinical trial setting, the systemspecific correction of GNL bias is best performed for perfusionsuppressed ADC maps before a combined populationwide analysis.
In conclusion, significant DW nonuniformity bias at offcenter locations results both in shifting and broadening of perfusionsuppressed ADC histograms for renal tissue. For this wellperfused, nearly isotropic tissue, ADC bias for offcenter measurements could be effectively removed by applying directionaverage DW bias correctors based on known gradient design specifications. Comparable performance was achieved using corrected DWIs, bvalues, or ADC maps independent of DWI orientation. No significant bias impact was observed for IVIM perfusion fraction with or without correction. The demonstrated systemspecific correction of GNL bias in DW for offcenter anatomy is feasible for clinical trials that utilize quantitative parametric maps based on the IVIM diffusion model.
Acknowledgments
This research was supported by National Institutes of Health grants U01CA166104, P01CA085878, and R01CA190299.
Conflicts of Interest: D.I. Malyarenko, T.L. Chenevert, and B.D. Ross are coinventors on intellectual property assigned to and managed by the University of Michigan for the technology underlying the DW bias correction described in this article.
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Research Articles
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TOMOGRAPHY, December 2015, Volume 1, Issue 2: 145151
DOI: 10.18383/j.tom.2015.00160
Correction of Gradient Nonlinearity Bias in Quantitative Diffusion Parameters of Renal Tissue with Intravoxel Incoherent Motion
Dariya I. Malyarenko^{1}, Yuxi Pang^{1}, Julien Senegas^{2}, Marko K. Ivancevic^{3}, Brian D. Ross^{1}, Thomas L. Chenevert^{1}
Abstract
Spatially nonuniform diffusion weighting bias as a result of gradient nonlinearity (GNL) causes substantial errors in apparent diffusion coefficient (ADC) maps for anatomical regions imaged distant from the magnet isocenter. Our previously described approach effectively removed spatial ADC bias from 3 orthogonal diffusionweighted imaging (DWI) measurements for monoexponential media of arbitrary anisotropy. This work evaluates correction feasibility and performance for quantitative diffusion parameters of the 2component intravoxel incoherent motion (IVIM) model for wellperfused and nearly isotropic renal tissue. Sagittal kidney DWI scans of a volunteer were performed on a clinical 3T magnetic resonance imaging scanner near isocenter and offset superiorly. Spatially nonuniform diffusion weighting caused by GNL resulted both in shifting and broadening of perfusionsuppressed ADC histograms for offcenter DWI relative to unbiased measurements close to the isocenter. Directionaverage diffusion weighting bias correctors were computed based on the known gradient design provided by the vendor. The computed bias maps were empirically confirmed by coronal DWI measurements for an isotropic gelflood phantom. Both phantom and renal tissue ADC bias for offcenter measurements was effectively removed by applying precomputed 3D correction maps. Comparable ADC accuracy was achieved for corrections of both b maps and DWI intensities in the presence of IVIM perfusion. No significant bias impact was observed for the IVIM perfusion fraction.
Introduction
Recent multicenter oncology trials have evaluated quantitative diffusionweighted imaging (DWI) as a radiological marker of tumor malignancy and response to therapy (1–3). The underlying physical principle for this technology is that oncogenic processes and therapeutic interventions induce regional changes in cellularity of the imaged tissue that can be detected and quantified by mean (isotropic) diffusivity (4, 5). In clinical applications outside of the brain, tissues with low fractional anisotropy are typically assessed by combining 3 orthogonal DWI acquisitions as a function of diffusion gradient weighting, quantified by a bvalue to provide a mean diffusivity measure of the tissue. The optimal number of acquired bvalues depends on the diffusion model utilized to appropriately characterize tissue diffusivity (6–8).
The default measure of mean diffusivity in current clinical trials is the apparent diffusion coefficient (ADC), which assumes monoexponential signal decay with increasing bvalues (4, 9–11). Advanced body oncology trials are designed to allow for multiexponential DWI signal decay, either because of true multicomponent diffusion or perfusion effects, such as intravoxel incoherent motion (IVIM) (7, 8, 12, 13). For IVIM, the typically derived metrics include perfusionsuppressed ADC values and perfusion fraction. Characterization and minimization of technical errors in diffusion metrics is imperative for standardizing DWI measurements so that meaningful and consistent clinical trial results can be obtained to further establish the diagnostic and clinical response value of DWIderived biomarkers (14, 15).
