Deep brain stimulation (DBS) has been demonstrated to be an effective surgical treatment for several movement disorders (e.g., Parkinson’s disease, essential tremor, and dystonia) and appears to be promising for other pathologies, such as epilepsy, pain, major depression, and Alzheimer’s disease. The process for all these diseases is to implant electrodes at different targets to modify the pathological activity in neural circuits by means of electrical stimulation. Microelectrode recording (MER) has long been known to be a reliable technique to identify neural structures [1].

One of these pathologies potentially treatable by DBS is intractable aggressivity, characterized by severe cases of unprovoked aggressive behaviour, usually associated with some degree of mental impairment and gross brain damage [2]. The aetiology can be due to genetic origin, perinatal insults, brain malformation, or posttraumatic, postencephalitic or epileptic seizures and is usually accompanied by self-aggressiveness, hyperkinesia, and destruction of objects. Patients usually need to be institutionalized and managed with major restraint measures. An early successful surgical treatment was posteromedial hypothalamomy [2, 3]. Deep brain stimulation (DBS) of the posteromedial hypothalamus (PMH) has widely replaced ablative procedures because the clinical benefits appear to be similar, but the treatment can be titrated, is reversible, and has a low risk of complications [4, 5, 6, 7].

The human hypothalamus is a complex structure composed of a number of groups of nuclei [8]. The identification of hypothalamic nuclei is particularly important to obtain good functional outcomes with DBS regarding optimizing battery life and decreasing secondary effects, especially considering that very sensitive nuclei related to arousal, circadian rhythms and hormone release are very close.

Most brain regions used for DBS have been described in terms of discharge patterns [9, 10, 11, 12, 13, 14, 15, 16], but less attention has been devoted to the analysis of extracellular action potentials (EAPs), with the exception of the pedunculopontine nucleus [17, 18] in a very limited way and some nuclei in the thalamus [19] and hypothalamus [20].

The hypothalamus is one of the least studied targets for DBS, probably because the pathologies treated with DBS in the hypothalamus have low prevalence. Descriptions of discharge patterns have been recently provided [21]. However, it have been described, for the first time, features of EAPs from the posteromedial hypothalamus (PMH) and adjacent regions [20]. In that work, it was described for the first time a type of cell with a highly anomalous EAP morphology, which was referred to as atypical (i.e., atypical mean action potential or amAP). Notably, amAPs were found mainly in the PMH, with lower concentrations in the regions above or below the PMH.

The morphology of amAPs is not the only electrophysiological feature of this region that is difficult to explain, as amAPs can be indicated by the presence of negative EAPs or the existence of a first phase that precedes the depolarization phase.

In this study, we aimed to analyse the electrophysiological features of amAPs recorded from the hypothalamus in anaesthetized patients. A detailed description of conventional mAPs will be used as a cornerstone for comparisons to amAPs.

Acronyms have been enlisted in Abbreviations.

We analysed traces from 9 consecutive locations spanning 4.0 mm from 7 trajectories. Overall, we analysed 337 units and 67 raw traces. Given that each mAP was composed of 34.8 $\pm$ 10.6 APs, the total number of unitary APs analysed was 11,700.

3.1 Types of Extracellular Action Potentials

Similar to thalamus recordings, in the hypothalamus, most mAPs were characterized by the following features: (i) a higher amplitude positive/negative phase followed by (ii) a phase of the opposite polarity, and (iii) the first phase was shorter and included the dV${}_{\text{max}}$ and dV${}_{\text{min}}$ values, and (iv) the later phase was clearly longer (Fig. 1A,B). The first phase was assumed to be depolarization, while the second was assumed to be repolarization [19]. We also found that most mAPs had an initial small and short phase, prior to depolarization, which was either positive or negative and could be interpreted as postsynaptic potentials, although this has not yet been conclusively demonstrated.

Fig. 1.

