# Improving tractography using anatomical priors & multimodal integration

Etienne St-Onge, Gabriel Girard, Kurt Schilling, Alessandro Daducci, Samuel

Deslauriers-Gauthier, Laurent Petit, Maxime Descoteaux

► To cite this version:

Etienne St-Onge, Gabriel Girard, Kurt Schilling, Alessandro Daducci, Samuel Deslauriers-Gauthier, et al.. Improving tractography using anatomical priors & multimodal integration. Handbook of Diffusion MR Tractography, Elsevier, pp.347-362, 2025, 978-0-12-818894-1. 10.1016/B978-0-12-818894-1.00021-5. hal-05472485

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Improving tractography using anatomical priors & multimodal integration

Etienne St-Ongeª, Gabriel Girardf, Kurt Schillingd, Alessandro Daduccie, Samuel Deslauriers-Gauthierc, Laurent Petitb, Maxime Descoteauxf

ªDepartment of Computer Science and Engineering, Université du Québec en Outaouais, QC, Canada

ᵇIstitut des Maladies Neurodégénératives, Université de Bordeaux, France

ᶜCRONOS, Inria Center at Université Côte d'Azur, Valbonne, France

ᵈVanderbilt University Institute of Imaging Science, Vanderbilt University, Nashville, TN, USA

ᶜDepartment of Computer Science, University of Verona, Italy

fDepartment of Computer Science, Université de Sherbrooke, QC, Canada

**Abstract**

Incorporating anatomical knowledge and alternative modalities is crucial to accurately estimate white matter architecture. Several techniques have been developed to improve tractography algorithm precision, leveraging high-resolution anatomical images alongside anatomical constraints, tissue segmentation, and cortical surface modeling. Additionally, microstructural information and functional imaging can further regularize tractography trajectory and enhance structural connectivity measures. This study details how these methods provide unique insights that simplify the overall complexity of reconstructing the brain's structural network.

**Introduction**

Enhancing diffusion MRI (dMRI) tractography with anatomical knowledge as priors can significantly improve the reconstruction of white matter architecture. This anatomical knowledge can encompass various levels of organization, ranging from macroscopic features such as gyri, sulci, gray nuclei, and white matter bundles, to the microarchitecture at the level of neurons. By incorporating this valuable information, tractography algorithms can achieve more accurate and precise reconstructions of the complex white matter pathways in the brain, overcoming the inherent limitations of dMRI, such as lower spatial resolution and complexities associated with crossing, kissing, and fanning fibers [Jbabdi and Johansen-Berg, 2011]. Without such prior information, the reconstruction is prone to generating a large number of “false positive” streamlines and incomplete reconstruction of “true positive” white matter bundles [Maier-Hein et al., 2017; Schilling et al., 2019b; Girard et al., 2020]. This integration of anatomical knowledge as priors in dMRI tractography holds great promise in advancing our understanding of the intricate connectivity patterns in the brain and their role in brain function and neurological disorders.

As evident in the preceding chapters [cross-ref det, prob, global, ML tracking chapters], various approaches have been developed to enhance the precision of tractography algorithms. In this chapter, we elucidate how incorporating information such as tissue segmentation, geometrical constraints, microstructure, and functional MRI as priors into the tracking process can significantly improve tractography reconstruction.
# 1. Guiding tractography with tissue maps

As seen in previous chapters, the effectiveness of tractography algorithms heavily depends on the precise characterization of brain tissues to ensure accurate tracking through the spatial exploration process. Therefore, brain tissue maps of white matter, but also gray matter (GM) and cerebrospinal fluid (CSF), are needed to guide the tractography algorithm, in particular to determine where streamlines should start and stop [Smith et al., 2012; Girard et al., 2014]. These maps are often named tissue “masks” when depicting the location of a single structure with a boolean value (e.g. 0 for the background and 1 for the white matter), or “probabilistic maps” when representing it with a probability or distribution. As seen in previous chapters, the most frequent way to obtain a white matter mask is by thresholding the DTI fractional anisotropy (FA) map at 0.15 [cross-ref]. However, FA thresholding has its limitations is often imprecise in crossing fiber regions, in partial volume regions at tissue boundaries and at the boundaries of the brain mask. To address FA thresholding limitations, tissue maps estimated from a T1-weighted or T2-weighted image are generally a good option (see Figure 1), since they are commonly acquired along dMRI and have typically higher spatial resolution than dMRI. Alternatively, white matter maps can be estimated from the dMRI data using the fODF value [Tournier et al., 2019; Raffelt et al., 2012; Jeurissen et al., 2014] or obtained through dMRI compartment modeling [Canales-Rodríguez et al., 2015]. This anatomical information is necessary to reliably assess structural connectivity and estimate white matter architecture. Multiple approaches to integrate tissue maps into tractography algorithms are described in this section, such as Anatomically-Constrained Tractography (ACT) and Particle Filtering Tractography (PFT) [Smith et al., 2012; Girard et al., 2014].