Recent multisite DWI phantom studies (16–18) have revealed the major sources of technical errors that confounded ADC metrics originating from diffusion weighting (DW) bias caused by spatially dependent deviations from the nominal bvalue for offcenter anatomic locations. In contrast, excellent reproducibility was demonstrated for ADC measurements acquired at the magnet isocenter (16–18) using a temperaturecontrolled (icewater) phantom (variability <3%). Multiinstitutional phantom studies conducted across the National Institute of Healthfounded Quantitative Imaging Network (19) confirmed that gradient nonlinearity (GNL) is a main contributor to spatial DW bias and variability in offcenter ADC measurements across clinical magnetic resonance imaging (MRI) platforms (17). This platformdependent bias was shown to stem from nonuniform DW that resulted from GNL (20–22) and ranged from −55% to +25% depending on the anatomic location and gradient system design (17). In fact, detected GNL bias accounted for ∼95% of the observed absolute ADC error on a single MRI platform and resulted in an average 20% variation across MRI scanners.
Our previous work has shown that the bulk of the ADC error resulting from spatial GNL bias could be effectively removed for monoexponential diffusion medium of arbitrary anisotropy using 3 orthogonal DWI measurements (21, 23). The proposed ADC correction framework was based on the rotation of the system nonlinearity tensor into the acquired DWI frame, where system GNL tensor characteristics were obtained empirically. In this work, the DW bias correction was tested for IVIM diffusion in (nearly isotropic) renal tissue on a clinical scanner with GNL characteristics provided by the vendor (24, 25). The theoretically predicted DW bias contribution resulting from GNL was validated by the ADC measurements on an isotropic flood phantom. The effect of GNL bias correction via the elimination of error from either DWI intensities or bvalues was compared for the perfusionsuppressed ADC and perfusion fraction.
Methodology
The experimental design for this study was tailored to illustrate the feasibility of GNL correction in the presence of IVIM. The renal tissue was chosen as a model IVIM medium (24, 25) for its known high (∼20%) perfusion fraction, relatively low anisotropy (fractional anisotropy <0.3), and because we could select substantial tissue regions of interest (ROIs) with reasonably uniform parametric maps. A large isotropic gel phantom was prepared to empirically confirm spatial GNL characteristics of the scanner within the imaged (torsosized) volume. The DWI acquisition was optimized to improve the signaltonoise ratio such that the random measurement errors (DWI SD) in the studied bvalue range were lower than the predicted systematic GNL bias at a chosen spatial location. All acquired data were stored in Digital Image Communication in Medicine (DICOM) format (26), and data analysis was automated using routines developed in MATLAB 7 (MathWorks, Natick, MA).
DWI of GelFlood Phantom
An isotropic floodDWI phantom was prepared in a large 300 × 380 × 150mm^{3} container using 1.8% weight gelatin (Gelita USA, Sioux City, IA) with 12.5 L of tap water. Coronal DWI scans of the phantom were acquired on a 3T Philips (Best, the Netherlands) Ingenia MRI scanner with large field of view (FOV = 480 × 480 mm^{2}) using three b values (0, 500, 1000), with DWI directions along primary magnet axis (LAB) and 8 excitations per b value. Other relevant scan parameters were as follows: retention time/echo time (TR/TE) = 4.0/0.066 s; 21 slices; slice thickness/gap = 4/1 mm; inplane resolution = 5 × 5 mm; and pixel bandwidth = 2686 Hz. The acquired DWI had a signaltonoise ratio >20 for the highest b (1000).
