26. Diffusion-Weighted MRI

26.1. DWI experiment and analysis

This section describes FireVoxel’s tools for the analysis of diffusion-weighted MRI (DWI).

A typical DWI experiment involves:

  • 4D images acquired using diffusion-weighted (DW) sequences, usually spin echo echo-planar imaging sequences (SE-EPI), at two or more diffusion weighting factors (b-values, in s/mm2) as the dynamic dimension, and

  • Model fitting of DWI data to calculate the apparent diffusion coefficient (ADC, mm2/s) and other parameters of tissues of interest.

26.2. Challenges of DWI quantification

Accurate quantification of tissue parameters from DWI presents a number of challenges, including:

  • Inherently low signal-to-noise ratio, especially at high b-values;

  • Artifacts (geometric distortions, ghost images, susceptibility artifacts, etc.);

  • Complexity of tissue diffusion (due to the presence of anisotropy, microperfusion, etc.) that may not be accurately captured by the diffusion model;

  • Computational challenges: Efficient voxel-based fitting, overfitting, etc.

26.3. DWI analysis in FireVoxel

FireVoxel offers a set of tools for the analysis of DWI data, including image loading, preview, signal visualization, motion correction, and model analysis.

26.4. Loading and viewing DWI data

DW images in DICOM format can be loaded into FireVoxel as 4D datasets using File > Open DICOM Single Document or Open DICOM Multiple Documents (DICOM Tree panel, Fig. 26.1).

DICOM Tree panel with DWI data

Fig. 26.1 DICOM Tree panel for loading DWI dataset.

In the DICOM Tree dialog, DW images are organized by PATIENT, STUDY, 4D volume lists (VL, volume_list), and 3D volumes (V, volume). The user may load the entire 4D series (VL) or individual 3D volumes (V) by checking the boxes next to the corresponding titles and clicking Load. If no boxes are checked, the entry highlighted with a red box will be loaded.

For most MRI systems, the b-values should be automatically read from the DICOM headers. Please contact the FireVoxel team about any issues with image loading. It is important to verify the correctness of the b-values once the images are loaded into FireVoxel. To do this, scroll through the images using the Right and Left arrow keys on the keyboard and check the b values displayed in the status bar in the lower left corner of the main software window (Fig. 26.2). To scroll through slices, use Up and Down arrow keys.

Status bar displays current b-value

Fig. 26.2 The status bar in the lower left displays the current b-value.

The signal change with b-value can also be viewed using Play 4D experiment play_4d_exp_icon tool on the main toolbar. The local signal behavior can also be visualized using Voxel Time Activity Browser voxel_tac_icon.

Before proceeding with the analysis, the user is advised to check the images for any issues, for example, motion artifacts, and decide whether any preprocessing, such as motion correction, may be necessary.

26.5. Preparing DWI for analysis

If the images are affected by motion, the user may use 4D coregistration tools to align images.

Prior to modeling, it is recommended to segment the organs or tissues of interest using FireVoxel’s segmentation tools and perform initial voxel-based analysis within these ROIs (Fig. 26.3).

Kidney ROIs on diffusion image

Fig. 26.3 The ROIs allow the user to examine parameters of tissues of interest.

26.6. Model analysis of DWI

The analysis of DWI data may be performed using Dynamic Analysis > Calculate Parametric Map command, also available via param_map toolbar icon. The command opens a dialog panel for setting up the model analysis (Parametric Map Calculation for Dynamic Experiment, Fig. 26.4).

Parametric Map Calculation Panel

Fig. 26.4 Parametric Map Calculation for Dynamic Experiment panel for DWI.

26.6.1. Model

The top part of the panel contains a drop-down menu with a numbered list of models compatible with the current dataset. The compatibility is determined by FireVoxel automatically based on the DICOM header information. Models that are not compatible with the current dataset are not shown.

The following models are compatible with the DWI data:

Model 17: IVIM bi-exponential diffusion (segmented fit):

S = S_0 (f \cdot exp(-b \cdot D_p)+(1-f)exp(-b \cdot D_t))

Model 18: IVIM bi-exponential diffusion (regular fit):

S = S_0 (f \cdot exp(-b \cdot D_p)+(1-f)exp(-b \cdot D_t))

Model 19: Monoexponential diffusion:

S = S_0 exp(-b \cdot ADC)

Model 21: Stretched exponential fit:

S = S_0 exp(-b \cdot DDC)^\alpha

Model 28: Diffusional kurtosis:

S = S_0 exp(-b \cdot D +b^2 \cdot D^2 \cdot K/6)

The following description will focus on Model 19 (monoexponential diffusion).