Correlations between pairs of variables. (A) V${}_{\text{Dep}}$ vs V${}_{\text{Rep}}$. (B) d${}_{\text{Dep}}$ vs d${}_{\text{Rep}}$. (C) d${}_{\text{Dep}}$ vs V${}_{\text{Dep}}$. (D) V${}_{\text{Rep}}$ vs d${}_{\text{Rep}}$. (E) V${}_{\text{Dep}}$ vs dV${}_{\text{max}}$. (F) $|$V${}_{\text{Dep}}$/V${}_{\text{Rep}}$$|$ vs d${}_{\text{Dep}}$/d${}_{\text{Rep}}$. P1N1 = white dots and black regression lines; V${}_{\text{Dep}}$ and V${}_{\text{Rep}}$ for N1P1, N1N2P1 and P1N1P2 mAPs were multiplied by -1 to preserve coherence with positive cells. N1P1 = empty dots and black lines; P1N1 = black dots and black dashed lines; N1PN2 = red dots and lines; P1P2N1 = blue dots and lines; N1N2P1 = yellow dots and lines; and P1N1P2 = green dots and lines.

We more deeply analysed the structure of the mAPs, defined as the arrangement of the components composing each of the waveforms [20]. Excluding atypical mAPs (amAPs), most of the mAPs were positive, 260/295 (81.1%), and fewer were negative, 25/290 (19.9%). Atypical mAPs were recorded in 42/337 cases (12.5%). Most of these atypical waveforms were positive, but in other cases, the polarity was difficult to identify. Moreover, they presented structures clearly different from the other conventional types. Negative mAPs were recorded simultaneously with positive ones. Usually, the mAP had more than two phases. Only 120/337 (35.6%) mAPs showed 2 phases. On the other hand, a more frequent occurrence was to observe either a small positive or negative deflection before the main component, which resulted in a three-phase structure. In 113/337 (38.3%) cases, an N1P1N2 structure was observed, followed in 106/337 (35.9%) cases with a P1N1 structure, and a P1P2N1 structure in 41/337 (12.2%), an amAP in 42/337 (12.5%), an N1P1 structure in 14/337 (4.7%), an P1N1P2 structure in 12/337 (4.1%), and an N1N2P1 structure in 9/337 (3.1%) cases.

3.2 Features of Canonical Forms

Theoretical considerations and empirical facts show that canonical forms of action potentials are composed of a high depolarization phase followed by a repolarization phase. Considering that both phases are part of the same process [28, 29, 30], a high correlation between them would be expected. The maximum and minimum values of the first derivative were located during the rising and falling periods of the depolarizing phase, respectively.

We plotted linear correlations between the different variables describing the P1N1 (n = 106), N1P1 (n = 14), N1P1N2 (n = 113), P1P2N1 (n = 41), N1N2P1 (9) and P1N1P2 (n = 12) cells in Fig. 1. We have added a new figure at Appendix (Appendix Fig. 7) to show the network for every kind of mAPs. Surprisingly, practically no correlations were observed between the durations of the phases or the durations and amplitudes (except for P1N1).

All the cells showed a strong relationship between V${}_{\text{Dep}}$ and V${}_{\text{Rep}}$ and between V${}_{\text{Dep}}$ and dV${}_{\text{max}}$. Moreover, the slopes of the regression lines for both pairs were similar. Consequently, these properties can be used to differentiate between typical and atypical mAPs.

We assessed these relationships as amplitude and duration ratios. We show these ratios to identify constant relationships between cells. In Fig. 2, we compare the amplitude and duration ratios for all typical cells. Considering all the pairs between each kind of mAP and each ratio, we have $4\times C_2^4+2\times C_2^6=54$ possibilities (C indicates combinations). However, we observed significant differences (post hoc Dunn’s test for ANOVA on ranks) only for the V${}_{\text{FP}}$/V${}_{\text{Dep}}$ and V${}_{\text{FP}}$/V${}_{\text{Rep}}$ ratios for the pair of P1P2N1 and N1N2P1 cells, where the first phase had an opposite polarity.

Fig. 2.

Amplitude and duration ratios for all the typical mAPs. No differences were observed for ANOVA on ranks, with the exceptions of the V${}_{\text{FP}}$/V${}_{\text{Dep}}$ and V${}_{\text{FP}}$/V${}_{\text{Rep}}$ for the pair of P1P2N1 (blue) and N1N2P1 (yellow) cells.

Therefore, these ratios can be considered nearly constant for different kinds of cells. It is quite interesting to observe that although no correlations between pairs d${}_{\text{Dep}}$ and d${}_{\text{Rep}}$ were obtained (Fig. 1B), the ratio d${}_{\text{Dep}}$/d${}_{\text{Rep}}$ can be considered nearly constant, with a value of 0.38 $\pm$ 0.01 (median and IP${}_{10-90}$: 0.37 (0.25, 0.57)).

