Inferring Deep Brain Stimulation Induced Short-term Synaptic Plasticity Using Novel Dual Optimization Algorithm

Abstract

Experimental evidence in both human and animal studies demonstrated that deep brain stimulation (DBS) can induce short-term synaptic plasticity (STP) in the stimulated nucleus. Given that DBS-induced STP may be connected to the therapeutic effects of DBS, we sought to develop an appropriate computational predictive model that infers the dynamics of STP in response to DBS at different frequencies. Existing methods for estimating STP – either model-based or model-free approaches – require access to pre-synaptic spiking activity. However, in the context of DBS, extracellular stimulation (e.g. DBS) can be used to elicit presynaptic activations directly. We present a model-based approach that integrates multiple individual frequencies of DBS-like electrical stimulation as pre-synaptic spikes and infers parameters of the Tsodyks-Markram (TM) model from post-synaptic currents of the stimulated nucleus. By distinguishing between the steady-state and transient responses of the TM model, we develop a novel dual optimization algorithm that infers the model parameters in two steps. First, the TM model parameters are calculated by integrating multiple frequencies of stimulation to estimate the steady state response of post-synaptic current through a closed-form analytical solution. The results of this step are utilized as the initial values for the second step in which a non-derivative optimization algorithm is used to track the transient response of the post-synaptic potential across different individual frequencies of stimulation. Moreover, we apply our algorithm to empirical data recorded from acute rodent brain slices of the subthalamic nucleus (STN) during DBS-like stimulation to infer dynamics of STP for inhibitory synaptic inputs.

Simulating Short-Term Synaptic Plasticity on SpiNNaker Neuromorphic Hardware

“…Theoretical knowledge of the long-term behaviour of a particular TM synapse also serves as a useful means of validating our implementation on SpiNNaker. We consider the steady-state resource variables u ∞ and R ∞ proposed by Markram et al (1998) and recently revisited in (Ghadimi, Steiner, Popovic, Milosevic, & Lankarany, 2021): from which we derive the peak of the postsynaptic current at steady-state where τ psc denotes the time constant of the postsynaptic exponential kernel which generates I psc,n .…”

“…Theoretical knowledge of the long-term behaviour of a particular TM synapse also serves as a useful means of validating our implementation on SpiNNaker. We consider the steady-state resource variables u ∞ and R ∞ proposed by Markram et al (1998) and recently revisited in (Ghadimi, Steiner, Popovic, Milosevic, & Lankarany, 2021):…”

Model-based closed-loop control of thalamic deep brain stimulation

“…Liu et al (2021) used the control system to suppress the beta oscillations in the cortex, and Fleming et al (2020) suppressed the beta power of LFP in the STN. Although these computational studies included methods for adjusting DBS in a closed-loop manner (Fleming et al, 2020;Grado et al, 2018;Liu et al, 2021), the models used were not validated for replicating/tracking experimental data nor did they incorporate DBS mechanisms of actions, e.g., DBSinduced short-term synaptic plasticity (Milosevic et al, 2021;Tian et al, 2023a;Ghadimi et al, 2022).…”