Diffusion MRI tractography for neurosurgery: the basics, current state, technical reliability and challenges

The cerebral WM forms the deeper component of the human brain. It contains bundles of nerve fibres (i.e. axons), the extended cellular processes from the nerve cell bodies (i.e. neuronal soma) located in the cerebral grey matter (GM). Cerebral WM provides the physical pathways through which the neurons interconnect and communicate. Similar to insulated electric cables, many axonal fibres are surrounded by laminated sheaths of lipid-dense tissue called myelin (figure 1), which gives WM its colour. In the central nervous system, myelin is produced by a type of glial cells, called oligodendrocytes. Each myelin sheath wraps around a segment of axon multiple turns (known as a myelin sheath or internode). One oligodendrocyte can form myelin internodes to as many as 50 axons (Lee et al 2021b). Between the neighbouring myelin internodes are approximately 1 μm wide gaps of bare axonal membrane, known as the Nodes of Ranvier (Susuki and Rasband 2008, Kiernan 2009, Lee et al 2021b). Ion channels are confined to these nodes. Action potential jumps from one node to the next, resulting in saltatory (rapid) conduction along neighbouring myelin internodes, providing up to 100 times faster conduction than through unmyelinated nerve fibres (Susuki and Rasband 2008, Kiernan 2009, Lee et al 2021b). Besides the axons, glial cells (neuroglia) make up the remaining cellular constituents in the cerebral WM; these include astrocytes, the aforementioned oligodendrocyte, its precursor cells (oligodendrocyte progenitor cells), and microglia (Walhovd et al 2014). The precise numbers and proportion of different cellular constituents of cerebral WM in humans are unknown ¹¹ .

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At a macrostructural level, the axonal fibres in the cerebral WM are often conceptualised as tightly packed, parallel bundles of myelinated axonal fibres, known as WM tracts or fibre bundles. The WM tracts are conventionally categorised into three main classes based on their connectivity patterns (see also figure 2):

• (1)  
  Commissural WM tracts—they provide inter-hemispheric cortical–cortical connections. The corpus callosum is the largest commissural tract in the human brain. Other examples include the anterior commissure, posterior commissure, and habenular commissure.
• (2)  
  Association WM tracts—they provide either long-ranged or short-ranged intra-hemispheric cortical–cortical connections. Arcuate fasciculus is an example of long association WM tract, providing perisylvian frontal, parietal and temporal cortical connections, critical for subserving language function. Other examples of long association tracts include the superior longitudinal fasciculus, cingulum, uncinate fasciculus, inferior fronto-occipital fasciculus, and inferior longitudinal fasciculus. Short association fibres, also known as the subcortical U-fibres, forming U-shaped connections between adjacent cortical gyri running just below the deepest portion of sulci.
• (3)  
  Projection WM tracts—they connect the cortex with subcortical structures, including the brainstem and spinal cord. They are afferent (outgoing) or efferent (incoming) fibres with respect to the cortex, forming the corona radiata and the internal capsule. Examples include the corticospinal tract subserving voluntary motor function, optic radiation, subserving primary visual function, and fornix, which forms part of the limbic system.

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While conceptually useful to aid neuroanatomical learning, the aforementioned terms, the 'association, commissural, and projection WM tracts', represent a rather over-simplistic view of the WM tract anatomy and patterns of its fibre arrangement. A WM tract can contain axons of different lengths, different sizes (diameters) and with different myelination extents. For example, the cingulum is often simply referred to as a long-range association WM tract, providing direct fronto-temporal connections. Evidence from both human cadaveric fibre dissection and non-human primate axonal neurotracer studies (Tournier et al 2011, Thiebaut de Schotten et al 2012) suggested it comprises both long- and short-range association fibres. The longest fibres connect the frontal subgenual region to mesial temporal lobe structures; while the shorter subcortical U-fibres pass in and out the cingulum, joining the adjacent cingulate, frontal and precuneus cortices. Similarly, histology studies of the human corpus callosum in the mid-sagittal plane revealed regional differences in axonal diameters and myelination extent, reflective of the need for different functional purposes and the associated nerve conduction speed (Aboitiz et al 1992).

Next, these WM tracts are arranged in a necessarily complex way, forming a 3D structural chassis through which the neurons communicate between and within the cerebral hemisphere, the cerebellum, and the brainstem. Locally, axonal fibres from different WM tracts, such as those contained within an MRI voxel, can be arranged either simply as tightly packed parallel axonal bundles; or organised in more complex ways, such as containing axonal fibres that are bending, kissing and crossing with each other, collectively termed the 'crossing fibre' phenomenon in the field of dMRI (Tuch et al 2002, Behrens et al 2007, Tournier et al 2011). Distinguishing different WM fibre sub-populations in these crossing fibre regions may not be possible, even with the meticulous cadaveric fibre dissection technique. It has been shown that such crossing fibre arrangement is highly prevalent, present in up to 90% of the brain WM regions in the human brain (Jeurissen et al 2013). This is an important point to bear in mind when considering the validity of dMRI models since the dMRI signal is sensitised by structural factors governing tissue microstructural environment, including axonal fibre arrangements (more to this in Q&A 2 and 3).

Achieving gross total lesion resection is the most important factor affecting survival following glioma neurosurgery (Kuhnt et al 2011, Capelle et al 2013, Li et al 2016), and the strongest predictor of achieving seizure freedom following lesion-based focal epilepsy surgery (Hamiwka et al 2005, Krsek et al 2009, Fallah et al 2015). Planning for and performing neurosurgery requires an in-depth understanding of individualised neuroanatomy, including the WM tract anatomy, as affected by pathology, to help survey surgical risks and to determine a safe surgical strategy. Not all WM tracts are considered equally important by neurosurgeons. This is particularly relevant when the lesion resides within or adjacent to eloquent brain cortices, such as areas controlling movement, language and vision, and the related WM tracts. Inadvertent injury to the WM tracts during surgery can lead to permanent functional damage and adverse neurocognitive sequelae (Kinoshita et al 2005, Duffau 2014, Nimsky 2014). The need for subcortical WM preservation makes having accurate and precise WM tract reconstructions foremost paramount for pre-surgical planning.

MRI-based neuroimaging is indispensable for modern neurosurgical practice, with critical roles in aiding pre-surgical planning and providing intraoperative imaging guidance (Upadhyay and Golby 2008, Enchev 2009). During surgery, the patient's head is co-registered with his or her preoperative MRI data using the image-guided neuronavigation software. Akin to a Global Positioning System, this enables subsequent intraoperative neuronavigation by accurately tracking the positions of the surgical instruments, and displaying these in relation to the patient's MRI dataset. Additionally, predefined image segmentations, such as the tumour volume, and the tractography images can be displayed into the operating microscope eyepiece, via augmented reality technology, and thus, be overlayed on the live microscope view as either semi-transparent or outlined objects (Kuhnt et al 2012, Sommer et al 2013). The ability to confirm the live resection view with MRI makes surgery more precise, while minimising injury to surrounding healthy brain structures. Conventional structural MRI sequences, such as T1-weighted, gadolinium contrast enhanced T1-weighted, T2-weighted, and fluid-attenuated inversion recovery (FLAIR) imaging, provide rich information concerning the relevant surgical anatomy. This includes demonstrating the regional surface sulcal-gyral and vascular anatomy, lesion extent, and the clarity of the tumour-brain interface. They also provide clues about pathological tissue properties and makeups, such as the presence of solid versus cystic component; the presence of acute intra-lesion haemorrhage; and suggestion of histopathologically high-grade tumour component with gadolinium-contrast enhancement. Despite being informative, none of these routine structural MRI sequences can depict the WM tract anatomy, specifically to demonstrate the tract disruption and/or displacement from its conventional trajectory, adjacent to the target surgical lesion (see figure 3(a)).

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Without being able to delineate affected WM tract location under direct vision, direct brain electrical stimulation (DES) performed during surgery is widely accepted as the surgical 'gold standard' confirming the WM tract position and its functional relevance (more details about the DES procedure is described in Q&A 7) (Penfield and Boldrev 1937, Ojemann et al 1989, Berger and Hadjipanayis 2007, Duffau 2015). Pre-surgical localisation of intrinsic tumours and functional cortical regions may be achieved by multiple non-invasive imaging modalities, such as positron emission tomography (PET); single-photon emission computed tomography; blood oxygen level-dependent functional MRI (BOLD-fMRI); magnetoencephalogram (MEG); and navigated transcranial magnetic stimulation (nTMS). Diffusion MRI tractography remains the only non-invasive technique enabling visualisation of in vivo WM tract anatomy (Jones 2008a), making it a powerful technique to complement neurosurgical planning and intraoperative execution (figures 3(b) and (c)). Coupled dMRI tractography with functional brain mapping strategies, such as BOLD-fMRI, or with intraoperative DES findings can improve the functional relevance of tractography reconstructions and offer insights into brain structural-functional relationship between the cortical–subcortical structural networks and patient's functional states both before and after the surgery (Berman et al 2004, Kinoshita et al 2005, Bello et al 2008, Sanvito et al 2020) (more to this in Q&A 5).

