Deep Brain Stimulation (DBS) is a surgical procedure for the treatment of motor disorders in patients with Parkinson’s Disease (PD). DBS involves the application of controlled electrical stimuli to a given brain structure. The implantation of the electrodes for DBS is performed by a minimally invasive stereotactic surgery where neuroimaging and microelectrode recordings (MER) are used to locate the target brain structure. The Subthalamic Nucleus (STN) is often chosen for the implantation of stimulation electrodes in DBS therapy. During the surgery, an intraoperative validation is performed to locate the dorsolateral region of STN. Patients with PD reveal a high power in the
Parkinson’s Disease (PD) is a common neurodegenerative disorder. Many successful pharmacological therapies and strategies have been developed to treat both the motor and nonmotor manifestations of PD. However, as PD progresses, it often becomes difficult to treat, typically because of motor complications. In these cases, Deep Brain Stimulation (DBS) is a therapy used to treat PD. Most recently, DBS is also being used in early stages of PD [
DBS involves the application of controlled electrical stimuli to a given brain structure by implanted stimulation electrodes. The implantation of the electrodes for DBS is performed by a minimally invasive stereotactic surgery where neuroimaging and microelectrode recordings (MER) are used to locate the target brain structure (Figure
(a) MER and stimulation electrodes in STN during a DBS surgery. (b) Basal nuclei of the brain: TH: Thalamus, STN: Subthalamic Nucleus, and SN: Substantia Nigra.
Neuroimaging studies, both Computerized Tomography (CT) and Magnetic Resonance Images (MRI), are used for surgery planning and validation of the implantation site. MER are obtained by recording the neuronal electrical activity using micro EEG technique during implantation surgery and they are used to perform an intraoperative validation of the electrode position. MER signals recorded during surgery are the sum of a variety of signals generated by several neural processes and elements. The extracellular activity captured by MER can be divided into three categories: Local Field Potential (LFP) < 300 Hz, MultiUnit Activity (MUA) > 300 Hz, and singleunit activity.
For PD, the Subthalamic Nucleus (STN) is often chosen as the target brain structure (Figure
Several researchers ([
From the mathematical point of view, in order to be able to retrieve frequency information from MER, and since the signals are random and only one segment of them is available, an estimation of the power spectrum must be considered [
However, for
For this study, MER recordings obtained from bilateral surgery performed on 9 patients with PD undergoing the implantation of stimulation electrodes for DBS in the STN were used. The surgical interventions took place at La Fe Hospital, in Valencia, Spain.
The recordings were obtained with the “MicroGuide” system (AlphaOmega Engineering, Nazareth, Israel). Neurophysiological activity was recorded through polyamidecoated tungsten microelectrodes (Alpha Omega). The signal was amplified 10000 times and it was filtered with a bandpass filter between 200 and 6000 Hz, using a 4th order Butterworth filter for the low cutoff frequency and 2nd order for the high cutoff frequency. The sampling frequency was 12 kHz, and a 12bit analog/digital converter was used.
Filtering the recordings with a highpass filter with cutoff frequency at 200 Hz implies that these signals are MUA and not LFP. This selection of filters, however, is helpful to avoid the recording of electrical noise in the operating room [
During electrode implantation surgery, two parallel MERs in each brain hemisphere were moved in small discrete steps of 0.2 mm starting at 8 mm above the calculated target (center of the dorsolateral STN). The recording times in each depth were variable (between 0.43 s and 278.92 s). In the study conducted by [
Signal processing and data analysis were performed with MATLAB software V8.5 R2015a (Mathworks, Natick, MA, USA) using
As reported by other authors ([
To assess signal stability, the strategy outlined by [
First, signals values whose modulus exceeded 150
This stability analysis rejects infrequent events, such as glitches (spurious electronic signals caused by peaks in electrical energy) or cell damage, but does not reject oscillatory activity greater than 1 Hz [
MER signals are produced by the superposition of multiple electrical sources corresponding to several neural processes. Since the acquisition was performed with a highpass online filter with cutoff frequency at 200 Hz, the signals used in this work are MUA signals; that is, they are composed by background activity and action potentials from neurons close to the recording electrode.
Because of this acquisition strategy, it is impossible to perform a direct frequency analysis in ranges lower than 200 Hz, which are the ones of interest in this study (
In [
In this study, the strategy proposed by [
Summarizing, to obtain the envelope, these steps were followed:
Full wave rectification: absolute value of each signal sample.
Extraction of the mean.
Smoothing to obtain the envelope: 4th order Butterworth lowpass filter: cutoff frequency at 100 Hz.
In studies where the
In this work, different PSD methods were analyzed with the purpose of selecting the one that allows the calculation of the
First, it was decided to compare different power spectrum estimation methods in order to identify other methods that could also be used. For this, after performing spectral estimation with different methods, a statistical analysis was performed to find significant differences among them. Then the computation time of some of the methods was compared.
