## 1 Introduction  
The brain's response to the brain's response is a function of the brain's response, which is a function of the brain's response. The brain's response is a function of the brain's response, which is a function of the brain's response. ## 1 Introduction  
Transcranial magnetic stimulation (TMS) is a non-invasive brain stimulation technique based on the application of brief magnetic pulses that induce localized intracranial electrical fields (E-fields) and result in the excitation and/or inhibition of cortical neurons [1]. Thus, the magnetic stimuli modulate brain activity at the targeted area, causing transient alterations of cortical excitability and brain connectivity that have therapeutic implications in patients with neurological or psychiatric disorders [2; 3; 4]. In addition, TMS holds significant potential as a diagnostic and prognostic biomarker in numerous neurological disorders, such as epilepsy [5; 6; 7; 8; 9], stroke [10; 11], multiple sclerosis [12; 13] and Alzheimer's disease [14; 15]. Despite this progress, the precise neural mechanisms underlying the effects of TMS as well as the exact relation between the properties of the E-field and the brain's physiological responses are incompletely understood and are a matter of active research [16]. Over the last couple of decades, the combination of electroencephalography with TMS (TMS-EEG) has emerged as a valuable clinical tool, but also as an innovative research approach for the investigation of brain circuits in health and disease [17; 18]. In parallel, various attempts at the computational modeling of the E-field have taken place, ranging from relatively simple spherical models that approximate the head shape and rely on generic assumptions about the conductivity properties of intracranial tissues [19; 20] to more advanced approaches, based on boundary or finite element methods (BEM and FEM, respectively) that take into full account the individual anatomy and scalp geometry [21; 22]. The main aim of E-field modeling is to compare real with theoretical TMS responses [23], compare and test coil designs [24; 25; 26], predict the exact stimulation location and optimize stimulation parameters by guiding TMS coil positioning, orientation and dosimetry [19; 27; 28; 29; 30; 31]. It is well known that in the case of TMS, the instantaneous E-field evokes action potentials in chains of excitatory and inhibitory cortical interneurons as well as principal output neurons in the cerebral cortex that are subsequently propagated intra- and inter-hemispherically, ultimately producing the recorded TMS-evoked potentials (TEPs). The overarching aim of the present work is to explore in detail the relation of the TMS-induced E-field and the brain's physiological response. To this end, we posed two specific research questions. The first one is as follows: What is the exact relation of the E-field induced at a certain stimulus intensity (SI), corresponding to a multiple (120% in our case) of the critical value of the lower cortical threshold (LT) to the ensuing global EEG response from a temporal (i.e., how does it change over time?) and spatial (i.e., where in the brain is it stronger?) point of view? The particular SI level was chosen on the basis of two criteria: (a) that it is clearly suprathreshold so as to secure the generation of TEPs, and (b) that it is sufficiently low so as to avoid the generation of biologic and non-biological artifacts, associated with high stimulus intensities, that may act as confounders. The second question is: What is, in mathematical terms, the relation of the E-fields, induced by a wide range of peri-threshold stimulus intensities, with TEPs recorded in a particular brain region of interest (ROI)? The ROI was determined based on the results of the spatial correlation analysis (vide supra) and included nine centrally located electrodes.