Abstract
The purpose of this research is to seek
connections and parallels between the concepts of chaos theory and the symptoms
of Posttraumatic Stress Disorder. If connections could be found then a holistic
model of PTSD may be developed. A computer assisted qualitative data analysis
software (CAQ DAS) program called ATLAS.ti was used. A total of 10 primary
documents on the topics of chaos theory, neurobiology, PTSD and psychology were
downloaded into the program. This material was formed into quotes, coded, and
then displayed in focused networks. The results showed at least four
connections between chaos theory and PTSD. These are the concepts of bifurcation,
fractals, limit cycle attractor and the periodic attractor.
The purpose of this research is to discover whether or not there are any links between the concepts of chaos theory and the major symptoms of Post Traumatic Stress Disorder. The purpose is also to discover if the literature on these symptoms reveals disrupted chaotic processes.
Statement
of the Problem
The American Psychiatric Association classifies Posttraumatic Stress Disorder (1994) as a psychiatric disorder, coded 309.81. It is listed under the heading of “Anxiety Disorders”. Many psychological symptoms are manifested; avoiding thoughts, feelings or conversations about the traumatic event, avoiding activities, situations, or people who arouse recollections of it, full or partial amnesia relating to the trauma, psychic numbing, nightmares, hypervigilance, angry outbursts and difficulty concentrating.
However, Van der Kolk (1996),( 1997) believes that there is a biological basis for posttraumatic stress disorder (PTSD). Recent biological findings include; increased urinary and blood catecholamines resulting in increased resting blood pressure and heart rate, increased corticotrophin-releasing factor levels in the brain resulting in the down-regulation of receptors for corticotrophin-releasing factor and ultimately decreased levels of cortical , increased startle response, increased plasma T3 levels, decreased sleep time with nightmares, a decreased hippocampal volume possibly impairing memory function, and decreased communication between right and left hemispheres of the brain (Van der Kolk,1997).
Because our most recent research demonstrates that PTSD is both a biological and psychiatric disorder we can no longer afford to think of the mind as somehow being dissociated from the body . Our psychological life is influenced by what happens in and to our bodies. Conversely, our bodies respond to our thoughts. And both the mind and the body respond to what is happening in our environments.
Because this is true, it seems that what may be needed is a holistic view of PTSD that would allow for an integrated perspective of mind/body effects. Such a view could have a positive impact on both diagnosis and treatment. But how do we develop such a view? And furthermore, do we have the language and tools available to do it? I believe that chaos theory may provide both the language and the tools necessary for the development of a holistic model of PTSD. This research represents an attempt to discover whether or not there are any relationships between the symptoms of PTSD and the major concepts of chaos theory. If such links are found to exist, then a holistic model may be developed from them.
Literature Review
Chaos
Theory
What is chaos theory and what does it have to offer by way of formulating a model for Posttraumatic Stress Disorder? In general terms, chaos theory represents a mathematical way to think about highly complex systems.
Chaos is variously defined depending on one’s frame of reference. Here are some definitions presented from the fields of mathematics and physics: “ A kind of order without periodicity.” , “Apparently random recurrent behavior in a simple deterministic system.”, “The qualitative study of unstable, aperiodic behavior in nonlinear systems.”, “The ability of simple models, without inbuilt random features, to generate highly irregular behavior.” (Sardar & Abrams, 1998. p.9).
Similarly, this definition is given to us from the field of neurobiology:
Chaotic systems are deterministic. The present variables depend entirely
on their recent, previous values. There is no element of chance. This is
called a dynamical system. Some dynamical systems are chaotic and
some are not. ...Mathematically...new values of the variables are computed
from the previous values of the same variables. ...A chaotic system has only
a small number of variables. The output of a chaotic system is very complex.
the data that are generated by a chaotic system are so complex that they
mimic the data generated by a system based on chance (Liebovitch, 1998. p.124).
Finally, a definition from the field of psychology states:
(Chaos is) the unpredictable evolution of the behavior of many nonlinear
dynamical systems. Because of their sensitive dependence on initial conditions,
the error in predicting the future states of such systems grows exponentially
with time, so that the future states of such systems becomes essentially
unknowable in a relatively brief period of time. Although chaos means
unpredictability, it should not be understood to mean that the system was
not or is not determined (Masterpasqua & Perna, 1997, p. 304).
The phenomenon of chaos occurs when something changes. The sort of changes that we are the most familiar with are those that have been previously studied by classical physics. Examples of this would be the Newtonian views of planetary motion and most machines. The behaviors of these systems are predictable. However, living systems must be perceived in another way. This is because living systems change over time. One pivotal view for applying chaos theory to human behavior states: ...human beings are intrinsically open, and therefore a nonlinear system.
Explicitly stated, the ontological assumptions underpinning all theoretical
formulations asserted here are that: human beings interact with the
environment, develop, choose how to develop within environmental
constraints (Blackerby, 1993, p.68).
In dynamical, open systems change is inevitable. And it is this change which gives rise to the possibility of chaos.