• The brain WM consists of myelinated and unmyelinated axonal bundles forming a complex 3D structural chassis, important for information relay between connected cortical and subcortical GM regions and brainstem.
• The majority of brain WM regions contain crossing fibres or more complex fibre arrangements, rather than simply tightly packed parallel fibre bundles.
• WM tract preservation is imperative for optimising post-surgical functional outcomes.
• Diffusion MRI is currently the only non-invasive imaging technique enabling in vivo mapping of WM tracts throughout the human brain.

Diffusion-weighted imaging (DWI) is a class of MRI method, whereby the signal obtained is sensitised by the diffusion of water molecules. In 1965, Stejskal and Tanner pioneered the famous PGSE sequence (Stejskal and Tanner 1965), which is still widely used by the typical dMRI scans nowadays. The PGSE sequence forms the basis of many modern dMRI methods. Following their PGSE experiments, they also proposed the Fourier relationship between the diffusion-weighted (DW) signal and the spin displacement distribution, which has laid the foundation of the q-space theory in diffusion imaging (Callaghan et al 1988) (see next paragraph). Stejskal–Tanner's PGSE pulse sequence employed a pair of magnetic field gradients with short duration (so-called 'diffusion gradients'), with equal magnitude and opposite gradient polarity, to record the diffusion-driven net dephasing of the spins (see figure 4) (Stejskal and Tanner 1965). The basic principle is that one diffusion gradient 'labels' the spins according to their spatial position (within the gradient), and the other diffusion 'unlabels' the spins—if no diffusion is present, the two effects cancel out; however, diffusion introduces a mismatch in the contribution from both gradients, leading to a net phase accumulation for each spin related to their diffusion. The PGSE sequence has a clear distinction between the diffusion encoding time and the diffusion time, defined as the duration and separation of the diffusion gradient pair, respectively. To correlate DW signal with molecular diffusion, Torrey considered the magnetisation transfer induced by diffusion and re-formulated the Bloch–Torrey equation by including an additional term (Bloch 1946, Torrey 1956). For an isotropic medium, the solution for such an equation is given as

$$\begin{eqnarray}&&S({\rm{T}}{\rm{E}},b)={S}_{0}\cdot {\rm{\exp }}\left(-\displaystyle \frac{{\rm{T}}{\rm{E}}}{{{\rm{T}}}_{2}}\right)\cdot {\rm{\exp }}(-bD)\end{eqnarray} \tag{ 1 }$$

in which D is the diffusion coefficient of the medium, S₀ is the initial MR signal without diffusion weighting at time t = 0, S is the MR signal obtained at the echo time (t = TE), T2 is the transverse or spin–spin relaxation time at which the transverse magnetisation decays to approximately 37% of its initial value (i.e. S₀), and b is the diffusion sensitising/weighting factor, or the so-called b-value, defined as

$$\begin{eqnarray}&&b=\displaystyle {\int }_{0}^{{\rm{T}}{\rm{E}}}k{(t^{\prime} )}^{{\rm{T}}}\,\cdot \,k(t^{\prime} )dt^{\prime} ,\,{\rm{with}}\,k(t)=\gamma \displaystyle {\int }_{0}^{t}G(t^{\prime} )dt^{\prime} ,\end{eqnarray} \tag{ 2 }$$

where δ is the nuclear gyromagnetic ratio, G(t) denotes the time-dependent gradient strength, and T means transpose operation. The diffusion gradient with a symmetric trapezoidal shape produces b-value as

$$\begin{eqnarray}&&b={\gamma }^{2}{G}^{2}\left[{\delta }^{2}\left({\rm{\Delta }}-\displaystyle \frac{\delta }{3}+\displaystyle \frac{{{\epsilon }}^{3}}{30}+\displaystyle \frac{\delta {{\epsilon }}^{2}}{6}\right)\right],\end{eqnarray} \tag{ 3 }$$

where δ is the duration, ∆ the separation, and ε the gradient rise time; the effective diffusion time (∆_eff) is usually defined as ∆_eff = ∆ − δ/3. Notably, without the diffusion weighting factor, i.e. at b = 0, the MR signal S in equation (1) is modulated by the T2 relaxation time of local tissue, thus producing a T2-weighted image contrast using the PGSE sequence.

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When using Stejskal–Tanner's PGSE pulse sequence (Stejskal and Tanner 1965), the accumulated phase shift for a single spin in the magnetic field gradients is given as

$$\begin{eqnarray}&&\phi (t)=\gamma {B}_{0}t+\gamma \displaystyle {\int }_{0}^{t}G(t^{\prime} )\,\cdot \,r(t^{\prime} )dt^{\prime} ,\end{eqnarray} \tag{ 4 }$$

where the first term represents the phase due to the static magnetic field B₀, and the second term is due to the effects of a magnetic field gradient. For a diffusing spin, the degree of phase accumulation owing to the applied gradient of a PGSE sequence is proportional to the spin displacement along the direction of the applied gradient. At TE, when the spin echo is formed, the net phase shift (φ) of one individual spin is therefore

$$\begin{eqnarray}&&\phi =\gamma \left(\displaystyle {\int }_{0}^{\delta }G(t^{\prime} )\,\cdot \,r(t^{\prime} )dt^{\prime} -\displaystyle {\int }_{\Delta }^{\delta +{\rm{\Delta }}}G(t^{\prime} )\cdot r(t^{\prime} )dt\right).\end{eqnarray} \tag{ 5 }$$

If the diffusion gradient pulse duration in a PGSE sequence is infinitely short (i.e. δ ≪ ∆), the diffusion distance under the diffusion gradient pulse duration is substantially smaller than the pore size of the medium. Under this narrow pulse approximation, the spin phase is then

$$\begin{eqnarray}&&\phi =\gamma G\delta ({r}_{0}-r),\end{eqnarray} \tag{ 6 }$$

where r₀ and r are the spin's position at the first and second instantaneous gradient pulse, respectively. For a given proton density ρ, the diffusion signal taking into account the spin displacement probability or diffusion propagator ${P}_{s}\left(r\left|{r}_{0},t\right|{t}_{0}\right),$ which is the conditional probability of finding a single spin at position r from its initial position r₀ after any diffusion time interval τ = t − t₀, is given as

$$\begin{eqnarray}&&S={S}_{0}\displaystyle \int \displaystyle \int \rho ({r}_{0}){P}_{s}\left(r\left|{r}_{0},{\rm{\Delta }}\right.\right)\exp \left[i\gamma G\delta ({r}_{0}-r)\right]d{r}_{0}dr.\end{eqnarray} \tag{ 7 }$$

Assuming that R = r₀ − r, this can be reformulated as

$$\begin{eqnarray}&&S={S}_{0}\displaystyle \int P(R,{\rm{\Delta }})\exp (i\gamma G\delta R)dR,\end{eqnarray} \tag{ 8 }$$

where P(R,∆) expresses the average probability for a spin diffusing a distance R within a time interval ∆. It is sensible to introduce the effects of the diffusion gradient pulses into the analysis by defining the reciprocal spatial vector q given as

$$\begin{eqnarray}&&q=\displaystyle \frac{\gamma G\delta }{2\pi }.\end{eqnarray} \tag{ 9 }$$

Hence, this q-space formalism can be rewritten as

$$\begin{eqnarray}&&S\left(q,{\rm{\Delta }}\right)=\displaystyle \int \left(R,{\rm{\Delta }}\right)\exp \left(i2\pi qR\right)dR={\Im }^{-1}\left\{P(R,{\rm{\Delta }})\right\}.\end{eqnarray} \tag{ 10 }$$

Based on this Fourier relationship, a mathematical q-space analysis method was developed by Cory and Garroway (1990) and by Callaghan (1993). They proposed that at a sufficient diffusion time, the displacement probability function may relate to the size and shape (e.g. spherical, cylindrical) of the compartment where diffusion occurs. These microstructural parameters will be reflected by the diffusion-diffraction peaks in the echo signal attenuation. Therefore, the q-space imaging technique can reveal direct microstructures of the biological tissues.

The driving force of diffusion MRI is to monitor the diffusion-driven displacements of water molecules at a microscopic level, which is well beyond the image resolution of both typical clinical and modern research-orientated MRI scanners that are at millimetre scale. The overall signal observed in DWI represents the statistical integration of all microscopic water molecular displacements presented in an MRI voxel. Accordingly, the complex diffusion processes that occur in a biological tissue on a voxel scale are often described with a global statistical parameter, named ADC (Le Bihan et al 1986):

$$\begin{eqnarray}&&S\left({\rm{T}}{\rm{E}},b\right)={S}_{0}\,\cdot \,{\rm{\exp }}\left(-\displaystyle \frac{{\rm{T}}{\rm{E}}}{{{\rm{T}}}_{2}}\right)\,\cdot \,{\rm{\exp }}\left(-b\cdot {\rm{A}}{\rm{D}}{\rm{C}}\right).\end{eqnarray} \tag{ 11 }$$

Such parameterisation of diffusion by a global ADC is intended to represent those physical processes that occur at scales smaller than the scales resolved by the method. The scale of an MRI voxel is imposed by technical limitations, e.g. by the strength of the imaging gradient field, whereas the actual scale of the diffusion processes and interactions with the local tissue environment is determined by physical phenomena at microscopic scale. The so-called partial volume effect averages and smooths some spatial inhomogeneity, making ADC parameter a summary metric of microscopic diffusion process within an MRI voxel in millimetric scale.

