Kurt G Schilling
email: kurt.g.schilling.1@vumc.org

Laurent Petit

Francois Rheault

Samuel Remedios

Carlo Pierpaoli

Adam W Anderson

Bennett A Landman

Maxime Descoteaux

Brain connections derived from diffusion MRI tractography

Keywords: Diffusion MRI, tractography, tracer, validation, white matter

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Introduction

Diffusion MRI Fiber Tractography is widely used to map the structural connections of the brain [START_REF] Conturo | Tracking neuronal fiber pathways in the living human brain[END_REF][START_REF] Mori | Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging[END_REF][START_REF] Basser | In vivo fiber tractography using DT-MRI data[END_REF][START_REF] Behrens | Characterization and propagation of uncertainty in diffusionweighted MR imaging[END_REF][START_REF] Parker | A framework for a streamlinebased probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements[END_REF][START_REF] Lazar | Bootstrap white matter tractography (BOOT-TRAC)[END_REF]. Tractography utilizes the directionality of diffusion of water molecules in brain tissue to estimate neuronal fiber orientation, and subsequently generates "streamlines" -typically by stepping along these orientation fields in some pre-determined ways [START_REF] Mori | Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging[END_REF][START_REF] Mori | Fiber tracking: principles and strategies -a technical review[END_REF]. These streamlines are representative of possible trajectories of white matter pathways of the brain and have been used to infer region-to-region connectivity (connectomics) or to identify and extract specific white matter tracts (bundle-segmentation). These techniques can additionally be informed by a priori knowledge of anatomy or trajectories of the pathways [START_REF] Wakana | Reproducibility of quantitative tractography methods applied to cerebral white matter[END_REF]. For instance, anatomical constraints can be employed by defining regions-of-interest (ROIs) to constrain the resulting streamlines, which is more generally used in bundle-segmentation applications. Most commonly, "seed" ROIs define where streamlines must start or end, "AND" or "inclusion" ROIs that pathways must include, and "NOT" or "exclusion" ROIs that pathways must not contact. These constraints are typically implemented post-tracking as a filtering technique [START_REF] Garyfallidis | Recognition of white matter bundles using local and global streamline-based registration and clustering[END_REF][START_REF] Yendiki | Automated probabilistic reconstruction of white-matter pathways in health and disease using an atlas of the underlying anatomy[END_REF][START_REF] Zhang | An anatomically curated fiber clustering white matter atlas for consistent white matter tract parcellation across the lifespan[END_REF][START_REF] Guevara | Automatic fiber bundle segmentation in massive tractography datasets using a multi-subject bundle atlas[END_REF], but can also be used during track generation [START_REF] Warrington | XTRACT -Standardised protocols for automated tractography and connectivity blueprints in the human and macaque brain[END_REF][START_REF] Behrens | Probabilistic diffusion tractography with multiple fibre orientations: What can we gain?[END_REF][START_REF] Catani | Atlas of human brain connections[END_REF][START_REF] Catani | Virtual in vivo interactive dissection of white matter fasciculi in the human brain[END_REF], and are most commonly associated with the field of bundlesegmentation (i.e., as a virtual dissection of specific pathways following seeding throughout the entire brain).

Despite these significant achievements in human brain mapping, the field of diffusion MRI has uncovered and detailed a number of limitations in the anatomical accuracy of fiber tractography techniques, particularly in recent years. Early validation studies were mostly aimed at proving sensitivity of these techniques, and only recently highlighted the specificity issues, especially as it relates to connectomics. These studies have convincingly shown a fundamental tradeoff between sensitivity (i.e., the ability to detect true connections) and specificity (i.e., the ability to avoid false connections) of tractography techniques [START_REF] Van Den | Comparison of diffusion tractography and tract-tracing measures of connectivity strength in rhesus macaque connectome[END_REF][START_REF] Azadbakht | Validation of High-Resolution Tractography Against In Vivo Tracing in the Macaque Visual Cortex[END_REF][START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF], and an overall limited accuracy in estimating both structural connectivity and spatial extent of pathways in the brain [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF][START_REF] Schilling | Limits to anatomical accuracy of diffusion tractography using modern approaches[END_REF][START_REF] Maier-Hein | The challenge of mapping the human connectome based on diffusion tractography[END_REF]. These results have been confirmed in simulations, in phantoms, and in a number of animal models -with sensitivity/specificity tradeoffs apparent across a range of tracking algorithms, parameters, and pathways under investigation [START_REF] Azadbakht | Validation of High-Resolution Tractography Against In Vivo Tracing in the Macaque Visual Cortex[END_REF][START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF][START_REF] Schilling | Limits to anatomical accuracy of diffusion tractography using modern approaches[END_REF][START_REF] Donahue | Using Diffusion Tractography to Predict Cortical Connection Strength and Distance: A Quantitative Comparison with Tracers in the Monkey[END_REF][START_REF] Knosche | Validation of tractography: Comparison with manganese tracing[END_REF][START_REF] Dyrby | Validation of in vitro probabilistic tractography[END_REF][START_REF] Dauguet | Comparison of fiber tracts derived from in-vivo DTI tractography with 3D histological neural tract tracer reconstruction on a macaque brain[END_REF][START_REF] Calabrese | A Diffusion MRI Tractography Connectome of the Mouse Brain and Comparison with Neuronal Tracer Data[END_REF][START_REF] Schilling | Anatomical accuracy of standard-practice tractography algorithms in the motor system -A histological validation in the squirrel monkey brain[END_REF][START_REF] Aydogan | When tractography meets tracer injections: a systematic study of trends and variation sources of diffusion-based connectivity[END_REF][START_REF] Neher | Fiberfox: facilitating the creation of realistic white matter software phantoms[END_REF][START_REF] Cote | Tractometer: towards validation of tractography pipelines[END_REF]. It is now well known that these techniques can be plagued not only by overestimation of the extent and connections of pathways (false positives), but also underestimation of the same (false negatives). One influential work presented by Thomas et al [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF] highlights "an inherent limitation in determining long-range anatomical projections based on voxel-averaged estimates of local fiber orientation obtained from DWI data that is unlikely to be overcome by improvements in data acquisition and analysis alone." Thus, it appears that high anatomical accuracy remains an elusive goal with current tractography algorithms and strategies, unless a "revolution" happens in the additional information provided to tractography algorithms [START_REF] Maier-Hein | The challenge of mapping the human connectome based on diffusion tractography[END_REF][START_REF] Poulin | Tractography and machine learning: Current state and open challenges[END_REF].

However, these limitations have largely been highlighted in validation studies that have implemented tractography in a manner most similar to that performed in connectomics studiesi.e., with little to no anatomical rules or constraints in a relatively "unsupervised" approach lacking advantages of prior information. Thus, they represent a lower-bound, or worst-case, scenario for tractography, and may not be indicative of the anatomical accuracy in the process of bundlesegmentation where filtering and anatomical rules are common [START_REF] Garyfallidis | Recognition of white matter bundles using local and global streamline-based registration and clustering[END_REF][START_REF] Yendiki | Automated probabilistic reconstruction of white-matter pathways in health and disease using an atlas of the underlying anatomy[END_REF][START_REF] Warrington | XTRACT -Standardised protocols for automated tractography in the human and macaque brain[END_REF][START_REF] Wasserthal | Combined tract segmentation and orientation mapping for bundle-specific tractography[END_REF][START_REF] Wasserthal | TractSeg -Fast and accurate white matter tract segmentation[END_REF][START_REF] Rheault | Bundle-specific tractography with incorporated anatomical and orientational priors[END_REF][START_REF] Wassermann | On describing human white matter anatomy: the white matter query language[END_REF][START_REF] Wassermann | The white matter query language: a novel approach for describing human white matter anatomy[END_REF]. In fact, several early works in this field share a quite optimistic view of the accuracy of tractography [START_REF] Catani | Virtual in vivo interactive dissection of white matter fasciculi in the human brain[END_REF][START_REF] Lawes | Atlas-based segmentation of white matter tracts of the human brain using diffusion tensor tractography and comparison with classical dissection[END_REF][START_REF] Mori | Human white matter atlas[END_REF], and "virtual" dissections of individual fiber bundles are qualitatively similar to cadaveric dissections [START_REF] Hau | Revisiting the human uncinate fasciculus, its subcomponents and asymmetries with stem-based tractography and microdissection validation[END_REF][START_REF] Wang | Subcomponents and connectivity of the superior longitudinal fasciculus in the human brain[END_REF][START_REF] Forkel | The anatomy of fronto-occipital connections from early blunt dissections to contemporary tractography[END_REF][START_REF] Sarubbo | Frontal terminations for the inferior fronto-occipital fascicle: anatomical dissection, DTI study and functional considerations on a multi-component bundle[END_REF]. Further, constraints have been heavily utilized in previous validation studies for not only verifying anatomical accuracy, but identifying advantages of comparative anatomy across species [START_REF] Jbabdi | Human and monkey ventral prefrontal fibers use the same organizational principles to reach their targets: tracing versus tractography[END_REF][START_REF] Mars | Diffusion-weighted imaging tractography-based parcellation of the human parietal cortex and comparison with human and macaque resting-state functional connectivity[END_REF][START_REF] Mars | The extreme capsule fiber complex in humans and macaque monkeys: a comparative diffusion MRI tractography study[END_REF][START_REF] Safadi | Functional Segmentation of the Anterior Limb of the Internal Capsule: Linking White Matter Abnormalities to Specific Connections[END_REF], and confirming the trajectory or cortical origin of white matter bundles [START_REF] Neubert | Comparison of human ventral frontal cortex areas for cognitive control and language with areas in monkey frontal cortex[END_REF][START_REF] Neubert | Connectivity reveals relationship of brain areas for reward-guided learning and decision making in human and monkey frontal cortex[END_REF][START_REF] Mars | Connectivity-based subdivisions of the human right "temporoparietal junction area": evidence for different areas participating in different cortical networks[END_REF][START_REF] Innocenti | The Crossed Projection to the Striatum in Two Species of Monkey and in Humans: Behavioral and Evolutionary Significance[END_REF]. While these studies, and many others incorporating prior information and anatomical constraints [START_REF] Rheault | Bundle-specific tractography with incorporated anatomical and orientational priors[END_REF][START_REF] Galinsky | A Unified Theory of Neuro-MRI Data Shows Scale-Free Nature of Connectivity Modes[END_REF][START_REF] Smith | Anatomically-constrained tractography: improved diffusion MRI streamlines tractography through effective use of anatomical information[END_REF][START_REF] Galinsky | Simultaneous multi-scale diffusion estimation and tractography guided by entropy spectrum pathways[END_REF][START_REF] Frank | Dynamic Multiscale Modes of Resting State Brain Activity Detected by Entropy Field Decomposition[END_REF], suggest tractography can accurately reconstruct not only broad pathways but also the topology of smaller bundles within those pathways, the sensitivity and specificity when implementing anatomical guidance has not been explicitly quantified.