## 1.1. Binary tissue masks

To constrain the reconstruction of tractography inside white matter voxels, tractography needs an input on valid tracking regions. One approach is to provide binary masks to describe where it can go and where it cannot. Anatomically, axons initiate and terminate in gray matter (GM) regions and propagate inside WM structures [cross-ref anat chapter]. Thus, both WM and GM binary masks can be provided to specify where streamlines, estimated with tractography, can go through (WM) and where they should stop (GM). These masks constitute a direct condition for every iteration of a streamline's reconstruction. Streamlines trajectory will progress inside WM and stop once they leave it. Different conditions can be applied based on endpoint location; e.g. if both endpoints reach GM the pathway is considered “valid”, otherwise it is rejected.

**Seeding mask** In addition to tissue segmentation, a seeding mask is often inputted to tractography algorithms to specify the starting location of streamlines. The starting point of each streamline, also called “seed”, is randomly chosen inside this seeding mask. This seeding mask can be directly derived from the previous WM or GM masks. Tractography’s seeding approaches are separated into two families: WM seeding, and WM/GM interface seeding. White matter seeding methods initialize streamlines from a point inside WM and propagate them in two opposite directions. In opposition, GM seeding techniques start streamlines inside GM and only propagate them toward the WM. Analogously, WM-GM interface seeding can be seen as a GM seeding, since it starts along the GM and behaves in a similar way. These seeding approaches are illustrated in Figure 2.
<figure><img src="image_2.png" /><figcaption>Figure 1: A) b=0 s/mm² image, 2mm isotropic resolution, B) T1-weighted image, 1mm isotropic, and C) tissue segmentation from the T1w: sub-cortical GM (white), WM (light gray), GM (gray) and CSF (black).</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2: Comparison of streamline initialization from seed positions, represented with a gray dot, inside a chosen mask: WM, GM and WM-GM interface seeding approaches. Reproduced with permission from St-Onge [2021].</figcaption></figure>

**Limitations of binary mask** Binary masks are prone to Partial Volume (PV) effects and a, so called, staircase artifact caused by the image discretization. Illustrated in Figure 3, these discretization artifacts impact the spatial precision of tractography near the interface of two different tissue structures. This PV effect impacts the accuracy of the segmentation, since multiple tissues values are averaged together. The staircase artifact affects the precision of the mask due to the domain discretization of an image, creating a cube-shaped profile, similar to a rasterization [Shirley et al., 2009]. This type of artifact can be reduced with continuous approaches such as level-set [Osher and Sethian, 1988] (see Figure 3-D).

## 1.2. Probabilistic tissue maps

State-of-the-art tractography methods, such as Anatomically-Constrained Tractography (ACT) [Smith et al., 2012] and Particle Filtering Tractography (PFT) [Girard et al., 2014], take advantage of probabilistic brain tissue segmentation (see Figure 4). These probabilistic segmentation maps, also called PV estimate maps, further increase the precision and facilitate image interpolation. The integration of probabilistic segmentation in tractography reduces PV effect especially in-between tissues, such as the WM-GM interface and near the ventricles. It also enables the filtering of streamlines based on each pathway probability. The incorporation of these probabilistic maps further improves the tractography algorithm spatial precision when obtained from a higher resolution T1w image.
<figure><img src="image_4.png" /><figcaption>Figure 3: A) Toy example with three different tissue types. B) Estimated image, where the Partial Volume (PV) effect is due to the averaging of different structures at each voxel. C) Voxel-wise segmentation with an observable staircase artifact. D) Surface based segmentation using level-set.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 4: Probabilistic tissue maps of the A) white matter (WM), B) gray matter (GM), C) cerebrospinal fluid (CSF) and D) subcortical structures (SC).</figcaption></figure>

The Anatomically-Constrained Tractography method interpolates probabilistic tissue maps to define tractography reconstruction behavior. At each position, PV estimates maps are describing the proportion of WM, GM and CSF, such that $PV^{WM} + PV^{GM} + PV^{CSF} = 1$. If the current tracking location is constituted of a majority of WM ($PV^{WM} > 0.5$), the tractography continues normally. However, if a position with $PV^{GM} > 0.5$ is reached, the streamline propagation is stopped and this streamline is included in the tractogram. Otherwise, every streamlines containing CSF voxels are excluded from the final tractogram (regions where the $PV^{CSF}$ has the highest proportion). In the end, the resulting tractogram contains only streamlines going through WM with both endpoints in regions with $PV^{GM} > 0.5$ or with one endpoint exiting the brainstem, suitable for connectivity analysis.