With these results, we defined the properties of cells considered canonical as those cells with (i) at least two opposite phases, with the higher, which is always the first of the two, considered depolarization, followed by a repolarizing phase; (ii) $V_{\text{Dep}}\in [1.2,2.7]\times |V_{\text{Rep}}|$ and strongly related by the function $V_{\text{Rep}}=-0.56\left(\pm 0.01\right)V_{\text{Dep}}-1.83(\pm 0.79)$; (iii) a very strong relationship between dV${}_{\text{max}}$ and dV${}_{\text{min}}$ given by the equation $d{V}_{\text{min}}=-0.91\left(\pm 0.03\right)d{V}_{\text{max}}-0.37(\pm 0.12)$, both of which were included in the depolarizing phase; (iv) a relationship with V${}_{\text{Dep}}$ by the equation $d{V}_{\text{max}}=0.08\left(\pm 0.001\right)V_{\text{Dep}}-0.28(\pm 0.14)$; and (v) $d_{\text{Dep}}\mathrm{~}0.38d_{\text{Rep}}$.

Nevertheless, most of the recorded cells (74.4%) showed an initial phase prior to the depolarization phase. For all of these cells, the 5 conditions stated above were applicable, and therefore, these cells can be included as typical or canonical cells. We analysed the different correlations between pairs of magnitudes affecting the first phase (Fig. 3) and other properties of the APs. However, none of these correlations were significant.

Fig. 3.

Correlations between the FP variable and other variables. (A) V${}_{\text{Dep}}$ vs. V${}_{\text{FP}}$. (B) V${}_{\text{Rep}}$ vs. V${}_{\text{FP}}$. (C) d${}_{\text{Dep}}$ vs. d${}_{\text{FP}}$. (D) d${}_{\text{Rep}}$ vs. d${}_{\text{FP}}$. V${}_{\text{Dep}}$ and V${}_{\text{Rep}}$ for N1N2P1 and P1N1P2 mAPs were multiplied by -1 to preserve coherence with positive cells, and the amplitude of the first phase was $|$V${}_{\text{FP}}$$|$. N1PN2 = empty dots and black lines; P1P2N1 = black dots and black dashed lines; P1P2N1 = red dots and lines; N1N2P1 = blue dots and lines.

Therefore, there were no correlations between FP and variables characterizing the depolarization or repolarization phases. Moreover, the coefficients of variation ($SEM/\overline{x}$) were $|V_{\text{FP}}/V_{\text{Dep}}|=0.08$, $|V_{\text{FP}}/V_{\text{Rep}}|=0.08$ and only 0.01 for $|V_{\text{Dep}}/V_{\text{Rep}}|$; the same measure for the duration ratios $d_{\text{FP}}/d_{\text{Dep}}$, $d_{\text{FP}}/d_{\text{Rep}}$ and $d_{\text{Dep}}/d_{\text{Rep}}$ were 0.11, 0.11 and 0.03 respectively, which implied that the variation was higher for ratios involving the FP.

These data suggest that the first phase was not associated with the same dynamic process of action potentials responsible for depolarization and repolarization.

3.3 Features of Atypical Forms

As previously stated, up to 12.5% of cases were amAPs, a percentage that cannot be considered anecdotal. Besides, this kind of cells was recorded from all the patients. As with the canonical cells, we considered depolarization as the phase where dV${}_{\text{max}}$ and dV${}_{\text{min}}$ occur. In Fig. 4 we have showed the canonical mAPs (upper row) and its atypical counterparts (lower row) for clarification.

Fig. 4.

Different phases of mAPs (red lines) and relationships with the first derivative (blue lines) for canonical and atypical cells. (A) P1N1 (B) N1P1N2 (C) P1P2N1 to (D) N1P1 cells for comparison with atypical cells in (E) wP1N1 (F) N1P1NLF (G) PbiN1 and (H) NbiP1. Horizontal dashed arrows indicate periods, and vertical dashed arrows indicate amplitudes of phases. Black dashed lines mark the maximum and minimum values of the first derivatives.

