Statistical analysis of MER data of STN Neurons with DBS in Parkinson`s movement disorders

Scientific-rationale

Parkinson’s disease is a foremost movement disorder and the prime root cause is damage to the central-nervous –system (CNS). In spite of every study on this malady, the formation-mechanism of its manifestations remained mysterious. But it is quiet obscure why damage to substantia nigra only which is, a tiny element of the brain (few millimeters), causes a wide-range of motor-symptoms? Still, the basic reasons of brain damages and injuries prolong to be wholly expounded and also understanding the brain function is very complex. Some cutting edge frontline engineering and technological tools and utilities are un-soothing to comprehend the behavioral actions and activities and performance of complex-systems.27 In this connection, mathematical frameworks and statistical signal modeling and then simulation modeling’s through computer (i.e., computer simulated prototypes through computational simulation techniques) is one of the most significant tools. Computational simulation models for the progression of this malady have begun in 1999 and today it is expanded profoundly. These engineering developmental tools are very helpful not only in improved perceptive and thoughtful of the PD, but also presenting innovative therapeutic-methods, and it’s envisage prediction and impediment, and in its early diagnosis. At present DBS is constrained to non-adaptive open loop stimulus method, without automatic adjustments or settings to the subject’s activity status, oscillations plus kinds of motoric-features, drug-medication (i.e., dosages) or neural markers of the disease. Adjustments of stimulation parameters are not conducted during real-time in real-time based on the ongoing neurophysiological variations in the brain. Hence, adverse effects on patient may be induced due to overstimulation of the brain. Whilst subject at home, every adjustment to DBS settings occur or during visits. Such constraints sometimes may lead to further health hazards and cross dyskinesias - side-effects like, cognitive dementia(CD) and cognitive impairment (CI), feelings, the doldrums, hallucinations, and both upper body symptoms (such as, dysarthria, deglutition, and respiratory-function) and lower body symptoms (like gait disorders, freezing of gait (FoG) and including symptoms associated groups like tremor-dominant (TD) and postural-instability gait difficulty (PIGD)) and axial symptoms (slurred inaudible speech). These features have a key impact on disease progression, and thus, the subjects’ quality of life (QoL) and the encumbrance of caregiver.

Significancy of the study and its importance to Biomedical engineering and Neuroscience

Subthalamic nucleus deep brain stimulation is a momentous therapeutic stereotactic neurosurgical operational technique which reduces tremors and restores motor function in subjects (patients) with advanced idiopathic Parkinson's disease both unilateral and bilateral STN-DBS, and for many disorders. The advances in stereotactic functional neurosurgical automatic operational techniques have fundamentally replaced ablative methods. Mahlon5 formulated a new model for the brain's circuitry and exposed a fresh target for this illness. Alim Louis Benabid 6 devised an effective and reversible intervention that remedies neuronal misfiring in Parkinson's disease. However, a well designed neuro bio marker perfectly giving vital information on the PD motoric and non motoric features in subthalamic-nucleus and also globus pallidus interna is not yet developed. In this study, we account the results of neural correlates of PD motor symptoms in the territory of subthalamic nucleus. Despite advances in magnetic resonance MRI particularly in connections with better spatio-temporal resolutions in latest 10 Tesla, the electrophysiological microrecording (MER) technique continues to be well applied for pinpointing on STN detection and discovery based on signatures (or MER signal patterns of STN neurons) with deep brain stimulating procedure.28, 29, 30, 3, 4 Hence, our results will give potentials for the construal explication of oscillatory-dynamics of STN and that these signatures or patterns which are confined very well by the intra op MER can be used as objective tools for future technologies of neuromodulation. The study also highlights the variability in spontaneous LFPs amongst the subjects and the neuronal data. Although the work deals with the signal processing Applications to the human motor sensory nervous system it deals with application of electro neuro physiological evaluation of dystonic and dexterous and movement disorders, in particular neuromuscular, writer's cramp with and without mirror movement (i.e., dystonic mirror movenets) it has broad implication in the development and innovation of newer signal processing and electrophysiological techniques and Improving the currently available EMG machines for Evaluating all types of neuromuscular diseases and disorders in Particular dystonias. It will be of great interest to the Scientists/engineers involved in biomedical research in the fields of biomedical instrumentation and signal processing applications to neuro electro physiology.