For isotropic free water diffusion, i.e. when the spin displacement probability is a three-dimensional Gaussian distribution, DW signal attenuation can be modelled using a monoexponential function characterised by ADC, as shown by equation (11). In biological tissue, water molecular diffusion or spin displacement is hindered by local tissue architecture. The movement of water molecules under typical diffusion time can be interfered by many biological elements, such as cell membranes, myelin sheaths, water contents and other macromolecules, leading to diffusion anisotropy (Moseley et al 1991, Beaulieu 2002).

In biological tissues containing some forms of coherent structural organisation, such as the brain WM tracts, water diffusion is hindered to a greater extent in a direction perpendicular to the principal axonal axis than parallel to it. Importantly, this means that DW signal and the derived ADC value within the same voxel would vary depending on the applied DW gradient direction. For example, the measured DW signal attenuates to a much greater extent in the direction aligned with the principal axonal axis than perpendicular to it, leading to a higher ADC value along this direction. This suggests that a set of gradient directions are necessary to obtain DW signal as a function of orientation, from which certain models can be imposed to estimate the underlying fibre organisation within a local MRI voxel. In 1994, Basser et al proposed the first model for this purpose, which is now well recognised in the field as the famous diffusion tensor model for analysing dMRI data, also known as 'DTI' (Basser et al 1994a, 1994b); see the next Q&A.

• The dMRI signal is sensitised by the underlying tissue microstructural environment, making it a unique and powerful tool to probe brain WM macro- and microstructures.
• The classic Stejskal–Tanner's PGSE pulse sequence is the basis of q-space theory that describes the diffusion-driven MRI signal attenuation.
• Isotropic free water diffusion can be modelled as a Gaussian distribution parameterised by the diffusion coefficient.
• Water diffusion in the brain WM tracts is anisotropic and non-Gaussian distributed. The ADC value parallel to the principal axonal axis is greater than those derived perpendicular to this axis.
• The DW signal is a function of gradient orientation in the brain WM.

The tensor model and tensor-based tractography remain the most widely adopted technique for the studying of in vivo brain WM tracts and their microstructural properties. The tensor provides a means to characterise the degree of diffusion anisotropy within DWI voxels, through an imposed assumption that the distribution of spin displacement is Gaussian. The term 'DTI' is often misinterpreted as synonymous with 'DWI', whereas it is not: DTI is only one of the many dMRI local modelling methods to analyse DWI data. The tensor model can be represented as a 3 × 3 matrix:

$$\begin{eqnarray}D=\left[\begin{array}{ccc}{D}_{xx} & {D}_{xy} & {D}_{xz}\\ {D}_{yx} & {D}_{yy} & {D}_{yz}\\ {D}_{zx} & {D}_{zy} & {D}_{zz}\end{array}\right].\end{eqnarray} \tag{ 12 }$$

The diagonal elements of the diffusion tensor correspond to the ADC value in the corresponding direction (e.g. D_xx  = ADC_x ); the off-diagonal elements reflect the correlation between diffusion in the corresponding two directions (e.g. D_xy is a measure of the correlation of the diffusion along the x and y directions). As the diffusion tensor, D, is a symmetric and positive definite matrix, it has six unknown coefficients to be estimated (as D_xy  = D_yx , D_yz  = D_zy , and D_xz  = D_zx ). Hence, the tensor model requires at least six DWIs (with diffusion sensitisation in six non-collinear directions) and one reference image without diffusion weighting to perform tensor decomposition:

$$\begin{eqnarray}&&D{\varepsilon }_{i}={\lambda }_{i}{\varepsilon }_{i},\end{eqnarray} \tag{ 13 }$$

where ε_i is the eigenvector of its corresponding eigenvalue λ _i (i = 1, 2, 3). The largest eigenvalue λ₁ gives the principal direction of the diffusion tensor, ε _i , and the other two eigenvectors span the orthogonal plane to it. Schematically, the DTI model can be represented as an ellipsoid with the principal axis parallel to the principal eigenvector (ε₁). The other two minor axes of the ellipsoid represent eigenvectors, ε₂ and ε₃, in orthogonal planes to the principal eigenvector. The relative difference between the three eigenvalues determines the size and the shape of the tensor ellipsoid. Some rotationally-invariant scalar measures have been defined based on this eigensystem decomposition in the literature, the most widely used are the mean diffusivity (MD, which reflects the overall size of the tensor ellipsoid) and the fractional anisotropy (FA, which is a quantitative measure of how the tensor ellipsoid deviates from a spherical shape) (Basser and Pierpaoli 1996). Figure 5 illustrates the maps of scalar metrics, ellopsoids, and principal eigenvectors that can be obtained using the tensor-based modelling.

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To complement these scalar maps with orientation information of the diffusion tensor, a directionally encoded colour (DEC) map is also typically generated based on the principal eigenvector. By convention, this DEC map uses a red–blue–green colour scheme (Pajevic and Pierpaoli 1999). The red colour represents the component of the principal eigenvector along the left–right orientation, the blue colour represents the component in the superior–inferior orientation, and the green colour represents the component in the anterior–posterior orientation.

Based on the analysis of the local tensor for every voxel within the brain, it is possible to infer the structural morphology of WM tracts using diffusion MR tractography (see below), and its cellular microstructure properties in both the healthy and disease states by quantifying diffusion tensor metrics.

As shown by equation (13), the decomposition of a local diffusion tensor yields three eigenvalues and the corresponding eigenvectors. A notable feature is that when an MRI voxel is occupied by coherent axonal fibres, there is a strong correlation between the fibre orientation and the direction of the principal eigenvector (ε₁) (Basser et al 2000, Lin et al 2001). The voxel-wise tensor decomposition provides a vector field of principal eigenvectors that can be connected between neighbouring voxels to form a curve or a streamline. This is the original concept of dMRI streamline tractography (Conturo et al 1999, Jones et al 1999, Mori et al 1999, Basser et al 2000), where WM tracts are delineated by streamlines generated through a stepwise integration process using a mathematical algorithm, based on the local fibre orientation distributions obtained from an applied signal or biophysical model. The diffusion tensor was the earliest model to provide such a vector field, and hence this is the information that most initial fibre-tracking algorithms were based upon. The simplest tractography algorithm is based on a deterministic model, which follows step-wise the estimated local WM fibre directions through the data until some termination criterion is reached. These methods are labelled as 'deterministic' since the trajectory is uniquely determined for a given starting point or so-called the seed point.

The first algorithm operating as such was the Fibre Assignment by Continuous Tracking algorithm (FACT) using the principal eigenvector of the tensor as the direction of propagation (Mori and van Zijl 2002), which became the most popular algorithm for over a decade. Starting from a predefined seed point, this method works by evaluating the direction of the fibre at the current location, stepping along this direction by a small fixed step size, and repeating until the track or streamline is terminated. Termination criteria typically include that the streamline has entered an area of low FA (since these methods typically rely on DTI to estimate fibre orientations), or that the streamline has made a sudden sharp turn (high curvature), deemed biologically implausible.

Using dMRI tractography, streamline trajectories can be generated that seem to follow the path of known WM tracts (figure 6). Importantly though, tractography does not reconstruct actual WM fibres or axons but only streamlines (or curves in 3D space) that are mathematical representations that delineate possible WM tracts—a crucial concept that has been misused quite frequently for applications in the field (Jones et al 2013, Jeurissen et al 2019).

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Deterministic tractography algorithms, like the FACT method, exploit the local orientation distribution information of the diffusion process (or fibres) to reconstruct from a starting seed, a virtual connection that corresponds to the most probable propagation path within this local orientation field. This retrograde and anterograde propagation process from the initial seed corresponds to a numerical integration scheme whose order can be adjusted to vary the integration step and accelerate the integration process. Deterministic tractography algorithms are inherently very sensitive to the presence of noise in the DWI data, which can lead to both false positive and false negative errors in estimating the local direction of the fibres in tractography output reconstructed over the whole brain. The quality of the estimated local orientation also depends on the ability of the chosen model to correctly represent the underlying reality.