Along these lines, we hypothesize that in order to overcome the sensitivity/specific curse, we simply (and intuitively) need to utilize anatomical knowledge and anatomically-informed rules as is commonly done in bundle segmentation studies, which will enable us to constrain where tracks can and cannot go [START_REF] Rheault | Bundle-specific tractography with incorporated anatomical and orientational priors[END_REF]. With this in mind, the aim of the current study is to investigate and quantify the upper bounds of current tractography methods. Whereas previous quantitative validation studies have asked how well we can map connections from a given region, we ask how well we can extract known bundles and connections of the brain, i.e., given detailed (and painstakingly acquired) knowledge of the ground truth pathways [START_REF] Schmahmann | Fiber pathways of the brain[END_REF] we ask if existing algorithms can reach high anatomical accuracy in segmenting these pathways. Thus, we propose, and show, that simple guidance can be used to achieve a high sensitivity and high specificity at the same time (i.e., if we a priori know, and constrain, where the pathways start, where they end, and where they don't go) -confirming that the process of bundle segmentation, with the incorporation of a prior knowledge, has the potential to results in highly accurate representations of the desired neural pathways.

To do this, we utilize the validation dataset originally introduced by Thomas et al. [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF], and subsequently employed in an international tractography challenge [START_REF] Schilling | Limits to anatomical accuracy of diffusion tractography using modern approaches[END_REF], both of which came to the conclusion that alternative or new strategies are needed for mapping the brain's fiber pathways. Here, we apply tractography methods to this ex vivo dataset of the macaque brain, and compare these methods to maps of known axonal projects from previous tracer studies in the macaque [START_REF] Schmahmann | Fiber pathways of the brain[END_REF]. Importantly, by utilizing the very same detailed tracer maps and explicit descriptions by the authors, we perform virtual dissections of a full brain tractogram. We constrain the streamlines using varying combinations of inclusion and exclusion regions in a manner consistent with common approaches in bundle segmentation. We assess the results using the code and analysis used in [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF], iteratively refining the constraints until both high sensitivity and high specificity are achieved. We use the subject-specific data to drive the results, but obey anatomical rules with clear landmarks, as one might when driving a car by following GPS instructions and road maps.

Results

The aim of the methodology is to duplicate the process of a clinician, neuroanatomist, or researcher that may be manually delineating a fiber bundle, i.e. by applying and adapting guidelines until the streamlines best replicate the ground truth WM anatomy of the pathway of interest (for example when comparing to neuroanatomy textbooks, prior knowledge, or tractography protocols). We selected the datasets and ground truth pathways from previous studies [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF][START_REF] Schilling | Limits to anatomical accuracy of diffusion tractography using modern approaches[END_REF], composed of anatomical locations of tracer-labeled regions from anterograde injections within (A) the precentral gyrus (PCG) corresponding to the foot region of the motor cortex (Case #28 in [START_REF] Schmahmann | Fiber pathways of the brain[END_REF]) and (B) the ventral part of area V4 (Case #21 in [START_REF] Schmahmann | Fiber pathways of the brain[END_REF]) of a rhesus macaque -the same injection sites utilized in [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF]. Tracer-labeled regions were transposed to the same space as the diffusion MRI data (Figure 1), and agreement between tracer results and tractography was assessed in terms of the number of true positive (TP), false negative (FN), false positive (FP), and true negative (TN) connections, which are used to compute specificity [TN/(TN+FP)] and sensitivity [TP/(TP+FN)], which are defined by regions of the brain manually delineated by the authors of [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF] (Figure 1).

Two different methods of streamline generation and subsequent pathway delineation were investigated, representative of the approaches and software the authors (KS and LP) chose in their own anatomical investigations. These are a manual-based approach and template-based approach. First, we utilized manually-drawn ROIs [START_REF] Wakana | Reproducibility of quantitative tractography methods applied to cerebral white matter[END_REF][START_REF] Catani | Atlas of human brain connections[END_REF], defining regions by hand where streamlines must go and where they must not go. These hand-drawn regions were typically in the form of planes or 2D free-form shapes, often orthogonal to the observed direction of streamline prorogation. Inclusion regions were placed in regions specific to the pathway of interest, whereas streamlines considered false positives were eliminated by placing exclusion regions where these were visually identified to share areas in common (most commonly along adjacent white matter bundles or at the sulcal depth of gyri). Example procedures and constraints are shown in Figure 2 and described in detail in Materials and Methods. Second, we made use of predefined anatomical regions defined in a macaque template to serve as inclusion and exclusion regions. The template was composed of labels in the form 3D volumes to be used as regions of interest. Example procedures and constraints shown in Figure 3 and described in detail in Materials and Methods.

Qualitative results of the final tractogram of connections to the injection region are shown in Figure 4 for PCG connections, and in Figure 5 for V4 connections. The reference atlas of digitized histological connections (i.e., the ground truth) is shown as well as a roughly anatomically matched MRI slice with tractography streamlines overlaid, showing both manual dissection results and template-based results. While the streamlines replicate the major pathways and connections from tracers, they do not do so on an individual axon/streamline basis. There are small inconsistencies from individual streamlines, however, on the scale of larger anatomical regions (see Figure 1D), streamlines exist where expected and do not occupy regions that tracer does not. Visually, the manual dissections better replicate the ground truth in many regions, due to the ability to make subject-specific and location-specific inclusion and exclusion decisions.

Quantifying accuracy (as done [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF] in and [START_REF] Schilling | Limits to anatomical accuracy of diffusion tractography using modern approaches[END_REF]) for PCG connections, we find manualdissections result in a sensitivity of 0.949, specificity of 0.956, and Youden index (sensitivity + specificity -1) of 0.906 (TP=132, FN=7, TN=328, FP=15), and template-generated dissections a sensitivity of 0.863, specificity of 0.869, and Youden index of 0.732 (TP=120, FN=19, TN=298, FP=45). For V4 connections, manual-dissections result in a sensitivity of 0.852, specificity of 0.925, and Youden index of 0.777 (TP=115, FN=20, TN=234, FP=19), and template-generated dissections a sensitivity of 0.770, specificity of 0.866, and Youden index of 0.636 (TP=104, FN=31, TN=219, FP=34). These results are plotted as ROC curves on top of the results of Thomas et al., 2013 [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF] and those of Schilling et al., 2018 [20] (Figure 5A for PCG connections, Figure 5B for V4 connections). It is clear that a high sensitivity and high specificity are achieved at the same time, with the values much higher than those from both the original investigation [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF], and the international community challenge [START_REF] Schilling | Limits to anatomical accuracy of diffusion tractography using modern approaches[END_REF]. The highest Youden indices observed previously on this dataset were 0.59 and 0.56 from [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF] and [START_REF] Schilling | Limits to anatomical accuracy of diffusion tractography using modern approaches[END_REF] for the PCG injection and 0.53 and 0.58 for the V4 injection. We note that this is not a comparison of algorithms, since we of course had access or direct knowledge of the ground truth to help choose constraints to improve sensitivity and/or specificity.

Discussion

In this study, we aim to investigate the upper bounds of tractography performance. If we are given a detailed description of the ground truth, either depicted in a map or written explicitly as a set of rules, and liberty in manual editing of pathways, we ask if it is possible to overcome the sensitivity/specificity limitations of current tracking algorithms and achieve a high anatomical accuracy. We find our answer is 'yes' -tracking can be highly accurate if we know where streamlines (or pathways) start, where they end, and (maybe most importantly) where they don't go.

The importance of prior knowledge

Importantly, a number of anatomical constraints were needed to achieve this accuracy. Thus, while our answer to the previous question is 'yes', it is not without caveats. Our conclusion should be amended to say that current algorithms, in combination with constraints, can achieve both high sensitivity and high specificity. Or alternatively, current algorithms "in combination with previous anatomical knowledge" can have high accuracy. This anatomical knowledge is what influences the regional constraints, and we find that both inclusion and exclusion regions were needed in our study. Thus, our results are exactly in agreement with previous literature [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF][START_REF] Schilling | Limits to anatomical accuracy of diffusion tractography using modern approaches[END_REF][START_REF] Maier-Hein | The challenge of mapping the human connectome based on diffusion tractography[END_REF], that simply utilizing local orientation information alone will not lead to accurate results, and more information is needed. However, we believe that this additional information can, and should, come in the form of existing knowledge of the trajectories of the white matter.

