The Unified Fractal Model of the External Ear for the Diagnosis and Treatment of Sympathetic Maintained/Mediated Pain Syndromes

Christopher R. Brown DDS, MPS Director of Scientific Affairs and Research Development

Fractal Analysis; A General Overview

Fractal geometry offers a platform to explain structure-function relationships of complex systems in biological science and engineering. The branching system in our body is characterized in a fractal nature: self-similar branching patterns and recursive bifurcation occurring in descending orders of magnitude to the cellular level illustrating biological iteration (the process of repeating a set of patterns or mathematical sets in which each set acts as a starting point for the next set) (1). The end result is that all components, in all dimensions, have a form similar but not identical to the whole (2). Natural fractal entities are mainly characterized by four properties: 1. Irregularity of their shape 2. Self-similarly of their structures 3. Non integer of fractional (fractal) dimensions 4. Scaling (the measured properties depend upon the scale by which they are measured) It is now recognized that "rough" shape is the most important property of every anatomical system strongly influencing its behavior and its relationship with surrounding components. This concept is often applied to biological systems described as ”closed areas” within the human body such as the lung, kidney, heart, and the external ear. Another fractal parameter is "lacunarity.” Lacunarity refers to a measurement of how fractal patterns fill a given space often producing gaps which, in the case of biological entities such as the lungs, heart, kidney, and for this discussion the external ear, are filled with other tissues and extra-cellular fluids. The external ear is a multi-fractal system meaning it cannot be explained by a single component. At both a macroscopic and microscopic level, the intrinsic complexity is apparent producing systems within systems (3). The result is an integrated continuum of multifractal components including neural, vascular, neuro-vascular bundles, lacunae and variations of tissues with different densities and therefore conductivity. The fractal properties occur at anatomical, functional, pathological, molecular and epigenetic levels and as a result no physiologic network is isolated making up self similar sub networks of interacting tissues. As long as the biological environment stays within homeostasis, systems will continue to function guided by complex positive and negative feedback mechanisms. A disruption in homeostasis occurs as a result of an almost infinite amount of variables resulting in changes in form and function. This is often referred to as the Chaos Theory which states that complex systems rely on underlying order and that simple homeostatic disruptions can result in complex changes, adaptations and plasticity (4). The afore-mentioned systems’ adaptations however will adapt in a fractal self-similar fashion The loss of homeostasis and dynamic feedback mechanisms often contribute to neurovascular plasticity which may be contingent upon but not limited to: 1. The presence of vascularity competing for the same space replicating in a self - similar fractal manner 2. The presence of intra-cellular lacunae which may directionally alter tissue expansion 3. Variations in density of tissues within the self-limiting space 4. Osmotic inter-cellular pressures created by biochemical inflammatory markers, cytokines, intercellular fluid, medications, pathology, and age. 5. A non-homeostatic condition which is caused by or is affected by inhibition of autonomic inhibition mechanisms resulting in a physiological imbalance such as chronic sympathetic or parasympathetic stimulation (5).