Analysis of Physiological Systems: The White-Noise Approach

SIAM Journal on Applied Mathematics
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This type of SS channel is used to acquire the noise in the superficial layer because the detected light in this case passes only through the superficial layer and does not reflect any cognitive activity [ 36 , 39 , 40 , 41 , 42 , 43 , 44 ]. Saager and Berger [ 39 ] and Saager et al.

Additionally, Zhang et al. In their study, the superficial noise estimated through the coefficient of one SS channel within the framework of RLSE. Recently, the long-separation measurement has been modeled as a linear form consisting of the expected HR and SS measurement [ 40 , 42 , 43 ]. It is noted that the weights of canonical functions i. Their proposed method revealed a significant improvement in both HbOs and HbRs when compared to those obtained by the traditional adaptive filter or the standard GLM model.

Additionally, Sato et al. Clearly, fNIRS data are contaminated by extra-cortical noises from the extra-cortical layers that occur when the light travels through the extra-cortical layers i. Superficial noises are exposed in either single-SS [ 42 ] or double-SS measurement [ 43 ]. Additionally, Gagnon et al.

In the fNIRS field, the canonical HR functions were usually generated by a combination of gamma functions [ 45 , 46 ]. However, the state-space model developed in [ 46 ] is specifically convenient when compared with the use of canonical HR functions in which the impulse HR for an impulse stimulation at a specific cortex was reconstructed as a state-space equation by using the subspace identification method.

It should be noted that the shapes of impulse HRs in individual cortices are different. Thus, the expected HR for an arbitrary stimulus is generated online or in real-time. In the study, we propose an adaptive-filter-based method to reduce physiological and superficial noises in fNIRS data. The mathematical model for filtering is a linear form comprised of the following four main components: the expected HR, SS data, the sum of sinusoidal functions representing physiological noises, and the baseline drift.

The expected HR is generated with given stimuli by using the state-space model developed in [ 46 ]. The SS data emitter-detector distance: 0. The physiological noises are modeled as a sum of three sinusoidal functions by following the method developed in [ 10 , 35 , 36 ]. In order to estimate the baseline value, the corresponding element in the regression vector is set to unity although its coefficient b 0 i.

The unknown parameter vector in the proposed model is estimated by using the RLSE with an exponentially forgetting factor.

Vasilis Marmarelis, PhD

Finally, the efficacy of the proposed method is demonstrated by using experimental right-finger-movement fNIRS data obtained from the left motor cortex. Our experimental results indicate that the proposed method significantly reduces physiological and superficial noises when compared with the existent approaches. Thus, it is possible to apply the proposed method to remove noises in both offline and online cases. In this study, the hemodynamic response caused by a brain activity is modeled in a linear form as follows:. According to previous works in the control field, the RLSE algorithm gives a good performance in parameter estimation [ 49 , 50 , 51 , 52 ] and could be utilized in real-time applications [ 53 , 54 , 55 , 56 ].

Thus, by using Eq. Its recursive update law is given as follows [ 57 ]:.

Analysis of Physiological Systems - The White-Noise Approach | Vasilis Marmarelis | Springer

We assume that s t is the arbitrary stimuli that activates a certain brain region, which corresponds the input signal to the state-space model. Additionally, its first and second derivatives are used in Eq. The difference between the measured data and the estimated data i. In the present study, the proposed method was applied to detect right-finger-movements in the left motor cortex.

Thus, to illustrate the necessity to estimate the frequencies of physiological noises, two cases are discussed i.

Lecture 04 - Principles of Systems Theory, Physiological and Psychological Stress

First, to eliminate a possible contribution of superficial noises in the comparison, the SS channels are ignored. Therefore, the two following models are utilized. It is noted that the fixed frequencies of f m 0. The main objective of the current study is to reduce both physiological and superficial noises.

It is noted that the physiological noise frequencies are estimated on-line and are subsequently included in 3. The parameters are estimated using the RLSE approach. Both numerical and real experimental data are processed. The RLSE method is utilized to estimate the weights of the linear combination of the expected HR and physiological noises i. Numerical simulations are performed to validate the appropriateness of using of the RLSE algorithm for decoding brain hemodynamics. First, five related signals are intentionally mixed, see Fig.

