This hypothesis is strongly supported by neuroimaging data. As described above, numerous neuroimaging studies have reported altered movement-associated neural activity after stroke. However, knowing where activity is altered after stroke does not allow to draw conclusions about how a particular region interacts with other parts of the brain. In the last two decades, several approaches have been developed to assess from time series of imaging data how different brain regions interact (Eickhoff and Grefkes 2011). In this context, two different types of connectivity concepts can be distinguished: (i) “functional connectivity” refers to correlations (or coherence) between the time-courses of different regions. Here, higher correlation parameters are interpreted as stronger functional connectivity between the regions of interest. However, functional connectivity cannot distinguish how interactions are mediated and whether one region drives activity of the respective other region. To this end, model-based approaches such as dynamic causal modeling (DCM) allow to estimate “effective connectivity,” i.e., the causal influences that one region exerts over another (Friston et al. 2003; Stephan et al. 2010). Grefkes and colleagues used DCM to evaluate cortical connectivity during simple unilateral hand movements in stroke patients with persisting motor deficits (Grefkes et al. 2008). In accordance to the TMS results of Murase and colleagues (2004), an inhibitory influence was exerted by contralesional M1 onto ipsilesional M1 during movements of the paretic hand, which was absent for movements of the unaffected hand or in healthy subjects. Moreover, the strength of this inhibition correlated with the degree of impairment across the cohort, with most severely impaired patients featuring strongest inhibitory influences targeting ipsilesional M1 (Grefkes et al. 2008). These findings corroborate a maladaptive role of the contralesional M1. As a consequence, suppressing the contralesional hemisphere might alleviate maladaptive influences exerted over the ipsilesional hemisphere, ultimately resulting in functional benefits for the paretic hand. Indeed, several studies have indicated that inhibitory rTMS applied to the contralesional M1 improves hand function in some patients (for further information see Chap. 4). A single application of inhibitory rTMS has been shown to also reduce neural over-activation of the contralesional hemisphere during movements of the paretic hand (Nowak et al. 2008). Hence, from a mechanistic perspective, reducing cortical excitability in the contralesional M1 transiently normalizes movement-related cortical activation. According to the interhemispheric competition model, reducing over-activation within the contralesional hemisphere will also reduce interhemispheric inhibition targeting the ipsilesional M1. Indeed, Grefkes and colleagues (2010) could show that inhibitory 1-Hz rTMS applied to contralesional M1 beneficially impacts on motor function of the affected hand and also reduces maladaptive interhemispheric inhibition targeting ipsilesional M1. Of note, the effects on motor behavior and connectivity significantly correlated, with stronger reduction in maladaptive inhibition observed in patients featuring strongest transient motor improvements after stimulation (Grefkes et al. 2010). Thus, rTMS-induced inhibition seems to promote motor function of the paretic hand through attenuating excessive interhemispheric inhibition onto ipsilesional M1.

The model of interhemispheric competition also supports the alternative rTMS-approach: enhancing motor activity within the ipsilesional hemisphere might strengthen IHI onto the contralesional hemisphere, which in turn could ultimately reduce pathological inhibition onto ipsilesional M1 (Grefkes and Fink 2012). One might argue that this hypothesis derived from the combination of electrophysiological data obtained via TMS and estimates of effective connectivity obtained via DCM from fMRI data seems far-fetched and that a beneficial impact of excitatory rTMS applied to the ipsilesional motor cortex rather stems from local effects within ipsilesional M1, such as induction of cortical plasticity or reduction of intracortical inhibition. However, we recently observed a strong relationship between reduced cortical excitability of the ipsilesional hemisphere (assessed via TMS) and reduced inhibition from ipsilesional M1 onto contralesional M1 assessed via DCM, which were both most reduced in chronic stroke patients suffering from severest motor deficits (Volz et al. 2015). Given these observations, enhancing cortical excitability within the ipsilesional hemisphere via rTMS could improve the interhemispheric balance of inhibition, ultimately alleviating maladaptive inhibition targeting the ipsilesional hemisphere. Support for this hypothesis stems from a study published by Ameli and colleagues, who observed that a single application of excitatory 10-Hz rTMS to ipsilesional M1 transiently increases motor function of the paretic hand and also reduces over-activation of the contralesional M1 (Ameli et al. 2009). Since the contralesional hemisphere was not directly stimulated, stimulation-induced changes in the ipsilesional hemisphere must have caused the observed reduction in contralesional activity, possibly via transcallosal connections on a cortical level. Of note, normalization of neural activation and motor function could only be achieved in patients suffering from subcortical stroke, whereas patients with cortical damage showed no reduction of contralesional activity (Ameli et al. 2009). This dependence on intact cortical tissue further corroborates that a beneficial effect of ipsilesional rTMS might, at least in part, derive from the modulation of cortical interactions within and across hemispheres.

In summary, the model of interhemispheric competition constitutes two hypotheses regarding systems-level mechanisms underlying beneficial effects of both excitatory rTMS applied to ipsilesional M1 and inhibitory rTMS applied to contralesional M1. Both approaches have been shown to transiently promote motor function, at least in certain patient populations. However, it must be kept in mind that the model of interhemispheric competition certainly oversimplifies the complex interactions between motor regions underlying the preparation and execution of voluntary movements and fails to include other important factors influencing motor recovery, e.g., lesion size and location. Furthermore, it contradicts observations that for some patients contralesional areas hold a compensatory role for motor recovery, especially early after stroke. Therefore, Di Pino and colleagues recently suggested combining both models (the vicariation model and interhemispheric competition model) by adding information on the individual extent of the structural damage caused by ischemia: size and location of a stroke lesion might determine whether motor areas of the non-lesional hemisphere rather hold a compensatory function or represent maladaptive plasticity (for further details see Di Pino et al. 2014).