Journal of Undergraduate Research
Volume 6, Issue 7 - May/June 2005

Linear Predictive Analysis for Targeting the Basal Ganglia in Deep Brain Stimulation Surgeries

J. Pukala, J. C. Sanchez, J. C. Principe, F. J. Bova, M. S. Okun

ABSTRACT

Intra-operative automated recognition of deep brain stimulation (DBS) targets from microelectrode recordings would improve the safety, efficiency, standardization, and accuracy of the surgical procedure. Our approach to the cellular classification problem is from a speech recognition perspective where linear predictive coefficient (LPC) analysis is used to model segments of thalamic and subthalamic nucleus cellular activity. We then cluster the linear prediction coefficients for three Parkinson’s Disease patients and develop discriminant surfaces with an artificial neural network to generate the target classes. The methods presented here yielded a significant separation of the cell types within a two-dimensional prediction coefficient data space. The results indicate that LPC analysis for DBS targeting warrants additional study for a larger variety of deep brain structures and patients.

INTRODUCTION

Parkinson’s Disease (PD) affects 1 in every 100 people over the age of 60 and is the second most common neurodegenerative disease after Alzheimer’s disease1. Surgical treatments for Parkinson’s disease (PD) are well established for relief of motor symptoms (tremor, bradykinesia, and rigidity) and drug-induced dyskinesia, as well as for motor fluctuations associated with chronic medical therapy2-10. Deep brain stimulation (DBS) is a relatively new surgical treatment that was developed as an alternative to lesioning. Problems with the surgery have been identified when leads are misplaced and result in changes in mood and cognitive dysfunction particularly when stimulation or lesions infringed on nonmotor areas11-13. In DBS, the goal is to affect motor circuits in the basal ganglia in order to improve clinical deficits in an individual patient. The precise mechanisms of DBS remain unknown, although many hypotheses have been recently presented4, 14-16. The placement of the deep brain stimulating electrode is a non-trivial task and is the single most important factor in clinical effectiveness of the procedure. The difficulty in placing the electrode lies in the fact that no high-resolution, real-time imaging tools are available for defining the borders/somatotopy of deep brain structures within the small number of millimeters needed for clinical accuracy. As a result, neurologists and neurosurgeons rely on pre-surgical imaging, stereotactic targeting, and functional electrophysiology to place the lead. The final selection of the DBS site is performed in the operating room by identifying cells and regions within a target utilizing multiple passes of a microelectrode. Each pass of the microelectrode is advanced in a stepwise fashion into the patient’s brain in order to obtain necessary information on the three dimensional location of the target. This process is time consuming and difficult and relies heavily upon the neurologist’s ability to use audio/visual cues to distinguish artifacts and noise from true signals.

The goal of our DBS research is to develop a targeting advisor that will automatically identify specific locations in the brain in real time. This technology would enable the neurologist/neurosurgeon team to locate the intended target faster and more accurately, thus potentially decreasing patient discomfort, morbidity, and expense. The appeal of our approach is that we can provide an additional tool to the neurologist that will quantitatively distinguish between the activity of deep brain structures. Since the current DBS procedure utilizes a neurologist that has been trained to listen and identify deep brain structures from neuronal recordings, we propose to address the DBS targeting problems from a speech recognition perspective. A speech analysis method called linear predictive coding (LPC) is the predominant method for estimating the basic speech parameters and for representing speech17. Here the LPC methodology was employed to ascertain the ability to discriminate subthalamic nuclei (STN) and thalamic cells.

DATA PREPARATION

The electrophysiological data presented here were collected from human subjects undergoing DBS for Parkinson’s Disease. Using an Axon recording unit (FHC, Bowdoinham, ME.), cellular voltage measurements were taken with respect to patient ground with a recording platinum/iridium (80%/20%) microelectrode. The microelectrode is a unipolar device with typical system impedances of 1 Mω as measured with a 1 kHz, 100 nArms sine wave. The data are digitized using a 20 kHz sampling rate with a range of ± 0.5 V and resolution of 500 nV. In Figure 1 we present representative recordings from STN and thalamus.

