3.3
Causality on the brain
Unfortunately, in a complex system where one would expect synchronization and coop- erative behaviour, the causal relationship is very complex [52] and the understanding of cause and effect in complex system is definitely lacking [17]. To approximate ‘causality’ for complex system such as the brain, we first need to have an idea of what we seek from the data sets.
3.3.1
Causal connectivity on the brain
We seek to understand the information transfer and causal connectivity of the brain. The main reason we wanted to establish ‘causality’ in the brain is to uncover the directed con- nectivity of the brain. The kind of ‘causality’ measures we utilize depend on what kind of connectivity we wish to uncover in the brain. In neuroscience, effective connectivity is the term often used for the connectivity that aims to identify the underlying physiological influ- ences of neurons using available time series data. The effective connectivity is defined as the directed influence that a neuronal populations in one brain area exerts on another [41].
Another type of connectivity that does not necessarily require any physiological veri- fication is coined as the dynamical connectivity [17]. The dynamical connectivity is valid when a few issues are taken into account. The first one is the fact that studies have demon- strated [92] that the same physical network structure on the brain can give rise to multiple distinct connectivity depending on interactions with environment. Secondly, neural dynam- ics is said to alter underlying structural dynamics [17], for example in terms of memory and learning.
Furthermore in our current state of knowledge, knowing all the variables involved with a certain structure will be quite impossible making effective connectivity perpetually pro- visional (unless perhaps validated by intervention procedures). On the other hand, the dy- namical connectivity is a description of dynamical relations between variables regardless. It will be best if one did obtain the effective connectivity where the dynamics and structure go hand in hand and one verifies the other, however in light of the brain as a complex sys- tem, this effective connectivity will surely be ever changing. We might want to take things one step at a time and make sure we understand the dynamics first.
Chapter 3. The question of ‘causality’ 47
3.3.2
Approaches to determining neural causal connectivity
There exist different approaches to achieving causal connections in the brain. One ap- proach to modelling the brain is by utilizing the knowledge of biology and neuroscience to preemptively make the best guess of a model that will fit the brain. Afterwards data sets are fitted to verify the model, this approach is called confirmatory approach [41]. The second approach called the exploratory approach takes the opposite position of inferring the model from the data. This approach does not rely on any preconceived idea and let the data from the brain shape the directed model of the brain. This view of modelling is also taken by other fields and there is a growing general view that biology should move from hypothe- sis directed research to exploratory methods [16]. Indeed, nature has so many secrets that humans might benefit from putting assumptions aside and listening to it without attaching preconceive notions.
One can think of the different approaches as being on a spectrum from purely confirma- tory to purely exploratory. An example of a method that is often classed as being near the confirmatory end of the spectrum is the Direct Causal Model (DCM) introduced by Fris- ton [41] and the graphical model [76]. DCM incorporates explicit model of the neuronal causes and is usually used to infer effective connectivity [17]. One can say that G-causality and Transfer Entropy resides near the other end of the spectrum since both derive infer- ences directly from data and conclusions are made based on distribution of the sampled data. Henceforth we will focus more on the exploratory end.
However, G-causality is also confirmatory in sense that it assumes autoregressive pro- cess. Transfer Entropy seems more exploratory than G-causality from this point of view. Recent implementations of DCM incorporate evidences from data in model selection pro- cess thus becoming somewhat exploratory [17]. The two approaches seems to be converg- ing more and more.
3.3.3
Establishing connectivity through EEG
If one intends to pursue ‘causality’ the exploratory way, EEG or MEG data would be the preferable to the fMRI. This is due to the fact that fMRI data changes with the structural model which implies that one cannot directly compare different regions of the brain without
3.3 Causality on the brain 48 a certain amount of structural model selection [41]. What we want to do is to get an insight of the inner workings of the brain through a method which does not require direct intervention in the brain by analysing EEG data sets. Wiener being keen on causality and information theory has pointed out how EEG may be useful for this purpose when he [107] wrote:
“Or again, in the study of brain waves we may be able to obtain electroen- cephalograms more or less corresponding to electrical activity in different parts of the brain. Here the study of the coefficients of causality running both ways and of their analogs for sets of more than two functions may be useful in de- termining what part of the brain is driving what other part of the brain in its normal activity”.
The normal activity Wiener is referring to here is activity on the brain without any inter- vention of artificial stimuli which he claims might bring about artifacts.
Artifacts such as movements and eye twitches (manually removed by neuroscientist) are usually an issue when dealing with EEG data sets because it gets in the way of time relation. The bandpass filtering that often has to be done on EEG data sets is also said to be damaging to G-causality estimation [17]. In terms of the data sets we have obtained, due to the use of the best possible equipments supplied by Bj¨orn’s team, almost no artifact removal is needed and very minimal filtering is required. Therefore we are confident that we have a good set of data to test our results on.
Recall that in our data sets, EEG refers to the recording of the brain’s spontaneous electrical activity over a short period of time, as recorded from eight electrodes placed on the scalp. It has been said that although the application of ‘causality’ measures on EEG data can be extremely useful due to its sub-millisecond time resolution, it also suffers from uncertainties in source space localization [17]. However, if we are focusing on the dynamical connectivity of the brain, this is a question that we can put aside for the moment. Here we assume that each electrode detects an average voltage of its surroundings thus each electrode represents a spatially averaged electrical activity at one point on the skull. We can think of it as the collective activity of neurons in that area of the scalp.
Chapter 3. The question of ‘causality’ 49 The notion that A causes B if A in the past incites B in the present (or it’s relative
future) is what we will define as ‘causality’ in our context. And this is what we will be looking for in the brain. In terms of EEG electrodes, if a certain electrode A in the past
consistently incites a certain electrodeB in the present, then we shall say that electrode A
causes electrodeB and this then translates to the area of the scalp. The general idea is that
if electrodeA causes electrode B we would want to be able to detect it.