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J Thorac Cardiovasc Surg 2003;125:12-19
© 2003 The American Association for Thoracic Surgery

Honored Guest's Address

Beyond Flatland

From Great Ormond Street Hospital for Children National Health Service Trust, London, United Kingdom.

Read at the Eighty-second Annual Meeting of The American Association for Thoracic Surgery, Washington, DC, May 5-9, 2002.

Received for publication May 29, 2002. Accepted for publication July 2, 2002. Address for reprints: Marc R. de Leval, MD, FRCS, Cardiothoracic Unit, Great Ormond Street Hospital for Children NHS Trust, Great Ormond St, London WC1N 3JH, United Kingdom (E-mail: delevm{at}gosh.nhs.uk).

	Introduction

Top Introduction Complexity and fluid dynamics Complexity and life sciences Appendix 1: examples of... References

 

Mr President, thank you for your kind introduction. Members of the Association, ladies and gentlemen, I am flattered to be the honored guest of The American Association for Thoracic Surgery. This is a unique opportunity to publicly express my gratitude to the Association for having been awarded the 1973 Evarts Graham Fellowship, which has been a cornerstone in my career.

It is a privilege to pay tribute to my North American mentors. Three of them were presidents of the Association: Frank Gerbode, Dwight McGoon, and Robert Wallace. I should also like to mention Donald Hill from the Pacific Medical Centre in San Francisco and Gordon Danielson from the Mayo Clinic. Finally, I should like to share today's honor with all my colleagues at Great Ormond Street Hospital, London.

The topic chosen for this lecture is an old one that I have, I am afraid, touched upon on several occasions. I will attempt today to show how my thoughts on these matters have evolved, but I must apologize for some inevitable repetition.

In 1884 a Victorian headmaster, Edwin Abbot, wrote the well-known story Flatland under the pseudonym of A Square. ¹ Flatland describes a race of beings who are 2-dimensional; triangles, squares, rectangles, polygons, and circles. They are unaware of the existence of anything else outside their universe. For A Square, it is truly impossible to appreciate the full reality of our 3-dimensional universe, called Spaceland. To illustrate this deficiency, Abbot imagines A Square watching a still pond being visited by a 3-dimensional being named A Sphere (Figure 1). A Sphere goes down into the water and rises again before disappearing. A Square can see only the part of the sphere intersecting his plane. He sees only a succession of 2-dimensional circles changing size in time. A Square cannot be convinced that A Sphere is a creature that extends spatially into a third dimension unknown to the Flatlanders. Flatland was written 25 years before Einstein's theory of relativity, before the days of space-time when time became the fourth dimension. To continue Abbot's metaphor, Einstein brought us to Timeland.

View larger version (13K): [in this window] [in a new window]   Fig. 1. The visitation of A Sphere through Flatland, perceived by A Square as a circle changing in time. (Illustration from Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimension by Thomas F. Banchoff, © 1990 by Scientific American Library. Reprinted by permission of Henry Holt and Company, LLC.)

Complex systems have a number of fundamental characteristics. First and foremost, the interactions between the numerous variables are nonlinear. In linear systems the variables are simply and directly related. Mathematically, a linear relationship can be expressed as a simple equation in which the variables appear only to the power of 1. In a nonlinear system, the many variables in the equations vary with respect to one another by powers of 2 or greater. Nonlinear systems do not obey the simple rules of addition. The whole is more than the sum of its components.

In complex systems there is high sensitivity to initial conditions. A tiny difference in initial conditions can be amplified over time to enormous differences.

Nonlinearity produces feedbacks; the outcome of an effect goes on to trigger more changes, leading to unexpected behaviors. Positive feedbacks amplify the output and tend to undermine the stability of a system. The larger the population, the larger it becomes. Negative feedbacks dampen the output and tend to maintain stability. Predator-prey relationships are regulated by negative feedbacks.

One of the most intriguing aspects of complex systems is that changes do not have to be related to external causes. They are, as already stated, capable of self-organization. Nonlinear interdependent dynamics can create patterns, coherence, networks, copying, synchronization, and synergy.

