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Observational data of natural systems, as measured in medical measurements are typically quite different from those obtained in laboratories. Due to the peculiarities of these data, wellknown characteristics, such as power spectra or fractal dimension, often do not provide a suitable description. To study such data, we present here some measures of complexity, which are basing on symbolic dynamics. Firstly, a motivation for using symbolic dynamics and measures of complexity in data analysis based on the logistic map is given and next, two applications to medical data are shown. We demonstrate that symbolic dynamics is a useful tool for the risk assessment of patients after myocardial infarction as well as for the evaluation of th e architecture of human cancellous bone.
Objective: Impairment of the baroreceptor reflex activity reflects an alteration of the autonomous regulation of the cardiovascular system and has proven to predict fatal outcome in patients after acute myocardial infarction. The following study was performed to analyse the baroreceptor sensitivity, heart rate variability and blood pressure variability in patients early after coronary surgery. Methods: Twenty-five male patients undergoing coronary artery bypass were examined in a prospective study; normal values were obtained from healthy volunteers. Arterial pressure signals were recorded from a radial artery catheter for 30 min preoperatively and in short intervals after surgery. Mechanical manipulations and pharmacological interventions were avoided during the sampling periods. Baroreflex function was calculated according to the dual sequence method, heart rate variability and blood pressure variability were calculated including nonlinear methods. Results: Initial values of the patients did not differ from healthy volunteers. The strength of baroreflex sensitivity (increase in blood pressure causing a synchronous decrease of heart rate) is low 2 It postoperatively. The number of delayed tachycardic changes of heart rate, which are caused by sympathetic activation, is only moderately reduced as compared to values obtained from healthy volunteers. Heart rate variability is widely unchanged as compared to preoperative values; blood pressure variability showed an increase of low-frequency components, again indicating sympathetic predominance. Nonlinear analyses revealed reduced system complexity at the beginning of the postoperative course. Conclusion: Obviously, there is a vagal suppression 20 h after surgery, while the sympathetic tonus works in a normal range. This unbalanced interaction of the autonomous systems is similar to findings in patients after myocardial infarction. The predictive value of these markers has to be elucidated in further clinical studies. (C) 2003 Elsevier B.V. All rights reserved
Objectives. Ventricular tachycardia (VT) provoking sudden cardiac death (SCD) are a major cause of mortality in the developed countries. The most efficient therapy for SCID prevention are implantable cardioverter defibrillators (ICD). In this study heart rate variability (HRV) measures were analyzed for short-term forecasting of VT in order to improve VT sensing and to enable a patient warning of forthcoming shocks. Methods. The lost 1000 normal beat-to-beat intervals before 50 VT episodes stored by the ICD were analyzed and compared to individually acquire control time series (CON). HRV analysis was performed with standard parameters of time and frequency domain as suggested by the HRV Task Force and furthermore with a newly developed and optimized nonlinear parameter that assesses the compression entropy of heart rate (H-c). Results. Except of meanNN (p = 0.02) we found no significant differences in standard HRV parameters. In contrast, H, revealed highly significant (p = 0.007) alterations in VT compared with CON suggesting a decreased complexity before the onset of VT. Conclusion: Compression entropy might be a suitable parameter for short-term forecasting of life-threatening tachycardia in ICD
Hypertensive pregnancy disorders are a leading cause of perinatal and maternal morbidity and mortality. Heart rate variability (HRV), blood pressure variability (BPV), and baroreflex sensitivity (BRS) are relevant predictors of cardiovascular risk in humans. The aim of the study was to evaluate whether HRV, BPV, and BRS differ between distinct hypertensive pregnancy disorders. Continuous heart rate and blood pressure recordings were performed in 80 healthy pregnant women as controls (CON), 19 with chronic hypertension (CH), 18 with pregnancy-induced hypertension (PIH), and 44 with pre-eclampsia (PE). The data were assessed by time and frequency domain analysis, nonlinear dynamics, and BRS. BPV is markedly altered in all three groups with hypertensive disorders compared to healthy pregnancies, whereby changes were most pronounced in PE patients. Interestingly, this increase in PE patients did not lead to elevated spontaneous baroreflex events, while BPV changes in both the other hypertensive groups were paralleled by alterations in baroreflex parameters. The HRV is unaltered in CH and PE but significantly impaired in PIH. We conclude that parameters of the HRV, BPV, and BRS differ between various hypertensive pregnancy disorders. Thus, distinct clinical manifestations of hypertension in pregnancy have different pathophysiological, regulatory, and compensatory mechanisms
In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated firstly from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE-algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and get again promising results. The thermally inducedaccuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems. errors can be estimated with 1-2 micrometer
In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated firstly from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE-algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and get again promising results. The thermally induced errors can be estimated with 1-2${mu m}$ accuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems.
Correlation dimension analysis of heart rate variability in patients with dilated cardiomyopathy
(2005)
A correlation dimension analysis of heart rate variability (HRV) was applied to a group of 55 patients with dilated cardiomyopathy (DCM) and 55 healthy subjects as controls. The 24-h RR time series for each subject was divided into segments of 10,000 beats to determine the correlation dimension (CD) per segment. A study of the influence of the time delay (tag) in the calculation of CD was performed. Good discrimination between both groups (p < 0.005) was obtained with tag values of 5 or greater. CD values of DCM patients (8.4 ± 1.9) were significantly lower than CD values for controls (9.5 ± 1.9). An analysis of CD values of HRV showed that for healthy people, CD night values (10.6 ± 1.8) were significant greater than CD day values (9.2 ± 1.9), revealing a circadian rhythm. In DCM patients, this circadian rhythm was lost and there were no differences between CD values in day (8.8 ± 2.4) and night (8.9 ± 2. 1). © 2005 Elsevier Ireland Ltd. All rights reserved