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Carlson-Sabelli L, Sabelli HC, Zbilut J, Messer J, Diez-Martin J, Walthall K, Tom C, Patel M, Zdanovics O, Fink P, Sugerman A.  Cardiac patterns of emotions demonstrated by the process method: Psychotic patterns.  New Systems Thinking and Action for a New Century: Proc. International Systems Society 38th Annual Mtg., B. Brady and L. Peeno (Eds.), Pacific Grove, CA, 1994, pp. 0419-0430.

         CARDIAC PATTERNS OF EMOTIONS DEMONSTRATED

           BY THE PROCESS METHOD:PSYCHOTIC PATTERNS

                NOT AFFECTED BY ANTIPSYCHOTIC DRUGS.

                 L. Carlson-Sabelli, H. Sabelli, J. Zbilut, J. Messer, Justo Díez-Martín*,

                K. Walthall, C. Tom, M. Patel**, O. Zdanovics, P. Fink, A. Sugerman.

                  Rush University, 1725 West Harrison, Chicago, Illinois, USA 60614

                                Phone 312-942-0118 or 2227. FAX 312-348-4499

                                           *Hospital Universitario de Valladolid

                                          **The University of Illinois at Chicago

         Electropsychocardiography [EPCG] studies these complex, patterned, and transient changes in cardiac timing to investigate emotional behavior and its influence on cardiac function. Twenty four hour recordings of the electrocardiogram are obtained from freely moving subjects, together with a recording of their activity and emotions. The electrocardiogram is sampled (128/sec) to measure the R-R interval, and the time series thus obtained is embedded 1 to 500 times using the time delay method. This data is used to plot the time course and to quantify organizational variables such as the percent of recurrences, patterned recurrences and their ratio (arrangement), using the methods of Eckmann et al. [7] and of Zbilut and Webber [50].  Time graphs of recurrence plots reveal distinct forms ("complexes") which repeat from subject to subject, and that correlate with the ongoing activity allowing one to distinguish wakefulness and sleep, anxiety and relaxation, work and play, etc., and suggest the existence of an "alphabet" of cardiac patterns that correspond to neurophysiological patterns. Measurements of recurrences, ratio a new measures introduced here, median dimensional complexity, and number of bigurcations, indicate that the physiological dynamics of schizophrenics are simpler and more rigid than that of normal or depressed subjects. The median dimensional complexity of the psychocardiological process is 58 + 4 in normal awake 52 + 25 in awake depressed and 24 +11 in awake schizophrenic subjects. The differences between the two non-psychotic groups and the schizophrenic group were statistically significant and visually evident in the time graphs or recurrences.  Electropsychocardiography may play a role in the understanding and diagnosis of mental illness, and in the elucidation of emotional factors in cardiac illness.

Key words: electropsychocardiography; depression, emotions; heart; process method; schizophrenia, psychotic.

            This article presents our current efforts in the development of electropsychocardiography (EPCG) as a comprehensive physiological technique potentially useful in psychiatry and cardiology [2,3,38,40]. Distinct and highly organized patterns of cardiac timing are associated with patterns of behavior and emotions [3,36,38].  Here we develop this methodology to reveal graphic (figure 1) and statistically significant (table 1) differences between psychotic and non-psychotic subjects. Our objective is to study objectively the dynamics of psychosis through the investigation of the dynamics of the associated cardiac rhythms.

            Ancient wisdom and popular language associate the heart with the soul because obvious changes in heart rate accompany emotions. Changes in cardiac timing accompany arousal and emotions because the circulatory system distributes the energetic metabolites required for behavior. Emotional behavior is an important factor in cardiac function and dysfunction [4,8,20,21,28,44,46]. Cardiological symptoms are prominent in panic disorder and other anxiety syndromes. Small but significant changes in heart rate variability have been reported in patients with panic disorder [47] or with depression [6,33].  Differences in verbal content during psychotherapy were found to be associated with differences in the instantaneous heart rate in two patients [31,32].   

