Complex Systems in Medicine: A Hedgehog’s Tale of Complexity in Clinical Practice, Research, Education, and Management

By David C. Aron

This unique title explores complex systems in clinical medicine and the subsequent implementation of that knowledge into practice.  Written conversationally and as a reflection on the journey of learning about complex systems, the book explores how knowledge of these systems can be applied to four key roles in academic medicine: clinical practice, education, research, and administration.  Further, this title emphasizes how gaining an understanding of complex systems can greatly help a physician deal with the many challenges found in academic medicine. Unlike other books on complexity in medicine, which tend to focus on only one aspect of the management of patients, Complex Systems in Medicine deals with the multifaceted roles of a physician. The approach in this book is uniquely qualitative rather than mathematical, and is written to make it not only of interest to physicians, trainees, and allied health providers, but also to make it more accessible to a non-medical audience. The inclusion of personal anecdotes by the author provides concrete examples of the application of knowledge of complex systems in academic medicine. A first-of-its-kind contribution to the literature, Complex Systems in Medicine: A Hedgehog’s Tale of Complexity in Clinical Practice, Research, Education, and Management is not only a novel reference for medical professionals, it is an accessible tool for the non-medical audience hoping to learn more about complex systems and their direct relevance to medicine, a field that deals with the infinite variety of humans and their ills. It illustrates the consequences of the interactive elements of patient care that make medicine both a science and an art.

• Language: English
• Publisher: Springer
• Release date: Aug 30, 2019
• ISBN: 9783030245931

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Part IStarting Out

© Springer Nature Switzerland AG 2020

D. C. AronComplex Systems in Medicinehttps://doi.org/10.1007/978-3-030-24593-1_1

1. Discovering Complexity

David C. Aron¹ 

(1)

School of Medicine and Weatherhead School of Management, Case Western Reserve University and Cleveland Veterans Affairs Medical Center, Cleveland, OH, USA

Keywords

SystemsComplexityQuality improvementDelivery of health careLearningDiabetes mellitus

If things were simple, word would have gotten around. – Jacques Derrida [1]

In the spring of 1973, I began my first clinical rotation – Obstetrics & Gynecology. One of the first patients I saw was in her 1930s. I was paired with an OB-GYN resident and we looked at the patient together. He noticed something – the patient just did not look right – and he suspected that she had some kind of hormone deficiency. This was not at all the reason why the patient was admitted. She had been referred because of a mass felt in her abdomen and some weight loss. However, his observation began a cascade. First, he asked a key question of the patient: Did you breast feed your last child? She responded that she was unable to produce any milk. Further history revealed that she had suffered a major hemorrhage during her last delivery and she had ceased to menstruate. Testing followed and confirmed that the patient had a deficiency of thyroid, adrenal, and gonadal hormones as well as deficiency of the hormone prolactin (which stimulates milk production). Everything pointed to a problem at the pituitary. The history was classic for Sheehan’s syndrome, post-partum pituitary necrosis, and the endocrine evaluation showed she had hypopituitarism, a deficiency of pituitary hormones [2]. Everything fit together. The resident was complimented for his perspicacity by the consulting endocrinologists and I mean multiple ones for she was deemed an interesting case. Many people stopped by to see her; none of them had seen a case of Sheehan’s before.¹ I got a pat on the back for looking up the literature on the subject before the endocrinologists did and I can still remember that article [3]. More importantly, the patient was treated with the appropriate hormone replacement and felt much better, not realizing until then how poorly she had felt before. The suspected abdominal mass turned out to be some fibrous adhesions of no significance, a welcome anti-climax. The patient went home happy and I left the rotation convinced that pursuing endocrinology, a subject that already interested me, was the right path.