This study serves as the link between the existing validation studies emphasizing inherent tractography limitations and the ever-present sensitivity/specificity tradeoffs [19, 22-24, 27, 30, 57-61], and those studies that suggest anatomically faithful white matter bundles visually matching independent cadaveric or tracer data [44-49, 51, 62, 63]. The sensitivity/specificity tradeoff has so far been quantified using algorithms or streamlines generated in a relatively unconstrained manner, without the use of prior knowledge or constraints. Alternatively, those that reveal accurate reconstructions of trajectories and connectivity patterns are nearly always performed using inclusion and exclusion criteria, chosen and implemented by those with expert a priori knowledge of the system or pathways under investigation. While the latter studies show similarities in bundle shape, location, and endpoints, the sensitivity and specificity has not been fully quantified. In this study, we quantitatively confirm that the use of a prior knowledge, in this case in the form of regional constraints, improves the anatomical accuracy of tractography. Thus, while false positives and false negatives still exist, the overall accuracy is significantly improved, suggesting that the use of constraints as is commonly employed in a number of studies using bundle-segmentation can indeed result in highly accurate reconstructions.

Relying on local orientation information alone is insufficient to ensure both sensitivity and specificity [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF]. Here, we show that current tractography algorithms can provide highly accurate maps of the white matter, utilizing prior knowledge to filter results. In this case, we chose an algorithm that was known to be highly sensitive (high TP), and utilized added constraints as the solution to improve specificity. The sets of utilized streamlines, prior to filtering, exhibited a high sensitivity and poor specificity (sensitivity=1, specificity=0.27, Youden index=0.27 for the probabilistic streamlines prior to manual filtering), in line with previous findings with similar reconstruction and tractography algorithms [START_REF] Schilling | Anatomical accuracy of standard-practice tractography algorithms in the motor system -A histological validation in the squirrel monkey brain[END_REF][START_REF] Schilling | Limits to anatomical accuracy of diffusion tractography using modern approaches[END_REF], showed a much higher overall accuracy after anatomical constraints were employed. This emphasizes that the high specificity and sensitivity is due to the exploited anatomical knowledge instead of tractography algorithm choices.

The challenge, then, was to find how to guide dissection that improved tractography. Here, we utilized inclusion and exclusion ROIs, as well as maximum streamline lengths. In order to improve future tractography results, it is crucial to understand what constraints are necessary (a task which is beyond the scope of the current study), and what additional constraints (i.e., clustering, seeding, filtering) may be successful. These constraints will almost certainly vary across the algorithm employed, and the system under investigation (i.e., the brain itself and the pathway of interest). In the human brain, these may vary on an individual subject basis (and animal regions will likely not be directly translatable to the human brain -see discussion below). For this reason, it is important to think critically about how these pathways are "defined" anatomically, the nomenclature used to describe them, and how best to replicate them using tractography tools. For example, pathways may be defined as connecting cortical region A to region B, or as a bundle that passes through/over/under region C [START_REF] Wakana | Reproducibility of quantitative tractography methods applied to cerebral white matter[END_REF][START_REF] Catani | Atlas of human brain connections[END_REF][START_REF] Wassermann | On describing human white matter anatomy: the white matter query language[END_REF][START_REF] Wassermann | The white matter query language: a novel approach for describing human white matter anatomy[END_REF][START_REF] Mori | Stereotaxic white matter atlas based on diffusion tensor imaging in an ICBM template[END_REF][START_REF] Landman | Effects of diffusion weighting schemes on the reproducibility of DTI-derived fractional anisotropy, mean diffusivity, and principal eigenvector measurements at 1.5T[END_REF]. In summary, it is clear that how a pathway is defined may influence constraints, and a consensus is not clearly within reach in humans, although efforts (or discussions) are underway [START_REF] Mandonnet | The Nomenclature of Human White Matter Association Pathways: Proposal for a Systematic Taxonomic Anatomical Classification[END_REF][START_REF] Panesar | Commentary: The Nomenclature of Human White Matter Association Pathways: Proposal for a Systematic Taxonomic Anatomical Classification[END_REF].

At first glance, these results may seem intuitive. If we choose a highly sensitive algorithm that connects everything to everything, the idea that we can detect connections to all areas of the brain seems obvious. However, the key is when ensuring specificity -the connections of these algorithms may go through regions the true pathways do not, and these are eliminated through exclusion regions. Despite these exclusions, we are still able to achieve high true positive rates. This is certainly an encouraging result, as it means that removing false positives does not also necessarily remove excessive true positives at the same time (i.e. streamlines not only connect to the correct regions, but also pass through the correct regions along their route). The alternative, brute force algorithm would be to connect every seed voxel to every target voxel, through every inclusion voxel, to guarantee that all true positive regions are able to be reached without traversing TN regions. However, current algorithms do not do this, and we are able to achieve successful results employing widely used algorithms in the literature.

Challenges in validation, tractography, and "gold" standards

The presented results tell us that on a region-by-region basis, we are able to achieve a high specificity and high sensitivity. However, it is clear that there are still spurious streamlines within both cortical and white matter regions (see Figure 3). While these will still contribute to false positive areas (if they are truly false positive over the defined regions), these results may not end up on the optimal end of the ROC curves if this was analyzed on a voxel-wise basis. However, the ground truth is only defined over anatomically meaningful gray and white matter regions rather than on the scale of voxels, an analysis which would be complicated because tracer and tractography are performed on different physical brains (although analysis on the same brain has been performed, we have chosen this dataset as it most clearly highlighted the fundamental accuracy limitations of tractography). As described in [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF], while connectivity strength may vary across animals and injections, the presence or absence of connections is likely to be similar across monkeys.

This highlights the significance, and importantly the limitations, of what we choose to call our gold standards, and the methods used to validate tractography [START_REF] Dyrby | Validation strategies for the interpretation of microstructure imaging using diffusion MRI[END_REF]. In this study, it is clear that we don't match the reference atlas perfectly, although our ROC analysis suggests near perfect results. When validating, it is important to ask how important are individual streamlines to the analysis, how large are the anatomical white and gray matter regions we should use to designate our ground truth, and how finely parcellated do we need these areas to be (entire gyral folds? Divisions into gyral crowns, walls, and sulcal fundi? Or on the scale of individual cortical columns?)? The answers to these questions may be based on the intended application of the tractography analysis. The use as a connectivity tool may require more finely detailed anatomical connections and localization, while the use as a segmentation tool may only necessitate accuracy on the coarser scale the size of the bundles themselves -although it is clear that accuracy in both cases requires prior constraints. However, use of tractography as an exploratory analysis (i.e., searching for new pathways, or connections to regions that are not well characterized) will have limited accuracy on both streamline and region-to-region bases without some prior anatomical knowledge, and results should be interpreted with care without strong independent validation (i.e., histological tracers and dissection).

Similarly, another major limitation is that the "gold" standard (chosen by Thomas et al. [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF]) is based on the very same reference used to constrain the tracking, which may bias the results. However, the aim was to investigate whether, with prior knowledge, it is possible to achieve a high sensitivity and specificity. In the human brain (or any brain), researchers and clinicians have the same ability to constrain streamlines to where they do/don't want them to go, which makes this a valid approach. And, again, we emphasize that given the ground truth defined previously, with anatomical accuracy defined and described as a ROI-based sensitivity/specificity measure, tractography can be highly accurate (at least for the pathways investigated). Finally, the present study presents a best-case scenario not only in terms of utilizing a priori knowledge, but also of the pathways chosen to validate (projection areas of M1 and V4) which are generally major projection systems with larger, well-defined projections. The use of these two systems was motivated by their use and careful manual delineations and ground truth definitions in [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF] which were chosen as two exemplar orthogonally oriented systems. Even in this ideal model system, a "perfect" sensitivity and specificity was not achieved, with false negatives observed at greater distances from injection site, and biases or inaccuracies at exact cortical terminations, in line with previous studies [START_REF] Donahue | Using Diffusion Tractography to Predict Cortical Connection Strength and Distance: A Quantitative Comparison with Tracers in the Monkey[END_REF][START_REF] Schilling | Confirmation of a gyral bias in diffusion MRI fiber tractography[END_REF][START_REF] Reveley | Superficial white matter fiber systems impede detection of long-range cortical connections in diffusion MR tractography[END_REF].