            Dynamic electrocardiography (Holter monitoring) provides a promising tool for investigating cardiac timing in freely acting subjects. The novel mathematical techniques of non-linear dynamics provide new avenues for the analysis of the data [15,16,49,], and the increasing availability of computers places these techniques in the hands of researchers and clinicians. As dynamic electrocardiograms are actively investigated with modern mathematical techniques, a number of basic physiological and clinical concepts have been reformulated, and the complexity of cardiac timing is becoming unfolded; increasingly higher dimensional frameworks have been found necessary to portray it appropriately. The unidimensional homeostatic model focussed on the maintenance of heart rate within physiological limits, and assumed variations in instantaneous heart rate (R-R intervals) to result from random disturbances, to be smoothed out with averaging techniques. However, variations in instantaneous heart rate have been shown to be clinically significant [9,10,18], and spectral analysis of cardiac timing has revealed periodicities associated with respiration and blood pressure [30].  The analysis of the electrocardiogram with the non-linear methods of modern mathematical dynamics has provided evidence for the existence of even more complex order behind the apparent beat to beat regulation of cardiac timing. Using methods to search for low dimensional attractors (stable patterns to which processes tend when undisturbed by transients), a number of investigators [16,35,43] found evidence suggesting that certain arrhythmias could represent the emergence of a chaotic attractor. On the other hand, Goldberger and co-workers [12-14] suggested that the cardiac timing of normal subjects corresponds to a chaotic attractor, and explained pathology by simplification to a periodic or static attractor. However, the timing of normal hearts is not stationary, and only when restricted by pathology is cardiac timing contained within the basin of an attractor, static, periodic or chaotic [48,50,51]. Using the recurrence plot method [7], Zbilut and co-workers studied relatively short electrocardiographic samples, presumably stationary periods, using 3-10 embeddings to reveal the dimensions of the process, and concluded that cardiac activity is governed by transients.  Transients need not be random, nor the result of a multiplicity of independent factors. The various functions of the organism are not independent from each other; rather, they all depend on the cardiac pumping of energetic supplies (biological priority), and all are controlled by neuropsychological processes (psychological supremacy [37]). Assuming that the organism functions as a unit, we studied dynamic electrocardiograms obtained during the course of the subject's normal activity via a sequence of recurrence plots (time graphs of recurrences). We found an intricate pattern made up of transient phases ("complexes") separated by bifurcations. We define complexes as organized, highly dimensional transients (with a beginning, internal phases, and an end), by way of contrast with low dimensional and stable attractors. Complexes appear to correspond to various activities, symptoms and emotions, such as anxiety, chest pain, sleep and awakening; differences were noted between manic, depressive and anxious individuals [3,38].  These observations suggested to us that cardiac timing cannot be understood in terms of one attractor, nor is it a collection of transients determined by a multiplicity of independent factors, but rather forms part of integrated patterns of behavior organized by the central nervous system ("action patterns") [22,23]. The detection of such patterns requires one to study 24-hour records of subjects leading their usual life [25], to examine the sequential patterns traced out by successive intervals; other approaches, such as frequency domain analysis, can only reveal the global features of the physiological state [41].  The clinical correlations observed suggest that the study of patterns may have diagnostic significance in psychiatry, and indicate the need to develop appropriate techniques for clinical use.

                                                                 Methods

To develop clinically useful methodology, we examine their ability to portray the most fundamental distinction in psychiatry, psychotic vs non-psychotic subjects. As in our previous studies, we used the recurrence plot method described by Eckmann and co-workers [7], quantified recurrences and ratio according to Zbilut and co-workers [50], and further expanded this methodology by creating time graphs of recurrences. In this article we develop two new measurements, the number of bifurcations, and the E₅₀--estimation of dimensional complexity. The complexity of a process can in principle be measured as the number of independent variables needed to specify its pattern; these are the dimensions of the process. The recurrence method approximates the number of dimensions as the number of embeddings needed to describe the process.  In this article we systematically compare recurrence graphs obtained during sleep and wakefulness in control and psychotic subjects.  The estimate of dimensional complexity was calculated as the embedding needed to reach 50% determined or patterned recurrences (E₅₀). The  Twenty-four hour recordings of the electrocardiogram were obtained in human subjects diagnosed according to DSM-III R: The non-psychotic group consisted of three normal and 3 bipolar depressed subjects; three schizophrenics made up the comparison psychotic group.  Subjects were asked to keep a diary of their activities and emotions; those from psychotic patients were very incomplete but recorded sleep and wakefulness. Here we compared 3 one-hour samples for each subject, obtained during normal daytime activity, and 3 hours during sleep. The electrocardiographic data were sampled at the rate of 128 observations per second to determine the intervals between R waves. From this time series, graphs of higher dimensions were created by the time displacement method [7], using a program that plots and measures recurrences developed by Zbilut and co-workers [48,50,51].  Whenever a relatively large number of equations is required to adequately describe patterns in natural processes, and a single sequence of numbers is the only available data, one can construct, artificially, N dimensional vectors from embedding the time series of 1 variable using the delay method. The embedding theorem [26] 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. 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 [11,17].  Thus computer constructed recurrence plots can reveal patterns of "almost" periodicities in complex processes whose description may need a number of partial differential equations [7]. In our study, vectors were constructed using a time delay of 1 beat. The time-ordered sequence of vectors were ordered in a square matrix, in which the horizontal axis represents the time index, x(i), and the vertical axis x(j) represents each of the successive vectors forward in time. When two vectors so constructed were approximately equal for a given embedding, a dot was plotted, indicating a recurrence. We used the Euclidean norm for the calculation of distances, and defined as "approximately equal" vectors that lie within 10% of the normalized mean distance of the first embedding.  We studied samples of 7000 beats (approximately 100 minutes at a rate of 70 beats per minutes) at various embeddings from 1 (comparing each beat against the next one) to 480 (comparing segments of approximately 7 minutes, at a rate of 70 beats per minute) .  Recurrence plots were made at 10, 50 and 480  embeddings for each subject for visual comparison of patterns and to  count bifurcations, transitions between patterns.  Using the methods of Zbilut and Webber [50], we measured the following organization qualities: (1) the number and percentage of recurrences; the percentage of recurrences is the proportion of the total number of possible recurrences, which is one helf of the matrix--in our case 7000x7000 / 2. If is a measure of order or rigidity. (2) Patterened recurrences--the number and percentage of "patterned recurrences" (recurrences occurring with simultaneous embedding segments (appearing in lines parallel to the diagonal, which Zbilut has called "determinism"); these are few or absent in plots of computer generated pseudo-random numbers at low embeddings (figure 1)  (3) Ratio, is the proportion of percentages of patterned (determined) recurrences and total recurrences in a given sample.  It is a number between 0 (none of the recurrences are patterned) and 1 (all recurrences are patterened). 

