The identification of a human "connectome" is a bit of a Holy Grail in modern systems neuroscience. It is a relatively recent idea, whose first appearance in the literature was a 2005 paper by Sporns and colleagues entitled The Human Connectome: A Structural Description of the Human Brain. In this article, the authors presented the term "connectome" as an analogue to the human genome, 90% of which was famously mapped through a large-scale collaborative effort called the Human Genome Project. They outlined a number of steps that in their view comprise the most sensible path to attaining a working description of the human connectome; these include the use of diffusion-weighted imaging (DWI) tractography to identify structural connections, functional correlations to identify interareal associations, and comparison of these findings to more biologically sound macaque tract tracing results.
There are some fairly crucial distinctions, however, between the idea of a genome and that of a connectome. While both attempt a population-level description of the human organism, a genome is a map of very specific nucleotide sequences which can be directly measured, while for the brain connectome we still lack a precise definition both of what is being connected, and how they are connected. The question of scale is particularly important: what constitutes a brain component — single neurons? Cortical microcolumns? Macroscale regions defined by cyto- or myelinoarchitecture? Regions defined by clustering of functional or structural connectivity patterns? Similarly, what constitutes a brain connection — a single axon? Coherent groups of axons (tracts)? Correlations in functional time series? DWI tractography? Each of these definitions requires a different set of assumptions, and has different implications for how we ultimately frame the discussion of human brain connectivity.
In recent publications, I've referred to "physical" connectivity as the quantity I believe to be the ultimate goal of "connectomics" approaches. The intention here was certainly not to invent yet another flavour of connectivity estimate, but largely to avoid the confusion which comes with pre-existing terms such as "structural", "functional", or "effective" connectivity. By physical connectivity, I mean the directed long-range axonal connections which originate with an excitatory neuronal soma, and terminate in the synapse formed by an axon terminal. This quantity is more or less directly measured by tract tracing experiments in animal models, where tracer substance is injected and actively transported along axons, to be deposited and measured at the other end (notably, there are both anterograde and retrograde tracer substances available to anatomists). Tract tracing is thus a legitimate gold standard for physical connectivity, and whatever connectome we eventually derive must demonstrate agreement with this method. Frustratingly, it is an intrinsically invasive approach, and therefore completely unavailable for human research. We are confined to indirect, noninvasive approaches, of which DWI tractography has been the most lauded.
In this blog entry, I want to revisit the idea of the connectome presented in the seminal paper by Sporns and colleagues. Over a decade has passed since this article was published, and many of its suggestions have been followed in various ways, most conspicuously in the form of the Human Connectome Project. How much closer are we to understanding human brain connectivity through DWI methods? What have we discovered about their limitations? Where can we go from here?
Diffusion-weighted tractography
MRI has afforded us incredible insight into the structure and function of the living human brain, and numerous innovative acquisition protocols have been designed over the past two decades to expand the breadth of these insights. DWI is one of the most promising of these approaches, allowing researchers to quantify the degree of anisotropy in the diffusion of hydrogen atoms with relatively high spatial (0.5-2 mm) and angular (~300 directions) resolution. DWI provides the basis for estimating orientation distribution functions (ODFs) in single voxels, and these can be sequentially sampled to approximate the axonal trajectories originating in one brain region and terminating in another. Moreover, if placed in a probabilistic framework, a "connectivity" distribution can be approximated by generating thousands of such "streamline" samples. In a typical DWI study, the number of streamlines originating in a region A and terminating in a region B is assumed to reflect the strength of "structural connectivity" between them. On its face, this method appears to be an excellent noninvasive alternative to tract tracing. It is, however, subject to several systematic biases that, while they remain unaddressed, severely undermine the utility of DWI for estimating physical connectivity.
What biases? The most obvious is distance: as streamlines sample sequential ODFs, they accumulate uncertainty; i.e., their probability of following a specific trajectory diminishes, because there is always a non-zero chance of following crossing or fanning fibres, or terminating at another part of the grey matter target mask. Thus, longer connections will necessarily result in fewer streamlines than shorter ones. One simple way to address this is to make a global correction for distance. However, as shown in the figure below, even in trivial examples such a correction is problematic. In this figure, I've given a basic tractography instance (A), in which the seed region (yellow node) is connected with equal connectivity strength (i.e., number of physical axons) to three target regions (green nodes). We generate 10 streamlines and assume that only at voxels represented by the red nodes do we have submaximal anisotropy, as represented by the ODF. For each such voxel, it is 70% probable that a streamline will continue straight and 30% probable that it will take the path towards a target region [1].
