We present a method for synthesizing two dimensional (2D)

Abstract:The Purkinje fibers are located in the ventricular walls of the heart, just beneath the endocardium and conduct excitation from the right and left bundle branches to the ventricular myocardium. Recently, anatomists succeeded in photographing the Purkinje fibers of a sheep, which clearly showed the mesh structure of the Purkinje fibers. In this study, we present a technique for modeling the mesh structure of Purkinje fibers semiautomatically using an extended L-system. The Lsystem is a formal grammar that defines the growth of a fractal structure by generating rules (or rewriting rules) and an initial structure. It was originally formulated to describe the growth of plant cells, and has subsequently been applied for various purposes in computer graphics such as modeling plants, buildings, streets, and ornaments. For our purpose, we extended the growth process of the L-system as follows: 1) each growing branch keeps away from existing branches as much as possible to create a uniform distribution, and 2) when branches collide, we connect the colliding branches to construct a closed mesh structure. We designed a generating rule based on observations of the photograph of Purkinje fibers and manually specified three terminal positions on a three-dimensional (3D) heart model: those of the right bundle branch, the anterior fascicle, and the left posterior fascicle of the left branch. Then, we grew fibers starting from each of the three positions based on the specified generating rule. We achieved to generate 3D models of Purkinje fibers of which physical appearances closely resembled the real photograph. The generation takes a few seconds. Variations of the Purkinje fibers could be constructed easily by modifying the generating rules and parameters.Key words: Purkinje fibers, L-system, heart simulation.A three-dimensional (3D) virtual heart model is often used for computer simulations and visualizations. Computer simulation is one way to understand the electrophysiological properties of the heart or to figure out the mechanisms of fatal arrhythmias [1][2][3][4]. Effective visualization of a 3D heart model is also a useful tool for education and communication between doctors and patients [1,5]. However, the creation of a 3D heart model is difficult and time-consuming because the heart has intricate structures containing various tissues, such as the atrioventricular node, bundle of His, Purkinje fi bers, and contractive myocardium. Our goal was to facilitate this process by providing effective modeling tools. In this study, we focused on the construction of Purkinje fi bers.The Purkinje fi bers are part of the ventricular conduction system and were originally discovered by Tawara [6]. These tissues conduct excitation (electrical activation) rapidly from the bundle of His to the ventricular myocardial tissue. The Purkinje fibers are located in the ventricular walls of the heart, just beneath the endocardium. Figure 1 is a PAS-stained stereomicrograph of a sheep heart provided by Shimada et al. [7], which shows the...

Abstract. L-system is a tool commonly used for modeling and simulating the growth of plants. In this paper, we propose a new tree modeling system based on L-system that allows the user to control the overall appearance and the depth of recursion, which represents the level of growth, easily and directly, by drawing a single stroke. We introduce a new module into L-system whose growth direction is determined by a user-drawn stroke. As the user draws the stroke, the system gradually advances the growth simulation and creates a tree model along the stroke. Our technique is the first attempt to control the growth of a simulation in L-system using stroke input.

We present an interactive modeling system for flower composition that supports seamless transformation from an initial sketch to a detailed three-dimensional (3D)