MER has been the gold standard for lead targeting in DBS, however patients must be awake during this surgery, it requires more instrumented passes into the brain, and operative time is longer. Targeting can be performed using intra operative MRI or intra operative computed axial tomography (iCT) to place electrodes with equal accuracy, which is appealing to patients since it is performed under general anesthesia and may result in lower morbidity and cost.

Provocative pathways

Whilst Mahlon began his experimental investigations in his research work (1960s), the basal-ganglia which is meant for body movement and control had been implicated in movement, principally for the reason that flaws there were connected amid infirmity such as PD in which motor turbulences feature notably. Little was known; yet, vis-à-vis how closely the basal ganglia contribute to movement. To find out, Mahlon embedded microelectrodes into rhesus-macaque-monkeys' brains and evaluated the activity of explicit neurons in the BG whilst the rhesus carried out imparted training exercises, actions and/or events. He thus matched neurons by tasks; some influenced and prejudiced, for instance, the direction, magnitude/size, or the pace or tempo of arm, leg, or facial movements. Thus, he mapped out the association of the motoric-circuit. Derived from his own research-work and that of other researchers plus existing anatomical-structural information, Mahlon proposed a model wherein BG neurons operate in separate circuits. Numerous pathways originate from distinct centers in the cerebral-cortex, run through BG, and end back at terminus point where they started; the circuits work alongside one another and allow concurrent operations that parallel processing the emotions, thoughts, and motor functions. This experimental work provided insights into the entrenched, ingrained, and deep rooted observation that cognitive and emotional problems accompany many motor disorders that stem from BG failings. Also, the findings provided a new framework for exploring how BG elements and mechanisms malfunction in a variety of illnesses, including PD. Although dopamine loss obviously causes the disease's motor perturbations, the associated changes in BG activities were unclear. Mahlon's model that included detailed maps-of-stimulatory, and inhibitory-signals through the BG given the ideas. For instance, the final-stop in the motor-circuit of the BG is a anatomical-structure that sends restraining and preventive and limiting instructions forward, thereby suppressing other components of the motor system. Anything that causes superfluous activity at that site might generate the symptoms that characterize-PD.

From aficionados to imminent and impendings

In the early 1980s, sporadic outbreaks of a syndrome that mimics Parkinson's disease started occurring among drug addicts and scientists traced it to a chemical, MPTP, that was contaminating some batches of synthetic heroin. Medical management of the compound to monkeys reproduced the key clinical and pathological features of PD, and thus offered a powerful new tool for studying the illness. Mahlon seized upon the opportunity. A part of the basal ganglia called the subthalamic nucleus drives the inhibitory output signal, and in 1987, Mahlon reported that MPTP triggers neurons in the subthalamic nucleus of monkeys to fire excessively. Perhaps, Mahlon reasoned, the over exuberant signals quash motor activity in PD. If so, inactivating the subthalamic nucleus might ameliorate some of the illness's worst symptoms. Next, he did an experiment that would transform PD treatment. He administered MPTP to two monkeys; as usual, they gradually slowed down until they sat motionless, their muscles stiffened, and they developed tremors. Mahlon then injected a second toxic chemical that inactivated the subthalamic nucleus. Within one minute, the animals began to move. Gradually, their muscles loosened and the tremors ceased. These findings strongly supported the hypothesis that hyperactivity in the subthalamic nucleus underlies PD symptoms.

Higher frequencies and greater confidences

Louis has been attempting the Parkinson`s neurodegenerative disease in America. In a throwback to the pre Levodopa era, the trickiest PD-patients those who did poorly with long term pharma ceutical treatment would wind up in the operating room. Louis craved a new tool—something safer that would quiet the most disabling symptoms of PD. In the year 1987, while operating in a PD subject he was about to create a lesion with essential tremor, a condition that causes tremulous in different parts of the subject. He was targeting an element of the thalamus that leads to tremor. Characteristically, the subject was awake so Louis could test whether he had positioned the right tissue; he placed a probe into the stain that he planned to lesion and sent an electrical-pulse to guarantee that distressing perturbing and tormenting this site did not cause or produce endangered and undesired-effects. As a rule he used γ-waves with ≤50Hertz frequency, although he determined to find out what would happen if he increased the frequency. Just below 100 Hertz (γ-waves range: 31Hertz –200Hertz), and that went unexpectedly occurred impressive and the tremor clogged. The Parkinson subject became so still, Louis thinking that he had caused an unintended unintentional muscle retrenchment. He switched off the stimulus and he contrite for his lapse or elapse. The subject told Louis not to express regret, as it was happened the first time in many years that his hand had not shaken. Louis continued the procedure, amid the similar result. Also, when he withdrew the current, the tremor recurred. Thus, the cause was reversible. So, Louis realized he was onto something exciting. (Figure 1)

