Keywords

Learning Points

  • Visual assessment of diffusion MR images can be supported by nonspecific quantitative measures that can be derived from DTI data, including fractional anisotropy and mean diffusivity.

  • Variation in image acquisition parameters in both individual cases and group studies affects both qualitative and quantitative analysis.

  • Fractional anisotropy can be modulated by numerous biological and methodological factors and should not be blindly interpreted as a quantitative marker of white matter integrity.

  • Interpreting changes of the axial and radial diffusivities on the basis of the underlying tissue structure should not be performed unless accompanied by a thorough investigation of their mathematical and geometrical properties.

  • Normal brain development and ageing, and the timing and severity of injury/pathology should be considered when interpreting DTI metrics.

Why Is Quantification Important in Medical Imaging?

Radiological diagnosis is based almost entirely on subjective visual evaluation and quantitative image analysis is rarely employed. While routine clinical diagnosis can be determined qualitatively, image quantification is essential for understanding the basic disease mechanisms which underlie neurological or psychiatric disorders of the human brain, and for the development of biomarkers of brain disease which can be used to evaluate pathology status and treatment efficacy.

Advanced and automated tools play an essential role in extracting such information about specific brain regions or structures within the patient population (e.g., hippocampal atrophy). These tools provide objective criteria, quantification, and a high level of precision (reproducibility), which can inform statistically driven conclusions. Without quantification, group differences cannot be statistically analyzed, and image-based findings cannot be correlated with clinical outcomes.

Whilst clinicians are well trained in reading scalar images, i.e., the grayscale images characteristic of computed tomography and conventional MRI sequences, they are less familiar with deriving quantitative information from complex imaging data such as captured using dMRI. As the preceding chapters of the book demonstrate, dMRI data provides additional information that requires nontrivial processing before the data can be analyzed and interpreted. Not only does it offer insight into tissue microstructure, but also the orientational information captured in the diffusion-weighted MR signal can be used to generate impressive and useful qualitative results on the shape of fibre bundles and the connection patterns of brain regions. However, whilst the orientation information contains important information on brain connectivity, it is important to remember that it is insufficient for its complete characterisation and there are many challenges in disentangling the true meaning of quantitatively derived metrics (see Chap. 11 for further details about using DTI to study brain connectivity).

The reduction of the measured diffusion information to a diffusion tensor and then to a scalar value means that when changes or differences are found in one of the scalar metrics, it is difficult to draw conclusions about the exact cause at a microstructural level. While this can be considered a drawback of dMRI, the systematic information reduction can also be advantageous. For example, the human brain is a complex system, the complete characterization of which is currently not possible. If we want to characterise its anatomical status, and compare it with different populations, we need to find a way to summarise the complexity in a more simple form. dMRI offers such a solution as it provides a quantitative means of systematically reducing the anatomical information into manageable scalar indices.

Which Quantitative Measures Can Be Calculated from a DTI Dataset?

Earlier chapters in this section (e.g., 4) describe how the dMRI signal can be used to calculate the diffusion tensor, the basic building block from which several quantitative measures describing the amount of diffusion and its orientational preference can be derived [4]. While direct visualisation of the diffusion tensor components is not readily interpretable, the ellipsoid model is perhaps the most widely used visual representation [4]. An ellipsoid is a three-dimensional representation of the diffusion distance in the X, Y, and Z planes by molecules in a given diffusion time. In the ellipsoidal representation (Fig. 5.1), the orientation of the axes is provided by the three eigenvectors e1, e2, and e3 while the radius of the ellipsoid along its axes is proportional to \( \sqrt{\lambda_1} \), \( \sqrt{\lambda_2} \), and \( \sqrt{\lambda_3} \) (see Box 5.1).

Fig. 5.1
figure 1

Schematic illustration of the relationship between the mathematical diffusion tensor and its ellipsoid representation. Decomposition of the tensor into eigenvectors and eigenvalues provides information on the orientation and amount of diffusion, respectively. Various mathematical formulas as a function of the eigenvalues and vectors form the basis of quantitative DTI parameters. Top left image: Adapted from Beaulieu C. The basis of anisotropic water diffusion in the nervous system – a technical review. NMR Biomed. 2002 Nov-Dec;15(7–8):435–55. With permission from John Wiley & Sons, Inc.

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Box 5.1 What Is the Difference Between Eigenvalues and Eigenvectors?

Eigenvalues: The ADC values of the tensor along the directions of the eigenvectors. They describe the shape and size of a tensor, independently of its orientation.

Eigenvectors: A new set of customized axes for a tensor, aligned along its specific orientation. They describe the orientation of a tensor, independently of its size and shape.

Eigenvalues are rotationally invariant, whilst eigenvectors are rotationally variant.

Having obtained the diffusion tensor for each voxel and having computed the eigenvectors and the corresponding eigenvalues, several metrics can be derived (Fig. 5.2), including standard metrics such as fractional anisotropy (FA), a measure of the diffusion anisotropy, and trace or mean diffusivity [6] which reflect the average amount of water diffusion in a voxel.

Fig. 5.2
figure 2

Example parameter maps derived from diffusion imaging. Note the changing contrast in the diffusion-weighted images (DWIs), reflecting tissue orientation changes relative to the applied diffusion gradients. The color FA map, bottom center, is generated by multiplying the direction-encoded color map, generated from the principal eigenvector of the diffusion tensor, with the FA map. The colour FA map therefore contains information about fibre orientation (color) and the degree of anisotropy (intensity). Abbreviations: B0, non-diffusion-weighted image, DWI, diffusion-weighted image, MD, mean diffusivity, AD, axial diffusivity, RD, radial diffusivity, A-P, anterior-posterior, L-R, left-right, I-S, inferior-superior, DEC, direction-encoding color, FE, first eigenvector, FA, fractional anisotropy

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It is important to note that some measures depend on the orientation of the tissue relative to the applied gradient (rotationally variant), whilst others do not (rotationally invariant) as this has implications for interpretation and for image registration (see Chap. 10). For example, eigenvector orientations are rotationally variant but FA and trace are rotationally invariant. Apparent diffusion coefficient (ADC) values , on the other hand, are rotationally variant. Recall from Chap. 4 that ADC quantifies the magnitude of diffusion along a given gradient direction and depends on the strength of the diffusion weighting, i.e., b-value. In the case of anisotropic tissue, for example, ADC is highest (diffusion is fastest) along the length of the pathway and lower in other directions [7].

