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Measuring electrical impedance of different segments of thebody, a.k.a. IP, has been widely used in different fields ofmedicine for decades. Examples of applications of plethysmog-raphy in medicine are measuring lung volume, blood volumevariations, blood flow, muscle contraction, eye movement, au-tonomic nervous system activity, and activity of brain cells [14].

Plethysmography is performed by injecting a high-frequencylow-amplitude sinusoidal current into the segment of interestusing a pair of skin electrodes (current electrodes) and measur-ing the imposed voltage difference between the injection pointsusing another pair of skin electrodes (voltage electrodes) [15].Electrical resistance of the tissue of interest is then calculatedusing the injected current and the measured voltage differencebetween the electrodes, which is caused by the passage of cur-rent through the tissue. The result is the IP signal, whose maincomponent is highly correlated with respiration [16], [17]. Therespiratory signal and the respiratory rate could be easily ex-tracted from the IP signal acquired from the thorax and abdomenarea when the subject is motionless. However, motion is anothermain source of blood volume variation. Motion can create dras-tic variations in the measured IP signal [18]–[22], resulting inartifacts whose amplitudes are much larger than the amplitudeof the respiratory component in many cases [23]. As a result, itis necessary to use filtering methods to eliminate MA’s beforethe signal can be used to monitor respiration. The IP signalsused in this study are measured on the subject’s back betweenthe third and tenth ribs. This setting has been used instead of thetraditional transthoracic electrode placement, since it is suitablefor portable acquisition of the IP signal.

The experiments that are presented in this study were con-ducted using a Biopac MP150 system, equipped with a BiopacEBI100C to measure the IP signal and a Biopac CO2100C tomeasure the EtCO2signal. All the signals were collected at250 Hz and were later down-sampled to 10 Hz for processingpurposes. The collected IP signals were filtered using a Butter-worth bandpass filter with cutoff frequencies of 0.001 and 2 Hz.A three-axis accelerometer sensor was used to capture the sub-ject’s movements. The module was placed on the subject’s rightarm and the signals were transferred to the Biopac machine andstored on a laptop. This setting was used because the movementsof the arm capture most of the movements that can induce MAinto the signal. However, choosing the optimal setting for theelectrodes and the accelerometer sensors is outside the scope ofthis paper and requires further investigation. The accelerometersignals were bandpass filtered using a Butterworth filter withcutoff frequencies of 0.05 and 2 Hz. A sample of the data thatis contaminated with MA is shown in Fig. 4.The plethysmograph’s electrodes were placed on the subject’sback between serratus posterior superior and serratus posteriorinferior muscles. Similarly, voltage electrodes were placed onthe back right beside the current electrodes along the path be-tween them. Fig. 5 shows the placements of the electrodes.Two experiments were conducted to assess the performanceof the proposedε-tube filtering method. The first experimentwas performed to compare the proposed method to the ICAalgorithm. The FastICA package, which maximizes the non-Gaussianity, was used in this study. For this experiment, thedata were collected from six subjects. The subjects performeda total of 272 maneuvers in 280.6 min (72.0 min of the signalswere contaminated by MA). The ICA algorithm requires atleast two readings of the IP signal from two different sights.The traditional transthoracic electrode placement was used asthe second channel of the IP signal. The second experimentwas conducted to compare the proposed method to the RLS andNLMS filtering methods. Thirteen subjects participated in thisexperiment where a total of 501 maneuvers were performed bythe subjects in 589.5 min, where 143.9 min of the signals werecontaminated by MA.

Subjects were asked to perform several maneuvers to imi-tate transient and periodic movements in both experiments. Theexperimented maneuvers are described in Table I. Maneuvers1–9 are transient movements while maneuvers 10–14 are pe-riodic. Each maneuver was performed roughly three times byeach subject, except maneuvers 13 and 14 which were each per-formed once. All the maneuvers except 7 and 8, 13 and 14 wereperformed while the subject was sitting on a chair.After removing the MA’s, the respiratory rate is extractedfrom both the filtered IP and the EtCO2signals. To do so, theS-transform of the signal is computed and the most dominantfrequency component between 0 and 2 Hz is considered to bethe respiratory rate at each timet. The S-transform is computedwithin a sliding window which is 30 s long and a step lengthof 10 s. The respiratory rate is extracted from 10 s of the signalin the middle of the window. Also, a threshold on the amplitudeof the signal is used to detect whether the subject is breathingor not. The extracted respiratory rates from the IP and EtCO2signals are then compared to assess the performance of the pro-posed filtering method. No postprocessing has been performedprior to the respiratory rate extraction.