In all spectrum estimations, parameters were adjusted to achieve a frequency resolution of 0.1 Hz.
Nonparametric methods for power spectrum estimation are based exclusively on the available data, without making any assumptions about the system that generates them. Due to the analyzed signals characteristics, it seems appropriate to use such an estimation method.
In this study, three nonparametric techniques of PSD estimation were analyzed, which are described below.
In this study, the results of three different window sizes were compared, always with an overlap of 50%:
0.5second Hamming window.
1second Hamming window. This is the most used window length in the consulted bibliography.
1.5second Hamming window.
To use this method, it is necessary to define the set of windows used and the NW parameter, which is related to the number of windows. In this work, the DPSS set of windows, proposed by Thomson, was always used. In order to select NW value, the values used in the consulted bibliography ([
Although MER signals characteristics do not seem to be described by a simple parametric model as they come from a system of great complexity, an autoregressive model (AR) was decided to be applied.
The order of the AR model provides a balance between bias and variance [
A statistical analysis was performed to compare the results of the different spectral estimators studied. For this, all of the signals coming from the 28 trajectories were used (each trajectory contained several signals, each of a different recording depth). In total, 1010 signals were used.
Since there were few samples and the distribution of the samples was unknown, it was decided to work with Friedman’s nonparametric method. This test was applied to two matrices. In both cases, each column represented a method of power spectral estimation and each row represented one signal, which was recorded at a specific depth, with a specific microelectrode, in a specific hemisphere, and in a specific patient.
In one of the input matrices, each element of the matrix contained the average
To obtain the significance value of the comparison between two methods, an ad hoc method for multiple comparisons, based on the TukeyKramer criterion, was used. The level of significance was
Since the final goal of this work is to apply one of these estimation methods to an intraoperative validation of the stimulation electrode implantation optimal location, it is necessary that signal processing is done in real time. Thus, processing speed is an important factor to consider.
The computation time of four of the estimators were compared, using a computer with an Intel® Core™ i76700HQ Processor, 16 GB SDRAM DDR3L, and running Windows 10 home 64 bits. The methods chosen for the calculation of the computational cost were those that are shown to be more adequate for the calculation of the spectral estimation.
An example of the stability analysis is shown in Figure
MER recording of patient 2, left hemisphere, central electrode, at a distance from target of 0.524 mm, processed to eliminate spurious data. (a) Original record. (b) RMS values of 50 ms signal segments; the red lines mark the limits corresponding to ±3 standard deviations of the median. (c) Portion of signal considered stable by the algorithm.
As a result of applying this stability analysis to all trajectories, stable portions were obtained from each of them. The length of the stable signals was 21.08 ± 12.18 s, being the minimum and maximum values of 1.55 s and 102.11 s, respectively.
To obtain the low frequency signal that modulates high frequency in the MER recordings, the method previously explained was applied over the stable segments of the signals.
As a result of full wave rectification, only positive values of the signal are present. However, the mean of the signal is then subtracted and then some samples may have negative values. Subsequent filtering, with a 4th order Butterworth lowpass filter with cutoff frequency at 100 Hz softens the signal, eliminating some of the original peaks. An example of this processing is illustrated in Figure
Low frequency modulation signal for patient 8, left hemisphere, central electrode (at a distance from the target of 1636 mm). Blue: stable MER segment. Red: rectified and filtered signal.
Since the actual spectrum of the signals is unknown, the results can only be evaluated by doing a comparison between the estimations obtained by each of the methods. That is, the bias of an estimate cannot be assessed without knowledge of the actual spectrum, but the differences in the variability of the different methods or of the same method with different parameters can be seen. Given that in studies where the
The goal of this comparison is to identify other methods that could also be used for this application.
In order to perform a qualitative comparison, power spectral estimation of an example signal, calculated with the different methods, is shown in Figure
Results of different power spectral estimation methods apply to the signal from patient 5, left hemisphere, central electrode, at a distance from target of 2.235 mm.
Periodogram
Welch: Hamming 0.5 s
Welch: Hamming 1 s
Welch: Hamming 1.5 s
Multitaper: NW = 2
Multitaper: NW = 6
AR order 4
AR order 15
From the observation of these estimations, and concerning the AR model with Burg coefficients, in the case of the AR model, 4th order, the spectrum (Figure
Statistical comparisons of the spectral estimations were performed with two different datasets: average power and highest power.
Comparison between Welch’s method with 1 s windows and the other estimators. Average power values in the
Table
Statistical results (
PGRM  Welch 0.5 s  Welch 1 s  Welch 1.5 s  Mult. 2  Mult. 6  AR 4  AR 15  

