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Translational Physiology
1 Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, Maryland 21218 2 Department of Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio 44195
Submitted 14 October 2003; accepted in final form 2 December 2003
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ABSTRACT |
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INTRODUCTION |
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). DBS results in clinical benefits analogous to those achieved by surgical lesions of the nucleus where the electrode is implanted. Three main targets have been identified that when ablated or stimulated result in beneficial clinical effects: the ventralis intermedius of the thalamus, the globus pallidus internus, and the subthalamic nucleus (Benabid et al. 1996; Gross and Lozano 2000; Obeso et al. 2001). Although the clinical benefits of DBS have been well documented, fundamental questions remain about the therapeutic mechanism(s) of action (Dostrovsky and Lozano 2002; Grill and McIntyre 2001; McIntyre and Thakor 2002; Montgomery and Baker 2000; Vitek 2002).
Because of the similarity in therapeutic outcomes achieved with DBS and lesions, it has been argued that high-frequency electrical stimulation (HFS) inactivates the structures being stimulated. Recordings made in the stimulated nucleus show inhibition and/or decreased activity during and after the stimulus train (Benazzouz et al. 1995, 2000; Boraud et al. 1996; Dostrovsky et al. 2000). However, recordings made in efferent nuclei of the stimulated nucleus indicate that the output of the stimulated nucleus is increased during DBS (Anderson et al. 2003; Hashimoto et al. 2003; Maurice et al. 2003; Windels et al. 2000, 2003). These results appear to be contradictory, with the former indicating that DBS inhibits the stimulated nucleus and the latter indicating that DBS excites the nucleus.
A significant obstacle in interpreting experimental results of DBS and developing a clear mechanism of action is the lack of quantitative understanding of the influence of HFS on the neural elements surrounding the electrode. Therefore we used detailed computer models of the stimulating electrode and surrounding neurons to determine the effects of stimulation in a controlled environment. Our approach combined a finite-element model of the clinical DBS electrode, a multi-compartment cable model of a thalamocortical (TC) relay neuron, and a distribution of excitatory and inhibitory synaptic inputs to the TC relay neuron. Each component of these models represents substantial improvement over our preliminary attempts to model the effects of thalamic stimulation where we used a point source electrode and ignored the effects of stimulation-induced trans-synaptic action (Grill and McIntyre 2001).
The first goal of this study was to determine whether HFS of the thalamus results in activation or inhibition of neurons surrounding the electrode. During extracellular stimulation, action potential initiation occurs in the axon (McIntyre and Grill 1999; Nowak and Bullier 1998a,b; Rattay 1999). Therefore we hypothesized that during HFS the activity recorded in the cell body of a neuron does not accurately reflect the efferent output, and a neuron could simultaneously exhibit suppression of activity in the soma and excitation of the axon (Grill and McIntyre 2001; McIntyre and Grill 2002). This hypothesis, if supported, resolves the apparently conflicting experimental results indicating that DBS both inhibits and excites the stimulated nucleus.
The second goal of this study was to determine the spatial extent of activation and/or inhibition of neurons surrounding the electrode generated with therapeutic stimulation parameters. Presently, the stimulus parameters used in clinical DBS (monopolar or bipolar stimulation; 120 to 180 Hz stimulus frequency; 0.06 to 0.2 ms pulse duration; 1 to 5 V stimulus amplitude) are derived by trial and error (O'Suilleabhain et al. 2003; Volkmann et al. 2002). Understanding the impact of parameter variation on the effects DBS represents an important step in developing rational methods for system design and tuning (Benabid et al. 2000).
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METHODS |
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DBS electrode model
We developed an axisymmetric finite-element model of the Medtronic 3387 DBS lead (Medtronic, Minneapolis, MN) positioned in a homogeneous isotropic volume conductor to solve for the potential distribution generated in the tissue medium (Fig. 1). The model was implemented using 4-node quadrilateral elements in a commercially available software package (ANSYS 5.7, ANSYS, Houston, PA). The voltages (V) at the nodes of the finite-element mesh were calculated using a frontal solution method of the Laplace equation
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= 350 
cm–1 (Sances and Larson 1975) was the electrical conductivity of the tissue medium (Fig. 1). The model consisted of 15,782 nodes. Along the surface of the electrode contact the separation between the nodes of the finite-element mesh was 25 µm, and in the tissue within 5 mm surrounding the electrode the spacing between nodes was <50 µm. The tissue box surrounding the electrode was 50 x 50 mm with the outer boundary set to 0 V, and the electrode contact set to the stimulus voltage. Doubling the density of the mesh or doubling the distance of the boundary from the electrode (i.e., the size of the tissue box) generated a potential distribution that differed by <2% when compared with the default model.