            All organizational measurements are derived from the number of recurrences calculated from the time series of RRIs.  We statistically compared differences between organizational variables at 3pm and 3am at the median emebedding dimension for non-psychotic (N=6) and Psychotic groups (n=3) with the Mtann-Whitney U test using BMDP statistical software(Berkeley, CA).

            The percentage of recurrences provides the ability to compare the degree of rigidity across beat segments of different durations or sampled at different times.  The percent patterened recurrences allows comparison of degree of patterning across samples.  The ratio provides an index to compare the proportion of "pattern or arrangement among groups of beat segments with when the total number of recurrences differ.   

                                                                  Results

            Visual comparisons. Figure 1 illustrates the obvious visual differences in geometric pattern between recurrence plots of cardiac data recorded from psychotic and non-psychotic subjects.  Because they are generated by a matrix, each recurrence plot has a square shape, and each complex within it also has a square shape (indicating that, within the complex, beats are related to each other, from its origin to its end). At 10 embeddings, recurrences are widely distributed in the matrix: records from random data are entirely uniform, whereas cardiac data are subdivided by brief breaks (bifurcations); at high embeddings (100-500) organic forms appear as the size of complex shrinks relatively to the embeddings framework, and bifurcations are easier to count. The records obtained from psychotics subjects have, at low embeddings, curvilinear forms such as those observed in the records of non-psychotic subjects at higher embeddings.

            Cardiac complexes have a limited number of forms, recognizable in many different individuals. The form of the complex displayed in figure 1 by the schizophrenic subject was also observed in records obtained from non-psychotic persons, often associated with reports of fear or anxiety in their diaries.   

            The number of bifurcations was greater (p < 0.04) in the samples obtained from psychotics (3.40 + 0.72 /hour) than in normals (2.00 + 0.00). No differences were found in the number of bifurcations between sleep and wakefulness samples, whereas there were obvious differences in pattern (figure 1) and number of recurrences.

            Numerical comparisons. Records from schizophrenic subjects had higher number of recurrences and patterned recurrences than controls at the median embedding dimension (Table 1).  The RRI was lower (indicating a higher heart rate) and its variability was lower in psychotic than in non-psychotic subjects.  During sleep, recurrences increased, while ratio decreased. The differences between wakefulness and sleep were smaller in the schizophrenics.

 *********************

Drop  because this actually has figures that aren't here, and it is better to keep it simpler.  We could also drop the bifurcation count???

            Embedding plots.  Measurements of organization of cardiac data varied in a non-linear manner with the number of embeddings, with obvious differences between normal and psychotic subjects. In contrast, in the case of random data, increasing the number of embeddings produce smaller and linear increases in most measures. The number of patterned recurrences grew faster with the number of embeddings in psychotic subjects, and during sleep. 

            At low embeddings, the number of recurrences and patterned recurrences were significant in cardiac records; in contrast, they were zero, or very low, in plots of pseudo-random data. Increasing the number of embeddings, decreased the number of recurrences in both normal and psychotic subjects, and then recurrences increased again. This inflection point occurred at 2 embeddings during sleep and at 6-8 embeddings during wakefulness in non-psychotic subjects, and it was higher in schizophrenics.

            Beyond 9-12 embeddings, increasing the number of embeddings increased most measurements, in a non-linear fashion. The curve flattened out towards 100 % patterning of recurrences about 70-100 embeddings in cardiac records, whereas less than 20 % of the recurrences appeared to be patterned with pseudo-random data even at 100 embeddings. Saturation points were reached at lower embeddings in specific cases; ratio increased with the number of embeddings in normals, from 10 to 480 during the day, but only up to 50 during the night; in schizophrenics, ratio increased only up to 50 embeddings during day or night time. At high embeddings, the data became distorted, as shown by the decrease in ratio at 480 embeddings in all data.