DWI Acquisition and IVIM Analysis for Renal Tissue
Sagittal DWI scans of an IVIM renal tissue (volunteer consented according to local institutional review board guidelines) were performed on a 3T Philips Ingenia MRI scanner near the isocenter and offset superiorly by 120 mm using a 32channel torso phasearray coil. Five b values (0, 100, 200, 500, and 800) were acquired for 2 sets of orthogonal DWI directions:U ( ″LAB″ ) = [ ( 1 , 0 , 0 ) T , ( 0 , 1 , 0 ) T , ( 0 , 0 , 1 ) T ] ; and U ( ″OVP″ ) = [ ( − 1 3 , − 2 3 , − 2 3 ) T , ( 2 3 , − 2 3 , 1 3 ) T , ( 2 3 , 1 3 , − 2 3 ) T ] . Two distinct gradient direction scenarios were used to empirically test for GNL bias dependence on DWI orientation both for individual directions and the trace. The offsets and angles for sagittal FOV = 375 × 375 mm^{2} were fixed to 0, whereas the table with the volunteer was physically moved from SI∼0 to SI∼120 mm, keeping the initial landmark and ignoring table position. Other acquisition parameters were as follows: TR = 4.0 s; TE (LAB/OVP) = 0.0937/0.08 s; 11 slices; slice thickness = 5.5 mm; inplane resolution = 1.67 mm; and pixel bandwidth = 2583 Hz. Eight freebreathing singleshot echoplanar imaging (SSEPI) dynamics were acquired and stored individually and then coregistered for each slice using homebuilt 2D fullaffine transformation (allowing inplane scale, shear, rotation, and translation) before averaging for each DWI direction and bvalue. Coregistration efficiency (for removing the breathing artifact) was visually evaluated from difference images with respect to b = 0 with and without coregistration.
The perfusionsuppressed ADC component in the presence of IVIM was obtained as a slope of monoexponential fit for b > 100 values (24, 25) of each pixel for logtraceDWI (directionaverage image) intensity ratios relative to the b = 0 image. The perfusion fraction was derived as an intercept of the linear fit. The original spatial ADC bias error offcenter (SI∼120 mm) was measured as the deviation from the “true” reference ADC at SI∼0 mm for the same anatomy. The anatomic slice with the most uniform parametric map close to RL∼0 mm was selected as a reference. The slice ROI was defined by manually tracing the kidney border on the T_{2}weighted (b = 0) image. The ROI edges were defined to exclude edge artifacts that resulted from susceptibility gradients near phantomcontainer walls or residual misregistration for kidney anatomy. The ADC histograms were binned with the step of 0.01 between 0.5 and 3.5 (×10^{−3} mm^{2}/s), while for perfusion fraction histograms, a bin size of 0.005 between 0.05 and 0.7 was used. All histograms were smoothed with a 3point movingaverage. The ROI histogram statistics were characterized by mean and SD.
Systematic Bias Prediction and Correction
System nonlinearity tensorL ( r ) (20) was constructed using gradient design (spherical harmonics) coefficients provided by the vendor. The Frobenius norm of the biased b ′ k = L b k L T matrix normalized to the nominal b value at the isocenter b n = ‖ b ( r 0 ) ‖ was used to generate (static) bias corrector maps for each ( u k ) gradient direction C k = 1 b n ‖ L b k ( r 0 ) L T ‖ = ‖ L u k u k T L T ‖ (21) on a Cartesian grid sampled every 5 mm within a 360mm FOV. As defined, the correction factors for each pixel were dimensionless and positive, with an allowed range between 0 and 1 for negative GNL and between 1 and 2 for positive GNL (C k = 1 at the isocenter, where GNL was absent). For experimental data, assuming a nearly isotropic medium, a single directionaverage corrector map C a v was constructed for each orthogonal DWI Uschema (LAB and OVP) and interpolated according to DICOM header information on imaged volume and resolution. Because of the cylindrical symmetry of the GNL model for the horizontalbore system, the predicted corrector maps were symmetric around the SI along the AP vs the RL direction (coronal vs sagittal slices).
The corrector was then applied pixelbypixel to yield corrected DWI intensities or b maps to derive an unbiased ADC (21, 23). A corrected ADC map was derived from pixelbypixel correction (21, 23) of traceDWI image intensities (Scorrection)S b c = S 0 C a v ( r ) − 1 C a v ( r ) S b ′ 1 C a v ( r ) or of bmaps (bcorrection) b c ( r ) = b n C a v ( r ) . (Here, image intensities acquired without DW were denoted as S_{0}, whereas S_{b′} referred to biased DWI intensities.) The effect of correction on logintensity dependence on the bvalue (utilized to derive ADC and perfusion fraction) was different for S versus b correction. Numerically, for each spatial location, Scorrection scaled biased logintensities by inverse correction factor (with unaltered bvalues) versus bcorrection resulting in a direct multiplication of nominal bvalues by correction factors (with preserved intensities). Note also that the bcorrection for the isotropic medium was equivalent to the direct correction of the “measured” ADC map by A D C c ( r ) = A D C ( r ) / C a v ( r ) . The correction efficiency was assessed by comparing histogram statistics (mean and SD) before and after correction for the reference ROI. The effect of both correction scenarios on the slope and intercept of linear regression fit was directly visualized for the mean ROI intensities as a function of b > 100.