In the older way of thinking we used to believe that the desirable state of each system was to be stable. We thought that there were certain forces that drove the system between these stable states. But the lessons of chaos have taught us that it is the nature of open systems to be unstable ( Liebovitch , 1998). In most cases this instability is seen as being desirable. “Hanging around for a while in one condition forces the system into another condition” ( Liebovitch , 1998 , p.235). A system living on the “edge of chaos” is said to be the most open to change. One of the most interesting phenomena of chaos theory is “sensitivity to initial conditions”. In his book, The Essence of Chaos, Lorenz relates his serendipitous discovery of this phenomenon. He says that one day while he was in the process of developing a statistical model of weather forecasting, he took a short cut with his weather machine. There was a certain sequence that he wished to examine in greater detail. This time, instead of starting with the beginning calculations he started halfway through. He tapped the numbers into his computer from an earlier print out. He started the computer and left to get some coffee. What he discovered when he returned and looked at the new printout, was that the newly generated weather system was nowhere near the original. They looked like two completely different systems! It seems that he had tapped in the number .506, the number copied from the printout instead of the number that had been used for the original weather system, which was .506127. The difference which was minute, less than one part in five thousand, had tremendous consequences. What Lorenz discovered was that minute differences could have catastrophic consequences. This is what is now referred to as the “butterfly effect” (Gleick, 1987). More importantly, if any error is made at all in observing the present state, and how can we help but make errors, making predictions about a future state may be impossible.
The idea of the attractor is important to chaos theory. Attractors have come to be seen as the states to which the system eventually settles. A simplistic way to understand an attractor would be to drop a marble into a bowl. The marble keeps going around the bowl until it eventually settles on the bottom. This point at which the marble settles “attracts” the marble. Attractors help to bring order out of chaos (Sardar & Abrams , 1998).
Attractors are said to exist in phase space. This is a mathematical space that has been plotted so that the coordinates can describe a system’s behavior. There appear to be various kinds of attractors towards which evolving dynamical systems tend to converge. Most non-linear systems tend toward “steady state attractors”. in which nothing much seems to happen , i.e. a pendulum at rest. A second type of attractor is the “limit cycle attractor”. In these we observe the never-ending repetitions of the same behavior, i.e. the swinging pendulum. The attractor associated with non-linear systems is called the “chaotic” or “strange” attractor. This term was first coined by David Ruelle to help explain turbulence in water (Ruelle , 1991). Fluid turbulence, he believed, was an example of chaos.
A chaotic attractor in phase space shows form and has definite boundaries. But within in these boundaries the behavior of the system is unpredictable. Chaotic attractors serve as boundaries for unpredictable behavior (Masterpasqua & Perna, 1997).
Bifurcations are closely associated with attractors as they represent any qualitative change from one kind of attractor to another. They may be seen as a jump in phase space. Robert May (Gleick , 1987) a researcher in population dynamics who first noticed this phenomenon in animal populations felt that the equations they were using to understand fluctuations were more complicated than they appeared. “ He discovered that, with the parameter at high levels, the system would break apart, and the population would oscillate between two alternating values “ (Sardar & Abrams, 1998, p.64). May’s ideas paved the way for finding chaotic processes in biological systems.
Fractals are formed when nonlinear forces in oscillating systems are turned back upon themselves creating feedback. That is when the output or result then affects the input of the system altering its operation. Mandelbrot coined the term “fractal” in 1975 . The word is taken from the Latin “fractus” which means broken up and irregular. In a fractal the same degree of irregularity exists on all scales of magnification.
Through the use of computer graphics fractals can expose the abstract, geometrical nature of chaos. This can be seen in the overall shape that the fractal takes, containing as it does, the repetitive patterns of self-similarity over many scales of magnification.
Benoit Mandelbrot has created a fractal that has become known as the most complex object in mathematics (Gleick , 1987 ). Though the fractal is complex, the formula contains only three variables, z z + c. Take a number, multiply it by itself and add the original number. Thus the equation becomes iterated and not solved. In this way the equation becomes a dynamic process instead of a static description.
The area of Mandelbrot’s fractal may be measured, but it’s circumference is infinite. It is the continuous iteration of numbers that causes the bending and folding into the self-similar and self-organizing designs that we see. The equation is used as a feedback loop, the result of one calculation is used as the input for the next calculation.
Psychology
and Chaos
The application of chaos theory to the life sciences and especially to psychology, is a rather new yet rapidly expanding area of research. Chaos represents a way to analyze complex dynamical systems which hitherto had not been possible.
Some of the concepts from chaos were first applied to certain aspects of family systems theory (Hoffman, 1981). Hoffman applies the idea of discontinuous change in an attempt to understand when and how change occurs within family systems. She believes that change occurs not in a smooth unbroken line but in discontinuous leaps. Further, these changes then precipitate a self-reorganization of the family. More recently, the principles of feedback, fluctuation, stability, bifurcation and disequilibrium has been applied to interacting family systems (Koopmans, 1996). In his research Koopman was seeking to understand where changes in dysfunctional families come from.
Schueler (1997), attempts what he calls an “interface” between Jungian psychology and chaos theory. He suggests that the personal unconscious represents a psychological “edge of chaos”. He believes that this “psychic region of complexity bridges the acausal gap between the collective unconscious and the conscious ego” (Schueler , 1997, p.1).