The numbers beside the blue paths represent the number of streamlines that will, on average, traverse that route. Thus, in A, we find streamline counts of 3.0, 2.1, and 1.5, for the nearest to farthest target regions — demonstrating a clear distance bias. Suppose, to correct for this bias, we apply a simple linear correction:
\[ c_{ij} = l_{ij} \cdot n_{ij}/N \]
where \(n_{ij}\) is the streamline count at target region \(j\), \(l_{ij}\) is the length of the route between the seed region \(i\) and \(j\), and \(N\) is the total number of generated streamlines. This is essentially the same correction used by the most popular tractography software, FSL's ProbtrackX. For our example A, let's assume all links between nodes are equal, with length 1. Applying the correction above, we get the values shown in parentheses; i.e., each target node gets assigned a corrected value of 0.6, and the correction appears to have worked. However, suppose we mix this up a bit. In B, we have changed the link lengths such that the first and second lengths are now 0.5, and the third length is 2. Applying the same correction results in an apparent overcompensation: the first and second target regions are now assigned smaller values than the third. Suppose we consider an even more realistic case, as shown in C: instead of the second target region, we now have a large fibre crossing our main route. Let's further suppose the ODF at the crossing fibre implies that it is 50% probable that a streamline follows it instead of the original fibre. This results in a reduced average streamline count of 1.0 at the farthest target region, and the distance correction does not sufficiently account for this reduction.
Even from these toy examples, it is clear that the distance bias does not have a trivial solution, largely because it is conflated with a second bias, which we could call the anisotropy bias. The streamline count between two regions will be highly dependent on the sort of ODFs it encounters along its trajectory, and the number of ODFs grows with distance. Put simply, a tract that encounters few uncertain ODFs will produce a higher number of streamlines than one of equal physical connectivity that encounters many. A satisfactory solution to this source of bias remains a critical challenge in the field.
As if that were not enough, a third source of bias is the organization of myelin in regions bordering cortical grey matter. The apparent anisotropy in these regions is critical for determining whether a streamline exits the white matter to terminate in a target region, or continues along the tract. This implies that regions in which axons coherently enter cortical grey matter are more likely to have higher streamline counts than regions in which axonal organization is less coherent. This issue has been highlighted impressively in a recent article by Reveley and colleagues, who performed DWI tractography alongside histological myelin staining in macaque monkeys. The authors demonstrated very clearly that 50% of the cortical surface was essentially inaccessible to DWI tractography methods, because the organization of axons in adjacent white matter was highly incoherent. Despite this, there was no apparent difference in the rate at which axons entered cortical grey matter in these regions. Failing to account for this bias entails neglecting connectivity patterns for essentially half of the cortical sheet!
Comparisons with tract tracing evidence
One of the main steps outlined in the Sporns article was to perform a comparison between the indirect connectivity estimates offered by DWI tractography and the direct evidence available through tract tracing experiments. Such a comparison is essential to evaluate the validity of this indirect approach as an estimate of physical connectivity. Several such comparisons have since been performed. My colleagues and I, for instance, have recently published a multimodal connectivity comparison which included a comparison of macaque tract tracing and human DWI tractography. To compare across species, we required a mapping between two rather different cortical surfaces, and a parcellation for which assumptions about homological relationships could be made. Despite the limitations of such assumptions, we did find a modest agreement between tract tracing evidence from the CoCoMac database and DWI tractography results obtained from two separate data sets (see figure below). When correlating the two on the basis of tract tracing label density (for CoCoMac) and distance-corrected streamline count (for DWI), we found an \(r^2\) of ~0.2, and when comparing binarized versions of the same networks, we found a random-normalized accuracy of ~0.3-0.4, indicating the position on a continuum between perfect agreement and agreement expected by random chance. These values are certainly well above random, but clearly a far cry from perfect. Added to the biases outlined above, this divergence is also likely due to the clear species differences, the incompleteness of CoCoMac with respect to contralateral connections, and the definition of cortical regions, among other issues.
More direct comparisons have been also performed with macaque monkey experiments. Azadbakht and colleagues, for instance, performed high angular resolution DWI tractography on two ex vivo macaque brains, and compared the resulting connectome to the famous Felleman and Van Essen (1991) tract tracing study of the visual system. On average, they found a rather promising 74% accuracy for the best of numerous tractography approaches tested. A similar approach was taken by Thomas and colleagues, who also performed high resolution ex vivo DWI tractography on macaques, but defined ROIs directly from the injection sites described in previous tract tracing studies. Their findings were less encouraging; in their own words:
Despite the exceptional quality of the DWI data, none of the methods demonstrated high anatomical accuracy. The methods that showed the highest sensitivity showed the lowest specificity, and vice versa. Additionally, anatomical accuracy was highly dependent upon parameters of the tractography algorithm, with different optimal values for mapping different pathways. These results suggest that there is 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.