Complexity theories are probably the broadest of all scientific discoveries of the last century, not only in basic sciences but also in life sciences, where it is now recognized that the main problems of mankind are global and complex. I should like to use my own research to illustrate that computer modeling has begun to explore the behavior of complex systems such as fluid dynamics but that in many of our endeavors we remain to the multidimensional universe of complexity as the Flatlanders were to Spaceland.

	Complexity and fluid dynamics

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Fluid dynamics studies are still based on nonlinear equations discovered more than 150 years ago, the Navier-Stokes equations. The application of supercomputers to the Navier-Stokes equations has given rise to computational fluid dynamics technology. This marriage has been one of the greatest achievements in fluid dynamics since the equations themselves were formulated. Computer simulation has become an essential tool in such fields as astrophysics, flow machinery, and aircraft design.

Computational fluid dynamics technology has also been applied to the human cardiovascular system to study, for example, the pathogenesis of atherosclerosis and the formation of aneurysms. ^4,5 In collaboration with the School of Bioengineering of Milan, Italy, I have applied computational fluid dynamics to the design and refinement of surgical procedures aimed at mending malformed hearts.

Because the Navier-Stokes equations describe continuous flow fields, and because digital computers are inherently discrete, the equations are necessarily approximated by dividing up space and time into a grid. A 3-dimensional geometric model of the flow domain is divided into a set of simply-shaped regions, called "finite elements." In each element, unknown functions such as pressure and velocity are determined in a number of points or nodes.

We have carried out numerous studies during the past 10 years. ^6-8 Recently we collaborated with Ed Bove and colleagues in Ann Arbor, Michigan, to compare the hemi-Fontan circulation with the bidirectional cavopulmonary anastomosis and the lateral tunnel with the extracardiac Fontan circulation (Figure 2).

View larger version (56K): [in this window] [in a new window]   Fig. 2. Three-dimensional grids of hemi-Fontan circulation combined with bidirectional cavopulmonary anastomosis (BCPA), lateral tunnel, and extracardiac Fontan circulation. TCPC, Total cavopulmonary connection.

	Complexity and life sciences

Top Introduction Complexity and fluid dynamics Complexity and life sciences Appendix 1: examples of... References

 
Complexity theories apply to human sciences as well, and I have chosen the analysis of surgical outcomes as an illustration. Medical outcomes result from complex interactions among three sets of complex variables: those related to the patients, those related to the treatments, and those related to the care providers. If computer modeling in fluid dynamics is still in its infancy, computer simulation in life sciences is at a gestational age. ⁹

Statistical methods, however, have become increasingly powerful in the investigation of complex interactions. At this point I should like to acknowledge the enormous contributions of John Kirklin and Eugene Blackstone on outcome analysis and to thank them both for the impact that they have had on my own work.

Most outcome analyses have concentrated mainly on patient-related variables or procedural variables. By and large, human factors related to the care providers have not been included in outcome analyses. Yet investment in human factors is expected to be the most important way to improve safety in high-technology industries such as aviation.

There is no reason to believe that this does not apply to high-technology medicine such as cardiac surgery. It is on these assumptions that we began a research project aiming at incorporating human factors in outcome analyses. ¹⁰ This was done in collaboration with Jane Carthey, human factors researcher, James Reason, the father of the organizational accident theory, and Vern Farewell, professor of statistics at University College London.

We took the neonatal arterial switch operation as a model of high-technology surgery. All 243 neonatal arterial switch operations for transposition of the great arteries with or without ventricular septal defect performed by all 21 United Kingdom cardiac surgeons in 16 institutions during an 18-month period were entered into the study. Three sets of data were collected: patient variables, procedural variables, and human factors data. The human factors data were collected by a human factors researcher who attended the operations from induction of anesthesia to admission to the intensive care unit. A detailed description of the operation was written down as the procedure was taking place. This included information on individual and team performance, information on communication with each team and between different teams, and situational and organizational data. From these reports, which I stress were written on-line without knowledge of the outcome to avoid hindsight bias, we extracted errors, or failures, which were categorized as minor or major negative events. Minor events were failures that disrupted the surgical flow of the procedure but in isolation were not expected to have serious consequences for the safety of the patient. Major events, on the other hand, were failures that were likely to have serious consequences for the safety of the patients. Examples of minor and major events are given in Appendix 1.