Results
Figure 1 illustrates how the nonuniformity in DW (bvalue) is directly reflected in the measured ADC map for a coronal slice through the isotropic gel phantom (Figure 1A). The apparent b value is symmetrically lower SI (negative GNL) and higher RL (positive GNL) than nominal (isocenter), leading to correspondingly under or overestimated ADC values (Figure 1A). The colorbar scale in Figure 1A (right) reports on the observed bvalue bias range between 0.8 and 1.2 with respect to the nominal value at the isocenter. Within a relatively large ROI (220 × 240 mm^{2}), such nonuniformity resulted in artificial broadening of the ADC histogram that was accompanied by a shift of the mean ADC value (Figure 1B). Knowledge of specific gradient design information allowed for the deterministic prediction of GNL bias and effective removal of nonuniformity in the ADC map (Figure 1C). Effective bias removal was demonstrated by narrowing the ADC histogram down to a measurement uncertainty of ±2.5% and shifting its mean to the isocenter reference value (Figure 1B). The observed ADC bias (Figure 1A), normalized to the isocenter reference value, agreed with the predicted by GNL model for the scanner (see Methodology), with ROI pixelbypixel difference falling within 3%. As expected for the cylindrically symmetric GNL model, the bias measured along the SI for coronal phantom orientation (Figure 1A) also agreed with that predicted for the sagittal orientation (Figure 2). Furthermore, the predicted average corrector maps (assuming isotropic medium) were identical for OVP versus LAB DWI orientations.
Figure 1.
(A) Measured ADC nonuniformity (left) for a coronal slice (AP offset of 70 mm) through a floodphantom is corrected (C) using the vendorprovided GNL model. (B) The wide (2SD∼20%) histogram bias is reduced by correction down to the measurement error (2SD∼5%) in (C). The DWbias color bar in (A) and topaxis scale in (B) reflect the relative deviation from the nominal bvalue at the isocenter (r_{0}). In the absence of GNL bias, this ratio is a unity (b(r)=b(r_{0})).
Figure 2.
(A) Predicted directionaverage (LAB or OVP) DWbias maps across kidney ROIs at scanned SI offsets (z = 0 and 120 mm). The same bias is predicted for LAB and OVP DWI orientations. The gray scale bar shows the range of predicted DW bias with respect to the nominal bvalue. Scale value of 1 corresponds to absent GNL bias (uniform DW) predicted for the z = 0 mm reference. (B) Predicted width of DWbias histogram, colorcoded as their corresponding ROIs in (A), changes depending on scan position consistent with the phantom measurements in Figure 1.
Figure 2A illustrates DW bias expected across kidney ROIs at 2 locations measured in this work. The corresponding bias histograms in Figure 2B show how steep GNL along the SI near z = 120 mm results in the broad and shifted ROI histogram compared to the reference at z = 0 mm. Figure 3, A and D, illustrate that the observed bias for the perfusionsuppressed ADC maps at z = 120 mm was consistent with the one predicted from the system GNL model (Figure 2) and virtually independent of DWI direction schemaU ( ″LAB″ or ″ O V P ″ ) as expected for the nearly isotropic medium. The strong nonuniform bias gradient along the SI was evident across the kidney parametric map at the z = 120mm superior offset location (Figure 3, A and D). Similar to the phantom data in Figure 1C, the uniformity of the kidney ADC map was nominally restored after GNL bcorrection (Figure 3, C and F), closely reproducing the ADC of the reference parametric maps acquired near the isocenter (RL∼0 mm) (Figure 3, B and E).
Figure 3.
Observation (A and D) and bcorrection (C and F) of GNL bias in perfusionsuppressed ADC for the parametric maps of the uniform sagittal slice (RL∼0 mm) through the kidney at the 120mm superior offset (A, D, C, and F) versus isocenter references (B and E) forU ( ″LAB″ ) (A–C) and U ( ″OVP″ ) (D–F) DWI. The common scale of the quantitative parametric ADC maps is given by the color bar.