For PFT, a Continuous Map Criterion (CMC) approach provides similar behavior by replacing threshold values (of 0.5) with probabilities. Thus, going through a higher $PV^{GM}$ estimate results in a higher likelihood that a streamline propagation will stop and be included in the final tractogram. Similarly, in regions of high $PV^{CSF}$ the trajectories are likely to be excluded. Moreover, multiple tractography steps in voxels with low CSF or GM partial volumes are likely to result by stopping
the streamline propagation. The probability of continuing the propagation at a position p is defined as

$$P_{p}^{continue} = (1 - PV_{p}^{GM} - PV_{p}^{CSF})^{\frac{s}{l}},$$

where s is the step size and l is the average length of a voxel edge of PV maps. Streamlines stopping without reaching gray matter, with $PV^{GM} > 0.5$, are also rejected from the final tractogram. When propagation stops, the probability of including a streamline in the final tractography is defined by

$$P_{p}^{include} = \frac{PV_{p}^{GM}}{PV_{p}^{GM} + PV_{p}^{CSF}}.$$

When a streamline reaches a location leading to a trajectory rejection, ACT tries to find an alternative trajectory using an iterative backtracking approach. The tractography restarts at a previous location, with each rejection increasing the backtracking distance by one step. If this process leads to backtrack to the initial seed location, the streamline is removed from the tractogram. By avoiding invalid regions, this backtracking strategy allows the tractography algorithm to follow WM in narrow corridors or high curvature that would otherwise be challenging to reconstruct with conventional tractography algorithms.

Both ACT and CMC can be generalized to use other tissue volume fraction or probability maps to guide streamlines propagation, such as including lesion maps to help determine whether the tracking should stop or continue, and if streamlines should be included or excluded. Also, subcortical structures (SC) are often segmented as GM along with the cortex, however some segmentation methods separate them in different labels (Figure 4). Having a distinct label for SC can be useful when distinct starting or stopping criteria are needed [Smith et al., 2012].

**Limitations of probabilistic mask** Nonetheless, incorporating tissue segmentation maps is still highly dependent on the precision of the segmentation algorithm. For example, voxels at the interface between WM and CSF are often mislabeled as GM due to PV effect, i.e. averaging a low (CSF) and high (WM) intensity results in a value similar to GM. This phenomenon is depicted in Figure 3 and can be observed in Figure 4 GM around the ventricles, specifically in the GM segmentation. Recent advanced segmentation methods, employing atlases or machine learning, could reduce those limitations resulting in a better reconstruction [Cabezas et al., 2011; Avants et al., 2011; Despotović et al., 2015; Dadar and Collins, 2021].

**Tissue maps from dMRI** Instead of using T1- or T2-weighted images, tissue maps could be obtained directly from dMRI data. This reduces scanning time by removing the requirement on an anatomical image acquisition. Moreover, extracting different tissue maps directly from the dMRI also removes the necessity of a registration step between the diffusion volume and the anatomical space [Liu et al., 2007; Yap et al., 2015; Nie et al., 2018; Ciritsis et al., 2018; Cheng et al., 2020; Little and Beaulieu, 2021; Zhang et al., 2021; Theaud et al., 2022]. However, doing a tissue segmentation only using the dMRI is challenging because it as a low spatial resolution, a lower contrast and more distortions. To alleviate these problems, alternative approaches of registration and segmentation could combine both diffusion and anatomical data.

**Segmentation recommendations** In general, segmenting tissues from a high resolution anatomical (T1) image results in better delineation of brain tissues, however, it requires the alignment of this anatomical image to the diffusion MRI space. This registration can introduce blurring
<figure><img src="image_6.png" /><figcaption>Figure 5: A) Cortical and subcortical surfaces over the T1w image. Streamline initialization from B) the WM-GM interface mesh, C) with a geometrical flow initialization. This geometrical modeling of the fanning structure near the gray matter can be represented with D) line trajectories or E) local orientation distribution. Reproduced with permission from St-Onge [2021].</figcaption></figure>

and a misalignment of brain structures, reducing the precision of those PV estimate maps. For this, the quality of the segmentation does not only rely on a good registration but also on a good distortion correction (eddy & topup) so that the geometry of brain in dMRI matches structural images. In opposition to binary masks that are limited to nearest-neighbor interpolation, probabilistic maps with scalar values can be continuously interpolated and transformed with minimal loss of precision.

### 1.3. Cortical surfaces

Recently, multiple surface-based tractography algorithms were proposed to improve the precision of the tractography near WM-GM interface [Cottaar et al., 2015; St-Onge et al., 2015]. Since meshes are not restricted to the voxel grid, they can be created with finer details (from a higher resolution image) and avoid the staircase artifact (see Figure 2-D). Cortical surfaces of the pial and the WM-GM interface are generally estimated from an high resolution T1w image using FreeSurfer [Dale et al., 1999], or other mesh reconstruction methods such as CLASP [MacDonald et al., 2000], CIVET [Kim et al., 2005] or BrainVisa [Auzias et al., 2013]. Depicted in Figure 5, the segmentation precision near the gray matter is essential for tractography methods to reconstruct pathways that reach the cortex accurately.