Diffusivity Measures

Trace

The trace (Tr) of the diffusion tensor (D) reflects the overall water content. Trace, Tr (D), is a commonly used clinical measure, which gives an indication of the overall diffusivity in a given voxel and is computed as the sum of the three eigenvalues λ 1, λ 2, and λ 3 or the sum of the diagonal elements of D (D xx , D yy , D zz ). Trace is completely rotationally independent, and therefore unlike with ADC, changes in Tr(D) can be attributed solely to changes in tissue structure. Trace has become an important metric in the assessment and diagnosis of stroke [1, 8]:

$$ \mathrm{T}\mathrm{r}(D)={\lambda}_1+{\lambda}_2+{\lambda}_3={D}_{xx}+{D}_{yy}+{D}_{zz} $$

Mean Diffusivity (MD)

Mean diffusivity characterizes the overall mean squared displacement of molecules (average ellipsoid size) and is simply a scaled version of the trace Tr(D) [9, 10]:

$$ D=\frac{Tr(D)}{3}=\frac{\lambda_1+{\lambda}_2+{\lambda}_3}{3}=\frac{D_{xx}+{D}_{yy}+{D}_{zz}}{3} $$

MD, sometimes denoted mathematically as D, is a measure of the overall diffusivity in a particular voxel regardless of direction. Just like Tr(D), MD is low within white matter but high, for example, in the ventricles, where the movement of water molecules is unrestricted. This measure of overall diffusion rate can be used to delineate the area affected by stroke, as demonstrated by van Gelderen [8].

Axial Diffusivity (AD )

Axial (or longitudinal or parallel) diffusivity, \( {\lambda}_{\left|\right|} \) is simply the diffusivity along the principal axis of the diffusion ellipsoid and is given by λ 1 (see Box 5.2).

Box 5.2: What Is the Difference Between ADC, Trace, and MD?

ADC: amount of diffusion in a single direction

Trace: sum of the eigenvalues, or “mean ADC”

MD: Trace/3

The ADC depends on diffusion anisotropy and is rotationally variant, whereas trace and MD are measures of the average amount of diffusion in a voxel irrespective of the gradient direction or underlying microstructure.

Radial Diffusivity (RD )

Radial (or transverse or perpendicular) diffusivity, \( {\lambda}_{\perp } \), is a measure used to express the diffusivity perpendicular to the principal direction of diffusion:

$$ {\lambda}_{\perp }=\frac{\lambda_2+{\lambda}_3}{2} $$

Westin Measures

In addition to the basic ellipsoidal representation, Westin et al. [11] proposed a set of geometrical diffusion measures to quantify the diffusion ellipsoid’s shape in terms of its linear (c l), planar (c p) and spherical (c s) anisotropy components:

$$ {c}_{\mathrm{l}}=\frac{\lambda_1-{\lambda}_2}{\lambda_1} $$
$$ {c}_{\mathrm{p}}=\frac{\lambda_2-{\lambda}_3}{\lambda_1} $$
$$ {c}_{\mathrm{s}}=\frac{\lambda_3}{\lambda_1} $$
$$ {c}_{\mathrm{l}}+{c}_{\mathrm{p}}+{c}_{\mathrm{s}}=1 $$

The linear component describes how prolate or cigar shaped the ellipsoid is, the planar component describes how oblate or disc shaped it is, and the spherical component describes how sphere or ball-like the ellipsoid is. See Fig. 5.3 for an illustrative example.

Fig. 5.3
figure 3

Westin measures: Panel (a) illustrates the geometric decomposition of the diffusion tensor, D, (yellow), into triangular barycentric space, characterised by cigar (red), disc (green), and ball-shaped (blue) ellipsoids. Axial maps of the corresponding Westin measure, c l, c p, and c s can be found beneath each ellipsoid. Panel (b) illustrates how useful additional information can be obtained by combining the measures in a single map. By omitting the spherical component, it is possible to more easily distinguish between linear and planar diffusion (bottom image). Compare to the fractional anisotropy map (top)

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The linear and planar diffusion tensor geometry indices have been used as criteria to distinguish single-fibre voxels from crossing-fibre voxels [12]. To some extent, voxels where the planar diffusion coefficient (c p) is largest, i.e., larger than linear (c l) and spherical coefficients (c s) can be classified as crossing-fibre configuration voxels; all voxels where linear diffusion is largest can be classified as single-fibre configuration voxels. A high c s may not only arise from multiple-fibre populations but also from partial volume effects with CSF [12].

Anisotropy Measures

The degree of anisotropy describes how molecular displacements vary as a function of orientation (ellipsoid eccentricity ) and is related to the presence and coherence of oriented structures [9].

Fractional Anisotropy (FA)

FA is a metric used to quantify the ratio between the magnitude of the anisotropic component of D and the entire magnitude of D, the diffusion tensor. FA values lie in the range [0, 1] and can be calculated in each voxel using the following expression based on the eigenvalues of the diffusion tensor:

$$ \mathrm{F}\mathrm{A}=\sqrt{\frac{3}{2}}\sqrt{\frac{{\left({\lambda}_1-\lambda \right)}^2+{\left({\lambda}_2-\lambda \right)}^2+{\left({\lambda}_3-\lambda \right)}^2}{\sqrt{\lambda_1^2+{\lambda}_2^2+{\lambda}_3^2}}} $$

This rotationally invariant, dimensionless measure, expresses the anisotropy of the tensor ranging from 0, when the tensor is completely isotropic to 1 when diffusion is bound to a single axis.

In addition to the FA, many other measures of anisotropy have been proposed, including, but not limited to, the relative anisotropy [6], dispersion of the principal diffusion direction [13] or mode of anisotropy [14].

Further discussion of how FA relates to tissue microstructure and other technical features of dMRI data are discussed in a later section of this chapter.