Generalizability

These results lead to an important set of open questions regarding generalizability. First, how should anatomical rules be defined to ensure they generalize not only across subjects, but also across tracking algorithms? The exact set of constraints are almost certainly not optimal for all methods of generating streamlines. Clearly, these rules will differ with varying bundle segmentation approaches, with much more flexibility and freedom in manually-placed ROIs, whereas atlas-based labels are fixed and may provide the ability to include and/or exclude desired regions depending on how fine-grained the parcellation is. Next, how do these guiding principles change in healthy versus diseased individuals? It is critical that any guidance in either segmentation or connectivity analysis generalize to subjects with anomalous diffusion and structural properties of both normal and abnormal (tumorous) tissue. Finally, while the filtering approach used here is most directly related to the field of bundle-segmentation, what physical, anatomical, or structural priors or rules can be used that will generalize to the connectomics field that will reduce invalid connections while ensuring the existence of valid connections? Major progress in the connectomics and bundle-segmentation field has taken place with advanced filtering and/or spatial priors based on anatomy [START_REF] Warrington | XTRACT -Standardised protocols for automated tractography and connectivity blueprints in the human and macaque brain[END_REF][START_REF] Rheault | Bundle-specific tractography with incorporated anatomical and orientational priors[END_REF][START_REF] Rheault | Tractostorm: The what, why, and how of tractography dissection reproducibility[END_REF][START_REF] Girard | Towards quantitative connectivity analysis: reducing tractography biases[END_REF][START_REF] St-Onge | Surface-enhanced tractography (SET)[END_REF], microstructure [START_REF] Girard | AxTract: Toward microstructure informed tractography[END_REF], and the diffusion signal itself (conservation of density) [START_REF] Daducci | COMMIT: Convex optimization modeling for microstructure informed tractography[END_REF][START_REF] Smith | SIFT: Spherical-deconvolution informed filtering of tractograms[END_REF]. We believe the next big steps involve multimodal integration of these and orthogonal techniques used to probe the human connectome -for example myelin [START_REF] Alonso-Ortiz | MRI-based myelin water imaging: A technical review[END_REF][START_REF] Ganzetti | Whole brain myelin mapping using T1-and T2-weighted MR imaging data[END_REF], BOLD contrasts [START_REF] Galinsky | A Unified Theory of Neuro-MRI Data Shows Scale-Free Nature of Connectivity Modes[END_REF][START_REF] Galinsky | Simultaneous multi-scale diffusion estimation and tractography guided by entropy spectrum pathways[END_REF][START_REF] Gore | Functional MRI and resting state connectivity in white matter -a minireview[END_REF][START_REF] Ding | Detection of synchronous brain activity in white matter tracts at rest and under functional loading[END_REF][START_REF] Huang | Voxel-wise detection of functional networks in white matter[END_REF], functional imaging [START_REF] Deslauriers-Gauthier | White matter information flow mapping from diffusion MRI and EEG[END_REF][START_REF] Galinsky | Joint Estimation of Effective Brain Wave Activation Modes Using EEG/MEG Sensor Arrays and Multimodal MRI Volumes[END_REF], and quantitative microdissection [START_REF] Benedictis | Photogrammetry of the Human Brain: A Novel Method for Three-Dimensional Quantitative Exploration of the Structural Connectivity in Neurosurgery and Neurosciences[END_REF], which will lead to a better understanding of the fundamental rules governing the structural organization and connectivity of the brain and endeavors to fully incorporate these into tractography algorithms. In essence, all of these facilitate the adoption of rules, for example ways to include, exclude, or generate streamlines in the same way approached through this study, which can lead to breakthroughs in the anatomical accuracy of tractographyas quantitatively shown in this study.

Finally, validation in animal models does not necessarily validate this methodology (or tractography in general) in humans. These results, and specifically these constraints, are not necessarily immediately generalizable -especially to different pathways, subjects, or pathology in particular. Additionally, non-anatomical constraints, such as path curvature or anisotropy thresholds are not immediately translatable from this non-human ex vivo model. In this study, we have the advantage of detailed histological tracings to define our constraints. In the human, there is a tremendous wealth of information from anatomists, gleaned from histological and blunt dissection methods. This knowledge, while it may not be able to constrain tracking to the degree used here, should be used on a pathway-by-pathway basis to define and refine constraints. Thus, collaboration between the anatomy and diffusion communities is needed to reach general agreement on defining pathways -a good first step would be describing locations, areas, or general boundaries where pathways start, where they end, and regions they do/do not pass through.

Conclusion

Tractography, even if performed on high quality diffusion MRI data with sophisticated methods, is faced with an inherent trade-off between sensitivity and specificity (the "sensitivity/specificity curse") and it seems that additional information is needed to overcome these limitations. In this work, we show that tractography implemented as a bundle segmentation technique, incorporating prior knowledge, can indeed be highly anatomically accurate. Importantly, this necessitates detailed knowledge of where pathways go and where they do not go. In this study, this knowledge is translated into constraints in the bundle dissection process which allows dissection and filtering of the desired streamlines from potentially many invalid streamlines. These techniques of using anatomical constraints to define inclusion/exclusion criteria have been utilized previously in bundle dissection studies, and we propose that connectomics studies should consider similar constraints guided by known anatomical, developmental, or microstructural rules.

Materials and Methods

The aim of the methodology is to duplicate the process of a clinician, neuroanatomist, or researcher that may be manually delineating a fiber bundle, i.e. by applying and adapting guidelines until the streamlines best replicate the ground truth WM anatomy of the pathway of interest (for example when comparing to neuroanatomy textbooks, prior knowledge, or tractography protocols). We first describe the ground truth dataset and accuracy assessment, followed by a description of how pathways were created and delineated.

Ground Truth and Accuracy Assessment

Figure 1 displays the datasets and ground truth derivation used in this study -for a detailed description of the histology we refer to [START_REF] Schmahmann | Fiber pathways of the brain[END_REF], and for the acquisition and delineation of MRI we refer to [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF]. Briefly, the ground truth is based on two anterograde tracer injections within (A) the precentral gyrus (PCG) corresponding to the foot region of the motor cortex (Case #28 in [START_REF] Schmahmann | Fiber pathways of the brain[END_REF]) and (B) the ventral part of area V4 (Case #21 in [START_REF] Schmahmann | Fiber pathways of the brain[END_REF]) of a rhesus macaque -these are the same injection sites utilized in [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF]. Slides were digitized and tracer substance (i.e. connection to the injection site) was delineated on individual slices of the reference atlas by the authors of [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF] (Figure 1,A).

MRI acquisition is performed on an ex vivo rhesus monkey brain, and scanned over ~71 hours using a 3D diffusion-weighted EPI PGSE sequence (b-value=4,800s/mm 2 , 7 b=0 volumes, 121 DWI's with directions distributed over a tessellated icosahedral hemisphere). The tracerlabeled regions were transposed to the same space as the diffusion data (by the authors of [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF]) for each MRI slice that was anatomically matched with the histology slice from the reference atlas. An example b=0 ("b0") slice from approximately the same anatomical location is shown (Figure 1B), along with the tracer results in MRI space (Figure 1C). Finally, gray and white matter ROIs were manually delineated on the high-resolution data [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF], and the agreement between tracer results and tractography was assessed in terms of the number of true positive (TP), false negative (FN), false positive (FP), and true negative (TN) connections, which are used to compute specificity [TN/(TN+FP)] and sensitivity [TP/(TP+FN)].

Tractography and pathway delineation

Two different methods of streamline generation and subsequent pathway delineation were investigated, representative of the approaches and software the authors (KS and LP) choose in their own anatomical investigations. First, we utilized manually-drawn ROIs [START_REF] Wakana | Reproducibility of quantitative tractography methods applied to cerebral white matter[END_REF][START_REF] Catani | Atlas of human brain connections[END_REF], defining regions by hand where streamlines must go and where they must not go. Second, we made use of predefined anatomical regions defined in a macaque template to serve as inclusion and exclusion regions.

Manual delineation

Local voxel-wise reconstruction and orientation estimation was performed using constrained spherical deconvolution [START_REF] Tournier | Resolving crossing fibres using constrained spherical deconvolution: validation using diffusion-weighted imaging phantom data[END_REF] (one of the techniques investigated in both [START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF] and [START_REF] Schilling | Limits to anatomical accuracy of diffusion tractography using modern approaches[END_REF]) implemented in the MrTrix3 software package [START_REF] Tournier | MRtrix: Diffusion tractography in crossing fiber regions[END_REF][START_REF] Tournier | MRtrix3: A fast, flexible and open software framework for medical image processing and visualisation[END_REF]. Probabilistic tractography was performed (iFOD2 algorithm) using software default parameters, propagating pathways from randomly selected points throughout the brain until 5 million streamlines were generated throughout the whole brain. From this set of whole brain streamlines, subsets of pathways from the injection sites were virtually dissected.

Pathways connecting to the dorsal part of area 4 in the PCG were constrained and extracted using both the written descriptions and tracer visualizations from Case #28 of "Fiber Pathways of the Brain" (pages 322-328) [START_REF] Schmahmann | Fiber pathways of the brain[END_REF], while those connecting the ventral part of V4 were extracted using the descriptions and visualizations from Case #21. Example delineations for 5 "pathways" from the PCG, and corresponding tractography constraints, are described in detail below (and shown in Figure 2). Importantly, this was an iterative manual process, where both inclusion and exclusion regions were added, removed, and translated until streamlines qualitatively matched the ground truth displayed in Figures 4 and5, as well as continually quantifying sensitivity/specificity until we determined that region placement was near-optimal for this set of streamlines. Importantly, the labelled regions used to quantify sensitivity/specificity were not used as exclusion/inclusion regions and were not used in the manual delineation process.

Local Association Fibers -Rostrally Directed Fibers (Figure 2, 1 st row)

Here, Pandya and Schmahmann [START_REF] Schmahmann | Fiber pathways of the brain[END_REF] describe "Diffuse terminations adjacent to the injection site are seen in area 4", thus we utilize 1 inclusion ROI (we note that the injection region is used as an inclusion ROI in all examples, thus is not included in the constraint count) -placed on two separate slices rostral to the seed at approximately atlas slices #85 and #89 [START_REF] Schmahmann | Fiber pathways of the brain[END_REF] -as well as a maximum streamline length of 6mm (which we found to be a tradeoff between including additional streamlines at the expense of streamlines extending caudally past the seed).

