Modeling absence seizure dynamics: Implications for basic mechanisms and measurement of thalamocortical and corticothalamic latencies

Abstract

A successful physiologically based continuum model of the corticothalamic system is applied to determine the relative contributions of axonal and intrinsic cellular delays to the waveforms of absence seizures. The predicted period of the absence seizure depends linearly on model parameters describing thalamocortical, corticothalamic, intracortical, and synaptodendritic delays, and these dependences are linked to the seizure mechanism by showing how time intervals between peaks in the waveforms depend on the parameters. Counterintuitively, it is found that a peak in the local field potential recorded in the thalamic relay nuclei can precede the peak in the cortical field that drove it, without violating causality, but rendering naive interpretation of time intervals between peaks invalid. We argue that a thalamocortical loop mechanism for absence seizures is consistent with intrathalamic cellular properties being the leading determinant of the frequency of spike-wave discharges in rat genetic models, with the combination of network and cellular properties providing a natural explanation for the lower frequency of human absence seizures. Finally, our results imply that the seizure frequency is not determined by the fastest thalamocortical and corticothalamic fibers, but rather depends on an effective weighted conduction velocity of all pathways present.

Introduction

In this paper we use a corticothalamic model to elucidate the temporal relationships between features of the absence seizure waveform as recorded in the cortex and thalamus. This has implications for the measurement of anatomical conduction delays along thalamocortical and corticothalamic pathways, and the open question of to what extent a thalamocortical network mechanism underlies human absence seizures, as opposed to the frequency being set solely by an intrinsic cellular pacemaker.

Absence seizures are a pathology characterized by a sudden brief period of unresponsiveness, identical pre- and post-seizure states, and a periodic, approximately 3 Hz, spike-and-wave morphology observed over most of the cortex in the electroencephalogram (EEG) (Stefan and Snead, 1997). The thalamus and cortex form a feedback loop, which has been implicated in pathologies such as epileptic seizures (Williams, 1953, McCormick and Contreras, 2001, Destexhe and Sejnowski, 2001, Meeren et al., 2002, Robinson et al., 2002, Pinault, 2003, Lopes da Silva et al., 2003, Aghakhani et al., 2004, Blumenfeld, 2005, Breakspear et al., 2006), as well as the normal healthy sensory (Nowak and Bullier, 1997, Usrey, 2002, Alitto and Usrey, 2003) and motor (Marsden et al., 2000, Sirota et al., 2005) systems. This feedback loop contains two pathways: thalamocortical, along which all sensory input (excluding olfaction) is relayed to layer IV of the cortex via the relay nuclei in the thalamus (Sherman and Guillery, 1996, Steriade et al., 1997); and corticothalamic, consisting of projections primarily from layer VI of the cortex terminating on both the relay and reticular nuclei of the thalamus (Sherman and Guillery, 1996, Steriade et al., 1997), and these two nuclei are reciprocally connected. The corticothalamic axons provide the largest single input to the thalamus, but their function is still largely unknown (Sherman and Guillery, 1996).

Despite their potential importance, the delays incurred by signals propagating around the corticothalamic loop are not yet well known in humans. Animal studies suggest the existence of multiple thalamocortical and corticothalamic pathways, with spike timing and correlation studies yielding a range of thalamocortical delays from 0.1 to 5 ms and longer corticothalamic delays from 1 to 30 ms in the mouse (Salami et al., 2003, Liu et al., 2001), rat (Sawyer et al., 1994, Beierlein and Connors, 2002), rabbit (Swadlow and Weyand, 1981, Swadlow, 2003), cat (Wilson et al., 1976, Tsumoto et al., 1978, Tsumoto and Suda, 1980, Dinse and Krüger, 1994, Miller et al., 2001, Sirota et al., 2005), and macaque monkey (Schiller and Malpeli, 1978, Briggs and Usrey, 2007). Scaling the above data to human brain size (Robinson et al., 2004), one can estimate delays of roughly 10 ms for the human thalamocortical pathway, and a few tens of milliseconds for the corticothalamic pathway. However, the trends with brain size are not clear cut between species, so values derived directly from human measurements would be far superior.

