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Carlson-Sabelli L, Sabelli HC, Zbilut J, Patel M, Messer J, Walthall K,
Tom C, Fink P, Sugerman A, Zdanovics O. How
the heart informs about the brain. A process analysis of the electrocardiogram.
Cybernetics and Systems`94. 2: 1031-1038, R. Trappl (Ed.), World Scientific Publ. Company,
Singapore, 1994.
HOW THE HEART INFORMS ABOUT THE BRAIN
A PROCESS ANALYSIS OF THE ELECTROCARDIOGRAM.
L. Carlson-Sabelli, H.C. Sabelli, J. Zbilut, M. Patel,
J. Messer, K. Walthall, C. Tom, P. Fink.
Rush University, and University of Illinois, Chicago, Illinois 60612, USA
ABSTRACT
Twenty-four hour recordings of the electrocardiogram are analyzed with
process methods derived from non-linear dynamics and integrated via a
comprehensive theory of processes that gives priority to simple, low dimensional
physical processes, and supremacy to complex, high dimesnional psychological
processes. Cardiac timing is shown to be patterned by emotions and activities;
patterned cardiac complexes associated with specific emotions are interpreted as
an alphabet.
FIGURE 1: Recurrence
plots from electrocardiograms of a normal and a schizophrenic subject. 7000 data
points, lag 1, 10 embeddings.
Complex and beautiful patterns of cardiac rhythmicity are associated with
psychobiological processes, with common features as well as personal
differences. Striking graphic (figure 1) and statistical differences between
psychotic and non-psychotic patients,1-3 as well as empirical
correlations with emotions and behavior (figure 2) suggest that such portraits
may potentially have clinical value. This technique, which we call electropsychocardiography
(EPCG)1-3, illustrates the process method, a two-pronged approach
that gives priority to the biological and supremacy to the psychological, in
diagnosis and treatment as well as in research.4,5 More generally, process
theory postulates the priority of the simple (energy-rich) and the supremacy
of the complex (information-rich).6 Accordingly, the function of the
cardiac energy-delivering system should reflect the supremacy of
neurophysiological processes in organizing the behavior of the organism as an
integrated whole. In a companion article3 we present the main
postulates of process theory. Here we shall describe them as components of a
process method and illustrate them by their application to the analysis of the
electrocardiogram: Process:
Focus on action, change and process, not on isolated events or permanent
structures. Obtain long recordings of the process, rather than instantaneous
snapshots, and obtain time graphs of rise and falls in magnitude (energy
intensity) and timing (instantaneous rate). Phase
plane of opposites: Study processes as a function of the interaction of opposites. We have
operationalized the union of opposites by means of the phase plane of opposites,
which can be applied in psychological testing, opinion polling, voting, and to
study conflictual beliefs, motivations and emotions.5-8 In the case
of heart timing, the opposites FIGURE
2: Twenty-four hour time graph of recurrences from an electrocardiographic
recording of a female outpatient with generalized anxiety disorder. 7000
points/matrix. Subjective reports: A: anger. B: anxiety. C: driving. D: shoppint.
E: sadness. F: work at computer. G: anxious. H: mood transition from anxious to
relaxed; note symmetric circle of recurrences indicating change in polarityh of
complexes. I: reading. J: phoning. K: planning events. L: cleaning house. M:
eating. N: reading to children. O: to bed. P: awakening. Q: reading in bed. R to
S: asleep. T: gets up. U: housework. are
the adrenergic system that increases rate and predominates during the day, and
the cholinergic system that reduces rate and predominates at night. Direct
evaluation of adrenergic and cholinergic inputs require invasive procedures.
Here we develop a method to study opposites in a time series using phase plane
portraits, and extend these concepts to time series which are a function of many
opposite factors, the number of which may change in time (factor processing).
Unity:
Study processes
as a unit, integrating findings at different levels of organization. The
organism functions as a unit integrated by the central nervous system. As higher
processes, such as biological and psychological, are complex forms of
organization of the simpler processes that serve as their building blocks --e.g,
emotions are made up of patterns of firing of neurons in specific brain nuclei,
and action potentials consist of the displacement of sodium ions--, lower and
higher level processes are necessarily isomorphic: neither is simpler than the
other. Lower levels predetermine the range of action of the higher processes.
