{"title": "Mechanism of Neural Interference by Transcranial Magnetic Stimulation: Network or Single Neuron?", "book": "Advances in Neural Information Processing Systems", "page_first": 1295, "page_last": 1302, "abstract": "", "full_text": "Mechanism of neural interference\n\nby transcranial magnetic stimulation:\n\nnetwork or single neuron?\n\nYoichi Miyawaki\n\nRIKEN Brain Science Institute\n\nWako, Saitama 351-0198, JAPAN\n\nyoichi miyawaki@brain.riken.jp\n\nMasato Okada\n\nRIKEN Brain Science Institute\n\nPRESTO, JST\n\nWako, Saitama 351-0198, JAPAN\n\nokada@brain.riken.jp\n\nAbstract\n\nThis paper proposes neural mechanisms of transcranial magnetic stim-\nulation (TMS). TMS can stimulate the brain non-invasively through a\nbrief magnetic pulse delivered by a coil placed on the scalp, interfering\nwith speci\ufb01c cortical functions with a high temporal resolution. Due to\nthese advantages, TMS has been a popular experimental tool in various\nneuroscience \ufb01elds. However, the neural mechanisms underlying TMS-\ninduced interference are still unknown; a theoretical basis for TMS has\nnot been developed. This paper provides computational evidence that in-\nhibitory interactions in a neural population, not an isolated single neuron,\nplay a critical role in yielding the neural interference induced by TMS.\n\n1 Introduction\n\nTranscranial magnetic stimulation (TMS) is an experimental tool for stimulating neurons\nvia brief magnetic pulses delivered by a coil placed on the scalp. TMS can non-invasively\ninterfere with neural functions related to a target cortical area with high temporal accuracy.\nBecause of these unique and powerful features, TMS has been popular in various \ufb01elds,\nincluding cognitive neuroscience and clinical application. However, despite its utility, the\nmechanisms of how TMS stimulates neurons and interferes with neural functions are still\nunknown. Although several studies have modeled spike initiation and inhibition with a\nbrief magnetic pulse imposed on an isolated single neuron [1][2], it is rather more plausible\nto assume that a large number of neurons are stimulated massively and simultaneously\nbecause the spatial extent of the induced magnetic \ufb01eld under the coil is large enough for\nthis to happen.\n\nIn this paper, we computationally analyze TMS-induced effects both on a neural population\nlevel and on a single neuron level. Firstly, we demonstrate that the dynamics of a simple\nexcitatory-inhibitory balanced network well explains the temporal properties of visual per-\ncept suppression induced by a single pulse TMS. Secondly, we demonstrate that sustained\ninhibitory effect by a subthreshold TMS is reproduced by the network model, but not by an\nisolated single neuron model. Finally, we propose plausible neural mechanisms underlying\nTMS-induced interference with coordinated neural activities in the cortical network.\n\n\fFigure 1: A) The network architecture. TMS was delivered to all neurons uniformly\nand simultaneously. B) The bistability in the network. The afferent input consisted of\na suprathreshold transient and subthreshold sustained component leads the network into\nthe bistable regime. The parameters used here are \u0001 = 0.1, \u03b2 = 0.25, J0 = 73, J2 =\n110, and T = 1.\n\n2 Methods\n\n2.1 TMS on neural population\n\n2.1.1 Network model for feature selectivity\n\nWe employed a simple excitatory-inhibitory balanced network model that is well analyzed\nas a model for a sensory feature detector system [3] (Fig. 1A):\n\n\u03c4m\n\nd\ndt\n\nm(\u03b8, t) = \u2212m(\u03b8, t) + g[h(\u03b8, t)]\n(cid:1))m(\u03b8\n(cid:1)) = \u2212J0 + J2 cos 2(\u03b8 \u2212 \u03b8\n(cid:1))\n\n(cid:1) \u03c0\n2\n\u2212 \u03c0\n2\n\nh(\u03b8, t) =\n\nJ(\u03b8 \u2212 \u03b8\n\n(cid:1)\n\nd\u03b8\n\u03c0\n\n, t) + hext(\u03b8, t)\n\n(1)\n\n(2)\n\n(cid:1)\n\nJ(\u03b8 \u2212 \u03b8\nhext(\u03b8, t) = c(t)[1 \u2212 \u0001 + \u0001 cos 2(\u03b8 \u2212 \u03b80)]\n\n(3)\n(4)\nHere, m(\u03b8, t) is the activity