Healthy systems exhibit complex dynamics on the changing of information embedded in physiologic signals on multiple time scales that can be quantified by employing multiscale entropy (MSE) analysis. Here, we propose a measure of complexity, called entropy of entropy (EoE) analysis. The analysis combines the features of MSE and an alternate measure of information, called superinformation, useful for DNA sequences. In this work, we apply the hybrid analysis to the cardiac interbeat interval time series. We find that the EoE value is significantly higher for the healthy than the pathologic groups. Particularly, short time series of 70 heart beats is sufficient for EoE analysis with an accuracy of 81% and longer series of 500 beats results in an accuracy of 90%. In addition, the EoE versus Shannon entropy plot of heart rate time series exhibits an inverted U relationship with the maximal EoE value appearing in the middle of extreme order and disorder.

Mode mixing is a limitation of the empirical mode decomposition (EMD) method appropriate for physiological signal analysis. In 2008, boundary condition map presented by Rilling and Flandrin provided the efficiency of separating the two components of a two-tone signal as a function of their amplitude and frequency ratios. Until 2019, their findings were still applied. However, their maps only give an uncertainty-like efficiency of mode mixing separation for two-tone signals. In this paper, we propose a criterion for mode mixing separation in EMD, which provides a binary judgment on mode mixing separation instead of the above-mentioned efficiency. By comparing the slopes of the two components, we found that the phenomenon of mode mixing occurs as the extrema of the high-tone component are suppressed by the low-tone component. Under this condition, the criterion shows the relation among their amplitude ratio, frequency ratio, and relative phase between the two components. Given with the values of the three parameters, one can affirm whether the two components are mixed according to the criterion. Accordingly, we derive a black/white three-dimensional (3D) map that plots the binary result of mode mixing in black or white as a function of the three parameters. Our map agrees with Rilling's map and the results obtained from our gait analysis. Among the 23 sets of center-of-mass trajectory signals, six sets encountered the mode mixing problem and their coordinates of the three parameters were found in the black region of the map, while the other 17 sets were in the white region.INDEX TERMS Empirical mode decomposition, mode mixing separation, improved EMD.

Static standing postural stability has been measured by multiscale entropy (MSE), which is used to measure complexity. In this study, we used the average entropy (AE) to measure the static standing postural stability, as AE is a good measure of disorder. The center of pressure (COP) trajectories were collected from 11 subjects under four kinds of balance conditions, from stable to unstable: bipedal with open eyes, bipedal with closed eyes, unipedal with open eyes, and unipedal with closed eyes. The AE, entropy of entropy (EoE), and MSE methods were used to analyze these COP data, and EoE was found to be a good measure of complexity. The AE of the 11 subjects sequentially increased by 100% as the balance conditions progressed from stable to unstable, but the results of EoE and MSE did not follow this trend. Therefore, AE, rather than EoE or MSE, is a good measure of static standing postural stability. Furthermore, the comparison of EoE and AE plots exhibited an inverted U curve, which is another example of a complexity versus disorder inverted U curve.

BackgroundTotal motile sperm count (TMSC) and curvilinear velocity (VCL) are two important parameters in preliminary semen analysis for male infertility. Traditionally, both parameters are evaluated manually by embryologists or automatically using an expensive computer-assisted sperm analysis (CASA) instrument. The latter applies a point-tracking method using an image processing technique to detect, recognize and classify each of the target objects, individually, which is complicated. However, as semen is dense, manual counting is exhausting while CASA suffers from severe overlapping and heavy computation.MethodsWe proposed a simple frame-differencing method that tracks motile sperms collectively and treats their overlapping with a statistical occupation probability without heavy computation. The proposed method leads to an overall image of all of the differential footprint trajectories (DFTs) of all motile sperms and thus the overall area of the DFTs in a real-time manner. Accordingly, a theoretical DFT model was also developed to formulate the overall DFT area of a group of moving beads as a function of time as well as the total number and average speed of the beads. Then, using the least square fitting method, we obtained the optimal values of the TMSC and the average VCL that yielded the best fit for the theoretical DFT area to the measured DFT area.ResultsThe proposed method was used to evaluate the TMSC and the VCL of 20 semen samples. The maximum TMSC evaluated using the method is more than 980 sperms per video frame. The Pearson correlation coefficient (PCC) between the two series of TMSC obtained using the method and the CASA instrument is 0.946. The PCC between the two series of VCL obtained using the method and CASA is 0.771. As a consequence, the proposed method is as accurate as the CASA method in TMSC and VCL evaluations.ConclusionIn comparison with the individual point-tracking techniques, the collective DFT tracking method is relatively simple in computation without complicated image processing. Therefore, incorporating the proposed method into a cell phone equipped with a microscopic lens can facilitate the design of a simple sperm analyzer for clinical or household use without advance dilution.

Static standing postural stability has been measured by multiscale entropy (MSE), which is used to measure complexity. In this study, we used the average entropy (AE) to measure the static standing postural stability, as AE is a good measure of disorder. The center of pressure (COP) trajectories were collected from 11 subjects under four kinds of balance situation, from stable to unstable: bipedal with open eyes, bipedal with closed eyes, unipedal with open eyes, and unipedal with closed eyes. The AE, entropy of entropy (EoE), and MSE methods were used to analyze these COP data, and EoE was found to be a good measure of complexity. The AE of the 11 subjects sequentially increased by 100%as the balance situations progressed from stable to unstable, but the results of EoE and MSE did not follow this trend. Therefore, AE, rather than EoE or MSE, is a good measure of static standing postural stability. Furthermore, the comparison of EoE and AE plots exhibited an inverted U curve, which is another example of a complexity versus disorder inverted U curve.

The complexity of biological signals has been proposed to reflect the adaptability of a given biological system to different environments. Two measures of complexity-multiscale entropy (MSE) and entropy of entropy (EoE)-have been proposed, to evaluate the complexity of heart rate signals from different perspectives. The MSE evaluates the information content of a long time series across multiple temporal scales, while the EoE characterizes variation in amount of information, which is interpreted as the "state changing," of segments in a time series. However, both are problematic when analyzing white noise and are sensitive to data size. Therefore, based on the concept of "state changing," we propose state change probability (SCP) as a measure of complexity. SCP utilizes a statistical hypothesis test to determine the physiological state changes between two consecutive segments in heart rate signals. The SCP value is defined as the ratio of the number of state changes to total number of consecutive segment pairs. Two common statistical tests, the t-test and Wilcoxon rank-sum test, were separately used in the SCP algorithm for comparison, yielding similar results. The SCP method is capable of reasonably evaluating the complexity of white noise and other signals, including 1/f noise, periodic signals, and heart rate signals, from healthy subjects, as well as subjects with congestive heart failure or atrial fibrillation. The SCP method is also insensitive to data size. A universal SCP threshold value can be applied, to differentiate between healthy and pathological subjects for data sizes ranging from 100 to 10,000 points. The SCP algorithm is slightly better than the EoE method when differentiating between subjects, and is superior to the MSE method.

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A novel design of an optical path length modulator is reported for ocular axial length measurement in an optical biometer. The relative optical path length modulator is designed to achieve a large optical path length change linearly over 52 mm with a tiny short translation stage movement of 3 mm to cover the entire axial lengths of all patients from infant to adult in an optical biometer. This design demonstrates a good benefit for the long-range scanning of ocular axial length from cornea to retina with small translation stage movement of reference arm.