Research ArticleDerivation of a measure of systolic blood pressure mutability: a novel information theory-based metric from ambulatory blood pressure tests
Introduction
Blood pressure (BP) can reach persistently elevated levels in what is usually called hypertension, a condition with one of the highest mortality rates worldwide. As it is well known a proper diagnosis of hypertension can help to save lives and to avoid vascular accidents that can limit the quality of life of some patients even if they survive.1 The cardiac cycle is very well established and can be found in the classical physiology textbook of W.F. Ganong for example.2 The systolic pressure (SP) is the maximum arterial pressure while the diastolic pressure (DP) is its minimum pressure, both of which are usually reported in units on mm of Hg. The SI unit for pressure is the Pascal (Pa) which corresponds to 1 N/m2; the kPa is found to be more convenient for usual BPs. The conversion can be easily achieved by means of the following expression: 1 mm Hg = 0.13332 kPa.
We can refer to the two previously mentioned circulatory pressures by an ordinate pair of numbers (SP,DP) for convenience with average values over a certain period of time denoted by (<SP>,<DP>). Thus, daily average pressures like (<125>,<75>) are usually thought to describe a person with normal BP; likewise, (<140>,<85>) describes a patient with some degree of blood hypertension. Although classifications of stages for hypertension may vary among different sources in this article, we follow here the study by H. Prat el al3 due to its local implications, since we will be dealing with data recorded in Chile.
Single measurements of BP may not have real significance for BP varies during the day. Therefore, a sequence of measurements is more appropriate since BP changes in intervals of minutes for the same person. An ambulatory 24-hour BP monitor (BP Holter) has been implemented, that periodically records SP, DP, and heart rate (HR) aiming to improve diagnoses. This monitoring system has been in use in Chile for decades using well-established protocols.4 The BP Holter examination can be adjusted to provide information after periods of certain number of minutes and during the course of many hours (usually one entire day). In this article, we will use this kind of data as described in the next section.
Usually, the data sequence provided by the BP monitors is subject to basic “static” statistics. In the present study, we propose a way to extract additional information from the ambulatory BP monitor, which can be used by the treating physician to determine “dynamic” variability in the series of measurements. By means of information theory, it is possible to recognize the degree of information content in any sequence as has been successfully applied in the case of magnetic systems.5 The same technique has been applied to study the dynamic variability of economic systems as well, such as stock markets.6 This new method introduces a quantitative indicator called mutability (μ) that recognizes the repetitive structures in the data chain. For the time being, let us just say that μ is a measure of the agitation of the system revealed by the fluctuations of the data sequence; high values of μ correspond to highly changing variables, while low values of μ correspond to monotonic data.
Although the importance of static variability in BP has been discussed in relation to prognosis and as a therapeutic target,7, 8, 9 it is not measured in clinical practice due to the lack of universally accepted definitions for normality or risk. We believe mutability may add information in relation to this field because it can deal with variability in a dynamic way which is not done by normal statistical methods. We will present evidence for recognition of different BP patterns by means of mutability, which could be an indication for risk. At present, there is no clinical evidence to sustain a risk indicator, so this represents the introduction of new techniques based on information theory. This should be considered as a first step research in relation to hypertension information and further studies relating these data with clinical outcomes are needed.
Section snippets
Data Description
The data used in the present study correspond to a random selection of 515 BP Holter tests obtained at Clinica Alemana de Temuco, between June 11, 2006 and November 10, 2011. Owing to Chilean laws and the regulations at Clinica Alemana de Temuco access to patient's personal or clinical information is not available to us; the only additional information that can be used here is some general demographic characteristics like gender, age, and medication or no medication. The Ethics Board of
Systolic Sequence
Let us begin by considering some general demographic characteristics of the sample. In Table 1, we separate the 515 patients according to their hypertension condition. According to previous conventional definition, the characteristics of the 181 patients with hypertension (average SP more than 130 mm Hg) are given in the column at the center, while those of the 334 patients without hypertension are given in the column to the right. This table is self-explanatory so it does not need further
Discussion
We begin this discussion by analyzing the main result of the approach proposed here: the mutability of the time sequences provided by the 24-hour BP monitors. This is an entirely new method in the field of data analysis and results reported here represent the first application to a biological sequence as it is the case for the ambulatory tests for the circulatory system. It can be quite easy to apply this method to other fields of physiology and clinical data analysis because the method is
Acknowledgments
The authors are grateful to Dr. Sergio Muñoz for helpful discussions on statistics.
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Conflict of interest: No conflicts of interest, financial or otherwise, are declared by the authors.
Funding: This work was partially supported by Millennium Scientific Initiative through grant P-06-022-F, Centro para el Desarrollo de la Nanociencia y Nanotecnología (CEDENNA) under contract FB0807 and by Fondecyt contracts 1100156 and 1150019.