Of all the areas taught in the pre-clinical curriculum, what had appealed to me the most was the field of endocrinology. That is probably why I was so eager to look up the literature on this patient. The approach to endocrine problems seemed logical and somehow the regulatory networks made sense – they constituted comprehensible systems. I don’t recall getting an explicit definition of what constituted a system in the pre-clinical years or after that for that matter in medical school, but I was taught that the endocrine system consisted of group of glands whose function was to regulate multiple organs within the body to (1) meet the growth and reproductive needs of the organism and (2) respond to fluctuations within the internal environment, including various types of stress, in order to maintain homeostasis [4]. This was accomplished by the secretion of hormones directly into the interstitial spaces and then absorbed into blood rather than through a duct. Hormonal secretion is regulated, usually by negative feedback loops. For example, as shown in Fig. 1.1, the hypothalamic–pituitary–adrenal (HPA) axis regulates the secretion of the steroid cortisol made in the adrenal cortex. The hypothalamus of the brain secretes a hormone (corticotropin releasing hormone or CRH) which stimulates the pituitary gland to secrete adrenocorticotropic hormone – (ACTH). ACTH stimulates the synthesis and secretion of cortisol from the adrenal. Cortisol feeds back negatively on the hypothalamus and pituitary to decrease the secretion of CRH and ACTH, respectively. We take advantage of the feedback dynamics of this system in our approach to diagnosis of conditions affecting the secretion of cortisol by the adrenal gland. For example, when we suspect deficiency of cortisol secretion, we try to stimulate the adrenal glands by administering ACTH and see if the adrenals respond by increasing cortisol levels. If the response is subnormal, we can assess the level of ACTH (after the effects of administration of the drug have dissipated). If the cortisol levels are low, then because there is decreased negative feedback on the pituitary so that more ACTH is secreted by the pituitary gland. The HPA axis as I have described it is a simple system, analogous to thermostat control of a heating system. There are few elements, few interactions between elements, and the interactions and their consequences are fairly predictable. Of course, it is more complicated than this; one of my first papers consisted of a series of cases in which the predictions turned out to be wrong. Nevertheless, as an endocrinologist, I had to be aware of systems and their dynamics and feedback.

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Fig. 1.1

The hypothalamic-pituitary axis – a simple system. (Modified from: Aron [5])

When I use a word, Humpty Dumpty said in rather a scornful tone, it means just what I choose it to mean — neither more nor less. The question is, said Alice, whether you can make words mean so many different things. – Lewis Carrol [6]

The definition of a system is not straightforward. The word system is used in many ways. There are healthcare systems, theological systems, the solar system, the Dewey Decimal System and The System, to name just a few. The Oxford Dictionary defined system as: a set of things working together as parts of a mechanism or an interconnecting network; a complex whole [7]. It is interesting that the word complex is part of one of the definitions as it is in the definition of Von Bertalanffy who developed general systems theory. He defined a system as a complex of interacting elements [8, 9]. Common to definitions of system are the inclusion of elements or items or things and their interactions [10, 11]. In fact, a fundamental notion of general systems theory is its focus on interactions. An additional aspect of a system is its function. The system accomplishes something not accomplished by the individual elements alone, absent that connected organization. This coherent organization may be derived from human action as in human-designed systems where the function is both consciously purposeful and obvious, e.g., a clock or an automobile. For naturally occurring systems, we as observers impute the purpose, though we may discover laws that inform us, e.g., Darwin’s theory of evolution [12].² Systems are delineated by their boundaries – spatial and temporal – which distinguish them from its environment.³ Simple systems are characterized by: a small number of elements, few interactions between the elements, predefined attributes of the elements, highly organized interactions with well-defined laws governing behavior, and system stability – the system doesn’t evolve. This begs the question about how small is small and how few are few. Nevertheless, as the number of elements and interactions increase, the system becomes more complicated. But, when does it become complex? I only learned about that later.

It is one thing to say with the prophet Amos, Let justice roll down like mighty waters, and quite another to work out the irrigation system.⁴ – Rev. William Sloane Coffin [13]

A decade after finishing an endocrinology fellowship, I became associate chief of medicine at the Cleveland Veterans Administration (VA) Medical Center⁵ where I had been a staff physician – endocrinologist and laboratory researcher. My major responsibilities involved ambulatory care and quality. These two overlapped in the implementation of a new organization of general medical care involving reorganization of the primary care clinic and the hospital medical wards [14]. This occurred at the time when the hospital accrediting organization (JCAHO – Joint Commission on Accreditation of Healthcare Organization) was requiring not only assurance of quality (QA), but also improvement in the quality of care that the hospital provided – quality improvement (QI). That required that I learn about the principles and methods of QI and how to put them into practice. I was a physician. How hard could it be? In fact, the principles and methods were straightforward, at least in theory.