In The Psychological Meaning of
Chaos: Translating Theory Into Practice,
Masterpasqua and Perna (eds.) (1997), have collected a series of papers by various authors containing the unifying theme that chaos has meaning and order occurs spontaneously. They state that chaos and self-organization are “inextricably linked in the dynamic development of living systems” (Masterpasqua and Perna, 1997, p. 1. ). However, in the forward to their book, they give us the understanding that the dynamical concepts are a source of ideas to be applied metaphorically to help us see the patterns in psychotherapy and other psychological processes.
Though I believe that the metaphorical applications of chaos theory to psychology help us to broaden our vision and to expand our language base , this move helps to continue the Cartesian split between the mind and body. The science of chaos is an holistic science . The application of it to psychology should help us to answer the basic questions of “what influence does the mind have on the body, and how do body processes influence our thinking, emotions and behavior?” “ How are the two connected?”
A
bridge between body and mind
The neurobiological substrate may be a bridge between the body and the mind. As we might expect, since our body contains many open systems, many chaotic properties and processes have been discovered on this neurobiological level. The fractal dimension has been measured on the following: the surfaces of proteins, the surface of cell membranes, the shape of herpes simplex ulcers in the cornea, in the growth of bacterial colonies, in the islands of types of lipids in cell membranes, the dendrites of neurons, the blood vessels in the eye, the heart and the lung, the blood flow in the heart, in the textures of x-rays of bone and teeth, and in the texture of radioisotope tracer in the liver ( Liebovitch , 1998). Temporally, fractal bursting patterns and scaling relationships have been observed in the kinetics of ion channels (Anderson , 2000). Scaling relationships have been found in the chemical reactions limited by diffusion and in the washout kinetics of substances in the blood. (Liebovitch , 1998).
Chaotic processes have also been found to be important to healthy heart functioning . Given normal circumstances there appears to be chaotic behavior in heart rate. The rhythm varies on a beat to beat basis. It also displays many fluctuations over time. When the variability becomes too regular it can lead to fibrillation or sudden death . These new discoveries are discussed in “An Interview with Dr. Yasha Kresh” (Date not given).
One of the foremost researchers in the field of neurobiology and chaos is Walter Freeman (1990). In his experiments with the olfactory bulb and cortex of rabbits he has discovered chaotic wave forms. He states, “ Chaos in the model arises when the bulbar loop is interconnected with the olfactory cortical loop, so that each excites the other. Each oscillator has its own characteristic period, but they differ and cannot agree. Neither can escape the other, so that perennial aperiodic oscillation results” (Freeman , 1990, p. 8).
Carl Anderson (2000) , has managed to isolate fractal-like bursting patterns in the REM sleep of fetal sheep. He believes that the burst patterns “provide a means to synchronize the linkage of movements in the fetus with other neuronal motor events such as the ingestion of amniotic fluid, allowing long-and short range coordination among different emerging behaviors” (Anderson, 2000, p.3). And further, Anderson induced stress in baby rats through maternal deprivation. He found that early stress caused disruptions in these burst patterns. He states:
Recent findings by many researchers, including the author, support the contention
that stress or abuse in early life induces functional hemispheric asymmetries and
disrupts the structure of REM sleep resulting in PTSD, predisposing one to
addictive and self-defeating behaviors resulting from the lifelong effects of
impaired interhemispheric integration (Anderson , 2000, p. 17).
If stress causes disruptions in chaotic processes , we may expect to find clues to these disruptions in the symptoms of posttraumatic stress. And this should be especially contained in the literature on PTSD symptomlogy. The purpose of this research then, is not only to discover whether or not there are any links between the concepts of chaos theory and the symptoms of posttraumatic stress disorder , but also to discover if the literature on symptomlogy reveals disrupted chaotic processes.
Research Design and Methods
For this research, I selected a computer assisted qualitative data analysis software (CAQDAS). Posttraumatic stress disorder is a complex phenomenon. I needed a tool that could deal with that complexity.
The CAQDAS that I chose for this project is Atlas.ti. I selected this program for several reasons. In the Atlas.ti program there is no limit on the units of coding and any amount of text can be coded as one unit. The conceptual networks are displayed visually and can be manipulated in a variety of ways. And most importantly for my purposes, it assists in creative and visualized theoretical thinking. This visual creativity I felt could assist me in the discovery of patterns and similarities.
The Atlas.ti program was constructed around the ideas of Glasser and Strauss’ grounded theory qualitative method of doing research. Grounded theory is an inductive approach that says theory must emerge from the data . In other words it must be “grounded” in the data. Its goal is to construct theories in order to understand phenomena.
The grounded theory process seems appropriate since I am not seeking to verify a theory but to generate a new one, i.e. an holistic model of posttraumatic stress disorder via chaos theory. One serious departure from the grounded theory approach that I will be taking, is that the data I use for my primary documents come from the literature and were not generated by myself through field research.
