Ken Kiyono

Critical Scale Invariance in a Healthy Human Heart Rate

We demonstrate the robust scale-invariance in the probability density function (PDF) of detrended healthy human heart rate increments, which is preserved not only in a quiescent condition, but also in a dynamic state where the mean level of the heart rate is dramatically changing. This scale-independent and fractal structure is markedly different from the scale-dependent PDF evolution observed in a turbulentlike, cascade heart rate model. These results strongly support the view that a healthy human heart rate is controlled to converge continually to a critical state.

Non-Gaussian heart rate as an independent predictor of mortality in patients with chronic heart failure

BACKGROUND Morbidity and mortality due to chronic heart failure remain unacceptably high despite effective drug therapies, and the search for a better risk predictor is ongoing. Statistics derived from beat-to-beat fluctuations in heart rate or heart rate variability (HRV) have been used for this purpose, but the current predictability level is low or moderate at best. OBJECTIVE The purpose of this study was to evaluate whether a recently proposed non-Gaussian index of HRV is a significant and independent mortality predictor in patients with congestive heart failure (CHF). METHODS Twenty-four-hour Holter ECGs from 108 CHF patients were evaluated. Thirty-nine (36.1%) of the patients died during the follow-up period of 33 +/- 17 months. Cox proportional hazards regression analysis was performed to determine factors related to all-cause mortality. The factors evaluated derived from clinical information, including plasma brain natriuretic peptide, conventional time- and frequency-domain and fractal HRV measures, and a recently proposed non-Gaussian index lambda of HRV. RESULTS The short-term (<40 beats) non-Gaussian index lambda(40) (hazard ratio per increment of unit standard deviation 1.64, 95% confidence interval [1.23, 2.18], P <.001) and the long-term (<1,000 beats) index lambda(1000) (hazard ratio 1.42, 95% confidence interval [1.07, 2.18], P <.02), together with brain natriuretic peptide (hazard ratio 2.26, 95% confidence interval [1.45, 3.53], P <.001), are significant univariate risk predictors of mortality. In a multivariate model, lambda(40) (1.49, [1.13, 1.96], P <.005) and brain natriuretic peptide (2.39, [1.53, 3.75], P <.001) are independent predictors of the survival statistics of patients. None of the conventional HRV measures have predicted the mortality of patients in a significant and independent manner. CONCLUSION The results of this study indicate the usefulness of the short-term non-Gaussian index of HRV for risk prediction in patients with CHF.

Modeling human postural sway using an intermittent control and hemodynamic perturbations

Ground reaction force during human quiet stance is modulated synchronously with the cardiac cycle through hemodynamics [1]. This almost periodic hemodynamic force induces a small disturbance torque to the ankle joint, which is considered as a source of endogenous perturbation that induces postural sway. Here we consider postural sway dynamics of an inverted pendulum model with an intermittent control strategy, in comparison with the traditional continuous-time feedback controller. We examine whether each control model can exhibit human-like postural sway, characterized by its power law behavior at the low frequency band 0.1-0.7Hz, when it is weakly perturbed by periodic and/or random forcing mimicking the hemodynamic perturbation. We show that the continuous control model with typical feedback gain parameters hardly exhibits the human-like sway pattern, in contrast with the intermittent control model. Further analyses suggest that deterministic, including chaotic, slow oscillations that characterize the intermittent control strategy, together with the small hemodynamic perturbation, could be a possible mechanism for generating the postural sway.

Multiscale probability density function analysis: non-Gaussian and scale-Invariant fluctuations of healthy human heart rate

For a detailed characterization of intermittency and non-Gaussianity of human heart rate, we introduce an analysis method to investigate the deformation process of the probability density function (PDF) of detrended increments when going from fine to coarse scales. To characterize the scale dependence of the multiscale PDF, we use two methods: 1) calculation of Kullback-Leibler relative entropy; 2) parameter estimation based on Castaings equation (B. Castaing et al., 1990). We compare scale-dependence of the increment PDFs between actual heart rate fluctuations and artificially generated Gaussian and non-Gaussian noise, including a widely used autoregressive model and a recently proposed multifractal model based on a random cascade process. Our analysis highlights an essential difference between heart rate fluctuations and those generated by other models. The outstanding feature of human heart rate is the robust scale-invariance of the non-Gaussian PDF, which is preserved not only in a quiescent condition, but also in a dynamic state during waking hours, in which the mean level of heart rate is dramatically changing. Our results strongly suggest the need for revising existing models of heart rate variability to incorporate the scale-invariance in the PDF.

Simulation of a Dripping Faucet

A dripping faucet system is simulated. We numerically show that a hanging drop generally has many equilibrium shapes but only one among them is stable. By taking a stable equilibrium shape as an initial state, a simulation of dynamics is done, for which we present a new algorithm based on Lagrangian description. The shape of a drop falling from a faucet obtained by the present algorithm agrees quite well with experimental observations. Long-term behavior of the simulation can reproduce period-one, period-two, intermittent and chaotic oscillations widely observed in experiments. Possible routes to chaos are discussed.