Cortical meshes were initially incorporated in the previously mentioned tractography algorithms (ACT and PFT), resulting in *Mesh-ACT* (MACT) [Yeh et al., 2017] and *Surface-Enhanced Tractography* (SET) [St-Onge et al., 2018]. Surfaces were also utilized in global tractography to better constrain streamlines projection near the cortex [Teillac et al., 2017]. Moreover, subcortical structures and ventricles can be included for more advanced filtering or connectivity analysis [St-Onge et al., 2021].
**Geometrical modeling** Geometrical approaches can be employed to mitigate tractography endpoint biases, such as gyral bias, since previous tractography algorithms overestimates the number of terminations along gyri [Van Essen et al., 2013; Reveley et al., 2015; Schilling et al., 2018]. Along with the integration of cortical surfaces, St-Onge et al. [2018]; Cottaar et al. [2021] suggested to estimate the white matter fanning structure in the superficial white matter. These geometrical models recreate the fanning structure of axons near the cortex, based on the shape of the brain (curvature, gyrification and folding). Similar geometrical approaches are also used to estimate the cortical thickness and boundary between layers [Tallinen et al., 2016]. This modeling further improves tractography reconstructions near the cortex and helps streamlines to reach gray matter regions. It can also distribute connections more evenly along the cortex [St-Onge et al., 2021], mitigating gyral bias effect and improving the overall cortical coverage. Illustrated in Figure 5, this can be used to both initialize pathways from the cortex towards the deep white matter, and to project streamlines to the cortex.

**Limitations of surfaces** The main limitation of a surface-based tractography algorithm is the requirement of an accurate reconstruction of cortical and subcortical surfaces. These estimated meshes frequently have geometrical imperfections, thus, the precision of the resulting interface may vary from one reconstruction to another. Other types of meshing error (flipped facet, degenerate triangles) will also directly impact any geometrical modeling, which are sensitive to local estimation (area, curvature). However, advanced meshes processing can reduce or remove these issues. New algorithms, or further improvements to existing cortical surfaces reconstruction methods, could significantly improve mesh quality and precision, resulting in more accurate modeling [Ren et al., 2022; Huo et al., 2016; Rickmann et al., 2022; Ma et al., 2022; Bongratz et al., 2022; Gopinath et al., 2021]. Finally, neurosurgical cases and abnormal anatomy can also be quite challenging for surface-based mesh reconstructions that should therefore be used with care on pathological anatomy [cross-ref chapter on tractography in pathological anatomy].

## 2. Anatomical constraints

Anatomical priors based on pathway shapes (length, curvature, loop) or positions (endpoints location, traversing invalid regions) are a useful way to constrain or filter streamlines. Some of these priors can be integrated directly to the tractography algorithm or applied afterward as a filtering step. This is done especially for assessing brain pathology along a specific fascicle or for neurosurgical planning around a particular WM area [Urbanski et al., 2008; Assaf and Pasternak, 2008; Dayan et al., 2015]. Streamline filtering approaches are well detailed Chapters 20 and 21 [cross-ref Forkel and Garyfallidis]. This section will focus on methods that combine anatomical priors directly into the tractography algorithms.

### 2.1. ROI-based tractography

When looking for a specific bundle or Region of Interest (ROI), reconstructing a whole-brain tractogram is not always the best practice. In fact, the seeding map (described in section 1.1) can be easily modified to focus on a specified ROI, such as the insula for example [Ghaziri et al., 2017]. Additionally, other tractography maps (tissues maps or atlases) can be adapted based on the target reconstruction, and then used to constrain streamlines [Wassermann et al., 2016]. ROI-based tractography reconstruction reduces the computation time and increases the specificity of the white matter reconstruction by reducing unwanted streamlines.
ROIs are often used to filter tractography with automatic algorithms or manual segmentation. This can be done to constrain or group white matter streamlines based on their general location, i.e. selecting specific way points or ending regions. When this knowledge is used prior to tractography, limiting the extent of the white matter reconstruction. Most of these approaches often heavily depend on anatomical knowledge of white matter fascicles and cortical regions, obtained from post-mortem dissection or tractography virtual dissection from neuroanatomists.

This type of approach is employed by ExTractor to extract anatomically plausible streamlines of the human brain [Petit et al., 2019]. From the most basic point of view, the human white matter is organized in fiber tracts, that are aggregations of axons running in close apposition to each other and sharing cortical and/or subcortical origins and destinations. With this goal, ExTractor aims to reduce the complexity of connections and pathways from a whole brain brain tractography employing a series of rules to organize the streamlines [Schmahmann and Pandya, 2006; Nieuwenhuys et al., 2007] :

A) Every cortical area is linked with other cortical and subcortical areas by pathways grouped into three distinct categories originally defined by Meynert [1885], namely the association, commissural and projection fibers [cross-ref Catani chapter].