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). During each time step of the simulation the Ve for each compartment was set either to zero when no stimulus pulse was being applied or to the potentials generated by the DBS electrode when a stimulus pulse was being applied (McNeal 1976). Thalamocortical relay neuron model
The DBS electrode model was coupled to a three-dimensional (3-D) multi-compartment cable model of a TC relay neuron. The model consisted of a dendritic tree, cell body, and myelinated axon with a geometry obtained from a 3-D reconstruction of a filled cell (Destexhe et al. 1998) (Fig. 2, Table 1). The membrane of the TC model consisted of the membrane capacitance (1 µF/cm2: cell body and dendrites; 2 µF/cm2: myelinated axon), in parallel with a complement of linear leakage and nonlinear calcium, potassium, and sodium conductances distributed in the different sections of the neuron (Fig. 2). The compartments were connected together with linear resistors based on the geometry of the connecting compartments and the intracellular resistivity (300 cm–1: cell body and dendrites; 70 cm–1: myelinated axon).
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; Huguenard and McCormick 1992; McCormick and Huguenard 1992; Williams and Stuart 2000). The cell body and dendritic compartments included the parallel combination of nonlinear fast Na+, delayed rectifier K+, slow K+, T-type Ca2+, and hyperpolarization-activated cation conductances, Na+ and K+ linear leakage conductances, and the membrane capacitance (Fig. 2; Table 2; see APPENDIX). The initial segment compartments included the parallel combination of nonlinear fast Na+, delayed rectifier K+, and slow K+ conductances, a linear leakage conductance, and the membrane capacitance (Fig. 2; Table 2; APPENDIX).
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). Between each node there were 2 MYSA compartments, 2 FLUT compartments, and 3 STIN compartments. The nodes included the parallel combination of non-linear fast Na+, persistent Na+, and slow K+ conductances, a linear leakage conductance, and the membrane capacitance. The paranodal and internodal compartments included 2 concentric layers, each including a linear conductance in parallel with the membrane capacitance, to represent the myelin sheath and underlying axolemma. The FLUT sections of the model also contained a fast K+ conductance in the axolemma.
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Previous work has shown that the threshold for extracellular stimulation of axonal terminals projecting to the region around the electrode is lower than the threshold for direct activation of local cells (Baldissera et al. 1972; Dostrovsky et al. 2000; Gustafsson and Jankowska 1976; Jankowska et al. 1975; McIntyre and Grill 2002). We modeled the trans-synaptic effect of extracellular stimulation on local cells by applying either excitatory or inhibitory synaptic conductances to each of the dendritic and somatic compartments of the TC neuron. The distribution of inhibitory and excitatory synapses was based on electron microscopic reconstructions of the glutamateric and GABAergic terminals on TC neurons (Sato et al. 1997). Each compartment was designated as either proximal (0–44 µm), medial (45–90 µm), or distal (>90 µm) relative to the cell body. The compartments within each group (proximal, medial, distal) were randomly assigned as either excitatory or inhibitory with proportions based on the experimental distribution of synaptic inputs: proximal: 30% excitatory, 70% inhibitory; medial: 50% excitatory, 50% inhibitory; distal: 70% excitatory, 30% inhibitory (Sato et al. 1997) (Fig. 6A).
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,b)
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and 
are the forward and backward rate constants, and R represents the fraction of open channels on the postsynaptic membrane. When the receptor is activated, C instantaneously changes from zero to 1 mM and remains there for 1 ms (AMPA, NMDA, GABAa) or 84 ms (GABAb). The postsynaptic current in the compartments receiving inhibitory stimulation-induced trans-synaptic inputs is given by
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,b).