Quantitative Parameters Derived from Multi-Shell dMRI

Anisotropy present at a microscopic level (for instance, in the presence of oriented structures, such as dendrites in the brain cortex) may not exist at a voxel level due to the averaging effect over the many different directions present in the voxel. This presents a problem for single-shell data (i.e., data acquired with one non-zero b-value, e.g., b = 1000 mm/s2), reconstructed with the diffusion tensor, which cannot model more than one orientation per voxel (see Chap. 20). However, new multi-shell approaches can be used to generate alternative metrics, which provide additional information about the underlying tissue microstructure. These multi-shell approaches are described in detail in Section VI of this book “Beyond DTI”; however, a brief summary of representative examples is provided below.

Diffusion Kurtosis Imaging

Diffusion kurtosis imaging (DKI ) is a recent MR technique that employs diffusion-sensitising gradients similar to that used in DTI, but acquires three or more diffusion weighting b-values instead of two [15]. While this technique is generally not used in a clinical environment due to time constraints (typical scan times are in the order of 20 min), DKI has been applied to study microstructural changes in a number of preclinical and clinical research populations [16–18]. Whilst DTI is concerned with modeling hindered Gaussian diffusion (see Chap. 3), DKI captures information about redistricted diffusion, which can be approximated to water bound by cell membranes and which is inaccessible to DTI. This means that DKI may provide more sensitive and specific markers for tissue injury than DTI data alone [19, 20]. Since the acquisition protocol used to obtain a DKI dataset includes all the information necessary to derive a standard DTI dataset, it can be used to calculate both types of indices. DKI measures include the kurtosis anisotropy (KA), mean, axial and radial kurtosis (MK, AK, RK, respectively). These measures quantify the degree of non-Gaussianity and can be regarded as indices of tissue compartmentalization or complexity [15]. For example, a high mean kurtosis may reflect an increase in tissue complexity. This is in contrast to high mean diffusivity, which would reflect an increase in freely diffusing water. Further information about DKI can be found in Chap. 21.

Tissue (Compartment) Model-Based Approaches

Whilst DTI and DKI do not assume a specific biophysical tissue model, other MRI based frameworks aim to incorporate additional features into their models that reflect some properties of tissue microstructure such as the behavior of water in intracellular and extracellular compartments [21]. For example, approaches such as CHARMED [22], AxCaliber [23], and ActiveAx [24] enable the extraction of a multitude of microstructural parameters (axon diameter distribution, mean axonal diameter, and axonal density) [25]. To date however, these approaches have been applied primarily in a research context owing to the complexity of analyzing such data and because of clinically prohibitive scan times. Neurite orientation dispersion and density imaging (NODDI) has recently been proposed as a more clinically feasible alternative and can be used to estimate the density and angular variation of neurites (dendrites and axons) in-vivo [26]. NODDI is based on a three-compartment tissue model and data is acquired using at least two shells differing from one another only in choice of b-values and optimized for clinical (research) feasibility (scan time <30 min).

It should be remembered however that all the techniques based on tissue models are still limited by the simplicity of the model and provide only indirect measures that may relate to tissue features, but do not actually directly quantify, for example, neurite density, in the same way as a histological examination .

Section Summary

  • The diffusion tensor provides a means to quantify the amount and orientational preference of diffusion at a voxel level.

  • A number of rotationally invariant scalar parameters can be derived from the diffusion tensor, including the FA, MD, AD, and RD.

  • The mean ADC, trace(D), and MD are all measures of the average diffusion in a voxel. They relate to the absence of barriers to water diffusion.

  • FA is the most widely used DTI measure and describes the degree of diffusion anisotropy in a voxel. It is related to the presence of barriers to diffusion, such as axonal membranes.

The Influence of Image Acquisition on DTI Parameters

Deriving scalar values from dMRI data and eventually comparing them between groups of subjects and/or correlating them with other parameters begins with the raw data acquisition, followed by a pipeline of image processing steps. Each one of these steps is susceptible to sources of bias, which may not only limit the accuracy and precision of DTI parameter estimation, but can lead to substantial errors. A more detailed coverage of this topic is performed in the following chapters of this section (Chaps. 6 and 7); however, a brief summary of selected influential factors is presented below.

Effect of Field Strength

Clinical MR systems typically used for routine DTI scanning of humans are 1.5 or 3 T, although a small number of specialist research centers offer the possibility of scanning (predominantly healthy) subjects at 7 T. As DTI parameters should not be dependent on the static magnetic field strength, the reproducibility of measures at different field strengths is largely dependent on signal-to-noise ratio and the effect of artifacts [27]. It is commonly accepted that scanning at higher field strengths increases signal-to-noise (SNR); therefore one would expect higher fields to equate with higher quality. Although this is the case for conventional imaging, the competing decreases in T2 time and increased b0 inhomogeneity associated with increasing field strength, coupled with increased distortions due to eddy currents, magnetic susceptibility, and chemical shift artifacts, off-set the gain in image quality in DTI. Nevertheless, it has been shown that the uncertainty of fitted DTI parameters decreases with increasing field strength, which may impact positively on fibre-tracking results [27]. Figure 5.4 illustrates the effect of field strength in a single subject.

Fig. 5.4
figure 4

Comparison of FA measured in two ROIs in the same subject at 1.5 and 7 T. Coronal DTI data of the human brain in the same subject acquired at 1.5 and 7 T. FA was calculated in the centrum semiovale at 1.5 T: FA mean = 0.48 (SD = 0.11) and 7 T: FA mean = 0.47 (SD = 0.08); and in the genu of the corpus callosum at 1.5 T: FA mean = 0.67 (SD = 0.18) and at 7 T: FA mean = 0.66 (SD = 0.14). Note the difference in image quality at different field strengths, which in this subject has a relatively minor effect on the FA when averaged across each ROI. SD = standard deviation [Legend data provided courtesy of FMRIB Centre, University of Oxford]

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Effect of Number of DWIs

Reconstruction of the diffusion tensor requires a minimum of seven MR images [28], one without any diffusion sensitizing gradients applied and at least six diffusion-weighted images with gradients applied in non-collinear directions. Mathematically, only six non-collinear diffusion-weighted directions are necessary to reconstruct the diffusion tensor; however, in practice more images should be acquired to improve the accuracy of tensor estimation [29].