Figure 1

The DBS had been inducing used for more than twenty years to treat ache and twinge, but no one had dialed up the frequency. Following the year, he attempted and also aimed the same approach for Parkinson subjects. In addition, he implanted a device which was on the market for pain relief and delivers constant stimuli. Some of the individuals benefited from the procedure, and no complications occurred. Louis in the early 1991 reported that high-frequency stimulus could be deployed bilaterally (in left and right brain) in people with essential tremor and PD; this strategy reduced tremor on two sides of the body. The gains were long lasting, and adverse effects were placid; also, any undesired outcomes could be reversed by reducing the stimuli.

Louis knew (although the technique quelled tremors) that this motoric-symptom was not the one that most debilitated people with PD. Perhaps high-frequency stimulus of brain regions and sub-structures other than the thalamus (i.e., the subthalamic nucleus) would alleviate the more troublesome aspects of the illness such as slowness of movement, postural instability and rigidity, he reasoned. In this state of mind, Louis read Mahlon's report that damage to the STN wipes out many symptoms of PD in primates and in non primate animals. This site was not an attractive target: Lesioning procedures and spontaneous lesions had established decades earlier that, when things went wrong, violent flailing could result. By that time, however, Louis had performed high-frequency stimulation of the thalamus and other brain regions' in ≥150PD patients. He was confident that he would cause no harm in the subthalamic nucleus; if necessary, he could remove the electrode.

In the year 1995, Louis reported his results in 1995 from the first humans who underwent bilateral, high frequency stimuli of the STN 3 subjects with severe PD. The treatment suppressed slowness of movement and muscle rigidity. 8 years later, he confirmed and extended these results in a study of individuals who had undergone the procedure 5 years earlier. The surgical-operation restored motor skills, suppressed tremor, and improved the ability to conduct normal activities of daily living. Furthermore, people were able to slash their dosage of L-dopa and related medications, which reduced associated complications. In the year 2002, the US Food and Drug Administration (FDA) approved high-frequency stimulation of the subthalamic nucleus for treating advanced idiopathic Parkinson's disease. The method is not a cure, and it does not reverse all aspects of the malady. In particular, the non motoric and axial feature symptoms such as speech, cognition and dementia continue to decline. Many questions remain about the mechanism of this intervention. It might jam or replace inappropriate circuit activity. Regardless how it works, functional neurosurgeons are using high-frequency deep brain stimulation to combat an ever-growing number of sites and diseases: essential tremor, dystonia—a condition of involuntary muscle contractions—and even psychiatric illnesses. The FDA approved its use for obsessive-compulsive disorder in 2009, and scientists are investigating applications for drug-resistant depression and Tourette Syndrome. Through their open-minded explorations and willingness to challenge dogma, Louis and Mahlon have delivered extraordinary medical innovations to humankind. By reaching deep into the brain sub structures, they have soothed some of the most troubling conditions that corrupt it.

Clinico statistical analysis

Variance (σ)

Variance is the average of the squared deviations of each data point from the µ-value. For a population of size N, the variance sigma square, is computed as,5, 32

σ2=1N[ ∑i=1Nxi-μ-2 ].............. (1)

Similarly for a sample size it is denoted by s square and is evaluated as,

S2∑i=1n(xi-x-)2(n-1)................(2)

The μ- [σ²] and the variance Var [σ²] of σ² are computed as,

Var [ σ² ] = μ- [( σ² − σ¯² )² ] = Var [ε] .........(3)

Because x is written as the convolution of σ and white Gaussian-noise W passed through H, the conditional distribution of x given σ² is Gaussian distribution with a µ of zero and a variance of σ²:

p(x/σ2)=1√2πσ2exp  -  - x22σ2 .......(4)

Standard deviation

The standard-deviation (or SD) of a sample is the square root of the variance which is measured as5,32,

s=s2=∑i=1n (xi-x-)2( n - 1 ) ..............(5)

as a result,

‘σ’ = σ 2......................(6)

is standard deviation of the given population.