Long Association Fibers -Rostrally Directed Fibers (Figure 2, 2 nd row)

Rostral to the injection site, "fibers travel in the white matter… [and] a small contingent of fibers near the inject site gathers at the upper bank and depth of the cingulate sulcus. These fibers terminate in the cortex at the depth of the cingulate sulcus…" in motor areas M3 (see slice #81 in for reference) [START_REF] Schmahmann | Fiber pathways of the brain[END_REF]. To replicate this, we utilize 2 inclusion ROIs, 3 exclusion ROIs, and a maximum length of 40mm. The inclusion ROIs (again, the injection region is also an inclusion ROI) force the pathways to go through the white matter adjacent and rostral to the seed, and reenter the cortex at the cingulate sulcus. The exclusion regions exclude interhemispheric crossing at the mid-sagittal plane, fibers extending anteriorly once entering the cortex, and fibers entering or adjacent to the striatal bundle.

Commissural Fibers (Figure 2, 3 rd row)

The commissural fibers descend into the white matter of the precentral gyrus [START_REF] Schmahmann | Fiber pathways of the brain[END_REF], and "move medially to enter the corpus callosum, and head towards the opposite hemisphere." For these fibers, we use 1 inclusion region at the mid-sagittal slice of the corpus callosum, and 3 exclusion regions excluding all other interhemispheric connections (i.e., incorrect "jumps" across hemispheres from the superior parietal lobe), fibers entering the cingulate, and fibers that project laterally before moving medially.

Striatal Fibers (Figure 2, 4 th row)

The striatal bundle and Muratoff bundle descend from the injection site and terminate in the body and head of the caudate nucleus. Some fibers additionally traverse the dorsal internal capsule to terminate in the putamen [START_REF] Schmahmann | Fiber pathways of the brain[END_REF]. For these systems, we utilized two large inclusion ROIs (one volume for the Putamen, one for the caudate nucleus) although we did not enforce streamlines to pass through both (i.e., they only had to pass/terminate in one or the other), thus these could be considered a single region. Additionally, we implemented 5 exclusion regions to prevent thalamic terminations, interhemispheric fibers (i.e. after traversing entirely through the caudate), and fibers extending too far laterally or posterior. Subcortical Fibers -pontine bundle (Figure 2, 5 th row) Fibers in the pontine bundle "descend in the central and medial parts of the rostral posterior limb…and enter the cerebral peduncle as they continue into the brainstem" [START_REF] Schmahmann | Fiber pathways of the brain[END_REF]. For these fibers, we included 1 simple inclusion region (following procedures very similar to that from Wakana et al. [START_REF] Wakana | Reproducibility of quantitative tractography methods applied to cerebral white matter[END_REF] for the corticospinal tract) and included several exclusion ROIs. These exclusion ROIs were drawn on a number of orthogonal and oblique slices to limit pathways that took tortuous trajectories to reach the internal capsule, travelled across hemispheres, or left and re-entered the expected pathways.

For case #28 (PCG), 15 separate bundles, or sets of fibers/streamlines, were extracted: 2 sets of local association fibers (1 rostrally and caudally directed), 3 sets of caudally directed long association fibers, 4 sets of rostrally directed long association fibers, 4 sets of commissural and subcortical fibers (1 commissural, 1 terminating in thalamic nuclei, 1 terminating in the subthalamic nucleus, and 1 set through the cerebral peduncles), and 2 sets of striatal fibers traveling through the putamen and caudate nucleus. For case #21 (V4), 10 sets of fibers were extracted: 2 sets of local association fibers, 2 sets of caudally directed long association fibers, 1 set of rostrally directed long association fibers, 1 set of commissural fibers, and 4 sets of striatal fibers (1 terminating in the genu of the caudate nucleus, 1 in the body and head of the caudate nucleus, 1 terminating in the putamen, and 1 with fibers entering the claustrum).

We note that sub-divisions and classification decisions are made based on written descriptions [START_REF] Schmahmann | Fiber pathways of the brain[END_REF], and decisions made during the iterative process, although it is likely that separate sets of streamlines could have been combined, for example by concatenating constraints.

This process was very much iterative. Regions were removed, added, or edited until pathways reached desired results. Once deemed "acceptable", sensitivity/specificity analysis was run, and more corrections performed based on quantitative results. Approximately 50 hours were spent in the process of creating and editing ROIs (see discussion on feasibility on human data and applicability to clinical and research applications).

Template based delineation

Local voxel-wise reconstruction and orientation estimation was performed using constrained spherical deconvolution [START_REF] Tournier | Resolving crossing fibres using constrained spherical deconvolution: validation using diffusion-weighted imaging phantom data[END_REF] implemented in the Dipy software package [START_REF] Garyfallidis | Dipy, a library for the analysis of diffusion MRI data[END_REF]. Probabilistic tractography was performed (LocalTracking algorithm) using software default parameters (step size = 0.5 x voxel size, max length = 800 steps), propagating pathways from randomly selected points throughout the brain until 1 million streamlines were generated.

As in the manually-drawn ROIs, pathways connecting to area 4 of PCG and V4 were extracted using both written descriptions and tracer visualizations from Case #28 and Case #21, respectively. However, in this case, we utilized a template of predefined anatomical regions defined in a standard atlas space. We chose the PennCHOP macaque template [START_REF] Feng | Population-averaged macaque brain atlas with high-resolution ex vivo DTI integrated into in vivo space[END_REF], which represents a good compromise of cortical, subcortical, and white matter ROIs. Example dissections for 2 pathways from the PCG, and corresponding constraints, are described in detail below (and shown in Figure 3). Again, this was an iterative process, typically involving defining the endpoints based on known anatomy, followed by refinement through exclusion regions or forcing pathways to go through specified WM regions.

Striatal Fibers

As described in [START_REF] Schmahmann | Fiber pathways of the brain[END_REF] the striatal bundles descend from the injection site, enter the corona radiata and dorsal aspect of the external capsule and "terminate in the dorsal segment of the claustrum as well as lateral sectors of the putamen throughout most of its rostrocaudal extent". Focusing first on putamen streamlines, we select only streamlines with an endpoint in the putamen. While streamlines do enter the corona radiata, spurious looping streamlines are apparent, which are removed through the use of 6 exclusion ROIs (anterior, posterior, and retrolenticular limb of the internal capsule, fornix, thalamus, and amygdala) in addition to a length threshold of 50mm.

Commissural Fibers

Again, the commissural fibers enter the corpus callosum and head towards the opposite hemisphere. For these fibers, we use the body of the corpus callosum as an inclusion region, followed by several exclusion regions that exclude regions where these fibers are known not to pass through before traversing hemispheres (cingulum, Thalamus, fornix, posterior limb of the internal capsule, extreme capsule, and posterior cingulate gyrus) For case #28 (PCG), 12 separate bundles, or sets of fibers/streamlines, were extracted (note that differences in manual delineations are due to constraints in template ROI parcellations): 3 sets of local association fibers (1 rostrally directed, 1 caudally directed, and one with a simple length threshold), 2 sets of caudally directed long association fibers, 1 set of rostrally directed long association fibers, 4 sets of commissural and subcortical fibers (2 commissural through the splenium and through the body of the corpus callosum, 1 passing through the cerebral peduncles, and 1 terminating in the thalamus), and 2 sets of striatal fibers (putamen and caudate nucleus), and 1 set of fibers projecting through the anterior corona radiata. For case #21 (V4), 12 sets of fibers were extracted: 4 sets of rostrally directed long association fibers (ending in the occipital gyrus, angular gyrus, inferior temporal gyrus, and middle temporal gyrus), 2 sets of caudally directed long association fibers (occipital gyrus and lingual gyrus), 1 set of commissural fibers (through the body of the corpus callosum), 3 sets of striatal fibers (1 terminating in the caudate nucleus, 1 in the putamen, and 1 in the claustrum), and 1 set of fibers projecting through the extreme capsule.

Compliance with Ethical Standards

The data collected here was collected as part of a prior study in which all procedures followed the Guide for the Care and Use of Laboratory Animals and were approved by the National Institute of Mental Health Animal Care and Use Committee. The authors have no potential conflicts of interest to declare. written and pictured in [START_REF] Schmahmann | Fiber pathways of the brain[END_REF]. Injection region (blue), inclusion ROIs (green), exclusion ROIs (red), and streamlines (yellow tubes) are visualized in 2D, with green and red arrows used to highlight hard-to-see inclusion and exclusion regions, respectively, that are either in a plane perpendicular or oblique to the image slice, or those partially obscured by streamlines. Detailed anatomical descriptions and decisions used in the dissection process are given in Materials and Methods.

Figures and Tables

Figure 3.

Example procedures and constraints for template-based virtual dissection. Bundles, pathways, or groups of streamlines were individually segmented based on a priori anatomical knowledge written and pictured in [START_REF] Schmahmann | Fiber pathways of the brain[END_REF]. Examples are shown for PCG injections for striatal and commissural pathways. ROIs are shown as colored volume renderings, and streamlines are colored based on directionality. Red arrows highlight apparent false positive streamlines that are removed through the use of exclusion regions, and white arrows emphasize the dense cord of the bundle matching anatomical descriptions. Detailed anatomical descriptions and decisions used in the dissection process are given in Materials and Methods. Briefly, for striatal streamlines, the original streamlines (A) are limited to those connecting to the PT (B), which pass through the CR (C) but still have false positives. These false positives pass through FX, TH, AM (D), and are eliminated using these as exclusion regions (E), resulting in the final Striatal bundle (F). The commissural streamlines pass through the BCC (G), however many false positives are apparent (H). Using a number of exclusion regions (I) eliminates erroneous streamlines (J) resulting in commissural streamlines trajectory agrees well with written descriptions (K).