When using the tensor model, the more directions that are acquired the better the angular resolution that can be achieved; however, research has shown that the “cost” (in this case scan time) versus benefit curve starts to flatten out at around 30–32 unique directions. Jones et al. [29] found that robust determination of mean diffusivity, FA and tensor orientation requires a dMRI sampling scheme in which at least 30 unique and evenly distributed sampling orientations are employed. However, for anisotropy measurement only, the measurements will be robust when at least 20 unique sampling orientations are used. When comparing indices derived from DT-MRI, if the number of sampling orientations is low (<30) and not uniformly distributed over the surface of a sphere, then the variance in derived indices can be strongly dependent on structural orientation [30]. For example, the lowest variance in a parameter such as FA is found when the fibre is aligned with one of the sampling orientations, and is largest when the fibre is at the greatest angle to the sampling vectors. These variations will effectively increase the standard deviation of measurements obtained from a region of interest (ROI) encompassing voxels containing tissue with different fibre orientations. Such increased variance will reduce the statistical power for quantitative analyses of mean diffusivity in different ROIs and will, in general, spuriously increase the heterogeneity of the apparent trace within ROIs (Fig. 5.5).

Fig. 5.5
figure 5

Illustrates synthetic color FA maps for (a) 16 (blue), (b) 30 (red), and (c) 60 (green) directions. Increasing the number of gradient directions increases SNR and therefore the accuracy of estimated the DTI measurements

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Combined with the number of diffusion weighting directions used, there is a requirement to acquire multiple non-diffusion-weighted images if large numbers of DWIs are acquired using different gradient orientations. The optimal ratio of diffusion weighted to non-diffusion-weighted images was calculated to be roughly 9:1 [31]. Typically one b = 0 image is acquired for every 8–9 diffusion-weighted images. HARDI methods typically use a higher number of gradient directions (>45) depending on the reconstruction method used, and similar to DTI, increasing the number of directions improves the angular precision achievable [32].

Effect of b-Value

The number and strength of b-values influence the derived measures of diffusion and anisotropy [30] (Fig. 5.6). Attention to the choice of diffusion sensitisation parameters is important when making decisions regarding clinical feasibility (acquisition time) and obtaining normative measures.

Fig. 5.6
figure 6

Illustration of change in contrast and SNR with increasing b-value [33 ]

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Within an ROI, the mean and variance of the trace will be dependent on the b-value [30]. The trace of the tensor is dependent on the amount of diffusion weighting used to characterise it [30]. As the diffusion weighting is increased there is an increasing dissociation between grey and white matter, with the trace in white matter being lower than in grey matter. This not only introduces more heterogeneity within ROIs, but also means that comparison with normative databases or data from other centres and, by extension, multicenter studies is problematic unless the same degree of diffusion weighting is employed (which is seldom the case).

The diffusion characteristics of a voxel containing a single-fibre population can be characterized by a tensor whose associated ellipsoid is prolate. In voxels containing multiple fibre populations (e.g., crossing-fibre regions), the diffusion characteristics observed at low b-values can still be described by a single tensor but the diffusion ellipsoid may be less prolate or may become spherical or even oblate. In such cases, the tensor model does not adequately reflect the underlying tissue microstructure. Unfortunately, this is the case in an estimated 60–90 % of brain voxels [34], which again emphasizes the need for caution when interpreting DTI measures. Several groups have proposed methods for elucidating complex tissue microstructure by examining the non-Gaussian diffusion behavior that only becomes apparent at higher b-values (see [32] for a review).

Effect of Image Quality

Noise

The effect of noise on anisotropy measurements derived from DT MRI was first described by Pierpaoli and Basser [35]. Noise in the diffusion-weighted signals will mean that, even in a perfectly isotropic medium such as a glass of water, it is not possible to obtain three identical eigenvalues. Low signal-to-noise ratios correspond to high eigenvalue discrepancies. Thus, there is a noise-induced bias in measurements of anisotropy. The variance in anisotropy increases as the added noise increases. However, the mean value remains approximately constant in the white matter, but increases rapidly in the grey matter [30]. Therefore unless the acquisitions are matched so that the SNR in the non-diffusion-weighted images is the same and, equally importantly, so that the same number of b = 0 images and diffusion-weighted images are acquired, then comparing anisotropy values across different subjects, time points, and centers is particularly problematic (see Box 5.3).

Box 5.3: Comparing DTI Measures in Different Studies

It is not trivial to directly compare DTI measures (e.g., FA) derived from data acquired on different scanners with different acquisition parameters (e.g., b-value).

Example: For a given patient, the FA in the corpus callosum is found to be 0.8. In another study, the FA in the corpus callosum in a healthy individual is reported to be 0.9. Intuitively, one may conclude that the patient has a lower FA than normal. This is incorrect because the FA was calculated based on data with different acquisition parameters, and possibly also using different tensor estimation and analysis techniques. The correct way to assess if a patient has a different FA value in the corpus callosum compared to a healthy individual would be to do a case–control group study with patients and healthy control subjects scanned with identical scan protocols and processed/analyzed in an identical manner.

The SNR depends linearly on the voxel volume. Clinical protocols typically limit voxel sizes to a minimum of about 2 mm3 at 3 Tesla (T) or 2.5 mm3 at 1.5 T. Reducing the edge length from 2 to 1.5 mm would reduce the SNR by more than half [36]. This reduction in SNR can only be compensated for by repeating and averaging the measurements, if averaging is performed in the complex domain and appropriate models of noise are invoked [36]. The SNR should never be below about 3:1 in any of the DW images in order to avoid the problems associated with the rectified noise floor [30]. Results reported in [37] and [38] suggest 10:1 as a safe minimum (Box 5.3).

It has also been found that that even within the three popular regression methods (linear least squares, LLS, weighted-linear least squares, WLLS, nonlinear least squares, NLLS) that do not explicitly account for the noise-floor, there are differential responses [37, 39]. This means that results will be different when using different estimation methods, and therefore, it is important when comparing measures of diffusion anisotropy to establish not only what acquisition was used, but also what tensor estimation routine was used (see previous Chap. 4 for further discussion on the topic of tensor estimation strategies).

