|Year : 2015 | Volume
| Issue : 2 | Page : 44-48
Endodontic inter-appointment flare-ups: An example of chaos?
Poorya Jalali, Gunnar Hasselgren
Endodontics, College of Dental Medicine, Columbia University, New York, USA
|Date of Web Publication||10-Jun-2015|
Dr. Poorya Jalali
154 Have Ave., Apt. 510, New York, NY 10032
Source of Support: None, Conflict of Interest: None
Introduction: Pain and/or swelling after instrumentation of a root canal constitute a significant complication during endodontic treatment. Despite a large number of articles discussing the causative factors behind endodontic flare-ups, the exact mechanism is still not understood. The Hypothesis: The seemingly irrational behavior of endodontic inter-appointment flare-ups may be due to sensitive dependence on initial conditions. A model based on Lorenz' chaos theory is presented as a possible explanation for the sudden emergence and unpredictability of flare-ups. Evaluation of the Hypothesis: All studies agree on some common traits regarding inter-appointment flare-ups: Careful instrumentation can still cause flare-up; the host inflammatory response behaves as a complex nonlinear network; and also the poly-etiologic nature of this phenomenon all illustrate the sensitive dependence on initial conditions of the system. Integrating more variables (e.g., different species of bacteria) into this already complex system will make it increasingly chaotic reflecting its unpredictable behavior.
Keywords: Chaos, endodontics, flare-up, nonlinearity
|How to cite this article:|
Jalali P, Hasselgren G. Endodontic inter-appointment flare-ups: An example of chaos?. Dent Hypotheses 2015;6:44-8
| Introduction|| |
Pain and/or swelling after instrumentation of a root canal constitute a significant complication during endodontic treatment. Despite a large number of articles discussing the causative factors behind endodontic flare-ups, the exact mechanism is still not understood. Inter-appointment flare-up has been defined as acute pain or swelling or a combination of both that occur soon after the initiation or continuation of the root canal treatment, which requires an unscheduled visit and active treatment.  The incidence of flare-up varies considerably in the literature, between 0.39% and 20%. ,,,,,,,,,,,,,, This variation reflects not only the differences in treatment procedures and methodology, but also a lack of definition. A meta-analysis of the literature showed that the average frequency of flare-up is 8.4%,  still the lack of consistency between the articles makes the average rather uncertain. According to the American Association of Endodontists  >15 million root canal treatments are performed every year and, therefore, this complication constitutes a major entity of pain, suffering, and cost. Although the etiology of exacerbations is unclear, several factors have been considered, including increase of the oxidation-reduction potential, over-instrumentation, apical extrusion of microorganisms, inadequate instrumentation, immunological factors, and psychological factors ,, and there may of course be combinations of these.
Modern scientific reasoning is still dominated by classical (Newtonian) concepts, which emphasize linear and proportional relationship of cause and effect. [20.21] Correspondingly, in endodontics, most researchers have focused on tracing specific causative factors which have a direct effect on the appearance of flare-ups. ,,,,,,,,,, However, biological systems are complex and often lack linear dynamics  and also subject to a large number of inputs and feedbacks. Edward Lorenz, a meteorologist studying a mathematical model of weather patterns, found that very small variations in initial conditions could result in drastic changes in weather conditions.  The mathematical description of this is known as sensitive dependence on initial conditions. In complex dynamic systems, two almost identical states may lose resemblance to each other as each evolves with time. Sensitive dependence implies more than a mere increase in the difference between two states followed over time. For instance, there are deterministic systems in which an initial difference of one unit between two states will eventually increase to a thousand units, while an initial difference of a millionth of a unit, may eventually increase to a thousand units also, even if the latter increase will need more time. , As a description of a minor happening causing a major event, Lorenz postulated the term "butterfly effect," which has become one of the most popular images of chaos theory-the flapping of a butterfly's wings in Brazil could set off a tornado in another part of the world. 
Complex nonlinear systems express properties that are referred to as emergence, meaning the ability of a system to generate negative entropy.  Emergence is a process in which a larger existence and pattern come out from smaller parts, and the whole pattern becomes greater than the sum of its entities. An example of it is the emergence of consciousness and memory from a complex nonlinear system of neurons. ,,, The emergent properties of a chaotic system arise from interactions between the lower-level components of the system. The result can be as elegant as a synchronized flock of fish schooling in the ocean or as destructive as a hurricane. Microorganisms also are able to give rise to spectacular emergent properties. The potency of bacterial communities is greater than the sum of the individual bacteria. A chaotic community of bacteria can react to a variety of stresses (e.g., starvation, crowding) by developing emergence of collective behaviors such as biofilm, which makes them more resistant to external forces. 
Due to the dynamic network of interactions in a complex nonlinear system, an infinite number of states may exist, but by self-organization the system may settle into a smaller number of stable forms.  It is conceivable, because of an infinite number of variables (e.g., different species of bacteria or components of immune system) and their interactions, a large number of states may arise in response to a root canal infection. The host response, which is also a complex nonlinear system, may react to it in only a few numbers of states like an acute apical abscess, a suppurating sinus tract, or just a slow growing, asymptomatic, chronic apical periodontitis. If a complex nonlinear system is broken into its component parts, the emergent properties of the system will be lost.  Consequently, in search of the causative factors behind flare-ups, studying individual interactions between the variables of the system may cause favoring or unintentional exclusion of certain factors.
| The Hypothesis|| |
A hypothesis is presented concerning the development of flare-up as a complex nonlinear system suggesting that its sudden emergence and unpredictability may be due to sensitive dependence on initial conditions. The following is a simple three-dimensional model of the host response to endodontic instrumentation that is based on the following clinical scenarios: An asymptomatic response in which patient does not have any signs and symptoms; a normal postoperative symptomatic response in which patient experiences tolerable signs and symptoms; a flare-up in which patient experiences intense pain and/or swelling that requires an unscheduled visit.