Figure 1. Representative thalamus and STN neuronal recordings.
Figure 1. Representative thalamus and STN neuronal recordings.


METHODS

In DBS target acquisition, we utilize the well-known signal processing methodology of linear autoregressive (AR) modeling to quantify the local time structure of the recorded time series. The purpose of fitting AR models to the spike trains is to capture the spike train rhythmicity within them, which may be what the neurologist/neurosurgeon exploits during audible manual discrimination.

We applied the AR modeling directly to the STN and thalamus time series segments described above. This method prescribed windowing the signal of interest and approximated future samples as a linear combination of previous samples using the equation


Equation

where s(n) is the original signal, ~s(n) is the predicted signal, αk are the predictor coefficients, and p is the prediction order. A unique set of predictor coefficients for any given signal may be determined by minimizing the sum of the squared differences between the actual samples and the linearly predicted ones. These predictor coefficients serve as the identification criteria in this study. We utilized the autocorrelation method for LPC to calculate the predictor coefficients. Minimizing the prediction error with this procedure leads to a Toeplitz matrix of the form:


Equation

R in the equation above represents the short-time autocorrelation function. The Levinson-Durbin recursion algorithm was used to solve this system of equations.

Preliminary investigation and experimentation found that applying the LPC method to unmodified neuronal voltage recordings sampled at 20 kHz yielded observable separation between thalamic and STN cells for a second-order linear predictor with a 2000 sample (100 ms) window size1. The procedure was repeated on subsequent data segments in the time-series to produce a collection of local models.

Figure 2 shows an example of the clusters of the first and second coefficients of all the AR models for STN and thalamus neurons (Patient #2, roughly equal amounts of data for each). As we can see, the distribution of model coefficients is quite distinct for each brain structure. Visual inspection would indicate that the classification of STN vs. thalamus could be achieved with a simple neural network.


Figure 2. Clusters of STN and thalamus LPC coefficients.

Figure 2. Clusters of STN and thalamus LPC coefficients.

To quantify the data separation seen above, we trained an artificial neural network (ANN) classifier with the topology shown in Figure 3. We use as inputs to the ANN the coefficients of each of the LPC models. The coefficients are weighted, summed, and passed through a hyperbolic tangent nonlinear processing element (PE). Our goal was to construct an optimal discriminant function18 for the classification of multidimensional coefficient data sets to produce a single output indicating the nuclei of the basal ganglia (i.e., STN or thalamus).

Figure 3. Topology of neural network DBS classifier
Figure 3. Topology of neural network DBS classifier

Optimal ANN weights were determined by training the topology using the backpropagation algorithm in batch mode for 1000 epochs19. Training data consisted of examples of both STN and thalamus LPC coefficients from three patients. Gradient descent was performed with a step size of 0.1 and momentum term of 0.7 to avoid local minima of the performance surface. Once the network was trained, the ANN’s weights were fixed, and novel LPC coefficients from the two cell type models were passed through the network to evaluate the testing performance for classifying STN from thalamus for three patients. The performance of each test set was evaluated using a confusion matrix.

RESULTS

The performance of the ANN in classifying STN from thalamus heavily depended upon the amount of overlap of the LPC coefficient clusters. Our test set LPC analysis resulted in significant overlap of STN and thalamus for patient 2 as shown by the LPC testing clusters in Figure 4. Results for patients 1 and 3 showed less overlap with thalamus. However, the variance of the coefficients was large. Clusters of thalamic LPC coefficients were tight with a center at values of (0.9, -0.2).

Figure 4. Overlap of STN and thalamus LPC coefficients from three patients.
Figure 4. Overlap of STN and thalamus LPC coefficients from three patients.

Our observations of LPC coefficient overlap were directly reflected in the testing ANN performance. In Table 1 we present the percentages of correct classification for each of the three patients. On average thalamus classification (83.91% correct) performance was better than STN (66.13% correct) across the patient population. We can attribute this result to the tightness of the thalamus LPC coefficient clusters. The distribution of thalamus model coefficients also relates that the neuronal firing of this structure is much more regular compared to STN. Individually, we observe that STN patient 2’s low percentages are due to overlap with thalamus LPC coefficients. However, in the case of STN patient 3, 99% of the examples was correctly classified because the ANN could easily place a discriminant surface between the clusters (see Figure 4. patient 3).