SNR of the diffusion-weighted images is also influenced by the diffusion weighting factor or b-value used. Low b-values provide higher SNR but at a cost of reduced angular resolution. Correspondingly, high b-values are better for HARDI acquisitions but SNR is significantly reduced.

Artifacts

Although general guidelines exist for optimizing a DTI acquisition protocol in terms of SNR, b-value, voxel size, diffusion gradient directions, and cardiac gating [40], large variations in data quality remain as a result of differences in scanner hardware, pulse sequences and available scan times. Tournier et al. [32] and Jones et al. [36] present excellent reviews on pre-processing dMRI data and the recommended quality assessment that should be performed. There are a number of artifacts that can be identified in DTI data, including geometric distortions, ghosting, and signal dropouts. Detailed information regarding the prevention, recognition, and correction of such artifacts is provided in Chaps. 6 and 7 of this book.

Such artifacts can affect the accuracy of the tensor estimation, and by extension, the derived DTI parameters. For example, FA values greater than one can result from negative eigenvalues in the diffusion tensor, which typically occur at the interface between the CSF and the surrounding white matter, as artificially low-intensity rims [36]. Correcting for CSF-contamination partial volume effects in the structures of interest on a voxel-by-voxel basis prior to drawing inferences about underlying changes in white matter structures is therefore recommended [41].

Not only the artifacts themselves, but also the strategies employed to correct them may also introduce errors. For example, when correcting for motion and eddy-current induced geometric distortions by performing affine registration of the diffusion-weighted images to one of the non-diffusion weighted images, it is important to also reorient the encoding vectors with the same rotation matrix [42]. Neglecting to perform this important step may have minimal impact on scalar indices such as FA but it can introduce biases of the order of a couple of degrees to estimates of the principal eigenvector, or peaks in the fibre orientation distribution (fODF) or diffusion orientation distribution (dODF).

It is also important to correct for any residual eddy currents along the phase-encode direction by modulating the signal intensity back to its correct value by scaling the intensity in proportion to the change in the volume of the voxel. Neglecting to do this can introduce biases in quantitative metrics and estimates of orientation [30].

Section Summary

  • DTI metrics are influenced by a number of factors related to data acquisition, including the magnetic field and gradient strength, the b-value, the number of gradient directions, and image quality.

  • Pre- and post-processing strategies used to estimate the tensor and correct for artifacts will affect the calculation of DTI measures.

Interpreting Quantitative Diffusion Measures

… in most in vivo DTI cases, all that is proven is that there is a change in the diffusion parameters of water in a specific neural region, the interpretation of which is merely a plausible hypothesis. (C. Beaulieu, [43]).

Diffusion-weighted MRI measurements reflect the amount of hindrance and restriction experienced by water molecules moving with a component of displacement along the axis of the applied gradient, averaged over a voxel. Exactly how restriction and hindrance influence the signal is an open and complicated question and relies on a number of modelling assumptions, which may or may not be correct [36]. The general mobility of water molecules depends on barriers and obstacles imposed by microstructure, e.g., cell membranes, myelin sheaths, and microtubules. Such barriers slow down the diffusing particles (“hindered diffusion”) or even impose an upper limit on their overall mean-square displacement (“restricted diffusion”). The distinction between restriction and hindrance is important when interpreting diffusion MR data. While the tensor parameters are influenced by both restricted and hindered diffusion, the tensor model assumes Gaussianity and therefore translates restricted into hindered diffusion.

It is important to understand that when there is any component of displacement along the applied gradient axis that this will lead to signal attenuation. In other words, if the gradient is applied along a given axis, water molecules do not have to be moving parallel to this axis to cause signal loss. It is only when the displacement is perfectly perpendicular to the encoding axis that there will be no contribution to signal loss since it is only at this orientation that there is no component of displacement along the encoding axis.

Relating DTI Parameters to Neurobiology

Fractional Anisotropy

Several DTI indices can be derived from the eigenvalues to quantify the properties of white matter noninvasively, but the most widely used is FA, which is an index of the amount of anisotropy. FA describes the directional coherence of water diffusion in tissue and is generally interpreted as a quantitative biomarker of white matter “integrity.” This is because pathological studies tend to show a reduction of FA associated with neurodegenerative processes [44–48] and developmental studies tend to show an increase of FA through infancy, childhood, and adolescence [49–53], whilst IQ or improved performance in particular cognitive domains often correlates with increased FA [54–56]. However, equating FA with an index of white matter “integrity” is an oversimplified interpretation because FA cannot disentangle the individual microscopic contributions (partly due to the relatively large voxel size) [12, 30, 36].

FA is influenced by large, oriented macromolecules, organelles and membranes . The degree of myelination, axon packing, the relative membrane permeability to water, the internal axonal structure, and the tissue water content all contribute to tissue anistropy [57]. The degree of anisotropy is often most strongly correlated with axon count and density [43], whilst the degree of myelination correlates with FA, but does not determine tissue anisotropy, which has also been demonstrated in non-myelinated fibres. Furthermore, as axon count and myelin are strongly correlated, it is impossible to differentiate between them when interpreting FA changes. For this reason, FA should not be equated with an index of myelination or myelin damage.

Large regional differences have been observed in WM FA measurements. These differences follow a typical pattern of high FA in the core of fibre bundles and low FA in the periphery [58], although there are exceptions. For example, in regions of where fibre bundles cross, FA is low. Regional anisotropy may arise from differential rates in developmental and degenerative trajectories for different fibre pathways [51]. For example the superior longitudinal fasciculus matures at a relatively later stage of development than other white matter fibre bundles, and an anterior-posterior gradient of FA decline in later adulthood has been observed [59, 60]. This regional heterogeneity introduces its own challenges with regard to both study design and the interpretation of results, as discussed later in this chapter and in Chaps. 8 and 13.

Mean Diffusivity

Recall that MD is a measure of the overall diffusivity in a particular voxel regardless of direction. It is highest in areas where water diffuses most freely, such as in the ventricles, and is lowest in areas of high tissue complexity and hence, more barriers to diffusion, such as in grey matter. MD or “mean” ADC is an important measurement when assessing the evolution of stroke as ischemia-induced changes in tissue water content can be visualized on DWI and ADC maps before they appear on T2-weighted images (see Box 5.4). In the adult brain, white matter water content is lower than that of the grey matter (65 % versus 85 %); however, the MD values for the two regions are virtually identical [61, 62]. This indicates that white matter is less restrictive to water diffusion than grey matter and may be related to the fact that water diffusion parallel to axons is relatively unrestricted, compared to diffusion perpendicular to axons or in grey matter.