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RESULTS |
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Electrophysiological properties of the thalamocortical relay neuron model
The firing properties of the model were compared with the electrophysiological properties of thalamic neurons measured in vitro (Emri et al. 2000; Jahnsen and Llinas 1984; Pape and McCormick 1995) (Fig. 3). The neuron model had a resting membrane potential of –70 mV, and an input resistance of 54 M as recorded in the soma. The model reproduced experimentally recorded membrane potential–dependent firing properties. A constant current stimulus injected in the soma elicited a passive response, burst response, or tonic firing depending on the membrane potential of the soma (Fig. 3A) (Jahnsen and Llinas 1984). The model exhibited rebound excitation from a hyperpolarizing stimulus that corresponded to experimental data. As the amplitude of the hyperpolarization was increased the degree of inward rectification increased and after release from the hyperpolarization bursts of action potentials were generated (Fig. 3B) (Pape and McCormick 1995). Constant current injection in the soma generated a firing frequency that matched well with experimental measurements (Fig. 3C) (Pape and McCormick 1995). In addition, decreasing the Na+ leakage conductance, increasing the T-type Ca2+ conductance, and shifting the voltage dependency of Ih resulted in a model that exhibited an intrinsic delta oscillation that corresponded to experimental bursting patterns (Fig. 3D) (Emri et al. 2000). Thus the model was able to replicate a wide range of experimentally documented excitation properties of thalamic neurons.
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The potentials generated by the DBS electrode model were applied to the TC relay neuron to determine the effects of extracellular stimulation. The application of extracellular electric fields results in regions of both depolarization and hyperpolarization in the same neuron (McIntyre and Grill 1999; Rattay 1999). The spatial distribution of polarization is dependent on the second derivative of extracellular potential along each neuronal process, and thus the position of the neuron with respect to the electrode affects its polarization. Figure 4 shows an example of the response of the TC relay neuron with its cell body located 1.5 mm from the geometric center of the stimulating contact and its axon oriented parallel to the electrode shaft. The cell body and dendritic arbor exhibited a complex pattern of depolarization and hyperpolarzation during the stimulus pulse, but the axonal elements near the cell body were all depolarized by the stimulus (Fig. 4). In this example, and in every neuron orientation we examined, action potential initiation took place in the axon.
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). Therefore we examined the response of the TC relay neuron to HFS. Intracellular stimulation applied in the cell body generated action potentials in the cell body that were transmitted down the axon in a 1:1 ratio with the stimulus frequency (Fig. 5). However, extracellular DBS of the neuron in Fig. 4 resulted in independent firing of the cell body and axon at high stimulation frequencies. As with intracellular stimulation, the axon responded one to one with the stimulus frequency, but the cell body was unable to follow high stimulus frequencies (Fig. 5). This decoupling of somatic firing and axonal firing was achieved without stimulation-induced transsynaptic inputs.
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; Dostrovsky et al. 2000; Gustafsson and Jankowska 1976; Jankowska et al. 1975; McIntyre and Grill 2002). Therefore a large number of synaptic inputs impinging on local cells will be activated by DBS, and can thus alter the firing of local cells during DBS. We determined the effect of stimulation-induced trans-synaptic activity on the TC relay neuron with a distribution of AMPA, NMDA, GABAa, and GABAb synaptic conductances on the dendrites and cell body (see METHODS). Figure 6 shows the influence of stimulation-induced trans-synaptic inputs on the efferent output of the TC neuron. The threshold to drive the efferent output of the neuron at the stimulus frequency decreased with increasing stimulus frequency, and this relationship was unaffected by the presence or absence of trans-synaptic inputs (also see Fig. 8C, below). In modeling the stimulation-induced trans-synaptic inputs the goal was not to reproduce a specific type of input to TC relay neurons but to simulate the effect of strong synaptic action generated during DBS as a result of simultaneous activation of large numbers of presynaptic terminals. We conducted a sensitivity analysis by examining the threshold of the TC relay neuron as a function of stimulus frequency after doubling or halving each of the synaptic conductance values (Fig. 6). In general, increasing or decreasing the individual synaptic conductances had limited effects on threshold. Most of the synaptic input parameter sets (including default) were unable to generate action potentials solely from the applied synaptic inputs because of the balance between the excitatory and inhibitory postsynaptic currents. However, in the cases of 2 gAMPA or 0.5 gGABAa the balance was shifted toward excitation and the stimulation-induced trans-synaptic inputs were sufficient to generate efferent output at the stimulus frequency, independent of the applied field. These 2 cases were not plotted in Fig. 6 because the threshold stimulus amplitude was not determined by application of the extracellular electric field to the TC relay neuron, but instead by the activation of axon terminals projecting to the TC relay neuron. Thus with weak GABAa and/or strong AMPA conductances the threshold to drive the efferent output of the TC relay neuron would be determined by the threshold for activation of afferent inputs.
