Fractals, fano planes, and perioperative teams: A narrative review

Background: Modern perioperative medicine represents a broad range of perioperative goals between and within institutions which necessitates a broad range of perioperative teams and governance structures, incorporating both manufacturing and complex adaptive system (CAS) approaches⁶. Methods: A close-reading of some of the seminal texts in leadership and management theory, while also drawing upon longstanding texts about natural and mathematical concepts allowed for a synthesis of theories to elucidate important ideas of leadership structure and organizational governance. No IRB approval was required for this narrative review of leadership concepts. Results: Organizational transformation in an evolving market dynamic calls for organizational ambidexterity, a dual capability to seek alignment among actors on both short and long-term goals⁸. Such ambidexterity calls for governance mechanisms that bring together a heterogenous constellation of actor networks with diverse goals and motives–outside of the control of the organization². By adapting semi-formal organizational governance structures, we lay out a framework for operating room governance based upon the organizational strength of triads, interconnectedness of “teams of teams” as modeled by Fano planes, and boundaries defined by fractal scalability as modeled by the Koch snowflake, all linked by the underlying strength of the social networks. Conclusions: While these mathematical principles were developed to explain and explore natural order, their application to organizational leadership theory validates current best practices and offers suggestions for refining leadership models in perioperative systems.