Major and minor events were judged to be either compensated for or uncompensated. An event was deemed to have been compensated for when the patient recovered or when the consequences of the event were negated by appropriate actions. The clinical outcomes were divided into four categories: (1) extubation within 72 hours with no complications, which occurred in nearly half of the patients; (2) prolonged intubation or reversible morbidity, which occurred in just over a quarter of the patients; (3) survival with near misses, which included major ischemic or hemodynamic problems at the end of the operation, mechanical support with extracorporeal membrane oxygenation (ECMO), severe postoperative arrhythmias, deep-seated infections, and permanent neurologic damage, which occurred in 17.7%; and (4) deaths, which occurred in 6.6% of this population. With grouping of near misses and deaths, the incidence of negative outcomes was about 25%.

The statistical analysis consisted of a multivariate analysis of patient- and procedure-specific variables to generate a baseline logistic regression model for two binary outcomes, the probability of death and the probability of death or near miss. The coronary arterial anatomy was the factor most closely related to both outcomes. Human factors data were then added to the logistic regression model after adjustment for coronary arterial distribution.

For both types of events, minor and major, two analyses were undertaken. The first looked at the total number of negative events for both death and death or near miss outcomes. The second analysis added both the total number of events per case and the number of uncompensated events per case so as to investigate the role of compensation.

Table 2 summarizes the results of adding major events to the baseline model. They have a strong relationship to both outcomes, death and death or near miss, with a P value less than .001. Compensated major events, even if multiple, however, did not influence the odds of death, whereas for an uncompensated major event the odds of death increased by a factor of 9 and the odds of death or near miss increased by a factor of 34.

Throughout this research we have established extensive contacts with high-technology industries such as the aviation industry and the car racing industry. One of the most important safety initiatives in aviation has been the introduction of crew resource management training in the 1980s. ^11,12 Crew resource management is about error management, which has three lines of defense: prevention, detection, and recovery.

Recent research has shown that the most successful organizations at managing potentially hazardous operations were those that created safety by anticipating and planning for unexpected events and future surprises. ¹³ There is no need to demonstrate to this audience that anticipation of problems is one of the characteristics of good surgery.

In Formula 1 motor racing, 90% of the outcome of the race depends on the pit stop. Each pit stop is videotaped and observed by human factors experts who score the errors. The highest scores go to the minor errors, those that go undetected by the performers. These are equivalent to the minor events of our study. The health care industry could, in my opinion, benefit greatly from the appointment of human factors observers to help detect errors and consequently improve quality of care.

Error recovery is the third line of defense in error management. It includes tolerance, compensation, and mitigation of adverse events. Errors will never be eradicated, and some are unavoidable. Our study has highlighted the importance of recovery or compensation from major negative events. The racing car industry has made huge investments in recovery, and these have paid off in sharply reduced human casualties, even after the most spectacular crashes. Recovery from major negative events, from serious complications, is known to be one of the hallmarks of the best institutions in healthcare. ^14,15 An example of recovery from a major negative event is the rapid deployment of ECMO support after a cardiac arrest in the intensive therapy unit, which has recently contributed to a reduction in mortality in pediatric cardiac surgery.

In the framework of complexity, surgical outcomes could be regarded as the result of synergetic nonlinear interactions between multiple interdependent variables related to patients, procedures, and care providers. As an example I will take again the arterial switch operation and look at the cost of the treatment as an outcome event. In the first scenario, the procedure is completely uneventful. The patient stays in the intensive care unit for 24 hours and returns home within 7 days. The cost is $40,000 (cost figures in this analysis were kindly provided by Dr Ed Bove, Ann Arbor, Mich). In the second scenario, a rotation of just a few degrees of the left coronary artery during its implantation to the pulmonary artery results in inadequate myocardial perfusion, so that the anastomosis has to be revised, the ventricular function remains poor at the end of the operation, and temporary mechanical support is provided by ECMO for 5 days. The patient spends 3 weeks in the intensive care unit and leaves the hospital in good health after 1 month. The cost is $94,000. In the third scenario, during ECMO support a kink on the arterial line remains unnoticed for a few minutes because of a faulty alarm system. This results in temporary but profound hypotension from which the patient sustains severe and permanent brain damage requiring lifetime care. The cost of treatment reaches astronomical figures, even without considering the human tragedy.

