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Relative contributions of local cell and passing fiber activation and silencing to changes in thalamic fidelity during deep brain stimulation and lesioning: a computational modeling study

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Abstract

Deep brain stimulation (DBS) and lesioning are two surgical techniques used in the treatment of advanced Parkinson’s disease (PD) in patients whose symptoms are not well controlled by drugs, or who experience dyskinesias as a side effect of medications. Although these treatments have been widely practiced, the mechanisms behind DBS and lesioning are still not well understood. The subthalamic nucleus (STN) and globus pallidus pars interna (GPi) are two common targets for both DBS and lesioning. Previous studies have indicated that DBS not only affects local cells within the target, but also passing axons within neighboring regions. Using a computational model of the basal ganglia-thalamic network, we studied the relative contributions of activation and silencing of local cells (LCs) and fibers of passage (FOPs) to changes in the accuracy of information transmission through the thalamus (thalamic fidelity), which is correlated with the effectiveness of DBS. Activation of both LCs and FOPs during STN and GPi-DBS were beneficial to the outcome of stimulation. During STN and GPi lesioning, effects of silencing LCs and FOPs were different between the two types of lesioning. For STN lesioning, silencing GPi FOPs mainly contributed to its effectiveness, while silencing only STN LCs did not improve thalamic fidelity. In contrast, silencing both GPi LCs and GPe FOPs during GPi lesioning contributed to improvements in thalamic fidelity. Thus, two distinct mechanisms produced comparable improvements in thalamic function: driving the output of the basal ganglia to produce tonic inhibition and silencing the output of the basal ganglia to produce tonic disinhibition. These results show the importance of considering effects of activating or silencing fibers passing close to the nucleus when deciding upon a target location for DBS or lesioning.

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Correspondence to Warren M. Grill.

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Action Editor: Gaute T. Einevoll

This work was supported in part by a grant from the US National Institutes of Health (NIH R01 NS040894) and in part by Singapore A*STAR BS-PhD National Science Scholarship.

Appendix A

Appendix A

Here we describe the equations and parameters used for each cell type and for the synaptic connections. All potentials have the unit of mV, conductances have the unit of mS/cm2, currents have unit of uA/cm2, and time constants have unit of msec. For all cell models the membrane capacitance is 1 uF/cm2.

Membrane potentials (v) of the TH cells were governed by the equations:

$$ \begin{array}{*{20}{c}} {{C_m}{v^{\prime}} = - {I_L} - {I_{{Na}}} - {I_K} - {I_T} - {I_{{GPi \to Th}}} + {I_{{SMC}}}} \\ {{h^{{\prime}}} = \left[ {{h_{\infty }}(v) - h} \right]/{\tau_h}(v)} \\ {{r^{{\prime}}} = \left[ {{r_{\infty }}(v) - r} \right]/{\tau_r}(v)} \\ \end{array} $$
Table 1 TH cell model equations and parameters

Membrane potentials (v) of the STN cells were governed by the equations:

$$ \begin{array}{*{20}{c}} {{C_m}{v^{\prime}} = - {I_L} - {I_{{Na}}} - {I_K} - {I_T} - {I_{{Ca}}} - {I_{{ahp}}} - {I_{{GPe \to STN}}} + {I_{{app}}} + {I_{{dbs}}}} \\ {{h^{{\prime}}} = 0.75\left[ {{h_{\infty }}(v) - h} \right]/{\tau_h}(v)} \\ {{n^{{\prime}}} = 0.75\left[ {{n_{\infty }}(v) - n} \right]/{\tau_n}(v)} \\ {{r^{{\prime}}} = 0.2\left[ {{r_{\infty }}(v) - r} \right]/{\tau_r}(v)} \\ {{c^{{\prime}}} = 0.08\left[ {{c_{\infty }}(v) - c} \right]/{\tau_c}(v)} \\ {C{A^{{\prime}}} = 3.75 \times {{10}^{{ - 5}}}\left( { - {I_{{Ca}}} - {I_T} - 22.5 \times CA} \right)} \\ \end{array} $$
Table 2 STN cell model equations and parameters

GPe and GPi cells were modeled similarly. Membrane potentials (v) of the GP cells were governed by the equations:

$$ \begin{array}{*{20}{c}} {{C_m}{v^{\prime}} = - {I_L} - {I_{{Na}}} - {I_K} - {I_T} - {I_{{Ca}}} - {I_{{ahp}}} - {I_{{STN \to GP}}} + {I_{{GPe \to GPe/GPi}}} + {I_{{app}}} + {I_{{dbs}}}} \\ {{h^{{\prime}}} = 0.75\left[ {{h_{\infty }}(v) - h} \right]/{\tau_h}(v)} \\ {{n^{{\prime}}} = 0.75\left[ {{n_{\infty }}(v) - n} \right]/{\tau_n}(v)} \\ {{r^{{\prime}}} = 0.2\left[ {{r_{\infty }}(v) - r} \right]/30} \\ {C{A^{{\prime}}} = 1 \times {{10}^{{ - 4}}}\left( { - {I_{{Ca}}} - {I_T} - 15 \times CA} \right)} \\ \end{array} $$
Table 3 GP cell model equations and parameters
Table 4 Parameters for synapses
Table 5 Applied currents to basal ganglia under healthy and parkinsonian conditions
Table 6 Differences between original Rubin and Terman Model and modified basal ganglia model

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So, R.Q., Kent, A.R. & Grill, W.M. Relative contributions of local cell and passing fiber activation and silencing to changes in thalamic fidelity during deep brain stimulation and lesioning: a computational modeling study. J Comput Neurosci 32, 499–519 (2012). https://doi.org/10.1007/s10827-011-0366-4

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