Box 5.4: The Effect of Timing on DTI Metrics : Stroke

The acute assessment and monitoring of stroke evolution remain the most useful and widely adopted clinical applications of DTI. Within several minutes of stroke onset there is a substantial decrease in mean ADC/MD in ischaemic brain tissue (by 30–50 %). The basic mechanism underlying this decrease remains unclear [1], but may be due to reduction in extra- and intracellular water mobility, a shift of water from the extracellular to intracellular space, an increase in the intracellular diffusion restriction due to changes in membrane permeability, an increased tortuosity in the extracellular space due to cell swelling [2] and the consequences of cytotoxic oedema. The initial drop in MD pseudo-normalizes around a week later, as a result of blood–brain barrier breakdown, damage to cell membranes, and vasogenic oedema, and gradually continues to rise over the following months. In contrast, anisotropy briefly increases in the hyper-acute phase (<7 h) before decreasing to below pre-lesion levels within 2 or 3 days [3].

Brain water content decreases with maturation . In the immature brain, the MD of white matter is almost twice that of the fully myelinated brain due to the large extracellular spaces present in unmyelinated white matter [63]. During brain maturation, structures such as cell and axonal membranes become more densely packed, and water molecule mobility becomes increasingly restricted. As white matter develops, changes in water diffusion perpendicular to white matter fibres may indicate changes due to premyelination (change in axonal width) and myelination [23]. Differences in water content could also affect the contrast between white and grey matter in the paediatric brain [64, 65]. Therefore, as with FA, it is important to consider the age of the study population when interpreting changes in MD.

Axial and Radial Diffusivities

Recall that axial diffusivity, \( {\lambda}_{\left|\right|} \) is simply the diffusivity along the principal axis of the diffusion ellipsoid (λ 1), whilst radial diffusivity, \( {\lambda}_{\perp } \) is an average of diffusion along its two minor axes, which expresses the amount of diffusivity perpendicular to the principal direction of diffusion, or, in single-fibre populations, perpendicular to the direction of fibre orientation. Some studies have related AD and RD to specific microstructural features. For example, axial diffusivity has been associated with axonal damage, and fragmentation in particular, whilst radial diffusivity has been associated with axonal density, myelin integrity, axonal diameter, and fibre coherence [3, 66].

However, it is important to emphasize that the diffusion direction associated with the axial diffusivity is not always preserved in pathological tissue and is not always aligned with the underlying expected tissue architecture [67]. Therefore, interpreting changes in axial and radial diffusivities in terms of underlying biophysical properties, such as myelin and axonal density is discouraged, unless accompanied by a thorough investigation of their mathematical and geometrical properties [68]. In this context, it also inappropriate to statistically compare the eigenvalues of the diffusion tensor without checking the alignment of the corresponding eigenvectors with the underlying tissue structures, especially when comparing patients with healthy controls [68]. The comparison of eigenvalues between different subjects or comparisons of the contralateral side of a tract affected by pathology in the same subject may be meaningless because they could represent completely different physical information.

Fibre Count

Although not strictly a DTI parameter, the “fibre count” (number of streamlines that pass through or between given regions of interest) can be derived from DTI-based tractography analysis (see Chap. 11). It is sometimes (incorrectly) used as a direct measure of connectivity or fibre density [36]. For this reason, the use of the term “fibre count” has been discouraged and it is proposed that reporting the number of streamlines is a safer and unambiguous way of reporting results [36]. Similarly, the number of streamlines passing through a voxel will be modulated by features of the pathway (curvature, length, width, myelination) and local variations in SNR and therefore interpreting this measure as fibre density is problematic. In this context, it may also be inappropriate to compare the streamline count between white matter structures that have different shapes [36].

DTI Parameters as Complementary Measures

Measures derived from the diffusion tensor, such as FA, essentially combine the contributions from the different sub-compartments of white matter into a single metric. Improving the biological specificity of diffusion MRI demands improvements in both acquisition and modeling schemes. Advanced MR methods may provide putative cellular markers, such as “axon/neurite density,” mean axon diameter, axon diameter distributions, and neurite dispersion (e.g., CHARMED [22], AxCaliber [23], ActiveAx [24], and NODDI [26]). As quantification of myelin via diffusion is extremely problematic, other MR contrast mechanisms may provide complementary information, for example, quantitative magnetization transfer imaging [69, 70] and multicomponent relaxometry (e.g., [71, 72]). Indeed, recent work has demonstrated the utility of this approach in the assessment of the microstructural basis of T2 hyperintensities in neurofibromatosis (NF1) [18].

Section Summary

  • DTI measures can be correlated with microstructural features such as axon count and density, myelination, and membrane permeability.

  • It is inappropriate to attempt to interpret DTI measures in terms of specific microstructural features or as a measure of white matter integrity

  • Fiber count cannot be equated with fibre or axon density. Reporting the number of streamlines is more appropriate.

  • Complementary information from other imaging modalities, advanced dMRI techniques, and histology can support the biological interpretation of DTI metrics.

Challenges of Interpretation

One of the great accomplishments of DTI is reducing complex information into a handful of simple, sensitive, useful measures. However, this oversimplification comes at a price, and that price is the lack of specificity of DTI metrics and their dependence on many methodological and biological factors. By extension, this means that changes in DTI metrics cannot be ascribed to a single factor (or biological/pathophysiological feature), and this makes the interpretation of changes in DTI metrics extremely challenging. For example, the demographics of subjects and controls, the timing and severity of injury or pathology, technical factors related to image acquisition and analysis, and the nature and location of abnormalities, are all important factors when relating DTI metrics to clinical outcome measures. This next section summarizes some of these issues.

Model Limitations

As described earlier in this chapter, and revisited throughout this book, DTI measures are derived from an oversimplified mathematical representation of the average diffusion in a given voxel given a number of assumptions, most of which cannot be satisfied in the “real-world” situation. Although it is beyond the scope of this introductory text to go into detail on this topic, it is useful to consider some of the limitations of the tensor model (further discussion can be found in Chap. 20).

