Tomoo Katsuyama

Behavior of the Dripping Faucet over a Wide Range of the Flow Rate

The time interval of successive water-drips from a faucet was examined over a wide range of the flow rate. The dripping interval alternately exhibits a stable state and a chaotic state as the flow ...

Neurodynamical Control of the Heart of Healthy and Dying Crustacean Animals

We analyzed the heartbeat-interval recorded from crustacean animals, using detrended fluctuation analysis (DFA) and delayed-time embedding method. EKG was obtained from freely moving animals in normal condition and then in terminal condition; we kept recording until the life was coming to an end. Our experimental purpose was to know whether DFA and embedding methods characterize quantitatively conditions of the cardiac control network, either in the brain or in the heart, or both, the brain and heart. We concluded that DFA exponents represent whether the subjects are under sick or healthy conditions. Here we show how the controller conditions of the brain changed and how pacemaker neural network in the heart deteriorated from time to time. This report demonstrates relationship between DFA and electro-physiological of the heart.Copyright

FRACTAL LIMIT DISTRIBUTIONS IN RANDOM TRANSPORTS

We analyze a random transport model of a scalar quantity on a discrete space-time. By changing a parameter which is a portion of the quantity transported at a time, we observe a continuous change of steady-state distribution of fluctuations from Gaussian to a power-law when the mean value of the scalar quantity is not zero. In the symmetric case with zero mean, the steady-state converges either to a trivial no fluctuation state or to a Lorentzian fluctuation state with diverging variance independent of the parameter. We discuss a possible origin of the intermittent behaviors of fully-developed fluid turbulence as an application.

A new probabilistic description for intermittent turbulence: Internal time

A new fractal model for intermittent turbulence is constructed on the basis of a hierarchical velocity-correlation function which represents a self-similar structure of turbulence. The hierarchy is assumed to be obtained by a class of transformations, such as the baker transformation. The hierarchical function allows describing stochastically the nonlinear dissipative dynamics of intermittent turbulence. The probabilistic description is done with time scales which have such a concept of age that the stronger the fluctuation is the younger it is in age. The velocity-correlation function which is observed in turbulent flow is expressed as having statistical weights proportional to the time scales. We propose that the time scale, called “internal time”, exists in the nonlinear dissipative dynamics of turbulence. A degree of intermittency is governed by the internal time. The numerical results of the one-dimensional energy spectrum function agree well over equilibrium range with experimental results. Mandelbrots fractal dimension takes values ranging from 2.3 to 2.7 for the experimental results.

Neurodynamical Control of the Heart of Freely Moving Animals Including Humans

Two kinds of nerves, acceleratory and inhibitory cardio-regulator nerves, innervate the heart. They are known to discharge concurrently to maintain an equilibrium state of the body. The nerves are also known to change their frequency of discharge in a reflexive manner to meet the demand from the periphery; such as augmentation of oxygen supply or vice versa. Consequently, the heart exhibits dynamic change in its pumping rate and force of contraction. If the control system fails, the heart exhibits unhealthy state. However, assessment of healthy/unhealthy status is uneasy because we are not able to monitor the nerve activities by non-invasive methods. Therefore, we challenged to detect state of the heart without nerve-recordings. We used the detrended fluctuation analysis (DFA) applying to heartbeat interval time series because DFA has been believed that it can quantify the state of heart. We performed DFA on the EKGs (electrocardiograms) from various living organisms including humans. The objective of this research was to determine whether the analytical technology, DFA, could function as a useful method for the evaluation of the subject’s quality of cardiovascular-related illness and transition to and from a normal healthy state. We found that DFA could describe brain-heart interaction quantitatively: the scaling exponents of (1) healthy, (2) sick-type (such as stressful or arrhythmic states), and (3) unpredictable-death type (such as ischemic heart disease) were corresponded to individuals who exhibited, (1) nearly one, (2) less than one, and (3) greater than one, respectively. We conclude that scaling exponents could determine whether the subjects are under sick or healthy conditions on the basis of cardiac physiology.Copyright

Detrended Fluctuation Analysis of Arrhythmia: Scaling Exponent as an Index of Heart Wellness