PGRM    0.9999  0.2284 


0.3520 


Welch 0.5 s  0.9999    0.4637 


0.6205 


Welch 1 s  0.2284  0.4637    0.6453  0.2741  1.0000 


Welch 1.5 s 


0.6453    0.9992  0.4884 


Mult. 2 


0.2741  0.9992    0.1697 


Mult. 6  0.3520  0.6205  1.0000  0.4884  0.1697   


AR 4 






 

AR 15 







 
With regard to parametric estimators, as expected, after visual inspection of the obtained spectra, the estimations based on AR models presented significant differences with all of the other methods and between each other
Comparison between 1 s windows Welch’s method and the other estimation methods. The values of the frequencies in which the maximum energy in the
Table
Statistical results (
PGRM  Welch 0.5 s  Welch 1 s  Welch 1.5 s  Mult. 2  Mult. 6  AR 4  AR 15  

PGRM   



0.9238  0.5155  0.9554 

Welch 0.5 s 








Welch 1 s 


  0.8801 




Welch 1.5 s 


0.8801    0.1680  0.5895  0.1262 

Mult. 2  0.9238 


0.1680    0.9963  1.0000 

Mult. 6  0.5155 


0.5895  0.9963    0.9906 

AR 4  0.9554 


0.1262  1.0000  0.9906   

AR 15 







 
Regarding parametric estimators, as in the previous comparison, AR models presented significant differences between each other
Since the final goal of this work is to apply one of these methods for intraoperative validation of the implantation’s optimal location, it is necessary that signal processing is done in real time. Thus, processing speed is a factor to consider.
The computation time of four of the estimators was compared. The methods chosen for the calculation of the computational cost were those that, from the previous comparisons, showed to be more suitable for the calculation of the spectral estimation, that is, Welch’s method with 1 s and 1.5 s window and multitaper method with NW = 2 and NW = 6. The evaluation of the computation time was done in the signals from patient 1, left hemisphere, posteromedial electrode, whose duration was
The computational times required by each of these methods for the PSD estimation are summarized in Table
Computation times for the trajectory corresponding to patient 1, left hemisphere, posteromedial electrode, whose duration is 27.9987 ± 11.9316 s.
Method  Computation times 