In the Atlas.ti program an overall “hermeneutic unit” is opened. The hermeneutic unit contains all the other elements of the research project in question. Primary documents are loaded into the hermeneutic unit from a word processor. The primary documents are then broken down into quotations. These are automatically numbered as to which primary document they come from and the order in which the quotation appears. After the quotations are formed, the quotation can then be coded. Memos may be derived from the codes and used later in the formation of the theories. Once this basic work is done, focused networks may be displayed. It is at this stage of the process that the links and patterns may be found. The focused networks consist of all the quotations that have been coded under a given concept.
The title that I gave to the Hermeneutic Unit was simply, “Chaos theory and posttraumatic stress disorder.” I then loaded ten Primary Documents into the Hermeneutic Unit. These documents were chosen for their relevance to chaos theory, to chaos theory in neurobiology, to chaos theory in psychology and to posttraumatic stress disorder. The following are the ten primary documents that I chose with a short explanation of my reason for selecting them:
1. Application of Chaos Theory to Psychological Models (Blackerby , 1993,
pp. 138-144.) These pages consisted of a glossary of the main concepts of
chaos theory presented from a more mathematical perspective.
2.The Psychological Meaning of Chaos (Masterpasqua & Perna (eds) , 1997,
pp. 303-307). These pages consisted of a glossary of the main concepts of
chaos theory presented from a more psychological perspective.
3.Fractals and Chaos Simplified for the Life Sciences (Liebovitch , 1997,
pp. 8, 12, 14, 16, 18, 28, 34, 36, 38, 40, 41, 42, 46, 68, 69, 70, 108, 109,
124, 126, 132, 172, 176, 180, 188, 192, 196, 198, 226, 234, 235, 238).
These pages presented explanations of the main concepts of chaos theory
and their application to neurobiology.
4.Chaos In The CNS: Theory and Practice (Freeman , 1994, pp. 1-8)
Representations: Who Needs Them? (Freeman & Skarda, 1990, pp. 1-6 ).
In these pages Freeman presents his discovery of chaotic processes in
neurobiological systems , practical applications of and implications for
neuroscience.
5.The Geometrization of Thought (Peat, not given , pp. 1-15). In these pages
Peat shows us how to apply the concepts of chaos theory to those of psychology.
He gives us language and vocabulary.
6. Spontaneous Fractal Behavior
from Ion Channels to the Internet:
A Bridge From Molecules to Minds. ( Anderson , 2000, pp. 17, 19, 20,
21, 22 ). In these pages Anderson applies chaos theory to the neurobiological
development of newborn rats. He demonstrates how posttraumatic stress may
develop in children leading to lifelong psychological and emotional problems.
7. Common Biological Findings in PTSD Patients (van der Kolk, 1997,
pp. 1-3). In these pages the neurobiological abnormalities of those suffering
from PTSD are presented .
8. Trauma and Recovery: The aftermath
of violence-from domestic
abuse to political terror ( Herman , 1992, pp. 33-50). These pages contain
descriptions of the major symptoms of PTSD . They also contain anecdotes
for each description.
9.Diagnostic and Statistical Manual of Mental Disorders-IV ( American
Psychiatric Association, 1994, pp. 424-427 ). These pages represent the
official descriptive features of Posttraumatic Stress Disorder 309.81.
10. Post Traumatic Stress
Disorder: The Latest Assessment and Treatment
Strategies (Friedman , no date given, pp. 33-50). These pages contain a
glossary of concepts important for an understanding of PTSD.
Once these documents were loaded into the Hermeneutic Unit, the process of analyzing began. The primary documents were read and re-read then quotations were formed from those sections containing material that might possibly provide links, similarities or patterns between the major concepts of chaos theory and the major symptoms of PTSD. As the quotations were formed they were coded according to a concept from chaos theory which they were thought to represent. For instance, a quotation that contained a description of constrictive behavior in someone suffering from PTSD was coded with “ limit cycle attractor” and so on. Memos , which are comments on the coded material, were also written at the time of the coding. These memos provided core ideas which come to mind in the forming of the quotations and in the assigning of the codes.
When the coding was completed , focused networks could then be displayed. A code is first displayed on the screen , then “neighbors” are imported . The “neighbors” are all of the quotations that have been assigned the code in question. Each coded quotation becomes a “node” on the visual map. The nodes that contained a definition or an explanation for the code were opened first. Quotations that appeared to be repetitive were deleted. Then the nodes that contained descriptions of symptoms were opened. In most cases , I placed the code at the bottom center of the screen. Directly above it I placed the nodes containing the definitions or explanations. These I thought of as the trunk of a tree. All of the nodes containing descriptions of PTSD symptoms I placed above and to both sides. The configuration that I ended up with depended largely on how many nodes the focused network contained. The symptoms were the branches of the tree. All of the nodes were automatically linked with a line from the code. Besides this, I linked the definitions that made up the trunk to each other with (?>). This means that one explains the other. I also made links between the trunk and each of the branches using the same symbol.
In the final analysis I accepted only those focused networks that contained three elements, at least one good definition of a concept from chaos theory, the related neurobiological application and the quotations of the descriptions from the literature on PTSD that appeared to be related to the other two elements. This final move eliminated most of the focused networks as they did not meet the requirements as stated above. I believe that if a concept from chaos theory has been applied with some success to neurobiology , then it may be a good indication that relevant material probably does exist on a psychological level. While the absence of a neurobiological finding does not mean that no relationship exists-it may be found with more research-applying a concept from chaos theory directly to the psychological level becomes too metaphorical.