B) According to Schmahmann and Pandya [2006]: commissural, projection and long-range association fibers travel within the central WM part of the core of a gyrus, forming a convergence of fibers also known as “the cord”. In other words, these fibers enter or leave a gyrus via a gyral stem and therefore never from the side of a gyrus by traversing a sulcus.

C) Shorter U-shaped association fibers connect adjacent gyri by running in a thin band immediately beneath the GM constituting the most external part of the gyral stem.

Illustrated in Figure 6, ExTractor employs these rules with ROIs from the Johns Hopkins University (JHU) template [Oishi et al., 2009] to define anatomical filtering rules respecting the principles of brain organization listed above. The resulting filtered and partitioned tractogram, obtained from ROIs and anatomical rules, can be used as a set of plausible streamlines for further analysis.

Other specialized approaches adapt local diffusion models or tractography parameters in specific ROIs to improve the reconstruction. This can be used in edema or near glial tumor, where tractography pipelines need to be adapted to work properly [Deslauriers-Gauthier et al., 2018; Parker et al., 2018; Vanderweyen et al., 2020].

## 2.2. *Bundle-specific tractography*

Some diffusion MRI and streamlines analysis often focus on a specific Bundle Of Interest (BOI) instead of a whole brain tractogram for connectivity analysis. The implementation is similar to a ROI-based tractography, where the tractography is adapted to reconstruct a specific bundle. With this method, each BOI can be reconstructed from a series of anatomical rules. These bundle priors can be manually given or automatically extracted from a template.

This idea of reconstructing each bundle separately from anatomical priors was recently implemented in XTRACT [Warrington et al., 2020]. By incorporating tractography masks and seeding regions adapted to specific white matter pathways, XTRACT is able to reliably reconstruct 42 WM bundles. BOI specific rules are based on anatomical knowledge from previous WM study and analysis from both human and macaque, detailed in the supplementary material of Warrington et al. [2020]. A BOI-based tractography can be described in a few series of operations:
<figure><img src="image_7.png" /><figcaption>Figure 6: Diagram summarizing the main steps of ExTractorflow to filter out false-positive streamlines from a whole-brain tractogram by following brain neuroanatomy organizational principles. In this example, an original tractogram of a single subject initially composed of more than 3.5 million streamlines provides a final whole-brain tractogram of around 590 000 anatomically plausible streamlines once a series of filters (anatomical rules schematically represented with yellow lines) are applied (adapted Petit et al. [2019]).</figcaption></figure>

1) Generate seeding, termination, and tracking maps from prior anatomical studies, white matter analysis or brain atlases.

2) For each subject, compute the bundle-specific tractography with the previously generated maps, and by adapting tractography parameters (maximum curvature, streamlines lengths, etc.) for each white matter pathway.

3) Filter generated streamlines based on the prescribed template, using anatomical descriptors (location) and filtering methods.

When adapting local model orientations, BOI based tractography can overcome some typical reconstruction limitations [Jbabdi and Johansen-Berg, 2011], such as traversing crossing regions [Rheault et al., 2019]. In addition, this single bundle reconstruction has the flexibility to change and optimize the tractography algorithm or parameters for the desired bundle [Girard et al., 2014; Takemura et al., 2016]. Recently, few tractography methods use directional enhancement
to better reconstruct a specific WM bundle: MAGNETic Tractography (MAGNET) [Chamberland et al., 2017], bundle-specific tractography (BST) [Rheault et al., 2019], and tract segmentation & orientation mapping (TrackSeg) [Wasserthal et al., 2019]. Firstly, MAGNET was proposed to overcome a difficult fiber crossing configuration in tracking the optic radiations from thalamus, by manually encouraging streamlines to curve more and be attracted by local directions pointing towards the occipital lobe. In opposition, BST and TrackSeg automatically generate directional priors and adapt tissue maps based on a template bundle without any manual intervention. For BST, directional priors are estimated using Track Orientation Density Imaging (TODI) [Dhollander et al., 2014], whereas TrackSeg employs deep learning techniques to generate those directions.

<figure><img src="image_8.png" /><figcaption>Figure 7: Bundle-specific tractography (BST) reconstruction of the corticospinal tract (CST) employing enhanced CST-fODF, combining fODF with CST prior orientations. Reproduced with permission from Rheault et al. [2018].</figcaption></figure>

These methods are able to enhance the local model directions for a chosen BOI, by recon-
structing a single bundle at a time with orientational priors (See Figure 7). This type of approach
significantly reduces the complexity of the tractography reconstruction by focusing on a single
pathway, thus avoiding the crossing/kissing/branching problem. Thus, BOI based tractography
can greatly improve tractography reconstruction in selected key areas. This can be more signifi-
cant in areas where tissues segmentation have difficulty (e.g. narrow regions with high PV effect),
since it also incorporates tracking maps (described in section 2.2). This approach is comparable
to a data-driven streamline registration, where the WM structure is reconstructed if the subject
directions are coherent with the atlas.