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). Driving the TC relay neuron at the stimulus frequency resulted in a chronaxie of 0.21 ms with stimulation-induced trans-synaptic inputs and 0.19 ms without them. These chronaxies were substantially shorter than the single pulse intracellular chronaxie of 6.3 ms, but slightly longer than chronaxies determined for tremor reduction during thalamic DBS (0.05–0.1 ms) (Holsheimer et al. 2000b).
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High-frequency efferent output generated by extracellular stimulation was characterized by limited somatic firing during the stimulus train. Figure 8C shows the firing frequency recorded in the cell body and axon as a function of cell body location during a 150-Hz train of –3 V, 0.1 ms stimuli (axons parallel to the electrode shaft). Stimulation with these clinically effective parameters resulted in efferent output at the stimulus frequency in neurons 
2.25 mm from the electrode but the soma either fired at a much lower frequency or not at all. This decoupling between the firing of the axon and cell body during DBS was independent of the presence or absence of stimulation-induced trans-synaptic inputs (Fig. 8C).
Extracellular stimulation of thalamic neurons: effects on firing neurons
The above results were from model neurons stimulated from rest (i.e., there was no activity in the neurons before the stimulus train was applied). However, thalamic neurons are often active in vivo. We examined the effects of DBS on intrinsically active neurons, firing in either a tonic or burst mode. Tonic activity was generated in the TC relay neuron by increasing the Na+ leakage conductance such that the model generated intrinsic 33-Hz output (Fig. 8). Bursting activity was generated in the TC relay neuron by decreasing the Na+ leakage conductance, increasing the T-type Ca2+ conductance, and shifting the voltage dependency of Ih such that the model generated intrinsic delta oscillations (Figs. 3D and 10).
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650 ms), followed by a return to 33-Hz firing (Fig. 9A).
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; Dostrovsky et al. 2002) (Fig. 9B). The origin of the transient quiescence after termination of the stimulation train has not been previously addressed, but our results indicate that it is the result of activation of GABAb receptors. The GABAb conductance was the only component of our model that could generate and/or modulate the transient quiescence in a manner that matched the available experimental data. Decreasing or removing the GABAb conductance decreased or eliminated the transient quiescence in a manner that was dependent on the stimulation frequency and train duration. Similarly, experimental recordings showed that increasing the duration and frequency of the stimulus train enhances the duration of the transient quiescence (Dostrovsky et al. 2002). Therefore our results predict that application of GABAb antagonists would abolish the transient quiescence observed after HFS of thalamic neurons. Figure 10 shows the activity of the cell body and axon of TC relay neurons firing in a burst mode before, during, and after a 500-ms train of –3-V, 0.1-ms stimuli at 150 Hz. The stimulus was suprathreshold for direct activation of the neuron 1.5 mm from the electrode and its axon fired in a 1:1 ratio with the stimulus train. The soma exhibited a stimulation-induced burst followed by tonic depolarization and a complete suppression of any subsequent burst activity. The stimulus was subthreshold for direct generation of efferent output in the neuron positioned further from the electrode (2 mm), but stimulation-induced trans-synaptic effects still suppressed the delta oscillation. This neuron exhibited a burst at the onset of the stimulus train followed by tonic depolarization and suppression of activity during the stimulus train in both the cell body and axon. The quiescence generated in bursting cells after HFS was the result of a transition in the operating mode of the cell induced by the stimulation. In dynamical terms, the rhythmic bursting activity of the TC relay neuron was generated by a stable limit cycle determined by the interplay between the hyperpolarization-activated cation current, T-type calcium current, and the potassium leakage current. Application of short-duration trains (10–200 ms) of high-frequency stimuli could disrupt the phase relation of the burst cycle, but did not transform the operating mode of the cell. Application of prolonged stimulus trains (>400 ms) completely disrupted the limit cycle and pushed the neural dynamics into a fixed point or stable resting point. The system would remain in the fixed point until a strong perturbation reintroduced the oscillatory activity.