To reduce this dependency on the noise present in the data and to compensate for the limitations of the tensor model to efficiently map the fibre configurations, probabilistic tractography methods have been introduced that fall into two broad categories: statistical sampling and Bayesian inference methods:

• (1)  
  In statistical sampling approach, probabilistic streamlines are generated in most aspects similar to deterministic streamline methods, except that streamline propagation is sampled from the distribution of fibre orientation during the integration process (Parker et al 2003, Jones 2008b), rather than a 'fixed' direction in the deterministic tracking algorithm. It is a convention to derive these candidate directions from a Gibbs sampler to favour the most plausible directions. Due to its probabilistic nature, these algorithms require generating many streamlines, to properly sample the available directional configurations. The tractography outcomes obtained from such methods are generally populated with good anatomical connections, but also with more false positive connections that should be removed by a posteriori filtering.
• (2)  
  The Bayesian approach does not reconstruct individual streamlines. Instead, it aims to construct for each point of interest within the brain, the connection probability maps to all points on the target region of interest (ROI) (Behrens et al 2007). The Bayesian approaches are also contaminated with false positives as the streamline approach above, whereas a posteriori cannot be applied to remove these errors.

It is important to understand that the choice of the local model is independent of the choice of the tractography algorithm (e.g. the tensor model can be combined with either the deterministic or probabilistic tracking strategies). Both components can be responsible for errors and lead to the creation of false positives in the connectivity maps.

The tensor model is simple and fast in terms of data acquisition and analysis, making it a popular technique to be applied in acute neurosurgical settings. In addition, tensor-based analysis including tractography has been implemented as a package by the major MRI scanner and surgical neuronavigation vendors, and thus is the default post-processing approach for the majority of clinical tractography analysis.

The fundamental problem of DTI framework is the assumption that spin displacement follows a Gaussian or normal distribution in the brain WM. As outlined previously (section 2.4), water diffusion can be hindered or restricted by several brain WM microstructural properties within the typical diffusion time. On the other hand, although the tensor model can deliver an accurate depiction of the fibre orientation in regions where there is only one coherent fibre population, a tensor can only model a single fibre population within a voxel. When a voxel is filled with 'crossing fibres' with more than one orientation, the principal eigenvector of the tensor will become ambiguous (shown in figure 5). Given the high occurrence of crossing fibres in the human brain (Jeurissen et al 2013), this will cause subsequent qualitative and quantitative tractography errors, if the principal eigenvector field serves as the input data upon which the fibre tracking algorithm operates. Furthermore, the tensor-based anisotropic metrics, such as FA, would also be affected by the incoherent fibre distributions (Tournier et al 2011). Limitations of the tensor model to deal with intravoxel incoherent fibre population motivated the invention and development of several 'higher-order' local methods. They are discussed in the following Q&A.

• The diffusion tensor model can be schematically represented using an ellipsoid, with its principal axis corresponding to the direction of the principal eigenvector of the diffusion tensor.
• The deterministic tensor-based fibre tracking is the simplest tractography algorithm that takes the principal eigenvector of the tensor model as the fibre direction.
• Probabilistic tractography samples the distribution of fibre orientations at each tracking step to provide a likely distribution of the WM tracts.
• The diffusion tensor and tensor-based tractography are problematic since the tensor model cannot differentiate 'crossing fibres' or other complex fibre arrangements that appear frequently in WM voxels of the human brain.
• DTI is not synonymous with DWI. It is only one of the many dMRI local modelling methods.

Obtaining voxel-wise orientation distribution functions (ODFs) is the main target of local modelling. The so-called 'high angular resolution diffusion imaging' (HARDI) data are acquired using a higher b-value (≥3000 s mm⁻²) and more non-collinear diffusion directions (≥45 directions), than those acquired for the tensor model (typical b-value is 1000 s mm⁻² with <30 diffusion directions) (Tournier et al 2011). As such HARDI estimates the additional higher angular frequency features of the DW signal that are not adequately modelled by the tensor model. The HARDI local modelling techniques can be broadly categorised into two main classes from their principles—one estimates diffusion ODF (dODF) and the other estimates fibre ODF (fODF). The following subsections provide a general description of these key ideas. To gain further methodological insights into various modelling techniques, the readers are referred to Daducci et al (2014) for more details.

4.1.1. Methods for deriving dODF

4.1.2. Methods for deriving fODF

This class of technique directly reconstructs the fODF which is represented as a mixture model of distinct fibre populations. The model-dependent reconstruction techniques can be divided into two categories: those based on an impulse response function of the fibre bundle to the diffusion process expressed as a parametric function, and those where the impulse response is estimated directly from the acquired data. Various parametric functions on the sphere have been used, such as Gaussian mixtures (Alexander et al 2001), Ball and Sticks (Behrens et al 2003), and among others (see (Jelescu and Budde 2017) for review). Back in 2004, the idea of spherical deconvolution of the DW signal was emerged, assuming a Gaussian kernel self-estimated from the most anisotropic voxels of a single-shell DWI dataset (Tournier et al 2004, Anderson 2005). The technique based on spherical harmonics was further improved, known as the non-negativity CSD technique, by ensuring the positiveness of the ODF values (Tournier et al 2007, 2008). While there is still no consensus about which local modelling technique outperforms the other, the CSD-based fODF estimation is increasingly widely used. A further improvement of CSD was achieved using a multi-shell q-space sampling and extending the deconvolution approach to take into account the existence of several diffusion kernels corresponding to the various brain tissue types that can be encountered within the voxels (i.e. the GM, WM, and CSF) (Jeurissen et al 2014; see figure 7). This multi-shell multi-tissue CSD technique is used growingly, providing more reliable fODF information for tractography. It is now also possible to perform reliable local multi-tissue CSD estimations using either a single-shell HARDI data (Dhollander and Connelly 2016), or a single-shell, non-HARDI dataset consisting of a lower b-value and/or lesser diffusion directions (Calamuneri et al 2018, Arrigoni et al 2020, Fekonja et al 2021). Of note, the tractography examples shown in figure 6 were reconstructed using the multi-tissue CSD model.

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4.1.3. Methods for quantifying tissue microstructure

Improving fibre orientation estimates is an essential step for voxel-wise ODFs reconstruction in tractography. While providing more accurate fibre orientation estimates over the crossing fibre regions than those estimated by the tensor model, ODF-based tractography methods are not problem-free. Concerns remained regarding the anatomical accuracy (Thomas et al 2014) and the propensities of generating many false positive streamlines for ODF-based tractography methods (Maier-Hein et al 2017). The discrepancy between the estimated WM fibres (in micrometre scale) and the dMRI voxel dimension (in millimetre scale) causes the partial volume effect. This leads to a 'bottleneck effect' on the accuracy of the fibre orientation estimate that can be achieved (Maier-Hein et al 2017). In WM regions with complex fibre configuration, the ODF-based algorithm may indiscriminately reconstruct all possible configurations that are compatible with the ODF field, leading to the downstream bias of retaining many false positive streamlines (Tournier 2019). This is particularly critical for whole-brain tractography and structural connectomics ¹³ analysis, where there is a need to address the tractography reconstruction bias by deriving quantitative metrics from the streamlines to approximate true WM fibre properties (see next section). In targeted tractography adopted in neurosurgical applications, the goal is to reconstruct a known WM tract. The use of a priori anatomical knowledge about the WM tract is fundamental to make the tractography technique 'less blinded' to the underlying biological reality. It is quite well established now that targeted tractography can be highly accurate if it can be a priori constrained by knowledge of where the WM tract starts, ends, and where it does not go (more to this in Q&A 5) (Schilling et al 2020a).

A step further to tractography reconstruction is to derive quantitative parameters for individual WM tracts. For instance, a common 'along WM tract profiling' (tractometry) approach combines WM tract segmentation with voxel-wise MRI metrics, allowing tract-wise microstructural quantification (Colby et al 2012, Yeatman et al 2012). While measures such as tensor-based FA and MD have been used frequently as imaging surrogates of tissue microstructures, the field has now gravitated toward implementing more direct imaging metrics representing proxies of the underlying cellular geometries as described in section 4.1.3. Such quantitative analysis is an important basis for brain structural connectomics research (Sotiropoulos and Zalesky 2019, Yeh et al 2021). Direct tissue validations of these tractography-based quantitative DWI metrics, in the healthy and the pathology states, remains an open issue in both the fields of neuroscience and clinical neuroimaging research. In recent years, DWI-based quantitative metric analysis, has moved on from tractography visualisation in pre-surgical planning to an entire field of clinical neuroimaging study, attempting to investigate the impacts of various neurosurgery-related pathologies on the tractography diffusion metrics, and to address postoperative outcome predictions based on DWI-based metrics derived from the preoperative tractography data. For example, in a clinical series of 30 mixed adult brain tumour patients, nTMS-based corticospinal tract tractography reconstructed using individualised FA thresholds, had been demonstrated to improve both the precision and functional relevance of the reconstructions, which in turn affected pre-surgical planning by directly modifying the surgical strategies and facilitating intraoperative neuronavigation and electrostimulation (Frey et al 2012). Both the tract-averaged and peri-tumoural FA reduction and ADC increase derived from the preoperative nTMS-based corticospinal tract tractography had been shown to predict postoperative motor deterioration in motor-eloquent adult high-grade gliomas (Rosenstock et al 2017). A recent publication by the same group extended the investigation to 65 motor eloquent high-grade glioma adults, using a more fibre-specific metric based on the CSD model derived along the corticospinal tract profile, showing they were more specific to tumour-induced changes compared to the ADC or FA values (Fekonja et al 2021). Nonetheless, detailed discussion about advanced quantitative tractography inferring brain microstructures, is beyond the scope of the present review and will only be briefly covered here with a short introduction.

