Diffusion tensor MRI-based estimation of the influence of brain tissue anisotropy on the effects of transcranial magnetic stimulation
Introduction
In this paper we investigate the influence of brain tissue anisotropy on the electric field distribution produced by transcranial magnetic stimulation (TMS). TMS is produced by passing a brief, high current electric pulse through an insulated coil over the scalp. This pulse induces a rapidly changing magnetic field which in turn induces an electric field in the underlying brain tissue. If the amplitude, duration and direction are appropriate, this electric field can depolarize cortical neurons and generate action potentials (Abdeen and Stuchly, 1994, Roth, 1994, Nagarajan and Durand, 1995, Hyodo and Ueno, 1996). By transiently interrupting normal brain activity, TMS can be used to produce reversible functional impairments (or, more rarely, improvements), and hence to test hypotheses about the role of the stimulated area in performing a given task (Walsh and Cowey, 2000). TMS is also a useful tool for investigating patterns of functional connectivity since the effect of the stimulation can be driven to areas distant from the area of stimulation through neuronal pathways (Paus et al., 1997, Paus et al., 2001, Ilmoniemi et al., 1997).
Though TMS is a popular tool in cognitive neuroscience, there is limited knowledge of the electromagnetic field distributions induced in biological tissue by the technique. Such information would be immensely valuable for interpretation of the resulting functional effects. To this end, theoretical models of these electromagnetic field distributions have been developed. To date, the majority of these models have employed infinite half-planes and perfect spheres to approximate the stimulated tissue (Tofts, 1990, Cohen and Cuffin, 1991, Roth et al., 1991a, Roth et al., 1991b, Esselle and Stuchly, 1992, Eaton, 1992, Ravazzani et al., 1996, Davey et al., 2003).
In recent studies, more realistic models have been constructed to investigate the effect of TMS. Structural MRI has been used to guide the construction of a human head model consisting of compartments corresponding to skin, skull, CSF, gray and white matter (Wagner et al., 2004). Each of these compartments was assigned a biologically plausible conductivity allowing investigation of tissue boundary effects on the induced current densities. Incorporation of tissue heterogeneity in these models is an important advance it can have a big impact on the location of the stimulation site (Wagner et al., 2004).
However, more detailed characterisation of the electric field distribution in the brain requires incorporation of tissue anisotropy measures, as the conductivity of a particular tissue type may differ with direction – a situation known to occur in white matter. Manipulation of tissue heterogeneity and anisotropy in a small region embedded in a spherical head model was found to significantly alter the simulated electric field distributions (Miranda et al., 2003).
Making accurate predictions about the effects of TMS depends not only on the estimation of the induced electric field, but also on the interactions between the electric field and the neural tissue. These mechanisms have been investigated in vitro (Amassian et al., 1992, Maccabee et al., 1993) and using theoretical models (Nilsson et al., 1992), showing that either the peak amplitude or gradient of the electric field can be most relevant to stimulation depending on the geometry of the axons. However, TMS experiments reported both on the human visual cortex (Amassian et al., 1994) and motor cortex (Boroojerdi et al., 1999, Wassermann et al., 1996, Krings et al., 1997), support the hypothesis that stimulation occurs at the peak of the electric field rather than at the peak of its gradient.
Despite this knowledge it still remains difficult to estimate the electric field intensity that is necessary to stimulate the targeted area. TMS threshold is usually estimated by measuring the minimum TMS stimulus intensity required over the motor cortex to elicit an electromyographic (EMG) potential in a target muscle. This threshold can be influenced by many important factors such as effects of background activity and orientation of the coil.
Theoretically it is very hard to predict a priori the electric field strength capable of stimulating neural tissue and therefore the area of tissue that a given electric field can affect. To derive an idea about the size of the stimulated area, the definition of focality introduced by Ruohonen and Ilmoniemid (1998) is often used; this refers to the area of the spherical surface bound by the half maximum of the induced electric field in a spherical model.
Here we use MRI-derived structural and conductivity information to model the electromagnetic field distribution caused by a TMS pulse on the human brain. In vivo conductivity estimates are possible due to the development of diffusion tensor imaging (DTI) which allows the localized measurement of the effective water self-diffusion tensor (Basser et al., 1994). The conductivity tensor can then be inferred from the diffusion tensor on the basis of a model of the close link between the two transport processes – of the water molecules and ionic motion along fibers (Tuch et al., 1998). The model predicts a strong linear relationship between the two tensors because the transport for the two processes is mainly constrained by the same extracellular space (Tuch et al., 2001).
We compare the electromagnetic field distribution due to a TMS pulse in the case of a full DTI conductivity model (taking into account tissue anisotropy) with the case of a simple scalar (non-directional) conductivity model. These two cases will be referred to as the DTI case and the isotropic case, respectively. We consider three commonly investigated sites of stimulation, motor cortex (M1), frontal eye field (FEF) and posterior parietal cortex (PPC) (Muggleton et al., 2003, Hung et al., 2005). The aim is to assess the impact of these measures on the estimated electromagnetic field distribution and discuss the relevance of these results for future interpretation of TMS-induced effects.
The estimate we make here is static in the important sense that it does not take into account the initial state of neuronal excitation (Silvanto et al., 2007) nor the effects of interactions between physiological factors and the induced field. This is a goal of future modelling.
Section snippets
Conductivity models
In the following we present two models of the conductivity distribution of the head, assigning appropriate conductivity to skin, bone, CSF and grey and white matter (Fig. 1(A)). The difference between the two models is that in one the conductivity assigned to grey and white matter is isotropic, whereas in the DTI case the influence of the brain tissue microstructural anisotropy on the induced electric field distribution is assessed. Within the cerebral tissues, the white matter has the highest
Maximum induced electric field
The maximum of the vector potential for the three stimulation sites occurs at about 2 cm beneath the intersection of the figure-of-eight coil (Table 1, left column and Fig. 3, Fig. 4, Fig. 5(B)). In the three cases considered, we kept the same distance between the centre of the coil and the skull. The differences in the induced electric field arise from variations in the distance between external skull surface and cortex, mainly due to differences in the skull thickness. The vector potential
Discussion
Despite the widespread and successful application of TMS in physiological and behavioural studies, there remain difficulties in assessing the spread and strength of the electromagnetic field induced by the pulse. Several experiments have shown that the secondary effects produced by the stimulus are even harder to predict due to the effects of the electromagnetic field on functional and anatomical connections (Paus et al., 1997, Paus et al., 2001, Ilmoniemi et al., 1997). These experimental
Acknowledgments
We would like to thank Julien Pommier for help with GET F EM ++ Software.
We acknowledge MRIcro for the support in the figures display.
M D L acknowledges the Marie Curie training site programme. K E is funded by MRC grant number G0300952. Royal Society and Wellcome Trust partly support V W.
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