Fig. 5: A cortical network model predicts distinct response thresholds for TUS and hTUS.

a, Schematic description of the sCNM, illustrating the network architecture (left) and the point-neuron electrical circuit at each network node (right), where the transmembrane potential (V_m = V_in − V_out, where V_in and V_out refer to intracellular and extracellular voltages, respectively) across the membrane capacitor (capacitance C_m) is regulated by a set of ionic currents each associated with a specific conductance (g) and reversal potential (E). b, Time course of model internal variables upon application of a 150-ms-long 1.9 MPa TUS stimulus. From top to bottom: peak pressure amplitude (P), local temperature (T) and conductance of thermally activated potassium current (g_KT). c, Left: time course of local transmembrane voltage in an isolated network node induced by a 150-ms-long TUS stimulus at 0.9 (top) and 1.1 (bottom) times the threshold activation pressure (P_thr); fast membrane potential fluctuations were driven by a Gaussian-noise current with an amplitude of 2 μA cm⁻²; the grey area marks the stimulation window. Middle: time course of transmembrane currents (bounded to ±1.2 μA cm⁻²) for the same stimuli, including the TUS-induced depolarizing current (I_TUS), spike generation currents (I_Na and I_Kd) and excitability modulation currents (I_KT, I_M and I_Leak); by convention, negative currents are depolarizing, while positive currents are hyperpolarizing. Right: breakdown of the cumulative charge injected by depolarizing currents (q⁺, that is, I_TUS) and hyperpolarizing currents (q⁻, that is, I_KT, I_M and I_Leak) during the first and second halves of the stimulation window (referred to as ‘early’ and ‘late’ phases, respectively), illustrating the increased influence of excitability modulation currents as the stimulus progresses. Spike-generating currents were voluntarily omitted to specifically examine changes in nodal excitability. d, Time course of transmembrane voltages (in black) and synaptic currents (I_AMPA, in brown) in two representative nodes of a fully connected three-node network, upon application of a 150 ms stimulus at 1.1 times the threshold activation pressure, either to a single network node (top, conventional TUS) or to all three network nodes (bottom, hTUS). e, Breakdown of the cumulative charge injected by depolarizing currents (q⁺, that is, I_TUS and I_AMPA) and by hyperpolarizing currents (q⁻, that is, I_KT, I_M and I_Leak) during the stimulus window for the same representative nodes, illustrating the role of the excitatory synaptic current (I_AMPA) in maintaining a depolarized state enabling sustained firing in the hTUS case. f, Number of evoked spikes in sonicated nodes as a function of peak pressure amplitude, for both TUS (red) and hTUS (blue) 150 ms stimulation. Traces and shaded areas denote the mean ± s.e.m. of 50 simulations where membrane potential fluctuations were driven by a Gaussian-noise current. The dashed horizontal line denotes a theoretical fluorescence detection threshold. Currents nomenclature is as follows: Na, sodium; Kd, delayed rectifier potassium; M, slow non-inactivating potassium; KT, thermally activated potassium; AMPA, AMPA receptor post-synaptic current; Leak, non-specific leakage.