Higher processes organize the lower levels that constitute them, in their
own degree of complexity; hence, to understand the pattern of lower processes
requires the examination of the higher processes that control them. These
concepts lead us to the development of electropsychocardiography as a
comprehensive technique that integrates psychology into the interpretation of a
biological function. Priority
of the simple and supremacy of the complex: bio-socio-psychological method in research and
clinical practice: Study each process from the dual perspective of its
simpler foundations (as in analytical methods) and of the more complex processes
to which it serves as a foundation. Thus, we examine in every clinical case the
priority of the objective (e.g. metabolic dysfunctions as a cause for
psychiatric syndromes) and the supremacy of the subjective (e.g., psychological
changes as cause for metabolic changes).9-11 More generally, one
should examine each process from the double perspective of the simpler levels
that have priority (mathematics, physics, biology, economics) and the more
complex levels (sociology, psychology) that have supremacy. For instance, as the
heart distributes the energy supplies required for behavior, its function must
be adapted to the needs created by neuropsychological processes, behavior must
leave its imprint on cardiac timing. Hence the timing of the cardiac
energy-delivering system not only provides a quantifiable estimate of the rate
of consumption of biological energy, but also offers a portrait of its
modulation by behavior. Mathematical
priority and psychological supremacy: Combine mathematical and psychological analysis in the
study of processes. Psychological processes are complex forms of physical energy
--differing in form, not in composition from simpler phenomena--, and
mathematical form (including number) is the simplest level. These concepts lead
us to the development of electropsychocardiography as a comprehensive technique
that combines mathematics and psychology in the study of a biological function.
This dual approach is a general methodological principle equally applicable to
physics and logic, two disciplines in which psychological and ideological
attachment to conservative viewpoints delayed the acceptance of the evolutionary
perspectives championed by biologists, historians and dialecticians.8
Dimensional
formulation of priority and supremacy: Measure the complexity of a process by estimating the
number of its dimensions. The mathematical concept of dimension is an extension
of the perception of spatial dimensions. As a an ordered set of 3 numbers
describes the position of a point in the 3 dimensions of space, a set of N
ordered numbers defines a point in N dimensional space. Qualitative dynamics
studies processes by plotting their trajectory in a phase space of an
appropriate number of dimensions; the "element" of such a plot is not
a symmetric dot but an asymmetric arrow, representing instantaneous change or
action, to be connected to form trajectories. The choice of axes, and the number
of dimensions to be studied are fundamental questions. The process method
provides definite guidelines. We begin with the search of low dimensional
components because every process, and every level of organization in each
process, has the one dimension of time (unidirectional flow), two dimensions of
information (because opposites are both similar and antagonistic), and the three
dimensions of physical space. Thus every process is studied in: (1) one
dimensional time-graph of action (asymmetry), such as changes in either
timing rate [frequency modulation, FM] or energy amplitude [amplitude
modulation, AM]; for instance, the timing of R-R intervals serves as an estimate
of the energy consumed by the organism. Describing processes as flows of energy
in time allows the joint consideration of physical and human processes. (2) two
dimensions of information (opposition) using the two-dimensional phase plane
to measure separately the interacting opposites, or reconstructing them by
plotting change versus acceleration. (3) three dimensions of structure
(space): a tridimensional phase space is constructed by separate recording
of 3 variables or reconstructed by the delay method. (4) higher dimensions of
organization, attempting to investigate the process of co-creation of
complexity. In this article we explore the possibility that the notions of
priority and supremacy may be rendered operational by examining complex
processes using frameworks with a wide range of dimensions: the simpler
components may be revealed by mathematical portraits process in few dimensions,
and the more complex ones by phase portraits of higher dimensions.