Figure

  Figure 1. Definition of ground truth and analysis. (A) Tracer substance delineated on individual slices (reproduced from[START_REF] Schmahmann | Fiber pathways of the brain[END_REF]). For the PCG injection (Case #28) tracer was described and detailed on 14 slices. (B) Example MRI b0 slice from approximately similar location. (C) Tracers were transposed to MRI data, as described in[START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF], and digitized as binary "ground truth" volume of pathways. (D) Gray and white matter ROIs were manually delineated on the high-resolution data in order to assess agreement between tracer and tractography results.

1 .

 1 Figure 1. Definition of ground truth and analysis. (A) Tracer substance delineated on individual slices (reproduced from[START_REF] Schmahmann | Fiber pathways of the brain[END_REF]). For the PCG injection (Case #28) tracer was described and detailed on 14 slices. (B) Example MRI b0 slice from approximately similar location. (C) Tracers were transposed to MRI data, as described in[START_REF] Thomas | Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited[END_REF], and digitized as binary "ground truth" volume of pathways. (D) Gray and white matter ROIs were manually delineated on the high-resolution data in order to assess agreement between tracer and tractography results.

Figure 2 .

 2 Figure 2. Example procedures and constraints for manual dissection. Bundles, pathways, or groups of streamlines were individually segmented based on a priori anatomical knowledge

Figure 4 .

 4 Figure 4. Qualitative comparison of tracer and tractography for PCG injection. Tracer digitized on the reference atlas from [56], are shown alongside the anatomically matched b0 slice with streamlines shown in black (only streamlines within +/-1 slice are displayed) for both the manualbased dissection and the template-based dissection.

Figure 5 .

 5 Figure 5. Qualitative comparison of tracer and tractography for V4 injection. Tracer digitized on the reference atlas from [56], are shown alongside the anatomically matched b0 slice with streamlines shown in black (only streamlines within +/-1 slice are displayed) for both the manualbased dissection and the template-based dissection.

Figure 6 .

 6 Figure 6. Sensitivity and specificity results compared to previous tractography validation studies. Results of the current study are shown as a filled-star for manual-dissection and outline-start for template-based dissection, overlaid on plots and results from Thomas et al [19], and Schilling et al [20] (left column and right column, respectively), which utilize the same data, same ground truth, and same quantitative analysis. ROC curves for PCG connections are shown on top row, with V4 ROC curves shown on bottom row.

Acknowledgments

This work was supported by the National Institutes of Health under award numbers R01EB017230, and T32EB001628, and in part by ViSE/VICTR VR3029 and the National Center for Research Resources, Grant UL1 RR024975-01. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.

Supplementary Data

Data has previously been made available through an international challenge, described at (https://my.vanderbilt.edu/votem/registration-and-data-access/). Data will also be uploaded to NITRC (link provided upon revision), along with ground truth and evaluation code.


B Sung

H H Wensink

E Grelet

DEPLETION-DRIVEN MORPHOLOGICAL TRANSITIONS IN HEXAGONAL CRYSTALLITES OF VIRUS RODS

The assembly of nanometer-sized building blocks into complex morphologies is not only of fundamental interest but also plays a key role in material science and nanotechnology. We show that the shape of self-assembled superstructures formed by rod-shaped viruses can be controlled by tuning the attraction via the depletion interaction between the rods. Using non-adsorbing polymers as a depleting agent, we demonstrate that a hierarchical unidimensional selforganization into crystalline clusters emerges progressively upon increasing depletion attraction and enhanced growth kinetics. We observe a polymorphic change proceeding from twodimensional (2D) crystalline monolayers at weak depletion to one-dimensional (1D) columnar fibers at strong depletion, via the formation of smectic fibrils at intermediate depletion strength. A simple theory for reversible polymerization enables us to determine the typical bond energy between monomeric units making up the smectic fibrils. We also demonstrate that gentle flowassistance can be used to template filament-like structures into highly aligned supported films.

Our results showcase a generic bottom-up approach for tuning the morphology of crystalline superstructures through modification of the interaction between non-spherical building blocks. This provides a convenient pathway for controlling self-organization, dimensionality and structure-formation of anisotropic nanoparticles for use in nanotechnology and functional materials.

Introduction

The ability to control the shape and symmetry of structures formed through self-assembly processes is of fundamental importance in fabricating highly-ordered nano-and micro-structures (1) [START_REF] Grzybowski | Self-assembly: from crystals to cells[END_REF]. The large diversity of morphologies emerging from such superstructures finds applications in photonics (3) (4) [START_REF] Wang | Self-assembled colloidal superparticles from nanorods[END_REF], electronics [START_REF]Chemical self-assembly for electronic applications[END_REF] [START_REF] Parviz | Using self-assembly for the fabrication of nano-scale electronic and photonic devices[END_REF], sustainable energy (8) (9) [START_REF] Lee | Virus-based piezoelectric energy generation[END_REF], drug delivery [START_REF] Lasic | Polymorphism of lipids, nucleic acids, and their interactions. Self-Assembling Complexes for Gene Delivery[END_REF] [START_REF] Drummond | Surfactant self-assembly objects as novel drug delivery vehicles[END_REF] and bioengineering [START_REF] Sanchez | Biomimetism and bioinspiration as tools for the design of innovative materials and systems[END_REF] [START_REF] Merzlyak | Genetically engineered nanofiber-like viruses for tissue regenerating materials[END_REF]. Finding ways to guide nanoparticle self-assembly into mono-and multi-layer structures, bundles, tubes, spherical or polyhedral shells, and more complex geometries has been one of the most pursued research themes in nanoscience. One of the main driving forces for studying controlled nanoparticle self-assembly is the many applications in nanotechnology ranging from tunable optical properties [START_REF] Zhang | Self-assembly of photonic crystals from polymer colloids[END_REF] [START_REF] Li | Pyrite nanocrystals: shape-controlled synthesis and tunable optical properties via reversible selfassembly[END_REF], anisotropic electron transport [START_REF] Saunders | Columnar self-assembly of colloidal nanodisks[END_REF] [START_REF]Hierarchical self-assembly of metal nanostructures on diblock copolymer scaffolds[END_REF], to functional surface topography [START_REF] Lin | Self-directed self-assembly of nanoparticle/copolymer mixtures[END_REF] [START_REF] Fang | Gold mesostructures with tailored surface topography and their self-assembly arrays for surfaceenhanced raman spectroscopy[END_REF]. Among such complex architectures, unidimensional (1D) fibers and bidimensional (2D) superlattices composed of rod-shaped building blocks are of particular interest in view of their intrinsic anisotropic properties. For example, fibers of 1D aligned carbon nanotubes, obtained from various spinning techniques, exhibit high mechanical stiffness and outstanding electrical performance [START_REF] Koziol | High-performance carbon nanotube fiber[END_REF] [START_REF] Dalton | Super-tough carbon-nanotube fibres[END_REF] (23).

Moreover, 2D long-ranged crystalline monolayers of inorganic nanorods can be used for generating surface plasmonics or piezoelectricity, or for creating photonic crystals (24) (25) (26) [START_REF] Liang | Symmetry control of nanorod superlattice driven by a governing force[END_REF].

Contrary to spherical nanoparticles, reports on controlled self-assembly of rod-shaped particles are scarce, and no clear indications of polymorphisms in their self-assembled structures have been adequately demonstrated so far. In view of this, we address the following two questions. First, what variety of ordered anisotropic superstructures can be expected if we were able to systematically tune the interparticle forces in a colloidal suspension of rods? And more specifically, is it possible to define a pathway enabling us to control the shape of these selfassembled objects from predominantly unidimensional (fiber-like) to bidimensional (disk-shaped) without compromising their long-range crystalline order? For this purpose, the depletion interaction [START_REF] Asakura | Interaction between particles suspended in solutions of macromolecules[END_REF] appears to be a suitable and versatile mechanism for controlling particle interaction, as the range and strength of depletion interaction are determined by the polymer size and concentration, respectively [START_REF] Lekkerkerker | Colloids and the Depletion Interaction[END_REF]. We will show that introducing tunable depletion interactions with a suitable range indeed leads to a high degree of controlled self-assembly generating a wide variety of crystallite morphologies without the need to use microscale confinements [START_REF] Zhang | Controllable synthesis and self-assembly of PbCO3 nanorods in shape-dependent nonionic w/o microemulsions[END_REF] or interfacial effects [START_REF] Lee | Phage-based structural color sensors and their pattern recognition sensing system[END_REF] [START_REF] Xie | Self-assembly of gold nanorods into symmetric superlattices directed by OH-terminated hexa(ethylene glycol) alkanethiol[END_REF].