Tractography is a mathematical computing process that has no direct quantitative physical and biological attributes (Jones et al 2013). One intuitive (but wrong) manner to make conventional tractography quantitative is by measuring the streamline density or streamline counts, within a WM tract. These streamline metrics are commonly adopted as an edge metric in connectome analysis to indicate the connection 'strength' of a WM tract. It has been increasingly recognised in the field that the reconstructed streamline density from conventional tractography cannot represent a valid imaging biomarker of the biological WM fibre density (Jones et al 2013). Studies have adopted other edge metrics, such as the mean FA value along a WM tract, as surrogates to biological WM connectivity (see Yeh et al (2021) for more details). There is still no clear evidence to verify which of these imaging metrics more closely approximates the true biological connectivity. Nevertheless, some clinical investigators have adopted the large-scale network connectome approach to assess or predict the post-surgical properties of WM tracts in clinical neurosurgical tractography reconstructions (Bonilha et al 2013, 2015, Hutchings et al 2015, Aerts et al 2018, Gleichgerrcht et al 2018, 2020, Henderson et al 2020). Together with the functional connectome derived from the resting-state fMRI data, such a network-based approach has the added benefit of addressing the issue of localism versus distributed function that arises in targeted tractography.

Outstanding progress made about advanced quantitative tractography methods in recent years has led to improved biological relevance of the reconstructed quantitative WM connectomes. Many of them exploit the quantitative microstructural information derived from advanced local modelling to estimate the contribution of reconstructed streamlines. For a more comprehensive introduction of this area, readers are advised to check out the recent articles (Daducci et al 2016, Jeurissen et al 2019, Rheault et al 2020, Zhang et al 2021) and book chapters (Smith et al 2020) dedicated to reviewing the key aspects of quantitative tractography reconstruction.

• Local models beyond the diffusion tensor aim at resolving the 'crossing fibres' problem by improving the accuracy of fibre orientation mapping; they can be broadly categorised into the method measuring dODF and fODF.
• Modern ODF-based tractography is not problem-free. The anatomical accuracy and false positive streamline generation are two major issues.
• Incorporating a priori anatomical knowledge about the WM tract into tractography is the key to improve the biological accuracy of the streamlines generation.
• Many advanced quantitative tractography methods exploit the brain WM tissue microstructural information derived from the advanced local modelling techniques. They are more relevant for whole-brain tractography reconstructions and quantitative structural connectomics research, and less relevant for tractography used in neurosurgery.

Targeted tractography utilises strategically placed ROIs typically based on a priori knowledge about the WM tract anatomy, to impose anatomical constraints for streamline propagation/tracking (see figure 8). They include: the seed ROI, which defines the starting point of streamline tracking; the inclusion ROI (also known as the 'AND' ROI or 'waypoints'), which defines the obligatory tract passage where the tract is known to pass through; and the exclusion ROI (also known as the 'NOT' ROI), which defines the region the tract is known not to pass through. Streamlines intersecting the exclusion ROI are rejected.

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The streamline tracking in targeted tractography is also dependent on the spatial and angular resolution of DWI data (Vos et al 2016, Schilling et al 2017), and many algorithmic variables that can be subjectively selected by the tracking operator. These include the dMRI model (e.g. DTI versus high-order models, such as CSD), the tracking algorithm of choice (e.g. deterministic versus probabilistic); and a set of pre-defined tracking parameters, e.g. the retained streamline numbers, the maximum and minimum retained tracking lengths, the size and angle between successive per-voxel streamline steps, and the criteria defined for track termination (Jeurissen et al 2019). Thus, performing targeted tractography in neurosurgical settings requires delineation of tracking ROIs by operators with expert anatomical knowledge, experience in adapting the ROI strategies in the presence of pathology, and expertise with chosen tractography techniques and their related technical limitations.

The following section will describe the two main classes of ROI strategies for targeted tractography in more detail: the anatomy-based ROI and functional-based ROI.

5.1.1. Using anatomy-based ROIs

These are typically delineated manually based on the recognisable anatomical structures or regions (such as the cerebral peduncle for corticospinal tract reconstruction) or based on the WM regions delineated by the contrast related to the principal diffusion direction, as evident on the DEC map (Pajevic and Pierpaoli 1999, Calamante et al 2010). For example, the sagittal stratum, a deep WM region adjacent to the occipital ventricular trigone, is an obligatory passage for optic radiation, thus commonly adopted as the inclusion ROI for its tractography reconstruction (Yang et al 2019) (see also figure 9). The sagittal stratum can be identified and delineated on the DEC map as a green-colour region adjacent to the ventricular trigone, containing predominantly anterior-to-posterior oriented WM fibres (Yang et al 2019). In addition to manually defined ROI, further anatomical constraints to specific cortical and subcortical GM regions can be defined by using automated individual brain GM parcellation schemes derived from structural MRI or using warped atlas-based brain regions into the subject native imaging space. Targeted tractography based on manually placed or template-driven anatomical constraints can result in reconstructions that very accurately reflect the ground truth WM connections mapped by axonal neurotracer in sectioned macaque brain (Schilling et al 2020a). Increasing adding well-chosen ROIs, based on a priori anatomical knowledge about the WM tract, can further improve the anatomical precision of the tractography result (see figure 9).

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The aforementioned ROI strategy will need to be modified if the brain anatomy is obscured by the presence of pathology or by the previous neurosurgical intervention (tracking in the post lesion resection regions, for example). While the decision is likely to be individualised, the general principle is to place ROIs only in areas with recognisable anatomy, and avoid placing precise ROIs in areas affected by pathology or surgery, which would introduce tracking bias due to ambiguous a priori anatomical knowledge. The presence of pathology may also render automated brain parcellation regions useless (see figure 9), or manual editing by expert raters is mandatory to ensure the delineated ROI satisfactorily encompasses the targeted anatomy (although the editing process may itself introduce further bias). This process, however, can be more time consuming than manually defining the ROI in the first instance.

5.1.2. Using functional-based ROIs

Targeted tractography has been widely applied in neurosurgery, with indications ranging from, resective surgery for wide spectrums of intrinsic brain lesions, examples including both high-grade and low-grade gliomas, cerebral metastases, vascular lesions (such as arteriovenous malformation and cavernoma); epilepsy surgery (such as resection of focal cortical dysplasia; anterior temporal lobectomy for hippocampal sclerosis and mesial temporal lobe epilepsy); cranial nerve mapping for skull-base neurosurgery (identify facial nerve location in vestibular schwannoma surgery, for example); functional neurosurgery (identifying thalamocortical connections adjacent to the targeted deep GM nuclei in deep brain stimulation surgery, for example), to intramedullary spinal cord tumour neurosurgery. The readers are referred to several comprehensive updated reviews and related studies for further information (Potgieser et al 2014, Egger et al 2016, Essayed et al 2017, Antherieu et al 2019, Henderson et al 2020, Vanderweyen et al 2020).

In high-grade glioma surgeries, DTI-based functional neuronavigation led to improved gross total resection with corticospinal tract involvement, prolonged survival, and a significant decrease in a postoperative motor deterioration compared to the control surgery group carried out without DTI-based tractography (Wu et al 2007). Similarly, improved lesion resection extent, survival rates, and greater motor functional preservation had been reported in retrospective DES-assisted glioma surgical series, complemented with DTI- and fMRI-informed neuronavigation (Bello et al 2008, Ius et al 2012). In a recently reported language dominant, insular-opercular paediatric epilepsy surgical case series, when performing DES or awake surgery was contraindicated (Yang et al 2020), combining expert generated probabilistic CSD-based targeted tractography and BOLD-fMRI were used to inform pre-surgical planning and intraoperative functional neuronavigation. The authors reported good surgical outcomes with minimal post-surgical morbidities. These children also avoided the added anaesthetic and surgical risks needed for further invasive intracranial electrode monitoring to localise epileptogenic focus and eloquent brain. The reported seizure freedom rates and post-operative morbidity profiles were comparable to other surgical series utilising high-density stereo-electroencephalography and open resection (von Lehe et al 2009, Dylgjeri et al 2014, Weil et al 2016, Freri et al 2017) or with invasive laser interstitial thermal ablation therapy (Freri et al 2017, Hale et al 2019). Finally, the use of targeted tractography in functional neuronavigation has been shown to improve efficiency in cortical and subcortical DES brain mapping (Bello et al 2008, Gonzalez-Darder et al 2010).