As an example of a periapical host response system, we use the Lorenz equations. , According to the Poincaré-Bendixson theorem  in order to have a nonperiodic chaotic behavior at least three variables are needed. There are a vast number of variables that play a role in the pathogenesis of flare-ups, but in order to simplify our model it consists of only three variables representing three major areas involved in flare-ups-infection, defense, and environment:
(x) Number of apically extruded pathogenic bacteria;
(y) Number of activated neutrophils;
(z) Amount of oxygen entering canal during treatment.
a, b, c are the system parameters, and t is time.
dx/dt = a (y − x).
dy/dt = x (b − z) − y.
dz/dt = xy − cz.
In this model, the evolution of the periapical state after instrumentation is reduced to a simple equation. Each point (x, y, z) in space represents a state in the periapical tissues, and the evolution of the three variables follows a vector field and traces out a strange attractor with an infinite number of trajectories.  Hypothetically, as illustrated in [Figure 1], the left wing of the attractor represents the asymptomatic state, the majority of the right wing represents a normal postoperative symptomatic state and the area corresponding to flare-up is the red circle on the right wing [Figure 1]. Starting points determine the future trajectories, and nearby trajectories diverge or grow away from each other eventually proceeding into completely different states. Therefore, two initial points very close to each other may have different destinies, and consequently a little change in one of the variables can completely change the future of the system. For instance, in studying host response under strict controlled conditions, a mere increase in number of extruded bacteria (e.g., extrusion of only 10 more bacteria) could shift an asymptomatic state to a painful acute apical abscess.
|Figure 1: Hypothetical model showing two nearby trajectories (blue, green) in the strange attractor starting at two initial points that differ only by 10-4 in the x-coordinate. The red-dot can be imagined as a flare-up state, traceable only by the green trajectory|
Click here to view
Another way to visualize this process is by utilizing the concept of the edge of chaos. In a dynamic system, there is a boundary in complexity space in which a phase transition happens from order to chaos. This region is called the edge of chaos, and has the greatest complexity. Hence, at some place between the order and chaos in the system there is a thin boundary, where the system follows ordered rules, but where there is a chance that something new will emerge just by a small change. An analogy for this is the accumulation of a large pile of snow on a mountainside. Snowflakes are dropping on it one-by-one, and eventually it becomes so large that the addition of just one more snowflake can trigger an avalanche. Likewise, a very small change in any of the variables in the periapical tissue may trigger an abscess formation.
| Evaluation of the Hypothesis|| |
In the many different studies on endodontics flare-ups, there are some common traits on which all authors agree. ,, First, even with a careful instrumentation technique a flare-up can happen  which can illustrate the sensitive dependence on initial conditions of the system. Second, the host inflammatory response behaves as a complex nonlinear network,  therefore integrating more variables (e.g., different species of bacteria) into this already complex system will make it more chaotic. Finally, the lack of a unified opinion on the etiology of flare-up and also the poly-etiologic nature of this phenomenon  may reflect its unpredictable, chaotic behavior.
In addition to the emergence of periapical flare-ups, there are other endodontics events that may be explained by chaos theory. For instance, previous studies have shown that it is not possible to make a histo-pathologic pulp diagnosis based solely on clinical signs and symptoms.  In other words, there is not a good correlation between histo-pathology and clinical findings, and pulps that histologically look the same often have different clinical symptoms. The question is what makes our body respond to a tooth infection in one way or another? The answer may be found in the complex nonlinear paradigm of the system. As mentioned earlier, the system dramatically reduces the number of possible states to a few numbers of stable states, and by sensitive dependence on initial conditions or seemingly random behavior it will emerge as either an asymptomatic or symptomatic pulp inflammation. This discrepancy may be due to differences at the molecular level which cannot be measured by current techniques. A possible explanation for this is the complex nature of the pulpal tissue and the caries flora so that even a small difference at the molecular level can result in a huge dissimilarity in clinical signs and symptoms.
One of the challenges for future work is to find out ways to predict and control chaotic flare-ups. Unfortunately, the complex nonlinearity in the system is responsible for making it impossible to perfectly predict flare-ups. Due to sensitive dependence, since neighboring trajectories separate exponentially with time, not only it is extremely difficult to guess the exact fate of each trajectory, but even vague predictions into the near future are presently impossible. , Therefore, based on this hypothesis it would be prudent to inform patients that flare-ups may occur even when the most judicious instrumentation techniques are used.
How can we control or take advantage of a chaotic evolution? This question is a challenge for future. Recently, several works in different areas of science have aimed at controlling chaos with novel approaches.  It has been stated that it is easier to control chaos than to predict it.  For instance, it has been postulated that in a chaotic system, by very small, careful perturbations in the parameters the trajectories could be directed to a desirable state.  In addition, to follow up on these promising ideas, further studies using a combination of systems biology and laboratory approaches are needed to explore innovative strategies to manage chaotic behavior of flare-ups.
This article suggests a chaos theory explanation for inter-visit endodontic flare-ups. However, there may be other clinic situations involving multiple factors in which chaos theory is applicable.
| Acknowledgment|| |
We would like to thank Dr. Kian Mehravaran for generating the strange attractor.
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