*******************************************

            E₅₀ ranged from 13 in a schizophrenic subject to 80 in a control subject. There were significant differences between individuals, and within individuals, according to the time of the day. . Calculating E₅₀ by interpolation between 10 and 50 embedddings produced reasonable estimates in non-psychotics but not in the psychotic subjects.

                                                                Discussion

            The visual contrasts, and the statistically significant differences, between cardiac and random data indicate that the observed variations in cardiac timing are not primarily due to random factors such as external circumstances. Recurrence plots of pseudo-random data showed forms similar to those recorded from cardiac data only at much higher embeddings. The temporal patterns (complexes) visualized in recurrence graphs must thus reflect ongoing behavior and emotion, pathological processes, or drug action. The observed distribution in the populations examined, and correlations with diaries indicate that some of these patterns are associated with emotions such as anxiety, not with diagnosis or treatment, while others appear to be due to either psychosis or antipsychotic treatment. The pattern associated with anxiety (exemplified by the schizophrenic subject in figure 1) was also observed in normal, cardiac, anxious and depressed persons, often associated with reports of fear, apprehension or anxiety [38]. In contrast, the increase in recurrences and the decrease in E₅₀ noted in schizophrenics was observed at all times during the day, regardless of the emotion or activity reported. 

         Psychotic and non-psychotic subjects differ in a wide variety of electrocardiographic parameters, from heart rate to number of recurrences. Even simple inspection of the color of the graphs allowed to differentiate these two groups.  The observed differences indicate that schizophrenics have an increase in simple order (higher number of recurrences, lower E₅₀), a reduction in the range of variation (lower standard deviation), a decrease in complex organization (lower ratio), and a greater fragmentation (greater number of bifurcations).

            The differences noted appear to be the sole result of nosological differences. The observed reduction in R-R interval variability, and the increase in the number of recurrences, indicates that order is greater in psychotics than in normals. Correspondingly, psychotics had more curvilinear, organic forms in low embedding recurrence plots, indicating a greater degree of simpler order. That simple processes determine much of the order in the cardiac behavior of psychotics is also shown by the fact that the number of patterned recurrences grows faster with the number of embeddings in psychotic subjects than in non-psychotics.        

            Almost invariably, the differences between normals and psychotics, and between wakefulness and sleep, were in the same direction. Further, the differences between sleep and wakefulness were greater in normals than in schizophrenics. In comparison with wakefulness, sleep records showed more recurrences and less arrangement, as expected from the fact that wakefulness represents a more varied and complex process, while sleep is more stereotyped and oscillates between only two states--slow wave and REM sleep. We thus speculate that psychosis represents a reduction in the level of complexity of consciousness. In fact, complex order, as measured by the degree of arrangement at higher embeddings, was lower in schizophrenics than in controls during wakefulness. The inability to recognize reality, would be a critical reduction in the dimensions of psychophysiological processes. Shannon [42] pointed out that simpler systems are unable to obtain information from their more complex surroundings; the simplicity of the psychotic would account for his isolation. These ideas are consistent with the notion of schizophrenia as a dynamic insufficiency [19], the recognition of the importance of defective and negative symptoms [1,5,27], and a Jacksonian concept of positive symptoms as disinhibition [34]. In brief, schizophrenia represents a simplification of mental complexity.

            Although electrocardiograms from psychotics showed a lower beat to beat variability, their recurrence plots showed a greater number of bifurcations (separations between complexes). This increase in bifurcations may relate to the greater fragmentation of psychological processes in the psychotic.  

         With regard to methodology, our results indicate that the calculations of bifurcation rate, organization qualities and embedding dimensions introduced in this article are potentially useful in diagnostic and/or pharmacological studies. The quantification of bifurcations revealed significant differences between population psychotics and non-psychotics. Recurrence plots [7] and measurements [51] are best adapted to study relatively stationary processes (e.g sleep vs wakefulness, or anxious vs relaxed). Recognizing that patterns of behavior are pathways from a sequence of appetitive acts to consummatory acts, which are in turn followed by relaxation [22,23], the study of bifurcations should be as important as the study of stationary patterns. The study of multiple embeddings seems useful to explore the complexity of the process. Recordings obtained during wakefulness and sleep, and from psychotics and non-psychotic subjects, differed in variations of geometric pattern and of recurrence measurements as a function of embeddings. This indicates that the study of embedding dimensions may yield meaningful data. What is their significance?  Comparison between the cardiac data and measurements obtained from known curves indicates that a larger number of embeddings is necessary to represent more complex processes. Ratio increases with the number of embeddings, and it does more so during wakefulness than during sleep, and more in normals than in psychotics, indicating that the number of embeddings reveals the complexity of the process under study. One could then measure the complexity of cardiac behavior by examining its characteristics at various embeddings. One way to interpret the results, albeit not the only possible one, is to consider that measurements obtained at low embedding dimensions may reflect the contribution of simple processes, while the organization and energy of higher processes is portrayed by measurements at high embeddings.