 

Table 1.
Percentages of Correct Classification
Patient Thalamus (%) STN (%)
Test Patient 1 99.06 65.99
Test Patient 2 82.67 33.31
Test Patient 3 69.99 99.08

Analysis of the mean and variance of the LPC model coefficients and their relationship to the original time-series recordings motivated us to perform a frequency analysis of the autoregressive models generated. Recall that the LPC analysis generated a series of all pole filters with frequency response of the form

Equation

where _1 and _2 are the coefficients of each of the LPC models. To obtain perspective on the features of the original time-series being exploited by the models for STN and thalamus, we computed the average frequency response of all the filters and plotted them in Figure 5. We observed that the STN filters had a broader pass band (up to 2kHz) than the thalamus and then quickly rolled off. In comparison, the majority of the thalamus filter energy was in lower frequencies with a gradual roll off. This result made sense with respect to the raw recordings observed offline and in the operating room in terms of STN cellular density, bursting activity, and sparseness of neuronal activity compared to the thalamus.

Figure 5. Average frequency response of the LPC models.

Figure 5. Average frequency response of the LPC models.

DISCUSSION

Using the speech recognition analogy for target acquisition in DBS surgery has proven to be a viable approach for a handful of patients and recordings. The simplicity and ease of implementation of this approach may be well suited for the operating room environment. In many circumstances, researchers alternatively characterize the activity of the basal ganglia in terms of neuronal firing rates which if required could significantly complicate the analysis process. We believe that the LPC/ANN approach efficiently focuses on frequency features of the recorded time-series that the neurologist/neurosurgeon utilizes for audible discrimination. Differences in the average frequency responses of the STN and thalamic models (Figure 5) attest to this conclusion, and it is this difference that makes it possible for the ANN to develop a classification surface.

Ultimately, we need to test how this approach generalizes to a variety of patients and deep brain structures. This analysis will be the subject of future investigations. Just as speech signals vary from speaker to speaker, so do the voltage signals of brain cells from patient to patient. The success of generalization will rely heavily on how repeatable the neuronal activity of the basal ganglia is from brain to brain. Since the basal ganglia is heavily involved with the fundamentals of movement, it is possible that the activity may lie within some range of LPC model values. An additional aspect of generalization is related to the regularity of firing from normal and abnormal brains. Detailed LPC frequency response analysis may provide an additional tool for quantifying these differences.

Future research regarding the application of LPC analysis for intra-operative targeting could proceed in a variety of directions. We believe that one of the most important aspects would be the development of new clustering techniques that would help to deal with overlapping classes of cells. Another area to explore will be the use of more powerful classifiers such as support vector machines that could project the LPC coefficient data into a higher dimensional space where the margins are more easily separable.

If LPC/ANN analysis for intra-operative targeting proves to be robust, we envision that it can be used as an additional tool for the neurologist/neurosurgeon in conjunction with presurgical imaging, anatomical atlases, and somatosensory responses. The combination of these tools could be used to improve the DBS procedure and to ensure maximal clinical benefit is obtained.

FOOTNOTES

  1. Higher order models (up to 6th order) and a variety of window sizes (500-5000 points) were explored and yielded separation in the classes. The significance of these other parameter choices is the subject of future investigations. Back