For example, the tensor model assumes that diffusion follows a Gaussian distribution, when in fact, typical dMRI sequences primarily capture signal from intracellular water, which is restricted and hence follows a non-Gaussian distribution. It also assumes a single fibre direction in each voxel, but we know that this condition is rarely satisfied in (complex mammalian) neural tissue. Other, perhaps less intuitive assumptions are that the temperature of the diffusing molecules remains constant and they remain in the same environment, e.g. there is no exchange between intra and extracellular compartments. In reality, variations in temperature will occur as a function of the thermal conductivity of the examined tissue and the proximity of blood vessels, and water molecules may move between compartments during the application of the diffusion-sensitizing gradients.

Another important limitation concerns the ellipsoid representation of the diffusion tensor. Recall that the degree of eccentricity of the ellipsoid reflects the degree of anisotropy, i.e., a long, thin ellipsoid reflects highly anisotropic diffusion (i.e., high FA), and a more spherical ellipsoid reflects more isotropic tissue and (i.e., low FA). However, FA reflects the relative contributions of the axial and radial diffusivities, such that different combinations of axial or radial diffusivity can give rise to the same FA. In this context, by only examining FA, it is not possible to identify the origin of the observed values. For instance, the prolate ellipsoid with λ 1 = 3, λ 2 = 1, λ 3 = 1 and oblate ellipsoid: λ 1 = 7, λ 2 = 7, λ 3 = 1 (arbitrary units) have the same FA value of 2/√11, but have different AD and RD values [73].

Biological Confounds

Demographics

Abnormalities in DTI pararmeters are typically defined on the basis of comparison with a healthy control group because universal thresholds for abnormality have not yet been established. In this context, a number of studies have examined DTI changes in healthy controls across the lifespan. As described earlier, FA typically increases and MD decreases through childhood and adolescence [74] until the fourth decade when white matter volume begins to decrease [51, 75]. However, the lack of standardized DTI acquisition and analysis protocols, means that standard, normative data describing thresholds of normality across the general population are presently unavailable. This situation is likely to change in the future as large-scale, harmonized multicenter studies and data-sharing gain ground.

In addition to age-related effects, other factors may confound DTI findings, including brain volume, gender, ethnicity, level of education, handedness, medical comorbidity, alcohol and smoking use, and medication status, to name but a few (see Chap. 13 for further information ).

Timing

In addition to age, sex and anthropometrics, injury mechanism and the chronicity of injury can greatly influence DTI metrics and it is therefore important that these issues are considered when designing studies and interpreting results. Primary injury and secondary injury play different roles in the evolution of pathology as a function of time post-injury. Microstructural pathology, as detected with DTI, may change over time and it is therefore important to systematically assess the timing of DTI after injury, particularly in the acute and sub-acute periods (between 2 weeks and 1 year) [76] (see Box 5.4).

Complex Tissue Architecture and Crossing Fibres

One of the most important confounds in DTI analysis is the inability of the tensor model to correctly characterise diffusion in regions of complex fibre architecture (i.e., when an image voxel contains fibre populations with more than one dominant orientation, such as in bending or interdigitating fibre configurations at the voxel level) [32] (Chap. 20). The impact of crossing fibres on the main DTI metrics is summarized below.

Impact of Crossing Fibres on FA

The FA, in particular, is strongly affected in areas of complex fibre architecture [35]. FA values are lower in such areas because there is no single dominant diffusion direction and the diffusion profiles of the different fibre configurations average out. Consider how the shape of the diffusion ellipsoid would change in a voxel with more than one fibre bundle. This effect is clearly visible on a standard mid-coronal FA in the semiovale region, at the intersection of multiple fibre pathways (Fig. 5.7).

Fig. 5.7
figure 7

The dark, low-anisotropy region (silver box) that is typically visible in the centrum semiovale on coronal FA maps (a) reflects the inability of the tensor to characterize more than one dominant fibre direction in a given voxel. Compare the more spherical tensor ellipsoid glyphs in this region (b), with those obtained from higher order models (in this case, constrained spherical deconvolution) (c)

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In neurodegenerative conditions, the deterioration of one fibre bundle could result in an adjacent or functionally related fibre bundle becoming more dominant, resulting in a paradoxical increase in FA. In some neuropathological studies, for example, investigating Wallerian degeneration and mild cognitive impairment, higher FA values have been observed in patients than in healthy controls [77, 78].

Impact of Crossing Fibres on the Trace

The b-value and the number, orientation, and trace of individual fibre populations within a voxel affect the trace [48]. In a voxel with two fibre populations, the trace in that voxel is not only dependent on the trace values of the underlying fibre populations but also depends on the angle of intersection between these two fibre populations. As the angle between the two populations increases, the trace in a crossing fibre region gradually decreases with respect to trace in a region with only a single population, reaching its minimum when the populations are orthogonal. The trace therefore depends on the configuration of the crossing, i.e., the angle of intersection between populations and the volume fraction of each of the fibre populations in a voxel [12].

Impact of Crossing Fibres on Mean Diffusivity

There are a number of factors that may influence the estimate of MD, for example the choice of tensor estimation routine or the set of gradient sampling vectors [79]. Vos et al. [12] demonstrate that the MD is lower in complex white matter configurations, compared with tissue where there is a single dominant fibre (SF) orientation within the voxel. They also show that the magnitude of this reduction depends on various factors, including the relative contributions of different fibre bundles, microstructural properties, and acquisition settings such as the b-value.

The dependence of the MD on the tissue geometry has implications for statistical testing. In regions that are comprised of voxels with purely SF-configurations, the MD will be relatively uniform. Likewise, for areas of tissue where there is uniformity in the complexity of the tissue, the MD may be lower but it will be uniformly lower. However, in regions that contain a mixture of SF and crossing fibre configurations that take different geometrical forms, there will be a larger variation in MD. Consequently, there will be a higher variance in such regions, and therefore less statistical power to detect differences in MD .