Psychobiological processes may be expected to be high-dimensional, complex and
creative --that is to say, organized but not "deterministic" (in the
strict meaning of the term), lying between, and including, processes produced by
a low-dimensional deterministic source, and components of infinite-dimensional
stochastic origin. Given such large number of dimensions, it is impossible to
measure all the relevant variables, but high dimensional plots can be obtained
by examining changes in one variable at various lags, and in this manner infer
the complexities introduced by the interaction of the many variables that affect
the process. Each variable necessarily reflects to some extend the influence of
all others --and, conversely each variable influences many others. One is many
and many is one, said Heraclitus. The embedding theorem shows that a vector of
time-delayed copies of the observable will generate a trajectory in the
dimensional space so created that is similar to the original,12,13
and the Whitney embedding theorem indicates that it is possible to make
quantitatively meaningful inferences about the dynamical structure of a complex,
multidimensional dynamical system by measuring one variable for a sufficiently
long period of time.12-14 Modular
and semantic analysis: Compare levels of organization, attempting to decode the meaning of
modules as letters of an alphabet in which complex messages are written. The
behavior of the organism consists of well organized, patterned processes, such
as sleep, and wakefulness cycles, feeding, sexual behavior, and emotional
behaviors such as fear, anger, submission and dominance ("action
patterns"). Each of these genetically inherited behaviors, embodied in
brain structure and available for activation by the release of synaptic
transmitters and modulators, include a subjective state, an outward behavior,
and physiological changes. Since by necessity cardiac activity is part of each
of these integrative patterns of behavior, we have explored if methods could be
devised to reveal the behavioral alphabet of the heart. Our objective is to
provide a physiological method to study emotions in clinical practice. To this
effect, we explored several methods of interpreting the pattern of R-R intervals
(the timing of heart action potentials) in day-long dynamic recordings of the
electrocardiogram (Holter monitoring).
Electrocardiographic recordings (24-48 hours) were obtained during the
course of daily activities from normal volunteers and psychiatric patients with
anxiety, depressive and psychotic disorders diagnosed according to DSM-III R.
Data were sampled at the rate of 128 observations per second to determine the
R-R intervals. While wearing the Holter monitor, subjects recorded in a diary
their activities (working, driving, eating, sex, sleep) and emotions (glad, sad,
angry, fearful, each 0 to 5), physical and psychological symptoms, and
medications. Data were studied by means of time graphs of RR intervals;
two-dimensional phase plane portraits [(RRIi) versus change in rate (RRIi
vs RRIi+1)]; factor processing (factor analysis of a time series
using the time delay method, as described in Results); and recurrence plots15
which construct N dimensional vectors from 1 variable using the delay method.
Using a program developed by Zbilut and Webber,16 a recurrence plot
was generated from the time series by constructing a square matrix in which the
R-R intervals were plotted along the horizontal and the vertical axes. For each
beat, we constructed a vector which included the R-R interval itself, and each
of the following intervals up to a number N, the number of embeddings. When two
vectors were equal (within 10%), a dot was plotted in the graph; a diagonal line
was thereby formed, because the vector corresponding to each R-R is identical to
itself. Colors were used to grade the degree of similarity of recurrences.
Guided by process theory, here we extend the use of recurrence plots in two
directions: we studied 24 hour recordings (rather than short, relatively
stationary samples), constructing time graphs of recurrences, and
analyzed them with a wide range of embeddings (from 10 embeddings, each vector
representing approximately 5-15 seconds to 480 embeddings, each vector
encompassing about 7 minutes at a rate of 70/min), a technique that provides
graphic and distinct portraits of long and complex processes.
RESULTS 1
Dimension: Time graphs of heart rate: Time graphs indicate an increase in heart rate in
psychotic patients and a decrease in depressed subjects, although both groups
received medications that increase heart rate. There was a marked decrease in
variability (as measured by the normalized standard deviation) in manic and
schizophrenic subjects, which contrasts with the excited behavior displayed by
some of these acutely-ill patients. These differences may have no diagnostic
significance, but may be relevant regarding cardiac function. 2
Dimensions: Phase plane of opposites: Process theory studies processes in terms of opposites.