At best, it appears that we can reach a modest level of accuracy in the estimation of physical connectivity from DWI tractography, if we tailor our tractography parameters to some limited subnetwork of interest. This is rather arbitrary, and not particularly enheartening, if our aspiration is to achieve an unbiased description of the whole brain human connectome.
Abandon all hope?
Surely not. Here's where I inject a bit of optimism into my dreary critique of our collective quest for the connectome. The crippling limitations of our current DWI-based approaches don't mean that the situation is hopeless. On the contrary, the methods that have been proposed and refined, and the regular improvements to MRI technology, all suggest that we are still only in the pioneering stage of human connectivity research. The identification of biases and other limitations is a necessary step towards realizing the connectome envisaged by Sporns and colleagues. Here are some possible goals that we can move towards:
Bayesian modelling. Instead of sending streamlines out like blind scouts to evaluate the diffusion space, we can instead frame the problem to incorporate our prior knowledge of the system. If we assign a prior probability to the existence of a connection between areas A and B, our problem becomes one of estimating the posterior probability, given the diffusion evidence. Given all possible paths through white matter between A and B, which are most probable, and how confident are we about that? Such a framework can forego the necessity of accumulating uncertainty with subsequent advances of a streamline sample, because the uncertainty of a connection can be considered on the basis of more biological constraints. For example, a path which takes a detour and returns to the same point is less probable than one which avoids that detour; and a path which makes an acute turn through an area of uncertainty is less probable than one which proceeds in a straighter trajectory through it. I'm being intentionally vague here because such an approach is still vague in my mind; the point is that there are plausible alternatives to the generic streamline sampling approach.
Mechanistic models. We can estimate, from histological observations and imaging techniques such as magnetization transfer ratio (MTR), the distributions of calibre and myelination (the so-called g-ratio) of axons in the white matter. We can also image myelinated fibres at the interface with cortical grey matter, both through myelin staining and polarized light imaging (PLI). From this information, we can put mechanistic constaints on our connectivity model. There is a finite number of axons of a specific calibre that can occupy a given region of space (such as a voxel). Likewise, there is a finite number of axons that can cross a specific cross sectional area of the cortical sheet. This information places upper and lower bounds on the physical connectivity between two defined regions of cortex; thus, integrating mechanistic models with DWI information may allow us to approximate connectivity as a physical quantity.
Multimodal integration. This has been a hot topic lately, but is still very much in its infancy. The challenge here is to find ways to integrate evidence from multiple modalities — including functional activation time series from BOLD, MEG, EEG, or calcium imaging; structural information from DWI, T1- and T2-weighted images; functional manipulation through methods such as TMS, induced currents, deep brain stimulation, or (in animal models) optogenetics; and histological evidence from postmortem human or animal models. All of these independent observations, if modelled appropriately, should provide converging evidence of the underlying physical connectivity structure, as well as the functional causal relationships (information transfer) subserved by it. This integration will likely require biophysical forward modelling approaches, such as mean field modelling — here is an example.
Ultra-high-field imaging. I know of at least one ongoing attempt to use ultra-high-field (9.4T) MRI to obtain DWI images from postmortem brains, with unprecedented spatial and angular resolution — see this page. I'm sure there are more. The major advantage to this approach is that you can scan a postmortem brain for days if you want to, without having to worry about motion or respiratory artifacts. You can also fabricate custom EM coils that fit tightly to the brain under investigation. When you are finished scanning, you can follow up by sectioning the tissue and acquiring histological information such as PLI, myelin staining, or other high-resolution quantities that can subsequently be compared with your DWI data. This approach requires a good deal of time and energy (man hours, CPU time, and analysis development), and will generate vast amounts of data. Its utility for obtaining whole-brain estimates of connectivity is still subject to these practical constraints, but it is a very promising avenue for the future.
There are most certainly other promising avenues we can pursue. The take home point I want to convey (without pointing fingers) is: let's not pretend we're there yet.
- It is noteworthy that the ProbtrackX approach actually expects white matter voxels as seeds, and streamlines generated from these voxel are extended in opposite directions until both ends terminate in target regions. This is likely a more robust approach than using cortical grey matter as streamlines, although it does nothing to address the systematic biases described here.