of neuron \u03b8 and \u03c4m is the microscopic characteristic time\nanalogous to the membrane time constant of a neuron (Here we set \u03c4m = 10 ms). g[h] is a\nquasi-linear output function,\n\n(cid:2) 0\n\u03b2(h \u2212 T )\n1\n\ng[h] =\n\n(h < T )\n(T \u2264 h < T + 1/\u03b2)\n(h \u2265 T + 1/\u03b2)\n\n(5)\n\nwhere T is the threshold of the neuron, \u03b2 is the gain factor, and h(\u03b8, t) is the input to neuron\n\u03b8. For simplicity, we assume that m(\u03b8, t) has a periodic boundary condition (\u2212\u03c0/2 \u2264 \u03b8 \u2264\n\u03c0/2), and the connections of each neuron are limited to this periodic range.\n\u03b80 is a stimulus feature to be detected, and the afferent input, hext(\u03b8, t), has its maximal\namplitude c(t) at \u03b8 = \u03b80. We assume a static visual stimulus so that \u03b80 is constant during\nthe stimulation (Hereafter we set \u03b80 = 0). \u0001 is an afferent tuning coef\ufb01cient, describing\nhow the afferent input to the target population has already been localized around \u03b80 (0 \u2264\n\u0001 \u2264 1/2).\n(cid:1)), consists of the uniform inhibition\nThe synaptic weight from neuron \u03b8 to \u03b8\nJ0 and a feature-speci\ufb01c interaction J2. J0 increases an effective threshold and regulates\nthe whole network activity through all-to-all inhibition. J2 facilitates neurons neighboring\nin the feature space and suppresses distant ones through a cosine-type connection weight.\n\n, J(\u03b8 \u2212 \u03b8\n\n(cid:1)\n\n\fm0(t) = \u2212m0(t) +\n\nm2(t) = \u2212m2(t) +\n\n\u03c4m\n\n\u03c4m\n\nd\ndt\n\nd\ndt\n\ng[h(\u03b8, t)]\n\ng[h(\u03b8, t)] cos 2\u03b8\n\nd\u03b8\n\u03c0\n\nd\u03b8\n\u03c0\n\n(6)\n\n(7)\n\n(cid:1) \u03c0\n2\n(cid:1) \u03c0\n\u2212 \u03c0\n2\n2\n\u2212 \u03c0\n2\n\nThrough these recurrent interactions, the activity pro\ufb01le of the network evolves and sharp-\nens after the afferent stimulus onset.\n\nThe most intuitive and widely accepted example representable by this model is the orienta-\ntion tuning function of the primary visual cortex [3][4][5]. Assuming that the coded feature\nis the orientation of a stimulus, we can regard \u03b8 as a neuron responding to angle \u03b8, hext as\nan input from the lateral geniculate nucleus (LGN), and J as a recurrent interaction in the\nprimary visual cortex (V1).\n\nBecause the synaptic weight and afferent input have only the 0th and 2nd Fourier compo-\nnents, the network state can be fully described by the two order parameters m0 and m2,\nwhich are 0th- and 2nd-order Fourier coef\ufb01cients of m(\u03b8, t). The macroscopic dynamics\nof the network is thus derived by Fourier transformation of m(\u03b8, t),\n\nwhere m0(t) represents the mean activity of the entire network and m2(t) represents the\ndegree of modulation of the activity pro\ufb01le of the network. h(\u03b8, t) is also described by the\norder parameter,\n\nh(\u03b8, t) = \u2212J0m0(t) +c(t)(1 \u2212 \u0001) + (\u0001c(t) + J2m2(t)) cos 2\u03b8\n\n(8)\n\nSubstituting Eq.8 into Eq.6 and 7, the network dynamics can be calculated numerically.\n\n2.1.2 TMS induction\n\nWe assumed that the TMS perturbation would be constant for all neurons in the network\nbecause the spatial extent of the neural population that we were dealing with is small com-\npared with the spatial gradient of the induced electric \ufb01eld. Thus we modi\ufb01ed the input\nfunction as \u02c6h(\u03b8, t) = h(\u03b8, t) + ITMS(t). Eq.6 to 8 were also modi\ufb01ed accordingly by re-\nplacing h with \u02c6h. Here we employ a simple rectangular input (amplitude: ITMS, duration:\nDTMS) as a TMS-like perturbation (see the middle graph of Fig. 2A).