We can study how opposing processes interact with each other by examining
accelerations and decelerations in heart rate. Two-dimensional phase plane plots
of instantaneous heart rate (RRI) versus change in rate (RRIi - RRIi+1)
draw irregular shapes around the 450 axis. The minor axis represents
the interbeat variation, the difference between successive beats, determined by
the opposing processes of adrenergic acceleration and cholinergic deceleration
(difference of opposites), while the joint variation of successive beats as
parts of a pattern determines the major axis (union of opposites). There is a
reduction in the range of patterned variations (major axis) in the depressed and
the anxious patients, and even greater in psychotic subjects, without change in
the beat to beat variations. 3
Dimensions: Factor
processing: To investigate the evolution of a process as a function of more
than two complementary factors, we introduced factor processing as a method to
identify them from the data contained in a time series. To this effect we
studied the correlation of the original time series with time-delayed replicas
from 1 to 30 lags, for samples of 1000 consecutive beats. We identified the
statistically significant factors that describe these 30 variables, rotated them
to separate orthogonal opposites. We plotted the factor loadings for each factor
against the factor loadings of the other. Plotting the trajectory determined by
the three most significant factors in a three dimensional space produced a
disorganized cluster of points for random data and a unidirectional trajectory
for patterns (cardiac or computer generated). The shape of the trajectory
changes in time indicating the presence of gradual and sudden bifurcations. The
trajectories themselves represent change, such as from the predominance of
factor 1 to that of its opposite factor 2, or vice versa, or may cycle between
the opposites. Often the flow from factor 1 to its opposite factor 2 was
mediated by non-linear changes in factor 3, creating an inverted U). In manic,
anxious and depressed individuals, daytime records had 2-3 factors, as in most
normal persons, whereas night time recordings had multiple factors, as random
data. N
Dimensions. Time graph of recurrences-complexes and bifurcations:
If one assumes that it might require up to N equations to adequately describe
the pattern of heart action potentials, one can construct, artificially, N
dimensional vectors from 1 variable--the R-R Interval--using the delay method.
When two vectors so constructed are approximately equal, a dot is plotted
(recurrence). In this manner we can reveal patterns.1,2,15-17 The
recurrence plots reveal the existence of a complex order, not evident in time
graphs and phase space portraits. The distribution of recurrences in plots
changed at different times. Assuming that patterns of change carry significant
information led us from
recurrence plots, that are "snapshots" of "stationary
processes" to the time graph of recurrences of dynamic
electrocardiograms (figure 2). The time graph of recurrences were clearly
different during sleep (figure 2, R to S) and wakefulness. These visual
differences were confirmed statistically: during sleep there is an increase in
the number of recurrences and a decrease in the proportion of patterned
recurrences, indicating a decrease in variability and in patterning. Over and
above these overall changes between the opposite phases of adrenergic and
cholinergic predominance, the recurrence graphs are naturally divided into
shorter phases ("complexes"), different in form and in the
number of patterned recurrences, variable in duration, and separated from each
other by short or long interruptions of recurrences (figure 2, I) which
represent bifurcations. The complexes appear to be symmetric, but this is
an artifact resulting from the use of a matrix to construct the recurrence
plots. Within their overall square boundaries, which indicate the beginning and
end of beats related to each other as detected by the recurrence method,
complexes have characteristic forms. These forms are engendered by the
distribution of recurrences within the complex, repeat from individual to
individual. High
Dimensions.