As a final step, I charted my findings. Each chart has four columns, the first one is titled “Chaos Concept”. Underneath, one or two definitions from the same concept in chaos theory are given. The second column is titled “Neurobiological Application”. This category turned out to be applicable to the areas of both chaos theory and PTSD. The third column is quotations from “PTSD Symptomology”. And the fourth column called “Relationship/Link” is a short explanation of how all three elements , chaos theory, neurobiology and PTSD may be linked.
Results
Bifurcation , chart # 1
My findings indicate that the concept of bifurcation from chaos theory may help to explain three different phenomenon usually associated with posttraumatic stress disorder. A small change in the value of a parameter in a nonlinear system can cause dramatic changes in behavior. On a neurobiological level, an external stimulus leads to unpatterned chaotic states which allow for the formation of new nerve cell assemblies. These new nerve cell assemblies then form new attractors and their basins of attraction. (Liebovitch. 1997). In PTSD, the literature indicates that the likelihood of developing this disorder increases as the intensity and proximity to the stressor increases. New attractors may be formed as a result of traumatic stress. This bifurcation process then leads to changed psychological processes and externalized behaviors.
Bifurcation may also help to explain the existence of other co-morbid disorders in those who suffer from PTSD. Since bifurcation takes place in discontinuous leaps, the specific type of attractor that is formed is not predictable. It may be that many types of attractors can be formed from traumatic stressors. Each attractor may represent a different bifurcation from stressors at various time periods in an individual’s life. This may help to explain the existence of the other related disorders such as Panic Disorder, Agoraphobia, Obsessive-Compulsive Disorder, Social Phobia Disorder and Substance Related Disorders.
Finally, we know that extreme stress changes the parameters of the original chaotic attractors leading to bifurcation. This may explain why individuals without any predisposing conditions may develop PTSD if the stressor is extreme. However, since it takes only a small change in parameters to effect bifurcation , it may be that a seemingly insignificant stressor could cause PTSD symptoms in some individuals. (Please see Chart #1-Results From Focused Network on Bifurcation).
Fractals,
chart #2
The Focused Network on Fractals displayed an interesting link between the disruptions of the vertical integration of fractal patterns leading to fewer spontaneous episodes of rapid eye movement in stressed baby rats (Anderson, 2000) and some of the different types of psychological fragmentation that is seen in PTSD. Anderson equates this lack of integration with the oversized right brain hemisphere often seen in PTSD patients.
In the same vein, this lack of vertical integration of fractal firing patterns may be at the root of traumatized individuals inability to integrate the experience on a conscious level. This lack of integration helps to maintain the memory in its nearly original form, giving it a life of its own.
Certain dissociative states may also be affected by the lack of vertical integration of fractal firing patterns. This lack of integration would tend to preserve the traumatic memory in its original state. Each time that there is a reminder of the event, the person would dissociate and experience the event as at first. Though the inability to integrate plays an important role in dissociative events , there is another phenomenon that makes it even more certain. (See Chart #2-Results From Focused Network on Fractals).
Limit cycle attractor, chart #3
Probably the most interesting findings are demonstrated in Charts # 3 and #4. I subdivided the chaos concept of the attractor into two focused networks. Chart # 3 deals with the limit cycle attractor and Chart #4 with the periodic attractor. These two types of attractors are the same thing. However, the limit cycle attractor is described as a “system trapped to move within the confines of a deep circular valley”(Peat, 2000, p 2) . While the periodic attractor is described as “ never-ending repetitions of the same behavior”(Masterpasquq & Perna, 1997 p.303). The language used to describe the limit cycle attractor speaks to the constrictive behavior of a person suffering from PTSD and the language used to describe the periodic attractor speaks to the repetitive thoughts and behaviors of those who suffer. In both cases it appears to be the over sensitized neurobiological substrate that then affects outward thoughts, emotions and behaviors. It also may be that becoming trapped in the limit cycle attractor may contribute to the fragmentation of the psyche and to certain types of dissociation by preventing the vertical integration of fractal firing patterns as observed by Anderson.
The
Periodic Attractor
We may think of the constrictive behavior, the repetitive thoughts and actions of the PTSD patient as being trapped in a periodic attractor. Most notably, a portion of the brain called the locus coeruleus is found to be hyperactive. The influence of the locus coeruleus is pervasive. It helps to regulate attention, arousal and sleep-wake cycles and affects learning, memory, anxiety, pain, mood and brain metabolism. It is possible that through the process of bifurcation (explained above) the locus coeruleus is changed from a chaotic attractor into a periodic attractor. Is it any wonder then that people tend to re-experience the traumatic event?
