Biophysical network models and the human connectome
Introduction
The Human Connectome Project (HCP) is collecting a wealth of state-of-the-art data across a range of imaging modalities; in particular, functional MRI, magnetoencephalography (MEG) and diffusion MRI (Van Essen et al., 2012). Arguably, each of these modalities could be used to obtain a different connectome (Behrens and Sporns, 2012, Friston, 2011). For example, FMRI can provide us with a map of functional/effective connectivity (Biswal et al., 1995, Friston, 2011), and diffusion MRI with a map of anatomical white matter connectivity (Basser et al., 1994, Basser et al., 2000, Behrens et al., 2007). But it is not immediately clear how these different modalities can be related. Or indeed, what governing principles we should use to resolve differences among these connectomes.
A useful unifying principle is that the anatomical connectome underlies (is necessary for) the functional connectome. This idea has previously been expressed in terms of the concept of “connectional fingerprints” (Passingham et al., 2002), which postulates that the functional profile of any given cortical area depends on the structural pattern of its incoming and outgoing connections. More recently, it has been demonstrated that models of effective connectivity are improved when formally integrating quantitative anatomical information (Stephan et al., 2009b). This is not to say that structural connectivity is a sufficient or complete description of connectivity, but rather that function depends on structural connectivity. Armed with this perspective, we can start to consider how we might characterise the architecture of a multi-modal human connectome.
Firstly, diffusion MRI data is not a panacea even for inferring vanilla anatomical connectivity — it has blind spots. Comparison with invasive studies in non-human primates reveal that current tractography approaches can suffer from both false positive and false negative results (Behrens and Sporns, 2012). Functional connectomics can help inform the anatomical connectome when structural information is missing, or is inaccurate. Arguably, the best way to do this is through network models; because these can embody both the structural and functional architecture, and allow information from the different modalities to be fused in a mathematically principled way.
We also want to go be able to go beyond the characterization of the anatomical connectome, to understand the brain function that rests upon it. Patterns of functional network connectivity emerge as the result of neuronal interactions taking place on this anatomical skeleton (Deco et al., 2011, Honey et al., 2007). The best way we can understand these patterns is by using biophysical network models that combine models of the anatomy with dynamic models of neuronal interactions. In principle, if we had sufficient knowledge of the system, including information at the level of synapses, we could predict context sensitive coupling or the dynamics one might expect to see, i.e. how functional pathways are modulated depending on task or cognitive set. This requires biophysical models that can be informed by experimentally controlled context, and can represent connection strengths as a function of activity (non-linear postsynaptic effects) or time (synaptic plasticity).
FMRI has a key role to play, and has already been successful in mapping functional networks, for example, using resting state data (Beckmann et al., 2005). However, evidence from MEG suggests that these network interactions are likely underpinned by oscillatory activity in particular frequency bands (Brookes et al., 2011a, Hipp et al., 2012). Understanding these oscillations and the biophysical models that underpin them will provide unique and important insights into the function of the brain. For example, one possibility is that long-range connectivity may be mediated by synchronisation of oscillatory activity (Fries, 2005). To illuminate these models, direct measures of neural activity at high temporal resolution are needed, such as can provided by the increasingly relevant modality of MEG.
Eventually, the understanding we can gain about the physiology of network dynamics can be used to elucidate the mechanisms of aging and disease in a clinical setting. Through approaches like generative embedding (Brodersen et al., 2011), we can investigate disease mechanisms; e.g. by looking at the population variability in certain biophysical model parameters. By moving closer to the actual mechanisms of brain function, this approach should ultimately be more sensitive and more interpretable than descriptive or normative approaches.
This paper will focus primarily on systems-level biophysical network models of non-invasive neuroimaging data at the macroscopic, whole brain, system level. There is a particular focus on biophysical network models of function. However, we will also consider models of anatomical connectivity, particularly with regards to informing models of network dynamics using the anatomical connectome.
Section snippets
Functional biophysical network models
In recent years there has been a noticeable move away from the spatial mapping of task related activity towards inferring brain connectivity. This is motivated by the idea that connectivity brings us closer to the distributed mechanisms of brain function.
A popular approach to looking at connectivity in functional data has been to look at measures of statistical dependency, otherwise known as functional connectivity. This includes approaches such as partial or full correlation (Smith et al., 2011
Biophysical functional network models
Here, we consider a biophysical functional network model as a mathematical description of how we can generate measurements of brain activity (e.g. using MRI). This modelling assumes that we know the underlying dynamic interactions between, and within, different brain areas; and the stochastic or deterministic properties of the exogenous or endogenous fluctuations that drive the network. As such “biophysics” includes the neurophysiology of the brain, and the physics of the measurement device.
We
Choosing the parcellation
A core goal of the HCP – to describe the connections between different brain areas – requires the specification of a set of brain areas between which to characterise the connectivity. This raises the question as to what makes for an appropriate parcellation for a given model and modality (or modalities). While this is a topic for other articles in this special issue, we consider here some of the key issues in the context of generative network modelling.
Estimation/inference on biophysical models
Biophysical models are typically used in one of two modes:
- 1)
To predict emergent spatiotemporal characteristics observed in neuroimaging data.
- 2)
As generative models that are inverted using (fitted to) neuroimaging data.
Although the boundaries between these two options can often get blurred, we will discuss them in turn.
What can we do with biophysical network models?
Since they are generative models (see above), a general trait of biophysical network models is their ability to allow for inference on hidden variables. So far, we have mainly referred to inference on the hidden parameters describing the effective connectivity between brain areas. However, this idea extends to other hidden variables; for example, those relating to network nodes for which we have little, or no, sensitivity in our measurements. In other words, even when we are not able to measure
Summary
We have considered the key role that biophysical functional network modelling has to play in characterising the human connectome using multi-modal non-invasive neuroimaging data. Furthermore, network models provide the means by which we can understand the relationship between structural and functional connections; and can provide us with more sensitive and interpretable parameters — through which we can better understand normal and diseased brain function. The suggestion here is that there is
Acknowledgments
The authors would like to thank Prof. Karl Friston for his extensive and invaluable comments on the paper, and also thank Faysal Kahn for useful discussions. MWW is funded by the Wellcome Trust, and supported by the National Institute for Health Research (NIHR) Oxford Biomedical Research Centre based at Oxford University Hospitals Trust Oxford University (the views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR or the Department of Health). KES is supported
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