The observed amAPs have been named wide P1N1 (wP1N1, Fig. 4E) cells, cells with a last phase (N1P1NLF, Fig. 4F), and positive bimodal (PbiN1, Fig. 4G) and negative bimodal (NbiP1, Fig. 4H) cells. Each type of cell is plotted below its canonical cell counterpart to clarify the difference. Explicitly, wP1N1 cells (2/42, 5%) have a longer d${}_{\text{Dep}}$ than P1N1 cells. N1P1NLF cells (27/42, 64%) show an initial negative phase with dV${}_{\text{max}}$ and dV${}_{\text{min}}$; therefore, this pattern could be considered a depolarization phase followed by a repolarization phase and by a third negative phase smaller than the first, referred to as the last phase. PbiN1 cells (12/42, 29%) are characterized by the presence of two positive waves of similar amplitude; in fact, dV${}_{\text{max}}$ is included in the first wave, in contrast to P1P2N1 cells, where dV${}_{\text{max}}$ is located in the second positive wave (Fig. 4C). Finally, NbiP1 cells (1/42, 2%) are similar to PbiN1 cells but with opposite polarity.

The first aspect we had to assess with respect to these amAPs was the possibility that such strange morphologies would arise from an erroneous sorting method that mixed different canonical forms. Therefore, it was extremely important to show atypical cells obtained from raw records. Fig. 5 shows three examples of amAPs obtained directly from the raw records before any sorting process.

Fig. 5.

Atypical extracellular action potentials recorded directly from the raw records before sorting. (A) NbiP1 (B) PbiN1 and (C) N1P1NLF. The horizontal lines under each record are expanded in the bottom panels. The horizontal calibration bar for every column corresponds from the upper to the lower row.

Therefore, it can be concluded that amAPs are truly extracellular action potentials and were not artificially constructed. In this sense, the amplitude and duration ratios of the amAPs were quite different from those of the canonical mAPs . From a total of 14 ratios, in 10 cases, a significant difference was observed (71%); a difference was observed with 6/7 amplitude ratios (86%), with the only exception being V${}_{\text{Dep}}$/V${}_{\text{Rep}}$ for the pair of P1N1 and wP1N2 cells, while the difference was observed with 4/7 (57%) duration ratios.

The structures of atypical PbiN1, NbiP1 and wN1P1 cells suggested a composition of simple mAPs. In fact, a summation of two P1N1 cells delayed by 0.20–0.24 ms resulted in mAP quite similar to PbiN1 and wP1N1 (Fig. 6B,C). The same process using two consecutive N1P1 cells gave rise to a structure highly similar to NbiP1 (Fig. 6D).

Fig. 6.

Composition of atypical mAPs from simple cells. (A) Theoretical cell (not actually recorded) with a delay between unitary mAPs = 0.16 ms (B) wP1N1, delay = 0.21 ms (C) PbiN1, delay = 0.24 ms (D) NbiP1, delay = 0.24 ms. Blue = true unitary mAPs at different delays; red = theoretical mAPs formed by combining the two unitary mAPs; black = recorded amAP.

Unfortunately, we had no hypothesis about the sources leading to N1P1NLP cells, which are the most frequent amAPs.

To the best of our knowledge, this is the first study describing in detail the features of the atypical structure of EAPs in the human brain and, specifically, in the hypothalamus.

Recently, it has been shown that the types of mAPs in the hypothalamus are similar to those described in the thalamus [19, 20], with the majority of cells showing three phases. Despite the similar morphology in both brain structures, the properties of the mAPs were different, showing that mAP morphology is region specific. However, in the thalamus, we did not record the amAPs that were recorded in the hypothalamus [20]. This fact adds another element of regional specificity regarding the structure of action potentials. EAPs can provide information about several properties of intracellularly recorded action potentials [28, 29]; therefore, the MER goal should not exclusively consider EAPs as binary events (present/absent). To date, scarce attention has been devoted to the analysis of EAPs. In fact, only EAP width has been reported from recordings in the pedunculopontine nucleus in humans, and a bimodal distribution has been observed with a longer APs attributed to cholinergic neurons and shorter APs attributed to glutamatergic transmission [18, 30, 31]. However, no other properties have been analysed (number of phases, features of phases, derivatives, etc.) until our previous studies in thalamic nuclei [19] and hypothalamic nuclei [20].

