Comment on "Kullback-Leibler and renormalized entropies: applications to electroencephalograms of epilepsy patients".

In a recent paper Quian Quiroga et al. [R. Quian Quiroga et al., Phys. Rev. E 62, 8380 (2000)] found renormalized entropy, formerly introduced as a complexity measure for the different regimes of a dynamical system, to be closely related to the standard Kullback-Leibler entropy. They assure this finding by reanalyzing electroencephalographic data of epilepsy patients, previously examined by exclusive use of renormalized entropy [K. Kopitzki et al., Phys. Rev. E 58, 4859 (1998)]. We argue that the general considerations undertaken by the authors and the experimental results do not justify this conclusion.

Bone modeling and structural measures of complexity.

We test sensitivity and powerfulness of recently suggested Structure Measures of Complexity (SMC) with simulated test objects, represented by simple structures or modelled on the basis of a real bone image. We check how these SMC reflect the local and global disordering processes, as well as a deterioration of the bone structure. We show that applications of SMC provide additional information about any changes of the bone structure in comparison to bone mineral density (BMD), and that they can be potentially helpful in the diagnosis of osteoporosis.

Bone architecture assessment with measures of complexity.

Architectural changes in trabecular bone by osteoporosis were utilized as a model for the changes which probably occur in human bone while exposed to microgravity conditions. Although there are many concerns about microgravity-induced bone loss, little is known about the impact of microgravity on the three-dimensional architecture of the skeleton. 50 (level L3) and 57 (level L4) vertebral bones harvested from human cadavers were investigated by computed tomography (CT) and quantified in terms of bone mineral density (BMD). Based on the symbol-encoded transformed CT-images, five measures of complexity were developed which quantify the structural composition of the trabecular bone. This quantification determines the bone architecture as a whole. Depending on the specific measure of complexity and its relation to BMD, a 5-10% change of BMD is related to a 5-90% change in structural composition. The method requires a non-invasive CT-procedure of the lumbar spine resulting in a radiation exposure of about 30 microSv effective dose. The technique is useful for the evaluation of the bone status of space-flying, personnel as well as for patients on ground. Grant numbers: BMH1-CT92-0296.

Measures of complexity for cancellous bone.

The problem of quantifying the structure of cancellous bone has been addressed in the past by histomorphometry and more recently by imaging techniques using X-ray attenuation. The current approaches compute and describe parts of the construction of the trabecular net. We developed a new technique which quantifies cancellous bone of human lumbar vertebrae as a whole. The interactions, transactions, and interrelationships of all parts of the structural composition of the trabeculae are accounted for and quantified. The method is based on the concept of structural complexity within the framework of nonlinear dynamics. The methodology was developed by using axial high resolution computed tomography images. The technique was transferred to quantitative computed tomography images and is based on the non-invasive assessment of 50 human L3 specimens. The value of Houndsfield units per pixel representing trabecular bone of the vertebrae was transformed into color-encoded and alphabet-encoded symbols. The procedure of transformation of the X-ray attenuation pixels into symbols was necessary as a basis on which measures of complexity were introduced to assess the composition of symbols within the images. The development of a generalization of symbolic dynamics, a mathematical method, to work with two-dimensional images was a prerequisite. The results of this study demonstrate that the structural composition of cancellous bone declines more rapidly than bone mineral density during the loss of bone. This outcome strongly suggests an exponential relationship between bone mineral density and the architectural composition of cancellous bone. Normal trabecular bone has a complex ordered structure. The structural composition during the osteopenic phase of bone loss is characterized by lower structural complexity and a significantly higher level of architectural disorder. A high grade of osteoporosis leads again to an ordered structure, although its structural complexity is minimal.

The application of methods of non-linear dynamics for the improved and predictive recognition of patients threatened by sudden cardiac death.

OBJECTIVES: This study introduces new methods of non-linear dynamics (NLD) and compares these with traditional methods of heart rate variability (HRV) and high resolution ECG (HRECG) analysis in order to improve the reliability of high risk stratification. METHODS: Simultaneous 30 min high resolution ECG's and long-term ECG's were recorded from 26 cardiac patients after myocardial infarction (MI). They were divided into two groups depending upon the electrical risk, a low risk group (group 2, n = 10) and a high risk group (group 3, n = 16). The control group consisted of 35 healthy persons (group 1). From these electrocardiograms we extracted standard measures in time and frequency domain as well as measures from the new non-linear methods of symbolic dynamics and renormalized entropy. RESULTS: Applying discriminant function techniques on HRV analysis the parameters of non-linear dynamics led to an acceptable differentiation between healthy persons and high risk patients of 96%. The time domain and frequency domain parameters were successful in less than 90%. The combination of parameters from all domains and a stepwise discriminant function separated these groups completely (100%). Use of this discriminant function classified three patients with apparently low (no) risk into the same cluster as high risk patients. The combination of the HRECG and HRV analysis showed the same individual clustering but increased the positive value of separation. CONCLUSIONS: The methods of NLD describe complex rhythm fluctuations and separate structures of non-linear behavior in the heart rate time series more successfully than classical methods of time and frequency domains. This leads to an improved discrimination between a normal (healthy persons) and an abnormal (high risk patients) type of heart beat generation. Some patients with an unknown risk exhibit similar patterns to high risk patients and this suggests a hidden high risk. The methods of symbolic dynamics and renormalized entropy were particularly useful measures for classifying the dynamics of HRV.

Quantitative analysis of heart rate variability.

In the modern industrialized countries every year several hundred thousands of people die due to sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, noninvasive diagnostic tools like Holter monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyze the HRV. Especially, some complexity measures that are based on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients. (c) 1995 American Institute of Physics.

[New methods for the detection of high risk patients in cardiology]. / Neue Methoden für die Erkennung von Hochrisikopatienten in der Kardiologie.

Common non-invasive diagnostic methods like Holter monitoring or the analysis of high-resolution ECG and heart rate variability are unable to accurately assess the individual risk for sudden cardiac death, since they describe only statistical, linear or strictly periodic parameters. Using new methods of non-linear dynamics one can now calculate parameters which much better describe the dynamic behaviour of complex systems. The application of these new methods should therefore lead to an improved identification of high-risk patients. The results of this first pilot investigation show on the one hand that ventricular arrhythmias are quick detectable using phase space plots, and on the other hand that the new methods of non-linear dynamics could lead to a new classification of high-risk patients.