**Region-based and bundle specific tractography** Overall, adapting tracking maps and masks in tractography serves to minimize, or even eliminate, local uncertainty in the tracking process. However, both ROI and BOI based approaches heavily depend on strong anatomical
priors and rely on atlases and templates. Additionally, they are optimal for only a limited number
of white matter pathways with established anatomical knowledge from post-mortem dissection and
tracing validation. In future tractography algorithms, the integration of additional anatomical rules
could further enhance the reconstruction of white matter pathways. These methods significantly
reduce reconstruction variability and are particularly useful when reconstructing specific bundles
or connections.

3. Tractography with microstructure information

Recent work in microstructural mapping, in particular axon radii mapping [Veraart et al., 2020], suggests that while microstructural properties are not perfectly homogenous along a pathway, they are at least continuous and slowly varying. These white matter properties, often obtained from diffusion models, can be exploited to regularize tractography connectivity or orientations.

3.1. *Filtering tractograms with microstructure information*

Proposed by Daducci et al. [2015], the COMMIT framework exploits microstructural prop-
erties in a top-down approach by associating a microstructure model of the neuronal tissue to
streamlines to improve the anatomical accuracy of the estimated tractogram and the biological
interpretability of the reconstructions. COMMIT is detailed in [cross-ref Daducci chapter] as well
as other tractogram filtering techniques such as SIFT and LIFE [Smith et al., 2015; Qi et al.,
2016]. Combining tractography with microstructure information allows filtering from an input
tractogram those streamlines with trajectories that are inconsistent with the imaging data and the
chosen model, as well as estimating the actual contribution, or weight, of the plausible ones. In the
original formulation [Daducci et al., 2015], a stick model represents the intra-axonal dMRI signal,
but COMMIT was later extended to consider multi-modal data and more advanced microstructure
models. For instance, in Schiavi et al. [2022] the candidate collection of streamlines is fit to a
myelin water fraction map, thus allowing one to infer the myelin content of fibers along the plausi-
ble trajectories. Besides, Barakovic et al. [2021a] proposed an extension to allow COMMIT to use
more advanced biophysical model for microstructure and map the axon diameter index along the
trajectories, whereas in Barakovic et al. [2021b] the tractogram is fit to multi-echo diffusion data
to estimate the distribution of T2 relaxation times of each streamline.

It is important to note that being able to weigh streamlines based on microstructural measures provides a way to quantitatively map microstructure to the streamlines, and provides an alternative to using streamline count for quantitative connectivity analysis [*cross-ref* Daducci and Zalesky chapters].

3.2. *Guiding trajectories using microstructure information*

Girard et al. [2017] proposed a bottom-up approach to microstructure-informed tractography mapping with the AxTract method. The AxTract method extends deterministic streamline propagation methods [cross-ref Leemans] by adding the active use of the local axon diameter information to guide trajectories. In this specific work, the AMICOX [Auría et al., 2015] framework was employed to estimate the diameter information for every peak of the fODF at the tracking location. Classical FOD-based deterministic streamline tractography methods iteratively follow the local peaks forming the smallest angle with the previous tracking orientation among all peaks of the voxels. AxTract relaxes this constraint by allowing the tracking algorithm to select any peaks within a predefined maximum angle. Instead of solely minimizing the angular deviation, AxTract
method selectively chooses the local white matter orientation based on estimated diameter information that closely aligns with the diameter information of the previously tracked orientation. Assuming a microstructure estimation method provides a reliable estimate of the axon diameter differences from the dMRI data, AxTract can change the propagation direction to resolve complex white matter configurations [Girard et al., 2017].

Although AxTract employs axon diameter measures, this concept could be extended to other microstructure properties that are constant or change smoothly along the trajectory of white matter bundles, such as myelin or T2 relaxation time. Even though it relies on the estimation of such diffusion properties for each peak independently and increasing the complexity of the model fit, it could improves the anatomical accuracy of the reconstructions by increasing its coherence with the underlying microstructure environment [Daducci et al., 2016].

# 4. Tractography with functional maps

In a parallel to diffusion MRI applications to map the structural connectivity of the brain, functional connectivity is used and interpreted as mapping the functional activations of the brain. With the intuition that brain structure guides brain function, functional signal contrast seems a logical modality to guide or inform tractography algorithms. Functional MRI (fMRI) relies on detecting small signal changes generally often associated with neural activity, an observation known as the BOLD (Blood Oxygenation Level-Dependent) effect [Friston et al., 1994; Attwell and Iadecola, 2002; Logothetis, 2003; Poldrack et al., 2011]. For example, an experiment may include presenting a stimulus or performing a task (such as a visual stimulus or motor task), which leads to neural activity, hemodynamic changes, and a detectable MRI signal change. With appropriate analysis tools, locations of signal changes may be related to specific functions. Additionally, rather than using a stimulus, recording the brain at rest (i.e., resting state fMRI), allows calculating correlations in time between MRI signals from different regions, which are widely used to reveal neural circuits (for example motor, language, or default mode networks).