\n\n2.1.3 Bistability and afferent input model\n\nTMS applied to the occipital area after visual stimulus presentation typically suppresses its\nvisual percept [6][7][8]. To determine whether the network model produces suppression\nsimilar to the experimental data, we applied a TMS-like perturbation at various timings\nafter the afferent onset and examined whether the \ufb01nal state was suppressed or not. For this\npurpose, the network must hold two equilibria for the same afferent input condition and\nreach one of them depending on the speci\ufb01c timing and intensity of TMS. We thus chose\nproper sets of \u03b2, J0, and J2 that operated the network in the non-linear regime. In addition,\nwe employed an afferent input model consisting of suprathreshold transient (amplitude:\nAt > T , duration: Dt) and subthreshold sustained (amplitude: As < T ) components (see\nthe bottom graph of Fig. 2A). This is the simplest input model to lead the network into\nthe bistable range (Fig. 1B), yet it still captures the common properties of neural signals in\nbrain areas such as the LGN and visual cortex.\n\n2.2 TMS on single neuron\n\n2.2.1 Compartment model of cortical neuron\n\nWe also examined the effect of TMS on an isolated single neuron by using a compartment\nmodel of a neocortical neuron analyzed by Mainen and Sejnowski [9]. The model included\n\n\f \n\nFigure 2: A) The time course of the order parameters, the perturbation, and the afferent in-\nput. B) The network state in the order parameter\u2019s plane. The network bifurcates depending\non the induction timing of the perturbation and converges to either of the attractors. Two\nexamples of TMS induction timing (10 and 20 ms after the afferent onset) are shown here.\nThe dotted lines indicate the control condition without the perturbation in both graphs.\n\nthe following membrane ion channels: a low density of Na+ channels in soma and den-\ndrites and a high density in the axon hillock and the initial segment, fast K+ channels in\nsoma but not in dendrites, slow calcium- and voltage-dependent K+ channels in soma and\ndendrites, and high-threshold Ca2+ channels in soma and dendrites. We examined several\ntypes of cellular morphology as Mainen\u2019s report but excluded axonal compartments in or-\nder to evaluate the effect of induced current only from dendritic arborization. We injected a\nconstant somatic current and observed a speci\ufb01c spiking pattern depending on morphology\n(Fig. 5).\n\n2.2.2 TMS induction\n\nThere have been several reports on theoretically estimating the intracellular current in-\nduced by TMS [1][2][10]. Here we brie\ufb02y describe a simple expression for the axial and\ntransmembrane current induced by TMS. The electric \ufb01eld E induced by a brief mag-\nnetic pulse is given by the temporal derivative of the magnetic vector potential A, i.e.,\nE(s, t) = \u2212\u2202A(s, t)/\u2202t. Suppose the spatial gradient of the induced magnetic \ufb01eld is so\nsmall compared to a single cellular dimension that E can be approximated to be constant\nover all compartments. The simplest case is that one compartment has one distal and one\nproximal connection, in which the transmembrane current can be de\ufb01ned as the difference\nbetween the axial current going into and coming out of the adjacent compartment. The\naxial current between the adjacent compartment can be uniquely determined by distance\nand axial conductance between them (Fig. 5B),\n\n(cid:1) sk\n\nsj\n\nI TMS\na\n\n(j, k) = Gjk\n\nE(s) \u00b7 ds = GjkE \u00b7 sjk.\n\n(9)\n\nHence the transmembrane current in the k-th compartment is,\n\n(j, k) \u2212 I TMS\n\na\n\n(k, l) = E \u00b7 (Gjksjk \u2212 Gklskl).\n\nm (k) = I TMS\nI TMS\n\na\n\n(10)\nNow we see that the important factors to produce a change in local membrane potential by\nTMS are the differences in axial conductance and position between adjacent compartments.\nAs Nagarajan and Kamitani pointed out [1][2], if the cellular size is small, the heterogeneity\nof the local cellular properties (e.g. branching, ending, bending of dendrites, and change in\ndendrite diameter) could be crucial in inducing an intracellular current by TMS. A multiple\nbranching formulation is easily obtained from Eq.10. For simplicity, the induced electric\n\ufb01eld was approximated as a rectangular pulse. The pulse\u2019s duration was set to be 1 ms, as in\nthe network model, and the amplitude was varied within a physically valid range according\nto the numerical experiment\u2019s conditions.