The relationship between the above delays and the mechanisms of absence seizures is poorly understood, even though the delays occur in pathways implicated in seizure generation (Williams, 1953, McCormick and Contreras, 2001, Destexhe and Sejnowski, 2001, Meeren et al., 2002, Robinson et al., 2002, Pinault, 2003, Lopes da Silva et al., 2003, Aghakhani et al., 2004, Blumenfeld, 2005, Breakspear et al., 2006). This bears on the controversial issue of the relative contributions of network and cellular mechanisms to the generation of absence seizures (McCormick and Contreras, 2001, Blumenfeld, 2005). Network mechanisms are concerned with the interconnected cortex and thalamus as a unified system, while cellular mechanisms emphasize intrinsic pacemaker properties of neurons. The details of how network and cellular mechanisms work in concert are inadequately understood, as the thalamocortical loop is often assumed to provide a synchronizing influence on the otherwise independent pacemaker oscillations in the cortex and thalamus (e.g., Steriade, 2001, Steriade, 2006), although the precise nature of this influence is not clear from the literature. Unavoidable axonal delays are not given any consideration, despite the fact that they constrain the allowable frequencies of any network oscillation that may exist (Robinson et al., 2001a, Robinson et al., 2002). Latencies have been measured between cortical and thalamic recordings during spontaneous spike-and-wave seizures in rat genetic absence epilepsy models (Seidenbecher et al., 1998, Pinault, 2003, Paz et al., 2007), which involve rats that are genetically predisposed to exhibit spontaneous 6–11 Hz spike-and-wave seizures assumed to correspond to human absence seizures, despite having a different frequency (Seidenbecher et al., 1998, McCormick and Contreras, 2001, Blumenfeld, 2005). These studies yielded values for rat thalamocortical delays of 5–15 ms, which are significantly longer than the $<5\mathrm{ms}$ delays measured via poststimulus spike timing in rats (Sawyer et al., 1994, Seidenbecher et al., 1998, Beierlein and Connors, 2002). This highlights the need to relate seizure waveforms to more direct measures of latency. An early study of local field potentials recorded in human cortex and thalamus during absence seizures yielded an estimate of (assumed equal) thalamocortical and corticothalamic delays of 14 ms in a 4 year old boy (Williams, 1953), but we argue that interpretation of the data relied on a flawed seizure mechanism. If a network mechanism (rather than an intrinsic pacemaker) is responsible, the short loop delay obtained cannot be reconciled with the low frequency of the absence seizure, as $\sim 300\mathrm{ms}$ of the period is unaccounted for and difficult to explain, even noting the slow ${\mathrm{GABA}}_B$ receptors in the thalamus. Nonetheless, the latencies between EEGs and field potentials recorded during seizures are a potentially useful probe of thalamocortical and corticothalamic delays when backed by modeling, and their use does not appear to have been explored since.

Physiologically based continuum modeling has provided a new tool with which to interpret neurophysiological data. Quantitative modeling of the EEG has progressed significantly since the 1970s (e.g., Wilson and Cowan, 1973, Lopes da Silva et al., 1974, Lopes da Silva et al., 1980, Nunez, 1974, Freeman, 1975, Nunez, 1981, Nunez, 1995, Wright and Liley, 1996, Jirsa and Haken, 1996, Steyn-Ross et al., 1999; Robinson et al., 1997, Robinson et al., 2001a, Robinson et al., 2001b, Robinson et al., 2002, Robinson et al., 2004, Robinson et al., 2005; Robinson, 2005, Robinson, 2006). Central to this approach is a procedure of averaging over neuronal populations, yielding description of brain activity on scales from tenths of a millimeter to the whole brain—those scales most relevant to the generation of the EEG. A recent corticothalamic model has successfully reproduced resting EEG spectra, evoked potentials, correlations, seizure dynamics, and other phenomena (Robinson et al., 1997, Robinson et al., 2001a, Robinson et al., 2001b, Robinson et al., 2002, Robinson et al., 2004, Robinson et al., 2005; Breakspear et al., 2006). The model is also able to fit a wide variety of clinical data, providing a novel noninvasive method of probing underlying physiology of the brain (Robinson et al., 2004, Rowe et al., 2004). The model fits yield values for the total corticothalamic loop delay $t_0$ in healthy adult humans of $t_0\approx 85\mathrm{ms}$ (Robinson et al., 2004, Rowe et al., 2004), higher than expected from the animal estimates above, but this is not surprising since $t_0$ is an average over all fibers present, not just the fastest few. The model naturally accommodates effective delays between connected structures, incorporating the aggregate effects of multiple pathways and latencies. It is important to determine how the value of $t_0$ obtained relates to the various experimental results as the model has successfully reproduced a wide range of behaviors, including dynamics strongly resembling epileptic seizures.

Recently it has been shown that the above model predicts the onset of limit cycle dynamics with key features of absence and tonic-clonic seizures (Robinson et al., 2002, Breakspear et al., 2006, Kim and Robinson, 2007). Seizures arise from stable states associated with healthy brain activity under moderate physiologically motivated parameter changes, and do not require a change in the corticothalamic loop delay from that of resting EEG. Generation of the model absence seizure relies on increased involvement, relative to the tonic-clonic case, of the inhibitory corticothalamic pathway via the reticular nucleus, yielding among other features the $\sim 3\mathrm{Hz}$ frequency. Although some spike-wave phenomena may have a purely cortical mechanism, there is considerable evidence for the involvement of the thalamus in absence seizures and thus it is this situation that we focus on. The model enables determination of the period and the time intervals between peaks of the absence waveform in terms of physiologically meaningful parameters, shedding light on the mechanisms underlying absence seizures. Here we focus on the dynamics once the seizure is under way, rather than the onset or termination phases. We also extend previous work by incorporating asymmetry between the thalamocortical and corticothalamic delays.

The paper is organized as follows: Section 2 presents an overview of the corticothalamic model on which this work is based. In Section 3 we study the temporal relationship between signals propagating around the corticothalamic loop during the model absence seizures, with implications for the measurement of latencies and the underlying seizure mechanism discussed in Section 4.