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DISCUSSION |
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Model limitations
The results obtained with our model of thalamic DBS provide insights difficult to achieve experimentally; however, both the electrode and neuron models have important limitations that should be noted. One limitation of our electrode model is that we assumed the tissue medium was isotropic. Although this may be a valid approximation within the thalamus, the anatomical structures surrounding the thalamus, such as the internal capsule, are highly anisotropic. The anisotropic nature of the tissue surrounding the stimulated nucleus can affect the shape of the electric field and in turn neural polarization (Grill 1999). However, our previous experience with stimulation in a gray matter region surrounded by white matter fiber tracks suggests that the influence of the anisotropy is a secondary concern (McIntyre and Grill 2002).
The multi-compartment TC relay neuron model accurately captured dynamic firing properties recorded experimentally, but limitations in the model arise from our limited knowledge of the ion channel distribution of the TC relay neuron dendritic arbor (Antal et al. 2001; Emri et al. 2000; Williams and Stuart 2000). However, the results of this and previous work addressing the biophysics of extracellular stimulation of CNS neurons suggest that the neural output that results from the stimulation is primarily dependent on the myelinated axon of the neuron (McIntyre and Grill 1999; Rattay 1999). The myelinated axon model used in this study consisted of a detailed representation of the fiber morphology and ion channel distribution and was able to capture nearly every experimentally recorded firing property of myelinated axons (McIntyre et al. 2002).
Another limitation of our model was the lack of inclusion of activity-dependent changes in synaptic efficacy such as short- and long-term potentiation and/or depression. In addition, the afferent axons and terminals presynaptic to the TC relay neuron were not explicitly defined in the model. We acknowledge that these limitations in our stimulation-induced trans-synaptic inputs could play important roles in determining the transsynaptic effects of DBS. However, our sensitivity analysis of the role of individual synaptic conductances on neural output shows that doubling or halving the conductances resulted in <10% changes in threshold as a function of stimulus frequency (Fig. 6). Moreover, inclusion of trans-synaptic effects in our model did not strongly influence any of the results of this study (Figs. 6, 7, 8). Therefore we expect activity-dependent changes in the efficacy of synaptic inputs to have a minimal impact on the effects of thalamic DBS on TC relay neurons. However, activity-dependent changes in synaptic efficacy could have important consequences on the downstream effects mediated by high-frequency activation of efferent axons (Urbano et al. 2002; Wang and Kaczmarek 1998; Zucker and Regehr 2002).
Our model also ignored K+ accumulation in the extracellular space surrounding the neural structure. When neurons fire at high frequencies for extended periods of time they (and/or the surrounding glia) can release large amounts of K+ into the extracellular space, resulting in changes in osmolarity and excitability (Bikson et al. 2001; Lian et al. 2003). Increases in the extracellular K+ concentration ([K+]o) can result in depolarization block where the membrane becomes so depolarized that Na+ channels become inactivated (Hille 2001). The magnitude and time course of the changes in [K+]o that occur during DBS are presently unknown, and we did not attempt to model these phenomena. Therefore because of the lack of inclusion of activity-dependent changes in synaptic efficacy and K+ accumulation in the extracellular space our model is unable to predict accurately the long-term effects of DBS.
Activation and suppression of neuronal activity by DBS
Our results predict that thalamic DBS results in regions of both activation and suppression of efferent output. These results match well with experimental recordings from both the stimulated nucleus and nuclei receiving the efferent output during DBS. Single-unit recordings in the thalamus and basal ganglia consistently reveal a suppression of activity within the stimulated nucleus during HFS (Boraud et al. 1996; Dostrovsky and Lozano 2002; Dostrovsky et al. 2000). However, activity recorded in projection nuclei suggests that there is increased input from the stimulated nucleus during HFS (Anderson et al. 2003; Hashimoto et al. 2003; Maurice et al. 2003; Windels et al. 2000, 2003). These experimental results seem to be contradictory, although the results of our study match both of these findings. Recordings from the cell body of our model showed suppression of activity during HFS, but activity recorded in the cell body was not representative of the neural output generated in the axon (Figs. 8, 9, 10). Our results predict that the majority of neurons within about 2 mm of the electrode contact will generate efferent output at the stimulus frequency, providing high-frequency inputs to projection nuclei, even though activity in the somas of these neurons is suppressed.