At the core of QI is the Plan-Do-Study-Act (PDSA) cycle. This sequential, iterative model of testing and learning constitutes a scientific method. It reflects its origins in the world of manufacturing and industry and it takes a mechanical view of the systems created by humans and focuses on incremental change to reduce variation. The approach implicitly assumes a simple cause-effect relationship between Plan A and Effect B, by testing one hypothesis at a time. The quality improvement journey supposedly took a straightforward path of rapid small-scale tests of change that ramped up in terms of scale – the ramp of complexity (Fig. 1.2). Interestingly complexity was never really defined at this point. Several separate ramps could be ascended simultaneously as different aspects of a single problem were addressed. This is an oversimplification, but that is how things were presented early on.⁶ However, when applied in actual practice, things turned out to be completely different. The ramp of complexity was not linear and a simple PDSA cycle got you only so far [16]. We were trying to implement a new clinic model of care delivery by establishing two academic groups practices each with its own staff (of all types), trainees, primary care clinics and hospital wards. This model of care has been denoted a firm system [17, 18]. Although we didn’t really use this the quality improvement process in any formal sense and only discovered the fact that we were trying to adhere to the basic principles of QI, we did come across many issues that made the path to implementation anything but linear [14]. It was more like the path illustrated in Fig. 1.3. We reorganized services from a traditional departmental and vertical organization into a collaborative horizontal matrix structure revolving around patient- and trainee-centered needs. It was not possible to change the organization of the department of medicine incrementally. It had to be accomplished in one shot, although departments were added incrementally by necessity rather than design. This was more akin to punctuated equilibrium than gradualism in evolutionary theory [19]. In contrast with the relative ease in securing the enthusiastic support of departments of nursing and medical administration, the integration of the social work and nutrition departments involved a six-month negotiation process. We had some false starts and wrong turns, but the reorganization was accomplished and lasted for nearly 20 years until there was a mandate from VA Central Office to organize differently, although to be fair, it was showing its age. The new reorganization process was national in scope and it was similarly non-linear within facilities and across the country [20].

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Fig. 1.2

PDSA cycles driven by data are scaled up in scope, e.g., one provider to several providers in a clinic to many clinics. (From Nelson et al. [15])

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Fig. 1.3

The ramp of complexity in reality. The path was not linear. Barriers resulted in course changes. Results of one cycle could lead in different directions. Complete cycles could not always be conducted and the impact of individual cycles and their components varied. (From: Tomolo et al. [16])

I have been involved in many quality improvement projects since then, some success and many not. Although I had been schooled in the methods of QI, there was clearly something missing. Whether the problem was intrinsic to QI or its presentation or in my application wasn’t clear. In addition, the failures of QI (and its related methods) were increasingly recognized [21]. This occurred at the same time as the external pressures to improve care increased. Among the causes suggested for the failures of QI in healthcare were the lack of physician acceptance and the absence of physician leadership.

