Moving on from the Seizure Reservoir

One of the most challenging and puzzling issues for both patients and clinicians is the apparent unpredictability of seizures. Beyond a few general statements of things that increase your chance of having a seizure, it is difficult (impossible) to pinpoint, why a seizure happens at exactly the time that it does. The issue becomes even more intriguing when there is not even a focal ‘epileptogenic’ zone – as for children with idiopathic generalised epilepsy, whose brains will look completely normal on brain scans, but will suffer apparently unprovoked seizures again and again. 

Richardson (2011)
Drawing from Richardson MP (2011) J Progr Biophys Mol Biol, 105:5-13, originally from Lennox (1941) Science and Seizures, New Light on epilepsy and Migraine. Harper Bros, NY

The relationship of all the different aetiological factors and the intermittent occurrence of seizures has been quite nicely conceptualised as a ‘Seizures Reservoir’ (Figure above) by Lennox of Lennox-Gastaut Syndrome fame. You can see that there are certain features that make the system inherently more likely to overflow (e.g. the depth of the basin, representing hereditary causes), features that add water to the reservoir, and a ‘seizure threshold’ that can increase or decrease. Yet without external variation, this model would remains static, without much in terms of internal dynamics and switches between seizure and interictal, non-seizure state. 

And here is where one of my favourite papers from last year comes in – Viktor Jirsa and colleagues [1] use seizures and seizure-like events in a variety of settings (human seizure recordings, acute mouse hippocampus slices, zebrafish larval seizures) to inform the development of a dynamic model that explains seizure onset, duration and offset in all of those settings. 

What sets their model apart from the simple (yet usefully intuitive) explanatory model above is not just the exquisitely complicated maths it is build on (who doesn’t know the difference between homoclinic and saddle-node bifurcations…). Rather, Jirsa and colleagues offer a fully generative model: ‘The Epileptor’ model not only has a name making me think of Schwarzenegger. In addition to giving an explanation of how existing data (i.e. seizure recordings) were derived, it can actually generate example data itself. The model consists of a set of 5 parameters that are linked by integral-differential equations and where changes in one parameter therefore influence the trajectories of the others. 

Jirsa et al. 2014
A) Shows a seizure generated by the epileptor (blue, left), and the trajectory of its slow ‘permittivity’ state variable (red, left). B) Shows simultaneous recordings of mouse hippocampal seizure like events (red shows NADH levels as proxy for ATP use, yellow shows partial oxygen concentration) . Jirsa (2014) Brain, 137:2210-30.
The results are quite impressive: The figure above shows both the model’s self-generated seizure, and the recorded seizure in a mouse hippocampus below. The three dimensional graphs on the right illustrate the trajectories of the composite parameters x, y and the slow permittivity variable. One of the interesting features is that there seemingly are two paths to traverse z-planes – one with many squiggles in x and y directions, and one with few squiggles (right in A, left in B). For those values of Z where the system could follow either of those two trajectories, the system is bistable – has two stable configuration of parameters that it could be pulled towards. 

The model does not only help in explaining some of the subtler and less intuitive features of seizure activity (e.g. baseline shifts), but also describes the mathematically critical parameters and their dynamics around seizure generation. And despite being able to model a surprising amount of seizure dynamic complexity, the model runs on only 5 mathematical parameters. There is huge promise in this – once we know how to deconstruct a complex, unpredictable system into 5 variables, there is a much better chance for us to actually find out what these are.

There are a few next steps to be taken from this – one is to find a robust way to determine the parameters of the model from actual empirical measurements as well as to start relating the mathematical properties to biophysical features [2-3]. But a second question pertaining to the initially highlighted issue still remains – even this powerful model requires the underlying ‘permittivity’ state variable to slowly change in order to drive a seizure. What, therefore, is this state variable? This fundamentally the same question as ‘Why does a seizure happen at the specific time that it does’.

What the mathematical modelling adds, however, is a clear idea of what kind of thing we are looking for, and to make specific predictions about what changing this parameter would cause in a system to complex for an intuitive prediction. And this is a more general point – at the current complexity of our understanding of brain dynamics, we will rely on computational models to generate meaningful hypotheses and predictions.

As for the initial questions, I don’t think we can yet move away from our general comments of things that increase seizure susceptibility, or at least in the clinic will anytime soon. But I do think this kind of work will support therapeutic approaches attempting neuromodulation to suppress seizures to become more successful in the future. It’s a field to watch, I think.  
[1] Jirsa VK et al. (2014) On the nature of seizure dynamics. Brain, 137:2210-30. DOI: 10.1093/brain/awu143
[2] Nevaado-Holgado AJ et al. (2012) Characterising the dynamics of EEG waveforms as the path through parameter space of a neural mass model: Application to epilepsy seizure evolution. NeuroImage, 59: 2374-92. DOI: 10.1016/j.neuroimage.2011.08.111
[3] Friston KJ (2014) On the modelling of seizure dynamics. Brain, 137:2110-3. DOI: 10.1093/brain/awu147