What happens when other bodily systems become over-sensitized due to stress and trauma? The results may be very similar. Corticotropin-releasing-factor sees an increase in activity. CRF affects the limbic and cortical regions of the brain. If this system becomes trapped in a periodic attractor, it also may contribute to the reliving and re-creating of the traumatic event that is seen in many traumatized persons. Likewise the same phenomenon probably occurs in the hypothalamic-pituitary-axis, a system that participates hormonally in response to stress. Here the hypothalamus is affected along with the pituitary gland and the cortex of the adrenal gland. This system normally orients the body for danger. A hypersensitive HPA-axis would lend to the feeling of impending danger even when there is nothing at all to fear. On becoming trapped in a periodic attractor a sense of danger becomes pervasive. Perhaps even to the point of controlling a person’s life. Of course one’s thoughts, emotions and behaviors become repetitive, reflecting what is happening in the neurobiological substrate. The repetitious thoughts and actions may also reflect the self-similar patterns that are occurring through-out the body on many different scales and levels. (Please see Chart #4-Focussed Network on Periodic Attractor).
Conclusions
Summary
The original purpose of this research was to explore the possibility of whether or not any links, patterns or relationships exist between the concepts of chaos theory and the symptomology of Posttraumatic Stress Disorder. If such links could be found, then a holistic model of PTSD may be developed from them. A computer assisted qualitative data analysis software (CAQDAS) program called ATLAS/ti was chosen for this project.
A total of ten primary documents from the literature on chaos theory, neurobiology and PTSD were loaded into the Hermeneutic Unit. Quotations were formed from them then coded according to the concepts of chaos theory. Focused networks were displayed showing the possible relationships. Finally a chart of each of the usable focused networks was constructed.
Thus the new theory that arose from this process demonstrates at least four links between chaos and PTSD. They are bifurcation leading to changed psychological processes, externalized behaviors and other comorbid psychological disorders; The lack of vertical integration of fractal patterns leading to psychic fragmentation and certain types of dissociation; The limit cycle attractor forming as a result of bifurcation leading to an over sensitized neurobiological substrate that thus affects the emotional and behavioral life demonstrated in constrictive thoughts and actions; And finally , the formation of the periodic attractor leading to the constant repetition of the traumatic event in thought and action.
Limitations,
strengths and weaknesses
Using the CAQDAS program ATLAS.ti for this project gave me a way to systematically uncover the links, similarities and patterns between the concepts of chaos theory and the main symptoms of PTSD. Because the grounded theory method from which ATLAS.ti derives its inspiration is so specific, the project is easy to reproduce. I believe this method also allows for a more “comprehensive development of coherent theoretical ideas” (Barry, 1998, p. 14). The further development of these theoretical ideas, which were gleaned from the primary documents, will contribute to the formation a holistic model of PTSD.
One limitation of this project may be the very subjective, though logical, nature of the selection of the material that was used for the primary documents. Perhaps if different documents were chosen, the results would have been much different. Another researcher might possibly choose different quotations and code differently, also with the end result differing from my findings. The choice of documents, quotations and coding depend heavily upon the researcher’s depth of understanding concerning the topic at hand. This research required a working knowledge of four different fields, that of psychology, neurobiology, posttraumatic stress disorder and chaos theory. The final conclusions may be tainted by my ignorance in any of the above areas.
Finally, I am assuming that chaos is a real phenomenon when many experts are not yet believers and many more are at least wary of the ideas. Not only am I assuming that it is real , I am attempting to apply the concepts in a literal fashion , because certain evidences of these processes appear to have been found and measured in the body. Ian Stewart, a professor of Mathematics at the University of Warwick, and also a leading authority on chaos in Britain, is quoted by Sardar & Abrams (1998). He cautions us:
The role of chaos and complexity has been crucial and positive: they have
caused us to start asking sensible questions and to stop making naive
assumptions about the source of complexity or pattern. But they represent
only a tiny first step along a difficult path, and we should not let ourselves
be carried away by over ambitious speculations based on too simple a notion
of complexity ( p. 171).
Hopefully, the application of chaos theory to the complex phenomenon of Posttraumatic Stress Disorder is neither over ambitious nor speculative, but will contribute in a positive way to our understanding of this puzzling disorder.
Key: Meaning of the numbers: The first number (ex. 3) refers to the number
of a primary document.