Root Mean Square (R M S)

The root-mean square (RMS) or root mean square deviation (RMSD) or root-mean-square error (RMSE) (or sometimes root-mean-squared error) factor mostly used in engineering and medicine for a statistical significance. It is often used for computing the disparities among the values (sample or population values) predicted by a model or an estimator and the values observed. In our computation the sample size is N (= 12).

To compute the R M S of a given population N, in our case it is (N = 12), one has to square the given population in the N and then determine the arithmetic-µof the squares. Finally, take the square root of the findings and computed by using the following equation

R M S =[ (a12+a22+…an2)n ] ...................(7)

=∑i=1nai2n.....................(8)

In our 12 population computation, the RMS for the Left Hemisphere Brain during DBS “ON” is 1.1 ± 0.8 and during “OFF” it is 5.9 ± 11.9. Similarly, R M S for the Right Hemisphere Brain during DBS “ON” is 0.9±0.3 and during “OFF” it is 2.6 ± 4.7.

Normalizing Impedance and RMS

The estimation of the root mean square of unprocessed multi unit S T N - M E R local field potentials activity acquired by the micro electrodes at apiece and at every microelectrode-depth or intensity is defined as in the following equation

Root Mean Square = X- =  ∑i=1 n (Xi-μ)2( n-1 ) ...(9)

In this equation, X - vector-quantity of sampled analog M E R – L F P signal with µ, and X_i is every sample, and n is the total number of samples in the sub division. The root mean square values are prone to microelectrode properties, for instance, the impedance of microelectrode; thus the necessity of R M S normalization in order to be an absolute quantity or gauge. In the earlier investigations the normalization of R M S with the white - matter of the of pre S T N zero-line, i.e., base line R M S producing what the investigators defined as the “N R M S”. The technique is highly pragmatic for detecting S T N borders and for exhibiting the micro electrode signal recording of S T N trajectory graphically/ or diagrammatically.

In this study, we intend to contrast the µ mean - R M S in the S T N to clinical/diagnostic diagnosis and/or clinic prognostic parameters, such as feature-symptom rigorousness and progression of the post operation which is impelled or driven and provoked our re-evaluation of the normalization technique. It is observed that in spite of zero line/base line normalization, the S T N – N R M S still demonstrated significant correlation to the impedance of the microelectrode which was gauged#1kilo-Hertz at the start of every trajectory; R=00.3291, P=49.60001. The ρ coefficient point to 10% (R²) of µ of N R M S inconsistency in the S T N might be elucidated by the impedance of the microelectrode. This confounding result might masquerade basic medical correlation`s. We therefore employed an different technique for normalizing R M S in the S T N: impedance normalized R M S (I N R M S). The I N R M S in the S T N was computed with the below expression

R M S_i = I N R M S_i = - a × [I_i - Mean (µ) I] ............(10)

Here, R M S_i is the mean-µ of RMS in fastidious nuclei in µ micro volts and ‘I_i‘ is the equivalent impedance of microelectrode in megΩs which was gauged@1kilo-Hertz, the vector-quantity of all impedances are ‘I’, and ‘a’ is the 'linear’ which is a µ of I, that guarantees following the normalization of the impedance. Here, µ is not changed which is relative to the unprocessed, and not normalized the R M S. Here, N R M S has a singular-µ. We have initiated that the normalized mean of RMS (NRMS), i.e., normalized by pre-STN baseline activity did not correlate significantly with Parkinson’s disease symptoms or postoperative improvement. Normalizing the RMS by impedance removed the confounding impedance correlation and revealed a significant correlation with both preoperative rigidity and postoperative reduction in Unified Parkinson’s Disease Rating Scale (UPDRS) and F, respectively). It is this impedance normalizes the technique that employs to compute the PSD in order to normalize.