Two fundamental effects of extracellular stimulation support the finding of decoupling of activity in the axon and cell body during HFS: 1) action potential initiation in the axon and 2) stimulation-induced trans-synaptic inputs. The direct effect of an applied electric field on a neuron is related to the second derivative of the extracellular potential distribution along each process (McNeal 1976; Rattay 1986). In turn, each neuron (or neural process) surrounding the electrode will be subject to both depolarizing and hyperpolarizing effects from the stimulation (McIntyre and Grill 1999; Rattay 1999) (Fig. 4). In general, cathodic stimuli generate membrane depolarization in regions near the electrode and membrane hyperpolarization in regions that flank the region of depolarization. However, because of the 3-D branching and termination patterns of the dendritic arbor, soma–dendritic complexes near the electrode exhibit both depolarization and hyperpolarization. The applied field generates depolarization in dendritic processes that terminate closer to the electrode and hyperpolarization in dendritic processes that terminate further from the electrode (Fig. 4). Depending on the neuron's orientation and positioning with respect to the electrode, it is common for the cell body to be directly hyperpolarized by the stimulus pulse. However, the first few nodes of Ranvier are usually depolarized by the stimulus pulse because of the short internodal spacing of the axon compared with the spatial distribution of potentials generated by the macroelectrode (Fig. 4). In turn, action potential initiation occurs in the axon (McIntyre and Grill 1999, 2002; Nowak and Bullier 1998a,b).
The second effect of extracellular stimulation that supports the decoupling of activity in the axon and cell body during HFS is the activation of trans-synaptic inputs. The threshold for extracellular stimulation of axonal terminals projecting to the region around the electrode is lower than the threshold for direct activation of local cells (Baldissera et al. 1972; Dostrovsky et al. 2000; Gustafsson and Jankowska 1976; Jankowska et al. 1975). The stimulation-induced trans-synaptic effects generated in postsynaptic neurons by the stimulation can affect their response to trains of extracellular stimuli. The relative distribution of excitatory and inhibitory synaptic inputs on the soma–dendritic membrane of TC relay neurons (and neurons in general) provides for a concentration of inhibitory inputs on the soma and proximal dendrites (Sato et al. 1997) (Fig. 6). Summation of an overall inhibitory synaptic effect on the cell body during high-frequency extracellular stimulation can aid in the generation of independent firing of the axon and cell body (Fig. 8).
Trans-synaptic effects applied to TC relay neurons subthreshold for direct excitation by DBS did reduce the activity of intrinsically active model neurons (Figs. 9 and 10). However, synaptic inputs did not dramatically alter the output of neurons during DBS with stimuli suprathreshold for direct excitation (Figs. 6, 7, 8). This result was robust to large changes in the synaptic conductance values (Fig. 6) because action potential initiation always occurred in the axon (Fig. 4). The change in excitability of the cell body and dendrites from the synaptic inputs had limited impact on the axon and, as a result, the output from suprathreshold stimuli was relatively unaffected by the synaptic influences.
Implications for understanding the therapeutic mechanisms of DBS
Presently, there are 4 general hypotheses to explain the therapeutic mechanism(s) of DBS: 1) stimulation-induced alterations in voltage-gated currents that block neural output near the stimulating electrode (Depolarization Blockade) (Beurrier et al. 2001); 2) stimulation-induced trans-synaptic inhibition of neurons near the stimulating electrode (Synaptic Inhibition) (Dostrovsky et al. 2000); 3) synaptic transmission failure of the efferent output of stimulated neurons as a result of transmitter depletion (Synaptic Depression) (Urbano et al. 2002); 4) stimulation-induced modulation of pathological network activity (Hashimoto et al. 2003; Montgomery and Baker 2000).