The second number refers to the quotation number within the same
primary document (ex. 3:16)
Chaos Concept |
NeurobiologicalApplication |
PTSDSymptoms |
Relationship/Link |
|
#3:16 The behavior of a nonlinear system can change dramatically when there
is only a small change in the value of a parameter. Such an abrupt change is
called a bifurcation. |
#4:6 Learning by trial and error and by insight takes place when a novel
stimulus with reinforcement leads to the emergence of an unpatterned chaotic
state during an orienting response….The chaotic activity provides the
substrate from which a new nerve cell assembly can form, leading to a new
attractor and its basin of attraction. This process constitutes a bifurcation
that may underlie adaptive voluntary behavior. |
#9:3 The likelihood of developing this disorder (PTSD) may increase as the
intensity of and proximity to the stressor increases. |
As the intensity and physical proximity to the stressor increases, the parameters of the original attractor are changed and a new attractor is formed. Bifurcation may lead to changed psychological processes and externalized behaviors. |
|
|
|
#9:9 There may be an increased risk of Panic Disorder, Agoraphobia,
Obsessive-Compulsive Disorder, Social Phobia, and Substance Abuse Related
Disorders. |
Since bifurcation takes place in discontinuous leaps, the specific type of attractor that is formed cannot be predicted. It may be that many types of attractors can be formed from traumatic stressors, each representing a different bifurcation from stressors at various periods of time. |
|
|
|
#9:12 This disorder (PTSD) can develop in individuals without any
predisposing conditions, particularly if the stressor is especially extreme. |
The extreme stress changes the parameters of the original attractor leading to bifurcation. Lesser stressors may also cause bifurcation to take place as small changes in parameters precipitates bifurcation causing the formation of new attractors. |
|
#1:6 A fractal is an irregular and recurring form or shape having the
property of self-similarity. |
#6:2 These findings suggest that early stress results in disruptions of
vertical integration of fractal firing patterns, leading to fewer numbers of
spontaneous episodes. (Rapid Eye Movement) |
#8:7 This kind of fragmentation, whereby trauma tears apart a complex
system of self-protection that normally functions in an integrated fashion, is
central to the historic observations on post traumatic stress disorder. |
Stress disrupts the vertical integration of fractal firing patterns
associated with REM. Fewer numbers of spontaneous episodes have been observed
under stressful conditions. Perhaps this lack of vertical integration of
fractal patterns contributes to the fragmentation of the psyche that we see
in PTSD. |
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# 8:8 …people with hysteria had lost the capacity to integrate the memory
of overwhelming life events. |
The lack of vertical integration of fractal firing patterns may be at the root of traumatized individuals inability to integrate the experience on a conscious level. This lack of integration helps to maintain the memory in its nearly original form, giving it a life of its own. |
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#8:29 Time sense may be altered, often with a sense of slow motion, and the
experience may lose its quality of ordinary reality. |
If there is a lack of integration of fractal patterns and an inability to integrate the trauma experience on a conscious level thus maintaining the memory in its original form; each time that there is a reminder of the event, the person would dissociate and experience the event as at first. |
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#9:4 In rare instances the person experiences dissociative states that
last from a few seconds to several hours, or even days, during which
components of the event are relieved and the person behaves as though
experiencing the event at that moment. |
The slowing down of REM during sleep, and the lack of vertical integration of fractal firing patterns may contribute to dissociation in the traumatized person. |
Chaos Concept |
Neurobiological |
PTSD Symptoms |
Relationship/Link |
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#5:4 Nonlinear dynamics also deals with limit cycles and quasi-periodic
behavior, that is with systems that settle into repetitive behavior highly
resistant to external perturbations. |
#7:9 Hyperactivity at the locus coeruleus is found in many PTSD patients
after exposure to trauma. |
#9:6 The person commonly makes deliberate efforts to avoid thoughts,
feelings, or conversations about the traumatic event and to avoid activities,
situations or people who arouse recollections of it. |
The locus coeruleus helps to regulate attention, arousal and
sleep-wake cycles and affects learning, memory anxiety, pain, mood and brain
metabolism. In PTSD, the locus coeruleus and its accompanying systems are
changed from a chaotic attractor into a limit cycle attractor. The result is
constricted behavior. |
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#5:5 Thus, for example, the mathematical description of a limit cycle can
be easily conceptualized in terms of a system trapped to move within the confines
of a deep circular valley. |
#7:10 Another phenomenon commonly seen in PTSD patients is an increase in
the activity of corticotrophin-releasing factor (CRF) in both the limbic and
cortical regions of the brain. |
#8:5 Each component of the ordinary response to danger, having lost its
utility, tends to persist in an altered and exaggerated state long after the
actual danger is over. |
In PTSD, cortical-releasing factor in the limbic and cortical regions
of the brain becomes trapped in a limit-cycle attractor. Thus the feelings of
persistent danger tends to linger even after the danger is past. If the
trauma was great enough the elevated CRF response may dominate through out
life. Perhaps this is what we refer to as “Generalized Anxiety Disorder”. |
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#10:19 Hypothalamic-pituitary-adreno-cortical axis refers to three anatomic
structures that participate collectively in hormonal response to stress: the
hypothalamus, in the brain, the pituitary gland, and the outer layer (cortex)
of the adrenal gland. |
#8:10 Hyperarousal reflects the persistent expectation of danger, intrusion
reflects the indelible imprint of the traumatic moment; constriction reflects
the numbing response of surrender. |
Systems such as the HPA-axis become trapped in a limit cycle attractor, thus constricting the emotions, thoughts and behaviors of the PTSD sufferer. |
Chaos Concept |
Neurobiological |
PTSD Symptoms |
Relationship/Link |
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#2:1 Most non-linear systems tend toward either steady-state attractors in
which nothing happens (e.g. a pendulum at rest) or periodic attractors in
which there are never-ending repetitions of the same behavior. (e.g. the
pendulum repeating the same back and forth motion). |
#7:9 Hyperactivity at the locus coeruleus is found in many PTSD patients
after exposure to trauma. |
#9:13 The characteristic symptoms from the exposure to the extreme trauma
include persistent reexperiencing of the traumatic event. |
The locus coeruleus regulates attention, arousal, and sleep-wake
cycles and affects learning, memory, anxiety, pain, mood and brain
metabolism. Traumatic stress sensitizes the locus coeruleus and its
accompanying systems causing them to change into a periodic attractor. This
may account for the persistent re-experiencing of the traumatic event. |
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#7:10 Another phenomenon commonly seen in PTSD patients is an increase in
the activity of corticotrophin-releasing factor in both the limbic and cortical
regions of the brain. |
#8:22 Adults as well as children often feel impelled to re-create the
moment of terror, either in literal or in disguised form. |
In PTSD, cortical-releasing factor in the limbic and cortical regions of the brain becomes trapped in the repetitive patterns of the periodic attractor. Since the emotional and cognitive centers of the brain are most affected by these constantly recurring memories and feelings, the urge to repeat may be most compelling. |
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#10:19 Hypothalamic-pituitary-adrenal axis refers to three anatomic
structures that participate collectively in hormonal response to stress: the
hypothalamus in the brain, the pituitary gland, and the outer layer (cortex)
of the adrenal gland. |
#8:20 Traumatized people relive the moment of trauma not only in their
thoughts and dreams but also in their actions. |
If we add the HPA-axis to the list of bodily systems that become trapped in the periodic attractor, repetitious behaviors of all types become clearly understandable. The receptiveness of the thoughts, emotions and actions are simply a reflection of the self-similar patterns that are occurring through-out the body on many different scales and levels. |
· American Psychiatric Association. (1994). Diagnostic And Statistical Manual of Mental Disorders. Washington, D.C.: Author.