The efficiency of bias correction is further quantified by the changes observed for ADC histograms of kidney ROIs in Figure 4A. ADC histograms for all ROI pixels of a uniform renal tissue slice were narrower in the vicinity of the isocenter (green) compared with the superior offset for both LAB and OVP DWI orientations (solid and dotted magenta). The steep DW nonuniformity bias across kidney ROIs observed in Figure 3, A and D, resulted in additional (nonbiological) broadening of the corresponding ADC histograms (Figure 4A, solid and dotted magenta). The mean ADC value for the reference histogram (Figure 4A, green) was ∼20% higher than mean ADCs at z = 120 mm either for OVP (dotted magenta) or LAB (solid magenta) DWI schema. With a similar initial bias resulting from GNL and identical corrector maps (Figure 2A), the effect of correction was similar independent of DWI orientation. The example of corrected ROI histograms for LAB DWI is shown in Figure 4A. The original mean bias of 20% (Figure 4, solid magenta) for ADC (z = 120 mm) was reduced to <2.5% after correcting the GNL bias either in DWI intensities (Scorrection; Figure 4A, orange) or in bvalues (bcorrection; Figure 4A, blue), nearly matching the unbiased reference histogram (green) for ADC (z = 0 mm). The bias correction by DWI intensity route apparently slightly overcorrected the ADC histogram, shifting it to somewhat higher values (orange trace) relative to the reference (green trace).
Figure 4.
(A) Perfusionsuppressed ADC histograms are shown for kidney ROIs corresponding to Figure 3A (solid magenta, LAB DWI) and D (dotted magenta, OVP DWI) before correction, and to Figure 3B (green histogram) and C (blue histogram) for the reference (isocenter) map and bvaluecorrected map of LAB DWI, respectively. The orange trace in (A) corresponds to a histogram of the corrected ADC map (not shown) achieved via Scorrection for LAB DWI intensity. (B) Mean ROI logintensity signal (symbols) and fit (lines) are plotted as a function of the bvalue for LAB DWI at the isocenter (green), before (magenta) and after bias correction via b values (blue pluses), and DWI intensities (orange crosses). Note the horizontal shift of data points with respect to measured (biased, magenta) signal after bcorrection vs vertical shift after Scorrection. The error bar of the mean reference signal at the highest bvalue (green) reflects the 2SD of the corresponding logintensity within the kidney slice ROI. The figure labels are colorcoded to mark correspondence between the histogram ROIs in (A) and mean data values shown in (B).
The slope error of linear fit for ROImean logintensity dependence on the bvalue shown in Figure 4B (magenta) is effectively corrected either for bvalues (blue pluses) or DWI signal Sintensities (orange crosses). As expected from the corresponding correction formalism, bcorrection scaled biased data points (magenta circles) horizontally along the baxis, whereas Scorrection scaled them vertically. Because bias is a multiplicative factor for bcorrection, the observed difference between the biased and corrected data location along the baxis was larger for higher bvalues. Both correction methods brought corrected data closer to the reference fit line (Figure 4B, green). The correction efficiency was similar by either method within measurement and fit uncertainty, as is evident from the proximity of the experimental and corrected data points to the fit lines. Although the original GNL bias and bias correction have a noticeable effect on the slope (ADC = 1.9 vs 1.5 × 10^{−3} mm^{2}/s) of the fit lines in Figure 4B, the effect on their intercept (∼0.23, perfusion fraction) was barely detectible. An insignificant change (<2%) resulting from the bias for the IVIM perfusion fraction (absolute intercept value ∼0.2) was likewise confirmed from observing the corresponding parametric maps and their histograms (without correction) in Figure 5. Both offset (Figure 5A) and reference (Figure 5C) parametric perfusion maps produce nominally overlapping histograms (Figure 5D, magenta and green) without GNL correction. For completeness, we confirmed that, like bcorrection (applied directly to ADC maps), Scorrection (Figure 5B) did not introduce significant sporadic bias into the perfusion maps and corresponding ROI histograms (Figure 5D).
Figure 5.
IVIM perfusion fraction maps for sagittal slice (RL∼0 mm) acquired with OVP DWI at a superior offset of 120 mm (A) and obtained after Scorrection (B) show negligible bias compared to the isocenter reference (C). Similar results are observed for their corresponding ROI histograms in (D). The figure labels are colorcoded to mark correspondence between the histogram ROIs in (A–C).
Discussion
The purpose of this study was to illustrate that GNL bias correction is feasible for quantitative diffusion metrics of the IVIM model. Although the current study design was tailored to emphasize the effect of GNL bias, similar effects may be observed routinely for large FOVs typical of body DWI applications. Consistent with previous findings (16–18), GNL causes nonuniform DW that follows a spatially static pattern for a given system independent of the nominal bvalue and is readily predictable from the deterministic gradient system design and applied DWI directions (20–22). For the isotropic medium, directionaverage bias is independent of the DWI schema. This further simplifies deriving spatial DW correction maps. In the multisite trial setting, the static GNL corrector maps would need to be calculated once for a specific system model and could then be applied to any acquired DWI scan according to its DICOM geometry.