In comparison to fMRI, electroencephalography (EEG) and magnetoencephalography (MEG) provide a direct measure of the electrical brain activity at a millisecond resolution [Baillet, 2017; Baillet et al., 2001; Schomer and Lopes da Silva, 2017]. However, because the sensors are located at the surface of the scalp or near the head, an ill-posed linear problem must be solved to extract brain activity from the recordings. Solving this problem typically involves the computation of a volume conductor model from anatomical MRI and in some cases dMRI. This volume conductor is then used to solve Maxwell's equations, referred to as solving the forward problem. Given the forward solution, brain activity can be recovered by inverting the model under suitable constraints, e.g. minimum norm or smoothness.

## 4.1. *Functional regions*

Functional areas revealed through functional activations have been used to inform, guide, and filter tractography. A simple, and intuitive, example is utilizing functionally defined ROIs to initialize or filter tractography streamlines. This is employed to further explore the link between brain function and structure. It also allows a direct visualization of the structural substrate (i.e., the white matter pathways) associated with areas of the activated cortex. This has been applied in both tasks and resting state fMRI, for example generating the underlying structural connections of resting state networks [Preti et al., 2012; Chamberland et al., 2015]. Additionally, a streamline
filtering step can be performed by extracting the BOLD time series from the endpoints of streamlines and performing correlations with the rest of the brain, keeping only those for which there is evidence of functional connections.

A similar idea can also be applied to more invasive imaging modalities like electrocorticography. Here, the location of the electrodes placed directly on the cortical surface is recorded, in addition to the location of electrical stimulation sites. By using the location of every stimulation and electrode pair as regions of interest, the underlying white matter fibers supporting the functional activations can be identified [Conner et al., 2011]. This allows the in-vivo quantification of physiological parameters of white matter bundles, for example their conduction velocity [Filipiak et al., 2021], and to relate them to micro-structural information provided by dMRI. The limitation of these approaches is their extreme invasiveness, allowing the procedure to be performed only on patients already scheduled for neurosurgery, for example during tumor resection.

In general, this approach is similar to ROI-based tractography (described in section 2), where regions are not obtained from anatomical knowledge but from subject-wise activation maps. This can further improve tractography reconstruction by integrating those functional maps. It can also segment and compare resulting streamlines based on activation correlation. These analyses may provide insight into structure-function relationships and a subject-specific basis, and may facilitate neurosurgical applications where the underlying structural network associated with a stimulated cortex is of paramount importance.

## 4.2. Functional connectivity

Structural connectivity, obtained from tractography along with diffusion measures, is often complemented with additional functional measures. For example, the functional correlations matrix can be used in addition to the dMRI connectivity to simultaneously map structure and function [Honey et al., 2009; Calamante et al., 2013; Abdelnour et al., 2018; Becker et al., 2018; Deslauriers-Gauthier et al., 2020b].

Recently, a way to combine functional signals from fMRI with tractography to gain insight into functional white matter has been introduced, called the functionnectome [Nozais et al., 2021]. Here, tractography-derived anatomical priors that describe the connectivity from every voxel to every other brain voxel are used to project gray matter fMRI signals into the white matter. Traditional fMRI analysis can then be performed on this whole-brain BOLD time series. This framework has been used to analyze the joint gray and white matter contribution to functional networks for motor systems, working memory, and language functions or to analyze the joint contribution to resting state networks of the brain and shows promise in using tractography to increase statistical power of fMRI in the white matter [Nozais et al., 2021]. Currently the functionnectome is based on a population-average tractogram in a standard space, but projecting functional data into white matter can also be done for subject-specific tractograms.

Strategies to inject white matter connectivity into the MEG and EEG inverse problem, which estimates cortical activity from recordings, have also been proposed. In addition to improving the ill-posed nature of the problem by limiting the space of solutions, these approaches also allow the projection of functional information onto the white matter substrate. For example, because of the millisecond temporal resolution provided by EEG and MEG, the white matter introduces observable delays into MEG and EEG data [Drakesmith and Jones, 2019]. This provides a unique opportunity to estimate the directionality of white matter connections, which is not possible from dMRI alone. A first strategy is to represent brain network dynamics using a multivariate auto regressive (MAR) model with constraints on the coefficients being driven by both dMRI and fMRI. The parameters
of the model are then estimated using a variational Bayesian algorithm to explain the MEG data,
yielding an estimate of the effective connectivity [Fukushima et al., 2015; Filatova et al., 2018].
A second strategy is to model the possible interactions between brain regions at different times
using a Bayesian network derived from dMRI. In addition to being subject specific, this Bayesian
network also encodes tract specific information, such as delays. By introducing EEG or MEG
measurements as evidence into this model, it is possible to infer information flow in white matter
connections at each time sample for both the afferent and efferent directions [Deslauriers-Gauthier
et al., 2019, 2020a]. Finally, more straightforward linear approaches have also been proposed to
constrain the EEG and MEG inverse problem using structural connectivity [Hammond et al., 2013;
Kojčić et al., 2021].