Presently, targeted tractography applications in neurosurgery are dominated by the use of the tensor model and FACT tracking algorithm as originally proposed in dMRI research 25 years ago. Contextually, this is likely due to the fibre-tracking tools from available commercial navigation software packages only supporting the use of this outdated dMRI tractography technique.

In a recent survey conducted from 36 out of all 40 neurosurgical units in the UK and Ireland, 90% of the neurosurgical units use tractography regularly, and they are predominantly DTI-based reconstructions. Concerningly, many neurosurgeons remain unfamiliar with the underlying methods used to produce tractography visualisations (Toescu et al 2020). An alternative way to provide a snapshot of clinical practice is to look at relevant tractography surgical cohort reporting. An author-initiated PudMed-based search for relevant literature over the last 25 years, demonstrating the striking contrast between the advanced dMRI-informed tractography research and what is being utilised and published from the clinical neurosurgical practice. Overwhelmingly, 94.7% of neurosurgical publications utilised DTI-based tractography, with the remaining 5.3% of studies utilised higher-order dMRI modelling techniques. Importantly, although many of these studies recognised the limitation of DTI-based tractography, and emphasised the need to introduce more advanced methods, none had actually proceeded with furthering research and industry partnership, working towards translating advanced dMRI methodologies into neurosurgical practice (Kuhnt et al 2012, Bucci et al 2013, Farquharson et al 2013, Kuhnt et al 2013, Zhang et al 2013, Lim et al 2015, Mormina et al 2015, Ashmore et al 2020, Fekonja et al 2021). Figure 10 shows a clinical example of differences in tractography appearances based on the selected dMRI modelling and tracking techniques.

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Nonetheless, there remains a pressing need to bridge the evidence-practice gap between dMRI-informed tractography research on the one hand and clinical neurosurgery practice on the other. Establishing close clinical, research, and industry partnerships are key to further translate these novel techniques into the clinical neurosurgery realm (more to this in Q&A 8).

• Pre-surgical planning and intraoperative neuronavigation in neurosurgery utilise targeted tractography to visualise WM tracts adjacent to the resecting lesion.
• Expert manual delineations of tracking ROI based on a priori anatomical knowledge about the WM tract remains the reference standard for target tractography reconstruction used in the clinical setting.
• Alternatively, the tracking ROI can be based on eloquent cortical regions derived from functional brain data to improve the functional relevance of the tractography reconstructions. This is particularly the case in scenarios with distorted anatomy and concerns of functional reorganisation.
• Presently, targeted tractography applications in neurosurgery are dominated by the use of the tensor model and FACT tracking algorithm, as originally proposed in dMRI research 25 years ago. There remains a pressing need to 'move beyond DTI', and bridge the evidence-practice gap.

6.1.1. DWI acquisition and artefacts

6.1.2. Diffusion models and tractography parameters

6.1.3. ROI placements

To answer whether tractography is reliable for neurosurgical applications, we must consider and ideally satisfy three levels of evaluation: 'algorithmic', 'biological' and 'clinical' reliability. In this section, we will delve into these concepts. Issues concerning tractography validation will be discussed in Q&A 7.

The first level is algorithmic reliability, which is the primary goal for all tractography technical development. This includes features such as the sensitivity to the imaging noise and curvature overshoot. The second level is the biological reliability that defines how accurate tractography outputs can delineate the true WM tracts, in both the healthy and the pathological brains. These two levels of reliability are fundamentally different. An algorithmically reliable tractography method operates properly on a given FOD field (i.e. the tractography output is highly precise and reproducible). However, the tractography output is only biologically reliable if the underlying FOD field is biologically plausible or meaningful (i.e. the tractography output is anatomically and biologically accurate). For example, in WM voxels containing crossing fibres, an algorithmically reliable fibre tracking algorithm would not reconstruct an anatomically accurate WM tract if the underlying vector field is derived from an over-simplified diffusion model, such as the tensor model (as described in Q&A 2). The tensor-based deterministic tracking approach is thus highly reproducible but biologically inaccurate due to the intrinsic systematic modelling bias (Farquharson et al 2013). Likewise, it is generally not sufficient to claim biological reliability purely based on an assessment of algorithmic reliability.

The third level is clinical reliability, which describes whether the use of tractography can improve surgical outcomes or not. This level of reliability can only be indirectly assessed using clinical or functional outcome measures following surgery. Prospective comparison of different tractography techniques is not possible within the same surgery, since there is no way to 'redo the same surgery' in the same patient.

Paradoxically, existing objective evidence concerning the clinical reliability of tractography applications in neurosurgery has so far been disappointing due largely to inadequate clinical outcome reporting from uncontrolled retrospective clinical surgical cohorts. Notably, a Cochrane review concluded low to very low-quality evidence that intraoperative DTI-based tractography image guidance benefited the extent of resection and found no survival benefit in adult high-grade glioma surgeries (Barone et al 2014), contrary to the reporting by Wu et al which remains the only randomised control trial to date which demonstrated functional neuronavigation incorporating tractography led to prolonged survival in adult motor-eloquent high-grade glioma patients (Wu et al 2007). While this review reaffirmed the prevalence of utilising DTI-based tractography in neurosurgery, it has not evaluated (thus does not necessarily discredit) emerging clinical targeted tractography studies utilising advanced dMRI data acquisition, higher-order dMRI models, and a probabilistic tracking algorithm (Fernandez-Miranda et al 2012, Chamberland et al 2014, Yang et al 2019). While there is currently not enough evidence to support that the application of advanced tractography techniques gives better surgical outcomes than conventional approaches, the clinical reliability should be established on the basis of algorithmic and biological reliability. In our opinion, tractography methods that are superior in all three levels will ultimately provide more meaningful and trustworthy results for clinical neurosurgical use.

Reportedly, the same Cochrane review also identified a significant concern regarding the risk of bias in the studies being investigated, with incomplete reporting of post-surgical adverse events, and high attrition bias in follow-up data, highlighting the need for prospective study design, high-quality randomised clinical trials and improve quality of clinical outcome reporting for future neurosurgical tractography studies (Barone et al 2014, Vanderweyen et al 2020).

• The accuracy and reliability of targeted tractography output is strongly dependent on how the dMRI data are acquired and processed.
• Sources of tractography uncertainties include the different DWI artefacts, the chosen diffusion model and the tracking parameters, and the chosen method of ROI placement strategies.
• A reliable tractography technique for neurosurgical application should ideally fulfil algorithmic, biological and clinical reliability.
• An algorithmically reliable tractography method does not necessarily equate to a biologically reliable tractography method. The tensor-based deterministic tractography used routinely in the neurosurgical setting is a good example of this.
• Assessing for clinical reliability of the tractography method is difficult, and can only be achieved indirectly with post-surgical functional outcome measures or indirectly via functional brain imaging.

Various software tools have been developed to validate the algorithmic reliability of fibre tracking (e.g. Close et al (2009), Neher et al (2014)). One can synthesise DWIs through a numerical model or simulate the FOD field directly. Synthetic DWIs can also be generated via using more sophisticated productions of simulated fibre configuration, combining with Monte Carlo simulations of water diffusion within the virtual tissue substrate, and then computing MRI signal based on the Bloch equation. This allows a tractography algorithm to be assessed in a controlled way against various settings, such as varying b-value, the number of gradient directions, SNR, and artefacts (e.g. Balls and Frank (2009), Yeh et al (2013)).

More recently, a synthetic DWI dataset was 'reversely' generated based on the predefined outcomes of targeted tractography (Maier-Hein et al 2017). Those predefined WM tracts, identified by one expert radiologist who performed and checked the quality of reconstruction, were utilised as the ground-truth WM pattern in the human brain. While more complex and realistic than previous numerical phantoms, this synthetic phantom does not fully capture the brain complexities, as only a subset of WM tracts are included in the model. Currently, such targeted tractography based on the manual delineation of ROIs would likely remain the ground-truth, which is dependent on raters' anatomical expertise. This highlights the need for a well-regulated and validated tractography methodology, to allow expert raters to assess and maximise the anatomical accuracy of tractography outputs, as alluded in section 6.1.3.

The other option is to construct a physical phantom model (Poupon et al 2008, Tournier et al 2008). Compared to computational synthetic data, building a physical phantom is challenging, sometimes expensive and time-consuming. It is also not as flexible as the computer simulation in terms of designing different fibre configurations for testing purposes. Nevertheless, this allows the testing to be performed using a realistic data acquisition and can be used to evaluate the stability of DWI scans, including cross-scanner calibration.