\n\n\fFigure 3: A) The minimum intensity of the suppressive perturbation in our model (solid\nline for single- and dashed line for paired-pulse). The width of each curve indicates the\nsuppressive latency range for a particular intensity of the perturbation (e.g. if At = 1.5 and\nITMS = 12, the network is suppressed during -35.5 to 64.2 ms for a single pulse case; thus\nthe suppressive latency range is 99.7 ms.) B) Experimental data of suppressive effect on\na character recognition task replotted and modi\ufb01ed from [7] and [11]. Both graph A and\nB equivalently indicate the susceptibility to TMS at the particular timing. To compare the\nabsolute timing, the model results must be biased with the proper amount of delay in neural\nsignal transmission given to the target neural population because these are measured from\nthe timing of afferent signal arrival, not from the onset of the visual stimulus presentation.\n\n3 Results\n\n3.1 Temporally selective suppression of neural population\n\nThe time course of the order parameters are illustrated in Fig. 2A. The network state can\nbe also depicted as a point on a two-dimensional plane of the order parameters (Fig. 2B).\nBecause TMS was modeled as a uniform perturbation, the mean activity, m0, was tran-\nsiently increased just after the onset of the perturbation and was followed by a decrease\nof both m0 and m2. This result was obtained regardless of the onset timing of the per-\nturbation. The \ufb01nal state of the network, however, critically depended on the onset timing\nof the perturbation. It converged to either of the bistable states; the silent state in which\nthe network activity is zero or the active state in which the network holds a local excita-\ntion. When the perturbation was applied temporally close to the afferent onset, the network\nwas completely suppressed and converged to the silent state. On the other hand, when the\nperturbation was too early or too late from the afferent onset, the network was transiently\nperturbed but \ufb01nally converged to the active state.\n\nWe could thus \ufb01nd the latency range during which the perturbation could suppress the\nnetwork activity (Fig. 3A). The width of suppressive latency range increased with the am-\nplitude of the perturbation and reached over 100 ms, which is comparable to typical experi-\nmental data of suppression of visual percepts by occipital TMS [6][7]. When we supplied a\nstrong afferent input to the network, equivalent to a contrast increase in the visual stimulus,\nthe suppressive latency range narrowed and shifted upward, and consequently, it became\ndif\ufb01cult to suppress the network activity without a strict timing control and larger ampli-\ntude of the perturbation. These results also agree with experiments using visual stimuli of\nvarious contrasts or visibilities [8][13]. The suppressive latency range consistently had a\nbell shape with the bottom at the afferent onset regardless of parameter changes, indicating\nthat TMS works most suppressively at the timing when the afferent signal reaches the target\n\n\fFigure 4: Threshold reduction by paired pulses in the steady state. A) Network model\nand B) experimental data of the phosphene threshold replotted from [12]. The dashed line\nindicates the threshold for a single pulse TMS.\n\nneural population.\n\n3.2 Sustained inhibition of neural population by subthreshold pulse\n\nMultiple TMS pulses within a short interval, or repetitive TMS (rTMS), can evoke\nphosphene or visual de\ufb01cits even though each single pulse fails to elicit any perceptible\neffect. This experimental fact suggests that a TMS pulse, even if it is a subthreshold one,\ninduces a certain sustained inhibitory effect and reduces the next pulse\u2019s threshold to elicit\nperceptible interference.