The methods mentioned above make use of functional information to complement, enhance, or
prune the structural connectivity captured by the tractogram, but never reconsider its relation to
the dMRI data. In contrast, it is possible to fit the dMRI data in a manner similar to COMMIT, but
simultaneously promoting fiber bundles that are coherent with resting state fMRI measurements.
The resulting tractogram is not only coherent with the structural data, but also in agreement with
the functional connectivity matrix [Frigo et al., 2019].

Furthermore, mapping streamlines endpoints along cortical surfaces (presented in section 1.3) is
a compelling way to apply multimodal research. This integration of cortical surfaces with meshes
facilitates the analysis of tractography and other diffusion measures along the cortex. Meshes
(vertices) can be used as a domain to analyze cortical measures (thickness, area and volume),
structural connectivity (tractography and dMRImetrics), and functional activations (fMRI, EEG,
MEG). A similar approach was recently employed by Cole et al. [2021] to analyze structural and
functional connectivity with a continuous representation over cortical surfaces.

4.3. Functional local orientation

In the white matter, fMRI BOLD contrast has traditionally been ignored, or considered as false
positive results. This is because its origins may be unclear, with lower blood flow in WM, and it is
not clear if there is a hemodynamic response to required energy changes. However, recent studies
have suggested that although BOLD effects are weaker in the WM, using appropriate detection
and analysis methods they are robustly detectable in both resting and task fMRI. First, resting
state signals have been shown to have local anisotropic correlation within neighborhoods (i.e.
correlation with neighbors may be stronger in anterior-posterior directions than superior-inferior,
for example) prompting fitting of local correlation coefficients to tensor fits (in a technique dubbed
function tensor imaging) [Ding et al., 2016; Schilling et al., 2019a]. Displayed in Figure 8, these
maps look very similar to what is expected from diffusion tensor imaging and diffusion HARDI
techniques, and have been used for “functional” tractography, which suggests that these measures
of BOLD signal directionality may be used to inform connectivity measures.

Over and above orientation information, task induced BOLD activations have been shown to
occur in WM, suggesting a WM hemodynamic response function analogous to that in GM [Li et al.,
2019]. This could potentially identify or segment regions of WM based on response similarity, or
response to specific stimuli, and be used to inform tractography algorithms. One could imagine
using a motor task, in combination with activation regions and mapping of hemodynamic response
functions, to cluster, filter, or propagate streamlines. Alternatively, correlations between GM
cortical regions and specific WM regions may be a way to identify or segment specific patterns of
activated regions that could be used for subsequent filtering. However, these directional correlations
with functional signals could also be due to vascular drainage effects or correlations caused by
<figure><img src="image_9.png" /><figcaption>Figure 8: Resting state signals have local anisotropic correlations within neighborhoods, with directionality that largely follows the underlying white matter structure. A) T1-weighted structural image, B) local functional correlations, C) diffusion tensors in the same region, and D) an RGB colormap obtained without any diffusion weighting, and using only correlations in resting state fluctuations. Reproduced with permission from Ding et al. [2016].</figcaption></figure>

susceptibility fields [Andersson et al., 2020]. Overall, studies of both WM and GM bold signals may not only provide new insights into brain function, but present opportunities to understand how function and structure are linked.

## Conclusion

Several ways exist to improve tractography by integrating anatomical priors. The use of segmentation maps or surfaces extracted from high-resolution anatomical images is crucial for improving tractography accuracy, particularly near the WM-GM interface. Surface-based modeling can further enhance the quality of streamlines near the cortex and superficial white matter, reducing end-point biases. However, aligning these segmentation maps to diffusion volumes perfectly is challenging.

Anatomical constraints should be used, when applicable, to decrease the number of invalid streamlines. The difficulty of using anatomical constraints is often increased in brain disease and pathological brains. Care should be taken in such applications. As such, when studying specific white matter pathways, using ROIs can significantly reduce erroneous streamlines in the analysis, focusing results on the desired pathway and trajectory. In addition, exploiting pre-segmented tractography bundles from a WM atlas is a powerful way to enhance local orientations and filter streamlines with automatic procedures. Future neuroanatomical studies focusing on white matter organization will provide more priors and better validations for current tractography methods.

Microstructure measures, from diffusion MRI or any other acquisitions, along white matter trajectory provides regularization that can be exploited for both quantitative connectivity matrix weighting. Some information could also be extracted from functional imaging, providing tractography with temporal data. These additional features provide unique connectivity characteristics that could alleviate the complexity of the brain structural network. These applications remain preliminary and should be further researched to fully take advantage of their potential.

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