Increased Non-Gaussianity of Heart Rate Variability Predicts Cardiac Mortality after an Acute Myocardial Infarction

Non-Gaussianity index (λ) is a new index of heart rate variability (HRV) that characterizes increased probability of the large heart rate deviations from its trend. A previous study has reported that increased λ is an independent mortality predictor among patients with chronic heart failure. The present study examined predictive value of λ in patients after acute myocardial infarction (AMI). Among 670 post-AMI patients, we performed 24-h Holter monitoring to assess λ and other HRV predictors, including SD of normal-to-normal interval, very-low frequency power, scaling exponent α(1) of detrended fluctuation analysis, deceleration capacity, and heart rate turbulence (HRT). At baseline, λ was not correlated substantially with other HRV indices (|r| < 0.4 with either indices) and was decreased in patients taking β-blockers (P = 0.04). During a median follow-up period of 25 months, 45 (6.7%) patients died (32 cardiac and 13 non-cardiac) and 39 recurrent non-fatal AMI occurred among survivors. While all of these HRV indices but λ were significant predictors of both cardiac and non-cardiac deaths, increased λ predicted exclusively cardiac death (RR [95% CI], 1.6 [1.3-2.0] per 1 SD increment, P < 0.0001). The predictive power of increased λ was significant even after adjustments for clinical risk factors, such as age, diabetes, left ventricular function, renal function, prior AMI, heart failure, and stroke, Killip class, and treatment ([95% CI], 1.4 [1.1-2.0] per 1 SD increment, P = 0.01). The prognostic power of increased λfor cardiac death was also independent of all other HRV indices and the combination of increased λ and abnormal HRT provided the best predictive model for cardiac death. Neither λ nor other HRV indices was an independent predictor of AMI recurrence. Among post-AMI patients, increased λ is associated exclusively with increased cardiac mortality risk and its predictive power is independent of clinical risk factors and of other HRV predictors.

Dripping Faucet Dynamics by an Improved Mass-Spring Model.

An improved mass-spring model for the dripping faucet is presented, which is constructed on the basis of numerical results recently obtained from our fluid dynamical computations. Both the fluid dynamical computations and the present mass-spring model exhibit a variety of complex behavior including transition to chaos in good agreement with experiments. The mass-spring model reveals further fundamental dynamics inherent in the dripping faucet system.

The lack of long-range negative correlations in glucose dynamics is associated with worse glucose control in patients with diabetes mellitus.

Glucose dynamics measured in ambulatory settings are fluid in nature and exhibit substantial complexity. We recently showed that a long-range negative correlation of glucose dynamics, which is considered to reflect blood glucose controllability over a substantial period, is absent in patients with diabetes mellitus. This was demonstrated using detrended fluctuation analysis (DFA), a modified random-walk analysis method for the detection of long-range correlations. In the present study, we further assessed the relationships between the established clinical indices of glycemic or insulinogenic control of hemoglobin A(1c) (HbA(1c)), glycated albumin (GA), 1,5-anhydroglucitol, and urine C-peptide immunoreactivity and the recently proposed DFA-based indices obtained from continuous glucose monitoring in 104 Japanese diabetic patients. Significant correlations between the following parameters were observed: (1) HbA(1c) and the long-range scaling exponent α(2) (r = 0.236, P < .05), (2) GA and α(2) (r = 0.254, P < .05), (3) GA and the short-range scaling exponent α(1) (r = 0.233, P < .05), and (4) urine C-peptide immunoreactivity and the mean glucose fluctuations (r = -0.294, P < .01). Therefore, we concluded that increases in the long-range DFA scaling exponent, which are indicative of the lack of a long-range negative correlation in glucose dynamics, reflected abnormalities in average glycemic control as clinically determined using HbA(1c) and GA parameters.

Universal and individual characteristics of postural sway during quiet standing in healthy young adults

The time course of the center of pressure (CoP) during human quiet standing, corresponding to body sway, is a stochastic process, influenced by a variety of features of the underlying neuro‐musculo‐skeletal system, such as postural stability and flexibility. Due to complexity of the process, sway patterns have been characterized in an empirical way by a number of indices, such as sway size and mean sway velocity. Here, we describe a statistical approach with the aim of estimating “universal” indices, namely parameters that are independent of individual body characteristics and thus are not “hidden” by the presence of individual, daily, and circadian variations of sway; in this manner it is possible to characterize the common aspects of sway dynamics across healthy young adults, in the assumption that they might reflect underlying neural control during quiet standing. Such universal indices are identified by analyzing intra and inter‐subject variability of various indices, after sorting out individual‐specific indices that contribute to individual discriminations. It is shown that the universal indices characterize mainly slow components of sway, such as scaling exponents of power‐law behavior at a low‐frequency regime. On the other hand, most of the individual‐specific indices contributing to the individual discriminations exhibit significant correlation with body parameters, and they can be associated with fast oscillatory components of sway. These results are consistent with a mechanistic hypothesis claiming that the slow and the fast components of sway are associated, respectively, with neural control and biomechanics, supporting our assumption that the universal characteristics of postural sway might represent neural control strategies during quiet standing.

Unique very low-frequency heart rate variability during deep sleep in humans

We investigate heart rate variability (HRV) in the very low-frequency (VLF) range (0.003-0.04 Hz) during deep sleep in good sleepers. Spectral analysis of HRV during deep sleep reveals consistent peaks at <0.04 Hz. By using wavelet analysis, we find both stationary and nonstationary periodic patterns in the VLF range, the presence of which has been discussed but has not been fully established to date. Although the mechanism(s) behind the unique VLF oscillations remain to be fully explored, we conjecture that there is an endogenous rhythmic component in human HRV in the VLF range. Further, our results also suggest a need for caution in the interpretation of the VLF spectral power in HRV during deep sleep.