\n\nWe considered the effect of paired pulses on a neural population and determined the dura-\ntion of the threshold reduction by a subthreshold TMS. Here we set the subthreshold level\nat the upper limit of intensity which could not suppress the network at the induction timing.\nFor the steady state, the initial subthreshold perturbation signi\ufb01cantly reduced the suppres-\nsive threshold for the subsequent perturbation; the original threshold level was restored to\nmore than 100 ms after the initial TMS (Fig. 4A). The threshold slightly increased when\nthe pulse interval was shorter than \u03c4m. These results agree with experimental data of oc-\ncipital TMS examining the relationship between phosphene threshold and the paired-pulse\nTMS interval [12] (Fig. 4B).\n\nFor the transient state, we also observed that the initial subthreshold perturbation, indicated\nby the arrow in Fig. 3A, signi\ufb01cantly reduced the suppressive threshold for the subsequent\nperturbation, and consequently, the suppressive latency range was extended up to 60 ms\n(Fig. 3A). These results are consistent with Amassian\u2019s experimental results demonstrating\nthat a preceding subthreshold TMS to the occipital cortex increased the suppressive latency\nrange in a character recognition task [11] (Fig. 3B).\n\n3.3 Transient inhibition of single neuron by subthreshold pulse\n\nNext, we focus on the effect of TMS on a single neuron. Results from a layer V pyrami-\ndal cell are illustrated in Fig. 5. An intense perturbation could inhibit the spike train for\nover 100ms after a brief spike burst (Fig. 5C1). This sustained spike inhibition might be\ncaused by mechanisms similar to after-hyperpolarization or adaptation because the intra-\ncellular concentration of Ca2+ rapidly increased during the bursting period. These results\nare basically the same as Kamitani\u2019s report [1] using Poisson synapses as current inputs to\nthe neuron. We tried several types of morphology and found that it was dif\ufb01cult to sup-\npress their original spike patterns when the size of the neuron was small (e.g. stellate cell)\nor when the neuron initially showed spike bursts (e.g. pyramidal cell with more bushy\ndendritic arbors).\n\n\fFigure 5: A) Layer V pyramidal cell. B) Compartment model of the neuron and the trans-\nmembrane current induced by TMS. C1, C2) The spike train perturbed by a suprathreshold\nand subthreshold TMS. C3) The temporal variation of the TMS threshold for inducing the\nspike inhibition. Thin lines in C1\u2013C3 indicate the control condition without TMS.\n\nUsing a morphology whose spike train was most easily suppressed (i.e. a pyramidal cell in\nFig. 5A), we determined whether a preceding subthreshold pulse could induce the sustained\ninhibitory effect. Here, the suppressive threshold was de\ufb01ned as the lowest intensity of the\nperturbation yielding a spike inhibitory period whose duration was more than 100 ms. The\nperturbation below the suppressive threshold caused the spike timing shift as illustrated in\nFig. 5C2. In the single cell\u2019s case, the suppressive threshold highly depended on the relative\ntiming within the spike interval and repeated its pattern periodically. In the initial spike\ninterval from the subthreshold perturbation to the next spike, the suppressive threshold\ndecreased but it recovered to the original level immediately after the next spike initiation\n(Fig. 5C3). This fast recovery of the suppressive threshold occurred regardless of the\ninduction timing of the subthreshold perturbation, indicating that the sustained inhibitory\neffect by the preceding subthreshold perturbation lasted on the order of one (or two at most)\nspike interval, even with the most suppressible neuron model. The result is incomparably\nshorter than the experimental data as noted in Sec. 3.2, suggesting that it is impossible to\nattribute the neural substrates of the threshold reduction caused by the subthreshold pulse\nto only the membrane dynamics of a single neuron.