ORIGINAL PAPERS psychosis and unnecessary discontinuation in BLANCKAERT.N. & FEVERY.J. (1990) Physiology and patho- our cases led to relapses and further difficulties physiology of bilirubin metabolism. In Hepatology: A Textbook ojLiver Disease (eds T. Zakim & T. D. Boyer), in management. Reintroduction of psychotropic pp. 254-285. Philadelphia. PA: W. B. Saunders. medication decreased the incidences of relapses COHEN. L. S. & COHEN. D. E. (1992) Lithium induced and confirmed the safety of neuroleptics in hyperbilimbinaemia in an adolescent. Journal of Gilbert's syndrome as suggested by others Clinical Psychopharmacology. 11. 274-275. DURST.R.. JAUTINSKY-RUBIN.K.. DOREViTCH.A., et al (1993) (Cohen & Cohen, 1992: Durst et al. 1993). Idiopathic unconjugated hyperbilirubinaemia (Gilbert's Psychiatric illnesses are regarded as complex syndrome) and concurrent psychotropic drug disorders: disorders which show evidence of gene administration. P/iarmacopsycnialry. 26. 49-52. effect but do not show clear Mendelian patterns GILBERT.A. & LEREBOULLET.P. (1901) La cholemie simple of inheritance. Comorbidity of such illneses with familiale. Semaine Médicale.2l. 241-245. other genetic disorders might be of help in LoYD.D. W..TSUANG. M. T. & BENGE.J. W. (1982) A study of a family with Leopard syndrome. Journal of Clinical understanding their psychopathology. A hy Psychiatry. 43. 113-116. pothetical explanation for the higher incidence MULLER.N.. SCHILLER.P. & ACKENHEIL.M. (1991) Coinci of hyperbilirubinaemia and schizophrenia, genetic dence of schizophrenia and hyperbilirubinaemia. predisposition, was emphasised by Muller et cd Pharmacopsychiafry. 24. 225-228. (1991). Further reporting of similar cases to the SEIG. A.. STICH, A.. RAEDSCH.R.. et al (1986) Gilbert's present study may emphasise the significant syndrome: diagnosis by typical serum bilirubin pattern. comorbidity of Gilbert's syndrome and mental Clinical Chimica Acta. 154, 41-48. TAYLOR. S. (1984) Gilbert's syndrome as a cause of disorder which will need further clarification. postoperative jaundice. Anaesthesia. 39. 1222-1224. *A. S. Mahdi, Senior House Officer in Psychiatry, and M. S. Elameer, Consultant Psychiatrist, St References David's Hospital. Carmarthen. Carmarthenshire. DAVIDSON,A. R., ROJAS-BEUNO.A.. THOMPSON.R. P. H., et cd (1975) Reduced caloric intake of nicotinlc acid SA31 3HB provocation tests in the diagnosis of Gilbert's syndrome. Brilish Medical Journal, ii. 480. 'Correspondence

Butterflies, fractals and psychiatry

Steven Reid

In this paper concepts related to the field of non-linear Previously the application of basic sciences to dynamics and chaos theory are discussed, and their clinical medicine has relied upon linear, deter relevance to psychiatry is considered. ministic processes which were relatively easily understood and predictable. Classical deter minism as propounded by Laplace, viewed the 'In all chaos there is a cosmos, in all disorder a secret universe as a gigantic, intricate clockwork order' (Jung. 1954) machine in which all events were predictable and the magnitude of any evoked response was For many, chaos theory is a new branch of proportionate to the size of its stimulus. science that appears to involve 'the butterfly However, there are physical systems which are effect' and 'fractals', but which is little under seemingly non-linear and highly unpredictable stood and has no obvious relevance to psy such as turbulence in liquids (e.g. blood flow chiatry. The purpose of this paper is to unravel in the heart) and cerebral electrical activity. In a number of unfamiliar concepts, and describe these situations small changes can result in some of the influences this emergent mathema large and unanticipated effects. Since the 1960s, tical theory has had upon medicine and more scientists from a variety of backgrounds have specifically, psychiatry. been attempting to provide models for this