            Mathematical theory validates the use of low embedding recurrence plots. A number of observations indicate the need to be cautious in interpreting high embedding plots; for instance pseudo-random numbers generated patterns of recurrences at high embeddings.  Although this may be explained by the fact that computer-generated pseudo-random numbers are not truly random, the occurrence of artifacts cannot be ruled out. Undoubtedly the forms observed in recurrence plots at any number of embedddings are determined in part by the method, and there is of course no method without artifacts; the artifactual nature of the PQRST wave as a portrait of the cardiac action potential does not detract from its clinical usefulness. Portraits at different embeddings capture partially the process under study: if a finite-dimensional process is mapped into a space that is too small, it will be projected onto that space, while, if it is mapped into a space that is too large, its structure will be unchanged, simply occupying a lower-dimensional sub-space [11].  At low embeddings, the recurrence plots have a square shape (reflecting their identification by means of matrices, see figure 1), and the appearance of a Sierpinski square [24], revealing their fractal structure [38], at 480 embeddings, cardiac complexes "shrink", adopting organic forms. On the other hand, measurements of entropy and arrangement at low embeddings, in which only 1-3 % of recurrences are determined, while the majority are due to chance, seem doubtful as estimates of the organization of the process under study.

            As the number of embeddings represents the space in which we study recurrences, an intermediate number of embeddings probably provides a more accurate canvas. By analogy with the usual manner in which we compute statistical measures (such as the mean effective dose ED₅₀ of a drug), the measurement of the median embedding dimension, the embedding at which 50 % of recurrences are patterned, E₅₀, seems a more accurate evaluation of the process under study. Taking E₅₀ as an estimate of the global dimensionality of the process, psychocardiological phenomena have 40 to 60 or more embedding dimensions in normals, and 20 to 40 embedding dimensions in psychotics while awake, with a reduction in dimensional complexity during sleep.

            The dimension of a process is defined by analogy with the concept of spacial dimensions: as two numbers are required to locate a point in a plane, and three numbers are necessary to specify the position of an object in space, the number of numbers required to define the trajectory of a process at a given moment is its local dimension. The relation between embedding dimensions and actual dimensions is not known, but the data suggest that we are dealing with processes of high dimensionality. Mayer-Kress and co-workers have developed a correlation between dimensional complexity and embedding dimensions, but warn that their method can lead to underestimation of the true dimensional values. Unfortunately, the various methods developed to measure dimensionality have problems in producing reliable values with a realistic number of data points [25].  As classic dynamics attempted to reduce all processes to manifestations of a unidimensional tendency to equilibrium, entropy and disorder, traditional biology assumed a unidimensional flow towards homeostasis (health), and portrayed illness as disequilibrium towards another form of stability --death. However we now recognize the importance of periodic attractors (such as biological clocks), of non-periodic chaos (with fractal dimensions), and of higher dimensional dissipative and autocatalytic structures [29,45].  It is thus possible that biological and psychological phenomena be high dimensional processes. The observation that patterned recurrences achieved the 50% mark at 10 to 80 embeddings indicates that psychological processes are likely to be high dimensional. Even if we cannot as yet identify biological and psychological dimensions in the way in which we can recognize time and space, they are as real as physical dimensions, and we might be able to estimate their number by comparing recurrent plots obtained at a wide range of number of embeddings --this provides an operational definition for the vague concepts of "complexity" and "higher nervous function".

            The differences noted between sleep and wakefulness, and schizophrenics and controls, suggests to us that psychosis is a reduction in central nervous system dimensionality. The fact that normals and depressives lay between schizophrenics on the one hand, and random data on the other, regarding measurements of patterned recurrences and entropy, suggests to us that psychosis is a highly determined form of order, at variance with the notion of health as equilibrium and illness as disorder. The higher number of bifurcations in psychotic samples denotes a lesser degree of continuity of the process. The data suggests that health is a variable, complex and fairly continuous order; psychosis has greater order, and lesser complexity, variability and continuity. Undoubtedly these interpretations of the results are highly preliminary, but they provide hypotheses to test, and relate the results contributed by the novel methods of non-linear dynamics to neuroamine and psychodynamic theories of behavior. If indeed cardiac complexes reflect both illness and drug action, such comparisons might serve for rational selection of drug treatment.