This is an illustration of nonlinearity, the absence of proportion between input—the arterial switch operation—and output—the cost. A small change in the initial conditions, a few degrees of rotation of the left coronary artery, has a major impact on the outcome. A small event, a faulty alarm system, leads to catastrophic consequences.

This last scenario brings me to address in brief the issues of responsibility and excellence in nonlinear systems. The linear mechanistic view of causality remains the dominant paradigm of our legal system. In a linear model, the extent of an effect is believed to be similar to the extent of its cause. The punishment can consequently be proportional to the degree of damage effected. ¹⁶ Little has changed, I am afraid, since the code of Hammurabi, an extraordinary document set down in black diorite and currently in the Louvre Museum in Paris. This is the first legal document related to medical malpractice and dates from around 2000 bc. ¹⁷

In Law 215 it is stated, "If a doctor has treated a gentleman for a severe wound with a bronze lancet, and has cured the man, he shall receive 10 shekels of silver." This was actually enough to pay a carpenter for 450 working days. In Law 218, which relates to malpractice, one can read, "If a doctor has treated a gentleman for a severe wound with a bronze lancet, and has caused the gentleman to die, one shall cut off his hands." Linear thinking can be dangerous in a nonlinear complex reality, where tiny initial fluctuations may result in a global crisis, where one can become accountable for events that are to some extent uncontrollable.

We see the world of complexity with the eyes of the Flatlander visited by a 3-dimensional sphere, which is perceived as a circle of varying circumferences (Figure 1). We are the slaves of our dimensional prejudices, and we are encouraged to maintain that attitude because of our inability to understand and measure higher dimensions.

This conflict is beautifully illustrated in a wood engraving by Maurits Escher (Figure 3). It shows a 2-dimensional dragon trying very hard to fight his 2-dimensionality by sticking his head and his tail through an open 3-dimensional cube.

View larger version (100K): [in this window] [in a new window]   Fig. 3. M.C. Escher's "Dragon." From Hofstadter DR. Gödel, Escher, Bach: An Eternal Golden Braid. © 2002 Cordon Art B.V. Baarn, Holland. All rights reserved.

We are in a situation similar to that of the many sailors who, for hundreds of years, were aware of the existence of longitude but could not measure it until John Harrison designed a clock that kept time at sea. ¹⁸ This was the thorniest scientific dilemma of the 18th century. Lacking the ability to measure their longitude, sailors were literally lost at sea as soon as they had lost sight of land. Thousands of lives and fortunes of nations were hanging on a resolution of the longitude problem. In 1714, during the reign of Queen Anne, £20,000 of prize money was offered to anyone who discovered a method or device to measure longitude. Countless proposals were received, some of them from cranks and opportunists, but others were promulgating what we would now call surrogates for the chronometer. Today, we need surrogates to produce excellence in a multidimensional universe that we cannot measure.

The way we think about dimensions was shaken in the 1970s by Benoit Mandelbrot, who pointed out that we are surrounded by objects of irregular shapes that have fractions of dimensions. ¹⁹ Mandelbrot introduced the concept of fractured dimensionality, and coined the word fractals in 1975 to describe those objects. He also discovered that fractals could be generated by computers by means of simple mathematical equations, the output of which is fed back into the same equation as its next input, forming a recursive loop.