Welch 1 s windows  1.1137 ± 0.4831 s 
Welch 1.5 s windows  0.7253 ± 0.3168 s 
Multitaper NW = 2  2.3227 ± 0.8811 s 
Multitaper NW = 6  4.4735 ± 1.8008 s 
Comparisons were done in order to choose the best method to perform an intraoperative validation that takes into account frequency characteristics of MER recordings from PD patients to be performed in real time.
First, it was necessary to compare different power spectrum estimation methods in order to identify methods that could be used for this application. Since the actual power spectrum of the analyzed signals is unknown, it is not possible to evaluate an estimator by how close it is to the ideality. Therefore, a comparison was made between different estimators, taking as a reference the mostly used method in the consulted bibliography ([
The bias of an estimate cannot be assessed without knowledge of the real spectrum, but the differences in the variability of the different methods or of the same method with different parameters can be seen. Here parametric and nonparametric methods were considered.
Regarding parametric methods, the results obtained by the AR models confirm the previous assumption that, without making a much deeper study, these are not optimal for processing MER recordings. Their results are not only significantly different from the results of the other methods, but they are also different from each other.
Regarding nonparametric estimates, although qualitative comparisons showed certain morphological similarities between all methods, the quantitative analysis shows that they may be significantly different from each other.
For the particular case of the periodogram, it presented similarities with other nonparametric methods in the comparisons; however, it must be remembered that this is not a consistent estimator and a high variance was observed in the qualitative analysis. Although some of its results may not be significantly different from those of other estimators, we consider that it is not convenient to continue this work with an inconsistent estimator, since other options are available.
On the other hand, regarding the mostly used method in the consulted bibliography (Welch’s method with 1 s Hamming windows and 50% overlap), the results of our comparisons show that there are significant differences, at least in one of the two comparisons, with all of the other tested methods, except for Welch’s method with 1.5 s windows. This means that it does have significant differences with the case of 0.5 s windows, but—taking into account the qualitative comparison—a reason for these differences can be found. Welch’s method with 1 s window is a method with little variance but sufficient resolution so as not to lose all of the peaks. Estimations obtained with the same method but other window sizes are morphologically similar, but the 0.5 s windows provided a spectrum with no peaks. Having shorter windows allows the method to further soften the spectrum, but this can lead to missed peaks that should be taken into account. This could explain why the results with 0.5 s windows do not match those of the other window sizes when comparing the frequency values in which the maximum power in the
So, for Welch’s method, the results indicate that 1 s and 1.5 s windows provide results that are not significantly different from each other. Since this method with 1 s windows is the most used in the consulted bibliography and given that there are no significant differences with the one with 1.5 s windows, the possibility of working with one of these estimators indistinctly could be considered.
As for the multitaper method, in first place, these estimators do not present significant differences between them in any of the two comparisons. On the other hand, in the qualitative comparisons, it can be seen that these methods give more variable results than Welch’s method. The quantitative comparison reveals that they do not present significant differences with Welch’s method with 1.5 s windows. If this result is analyzed taking into account the explanation in the previous paragraph, the use of multitaper methods for the study of MER recordings could also be considered.
According to the statistical analysis performed, the methods that could be considered for PSD estimation in MER recordings are multitaper with NW = 2 and NW = 6 and Welch’s with Hamming windows of 1 s and 1.5 s.
However, in order to be able to do an intraoperative validation of the electrode position during implantation surgeries, the
In order to select a single method, then, the computational cost of each of them was considered. The results show that multitaper methods are computationally more expensive than those of Welch. In addition, the comparison suggests that Welch’s method with 1.5 s windows is the fastest: 35% faster than Welch with 1 s windows and 617% faster than
In this study, a comparison was made between different PSD estimation methods, taking into account a particular application. MER signal processing and particularly its frequency information can serve as an intraoperative validation tool for best electrode placement during DBS electrode implantation surgery in PD patients. The most used method for spectral estimation in the literature is that of Welch with 1 s Hamming windows and 50% overlap.
In this study we compared different spectral estimators and also the computational costs involved were taken into account. Finally, according to the discussion, we propose Welch’s method with 1.5 s Hamming windows and 50% overlap as the most appropriate realtime PSD estimator for MER signals of PD patients.
Even though the selection was based on the idea of performing an intraoperative validation in real time, the methods were not applied online. To further test the utility of the selected method, it would be appropriate to generate a hardware set, in which the registration of the signals could be simulated as if it was on the actual operating room, and the
The authors declare that they have no conflicts of interest.