Modelling of vertical nano-needles as sensing devices for neuronal signal recordings

Abstract

A design-oriented numerical study of vertical Si-nanowires to be used as sensing elements for the detection of the intracellular electrical activity of neurons. An equivalent lumped-element circuit model is derived and validated by comparison with physics-based numerical simulations. Most of the component values can be identified individually by geometrical and physical considerations. The transfer function and the SNR of the sensor in presence of thermal noise are derived, and the impact of the device geometry is shown.

Multiscale simulation analysis of passive and active micro/nanoelectrodes for CMOS-based in vitro neural sensing devices

“…the ones that are not directly part of the sensing elements and thus are not included in the FEM domain, are modelled by an equivalent circuit. Our previous work [58] suggests that an RC (i.e. resistors and capacitors) circuit representation with few lumped elements, neglecting the distributed nature of these domains, is adequate if clefts are sufficiently conductive.…”

“…In particular, the time-invariant HH model with compartmentalization has been used in [18,60], and in [19] in its transmembrane current-sources version; the model for the neuron-electrode junction is consistent with [17,29]. Concerning the value of the circuit components used in the models: R njm is taken from the experiments in [66], later confirmed by [39]; R njseal has been taken from [19] that slightly modified the value from the experiments in [66]; R jseal is computed as the disk resistance given the cleft thickness, and the hole and rim ring radii according to eqn (11) in [18]; C njm , C nm , C m are the capacitances obtained by scaling the value C m = 2.2 pF [19] according to the relative area of the different portions of the membrane based on the geometry of the system; C nano is computed according to the third expression in table 2 of [58], where the area is given by eqn (7) of [18] possibly adding the contribution of the cap for mushroom-shaped sensors; R nano is computed according to eqn (8) in [18] with or without the mushroom cap, as appropriate; C pad is computed according to the fourth formula in table 2 of [58]; R stray and C stray have been computed according to the last two expressions in table 2 of [58], employing the formulae for parallel plate capacitor and barrel resistor using realistic values for the geometry of the interconnects; R amp and C amp are the input resistance and capacitance of a typical OpAmp (taken from [19]); the g m of the active sensor is taken from [67] and refers to a realistic advanced 28 nm CMOS node. C njm , C nano and R nano have been also verified by means of TCAD simulations (as we will see later in §4b).…”

“…At first order, pristine cellular membranes can be described as a lossless insulating layer [58] with a relative permittivity and a capacitance equal to those of the biological neuronal membrane (εr,memb≈11, Cm≈1 μF cm−2, respectively [59]). To model the electrogenic functions of the biological neuron, we proceed as follows.…”

“…Alternatively (figure 2 b ), an independent voltage generator can be used, imposing the same AP waveform Vmfalse(tfalse) of the HH model (which accounts for the −70 mV physiological rest membrane potential) as an external boundary condition between the compartment contacts. This simple approach is adequate only when simulating intracellular sensing [58], as further discussed in the description of figure 4. Yet another possibility, figure 2 c , is to use an independent transmembrane current generator, Im, imposing the same total current flowing through the HH model’s membrane capacitance, Cm, in figure 2 a .…”

“…, f pn are the zero and pole frequencies, respectively. Following similar steps as in [58], we used open and short circuit time constants analysis [68] to determine approximate analytical formulae for the poles, zeros and in-band gain of the H(f ) (table 3) as a function of the lumped element parameter values reported in electronic supplementary material, table A1; the availability of free-distribution codes (e.g. SCAM [69]) could yield exact analytical expressions given the circuit topology.…”