The mixed signal of five signals is shown in Fig. In the process, the values of the amplitudes and frequencies of physiological noises were adopted from [ 36 ]. The proposed method of Eqs. Specifically, the estimated HbO the red thick curve in Fig. As shown in Fig. Furthermore, the estimated frequencies of cardiac 0. The result demonstrates that the proposed method effectively extracts the correct HbO and the physiological noises.

And each optode is used as either an emitter or a detector. Specifically, the pairs 1 — 2 , 3 — 4 , 5 — 6 , and 7 — 8 are SS channels 0. The long separation channels i. In Ch. Either measurement is included in Eq. Five long-separation channels are considered when optode 1 emits light. Similarly, an additional five channels are formed from the right to the left when optode 8 shoots light. Therefore, ten channels are created in each row. In the study, only a total of 40 channels eight channels for five distances: 1.

Five healthy male participants mean age None of the subjects exhibited any neurological impairments or mental disorders. Four of the subjects were right-handed. To eliminate any interference from the external noise, the experiments were conducted in a dark and quiet room. The subjects were asked to sit comfortably on a chair and not to move their body during the experiment. Prior to starting the experiment, the subjects were carefully trained in how to move their fingers. A laptop computer with a inch screen was utilized to display pictures indicating each finger.

The subjects were also instructed to keep their eyes open during the experiments. The optodes in Fig. Prior to the experiments, the nature of the experimental procedures was clearly explained to the subjects. All the experiments in the study were performed following the guidelines of the Institutional Review Board of Pusan National University, and informed consent were obtained from all the subjects based on the Declaration of Helsinki.

The intensities of the detected light were converted to hemoglobin concentration changes by using the MBLL. A total of 40 channels over the left motor cortex were configured at a sampling rate of 1. In the present study, the recorded fNIRS data drifted in time [ 45 , 58 , 59 ], and thus a baseline-correction method was applied. Specifically, a 4th order polynomial was fit to the data, and the obtained curve was subtracted from the original data to remove the drift [ 59 , 60 ]. The contrast-to-noise ratio CNR denotes the weighted difference between the mean of the signal during the task and that during the rest period [ 23 , 59 ].

To validate our proposed method, the CNRs were used to check the signal-to-noise ratio, since a high CNR value indicates a high ratio of the signal upon the task relative to that to noise.

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The CNR is computed as follows:. As observed, the averaged frequencies Mayer, respiratory, cardiac: 0. The result also agrees with those in previous studies [ 47 , 48 , 61 ]. However, variations exist per subject and per time, for e. Finally, the estimated frequencies were reflected as shown in 3. Our main objective involved reducing the physiological and superficial noises and subsequently extracting the correct HR from fNIRS data.

In extant studies, Abdelnour and Huppert [ 10 ] proposed a brain activity model including two main components, namely the expected HR and the sum of three sinusoidal functions representing the physiological noises. Their proposed method demonstrated a significant reduction in the physiological noises although the frequencies of those noises were assumed constant.

In the study, we use a linear model in which the physiological noise frequencies are estimated online during the initial resting state prior to the first trial. Additionally, those estimated frequencies are included into the f m in Eq. A SS measurement records the extra-cortical noise in the superficial layer while a long-separation channel includes the brain HR from both the cerebral cortex and the superficial layer [ 41 , 42 , 43 , 62 ].

In the current study, SS measurements were utilized as reference channels to remove noises in the superficial layer. In most channels, the correlation coefficients were less than 0. The peak s in the dashed line is due to the shift of an optode during the experiment. Additionally, in most cases, the correlation coefficients between the filtered SS data and the active long-separation signals were less than 0. Thus, it is concluded that the extra-cortical noise and the physiological noises are not correlated.

The experimental data confirmed that the SS data only contained the extra-cortical noise and did not include brain-activity related physiological noises. Comparison of a SS channel and an active long-separation channel Sub. To investigate the effectiveness of physiological noise frequency estimation, we compared the two brain activity models in 5 and 6 , respectively. In 5 , three frequencies i. The results show that the percentage improvement in terms of the number of improved channels of Subs. Thus, this indicates that the estimation of the physiological noise frequency did not result in a significant improvement.