26.6.2. Hyperparameters

This series of text boxes allows the user to specify the fixed input parameters (referred to below as hyperparameters) and the bounds of the fitted model parameters:

Low signal tail cutoff – If signal intensity falls below this cutoff value, the data at the corresponding b-value and all higher b-values are discarded from fitting.

Maximal ADC (mm^2/sec) – Upper limit on the ADC value.

[Tissue Concentration – Not relevant to DWI processing. Opens Concentration Conversion dialog for setting up the conversion from signal intensity to contrast concentration in contrast-enhanced CT and dynamic contrast-enhanced MRI experiments. By default, unconverted Signal values are selected, so no further action is needed for DWI analysis. This option will be removed in future builds.]

26.6.3. Output

These checkboxes allow the user to select the parameters that will be returned as the results of model analysis. At least one output parameter must be selected. For curve fitting models, the output parameters also include a measure of goodness of fit, such as the root-mean-square error

RMSE = \sqrt{\frac{1}{n} \sum{(y_i-\hat y_i)^2}},

where y_i and \hat y_i are the signal data and model fit values, respectively, at i-th value of the dynamic variable (i = 1,2,...n).

Model 19 (monoexponential diffusion) has two possible outputs: the apparent diffusion coefficient (ADC) and the fit residual.

Select All or Unselect All – Clicking these buttons selects or unselects all output parameters.

26.6.4. Optimization


This block controls the optimization options for the curve fitting models (for both voxel-based and average curve fitting analyses, see Fitting Options).

[Optimization method] – Dropdown menu with a choice of: 1) Simplex optimization or 2) Global optimization.

Simplex optimization is based on the simplex Nelder-Mead (or amoeba) method. As a heuristic, it finds an optimal solution by iteratively replacing the worst solution with a better solution at each step. The simplex method starts from multiple grid points for fitted parameters, which ensures a more optimal solution, but is not guaranteed to yield the global optimum. The precision of the simplex solution is determined by a combination of the number of simplex grid points and the number of iterations (see Simplex grid and #Iterations below). Simplex optimization can work efficiently with multiparameter models. In FireVoxel, all convolutional models currently use simplex optimization.

Global optimization is based on interval arithmetic, branch-and-bound approach that always searches for a guaranteed global optimum. The precision of global optimization is controlled by fitted parameter bounds (see Hyperparameters) and the maximum allowed number of iterations. Global optimization provides the exact solution bounds on the globally optimal parameters and fitting residual (which heuristic methods, such as simplex optimization, cannot provide). With increasing number of iterations, the solution bounds become tighter. For models with multiple parameters, global optimization may become impractical because of the high computational cost.

Simplex grid – Number of grid points Ng (typically 3 to 5) for simplex optimization. For the monoexponential model, the grid points are constructed by dividing the full ADC range from 0 to the maximum ADC into (Ng-1) equal subintervals. For other models, Ng applies to each of the fitted parameters.

#Iterations – Maximum number of iterations used as a stopping criterion in simplex fitting. Higher numbers may help achieve a better fit but will also require longer processing times.

26.6.5. Noise processing


Sets the parameters of noise and excluding unreliable data and/or results:

Noise – Noise level.

Exclude RRSE above – Checkbox and text box (for cutoff value) – Exclude voxels with poor quality fit. If the box is checked, replace with VOID any voxel for which RMSE is above the cutoff entered in the text box. Trial and error is often used to establish the desired cutoff.

Exclude parameters above (%) – Checkbox and text box (to enter percent cutoff) – Exclude voxels that yield exceedingly large or negative parameters. If the box is checked, replace with VOID any voxel where ADC is greater than percent cutoff as defined by maximum ADC.

26.6.6. Fitting options: Process All, Process ROI Only, Process ROI as a single curve

These buttons at the bottom of the panel enable the user to select how the model analysis is performed: on a voxel-by-voxel basis over the entire image, or within an ROI, or for an ROI-averaged curve. The available options depend on the presence of a visible ROI layer (or layers). If ROIs are invisible or not present at all, only the entire image can be modeled (voxel-by-voxel or as an average curve). If multiple ROI layers are visible and one of them is active, the model analysis is performed for the active ROI. If ROIs are visible, but none of them is active, modeling is available either for the entire image or for all of the ROI-averaged curves.

Process All – Fit the entire image voxel by voxel. For each output parameter, the result will be displayed as a color map residing in a new, automatically created real-valued layer. These new layers will be placed on top of all other layers in the same document window as the original data.

Process ROI Only – Enabled when the active layer is a visible ROI. The model analysis is performed on a voxel-by-voxel basis within the ROI. If more than one ROI is present, but none of them is active, this option is not available. The results will be returned as new, color map layers, as in Process All.

Process ROI/volume/All ROIs as a single curve – The functionality depends on the active layer:

1) The active layer is a visible ROI – Fit the curve obtained by averaging the signal within the active ROI.