We have analysed in detail the structure of canonical forms of mAPs in the hypothalamus, and we have identified five features defining conventional or canonical mAPs. These properties can be well fitted to the described basis of neuronal excitability in vivo by means of quantitative methods [32, 33, 34, 35]. The tight relationship between V${}_{\text{Dep}}$ and V${}_{\text{Rep}}$ and dV${}_{\text{max}}$ demonstrates that the three variables are components of the same dynamic process, as can be expected. In contrast, the absence of a correlation between durations was not as expected. Nevertheless, as we have shown in Additional materials (Appendix Figs. 8,9), the different orders of magnitude for voltages (82.2 $\pm$ 2.4 (69.3 [49.2, 130.2] $\mu$V)) and durations (1.66 $\pm$ 0.03 (1.63 [1.2, 2.2]) ms) makes the duration measures much more sensitive to noise (see Appendix). Most likely, the smaller amplitude of hypothalamic cells relative to the thalamus precludes a better correlation between d${}_{\text{Dep}}$ and d${}_{\text{Rep}}$.

The ratios of amplitudes and durations for the several phases of the canonical forms have been proven to be a robust way to characterize typical mAPs. It is quite interesting to observe that different types of mAPs share similar values of V${}_{\text{Dep}}$/V${}_{\text{Rep}}$ or d${}_{\text{Dep}}$/d${}_{\text{Rep}}$, even when no good correlation was obtained. These quasi-constant ratios endorse the unity of the dynamic system responsible for mAPs.

The shape of the EAP is similar and proportional to the total transmembrane current from the perisomatic region [28]. However, as we previously described in the thalamus [19] and hypothalamus [20], most cells have a small phase before depolarization. This first phase can be observed with either positive or negative polarities. Given that quantitative and experimental data have shown the presence of capacitive current prior to the large depolarizing phase, this origin could be hypothesized for the first phase described here. However, capacitive current is elicited by current spreading to dendrites from the soma and is always of the opposite polarity as depolarization; therefore, we would obtain only N1P1N2 and P1N1P2 types. Thus, capacitive current cannot explain cells such as P1P2N1 (12.2%) and N1N2P1 (3.1%). Moreover, the magnitude of this current is between 10 and 50 times lower than the perisomatic current and cannot explain the amplitude and duration of the FP described here. Another possibility could be that the first phase is related to postsynaptic potentials, which can explain the difference in polarity. This possibility is reinforced by the lack of correlation and the greater variance for V${}_{\text{FP}}$ and d${}_{\text{FP}}$ and other phases of EAPs. If this phase is related to the process of APs, we should expect a greater correlation, as described for V${}_{\text{Dep}}$ and V${}_{\text{Rep}}$, although perhaps not for d${}_{\text{FP}}$. In addition, we should expect values for amplitudes and duration ratios closer to those recorded in the depolarization and repolarization phases, but we truly found a variation in these ratios between 4 to 8 times greater than for ratios involving depolarization and repolarization. Another reason to consider the first phase as having a synaptic origin is the different features described in the thalamus [20]. A different morphology of the dendritic tree and the density and kind of receptors could give rise to different morphologies of postsynaptic potentials. A comparison with awake patients could shed light on this possibility because we can postulate similar features for action potential dynamics but some changes in the characteristics of synaptic activity. Although we cannot be sure whether synaptic potentials are the origin for the first phase, we can practically exclude its belonging to the dynamic system from which the EAP originates.

Another possibility to explain N1P1N2 cell morphology to capacitive or synaptic activity could be consider these kinds of cells as EAPs originating from axons, not the perisomatic region. Referential recordings from nonmyelinated fibres result in waveforms quite similar to a smaller first negative phase, followed by a higher positive and finally a third negative longer phase [36]. If this kind of mAP would be, in fact, in axons, it could be expected that its percentage would be greater in regions richer in white fibres, such as the hypothalamus (i.e., caudate-pallidal fibres and lenticular, tuberomamillar and dorsal longitudinal fascicles go through the hypothalamus), and lower in nuclei mainly composed of dendrite-soma structures, such as the basal ganglia [8]. This was true, because in the thalamus, the percentage of N1P1N2 was 19.4% (216/1114 cells), while in the hypothalamus, this percentage was nearly double (37.6%, 53/141 cells) [20]. In fact, the initial axon segment is the dominant contributor to the extracellular action potentials of cultured neurons [37].