In response to the need for physician leaders in the research and practice of quality improvement, the Veterans Health Administration (the medical care branch of the Dept. of Veterans Affairs) which was facing enormous political pressure to improve [22] established a training program in 1998 – the VA Quality Scholars Fellowship Program [23, 24].⁷ I became the director of one of the six sites. As a group, we site directors had relatively little experience in QI; mainly we were health services researchers schooled in the linear approaches of research. (Chap. 12 addresses some of the problems that complexity presents to researchers.) It was during our training that guest faculty (Paul Plsek and Sarah Fraser) introduced us to the topic of complexity in healthcare [25, 26]. Part of this introduction included a metaphor to describe different types of problems developed by Glouberman and Zimmerman [27]. They likened simple problems to following a recipe. The recipe has been tested so it can be easily replicated with the same (or at least extremely similar) results. Once the techniques involved in cooking or baking are mastered, success is pretty much assured. That success was defined as producing the standardized product. Of course, good cooks take a recipe as a starting point and that results in a non-standardized, albeit customized product. A complicated problem was likened to sending a rocket to the moon. Certainly, formulae are critical, but not only the components and factors more numerous, there is a need for specialized expertise and coordination. Success is highly likely, but as demonstrated by some of the tragedies and close calls in the space program, it is not assured.⁸ Complex problems are likened to raising a child. The is no single formula. In fact, there are many which contradict each other. How the first child turns out doesn’t predict how the second one will turn out. Every child is unique and there is considerable ambiguity and uncertainty. Taking the solution to one kind of problem and applying to a different type of problem leads to inappropriate actions and failure. This was a useful metaphor in helping me think about complexity and many long discussions with one of my colleagues, Sarah Fraser, forced me to question my own assumptions. What I learned about complexity was consistent with what I had personally experienced. This was particularly true when it came to implementing something developed in a different setting. This was the case with our ambulatory care reorganization in which adopted a model used at another hospital in Cleveland. We came up against a variety of ‘real world’ factors since our world was different from their world. Our worlds differed not only at the macro-level since we were part of a national government run health care system and the other hospital was a county supported hospital open to all, but also at the meso- and micro- levels because the facilities were organized somewhat differently and of course, the people were different. In other words, the context was critical and that context could not be easily described. The magnitude of the differences between healthcare facilities reflecting the differences in context even in the same system is summarized by the adage: ‘if you have seen one VA, you have seen … one VA. Disciplines from the social and behavioral sciences contributed to my understanding of specific aspects of the context, but I kept coming back to this idea of complexity. What was it?

Like the word system, the definition of complexity is not straightforward. The word complex is applied to diverse phenomenon and is used in many different ways, e.g., Oedipal Complex, industrial complex, DNA-protein complexes or meaning just hard or difficult to understand. In fact, one dictionary defines complexity as the state of having many parts and being difficult to understand or find an answer to [28]. A rocket engine may be considered complex in one colloquial meaning of the term because it is made up of so many parts. A problem can be considered complex because it is so difficult to solve, difficult to grasp, or just plain overwhelming [29]. Complex and complicated are often used synonymously, though their different etymologies suggest that they are different; the former is derived from a word meaning weave and the latter is derived from a word meaning fold.⁹ However, in all cases, complexity is an attribute, quality, or characteristic of something and for my purposes, that something is a system. Beyond stating that a complex system doesn’t have the characteristics of a small number of elements, few interactions between the elements, predefined attributes of the elements, highly organized interactions with well-defined laws governing behavior, and system stability, the definitions of complexity and complex system are more problematic because of the phenomenon’s wide scope and variability.

Defining complexity is either easy or difficult depending upon whether you are a glass is half full or a glass is half empty kind of person.¹⁰ It must be easy in the sense that there are dozens of definitions. It must be hard because there is no single generally accepted definition that can be universally operationalized. The various glossaries of the Encyclopedia of Complexity and Systems Science, a work more than 10,000 pages, provide no less than 11 different definitions [30]. Not only have many definitions been proposed, complexity has been parsed into different types [31, 32]. (This would be a good place for a footnote, but this philosophical digression ended up being several pages in length so I have appended it to the end of this chapter so as not to disrupt the flow.) Nevertheless, a system is complex when the number of elements is large, the number of interactions is large, and the consequences of the interactions and interdependencies are not readily predictable, but at least some of the time exhibiting regularity. I will address in later chapters issues like the nature of the elements, the interactions, their consequences and implications. But for now, this relatively simple definition will serve. This is a definition which works for me in part because it is somewhat elastic and the types of systems I deal with vary widely. Moreover, this unpredictability and with it an element of the unexpected, particularly the observation that the behavior of complex systems exhibits novelty, admittedly a subjective concept, not only is particularly apt in systems of humans, it also appeals to my intuitive side.¹¹ This unpredictability was also a key factor in my coming to appreciate complexity and the last piece of the puzzle that set me on this related to the patients for whom I provided care.