· Anderson, C. M., Ph.D. (2000). Spontaneous Fractal Behavior from Ion Channels to the Internet: A Bridge from Molecules to Mind. Retrieved October 24, 2000 from the World Wide Web: http://remfractal.mclean.org.8080/intro.html
· Barry, C. A. (1998). Choosing Qualitative Data Analysis Software: Atlas/ti and Nudist Compared. In Sociological Research Online (3rd ed., Vol. 3). Retrieved December 7, 2000 from the World Wide Web: http://http/3/3/4.html
· Blackerby, R. F. (1993). Application of Chaos Theory to Psychological Models. USA: Performance Strategies Publications.
· Freeman, W. J. (1994). Chaos in the CNS: Theory and Practice: Retrieved July 11, 2001 from the World Wide Web: http://sulcus.berkely.edu/FreemanWWW/manuscripts/IF2/94/html
· Freeman, W. J., & Skarda, C. A. ( 1990). Representations: Who Needs Them? In Brain Organization and Memory Cells, Systems, & Circuits (pp. 375-38). Retrieved July 11, 2000 from the WorldWideWeb:http://sulcus.berkeley.edu/FreemanWWW/manuscripts/IF2/94/html
· Friedman, M. J. (not given). Post Traumatic Stress Disorder: The Latest Assessment and Treatment Strategies. Kansas City, MO: Compact Clinicals.
· Gleick, J. (1987). Chaos: Making a New Science. N.Y.: Penguin Books.
· Herman, J. (1992). Trauma and Recovery. New York: Basic Books.
· Hoffman, L. (1981). Foundations of Family Therapy. USA: Basic Books.
· Kresh, Yasha (2000). The Brain and Heart of Chaos. Retrieved July 25, 2000 from the World Wide Web:http://husol.auhs.edu/chaosjk.1.htm
· Koopmans, M. (1996). Application of Chaos Theory to Family Interaction [Proceedings of the Winter Chaos Gathering in Vermont]. Retrieved January 24, 2000 from the World Wide Web: http://www.valdosta.edu/~whuitt/psy702/files/chaosfmy.html
· Leibovitch, L. S. (1998). Fractals and Chaos Simplified for the Life Sciences. New York: Oxford University Press.
· Lorenz, E. N. (1993). The Essence of Chaos. Seattle: University of Washington Press.
· Masterpasqua, F., & Perna, P. A. (1997). F. Masterpasqua & P. A. Perna (Eds.), The Psychological Meaning of Chaos. Washington, D.C.: American Psychological Association.
· Peat, D. F. (2000). Chaos: The Geometrization of Thought [Talk given to the Chaos in Psychology Association].Chaos in Psychology Association. Retrieved October 24, 2000 from the World Wide Web: http://www.fdavidpeat.com/bibliography/essays/oril.htm
· Ruelle, D. (1991). Chance and Chaos. Princeton, New Jersey: Princeton University Press.
· Sardar, Z., & Abrams, I. (1998). Introducing Chaos. USA: Totem Books.
· Schueler, G. (1997). Chaos Theory: Interface With Jungian Psychology. Retrieved December 12, 2000 from the World Wide Web: http://www.schuelers.com/chaos1.htm
· Van Der Kolk, B. A. (1996). The Body Keeps the Score: Approaches to the Psychobiology of Posttramatic Stress Disorder. In Traumatic Stress (pp. 214-241). New York , London: The Guilford Press.
· Van der Kolk, B. A. (1997). Common Biological Findings in PTSD Patients. In Journal of Clinical Psychology (pp. 1-3). Retrieved October 10, 2000 from the World Wide Web: http://www.unmc.edu/FamilyMed/ICE/PTSD/patho.html