         Clinically, the time graph of recurrences at various embeddings provides graphic and distinct portraits of relatively long and complex processes such as emotions and psychiatric syndromes, and thereby provide physiological objective measurements that may help in differential diagnosis, and in the evaluation of drug treatment. Although the sample sizes were small, the differences were statistically significant, and so large in the case of psychotics as to allow the application of these measurements to the individual patient.

         Theoretically, this study illustrates the methodology that springs from process theory, which adopts mathematical techniques of non-linear dynamics but modifies them in two directions: examining variations in time (instead of snapshots of stationary processes) and a range of dimensions (rather than seeking a single, low dimensional attractor).  Thus process theory adopts the concept of complex --a highly dimensional organized transient process-- as its central concept.

            In conclusion: First, the time series of R-R intervals consists of a sequence of transient and patterned phases (complexes) separated by transitions (bifurcations), which occur at an average rate of 1 every 30 minutes in normal subjects. Second, estimates of the median global dimension of cardiac timing indicate a high degree of complexity, ranging from 13 to 80 embedding dimensions during the day, and 14 to 45 during sleep. In both respects, the data are at variance with models that postulate that cardiac rate tends to low dimensional homeostatic equilibrium, periodic cycles, or chaotic attractors. Third, the short-lasting pattern of complexes corresponds to ongoing activities and emotions, such as anxiety or sleep, and are the same regardless of diagnosis. Fourth, these long-lasting, overall features of organization reflect the overall dynamics of the subject, in that treated schizophrenic subjects show an increase in the rate of bifurcations, and a decrease in the number of embedding dimensions, whereas treated depressives were similar to normals, except in measures of energy utilization. Insofar as cardiac behavior reflects the behavior of the organism, the results suggest that schizophrenia involves an increase in simple order, a reduction in the range of variation, a decrease in complex organization, and a greater fragmentation. The present data do not include untreated subjects, but the methodology here developed is potentially capable of differentiating the results of illness from the effects of drugs.

         Acknowledgements: This research was supported by gifts from Ms. María McCormick of the Society for the Advancement for Clinical Philosophy. We also wish to thank Rene Leucht for her technical assistance. J.D-M. participated in this study thanks to the pilot exchange program of Rush University. The Scientific Computer Workstation and the Biostatistics Facility of the Research Resources Center, University of Illinois at Chicago provided the equipment and assistance necessary to conduct some of our computations.

[1] N.C. Andreasen, 1982, "Negative versus positive schizophrenia. Definition and validation," Arch Gen Psychiatry 39:784-88.

[2] L. Carlson-Sabelli, H. Sabelli, J. Zbilut, M. Patel, J. Messer, K. Walthall, C. Tom, A. Sugerman, P. Fink, and O. Zdanovics, 1994, "How the heart informs about the brain. A process analysis of the electrocardiogram," Proc. European Meeting on Cybernetics and Systems Research, Vienna.

[3] L. Carlson-Sabelli, H.C. Sabelli, M. Patel, J. Messer, J. Zbilut, and K. Walthall, 1994, "Electropsychocardiography. Illustrating the application of process methods to comprehensive patient evaluation," Theoretic and Applied Chaos Theory in Nursing 1.

[4] M.A. Chesney, G. Sevelius, G.W. Black, M.M. Ward, G.E. Swan, and R.H. Rosenman, 1989, "Work environment, type A behavior, and coronary heart disease risk factors," Journal Occup Med 23:551-555.

[5] T.J. Crow, 1985, "The two syndrome concept: origins and current status," Schizophr Bull 11:471-85.

[6] G.W. Dalack and S.P. Roose, 1990, "Perspectives on the relationship between cardiovascular disease and affective disorder," J Clin Psychiatry 51 Suppl:4-9. Discussion 10-11.

[7] J.P. Eckmann, S.O. Kamphorst, and D. Ruelle, 1987, "Recurrence plots of dynamical systems," Neurophys Lett 4(9):973-977.

[8] R.S. Elliot and J.C. Buell, 1985, "Role of emotions and stress in the genesis of sudden death," J Am Coll Cardiol 6: 95B-98B.

[9] D.J. Ewing, 1991, "Heart rate variability: an important new risk factor in patients following myocardial infarction," Clin Cardiol 14:683-685.

[10] T.G. Farrell, Y. Bashir, T. Dripps, M. Malik, J. Poloniecki, D. Bennett, D.E. Ward, and A.J. Camm, 1991, "Risk stratification for arrhythmic events in post-infarction patients based on heart rate variability," Ambulatory Electrocardiographic Variables and the Signal-averaged Electrocardiogram 18(3):687-697.

[11] N.A. Gershenfeld, 1992, "Dimension measurement on high-dimensional systems," Physica D 55:135-154.

[12] A.L. Goldberger, V. Bhargave, B.J. West, and A.J. Mandell, 1985, "Nonlinear dynamics of the heart beat. II. Subharmonic bifurcations of the cardiac interbeat interval in sinus node disease," Physica D 17:207-214.