As previously described in the thalamus, negative mAPs have also been described in the hypothalamus. Absolute values of amplitude and duration for repolarization (what we to consider as the negative phase) are similar to repolarization in positive cells. If depolarization originates from the transmembrane current going into the cell [35, 38], we should think that negative depolarization originates from the transmembrane current coming from inside the cell. However, this case has not been described to date. The presence of these negative cells is high enough to discard an anecdotal finding; therefore, the transmembrane sources of current for these cells remain to be explained. In animal cortical recordings, a high amplitude positive action potential different from conventional negative spikes has been described, and the features of both types of spikes, such as amplitude and duration, were clearly different [39]. However, these findings were not observed in our case, where the properties of the positive and negative mAPs (absolute magnitudes for amplitudes and phase durations) were on the same order of magnitude.

To the best of our knowledge, this is the first description of EAPs that significantly differs from that conventionally described in animals and humans or quantitatively predicted [32, 34, 40]. First, it is important to keep in mind that despite their anomalous structure, they are real action potentials and not artefacts from erroneous sorting. Although we have denominated the amAPs in a similar way to canonical forms, the amplitudes and durations are strikingly different. The amAPs PbiN1 and NbiP1 have three well-defined phases. However, the first phase cannot be considered a canonical first phase because it is usually the higher amplitude phase. Obviously, neither a postsynaptic potential nor capacitive current can be so high. In fact, both dV${}_{\text{max}}$ and dV${}_{\text{min}}$ are placed inside the complex structure formed by the first two phases. Along with the high amplitude, as high as the V${}_{\text{Dep}}$, these facts suggest that the biphasic structure can be explained as two consecutive simple EAPs. In fact, the composition of two canonical P1N1 and N1P1 EAPs delayed between 0.16 and 0.24 ms reproduced the main features of PbiN1, wP1N1 and NbiP1. Therefore, consecutive canonical spikes separated by less than ¼ ms could explain these types of atypical cells. Synaptic communication takes an approximately 1-ms delay in addition to the time for travel along the axon [32, 33]. Therefore, even for very closely placed neurons, we can exclude synaptic mediation for a consecutive pair of spikes at this short delay, although we cannot exclude that both cells would be driven by a third cell. On the other hand, the refractory period excludes the possibility of a second spike from the same neuron. Therefore, one possibility to explain consecutive spikes from different neurons at such a short delay would be ephaptic communication or gap junctions (GJs). Connexins are expressed by grey but not white matter astrocytes [41]; they are important for the developing cortex [42] and are ubiquitous in the cortex between fast-spiking parvalbumin-positive interneurons and interneuron-neurons [43], although their presence in pyramidal cells from the adult cortex is still debated. Evidently, we cannot probe the presence of GJs in the human hypothalamus with these results, and further studies are needed, but it is an interesting suggestion.

Another possibility to explain the broad mAP could be the participation of calcium currents. It is well known that this type of conductance enlarges the duration of action potentials and can be located at dendritic sites [44].

The most frequently found amAP was N1P1N2LP. Although slightly similar at first sight to N1P1N2 canonical cells, there were some differences. For the canonical mAP, the ratio V${}_{\text{FP}}$/V${}_{\text{Rep}}$ was 0.32 $\pm$ 0.2, and for the amAP, it was 6.77 $\pm$ 2.63, indicating that phase N1 was a true first phase, but for the amAP, it was not. In fact, the maximum values for the first derivate, which in canonical forms are inside the depolarization phase, were located in the N1 phase in this atypical cell, suggesting that this waveform is in fact the depolarization phase. If this was true, the V${}_{\text{Rep}}$ $>$ V${}_{\text{Dep}}$, which is another anomaly. However, the volume conduction theory could explain this amAP as an EAP generated by axons, as we discussed in relation to N1P1N2 cells (see above) [36]. In fact, the different distances from the active electrode to the source could be the explanation for both kinds of waveforms. If this were true, regions with a higher density of nonmyelinated fibres would be more prone to show both types of mAPs, as we have recorded from the hypothalamus.