REFERENCES

  1. M. J. Aminoff and M. Di Minno, "A Primer on Parkinson Disease." www.parkinson.org/site/pp.asp?c=9dJFJLPwB&b=71354, 2004.
  2. A. L. Benabid, et al., "Stimulation of the Subthalamic Nucleus," presented at XIIth Meeting of the World Society for Stereotactic and Functional Neurosurgery Abstracts of Workshop on Parkinson's Disease, 1997.
  3. A. L. Benabid, et. al., "Stimulation of Subthalamic Nucleus Acutely Changes Clinical Status in Parkinson's Disease," Society for Neuroscience Abstracts, vol. 19, pp. 1052, 1993.
  4. A. L. Benabid, A. Benazzouz, D. Hoffmann, P. Limousin, P. Krack, and P. Pollak, "Long-term electrical inhibition of deep brain targets in movement disorders," Movement Disorders, vol. 13, pp. 119-125, 1998.
  5. A. L. Benabid, A. Benazzouz, P. Limousin, A. Koudsie, P. Krack, B. Piallat, and P. Pollak, "Dyskinesias and the subthalamic nucleus," Annals of Neurology, vol. 47, pp. S189-S192, 2000.
  6. M. S. Baron, J. L. Vitek, R. A. E. Bakay, J. Green, Y. Kaneoke, T. Hashimoto, R. S. Turner, J. L. Woodard, S. A. Cole, W. M. McDonald, and M. R. Delong, "Treatment of advanced Parkinson's disease by posterior GPi pallidotomy: 1-year results of a pilot study," Annals of Neurology, vol. 40, pp. 355-366, 1996.
  7. L. V. Laitinen, A. T. Bergenheim, and M. I. Hariz, "Leksells Posteroventral Pallidotomy in the Treatment of Parkinsons-Disease," Journal of Neurosurgery, vol. 76, pp. 53-61, 1992.
  8. R. Kumar, A. M. Lozano, E. Montgomery, and A. E. Lang, "Pallidotomy and deep brain stimulation of the pallidum and subthalamic nucleus in advanced Parkinson’s disease.," Mov Disord, pp. 73–82, 1998.
  9. R. Kumar, A. Dagher, W. D. Hutchison, A. E. Lang, and A. M. Lozano, "Globus pallidus deep brain stimulation for generalized dystonia: Clinical and PET investigation," Neurology, vol. 53, pp. 871-874, 1999.
  10. J. L. Vitek, R. A. E. Bakay, and M. R. DeLong, "Microelectrode-guided pallidotomy for medically intractable Parkinson's disease," in Advances in Neurology, Volume 74, vol. 74, Advances in Neurology, 1997, pp. 183-198.
  11. C. Junque, M. Alegret, F. A. Nobbe, F. Valldeoriola, R. Pueyo, P. Vendrell, E. Tolosa, J. Rumia, and J. M. Mercader, "Cognitive and behavioral changes after unilateral posteroventral pallidotomy: Relationship with lesional data from MRI," Movement Disorders, vol. 14, pp. 780-789, 1999.
  12. W. J. Lombardi, R. E. Gross, L. L. Trepanier, A. E. Lang, A. M. Lozano, and J. A. Saint-Cyr, "Relationship of lesion location to cognitive outcome following microelectrode-guided pallidotomy for Parkinson's disease - Support for the existence of cognitive circuits in the human pallidum," Brain, vol. 123, pp. 746-758, 2000.
  13. J. A. St. Cyr, et al., "Neuropsychological Outcome of Posteroventral Pallidotomy in Parkinsonian Patients," Movement Disorders, vol. 11(Supplement 1, Vienna Abstracts), pp. 161, 1996.
  14. J. L. Vitek, "Mechanisms of deep brain stimulation: Excitation or inhibition," Movement Disorders, vol. 17, pp. S69-S72, 2002.
  15. A. M. Lozano and F. Carella, "Physiologic studies in the human brain in movement disorders," Parkinsonism & Related Disorders, vol. 8, pp. 455-458, 2002.
  16. W. M. Grill and R. McIntyre, "Extracellular excitation of central neurons: implications for the mechanisms of deep brain stimulation," Thalamus and Related Systems, vol. 1, pp. 269-277, 2001.
  17. R. L. Rabiner and R. W. Schafer, Digital Processing of Speech Signals. Englewood Cliffs: Prentice-Hall, 1978.
  18. J. C. Príncipe, N. R. Euliano, and W. C. Lefebvre, Neural and adaptive systems: fundamentals through simulations. New York: Wiley, 2000.
  19. S. Haykin, Neural networks: a comprehensive foundation. New York: Toronto: Macmillan; Maxwell Macmillan Canada, 1994.

--top--

Back to the Journal of Undergraduate Research