Fractal objects are characterized by self-similarity or scale invariance. They are identical across a wide range of scales. Fractal structures are sensitive to initial conditions and the patterns that emerge are unpredictable, but they remain ordered and maintain their compelling beauty. Fractal geometry offers an algorithm to describe the complexity of nature that transects time frame and spatial scale. It is reasonable to suspect that fractal geometry represents a universal language that might apply to human sciences as well. ²⁰ Complex systems such as hospitals, operating rooms, intensive care units, and research laboratories, in which each team, each individual, each element, even at the smallest scales, display the same pattern of symmetry, harmony, and beauty, must have the ingredients of excellence. Each individual, even at the bottom of the ladder, must consequently be made aware of his or her importance and must be accorded the highest respect. Each task, even the ancillary duties, must be given the same attention, the same consideration.

Johann Sebastian Bach's canons, which are among the greatest accomplishments of human intellect, are examples of recursive loops found in fractal geometry. ²¹ They inspired Maurits Escher in his desire to capture infinity and perfection when he created the magnificent fractal entitled "Smaller and Smaller" (Figure 4). ²²

View larger version (165K): [in this window] [in a new window]   Fig. 4. M.C. Escher's "Smaller and Smaller." From Schattschneider D. M.C. Escher: Visions of Symmetry. © 2002 Cordon Art B.V. Baarn, Holland. All rights reserved.

	Appendix 1: examples of minor and major events

Top Introduction Complexity and fluid dynamics Complexity and life sciences Appendix 1: examples of... References

 

• Minor events
  
• Coordination problem with blood bank or intensive care unit
  
• Poor preoperative communication (scheduling of cases, fasting)
  
• Human resource problems (eg, no junior anesthetist)
  
• Positioning and tension errors by the surgical assistants
  
• Internal and external distractions
  
• Equipment breakdowns
  
• Communication errors between teams
  
• Absence of a senior team member in the operating room at safety-critical times, inadequate monitoring during transfer to intensive care unit
  
• Inappropriate task delegation (surgical, anesthetic, perfusion) to inexperienced individuals
  
• Cognitive tunnel vision
  

• Major events
  
• Preoperative events such as cardiac perforation during balloon atrial septostomy
  
• Anesthetic errors, including failure to gain sufficient vascular access, pin-cushioning during insertion of lines leading to a serious cardiac event, and delayed diagnosis of a major deterioration in the patient's condition
  
• Surgical errors, including laceration of the ductus arteriosus before bypass, serious cannulation problems, aortic tear or massive coronary air embolism during infusion of cardioplegia, damage of coronary artery or of neoaortic valve, and laceration of pulmonary artery
  
• Major perfusion errors, including pump failure
  
• Postbypass problems, including delayed diagnosis or misdiagnosis of a serious ischemic event, ventilation errors by the anesthetist, omission of pacing wires in a patient with serious arrhythmias, delayed diagnosis of serious deterioration during transfer to intensive care unit (tamponade), and severe bleeding from poorly secured indwelling catheter (left atrial line)
  

	References

Top Introduction Complexity and fluid dynamics Complexity and life sciences Appendix 1: examples of... References

 

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12. Helmreich RL. On error management: lessons from aviation. BMJ. 2000;320:781-4.[Free Full Text]
    
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14. Silber JH, Rosenbaum PR, Schwartz JS, Ross RN, Williams SV. Evaluation of the complication rate as a measure of quality of care in coronary artery bypass graft surgery. JAMA. 1995;274:317-23.[Medline]
    
15. Silber JH, Williams SV, Krakauer H, Schwartz JS. Hospital and patient characteristics associated with death after surgery: a study of adverse occurrence and failure to rescue. Med Care. 1992;30:615-29.[Medline]
    
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18. Sobel D. Longitude. London: Fourth Estate; 1996.
    
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20. Marks-Tarlow T. The fractal geometry of human nature. In: Robertston R, A Combs, editors. Chaos theory in psychology and the life sciences. Mahwah (NJ): Lawrence Erlbaum; 1995.
    
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This Article Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Add to Personal Folders Download to citation manager Permission Requests Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by de Leval, M. R. Search for Related Content PubMed PubMed Citation Articles by de Leval, M. R. Related Collections Cardiac - physiology Congenital - acyanotic Congenital - cyanotic