In this study, DW bias observed across a sagittal slice through the kidney followed the trends predicted from the system gradient design for both LAB and OVP DWI orientations. The spatially dependent bias resulted in significant (∼20%) nonuniformity error for the perfusionsuppressed ADC map offcenter (z = 120 mm) compared to the same anatomy close to the isocenter. DW nonuniformity as a result of GNL shifted and broadened kidney ADC histograms. For multisite clinical trials, such system and location specific errors would likely lead to significant technical variability that would confound a populationwide analysis of predictive power for obtained ADC metrics if left uncorrected (14, 15). The observed bias was independent of the nominal bvalue and the DWI direction schema and mainly affected the ADC derived from the slope of the linear fit for the perfusionsuppressed component of the IVIM diffusion. As expected, the IVIM perfusion fraction derived from the fit intercept was immune to the bvalue bias. DW bias correctors reduced the ADC nonuniformity and mean error to <3% for diffusion in the presence of perfusion. Similar to anisotropic monoexponential medium (23), the same correction efficiency (within measurement and fit uncertainty) was achieved for ADC extracted using either corrected trace DWI intensities or corrected bvalues. These corrections did not introduce sporadic bias into the perfusion fraction maps.
Although the described correction removes the errors related to GNLinduced bias in DW, it does not address other sources of nonGNL bias error in quantitative diffusion metrics or geometric distortions. Although these bias sources are presumed to have a minor effect on bvalues for most horizontalbore systems (17, 18, 22), including the scanner in this study, they may need to be treated differently depending on severity when observed for a specific scanner model. To reduce the variability of quantitative IVIM diffusion metrics derived in a multisite clinical trial setting, the systemspecific correction of GNL bias is best performed for perfusionsuppressed ADC maps before a combined populationwide analysis.
In conclusion, significant DW nonuniformity bias at offcenter locations results both in shifting and broadening of perfusionsuppressed ADC histograms for renal tissue. For this wellperfused, nearly isotropic tissue, ADC bias for offcenter measurements could be effectively removed by applying directionaverage DW bias correctors based on known gradient design specifications. Comparable performance was achieved using corrected DWIs, bvalues, or ADC maps independent of DWI orientation. No significant bias impact was observed for IVIM perfusion fraction with or without correction. The demonstrated systemspecific correction of GNL bias in DW for offcenter anatomy is feasible for clinical trials that utilize quantitative parametric maps based on the IVIM diffusion model.
Notes
[1] Abbreviations:
ADC
Apparent diffusion coefficient
DICOM
Digital Image Communication in Medicine
DWI
diffusionweighted imaging
DW
diffusion weighting
TE
echo time
FOV
field of view
GNL
gradient nonlinearity
IVIM
intravoxel incoherent motion
MRI
magnetic resonance imaging
ROI
region of interest
RL
rightleft
SI
superiorinferior
TR
retention time
3D
threedimensional
Acknowledgments
This research was supported by National Institutes of Health grants U01CA166104, P01CA085878, and R01CA190299.
Conflicts of Interest: D.I. Malyarenko, T.L. Chenevert, and B.D. Ross are coinventors on intellectual property assigned to and managed by the University of Michigan for the technology underlying the DW bias correction described in this article.
References
Journal Information
Journal ID (nlmta): tom
Journal ID (publisherid): TOMOG
Title: Tomography
Subtitle: A Journal for Imaging Research
Abbreviated Title: Tomography
ISSN (print): 23791381
ISSN (electronic): 2379139X
Publisher: Grapho Publications, LLC (Ann Abor, Michigan)
Article Information
Copyright statement: © 2015 The Authors. Published by Grapho Publications, LLC
Copyright: 2015, Grapho Publications, LLC
License (openaccess, http://creativecommons.org/licenses/byncnd/4.0/):
This is an open access article under the CC BYNCND license (http://creativecommons.org/licenses/byncnd/4.0/).
Publication date (print): December 2015
Volume: 1
Issue: 2
Pages: 145151
Publisher ID: TOM0016015
DOI: 10.18383/j.tom.2015.00160
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