[13] A.L. Goldberger, D.R. Rigney, J.E. Mietus, E.M. Antman, and S. Greenwald, 1988, "Nonlinear dynamics in sudden cardiac death syndrome: heart rate oscillations and bifurcations," Experientia 44:983-987.

[14] A.L. Goldberger and B.J. West, 1987, "Applications of nonlinear dynamics to clinical cardiology," in  Perspectives in Biological Dynamics and Theoretical Medicine: Annals of the New York Academy of Sciences, (S.H. Koslow, A.J. Mandell, M.F. Shlesinger, eds.) New York Academy of Sciences, New York, pp. 195-212.

[15] A.L. Goldberger and B.J. West, 1987(a), "Fractals in physiology and medicine," Yale J Biol Med 60:421-435.

[16] M.R. Guevara, L. Glass, and A. Shrier, 1981, "Phase locking, period-doubling bifurcations and irregular dynamics in periodically-stimulated cardiac cells," Science 214:1350-1354.

[17] V. Guillemin and A. Pollack, 1974, Differential Topology, Prentice-Hall, Englewood Cliffs, N.J.

[18] H.V. Huikuri, M.K. Linnaluoto, T. Seppanen, K.E.J. Airaksinen, K.M. Kessler, J.T. Takkunen, and R.J. Myerburg, 1992, "Circadian rhythm of heart rate variability in survivors of cardiac arrest," Am J Cardiol 70:610-615.

[19] W. Janzarik, 1987, "The concept of schizophrenia. History and problems," in Search for the Causes of Schizophrenia, (H. Hafner, W. Gattaz, F. Janzarik, eds.) Springer, Berlin, pp. 11-18. 

[20] J.R. Jennings, 1986, "Memory, thought, and bodily response," in Psychophysiology: Systems, Processes, and Applications, (M.G.H. Coles, E. Donchin, S.W. Porges, eds.)  Guilford Press, New York, pp. 290-308.

[21] D. Karakostas, C.L. Papadopoulos, A. Missiopoulou-Kokka, and A.D. Vassilopoulos, 1988, "Anxiolisis as a modifying factor of certain neuropsychiatric parameters in patients with coronary heart disease," Acta Therap 14:381-388.

[22] P.R. Killeen, 1992, "Mechanics of the animate," J Exp Anal Behav 57:429-463.

[23]. K. Lorenz, 1966, On aggression, (M.K. Wilson, Trans.) Harcourt Brace Jovanovich, New York.

[24] B.B. Mandelbrot, 1983, The Fractal Geometry of Nature, W.H. Freeman, San Francisco.

[25] G. Mayer-Kress, F.E. Yates, L. Benton, M. Keidel, W. Tirsch, S.J. Pöppl, and K. Geist, 1988, "Dimensional analysis of non-linear oscillations in brain, heart, and muscle," Math Biosci 90:155-188.

[26] N.H. Packard, J.P. Crutchfield, J.D. Farmer, and R.S. Shaw, 1980, Phys Lett. 45:712.

[27] D. Pickar, R.E. Litman, P.E. Konicki, O.M. Wolkowitz, and A. Breier, 1990, "Neurochemical and neural mechanisms of positive and negative symptoms in schizophrenia," in Schizophrenia: Positive and Negative Symptoms and Syndromes: Modern Problems in Pharmacopsychiatry, (N.C. Andreasen, ed.) Vol. 24,  Karger, Basil.

[28] S.W. Porges, P.M. McCabe, and B.G. Youngue, 1982, "Respiratory-heart rate interactions: psychophysiological implications for pathophysiology and behavior," in Perspect Cardiov Psychophysiology, (J. Cacioppo, R. Petty, eds.) Guilford Press, New York: 223-264.

[29] I. Prigogine, 1980, From Being to Becoming. Time and Complexity in the Physical Sciences, W.H. Freeman, San Francisco.

[30] F. Raschke, 1986, "The hierarchical order of cardiovascular-respiratory coupling," in Cardiorespiratory and Cardiosomatic Psychophysiology, (P. Grossman, K.H.L. Hansen, D. Vaitl, eds.) Plenum Press, New York.

[31] D.J. Redington and S.P. Reidbord, 1992, "Chaotic dynamics in autonomic nervous system activity of a patient during a psychotherapy session," Biol Psychiatry 31:993-1007.

[32] S.P. Reidbord and D.J. Redington DJ, 1992, "Psychophysiological processes during insight-oriented therapy: further investigations into nonlinear psychodynamics," J Nerv Ment Dis. 180(10):649-657.

[33] S.P. Roose and H. Glassman, 1989, "Cardiovascular effects of tricyclic antidepressants in depressed patients,"  J Clin Psychiatry Monograph Series 7(2).