Nevertheless, it is important to understand that our data were obtained from a small number of patients. Although these data seem to be robust, a larger cohort study is needed to corroborate our interpretation of various EAP patterns as atypical and to confirm a connection between the presence of atypical potentials and the target identification. To further corroborate our interpretations of the EAP, simulations with neural models incorporating ion channel dynamics could be helpful.

EAPs of hypothalamic cells in anaesthetized humans can be divided into canonical forms, sharing a set of properties that are highly robust, mainly concerning the relationship between V${}_{\text{Dep}}$ and V${}_{\text{Rep}}$. These cells show a three-phase structure in the majority of cases. However, there is another type of EAP that clearly differs from canonical. These atypical cells represent 12.5% of cells and clearly show different morphologies. To date, these atypical cells have been described only in the hypothalamus, although more research is needed to ascertain their presence in different brain regions.

The MATLAB® script is available upon request from corresponding author.

amAP, Atypical Mean Action Potential; AP, Action Potential; DBS, Deep Brain Stimulation; d${}_{\text{mAP}}$, Duration of the mean Action Potential; dtN/dtP, Duration of Negative/Positive phases at half-amplitude of EAP; d${}_{\text{Dep}}$, Duration of the Depolarization; d${}_{\text{FP}}$, Duration of the First Phase; d${}_{\text{Rep}}$, Duration of the Repolarization; dV${}_{\text{max}}$/dV${}_{\text{min}}$, Maximum/Minimum values of the first derivative; EAP, Extracellular Action Potential; Freq, Frequency of the raw trace; GJs, Gap junctions; ISI, Inter-Stimulus Interval; MER, Microelectrode Recording; mAP, Mean Action Potential; MRI, Magnetic Resonance Imaging; NbiP1, Negative bimodal (Dep) positive (Rep) phases cell; N1P1, Negative (Dep) and Positive (Rep) phases cell; N1P1N1, Negative (FP), Positive (Dep) and Negative (Rep) phases cell; N1P1NLF, Negative, Positive and Negative Last-Phase cell; N1N2P1, Negative (FP), Negative (Dep) and Positive (Rep) phases cell; PI, Pause Index; PR, Pause Ratio; PS, Power Spectra; P/N, Positive/Negative phase; P1N1, Positive (Dep) and Negative (Rep) phases cell; P1P2N1, Positive (FP), Positive (Dep) and Negative (Rep) phases cell; P1N1P2, Positive (FP), Negative (Dep) and Positive (Rep) phases cell; rnk, Rank for the matrix containing observations; SW, Schaltenbrand-Wahren; PbiN1, Positive bimodal (Dep) and negative (Rep) cells; PMH, Postero-medial Hypothalamus; V${}_{\text{AP}\pm }$, Positive/negative voltage thresholds of mAP; V${}_{\text{Dep}}$, Amplitude (voltage) of the Depolarization phase; V${}_{\text{FP}}$, Amplitude (voltage) of the First Phase; V${}_{\text{mAP}}$, Amplitude (voltage) of the mean Action Potential; V${}_{\text{max}}$/V${}_{\text{min}}$, Maximum/Minimum voltages of EAP; V${}_{\text{Rep}}$, Amplitude (voltage) of the Repolarization phase; V$\pm$, Maximum/minimum voltage threshold; wP1N1, Wide Positive (Dep) and Negative (Rep) phases cell.

JP is responsible of the idea. LV-Z and EM-A participated in data collection. JP developed the analytical methods and EM-A and LV-Z participated also in analysis and interpretation, and JP was responsible for manuscript preparation. All authors have approved the submitted version of this manuscript.

The experimental procedure was approved by the medical ethics review board of the Hospital Universitario de La Princesa and was deemed “care as usual”. Under these circumstances, written informed consent was not required because all procedures were done by clinical necessity and analysis was off-line. The study was accomplished according to standards for human research and in accordance with the Helsinki Declaration.

Authors want to acknowledge the collaboration during surgeries of neurosurgeons Marta Navas and Cristina Torres and anaesthesiologists María Luisa Meilán and Eva de Dios and Angel Nuñez by its comments during the elaboration of the manuscript.

This research received no external funding.