568 Psychiatric Bulletin (1998). 22. 568-570 ORIGINAL PAPERS unpredictable and complex behaviour. A similar irregularities whether viewed on a scale of meteorologist, Lorenz (1986) attempting to model 1 min or 100 min. Other examples include heart- global weather systems, noted the degree to rate variability, systemic blood pressure and which the components of a non-linear system variation in white cell counts. This fractal or interact, thereby producing a series of feedbacks scale-free organisation seems to be a central (both positive and negative) which can lead to a principle of physiological structure and function. tremendous variation in consequences. This It would therefore be a reasonable assumption explains the difficulty in long-range weather that with pathology there may be an associated forecasting, and led to the coining of the term breakdown of the fractal process which would 'the butterfly effect' (originating from the title of result in a fractal-free system dominated by his address to the American Association for the one scale. A system dominated by one scale is Advancement of Science in 1979, 'Predictability: by definition periodic and the appearance of does the flap ofa butterfly's wings in Brazil set off highly periodic events in disease is well- a tornado in Texas?'). This potential for such an recognised e.g. periodic tremors in neurological exaggerated range of outcomes is known as conditions, periodic fevers in Hodgkin's lympho- 'sensitive dependence on initial conditions'. ma and periodic electroencephalogram rhythms This area of study has expanded to become non during a seizure. It has been maintained on this linear dynamics and has been applied to fields basis that the normally functioning heart shows as diverse as meteorology, economics (with more chaotic behaviour than the diseased one. attempts to predict the rise and fall of cotton This seemingly paradoxical conclusion is at odds prices), car manufacture and medicine. All of with the traditional, 'common sense' view that these non-linear processes resist any form of the collapse of the rhythms of a healthy organism reductionist analysis but a common theme is the is at the root of many physiological disorders. potential for striking, unexpected effects arising The role of non-linear dynamics in clinical from minimal changes in initial variables. One medicine has only recently begun to be examined, such potential effect is the much vaunted but workers in the field are optimistic. As early as phenomenon, chaos. in the 1920s, two Dutch physiologists, van der Chaos theory, although pioneered by Lorenz, Pol and van der Mark had shown that by using was given its name in 1972 by the mathemati logistic equations (which are of fundamental cian James Yorke. Chaos refers to a seemingly importance in non-linear theory), in an attempt random type of variability that can arise from a to formulate a mathematical model of cardiac non-linear system. Despite its connotations, in pathology, they could generate cardiac arrhyth this context chaos is not completely unfettered, mias (Mackay & Glass. 1977). The arrhythmias random behaviour. It has the characteristic of were precipitated by abrupt non-linear transi appearing random and is unpredictable at tions known as bifurcations. A bifurcation is a certain scales, yet retains an overall degree of descriptive term for the situation in which a very organisation which can be modelled. Many small change in the value of a variable affecting a previously observed phenomena and patterns of system causes it to change abruptly from one behaviour, thought to be unpredictable and type of behaviour to another. Within cardio unexplainable, are now considered to operate vascular medicine there is an expectation of a on non-linear principles. This implies a potential number of practical applications in the short- for greater understanding of these processes. term (Goldberger, 1996). The use of non-linear The term fractal (derived from the Latin, dynamics in physiological monitoring has fractus, meaning broken) was introduced by a already shown promise in predicting those at French mathematician. Benoit Mandelbrot, in rick of electrophysiological instability such as 1975 (Peitgen & Richter, 1986) and is related to the automatic detection of the onset of patho chaos. A fractal is an object consisting of a logical changes in heart-rate beat-to-beat pattern that when magnified, reveals repetitive variability, which may be a precursor to ventri levels of detail so that a similar structure exists cular arrhythmias and sudden cardiac death. on all scales. This property is known as self- Other potential sites of application for chaos similarity. Mandelbroit found fractals every theory include the detection of subtle ST-T where - coastlines, trees, forked lightening, cauli alternans (alternating amplitude from beat-to- flower florets. Fractal structures abound in beat on an electrocardiogram) and the detection medicine e.g. the arterial and venous circulatory of a breakdown in fractal scaling also leading to systems, the central nervous sytem, the tracheo- arrhythmias. With a greater understanding of bronchial tree. Possessing self-similarity offers the origin of arrhythmias another possible these systems a great advantage; they are able to development involves the refinement of cardiac contain a vast surface area in a limited volume. defibrillators. Previously the design of defibrilla- Fractals are also evident in complex processes tors. such as the size and shape of the electrical with a timescale e.g. a graph of a series of charge, has been empirically based. Principles of fluctuations in respiration over time would reveal non-linear dynamics may provide a theoretical