[34] M. Roth, 1989, "Commentary on the contributions of Professor H. Sass, Dr. G. Gross and Dr. Ch. Mundt etal. on 'negative' and 'basic' symptoms of schizophrenia," Br J Psychiatry 155 (Suppl. 7):37-40.

[35] D. Ruelle, 1980, "Strange Attractors," Math Intelligence. 2:126-137.

[36] H.C. Sabelli, 1992, "From process theory to electropsychocardiography," plenary lecture, American Society of Hispanic Psychiatry, Chicago.

[37] H.C. Sabelli and L. Carlson-Sabelli, 1989, "Biological priority and psychological supremacy, a new integrative paradigm derived from process theory," Am J Psychiatry 146:1541-1551.

[38] H.C. Sabelli, L. Carlson-Sabelli, M. Patel, J.P. Zbilut, J. Messer, and K. Walthall, in press, "Psychological portraits and psycho-cardiological patterns in phase space," in Chaos theory in Psychology, (F. Abraham and A. Gilgen eds.) Greenwood Publishing Group, Inc., Westport, CT.

[39] H.C. Sabelli, 1994, "Entropy as symmetry: theory and empirical support," These Proceedings.

[40] H.C. Sabelli, L. Carlson-Sabelli, J. Zbilut, M. Patel, J. Messer, K. Walthall, and C. Tom, 1994, "Cardiac entropy in coronary and schizophrenic patients, and the process concept of entropy as symmetry," Proc. European Meeting on Cybernetics and Systems Research, Vienna.

[41] B. McA Sayers, 1973, "Analysis of heart rate variability," Ergonomics 16:85-97.

[42] C.E. Shannon, 1964, "The mathematical theory of communication," in The Mathematical Theory of Communication,  (C.E. Shannon, J. Weaver, eds.) University of Illinois Press, Urbana, Illinois, pp. 29-125.

[43] J.M. Smith and R.J. Cohen, 1984, "Simple finite-element model accounts for wide range of cardiac dysrhythmias," Proc Natl Acad Sci U S A 81:233-237.

[44] E.N. Sokolov, 1963, Perception and Conditioned Reflex, Permagon Press, Oxford.

[45] F. Varela, H. Maturana and R. Uribe, 1974, "Autopoiesis: the organization of living systems, its characterization and a model," Biosystems 5:187-196.

[46] R.B. Williams, J.D. Lane, C.M. Kuhn, W. Melosh, A.D. White, and S.M. Schanberg, 1982, "Type A behavior and elevated psychologic and neuroendocrine responses to cognitive tasks," Science 218:483-485.

[47] V.K. Yeragani, R. Pohl, R. Balon, C. Ramesh, D. Glitz, I. Jung, and P. Sherwood, 1991, "Heart rate variability in patients with major depression," Psychiatry Res 37:35-46.

[48] J.P. Zbilut, M. Koebbe, H. Loeb, and G. Mayer-Kress, 1991, in Proceedings, Computers in Cardiology,  1990 IECE Computer Society Press, Los Alamitos, Ca., pp. 263-266.

[49] J.P. Zbilut, G. Mayer-Kress, P.A. Sobotka, M. O'Toole, and J.X. Thomas Jr, 1989, "Bifurcations and intrinsic chaotic and 1/¦ Dynamics in an isolated perfused rat heart," Biol Cybern 61:371-378.

[50] J.P. Zbilut and C.L. Webber Jr., "Embeddings and delays as derived from quantification of recurrence plots," Physics Lett A 171:199-203.

[51] J.P. Zbilut, C.L. Webber Jr, P.A. Sobotka, and H. Loeb, 1993, "Recurrence analysis of heart rate variability,"  J Am Coll Cardiol 21(2, Suppl. 4A.):439-5.  C.L. Webber, J.P. Zbilut, in press, "Dynamical assessment of physiological systems and states using recurrence plot strategies," J Appl Physiol.

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Figure 1: Recurrence plots. Cardiac data obtained during wakefulness and sleep in a normal, a depressed and a psychotic subject, and random data with similar average. Recurrence plots of 7000 data points, at 10, 50 and 480 embeddings. 

Table I:  Comparison Between 3 Psychotic and 6 Non-psychotic Subjects During Wakefulness and During Sleep at the Median Embedding Dimension (E50).

* x 10^-4

Table I:  Comparison Between 3 Psychotic and 6 Non-psychotic Subjects During Wakefulness and During Sleep at the Median Embedding Dimension (E50), continued.

Comparison between 3 normal, 3 bipolar depressed, and 3 psychotic subjects during wakefulness and during sleep.  Average + S.D. of several variables at the embedding where the patterned recurrences are 50% (median embedding dimension). Lag 1, cutoff 0.1, 7000 beats per patient.  Statistical significance (Mann-Whitney U test).