Depolarization blockade and synaptic inhibition represent two of the earliest hypotheses to explain the similarity between the therapeutic benefit of ablation and DBS for the treatment of movement disorders. Both of these effects are supported by recordings of somatic activity in the stimulated nucleus from several different types of experimental preparations (in vitro and in vivo, humans and animals) (Benazzouz et al. 1995, 2000; Beurrier et al. 2001; Bikson et al. 2001; Boraud et al. 1996; Dostrovsky et al. 2000; Kiss et al. 2002; Lian et al. 2003). However, our results suggest the limitation of these hypotheses is that they do not take into account the possible independent activation of the efferent axon. The axon plays a critical role in the activation of neurons by extracellular stimulation, and the response of the cell body does not necessarily reflect the output of the axon (Figs. 8, 9, 10). Therefore although synaptic inhibition and/or depolarization blockade may occur in the cell body, the suppression of somatic activity will have limited impact on the output of neurons whose axons are directly excited by DBS.
How then can stimulation that results in efferent output of neurons around the electrode mimic the therapeutic effects of ablation? One possibility is that neurons activated by the stimulus train are unable to sustain high-frequency action on efferent targets because of depletion of neurotransmitter (Urbano et al. 2002; Wang and Kaczmarek 1998; Zucker and Regehr 2002). However, several in vivo experimental studies have shown increases in transmitter release and sustained changes in firing of neurons in efferent nuclei consistent with activation of neurons around the electrode and subsequent synaptic action on their target during HFS (Anderson et al. 2003; Hashimoto et al. 2003; Windels et al. 2000, 2003). Therefore the only general hypothesis on the mechanisms of DBS that is consistent with all of the available data on the effects of DBS (including the results of this study) is stimulation-induced modulation of pathological network activity. However, it should be noted that, although DBS may override pathological activity patterns, the activity patterns induced by DBS are not normal. Therefore it remains an open question to link the cellular effects of DBS with explicit therapeutic mechanisms.
The control of tremor with DBS may be explained by blocking low-frequency oscillations. Tremor is most likely generated by increased neuronal synchronization and low-frequency rhythmic oscillation within the basal ganglia and thalamus (Bergman et al. 1998; Deuschl et al. 2001). Our results suggest that DBS masks the underlying activity of neurons surrounding the electrode, independent of their original mode of operation: rest (Figs. 6, 7, 9), tonically active (Fig. 9), or bursting (Fig. 10). This masking can result from either stimulation-induced trans-synaptic suppression of activity or efferent firing time-locked to the stimulus frequency. In either case the firing patterns of neurons directly affected by DBS are no longer regulated by their network interactions, but instead by the constant and unchanging stimulation. Therefore we propose that, independent of their response to DBS, neurons directly affected by DBS represent a barrier for the transmission of synchronized low-frequency oscillations throughout the network.
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APPENDIX |
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) is given by
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) and Huguenard and McCormick (1992). The models were implemented in NEURON v5.3 (Hines and Carnevale 1997) using a time step of 0.01 ms and a temperature of 36°C. Individuals interested in reproducing the results of this study or using these models in their own work are encouraged to contact us for the appropriate NEURON files and instruction on their use. Times are in ms, voltages are in mV, concentrations are in mM, and currents are in mA/cm2. Soma and dendrite T-type Ca+ current
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Soma and dendrite hyperpolarization activated cation current
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Soma, dendrite, and initial-segment fast Na+ current
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Soma, dendrite, and initial-segment delayed rectifier K+ current
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Soma, dendrite, and initial-segment slow K+ current
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Nodal fast Na+ current
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Nodal persistent Na+ current
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Nodal slow K+ current
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Juxtaparanodal (FLUT) fast K+ current
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ACKNOWLEDGMENTS |
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GRANTS
This work was supported by National Institute of Neurological Disorders and Stroke Grants NS-40894 and NS-35528 and a postdoctoral fellowship supported by the Whitaker Foundation.
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FOOTNOTES |
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Address for reprint requests and other correspondence: C. C. McIntyre, Cleveland Clinic Foundation, Department of Biomedical Engineering, 9500 Euclid Avenue, ND20, Cleveland, OH 44195 (E-mail: mcintyre{at}bme.ri.ccf.org).
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