Copula as a dynamic measure of cardiovascular signal interactions

Vasopressin and cardiovascular autonomic adjustment in chronic hypertensive pregnancy

Chronic hypertensive pregnancy (CHP) is a growing health issue with unknown etiology. Vasopressin (VP), a nonapeptide synthesized in paraventricular (PVN) and supraoptic nucleus (SON), is a well-known neuroendocrine and autonomic modulator of the cardiovascular system, related to hypertension development. We quantified gene expression of VP and its receptors, V1aR and V1bR, within the PVN and SON in CHP and normal pregnancy, and assessed levels of secreted plasma VP. Also, we evaluated autonomic cardiovascular adaptations to CHP using spectral indices of blood pressure (BPV) and heart rate (HRV) short-term variability, and spontaneous baroreflex sensitivity (BRS). Experiments were performed in female spontaneously hypertensive rats (SHRs) and in normotensive Wistar rats (WRs). Animals were equipped with a radiotelemetry probe for continuous hemodynamic recordings before and during pregnancy. BPV, HRV and BRS were assessed using spectral analysis and the sequence method, respectively. Plasma VP was determined by ELISA whilst VP, V1aR, and V1bR gene expression was analyzed by real-time-quantitative PCR (RT-qPCR). The results show that non-pregnant SHRs exhibit greater VP, V1aR, and V1bR gene expression in both PVN and SON respectively, compared to Wistar dams. Pregnancy decreased VP gene expression in the SON of SHRs but increased it in the PVN and SON of WRs. Pregnant SHRs exhibited a marked drop in plasma VP concentration associated with BP normalization. This triggered marked tachycardia, heart rate variability increase, and BRS increase in pregnant SHRs. It follows that regardless of BP normalization in late pregnancy, SHRs exhibit cardiovascular vulnerability and compensate by recruiting vagal mechanisms. Pregnant SHR dams have reduced expression of VP in SON associated with increased V1bR expression, lower plasma VP, normal BP during late pregnancy and marked signs of enhanced sympathetic cardiac stimulation (increased HR and LFHR variability) and recruitment of vagal mechanisms (enhancement of BRS and HFHR variability).

Dose Correlation of Panax ginseng and Atractylodes macrocephala Koidz. Drug Pairs in the Chinese Medicine Prescription Based on the Copula Function

Objective

Panax ginseng and Atractylodes macrocephala Koidz. (AMK) are widely used in treating various diseases; however, research is insufficient on measuring the relationship that exists by combining this drug pair using the copula function.

Methods

In this study, 279 traditional Chinese medicine prescriptions containing the Panax ginseng and AMK drug pair were extracted from the prescription database for three types of screened indications, namely, diabetes mellitus, diarrhea, and insomnia. Following the principle of dose conversion, each dynasty unit was uniformly converted into a modern unit. Then, the kernel density distribution of Panax ginseng and AMK was fitted with their empirical distribution functions. Finally, the optimal copula function was selected from the copula function family as a t-copula function.

Results

The empirical distribution and probability density functions of Panax ginseng and AMK were obtained. From the results, their Kendall rank correlation coefficients with indications of diabetes mellitus, insomnia, and diarrhea were 0.8689, 0.7858, and 0.7403, whereas their Spearman rank correlation coefficients were 0.9563, 0.9276, and 0.8958. Results also indicated that the use of the t-copula function can better reflect the correlation between Panax ginseng and AMK doses.

Conclusion

From the three indications, the dose between Panax ginseng and AMK was positively correlated. This study, therefore, confirms the medicinal principle of Chinese medicine “combining” from the perspective of mathematical statistics. Results from this study are practical to evaluate the correlation between the drug pair doses, Panax ginseng and AMK, using the copula function model, which provides a new model for the scientific explanation of compatibility for Chinese medicines. This study also provides a methodological basis for more drug measurement studies and clinical medications.

Entropy Analysis of COVID-19 Cardiovascular Signals

The world has faced a coronavirus outbreak, which, in addition to lung complications, has caused other serious problems, including cardiovascular. There is still no explanation for the mechanisms of coronavirus that trigger dysfunction of the cardiac autonomic nervous system (ANS). We believe that the complex mechanisms that change the status of ANS could only be solved by advanced multidimensional analysis of many variables, obtained both from the original cardiovascular signals and from laboratory analysis and detailed patient history. The aim of this paper is to analyze different measures of entropy as potential dimensions of the multidimensional space of cardiovascular data. The measures were applied to heart rate and systolic blood pressure signals collected from 116 patients with COVID-19 and 77 healthy controls. Methods that indicate a statistically significant difference between patients with different levels of infection and healthy controls will be used for further multivariate research. As a result, it was shown that a statistically significant difference between healthy controls and patients with COVID-19 was shown by sample entropy applied to integrated transformed probability signals, common symbolic dynamics entropy, and copula parameters. Statistical significance between serious and mild patients with COVID-19 can only be achieved by cross-entropies of heart rate signals and systolic pressure. This result contributes to the hypothesis that the severity of COVID-19 disease is associated with ANS disorder and encourages further research.

On Entropy of Probability Integral Transformed Time Series

The goal of this paper is to investigate the changes of entropy estimates when the amplitude distribution of the time series is equalized using the probability integral transformation. The data we analyzed were with known properties-pseudo-random signals with known distributions, mutually coupled using statistical or deterministic methods that include generators of statistically dependent distributions, linear and non-linear transforms, and deterministic chaos. The signal pairs were coupled using a correlation coefficient ranging from zero to one. The dependence of the signal samples is achieved by moving average filter and non-linear equations. The applied coupling methods are checked using statistical tests for correlation. The changes in signal regularity are checked by a multifractal spectrum. The probability integral transformation is then applied to cardiovascular time series-systolic blood pressure and pulse interval-acquired from the laboratory animals and represented the results of entropy estimations. We derived an expression for the reference value of entropy in the probability integral transformed signals. We also experimentally evaluated the reliability of entropy estimates concerning the matching probabilities.

A Mobile Crowd Sensing Application for Hypertensive Patients

Mobile crowd sensing (MCS) is an application that collects data from a network of conscientious volunteers and implements it for the common or personal benefit. This contribution proposes an implementation that collects the data from hypertensive patients, thus creating an experimental database using the cloud service Platform as a Service (PaaS). The challenge is to perform the analysis without the main diagnostic feature for hypertension—the blood pressure. The other problems consider the data reliability in an environment full of artifacts and with limited bandwidth and battery resources. In order to motivate the MCS volunteers, a feedback about the patient’s current status is created, provided by the means of machine-learning (ML) techniques. Two techniques are investigated and the Random Forest algorithm yielded the best results. The proposed platform, with slight modifications, can be adapted to the patients with other cardiovascular problems.