Computing the PSD spectrum

To compute the spectrum, i.e., power-sepctral-density (PSD) spectrum, the unprocessed analogue signal was rectified by the absolute operator and the µ was subtracted (Moran et al., 2008; Moran and Bar-Gad, 2010). Using the rectified signal, which follows the envelope of multi-unit activity, we were therefore able to detect burst frequencies below the range of the operating room band-pass filter (250–6000 Hz). Since the local field potential frequency domain was filtered out by the recording apparatus, our resulting power spectral density represents only spiking activity. The average power spectral density was calculated in each trace using Welch’s method, with a 1s Hamming window (50% over-lap) and spectral resolution of 1/3 Hz. Values within 2 Hz of the 50 Hz power supply artifacts’ and their harmonics were removed and interpolated from the surrounding values. Two different methods were used to normalize the power spectral density: Dividing the power spectral density by the total power of the signal between 3 and 200 Hz (excluding power spectral density values within 2 Hz of the 50 Hz power supply artifacts’ and their harmonics) creating a relative power spectral density. This method exposed the ‘relative’ power across frequencies. For ex-ample two pure sine waves with the same frequency but of dif-ferent amplitudes would have identical relative power spectral densities. This method is particularly useful in identifying the dorsolateral oscillatory region of the STN (Zaidel et al., 2009). The relative spectrum i.e., power spectral density computing diagram be viewed in the following graphs/images.

Normalizing the power spectral density by electrode impedance in the identical manner as the described above for the RMS (i.e. by offsetting its correlation with the measured electrode impedance). This method retained the ‘absolute’ level of power, exposing the magnitude for each frequency in the signal. In the above example of two sine waves with the same frequency but of different amp-litudes (measured by equal impedance electrodes), the impedance normalized power spectral densities would be different. Since the dependence of power on electrode impedance could be different for specific power spectral density frequencies, the normalization was performed separately for each frequency band in question. In order to qualify this, we computed the correlations for 1–100 Hz power spectral density individually (in steps of 1 Hz)—all correlations were significant (P50.01; median P50.0001). Furthermore, re-analysis using a single value for normalization across all frequencies (the µ linear coefficient of the regression line) did not change our results presented below. This method was used for the regression analysis presented in Fig. 7. For all power spectral density normalization, correlation analyses and plotting in this manuscript, the logarithm of the power spectral density was used.

Entropy

To compute the local field potentials, the thermodynamic entropy is used. It is a measure of the fraction of the internal energy of a neuron which is not available to function. In neurons impulse progression, such as the flow of neuron from one state to another state, i.e., neuron sending impulses from one state to another state typically referred to as “divergency” and similarly receiving impulses from other state neurons is usually referred to as “convergency”. It is said that entropy is increases at all times.9

To establish the functional nonlinear multivariate (Taylor`s series) local field potentials, i.e., LFP signals, say F, in a deep brain stimulator ‘correlation’ or ‘relation’ r (t), then, we can establish the relation r (t) as,

r (t) = F[s(t)], .......................(11)

to discretize prior times:

s(t)=(s(t-Δt), …, s(t-LΔt))= (s₁, s_2, s₃…, s_L) ...................(12)

Consider the only current-response (r) then, we can write (r) as

(r) = r (0),  .................................................(13)

and F is a multivariate LFP signals for r in terms of s₁, s₂, s₃…, s_L.

So, to compute lower-order coefficients, we surmise that the others are as zero (0). Hence, the maximum-entropy is computed distributed as

K-exp-c(r-F(s1,…, sL) )2 .................(14)

In multivariate analysis, the µ and covariance’s controlled or conditioned as:

K-exp(x-mTC(x-m)} ....................(15)

and, in independent variable or analysis, with marginal’s

P (x), Q(y): P(x) × Q(y) or P(x)Q(y) ........................(16)

In this study, the entropy method is of non-linear-dynamics (signals with different phase amplitudes and with different frequencies) which computes negative (-Ve) natural-logarithm of the conditional-probability that two-sequences in a time series/time-domain which are analogous for ‘m’ number of points are analogous for m+1 points.33 In our computation, we obtained the entropy value which showed the tremor-complexity during DBS “ON” for the brain right-hemisphere (left side: 1.4±0.7) and “OFF” states (2.3±1.6), and for the right hemisphere the tremor complexity during DBS “ON” is (1.3±0.7) and during “OFF” state in left-hemisphere it is 1.5±1.6. So, if we observe, in our computation, carefully, as we already mentioned that entropy is increases at all times,9 and so the entropy is increased in either case. This also (the results) indicating that the PD-patients cardinal motor-symptoms were effectively reduced with DBS.