This section presents the results of comparing the respira-tory rates extracted from the filtered IP signal and the EtCO2(reference) signal using two criteria, the error and the correla-tion, where the error is defined as the amount of discrepancybetween the respiratory rates in breaths per minute (BPM). Thefilter parameters are selected using subject-wise cross valida-tion, i.e., the signals for one of the subjects is used as the testdata while the rest of the subjects are used to find the optimalparameters in each fold. The criterion used for selecting the op-timal parameters is the mean error. The filter orders forε-tubewerena=1andnb=6in all the folds, andc=20in nineandc=10in four folds. For the NLMS filter, the selected filterorder is 35 in all the folds, the step size is 0.1 in nine foldsand 0.05 in the others, and the leakage is 0.93 in six folds and0.95 for the others. The selected filter orders and forgetting fac-tors for the RLS filters are five and 0.99 in all the folds, respec-tively. For the ICA algorithm, cross validation selects the tangenthyperbolic AF witha1=10intanh(a1u)in five folds and theGaussian AF’s witha2=5anda2=10inuexp(−a2u2/2)forthe remaining two folds. The RLS and NLMS filters are cho-sen as the representatives of the family of adaptive filters sincethey are the most commonly used filtering methods in differentsignal processing applications, including MA reduction.The results of MA reduction usingε-TF, NLMS, RLS, andICA from a sample of maneuver five are shown in Fig. 6. Theamplitude of the filtered IP signal in Fig. 6(b) is within theimposed tube. On the other hand, the NLMS, RLS, and ICAmethods, as shown in Figs. 6(f) and (g) do not guarantee thatthe amplitude of the filtered signal is within the acceptable rangeof amplitudes for the IP signal. Furthermore, none of the meth-ods exceptε-TF are able to successfully recover the respiratory component of the signal. Hence, the proposed method seems tooutperform the existing methods. The proposed filter and ICAare compared in Table II using several different performancemeasures. A similar comparison between the proposedε-TF,NLMS, and RLS filters is shown in Table III. The first perfor-mance measure that is used,Corr, is the Pearson correlationcoefficient between the filtered IP signal and the EtCO2signal,which measures how much the morphological features of thetwo signals agree in the time domain. The error between theextracted respiratory rates is also used to compute several per-formance measures. The first measure,Exact, is the proportionof the times when the extracted respiratory rate from the IP andEtCO2signals are equal. Moreover,Dev1andDev3are the pro-portions of the times when the average error is less than 1 and 3BPM, respectively. Finally,Mean ErrandMax Errare the meanand maximum error between the respiratory rates extracted fromthe filtered IP signal and the EtCO2signal, respectively.Figs. 7 and 8 show the comparison between the proposed andthe conventional methods for different maneuvers using correla-tion. The results indicate that the proposed method outperformsthe other methods with no exceptions. Moreover, Figs. 9 and 10show a similar comparison using mean error. Again, the perfor-mance of the proposed method is superior to the other methodsin all the maneuvers. As a result, we can conclude that the pro-posed method is more successful in removing the MA comparedto ICA, NLMS, and RLS. The statistical significance of the dif-ferences are tested using Tukey’s honestly significant difference(HSD) for NLMS and RLS and using two-samplet-tests for ICA.The Box–Cox transform is successfully applied to the response variables to improve the normality and homogeneity of the vari-ances. The analysis includessubjectandreplication[subject](replicationnested withinsubject) as random effects, andfilter-ing methodas a fixed effect. It is performed separately for eachmaneuver.The statistical tests indicate that most of the differences inFigs. 7–10 are statistically significant. Tables IV and V showthe results of the statistical analysis. The results indicate that 33of the tests on correlations and 36 of the tests on mean errors outof the total of 42 tests that have been conducted in each case aresignificant. Similar results are obtained using pair-wiset-testsand Bonferroni’s correction, except for the difference betweenthe mean errors ofε-tube and RLS which becomes significantwhen pair-wiset-test is used. As a result, we can conclude thatthe proposed method outperforms the existing method and thedifferences between this method and the existing methods arestatistically significant.All in all, the results indicate that the proposed method issuperior compared to ICA, NLMS, and RLS.

Theε-tube filter proposed in this study is a novel approachfor removing high-amplitude MA’s from the IP signal with aregular pattern. The only assumption that is made is that theamplitude of the signal of interest does not change rapidly duringa short period of time. An ARX model is used to relate the inputaccelerometer signals to the filter output which is an estimate ofthe MA. Aε-tube is used to measure the estimation error. Thisallows for modeling the MA while refraining from modeling thesignal of interest. In order to choose the best filter coefficientsamong those that minimize the estimation error, a regularizationterm is introduced to maximize the regularity of the outputsignal. The results show that theε-tube filter with regularizationcan effectively reduce the MA in the IP signal. In particular,the proposed method outperforms ICA, NLMS, and RLS inall the maneuvers that were performed in the experiments. Thestatistical tests indicate that the differences betweenε-TF andthe conventional methods are statistically significant in most of the cases. Hence, the proposed method is more successful inremoving the MA from the IP signal than ICA, NLMS, andRLS.One of the future works of this study is to evaluate the per-formance ofε-tube filter in removing MA’s from other physio-logical signals, such as ECG and PPG. Moreover, the proposedmethod should be compared to other existing MA reductionmethods. The adaptive version of the same filter will also bedeveloped to be used in real-time applications View More