Comparison of correlation coefficients between the desired HRs and the estimated HRs blue bars: fixed frequencies, red bars: estimated frequencies : For Sub. The proposed method was compared with a conventional method. The low-pass filtering LPF approach was popular, and thus a cut-off frequency of 0. The result reveals that it was not possible to eliminate the physiological noises at 0. In the process, the number of source signals was assumed as equal to the number of measured signals [ 63 ]. The steps of ICA included preliminary whitening of the measured data and estimation of orthogonal ICA transform to obtain the weight vector of all channels.

Finally, the independent component IC or source signals were estimated from the estimated weight vector and measured data see [ 45 , 63 , 64 ] for more details. To further validate the proposed method, CNRs in Eq. The result demonstrates that the proposed method extracted the expected HR more precisely by significantly reducing noise. Comparison of HbOs obtained by the proposed model with red thick curve and without blue dashed curve by using the sum of sinusoidal functions Ch. Kalman filter is a recursive tracking estimator. The approach estimates the states of a process by using an updated regularized linear inversion scheme [ 38 , 52 , 66 , 67 ].

Therefore, the performance of our proposed method was compared with that of a Kalman filter. In the study, the same linear model in Gagnon et al. It is noted that the canonical HR is a set of 15 Gaussian functions. The results indicate that our proposed method was comparable with the Kalman filter. Comparison of the HbOs obtained by the proposed method red thick curve and a Kalman filter blue dashed curve.

To further evaluate the proposed method, the HbOs obtained by three different methods Kalman filter, LPF, and the proposed method for five subjects were compared. The results suggest that the proposed method is comparable with both the expected HbO black dotted-dashed curve and the Kalman-filter-based HbO. A one-way test of variance was performed to evaluate the obtained HRs in Fig. In the case of Kalman filter, the obtained HRs from Sub. This demonstrates that the proposed approach gives the extracted HR more consistently than LPF and Kalman filter methods. This revealed that the proposed method effectively removed physiological and superficial noises.

Additionally, the accuracy of the obtained HRs was significantly improved. To implement the proposed method for brain imaging, right-finger-movement tasks in the left motor cortex were performed by using a bundled-optode arrangement.

Key points

The values of CC norm have been multiplied with their absolute value to demonstrate that negative values only occur for SPE , but not for CC norm. This is particularly difficult because the responses of sensory neurons are inherently variable, even in response to repeated presentations of identical stimuli. Doc Ophthalmol. Estimates of the nonlinearity after trials. Citing articles via Web of Science The close similarity between the impulse responses measured at different positions indicates that the dynamic tracer concentration was almost identical within a volume of at least 10 mm diameter surrounding the fly.

In our experiment, the available sampling rate for the bundled arrangement a total of 32 optodes was limited to 1. Therefore, with respect to the acquired fNIRS data, the proposed method deduced the cardiac frequency as within approximately 0. Several relevant reports proposed that motion artifacts are measured by means of an accelerometer [ 2 , 22 ]. If motion artifacts are measured in this manner, then they are included in our model as a new additional component and estimated by the RLSE approach.

Specifically, we expect that motion artifacts are effectively reduced in this manner. In addition, in the future works, measured fNIRS data of different brain regions will be checked using our proposed method. Actually, the proposed method reduces noises online. Therefore, it is appropriate for BCI applications [ 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 ] based on effective classifiers e. The precisely extracted commands from measured data controls external devices if noises are perfectly removed, i.

In the study, we presented a novel adaptive-filtering-based approach to reduce physiological and superficial noises and decomposition of the HRs in fNIRS data. Our experimental results revealed that the proposed method improved the accuracy of the estimated HR and significantly reduced physiological noises. The results strongly suggest that the proposed model can be utilized for noise removal and HR extraction in both offline and online applications. Villringer A, Chance B. Non-invasive optical spectroscopy and imaging of human brain function. Trends Neurosci.

Comparison of principal and independent component analysis in removing extracerebral interference from near-infrared spectroscopy signals. J Biomed Opt. Parks NA.

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Introduction

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Linear parameter-varying model and adaptive filtering technique for detecting neuronal activities: an fNIRS study. Cerebral regulation in different maximal aerobic exercise modes. Recommend to Library. Email to a friend. Digg This.

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