Fig 1.
Descending volleys of spinal waves provide a window into motor cortical responses to TMS.
A) TMS coil with electric field (E) induced in the posterior–anterior (P–A) orientation over the motor cortex. L5 PTNs send axons into the spinal cord (corticospinal tract), and their activity is recorded epidurally at levels C1–C5. B) Epidural recordings of corticospinal waves in two human subjects. Individual trials are plotted with colored lines. The solid black lines are trial averages.
Fig 2.
High level diagram of methodology.
A network model was defined, and particle swarm optimization was used to constrain parameters using experimental data. A TVAT sensitivity analysis was conducted on the optimized model, and finally the network graph was used to identify structural patterns that predict the sensitivity analysis. E: Excitatory neuron. I: Inhibitory neuron.
Fig 3.
Overview of motor cortical macrocolumn model.
A) Block diagram of cortical connectivity. Arrowheads denote excitatory connections mediated by AMPA and NMDA receptors. Round heads denote inhibitory connections mediated by GABAA and GABAB receptors. B) Three-dimensional representation of neuron locations. (Left) Side view showing laminar distribution. (Right) Top view depicting microcolumn organization within macrocolumn. IT: Intratelencephalic neuron. PTN: Pyramidal tract neuron. BC: Basket cell.
Fig 4.
Optimization results and unified model.
A) Simulated epidural corticospinal activity for the optimized model (dashed colored lines) compared to experimental data (solid black line). The same underlying cortical model parameters were used for the D+ response (left) and D- response (right) except for the TMS activation parameters which activated different proportions of the cell populations to produce each response. B) Spike raster plots for all motor cortical neuron types. A band-pass filter was applied to the activity of the Layer 5 PTN (orange) to represent the corticospinal responses shown in A. C) Distribution of relative errors across corticospinal wave objectives. Average error is plotted on the right side.
Fig 5.
TVAT effect sizes and their relative contributions across corticospinal waves.
A) Rank sorted total effect sizes across all waves are shown. Only the 20 largest effect sizes are shown for legibility; the full results are shown in Fig F in S1 Appendix. The y-axis uses a log-scale. B) Relative effect sizes normalized across all waves by parameter. A and B share the same x-axis. Parameter names were shortened and hyphenated such that the label before the hyphen corresponds to the presynaptic source and the label after the hyphen corresponds to the postsynaptic target, e.g. TMS-L6 BC indicates the activation of L6 basket cells via TMS and L2/3 BC-L5 PTN indicates the projection of L2/3 basket cells to L5 pyramidal tract neurons. IT: Intratelencephalic neuron. PTN: Pyramidal tract neuron. BC: Basket cell. AFF: Afferent.
Fig 6.
Sensitivity was computed as the average effect size for a specific corticospinal wave across all relevant mechanisms. A) Sensitivity was divided based on activation vs the synaptic strengths of the network. B) Sensitivity to activation was divided into feedforward activation, i.e., activation of extracortical afferent terminals, and feedback activation, i.e., activation of the motor cortical circuit. C) Sensitivity to the synaptic strengths was divided into the feedforward circuit, i.e., the synaptic strengths of extracortical afferents, vs the feedback circuit, i.e., the synaptic strengths of intracortical projections. D) Sensitivity was divided into elements that were excitatory vs inhibitory. E) Feedforward activation was divided into feedforward excitation, i.e., afferents targeting excitatory neurons, vs feedforward inhibition, i.e., afferents targeting inhibitory neurons. F) The synaptic strengths were divided into synaptic strengths of afferents targeting excitatory neurons vs synaptic strengths of afferents targeting inhibitory neurons. G) Feedback activation was divided into feedback excitation, i.e., activation of excitatory motor cortical neurons, vs feedback inhibition, i.e., activation of inhibitory motor cortical neurons. H) The synaptic strengths were divided into the strengths of excitatory intracortical projections vs inhibitory intracortical projections. Note the differences in y-axis values.
Fig 7.
Effect sizes for parameters that preferentially affected a single I-wave.
For each corticospinal wave, effect sizes for parameters that preferentially affected the wave were normalized and rank sorted and visualized as bar plots. Examples of traces that demonstrate the preferential effects of the identified activations are shown. The solid black line represents responses for which the parameter was set to zero. The difference in the amplitude of the wave across the colored and black lines indicates that the parameter was important to the generation of that wave. The waves are labelled in the plots. Please note the difference in x-axis limits across the bar plots. IT: Intratelencephalic neuron. PTN: Pyramidal tract neuron. BC: Basket cell. AFF: Afferent.
Fig 8.
Classification of network features for effect size types.
A) Recursive feature elimination was conducted to identify feature pairs that could predict preferential activation of corticospinal waves. Higher probabilities of remaining after elimination indicated better classification accuracy. Only a partial number of pairs are shown for legibility. B) Logistic regression decision boundary for preferential parameters (light) versus non-preferential parameters (dark) using the best classification features identified in A. Dark filled dots indicate data that were preferential, and light filled dots indicate data that were not preferential. C) Recursive feature elimination to identify features that predict corticospinal wave preference for preferential parameters. Only 10 features are shown for legibility. D) Corticospinal wave probabilities obtained by support vector classification using the single best classification feature from C. The dashed lines represent the conduction delays of the data being classified.
Fig 9.
Histogram of number of waves for which L5 PTNs contributed a spike.
For each stimulus presentation, the spikes generated by each L5 PTN were divided based on the time windows for each corticospinal wave, and the total number of time windows during which spiking occurred was counted.
Table 1.
Total numbers of neurons in model.
Fig 10.
Analysis to select a time-step that both minimizes computation time and is numerically stable.
Each scatter-line plots shows the mean of a metric as a function of the time-step size in the log10 scale. At the bottom, the membrane potentials of the neuron model for different time-steps are shown. Offsets were added for the y-axis to allow all lines to be distinctly seen. The plots depict a key behavior that differentiates simulations at larger time steps. A pronounced afterhyperpolarization is seen with a 0.2 ms time-step that is absent from other time-steps. Additionally, spikes are generated at larger time-steps (0.1 and 0.2 ms) that are absent for smaller time-steps. These dynamics contribute to the larger numbers of spikes, lower mean ISIs, larger NRMSE, and larger spike distance observed for larger time-steps.
Fig 11.
Change in particle swarm optimization weights across successive iterations.
For approximately 100 iterations, optimization is exploratory with large cognitive, inertial, and gain weights before favoring convergence with high social weights for the final 150 iterations.
Table 2.
Sigmoid function constants underlying evolution of optimization hyperparameters.
Table 3.
List of Optimization Objectives.
Table 4.
Categories of optimized parameters.
Fig 12.
The unified model was selected by interpolating between the parameters of the subject-specific D+ and D- models. The cost function for selecting the unified model was the average of total error across both subject-specific models and the absolute difference in errors between both models.
Table 5.
Description of graph metrics used to characterize the network.