Patients, my dear boy patients.¹²

In the background and the foreground were the patients I was taking care of. I had learned the discipline of endocrinology, but patients didn’t behave according to the textbooks. In fact, one of my first papers addressed this problem [35]. Nevertheless, for the most part, endocrine diagnoses could usually be figured out with a combination of logic and intuition with an emphasis on the former and treatment was usually straightforward, at least in theory. For example, if one developed deficiency of thyroid hormone production due to an autoimmune disorder like Hashimoto’s thyroiditis, treatment consisted of thyroid hormone in a manner that was similar to what would happen if the individual were normal. Where things broke down was when you considered the whole patient in his or her context. This was most evident in my patients with diabetes, a chronic disorder.

Diabetes mellitus has a long history having been described in both ancient Egypt and India. In the modern era (beginning in the latter half of the nineteenth century), most cases in developed in children hence the name juvenile diabetes. These unfortunate children developed a deficiency of insulin secretion by pancreas islet cells. Absent insulin, they developed severe metabolic dysfunction associated with characteristic symptoms of polydipsia, polyuria, polyphagia, and weight loss. At first, treatment consisted primarily of diet and a starvation diet at that, designed to keep blood glucose under some control.¹³ Life expectancy of less than a year and a half was the rule. Conceptually, diabetes was simple and the corresponding model (biomedical) was simple. In the simplest case, diabetes mellitus could be induced by removal or destruction of the pancreatic beta cells producing absolute insulin deficiency (so-called Type 1 diabetes), which in turn resulted in alterations of carbohydrate, lipid and protein metabolism (Fig. 1.4). Treatment, conceptually, was also ‘simple’ – replace the missing hormone. In practice this was not easy and we are, nearly 100 years after the discovery of insulin, still making improvements in terms of types of insulin available, modes of delivery, and modes of adjustment. Nevertheless, even with the relatively crude preparations of the early 1920s, insulin was life-saving and extended life expectancy by more than 35 years. Not a complete cure perhaps, but a staggering improvement. It is not at all surprising that we make heroes of such discoverers [33]. As the century progressed, another type of diabetes was recognized in which insulin resistance also played a role. In fact, when insulin measurement became possible,¹⁴ it was found that many such patients had elevated insulin levels, but levels that were insufficient to bring the glucose levels down. This type of diabetes (Type 2 diabetes) most commonly developed in obese individuals. Since its description, many variations have been found and various underlying etiologies at the gene/cellular level identified. The question of etiology of diabetes has focused on the molecular and cellular aspects. This implies that what ‘gets’ diabetes is at the level of the genes or the cells or conglomeration of cells in organ systems. However, the epidemiology of diabetes also pointed to the influence of environment and lifestyle in addition to genetics. An expanded model was needed (Fig. 1.5). Meanwhile, taking care of patients with diabetes was not easy. It required a large and expanding knowledge base and an array of skills, particularly in communication. Short term benefits were not always apparent and when they were, e.g., in measurements of glycemic control, those benefits were not the same as preventing someone from going blind from diabetic retinopathy. There were competing priorities of the physician imposed by the health care system, the physician’s own values, and the multiple conditions that a single patient might have.

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Fig. 1.4

Biomedical model of (Type I) diabetes

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Fig. 1.5

An expanded linear model that includes the effects of environment and lifestyle in addition to genetics

Thus, many factors affect how physicians treat their patients and variation in quality, limitations on measurement notwithstanding, is large. However, if we physicians are to be honest with ourselves, our difficulties pale in comparison to those of the patient and what physicians do may add to the burden placed on the patient [37]. Ask any patient and s/he will say that it is not easy to live with diabetes. For all the factors that affect physicians, patient behavior is influenced by even more factors; for all the expertise that physicians bring to care, the patients have to become their own experts in management (Fig. 1.6). This is essential because in the 525,600 minutes that make up a year, direct contact between physicians and patients is typically less than 100. When one begins to consider the factors that affect the patient it raises questions about the etiology of diabetes. For example, Type 2 diabetes is most commonly associated with obesity, which has its origins not only in one’s genetic makeup related to control of metabolic rate but also on individual behavior (diet and physical exercise), as well as on other factors such as birthweight and early exposures, cultural norms, the commercial environment and the built environment, which combine to create an obesogenic environment [38, 39]. What is it that ‘gets’ diabetes? [40, 41] Is it the individual, the family or the community or all of them?¹⁵ Interventions that target only one level, e.g., using drugs that affect insulin levels or insulin resistance may have limited effectiveness if the patient’s context is ignored. In fact, the risk to the clinician is that she or he will focus on a manifestation of diabetes such as hyperglycemia and solely adjust medication rather than considering other factors that result in hyperglycemia such as stress at home and food insufficiency. Thus, the clinician must think in multiple dimensions in order to manage the acute situation and prevent its recurrence. Understanding underlying causes while important for the former is particularly critical for the latter. This will remain even after we have the genetic information that allows us to target our drug therapy with greater precision. Context matters.