Post-mortem fibre dissection studies are fundamental for understanding the organisation of WM tract architecture (Dejerine 1895, Dejerine 1901, Klingler and Ludwig 1956, Türe et al 2000, Schmahmann and Pandya 2007, Fernández-Miranda et al 2008, Lawes et al 2008, Martino et al 2013). When comparing the tractography outputs with the existing or classic descriptions of anatomical references about WM tract anatomy based on human post-mortem dissection studies, there are some important caveats to consider: despite over centuries of works by many, there is still no agreement to the exact anatomy of many WM tracts. In particular, disagreements exist with regards to the precise cortical origin or terminations of these WM tracts (Martino and Brogna 2011). Classic post-mortem fibre dissection technique requires WM tracts to be identified by an 'outside-in' approach through peeling away the cortex (Klingler and Ludwig 1956). Even with a meticulous dissection technique using an operative microscope, delineation of adjacent WM tract populations cannot be reliably guaranteed (Yasargil et al 2004). In addition, post-mortem fibre dissection is relatively coarse, and cannot reliably trace WM fibres through crossing fibre regions (Fernández-Miranda et al 2008). Tissue fixation-related artefacts during cadaveric specimen preparation can also affect the accuracy and validity of the dissection findings. For this very reason, the existence of some WM tracts, as distinct fibre tract entities, has been questioned (Tusa and Ungerleider 1985).

Ex vivo dMRI of tissues, in combination with histological stains or axon tracing techniques, is an important approach to investigate information of in vivo dMRI data (Schilling et al 2018, Yendiki et al 2021). This allows validation of WM orientation and tractography estimates to be performed on the same tissue sample, either from post-mortem human brains or animal models (Seehaus et al 2015). The advances in imaging techniques on ultra-high field MRI systems (with B₀ at 7 Tesla or above) can achieve high-quality high-resolution image acquisition at tens to few hundreds of micrometres, making the comparisons of fibre orientation mapping with histological sections even more feasible (Sato et al 2017, Roebroeck et al 2019, Yendiki et al 2021). Further, in vivo studies in mammalian tissue using endogenous fluorescent axonal labels have been an additional strategy to unveil the relationships between the dMRI signals and WM microstructures. Such experimental strategy has been adopted to provide quantitative tissue validation of advanced dMRI biophysical model metrics (Sato et al 2017), or to study the sensitivity of dMRI metrics for early detection of presymptomatic degenerative neurological diseases (Gatto et al 2018a, Gatto et al 2018b).

Histochemical staining of sectioned brain tissues is a classic way to study WM tract anatomy. Axonal anatomy is identified through tracing the course of Wallerian degeneration, or via staining the myelin content of either developing or degenerating axons (Englander et al 1975, Kretschmann 1988, Yagishita et al 1994). Histochemical staining studies can also be performed in animal brains through axoplasmic transport of either retrograde or anterograde tracers (Schmahmann and Pandya 2006, Schmahmann et al 2007, Morecraft et al 2009). These techniques offer the advantage of reducing the number of misidentified crossing fibres, and can reliably identify both the origin and the terminations of different WM tracts (Morecraft et al 2009). In particular, myelin-stained histology is popular for generating the ground-truth fODFs from the histological orientation profile using a structural tensor analysis approach.

Many studies have used manganese-enhanced MRI (MEMRI) for tractography validation (Lin et al 2001, Knösche et al 2015). The paramagnetic manganese ion (Mn²⁺) is a potent T1-shortening agent and can be uptaken and transported actively along the axon. Hence, manganese tracers can be identified on T1-weighted images and thereby used to characterise the connectivity of an injection site within the same brain, which is comparable to the connectivity profile of a seed region obtained by tractography (Knösche et al 2015). To date, the mechanism of Mn²⁺ within the brain is not very well understood, making the interpretations of the results obtained by MEMRI sometimes uncertain. For example, the apparent transport rates of Mn²⁺ could potentially vary among axons according to experimental modelling from dynamic MEMRI (Deng et al 2019).

More recently, tractography validation has moved towards using a multi-modality approach. Methods such as three-dimensional polarised light imaging can provide a multiscale reconstruction of FODs to evaluate diffusion modelling and tractography (Salo et al 2018, Alimi et al 2019). Tissue clearing methods combined with immunohistochemical staining, provide neuron-to-neuron connectivity at microscale cellular level, potentially to be adopted as ground-truth connectome data (Goubran et al 2019, Leuze et al 2021). These advanced neuroimaging techniques are promising but currently only applicable to imaging small blocks of biological tissue.

Performing DES is considered as the 'gold standard' in neurosurgery to validate the eloquent cortex location, WM tract position and its functional relevance (Penfield and Boldrev 1937, Ojemann et al 1989, Berger and Hadjipanayis 2007, Duffau 2015). A meta-analysis demonstrated brain tumour surgeries assisted by DES resulted in more extensive resection of the eloquent lesion, and fewer late severe neurological deficits compared to resections performed without DES (De Witt Hamer et al 2012). During DES-assisted surgery, a small amount of electrical current is passed directly to the targeted cortex, which elicits transient functional perturbation that could be identified by testing the patient's response during awake surgery (as in identifying transient language deficits in counting or object naming objects, for example), or while the patient is asleep under general anaesthesia (i.e. to elicit limb motor response following motor cortex stimulation, as evident by electrophysiological monitoring, i.e motor evoked potentials). Similarly, in subcortical stimulation, the anatomical location of the WM tract is confirmed if the functional perturbation was elicited when stimulating subcortically at the tractography-informed WM location. One should be aware that DES procedure is subjected to its own methodological consideration, including the stimulation parameter used, the stimulation types (i.e. monopolar versus bipolar stimulation), the size of the electrode tips and its effective stimulation radius (about 5–10 mm), false positive stimulation due to current afterdischarges, and false negative stimulation due to dysmyelination or neuronal migration disorders causing epilepsy (such as focal cortical dysplasia, and tuberous sclerosis) in paediatric cases (Chitoku et al 2001, Ng et al 2009, Tuxhorn 2010) or due to patient fatigue, as in the case of language mapping in awake surgery (Tuxhorn 2010, Mandonnet 2011).

Evidence concerning DES-based tractography validation studies was primarily derived from clinical glioma series performing motor stimulation and DTI-based corticospinal tractography reconstruction (Kamada et al 2005, Berman et al 2007, Mikuni et al 2007, Bello et al 2008, Kamada et al 2009, Gonzalez-Darder et al 2010, Zhu et al 2012, Bonney et al 2017). The correspondence between the tractography and subcortical DES findings were generally high, with reported sensitivity ranged between 90% and 98% and specificity ranged between 85% and 100% (Mikuni et al 2007, Bello et al 2008, Zhu et al 2012, Bonney et al 2017). Despite this, these studies consistently observed an up to ∼1 cm discrepancy between the tractography position and the positive direct stimulation points. This spatial discrepancy may represent cumulative errors relating to the stimulation procedure, image registration, technical nuances concerning the dMRI model and tractography method, and intraoperative brain shift (more to this point about brain shift in Q&A 8; (Berman 2009)). This has led to a recommended practice of a '1 cm' safety margin for tractography-informed neuronavigation, based on preoperative deterministic DTI-based tractography.

Considering DES is both invasive and time-consuming to perform, and contraindicated for some (i.e. young children, for example), it may not be a viable surgical adjunct in certain clinical scenarios. In these instances, functional imaging modalities, such as task-based BOLD-fMRI, and MEG, can be used to indirectly validate tractography by co-localising tractography streamline terminations with the eloquent cortices. This observation can be used as indirect means to improve the clinician's confidence about the tractography findings, although a perfect spatial concordance is not to be expected due to differences in the underlying imaging principles. Interestingly, quantifying the spatial extent of this structural-functional co-localisation has been adopted as a strategy to indirectly validate exploratory automated tractography techniques applied in temporal lobe epilepsy and brain tumour patients (O'Donnell et al 2017, Mancini et al 2019).

Lastly, functional outcomes following surgery can serve as indirect reminders about the validity of preoperative tractography, with knowledge of tract preservation or damage during the surgery or demonstrated by postoperative tractography. This form of indirect validation using functional interpretation is only possible if a WM tract or tract component has clearly defined topological functional representation. A good example is surgical injuries to the anterior temporal fibres of optic radiation (i.e. Meyer's loop) results in upper quadrant visual field defects (Hughes et al 1999). Preoperatively reconstructed Meyer's loop tractography and its distance from the temporal pole could predict the degree of postoperative visual field deficits following anterior temporal lobectomy epilepsy surgery performed in adults (Piper et al 2014, Lilja et al 2015). Incorporating intraoperative optic radiation tractography in anterior temporal lobectomy could significantly reduce the frequency of postoperative visual field deficits (Piper et al 2014, Cui et al 2015). In other scenarios, the possibility of functional reorganisation with either an adaptive or maladaptive neuroplasticity mechanism (Thomas et al 2007), makes speculation about the direct functional relevance of the tractography appearance uncertain. To this end, it is important to emphasise that tractography only infers WM structures. Combining it with postoperative functional imaging studies are mandatory to provide further insights into brain structural-functional relationships.