It is well known that adding non-adsorbing polymers to colloidal suspension provides an efficient method to induce effective particle-particle attraction that can direct hierarchical organization processes [START_REF] Hata | Macromolecular crowding for materials-directed controlled self-assembly[END_REF] [START_REF] Zhao | Directing colloidal self-assembly through roughness-controlled depletion attractions[END_REF] (35) [START_REF] Young | Assembly of reconfigurable one-dimensional colloidal superlattices due to a synergy of fundamental nanoscale forces[END_REF] [START_REF] Gibaud | Reconfigurable self-assembly through chiral control of interfacial tension[END_REF] [START_REF] Adams | Phase Behavior of Mixtures of Rods (Tobacco Mosaic Virus) and Spheres (Polyethylene Oxide, Bovine Serum Albumin)[END_REF] [START_REF] Saikia | Curvature instability of chiral colloidal membranes on crystallization[END_REF]. Experimental and theoretical studies on model systems of rod-like particles such as fd viruses have established that the experimental conditions are such that the formation of partially-ordered structures, such as nematic tactoids, membranes and their stacks, as well as twisted ribbons [START_REF] Gibaud | Reconfigurable self-assembly through chiral control of interfacial tension[END_REF] [START_REF] Yang | Self-assembly of 2D membranes from mixtures of hard rods and depleting polymers[END_REF] are strongly favored. These depletion-driven self-assembled morphologies have been obtained using high molecular-weight depletants such as Dextran (molecular weight, Mw = 500,000 g/mol; radius of gyration, Rg ~21 nm), whose size is larger than the particle diameter. This results in the virus rods self-assembling into super-structures with predominant liquid-like or short-ranged positional order in at least two spatial directions (37) (40) (41) [START_REF] Gibaud | Filamentous phages as building blocks for reconfigurable and hierarchical self-assembly[END_REF]. However, in order to fully benefit from the morphology effect in terms of enhanced anisotropic properties of the resulting materials, highly ordered structures with crystalline, i.e. long-ranged positional order are required (4) (5) [START_REF] Lee | Virus-based piezoelectric energy generation[END_REF].

In order to promote dense self-assembled structures with crystalline order short-ranged depletion attractions are required favoring small inter-rod distances, s. This effect can be achieved using a non-adsorbing polymer of small molecular weight (PEG, Mw = 8,000 g/mol; Rg ~4 nm) added to a suspension of fd virus. The key-point here is that corresponding polymer coil has about the same size as the virus diameter, 2.Rg ~ d =7 nm. Taking advantage of the micrometer length of fd virus we are able to analyze the structures formed by these filamentous rods at the single particle scale using fluorescence optical microscopy [START_REF] Saikia | Curvature instability of chiral colloidal membranes on crystallization[END_REF] [START_REF] Sung | Chirality-controlled crystallization via screw dislocations[END_REF]. We then investigate the detailed morphology of the virus-based superstructures upon varying both the depletion strength (polymer concentration) and rod volume fraction, while keeping the polymer size fixed thus ensuring the rod-rod interactions to be short-ranged.

Results and discussion

The experimental results are presented in Figure 1. Here, we demonstrate that subtle morphological changes occur in a hierarchical way upon increasing the depletion strength. At low polymer concentration, when the depletion attraction is weak, the rods tend to aggregate side-byside (44) thus minimizing their excluded volume. This results in the formation of 2D plate-shaped crystallites. These platelets have well-developed hexagonal facets (Figure 1a) and are composed of a single layer of hexagonally packed aligned viral rods with a protruding needle-like defect located at the core [START_REF] Sung | Chirality-controlled crystallization via screw dislocations[END_REF]. The core-defect acts as a steric deterrent preventing the platelets to stack on top of each other.

Enhancing the depletion attraction causes an increase in the density number  0 of plateshaped nuclei and a simultaneous decrease of the platelet diameter (D=1-2 μm) as well as a length reduction of the central core defect (Figures 1b andS2). This results in a decrease of the average platelet diameter D with increasing the depletion strength (Figure S3), since  0 1/D 2 as dictated by particle mass conservation. Upon increasing the depletion strength, the self-assembly process speeds up considerably resulting in much shorter typical growth times. Pushing the depletion strength even further we observe a high population of small platelets (of about D~1 μm). Without a detectable central defect preventing their clustering, the small platelets begin to stack up and finally self-assemble into smectic fibrils in which each layer represents a small hexagonal platelet with a width of about one rod length (Figure 1c). This quasi-1D morphology referring to the overall resulting shape of the self-assembly can be interpreted as the result of fast-growing hexagonal platelets reversible polymerizing into smectic filaments. Clearly, the effective depletion attraction acting between platelets promotes face-to-face stacking in order to maximize the free volume available to the polymer [START_REF] Lekkerkerker | Colloids and the Depletion Interaction[END_REF]. In order to estimate the typical bond energy between monomeric platelets making up a smectic fibril, we invoke a simple reversible polymerization model described in the Supporting Information. This theory assumes the smectic fibrils to operate in thermodynamic equilibrium in which case the fibril height distribution can be determined analytically and compared to experimental results depicted in Fig S4a . From the fits (see Supporting Information) we estimate a typical bonding energy between monomeric platelets of about 10 kBT and a typical 'bonding volume' of effective range of attraction of about 8-10 times the polymer volume. The 'bonding volume' which can be interpreted as the bonding range times the platelet area is considerably less than the volume ~ R 2 .Rg with R the radius of a flat plate one would naively obtain from free-volume theory [START_REF] Lekkerkerker | Colloids and the Depletion Interaction[END_REF] if the face-to-face bonding was entirely due to ideal depletion attractions. Complicating factors such as thermal corrugation of the plate surface (due to fluctuations of the rods around their centers of mass), electrostatic interactions and semiflexibility of the filamentous virus rods may account for the strongly reduced bond energy but these effects are notoriously difficult to capture within a simple, tractable model. At the highest depletion attraction the growth kinetics speeds up dramatically resulting in the rods self-assembling into columnar bundles (Figure 1d). In these structures, there is no layered organization along the main axis of the fiber but the hexagonal crystalline structure transverse to the bundle director n is preserved. The time required for the self-assembly processes, or growth time, is reduced dramatically when the growth morphology changes from the predominantly bidimensional platelets to the unidimensional fibers and bundles.

Throughout the range of cluster morphologies observed, the typical growth time varies by more than six orders of magnitude, taking up days for large platelets to form, a few minutes for the smectic fibrils, down to milliseconds for the fast formation of columnar fibers. Apart from the intrinsic rod-rod attraction, kinetics play an important role in templating the self-assembled structures obtained. In view of the ultrafast growth process, we expect the formation of columnar bundles to be strongly marked by non-equilibrium effects, as columnar structures composed of long rods usually do not emerge from thermodynamic considerations (32) [START_REF] Grelet | From soft to hard rod behavior in liquid crystalline suspensions of sterically stabilized colloidal filamentous particles[END_REF]. In all the observed superstructures, the orientation of the rods (n) remains parallel to the main axis of the crystallite, as evidenced from the presence of a small fraction of virus rods labelled with a red fluorescent dye (Figure 1) and using a full-wavelength retardation plate (Figure S1). The absence of any detectable particle self-diffusion within the clusters (Movies S1 to S5) is consistent with the long-range positional order along the direction normal to n observed by small-angle X-ray scattering (SAXS) experiments (Figure 2). The SAXS experiments have been conducted at a fixed rod concentration but at varying polymer concentration and depletion strength. All SAXS spectra (Figure 2a) display (100) and

(110) diffraction peaks, characteristic of local hexagonal rod packing. The interaxial distance between the neighboring rods can be directly obtained from the position of the main diffraction reflection. There is only little variation of the distance s (Figure 2b) accompanying the vast morphological changes observed throughout the same range of conditions.

Since the interaxial rod distance s probed by SAXS is about two orders of magnitude smaller compared to the rod length ℓ, a 2D swelling law (q100 = .Crod 1/2 ) of the hexagonal lattice is expected, with [START_REF] Grelet | From soft to hard rod behavior in liquid crystalline suspensions of sterically stabilized colloidal filamentous particles[END_REF]. From this, the local rod concentration associated with the various self-assembled morphologies can be deduced. This gives a value of around 300 mg/mL for the platelets, 350-400 mg/mL for the smectic fibrils, and 450-550 mg/mL for the columnar bundles (Figure 2a).

The depletion interaction between the virus rods can be accounted for by invoking a polymer-generated osmotic pressure Π acting on the virus arrays. Here, one simply assumes that most of the polymer is excluded from the virus-based superstructures [START_REF] Gibaud | Direct Liquid to Crystal Transition in a Quasi-Two-Dimensional Colloidal Membrane[END_REF]. Such models, described in the Supporting Information, have been successfully applied to many charged rodlike particles (46) [START_REF] Stanley | Measuring osmotic pressure of poly(ethylene glycol) solutions by sedimentation equilibrium ultracentrifugation[END_REF], and give an accurate description of the experimental data as shown in Figure 2b. Figure 3 displays the crossover from one self-assembled superstructure to another in terms of the aspect ratio AR=h/D of the typical cluster morphology, with h and D indicating the height and diameter of the superstructure measured parallel and perpendicular to the rod director n, respectively. Throughout the range of attractions, the diameter decreases from 20-30 μm for the platelets while reaching a minimum of around 0.9 μm for the smectic fibers and columnar bundles (Supporting Information, Figures S3 andS4). The height increases from one rod-length for single platelets to 10-20 μm for smectic fibers and columnar bundles (Supporting Information, Figures S3 andS4). Consequently, the aspect ratio AR of the cluster morphology varies by almost three orders of magnitude throughout the probed range of depletion strengths. This demonstrates a high degree of shape-tunability of the self-assembled clusters, while guaranteeing the long-ranged positional order within the structures as demonstrated by the SAXS experiments. orientational order parameter, S=<2.cos 2 ()-1>=0.91, can be obtained after numerical integration.