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Fig. 1.6

A further expansion of the linear model that in addition to including the effects of environment and lifestyle in addition to genetics, also includes the effects of the physician and patient on treatment. Rather than cure, there is management

There is nothing new about the importance of context. George Engel’s biopsychosocial model included an abundance of factors and even suggested that systems theory could provide "a conceptual approach suitable not only for the proposed biopsychosocial concept of disease but also for studying disease and medical care as related processes [42].¹⁶ However, though it is often ignored, and the importance to physicians of having a broad view rather than an overly narrow focus [43]. For example, in the classic paper ‘The Care of the Patient’ published nearly 90 years ago, Francis Peabody wrote: Everybody, sick or well, is affected in one way or another, consciously or subconsciously, by the material and spiritual forces that bear on his life…What is spoken of as a ‘clinical picture’ is not just a photograph of a man sick in bed; it is an impressionistic painting of the patient surrounded by his home, his work, his relations, his friends, his joys, sorrows, hopes and fears. Now, all of this background of sickness which bears so strongly on the symptomatology is liable to be lost sight of in the hospital: I say ‘liable to’ because it is not by any means always lost sight of, and because I believe that by making a constant and conscious effort one can almost always bring It out into its proper perspective. The difficulty is that in the hospital one gets into the habit of using the oil immersion lens instead of the low power, and focuses too intently on the center of the field [44]. When I was an intern, Dr. Paul Friedman conducted a radiology conference daily for the inpatient teams. He would sit in front of the room where there was a giant light box so he could review the x-rays on our patients. Every now and again he would pick up what looked like a magnifying glass but held it close to his eye but far from the x-ray. This enabled him to see the image as a whole. He called it his ‘minifying’ lens. I needed not only a minifying lens but a lens with a wide focal length so that I could zoom in or out as necessary. The lens was not made of glass but consisted of a different way of thinking that incorporated the principles of complex systems. Apropos, because this chapter’s diagrams are models, it is worth taking a detour to address the issue of models.

1.1 Philosophical Digression

Speaking of detours, what follows is a philosophical digression which can be read or not as you please. From a philosophical perspective, Rescher divided complexity into three groups – epistemic modes, ontological modes, and functional complexity [12]. Epistemic modes constitute formulaic complexity whether descriptive – length of the account that must be given to provide an adequate description of the system at issue; generative – length of the set of instructions that must be given to provide a recipe for producing the system at issue; or computational – amount of time and effort involved in resolving a problem. Ontological modes are compositional or structural complexity. Compositional complexity refers to the number of constituent elements while taxonomical complexity or heterogeneity refers to the variety of kinds of components. Structural complexity may be organization – the variety of different possible ways of arranging components in different modes of interrelationship or hierarchical complexity – elaborateness of subordination relationships in the modes of inclusion and subsumption or organizational disaggregation into subsystems. There has been much written about these three groups.

Some have defined complexity based on the difficulty of description of in terms of how many bits are required. For example, the sequence ababababab…ab can be easily described as (ab)∗n where n = number of times ab appears. A completely random sequence of a’s and b’s could be described only be repeating the entire sequence. There are many such measures. Lloyd listed more than 40 different measures dividing them into three groups – effort to describe; effort to create; and degree of order. Nagaraj and Balasubramanian changed ‘effort to create’ into ‘effort to compress’ and provided an easily computable (so they claim) measure [45]. An illustration of the differing degrees of difficulty in describing something is found in art. Although whether a painting is a system or not is arguable, a painting can be considered complex by virtue of the difficulty of describing it in detail. For example, a detailed description of a drip painting of Jackson Pollock would be much longer than that of a line and rectangle painting by Piet Mondrian. Taylor and Pollock described this idea [46]. Whether there are fractal patterns (self-similarity across scales) underlying paintings by Pollock is a controversial subject. It has even been suggested that the tree paintings of Mondrian are fractal, an issue discussed in papers by Oancea and Rapa [47] and by Bountis et al. [48]