Using a higher number of embeddings, it is easier to identify a sequence of
complex forms (which we shall call "complexes"), each a distinct
pattern, separated by "interruptions". In the 40 subjects studied thus
far, we have learned to recognize a series of forms so distinct as to encourage
the possibility of using recurrence plots to uncover hidden associations between
physiological and psychological processes in health and illness, that could
improve diagnosis and prevention. The morphological differences between
wakefulness and sleep were consistent in all subjects studied. We
have noted drastic changes associated with changes in activity, including
working versus playing, going from one task to another, etc. Using windows of
different size, it was observed that the same forms repeated with various
magnitudes, indicating a self-similarity characteristic of fractals. Cardiac
complexes observed are chaotic and fractal-like, but are neither static nor
stable, and hence do not represent attractors. In high embedding graphs we have
identified a number of modules and complexes that reoccur in many individuals. Cardiac
language: alphabet and punctuation: This relatively small number suggests the idea of an
alphabet in which messages can be written; interruptions between complexes would
represent punctuation. In fact complexes appear to have meaning. First, there is
a correlation between the form of the complex and the activity of the individual
as reported in the diary. In figure 2, note the temporal association of distinct
complexes with anger (A), anxiety (B), sadness (D), eating (M), the interruption
of pattern when going to sleep (O), etc. Cardiac
meanings: the lattice of anxiety: A greater magnification of the complex in figure 2, O
reveals a lattice pattern of recurrences, which was observed also in many other
patients who concomitantly reported brief feelings of fear or anxiety. We have
also noted that the patterns associated with sadness and anger repeat in many
subject. Opposite emotional patterns (e.g. anxiety and relief) appear to
correspond to opposite polarities in the cardiac complexes. A number of other
patterns reoccur in many subjects, but we have been unable to correlate them
with behavior.
DISCUSSION
Clinically, the observed cardiac patterns may assist
cardiologists to study the influence of emotions on cardiovascular illness, and
mental health professionals to devise a system of physiological diagnosis. Physiologically,
the sequence of patterned complexes indicates that cardiac behavior is governed
by the sequence of integrated patterns of behavior of the organism, each with a
distinct beginning and end, rather than being organized into a single attractor,
whether homeostatic, periodic or chaotic, or simply being regulated on a beat to
beat basis by a number of independent factors (respiration, blood pressure,
endocrine, etc). Hence, one needs to study the influence of emotions to
understand the dynamics of the heart. In our view, cardiac complexes represent
transient phase attractors, that include three internal stages: rise, stationary
(phase attractor) and fall. This is in contrast to a structural model of
deterministic dynamics that assumes processes tend to stable patterns
(attractors), that would be reached in the absence of transients created by
external interactions, and that are separated by relatively sudden bifurcations.
Methodologically, these observations illustrate a manner of thinking
which focuses on change rather than static structures.: (1) Searching for
temporal changes --i.e. bifurcations rather than stable attractors-- in
longitudinal recordings; short samples of stationary periods may be useful to
investigate more or less permanent features of the system, such as
cardiovascular pathology, but to reveal the dynamic changes that accompany
neurophysiological processes, Holter monitoring is necessary. (2) Focusing on
multidimensional forms, rather than seeking low dimensional attractors. (3)
Attempting to understand meanings through simultaneous observations of different
levels of integration --e.g. understanding the meaning of cardiac complexes by
examining the accompanying emotional behaviors. The observation of similar
patterns of cardiac timing accompanying anxiety and other behaviors1,2
in a number of different subjects, suggest to us the possibility of deciphering
complexes as letters of a cardiac alphabet. Albeit this aspect of our
investigations should be considered as highly preliminary, the centuries-old
idea that natural patterns represent the language of nature ("logos")
has been supported by understanding the coding of genetic information in the DNA
bases, and the coding of emotions in patterns of release of brain
neurotransmitters. The letters of the cardiac alphabet may be identified through
the recognition of complexes of different form, and reports of subjective
feelings. Theoretically, data support the three postulates of process
theory: 1) all is a process ordered by the irreversible asymmetry of time
(Pasteur's cosmic asymmetry) into a lattice structure:5,6 cardiac
behavior is made of patterned processes (cardiac complexes), not of independent
events (beat to beat regulation), with an overall lattice form, which we see in
a condensed form during periods of fear. This lattice organization may represent
the bifurcation of one process into many, and the subsequent reunion of many
processes into one. Mathematical logic has a lattice structure: processes are
lattices because they are logical --nature is a logos, said Heraclitus.
Regarding the 2) Union of opposites: we found that complexes associated
with opposite emotions have opposite polarities; opposite patterns have been
observed in some subjects when getting up and when falling asleep. Further
illustrating the constant interaction of opposites, in factor processing,
trajectories go from the predominance of one factor to that of its opposite. The
creation of higher dimensional structures is discussed in a companion
article.3 Acknowledgements:
We thank Ms. Marķa McCormick for her indispensable support.
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