2) The active layer is an image layer and no ROIs are visible or present – Fit the signal averaged over the entire volume.

3) The active layer is an image layer, and multiple visible ROI layers are present – Fit the curves obtained by averaging each visible ROI.

Extrapolate – Create an extrapolated 4D volume corresponding to the user-specified values of the dynamic variable (b value for DWI), with signal in each voxel computed based on the model formula and fitted parameters. The extrapolated 3D volumes are added to the original image set and displayed in a new document window titled [original document]_extrapolated.

26.6.7. Results

The results correspond to the fitting options selected in the previous step:

Process All – Parametric maps, displayed as color maps, for the entire image. The appearance of the color maps can be customized using ViewFilter command on the Layer Control panel (Fig. 26.5).

Parametric map - Process All results

Fig. 26.5 Process All results showing whole-image ADC map.

Process ROI Only – Parametric maps within the filled (non-zero) ROI voxels; all other voxels remain fully transparent. Again, the appearance of the color maps can be customized using ViewFilter (Fig. 26.6).

Parametric map - Fit ROI only results

Fig. 26.6 Fit ROI Only results showing map of ADC for the right kidney.

Process volume/ROI/ROIs as a curve – Opens the output panel (Dynamic Experiment Single Curve Results: [Model name], Fig. 26.7). The panel consists of three parts.

Dynamic Experiment Single Curve Results

Fig. 26.7 Dynamic Experiment Single Curve Results panel.

The top part of the panel displays a plot of the signal data and the model fit as a function of the dynamic variable (here b-value, s/mm2). The bottom right part shows the current ROI (and a dropdown menu to select other ROIs, if multiple ROIs were fitted). Below the ROI menu are the color swatches for the data curve, fit curve, and the plot background. The buttons next to the color swatches open the standard color picker for selecting the colors of the curves and the background.

The bottom left part under the plot contains a table of fitted parameters with the columns showing parameter name, fitted value, and units (if applicable). For Model 19, the table lists the ADC and residual as the output parameters.

For global optimization, the table also shows the lower and upper solution bounds [LB, UB] on the globally optimal parameter value OV and percent spread = 100%*max(OV-LB, UB-OV)/OV.

Offset signal (checkbox) – Toggles on/off the vertical axis offset. If checked, the vertical axis range is restricted to the interval between the smallest and largest value of the data or fitting curve. If unchecked, the vertical axis range is from zero to the largest data/fit value.

Copy results to clipboard – Copies fitted parameters to the clipboard and makes them available for posting into a text file or spreadsheet. For each ROI, each parameter is recorded in a separate line (ROI name, parameter name, fitted parameter value, and units, if applicable).

OK – Closes the panel.

26.6.8. Analyzing parametric maps with ROI Stats 3D

To explore the ADC voxel values within an ROI, make sure that this ROI is the only visible ROI layer and the ADC map is the active layer, then click ROI Stats 3D on the Layer Control panel. This command opens a panel (ROI Stats 3D) that provides the histogram, selected features, and other statistics of the parameter distribution.

ROI Stats3D panel showing ADC statistics within ROI

Fig. 26.8 The ROI Stats 3D panel showing ADC statistics within the left kidney ROI.

The top part of the panel shows the histogram of the voxel distribution of the parameter values. The options controlling the histogram are located below the histogram. These options include the Range, Number of bins, and Bin Width.

By default, the full range of values is displayed. To adjust the range, click Range to open dialog showing the lower and upper bounds and type new values. If Clip box is checked, the values outside the Range are not included into the histogram and from statistics calculation. This is reflected in the first order features and ROI voxel count (under Geometrical features). In response to the change of Range, the Number of bins is automatically updated (if Bin Width stays unchanged).

The range may also be set via specifying the low and high percentile bounds to be displayed (by clicking the % button and entering the corresponding values). Clicking Full restores the full range of values included into the histogram.

The lower left part of the panel lists the first order features of the voxel values distribution, including the mean, standard deviations, etc., as well as a selection of percentile values between 1% and 95%.

All values are displayed in scientific notation, e.g., mean ADC = 3.487193e-03 = 0.003487193.

Geometrical features list the voxel count and ROI volume and other parameters.

The Segmentation\Modeling options on the lower right enable partitioning (segmentation) of ROI voxels into subgroups, such as viable tissue versus necrotic tissue, based on the voxel value distribution. Voxels within each subgroup are presumed to have similar parameter values.

Clicking Save Stats opens a text file with the main statistical results (named RoiStats3D.txt), including ROI volume, first order features, and histogram. By default, this file is created in FireVoxel’s Temp directory, but can be saved in any user-selected directory.