Impact of Crossing Fibre Configurations on AD and RD

Wheeler-Kingshott and Cercignani [68] have demonstrated the challenges of interpreting changes in axial diffusivity (AD) and radial diffusivity (RD) in crossing fibre regions. Their experiments revealed that AD increased when the RD of one of the underlying fibre populations was increased. Similarly, RD decreased when there was a reduction in AD in one of the underlying populations. They propose a framework to address some of these issues [80]. Vos et al. [12] have also shown an associated reduction in one or more of the tensor’s eigenvalues with lower MD values in regions of complex fibre architecture. With two fibre populations in a voxel, the diffusivity becomes more planar, leading to an underestimation of λ 1 and an overestimation of λ 2.

Technical Issues

Partial Volume Effects

Spatial resolutio n is an important consideration when assessing anisotropy and the aggregate range of diffusivities across the tissues composing the voxel, as it will determine to a large extent, the influence of partial volume effects (PVEs) (Fig. 5.8).

Fig. 5.8
figure 8

The thickness of a fibre bundle modulates the DTI metrics along its length, with smaller, thinner bundles being more susceptible to PVE than larger, thicker bundles. In this example, FA is highest in the middle of a cross-sectional ROI of the cingulum compared to at the bundle periphery. The scatter plot (left bottom) is based on data from Szczepankiewicz et al. 2013 [81]

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PVE is defined as the intra-voxel heterogeneity of different tissue organizations. For example, within one voxel, a variety of tissue types (grey matter, white matter, CSF, vascular tissue) may be present, each with a different type and degree of cellular architecture and fluid content. When averaged out over the voxel as part of the tensor reconstruction, the contribution of all these different tissue structures will give rise to a single dominant diffusion direction. The relative contribution of each tissue type will determine the dominant diffusion direction, so for example, a voxel located in the core of a white matter bundle will be less influenced by PVE than for example, a voxel at the edge of a bundle, or near the ventricles. Vos et al. demonstrated that FA and MD are modulated by fibre bundle thickness, orientation and curvature as a result of PVE [36] and recommend accounting for these features in DTI analysi s.

Impact of CSF Contamination on Diffusion Metrics

Given that diffusion in CSF is isotropic and has a mean diffusivity that is approximately four times larger than water in tissue, it is clear that partial volume contamination any voxel by CSF will influence DTI parameter measurements [82]. This is particularly problematic at the interfaces of tissue with CSF-filled spaces [83] and is an important confound in studies of development and ageing, and in pathological volume change [82].

CSF-suppression techniques such as FLAIR have been used to ameliorate CSF contamination at the point of acquisition [84] but this can prolong acquisition time. Jones et al. [36] recommend the use of a multicomponent modeling solution [85, 86].

In a recent study, Metzler-Baddeley et al. [41] highlight the importance of correcting for CSF-contamination partial volume effects in structures of interest on a voxel-by-voxel basis prior to drawing inferences about underlying changes in white matter structures. They found that diffusivity metrics (mean diffusivity, axial and radial diffusivity) were more prone to partial volume CSF contamination errors than fractional anisotropy. After free water elimination (FWE) based voxel-by-voxel partial volume corrections [85], the significant positive correlations between age and diffusivity metrics, in particular with axial diffusivity, disappeared whereas the correlation with anisotropy remained. Free water elimination may be a more useful strategy than correcting for whole brain volume, which had little effect in removing these spurious correlations [41].

The Role of the Analysis Technique

DTI can be used to study brain structure at a voxel, regional or whole-brain level (See Section III). Regional analyses include those in which an a priori region of interest is chosen for study, and tractography-based analysis, in which an a priori fibre bundle (or bundles) of interest is selected for investigation. In both approaches, typically, average diffusion values such as FA are extracted from voxels within the ROIs or tracts for subsequent analysis. Whole-brain analyses include voxel-based analysis (VBA) (Chap. 10) and histogram analyses of all the voxels in the brain image or in a white matter mask.

Because the different analysis approaches utilize different assumptions and image processing strategies, it is possible that different results can be obtained from each type of analysis. For example, in a recent investigation of bipolar disorder endophenotypes, Chaddock et al. [87] and Emsell et al. [88] report differences in the extent of regional FA changes and association with genetic risk in the same dataset. This does not necessarily mean the results from one type of analysis are correct and the other incorrect. In fact using multiple analytic strategies is important for cross-validation of results. The most commonly implicated regions are generally similar across approaches, whilst subtle, more local effects or spurious findings tend to occur less frequently .

Section Summary

  • Disentangling the relative contributions of biophysical, pathological and methodological factors to DTI measures is challenging and confounds their interpretation.

  • The tensor model is an over-simplification, which provides useful summary measures in single-fibre regions such as the corpus callosum and fornix, but has limited applicability in regions of complex microstructure or “crossing-fibres.”

  • Investigators should consider biological confounds such as subject demographics, the timing and severity of pathology and the location of DTI changes when interpreting results

  • Cross-validation of results using different analysis techniques can yield useful information about the reliability and location of DTI metric changes.

Chapter Summary

Qualitative assessment of diffusion MR images can be supported by quantitative measures derived from DTI data. However, such metrics are influenced by many biological and methodological factors, and should therefore be interpreted with due caution. Fractional anisotropy is a summary measure derived from DTI, which describes the directional coherence (anisotropy) of water diffusion within tissue, while mean axial and radial diffusivity may more specifically describe the direction and magnitude of tissue water diffusion.

Equating FA with an index of white matter integrity is an oversimplified interpretation because FA cannot disentangle individual microscopic contributions at the voxel level. Similarly, the interpretation of measures that are sensitive to the sorting of the eigenvectors or to the effect of noise and partial volume, such as the axial and radial diffusivities, should be discouraged unless accompanied by a thorough investigation of their geometrical properties.

It is important to emphasise that comparing data that have been acquired using different acquisition parameters may be meaningless. This is particularly important in ROIs that contain complex tissue geometry, which will result in greater variation in diffusion measures leading to higher variance in ROIs across subjects and therefore less statistical power to detect differences in diffusion measures.

The accuracy and reliability of DTI based results can be improved by undertaking quality assurance, appropriate pre- and post-processing to correct for artifacts, and by incorporating PVE-related covariates into statistical analysis.