Films of highly aligned smectic fibers can be obtained upon applying weak shear flow, as

shown in Figures 4a. The degree of alignment can be established from a 2D nematic order parameter S=<2.cos 2 ()-1> that we can extract from the orientational distribution of smectic fibrils (Figure 4c). Typical values we found are of about S=0.90 (note that S=1 indicates perfect alignment, and S=0 complete orientational disorder). This shows that these self-assembled superstructures are strongly susceptible to external orientation stimuli and can be readily shaped into macroscopically aligned domains. The facile processability of these rod-based superstructures opens perspectives for applications requiring anisotropic stimuli-responsive materials with internal crystalline order (9) (10) (14) (29) [START_REF] Reynolds | Competition between crystal and fibril formation in molecular mutations of amyloidogenic peptides[END_REF].

Conclusion

In conclusion, we have described a tunable self-assembly process of rod-like particles forming superstructures with an unprecedented control of their cluster morphology, effective dimension and internal microstructure. In our system of filamentous fd virus rods mixed with PEG polymer, controlled self-assembly is achieved through the use of tunable short-ranged depletion interactions between the rods generated by the presence of non-adsorbing polymer with typical size comparable to the rod diameter. A systematic increase in the polymer concentration causes a number of morphological transitions affecting the principal dimensionality of the selfassembled structure. These range from isolated quasi-bidimensional platelets and stacked oligomeric platelets at weak depletion to unidimensional polymeric smectic fibrils, and columnar fibers at strong depletion. These polymorphological changes occur without compromising the long-ranged hexagonal crystal order within the superstructures. The average inter-rod distance is only weakly affected by the depletion strength. Simple thermodynamic considerations enable us to predict the typical fibril length and infer the typical bond energy between monomeric platelets within these structures. Last but not least, we have demonstrated the possibility of flow-assisted templating of such anisotropic superstructures into highly aligned supported films demonstrating a high degree of processability. By expanding the spectrum of bottom-up approaches towards anisotropic nanoparticles we argue that depletion-driven rod suspensions displaying hierarchically-tunable morphogenesis constitute a promising candidate for fabricating selfassembled structures for use in devices depending on anisotropic stimuli-responsive materials.

Materials and Methods

Virus stock suspensions

Wild-type fd bacteriophages were grown with ER2738 strain of E. coli as host bacteria, and were purified according to standard protocols [START_REF] Sambrook | Molecular Cloning: A Laboratory Manual[END_REF]. The fd-wt (wild type) viruses are rod-like particles, monodisperse in size and shape, with contour length ℓ = 880 nm and diameter d = 7 nm. In suspension, the virus rods have been shown to behave as near-hard rods exhibiting a well-defined liquid-crystalline phase behavior (41) (39) (40) [START_REF] Grelet | From soft to hard rod behavior in liquid crystalline suspensions of sterically stabilized colloidal filamentous particles[END_REF]. Virus suspensions were extensively dialyzed against TRIS-NaCl-HCl buffer (pH 8.2) at 110 mM of ionic strength, to ensure the electrostatic repulsion between viral particles is strongly screened (Debye screening length, λD = 0.9 nm). The rods were subsequently concentrated using ultracentrifugation and redispersed at 30-35 mg/mL in the same buffer solution. The virus concentration was determined using spectrophotometry at the peak absorption wavelength of 269 nm with an optical density of 3.84 cm 2 /mg [START_REF] Barry | A model liquid crystalline system based on rodlike viruses with variable chirality and persistence length[END_REF].

Fluorescently-labeled virus batches were separately prepared by conjugating Alexa Fluor 488-TFP ester (Invitrogen) or Dylight550-NHS ester (ThermoFischer) to their coat proteins. These labeled viruses were added in tracer amounts (0.001% (w/w) to 0.1% (w/w)) to the non-labeled virus batches for tracking by fluorescence microscopy.

Sample preparation

Polyethylene glycol (PEG) of Mw = 8,000 g/mol (Sigma-Aldrich) was used as a non-absorbing polymer with a radius of gyration (Rg) of 4 nm in aqueous solution [START_REF] Devanand | Asymptotic behavior and long-range interactions in aqueous solutions of poly(ethylene oxide)[END_REF]. All polymer-virus mixtures were prepared in TRIS-NaCl-HCl buffer (pH 8.2) adjusted at 110 mM of ionic strength, and injected into optical microscopy cells. The cells were made by a glass slide and a coverslip (initially cleaned with sulfochromic acid) separated by a Mylar or Parafilm spacer, to obtain a cell thickness of about 100 μm. The cells were then sealed with UV-cured glue (NOA81, Epotecny).

For the film of aligned smectic fibers, the samples were either prepared by drop casting on a cover slip, or loaded and oriented in the cell through capillary forces. Samples for small-angle Xray scattering (SAXS) experiments were prepared in cylindrical quartz capillaries (diameter ~1.5 mm; Mark-Röhrchen), filled with aqueous virus-polymer mixtures (~20 µl for each), and sealed by flame. The capillaries were positioned vertically (gravity along the main axis of a capillary) for about 4 weeks in order to induce macroscopic phase separation through sedimentation of the selfassembled structures at the capillary bottom.

Optical microscopy

Differential interference contrast (DIC) and epifluorescence images were obtained using an inverted microscope (IX71, Olympus) equipped with an oil-immersion objective (NA 1.4, ×100

Figure 1 .

 1 Figure 1. Overview of morphological and dimensional changes in self-assembled structures formed by rod-like fd viruses driven by increasing depletion attraction. The kinetic processes determining the typical growth time for the various structures speeds up considerably with increasing inter-rod attraction. The self-assembled morphology changes from (a) hexagonal platelets composed of a one-rod thick monolayer of aligned fd rods with a central core defect (indicated by a white arrow), (b) small hexagonal platelets and their stacks. When the attraction increases further, the rods self-assemble into (c) smectic fibrils composed of small polymerized platelet monomers, and then to (d) columnar fibers. The fluorescently labeled viruses in the DIC/fluorescence overlaid images show that the rods are aligned parallel to the main axis n of the cluster (black double arrow). Scale bars, 5 µm for (a) and 1 µm for (b-d).(e) Phase diagram as a function of the rod (Cfd-wt) and polymer (CPEG) concentrations, where the typical growth time is also indicated. At each phase boundary, a gradual change of morphology occurs rather than a sharp transition.

Figure 2 .

 2 Figure 2. SAXS data of the different virus-based self-assembled superstructures obtained by varying the concentration of PEG depletant (CPEG). The initial virus concentration is set at 10 mg/mL. (a) SAXS spectra characteristic of hexagonal long-ranged positional order with the presence of sharp 100 and 110 Bragg reflections. The virus concentration within the self-assembled clusters, referred to as the local concentration, is calculated from the 2D swelling law associated with a hexagonal ordering of long rods (46) for a given (100) peak position. (b) Osmotic pressure (Π) obtained from the PEG concentration (47) as a function of inter-rod distance, s . The fit (black curve) is based on the model of Yasar et al. (48) described in the Supporting Information.

Figure 3 .

 3 Figure 3. Morphological transition from 2D to 1D self-assembled structures observed by enhancing the inter-rod attraction, in turn controlled by the strength of the depletion interaction. The cluster aspect ratio AR, defined as the dimension parallel to n (h; height) over the dimension perpendicular to n (D; diameter) where n denotes the main axis of the cluster morphology, is plotted (black and white squares) as a function of the depletant concentration. Experimentally, the largest measurable length is around 20 µm (the corresponding aspect ratio is indicated by a dotted line), since longer fibrils no longer lie within the same focal plan. The red triangular symbols represent the theoretical predictions from a simple reversible polymerization theory describing the formation of smectic fibrils (see Supporting Information), and they show a good quantitative agreement with experimental data. The typical bond energy between monomeric platelets within the smectic fibrils is estimated to be about 10 kBT.

Figure 4 .

 4 Figure 4. Flow assisted alignment of smectic fibrils deposited on a glass substrate. (a) DIC image of the smectic fibrils, whose main axes (n) are along the flow direction. Scale bar, 10 µm. (b) Fourier transform pattern of the DIC image in (a), with the one-rod-thick smectic layer spacing indicated. (c) Distribution of smectic fibril orientations fitted by a Gaussian function (red line), from which the 2D

Acknowledgments: This work was supported by the French National Research Agency (ANR) through the project AURORE. We thank J. Perez from the SWING beamline for his kind assistance.

UPLSAPO), a mercury-halide excitation source (X-cite120Q, Excelitas), and a fluorescence imaging camera (NEO sCMOS, Andor Technology). To enable simultaneous acquisition of DIC and fluorescence images, an optical splitter setup (Optosplit II, Cairn Research) was used to divide each image into two channels thanks to a dichroic beamsplitter and band pass filters. The images obtained from both channels were then overlaid. The whole imaging system was operated by computer-interface software (Meta-Morph, Molecular Devices).

Small angle X-ray scattering (SAXS)

SAXS measurements were performed at the SWING beamline at the synchrotron facility SOLEIL (Orsay, France) operating at a source wavelength of λ = 0.0995 nm. The diffraction pattern was recorded by an AVIEX CCD detector, which was located in a vacuum detection tunnel with a sample-to-detector distance of 1.49 m. Angular integration was applied on the 2D SAXS pattern to obtain the scattering intensity as a function of scattering vector modulus, q.

Conflicts of interests:

There are no conflicts to declare.

Corresponding author: eric.grelet@crpp.cnrs.fr