Butterßies.fractals and psychiatry 569 ORIGINAL PAPERS basis for improving their efficiency and thereby predicting the pathway of affective change and success rate. developing a pulsed or phasic treatment which Applications of non-linear dynamics have yet could be used in anticipation. Unfortunately, to make a significant impact upon clinical this study was small (using seven bipolar psychiatric practice. They have been useful in patients) and warrants replication on a larger developing models for research e.g. Hubermans' scale but the authors do demonstrate that both simulation of the scanning abnormalities in the biomédical and psychological contributors to eye movements of patients with schizophrenia mood and behaviour can be employed in non and their relatives (Gleick. 1988). More recently. linear models. Paulus et al (1996) have used non-linear theory Non-linear dynamics has some determined in their analysis of people with schizophrenia advocates. Mandell (1985), a US psychiatrist being tested by their responses to a simple choice criticised previous psychiatric practice for being task. They were able to demonstrate a signifi narrow-minded and upsophisticated . . . "psy cantly greater degree of perseveration and chiatry is soon to be faced with a radical unpredictability compared with controls, and paradigmatic shift in neuropsychobiology that were able to quantify the degree of behavioural may have far-reaching implications for patho- disorganisation. physiology and treatment. Current paradigms of Work by Gottschalk et cd (1995) has high medical research will collapse because of their lighted more practical implications of non-linear failure to deal with diseases that emerge auto dynamics. They introduced principles of chaos nomously". This comment would appear to be theory in their study of a group of patients with somewhat overblown, but chaos theory clearly rapid-cycling bipolar affective disorder as a does offer solutions to several problems in means of analysing the temporal variation in contemporary physiology and biology. The likely their mood. Pre-existing models of mood vari impact of non-linear dynamics upon psychiatry ation in this disorder consisted of (a) aberrant remains unclear at present, but its potential biological rhythms, based on short-term, inten value in elucidating the mechanisms of mental sive monitoring of mood cycles in which there is a illness merits continuing investigation. marked tendency for periods of mania to follow periods of depression, and (b) the kindling model, in which episodes of mood disorder References become more frequent as the disorder persists GLEICK,J. (1988) Chaos. London: Heinemann. and later episodes seem to arise spontaneously GOLDBERGER, A. L. (1996) Non-linear dynamics for rather than being related to précipitants. Both of clinicians. Lance!, 347. 1312-1314. these models fail to explain the irregular fluctua GOTTSCHALK.A.. BAUER. M. S. & WHYBROW.B. C. (1995) Evidence of chaotic mood variation in bipolar disorder. tion of mood which is often observed in the Archives of General Psychiatry. 52. 947-959. clinical situation. Gottschalk et al found that JUNG, C. G. (1954) The Development of Personality. London: the mood variation in this group of patients Routledge. showed a chaotic pattern, without true periodi LORENZ. E. N. (1986) Large-scale motions of the city or progressively accelerating course, and atmosphere. In Advances in Earth Science (ed. P. M. interestingly this pattern had a degree of Hurley), pp. 95-109. Cambridge. MA: MIT Press. MACKAY,M. & GLASS. L. (1977) Oscillation and chaos in organisation and predictability that was absent physiological control systems. Science, 197. 287. from the euthymic controls. This is comparable MANDELL. A. J. (1985) From molecular biological with electroencephalogram wave patterns in simplification to more realistic central nervous system epilepsy - abnormality being associated with dynamics: an opinion. In Psychobiological Foundations order. This chaotic model also offers a coherent of Clinical Psychiatry (ed. O. Cavenar). pp. 361-366. New York: Lippincott. explanation of the role of psychosocial Stressors PAULUS.M. P., GEYER,M. A. & BRAFF,D. L. (1996) Use of in bipolar disorder. An appropriate timed sti methods from chaos theory to quantify a fundamental mulus (stressor) of sufficient amplitude may dysfunction in the behavioural organisation of schizo exacerbate symptoms by driving a vulnerable phrenic patients. American Journal of Psychiatry. 153. system into sustained chaotic dynamics. In this 714-717. way a stressor may produce long-lasting effects, PEITGEN,H. & RICHTER.P. (1986) The Beauty of Fractals. Berlin: Springer-Verlag. with subsequent episodes apparently unlinked to any precipitant, which may explain why later episodes in bipolar disorder appear to arise Steven Reid, Senior Registrar in General spontaneously. The high level of organisation of Psychiatry, Springfield Hospital, 61 Glenburnie these patients' moods suggests the possibility of Road. London SW17 7DJ

570 Reid