The authors declare no conflict of interest. JP and LV-Z are serving as the guest editor of this journal. We declare that JP and LV-Z had no involvement in the peer review of this article and has no access to information regarding its peer review. Full responsibility for the editorial process for this article was delegated to GP.

To assess the influence of the signal-to-noise ratio (SNR) in the relations between different parts of mAP we have mixed different degrees of known noise ($n_{i,},i=1,2,\mathrm{\dots }N$) with the numerical model of mAP $(s_{i,},i=1,2,\mathrm{\dots }N)$. The definition of SNR is given as

(2)$$SNR=10{\log }_{10}\frac{{\sum }_{i=1}^N{s}_i^2}{{\sum }_{i=1}^N{n}_i^2}$$

We have simulated a P1N1 mAP fitting the next properties (i) two opposite phases of depolarization followed by repolarization, (ii) $V_{\text{Dep}}=\mathrm{\hspace{0.25em}1.63}\times \left|V_{\text{Rep}}\right|$and v) $d_{\text{Dep}}\mathrm{~}0.38d_{\text{Rep}}$. We were not interested in properties (iii) and (iv) related to dV${}_{\text{max}}$ and therefore they have not been modeled.

To simulate noise, we have chosen a function like this $n\left(t\right)=A\sin \left(2\pi ft+\phi \right)$, with amplitude (A) and phase ($\phi$) random and $f=1920Hz$. We have performed 7 simulations, with the first without noise. Every simulation included 30 repetions with a random phase. The probability density function for all repetitions fitted well to Gaussian distribution by effect of the random phase. For the resulted waveform (mAP + noise) we determined the fiducial points (Appendix Fig. 8).

We have plotted these results at Appendix Fig. 8. We can observe that there was a very good correlation between A and V${}_{\text{Dep}}$, V${}_{\text{Rep}}$ and d${}_{\text{Dep}}$, but not with d${}_{\text{Rep}}$. Besides, it was a very good correlation between V${}_{\text{Dep}}$ vs V${}_{\text{Rep}}$ and between V${}_{\text{Dep}}$ vs d${}_{\text{Dep}}$, but not between d${}_{\text{Dep}}$ vs d${}_{\text{Rep}}$ or V${}_{\text{Rep}}$ vs d${}_{\text{Rep}}$. Interestingly the V${}_{\text{mAP}}$ did not correlate with A, because, in fact, can be considered as constant independent of noise, at least for a SNR between 33.5 (A = 0.8 $\mu$V) and 7.1 (A = 16.3 $\mu$V). However, although d${}_{\text{mAP}}$ was not correlated with A, cannot be considered as a constant.

But, not only no correlation between durations were obtained, besides the coefficient of variation was higher for d${}_{\text{Dep}}$/d${}_{\text{Rep}}$ (0.266) than for V${}_{\text{Dep}}$/V${}_{\text{Rep}}$ (0.153), what mean that noise increase the dispersion for measurement of duration.

Fig. 7.

Network plot for correlations between variables for all the kind of mAP. The strength of correlation is indicated by the thickness of line.

Fig. 8.

Different mixtures of the model of mAP with noise. (A) Signal without noise. (B) SNR = 17.1, A = 5.2 $\mu$V. (C) SNR = 12.7, A = 8.6 $\mu$V. Red = waveform resulting from numerical model of mAP + noise; dotted blue = high frequency noise; dashed black = basal zero-voltage. Inset: bar histrogram for an overall analysis of 30 repetitions.

Fig. 9.

Relationships between variables from different mixtures of mAP + noise. (A) A vs V${}_{\text{Dep}}$ (red dots) and A vs V${}_{\text{mAP}}$ (blue dots) (B) A vs V${}_{\text{Rep}}$ (C) A vs d${}_{\text{Dep}}$ (D) A vs d${}_{\text{Dep}}$ (red dots) and A vs d${}_{\text{mAP}}$ (blue dots) (E) V${}_{\text{Dep}}$ vs V${}_{\text{Rep}}$ (F) d${}_{\text{Dep}}$ vs d${}_{\text{Rep}}$ (G) V${}_{\text{Dep}}$ vs d${}_{\text{Dep}}$ (H) V${}_{\text{Rep}}$ vs d${}_{\text{Rep}}$. Dashed lines are regression functions. Values of r and statistical significance (p) for every regression function are indicated. Vertical error bars inside the symbols.