• In vivo dMRI tractography validation is fundamentally limited and remains one of the greatest challenges in the field due to the lack of ground-truth information.
• Tractography validation can be performed using numerical or physical phantoms, post-mortem fibre dissection, myelin-stained histological sections, or axonal neurotracers in non-human primates. Direct translation of these findings to in vivo tractography is confined by the methodological limitations of these techniques.
• Concordance of multimodal structural-functional imaging findings improves clinical confidence of the tractography findings.
• DES remains the 'gold standard' for functional brain mapping in neurosurgery, including validation of both the position and functional relevance of WM tracts during the surgery.
• Functional neuronavigation informed by tractography and functional imaging modalities, such as BOLD-fMRI, are used to complement the DES findings, and to improve the efficiency of the stimulation procedure performed during surgery.

8.1.1. Intraoperative brain shift

Conventional intraoperative image-guidance is based on preoperatively acquired MRI. The main drawback is the inability to account for the effects of brain shift that occurred throughout the course of surgery (Dorward et al 1998, Nabavi et al 2001) (see also figure 11). The brain shift is a progressive, dynamic process affecting the whole brain and is influenced by multiple intraoperative factors, such as the craniotomy and dural opening sizes, resection size, and the presence of brain oedema (Romano et al 2011, Gerard et al 2017, Yang et al 2017). The direction of WM tract shift can be unpredictable, impacted by the type of WM tracts studied, and the proximity of WM tracts to the lesion (Nimsky et al 2006, 2007, Maesawa et al 2010, Yang et al 2017). It remains unclear how different surgical factors contribute to the magnitude and direction of the intraoperative WM tract shift. As alluded to previously, the presence of brain shift contributes to the proposed '1 cm' safety resection margin relating to neuronavigation errors guided by preoperatively reconstructed deterministic DTI-based tractography (Kamada et al 2005, Berman et al 2007, Mikuni et al 2007). A recent probabilistic CSD-based tractography study in paediatric epilepsy and brain tumour surgeries had demonstrated intraoperative WM tract shift accounts for one-third to half of this distance (Yang et al 2017). A revised '5 mm' resection margin was proposed, representing combined errors from electrical stimulation, tractography methodology, and image registration.

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Acquiring updated intraoperative images using intraoperative MRI scans remains one of the most practical solutions addressing the registration inaccuracy caused by brain shift (Dorward et al 1998, Nabavi et al 2001). While other imaging techniques, such as intraoperative ultrasound, can be performed directly by the operating surgeon allowing for rapid assessment of updated lesion status, it does not enable tractography visualisation (Sosna et al 2005, Liang et al 2019, Yeole et al 2020). Intraoperative MRI remains the most direct method that can obtain updated tractography during the surgery. Recent developments in MRI have produced intraoperative high-field 3 Tesla MRI scanners acquiring high-resolution DWI data possible during surgery. The accuracy of surgical neuronavigation can be improved by the real-time update of WM tract positions, compensating for the effects of intraoperative WM tract shifts. Open-source software tools enabling live, interactive visualisation of streamline reconstructions are now emerging (e.g. Fibernavigator ¹⁴ (Chamberland et al 2014)). In line with the aforementioned challenge of bringing advanced dMRI data and higher-order dMRI WM modelling technique to neurosurgical settings, there remains a pressing need to examine the computation efficiency of dMRI data acquisition and tractography processing pipeline, in order to bring intraoperative real-time tractography into surgical reality.

8.1.2. Optimising peri-lesion WM fibre tracking

Many neurosurgeons are now increasingly recognising the need to 'move beyond DTI' in neurosurgical practice (Kinoshita et al 2005, Tournier et al 2011, 2013, Duffau 2014, Nimsky 2014, Kinoshita et al 2016, Toescu et al 2020, Fekonja et al 2021). Unfortunately, to date, advanced MRI tractography techniques have yet to be incorporated into commercial neurosurgical navigation software, which are the ones most widely used in clinical practice. The impediment to this clinical translation is multifactorial, in part, stemmed from the clinician's lack of awareness or misconception surrounding the dMRI theory, and technical nuances that underpin the tractography outputs (Toescu et al 2020). Many perceive that the advanced techniques are 'too complex' to implement and involve 'long acquisition and processing times incompatible with clinical practice' (Kinoshita et al 2016). There remains a need to improve the technical efficiency of advanced methods to be comparable with acute neurosurgical time. For example, it is currently not feasible to apply the advanced methods to a high-grade glioma patient who presented with acute neurological decompensation, and brain herniation related to the tumour mass effect, which warrants immediate surgery for tumour debulk. On the contrary, the application of advanced tractography methodologies is highly feasible for many lesion-based neurosurgery performed on either a semi-urgent or elective basis. This includes most of the benign intrinsic brain lesions, such as low-grade glioma, developmental brain tumours, cavernoma, and majorities of the lobectomy and lesionectomy-based epilepsy surgeries (Mormina et al 2015, Caverzasi et al 2016, Mormina et al 2016, Yang et al 2017, Hales et al 2018, Yang et al 2019, Becker et al 2020, Yang et al 2020). Additionally, continual advances in MRI hardware and dMRI acquisition scheme, such as the simultaneous multi-slice imaging (Feinberg and Setsompop 2013) have reduced the data acquisition time down to clinically acceptable times.

On the other hand, many advanced MRI techniques were developed with little consideration to clinical use, driven mainly by imaging scientists, MR physicists and signal processing experts, with little input from clinicians and neuroanatomists. These were based on studies usually in healthy and typically developed individuals without demonstrating methodological feasibility and reliability using clinical neurosurgical patient data. These methods are only possible through open-source MRI software packages, and the tractography outputs are incompatible with current surgical navigation software, thus preventing immediate clinical uptake. Open-source tools are being developed and now made available in the public domain to transfer such tractography outputs and import them into selected surgical navigation platforms, enabling intraoperative image-based navigation by integrating tract visualisations with other image data (e.g. Karawun ¹⁵ ). Alternatively, there are novel tools (e.g. OpenIGTLink ¹⁶ ) to integrate open-source viewing platforms and real-time surgical neuronavigation data. This is an area of ongoing research development with the potential of significant clinical impact.

Thus, it is clear that clinicians, researchers, MRI and surgical navigation vendors need to work collaboratively to help bridge the evidence and practice gap, to introduce advanced tractography methodologies into the routine clinical neurosurgical realm. In line with the recommendations provided by a recent tractography review (Vanderweyen et al 2020), we believe continued and improved communication and education between all parties involved will likely lead to clinicians being better informed of the technical nuances; researchers and industry vendors to better appreciate the focus of clinical needs; and greater potential for translating advanced sequences and modelling techniques into MRI and surgical navigation devices. Pleasantly, such collaborative efforts are already underway, as highlighted by a recent multi-institution, multi-disciplinary dMRI tractography project with the aims to both survey the different in vivo fibre dissection approaches, and attempting to reach a consensus definition of WM tract anatomy and nomenclature between the clinical and research communities (Schilling et al 2020b).

Many international tractography challenges held to date, for example, ranging from using MRI phantom (Fillard et al 2011, Cote et al 2013), synthetic dMRI data (Maier-Hein et al 2017), high-resolution human dMRI data (Neher et al 2015, Schilling et al 2020b) and selected clinical brain tumour MRI data (Pujol et al 2015), all, more-or-less, revealed a common feature: a high degree of inter-rater tracking variability of tracking reliability and reproducibility; and different groups adopted their preferred in-house advanced tractography algorithms. (For a comprehensive review about these tractography challenges, see Schilling et al (2019).) Thus, before a methodological consensus can be considered for clinical neurosurgical tractography applications, more comprehensive surveys of clinical tractography usages in neurosurgery, like the recently conducted UK-based clinical survey mentioned previously (Toescu et al 2020), and more high-quality studies are required to quantify the performance of different advanced methodologies using in vivo clinical MRI data (Vanderweyen et al 2020). Similarly, more in vivo tractography validation studies are needed in DES-assisted neurosurgical cases to map out WM tract position. We advocate for all future clinical tractography studies to include comprehensive clinical outcome reporting, preferably with formal neurological and objective functional assessments conducted both before and after surgery. Lastly, high-quality prospective randomised clinical trials involving a tractography intervention and a patient control group, similar to the study performed by Wu et al (2007), are desired in order to formally evaluate the clinical value of advanced dMRI tractography methods in a less biased manner.

• Intraoperative brain shift compromises the accuracy of tractography-informed neuronavigation based on preoperatively acquired MRI, highlighting the need for intraoperative real-time imaging updates.
• The accuracies of dMRI modelling and fibre tracking are uncertain within the pathology and in the peri-lesion WM. Promising methods are being proposed but remaining largely confined to the research domain.
• Clinical translation of advanced dMRI modelling and tractography methods requires a collaborative approach involving close clinical, research and industry partnership.
• Further high-quality methodological and prospective studies are required to: (1) survey more comprehensively the current landscape of clinical tractography use worldwide; (2) quantify tracking variability based on different advanced methods, using clinical MRI datasets; (3) further in vivo tractography validation works in DES-assisted neurosurgery and myelin-stained histopathology validation based on the resected surgical specimens; (4) improve clinical outcome reporting in tractography-informed neurosurgical case series.