Mapping the human lung using Delaunay tessellation.

Abstract

A computer protocol is (1) developed and (2) applied to the human body for medical research. Delaunay tessellation is used to derive an algorithm to describe the structure of the lung. This may be the first application of that mathematical concept to a physiological system. The lung is a complex yet systematic network of pathways described herein with cited dimensions and angles. Its terminal points are the most distal airways, alveolar sacs, defined by their (x, y, z) coordinates. We have addressed that spatial array as a set of points in 3-D space, and, visualized the physical boundary of a lung as the surface of the convex hull of that set in R3. As documented, the enveloping surface of the computer lung closely describes the outer contours of human lungs depicted in clinical studies. Therefore, the model has immediate and salient implications to problems in medicine where respiratory function and morphology have integral roles, specifically, thoracic surgery and aerosol therapy. Examples include the removal of lobes damaged by respiratory diseases such as cystic fibrosis and cancer, and the definition of lung boundaries for gamma camera, PET, and SPECT images. Importantly, the model can be varied to simulate the intersubject differences that physicians experience among a patient population. The mathematical simulations performed in this work are intended to be complementary to laboratory investigations in the medical arena. By providing accurate 3-D, quantitative descriptions of human lungs the supercomputer can be actively integrated into the clinical environment.