\n\n4 Discussion\n\nThis paper focused on the dichotomy to determine what is essential for TMS-induced\nsuppression\u2013a network or a single neuron? Our current answer is that the network is es-\nsential because the temporal properties of suppression observed in the neural population\nmodel were totally consistent with the experimental data. In a single neuron model, we\ncan actually observe a spike inhibition whose duration is comparable to the silent period\nof the electromyogram induced by TMS on the motor cortex [14]; however, the degree of\nsuppression is highly dependent on the property of the high-threshold Ca2+ channel and\nis also very selective about the cellular morphology. In addition, the most critical point is\nthat the sustained inhibitory effect of a subthreshold pulse cannot be explained by only the\nmembrane mechanisms of a single neuron. These results indicate that TMS can induce a\nspike inhibition or a spike timing shift on a single neuron level, which yet seems not enough\nto explain the whole experimental data.\n\n\fAs Walsh pointed out [15], TMS is highly unlikely to evoke a coordinated activity pattern\nor to stimulate a speci\ufb01c functional structure with a \ufb01ne spatial resolution in the target corti-\ncal area. Rather, TMS seems to induce a random activity irrespective of the existing neural\nactivity pattern. This paper simply modeled TMS as a uniform perturbation simultaneously\napplied to all neurons in the network. Walsh\u2019s idea and our model are basically equivalent\nin that TMS gives a neural stimulation irrespective of the existing cortical activity evoked\nby the afferent input. Thus inactive parts of the network, or opponent neurons far from\n\u03b80, can be also activated by the perturbation if it is strong enough to raise such inactive\nneurons above the activation threshold, resulting in suppression of the original local exci-\ntation through lateral inhibitory connections. To suppress the network activity, TMS needs\nto be applied before the local excitation is built up and the inactive neurons are strongly\nsuppressed. In the paired-pulse case, even though each TMS pulse was not strong enough\nto activate the suppressed neurons, the pre-activation by the preceding TMS can facilitate\nthe subsequent TMS\u2019s effect if it is applied until the network restores its original activity\npattern. These are the basic mechanisms of TMS-induced suppression in our model, by\nwhich the computational results are consistent with the various experimental data. In addi-\ntion to our computational evidence, recent neuropharmacological studies demonstrated that\nGABAergic drugs [16] and hyperventilation environment [17] could modulate TMS effect,\nsuggesting that transsynaptic inhibition via inhibitory interneuron might be involved in\nTMS-induced effects. All these facts indicate that TMS-induced neural interference is me-\ndiated by a transsynaptic network, not only by single neuron properties, and that inhibitory\ninteractions in a neural population play a critical role in yielding neural interference and its\ntemporal properties.\n\nAcknowledgments\n\nWe greatly appreciate our fruitful discussions with Dr. Yukiyasu Kamitani.\n\nReferences\n[1] Y. Kamitani, V. Bhalodi, Y. Kubota, and S. Shimojo, Neurocomputing 38-40, 697 (2001).\n[2] S. Nagarajan, D. Durand, and E. Warman, IEEE Trans Biomed Eng 40, 1175 (1993).\n[3] R. Ben-Yishai, R. Bar-Or, and H. Sompolinsky, Proc Natl Acad Sci USA 92, 3844 (1995).\n[4] H. Sompolinsky and R. 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Cowey, Nat Rev Neurosci 1, 73 (2000).\n[16] U. Ziemann, J. Rothwell, and M. Ridding, J Physiol 496.3, 873 (1996).\n[17] A. Priori, A. Berardelli, B. Mercuri, M. Inghilleri, and M. Manfredi, Electroencephalogr Clin\n\nNeurophysiol 97, 69 (1995).\n\n\f", "award": [], "sourceid": 2395, "authors": [{"given_name": "Yoichi", "family_name": "Miyawaki", "institution": null}, {"given_name": "Masato", "family_name": "Okada", "institution": null}]}