Well-established technologies to analyze biological signals including rhythmic heartbeat are available and accessible to scholars. However, stronger empirical evidence is required to justify the use of these technologies as practical tools in the field of biomedicine. Here we conducted analyses of heartbeat interval time series using an analytical technology developed across three decades—detrended fluctuation analysis (DFA)—to verify the power-law/scaling characteristics of signals that fluctuate in a regular, irregular, or erratic manner. We believe that DFA is a useful tool because it can quantify the heart condition by a scaling exponent, with a value of one (1) set as the default for a healthy state. This baseline value can be compared to a clinical thermometer, where the baseline is 37 °C for a physiologically healthy condition. Our study aimed to ascertain and confirm the utility of DFA in evaluating heart wellness, specifically in the context of studying arrhythmic heartbeat. We present case studies to confirm that DFA is a beneficial tool that quantifies the scaling exponent of a heart’s condition as “nonstationarily” beating and dynamically controlled. From an engineering perspective, we show that the heart condition can be classified into two typical categories: a healthy rhythm with a scaling exponent of one (1.0), and arrhythmia with a lower scaling exponent (0.7 or less).Copyright

DFA, a Biomedical Checking Tool for the Heart Control System

We made our own detrended fluctuation analysis (DFA) program. We applied it to the cardio-vascular system for checking characteristics of the heartbeat of various individuals. Healthy subjects showed a normal scaling exponent, which is near 1.0. This is in agreement with the original report by Peng et al. published in 1990s. We found that the healthy exponents span from 0.9 to 1.19 in our temporary guideline based on our own experiments. In the present study, we investigated the persons who have an extra-systole heartbeat, so called as premature ventricular contractions (PVCs), and revealed that their arrhythmic heartbeat exhibited a low scaling exponent approaching to 0.7 with no exceptions. In addition, alternans, which is the heartbeats in period-2 rhythms, and which is also called as the harbinger of death, exhibited a low scaling exponent like the PVCs. We may conclude that if it would be possible to make a device that equips a DFA program, it might be useful to check the heart condition, and contribute not only in statistical physics but also in biomedical engineering and clinical practice fields; especially for health check. The device is applicable for people who are spending an ordinary life, before they get seriously heart sick.

Evaluation of Wellness by Detrended Fluctuation Analysis of Heartbeats

We used detrended fluctuation analysis (DFA), which was originally developed by Peng et al. (1995) to check power-law characteristics, to study the heartbeats of various subjects. Our purpose was to determine whether DFA is a useful method for the evaluation of a subject’s quality of recovery from cardiovascular-related illness and transition to a normal healthy state. Here, we report on subjects who underwent rehabilitation thermal therapy, subjects who developed premature ventricular contractions, and other subjects, including healthy subjects. The perceived level of wellness varies among subjects because the physiology of no 2 individuals is identical. However, several case studies have shown how wellness of subjects can be evaluated using heartbeat recordings. We conclude that DFA is a new, useful numerical method for quantifying the degree of wellness and the transition from sickness to wellness.Copyright

Premature ventricular contractions, a typical extra-systole arrhythmia, lowers the scaling exponent: DFA as a beneficial biomedical computation

We made our own DFA (detrended fluctuation analysis) program. We applied it to the heartbeat of various individuals. Healthy subjects showed a normal scaling exponent, which is near 1.0 (ranging 0.9 to 1.19 in our own temporary guideline). This is in agreement with the original report by Peng et al. long time ago. In the present study, we investigated a person who has an extra-systole heartbeat, called PVCs (premature ventricular contractions), and found that their arrhythmic heartbeat exhibited a low scaling exponent (around 0.7). Alternans, which is the heart beating in period-2 rhythms, exhibited a much low scaling exponent (around 0.6). We suggest that a device that employs a DFA program might be useful to check the heart condition, and would contribute not only in nonlinear physics but also in biomedical fields especially as a device to routinely check for predictors of heart disease in otherwise normal people.

An Extra-Systole Arrhythmia Lowers the Scaling Exponent: DFA as a Beneficial Biomedical Tool

We made our own DFA (detrended fluctuation analysis) program. We applied it for checking characteristics for the heartbeat of various individuals. Healthy subjects showed a normal scaling exponent, which is near 1.0 (ranging 0.9 to 1.19 in our own temporary guideline). This is in agreement with the original report by Peng et al. long time ago. In the present study, we investigated the person who has an extra-systole heartbeat, which is so called as PVCs (premature ventricular contractions), and revealed that their arrhythmic heartbeat exhibited a low scaling exponent (around 0.7). Alternans, which is the heart beating in period-2 rhythms, exhibited a much low scaling exponent (around 0.6). We may conclude that if it would be possible to make a device that equips a DFA program, it might be useful to check the heart condition, and contribute not only in nonlinear physics but also in biomedical fields; especially as a device for health check, which is applicable for people who are spending an ordinary life, before they get seriously heart sick.