There is something beyond the difficulty of description, i.e., whether description itself can be accomplished. Edmonds wrote that complexity is The property of a language expression which makes it difficult to formulate its overall behavior even when given almost complete information about its atomic components [49]. For Law and Mols There is complexity if things relate, but don’t add up, if events occur but not within the process of linear time, and if phenomena share a space but cannot be mapped in terms of a single set of three dimensional coordinates [50]. An early view of complexity focused on interactions. In 1948 when the mathematician Warren Weaver used a billiard ball analogy to distinguish between simplicity (the interaction of two billiard balls – a two variable issue) and what he called disorganized complexity (the interactions of millions of billiard balls which can be handled statistically) [51]. Everything in between consisted of problems which involved dealing simultaneously with a sizable number of factors which are interrelated into an organic whole for which he proposed the term problems of organized complexity. Thus, although the number of elements was important, it was the nature of the interrelationships that were key. Rosen considers complexity to be a relational property rather than an intrinsic property so that complexity depends on whether or not there is one largest model that A system is simple if all its models are simulable. A system that is not simple, and that accordingly must have a nonsimulable model, is complex [52]. Simulable means Turing compatible, i.e., there are a system of data-manipulation rules (such as a computer’s instruction set, a programming language, or a cellular automaton) is said to be Turing complete or computationally universal if it can be used to simulate any Turing machine.

Manson proposed a division of complexity research: deterministic complexity which deals with chaos theory and catastrophe theory; aggregate complexity which deals with how individual elements work in concert to create systems with complex behavior; and algorithmic complexity which involves mathematical complexity theory and information theory [53]. The first and third are more straightforward than the second even though there are many definitions and measures used for algorithmic complexity. Although all three apply to medicine, it is aggregate complexity which tends to be discussed most as it plays out in the multiple levels that make up the field of medicine from the cell to the organism to the population and health care system. In fact, Coveney and Highfield focused on what might be considered aggregate complexity, defining complexity as The study of the behavior of macroscopic collections of simple units (e.g., atoms, molecules, bits, neurons) that are endowed with the potential to evolve over time [54].

Most interesting to me has been a particularly insightful review by Zuchowski [32]. She conducted a systematic study of a large number of definitions and complexity and concluded that the vast majority of them could be viewed as requiring different combinations of different technical embodiments of five core criteria for the diagnosis of complexity: the three dynamical criteria of the existence of many components, determinism, and indeterminism; and the two phenomenological criteria of regularity and irregularity. She uses the term ‘dynamical’ to refer to properties of the underlying mechanisms of a system, e.g. the formalism of a model (see note as below), while ‘phenomenological’ refers to those properties of a system’s behavior that are observable without any knowledge about these underlying mechanisms, e.g. the output of a model. This is where unexpectedness comes in. In a deterministic system in which there is only one possible outcome, given the initial state of the system, one would expect that the outcome would exhibit regularity, i.e., pattern of behavior. (A deterministic system is a system in which no randomness is involved in the development of future states of the system. A deterministic model will thus always produce the same output from a given starting condition or initial state.) Although regularity may be a case of ‘one knows it when one sees it,’ (see note b. below) there are numerical measures, e.g., pattern entropy which is the number of patterns in a suitable representation of a model’s phenomenology. Similarly, in a non-deterministic system in which there are several possible outcomes for a given initial state, one would expect irregularity and not regularity. She then defines complexity based on the contrast between the expectation of the dynamics and the behavior or the system. A system is complex if it is deterministic and has at least some regularity (it need not be completely regular) or if it is non-deterministic and exhibits regularity. She limits systems of interest to those with many components.

Note a. An example of such a formalism is the logistic equation that is a mathematical model for mapping growth: xt + 1 = xt (1 + r(1 – xt)) where xt is the population at time t