Reducing the Memory Requirements of High Resolution Voxel Phantoms by Means of a Binary Tree Data Structure

Computational human phantoms are a well-established tool used to simulate the performance of medical imaging devices. The maximum resolution of voxelized phantoms is bounded in practice by the available computer memory, which is especially limited for graphics processing unit (GPU)-based simulations. For phantoms that have been segmented into a small number of tissue types, the use of a uniform grid is inefficient because large numbers of adjacent voxels are composed of the same tissue. The computer files used to store these phantoms can be compressed into a small fraction of their original size using standard lossless compression algorithms. Compression is used for storage and distribution, but not during the simulations because compression algorithms compress the data incrementally from the first byte to the last. This approach intrinsically prevents access to random locations along the data stream, which is an essential requirement of the majority of simulation algorithms. In this paper, we propose to store voxelized phantoms in memory using a binary tree structure, as a way to accomplish both data compression and fast random access. The composition of a particular voxel can be efficiently retrieved by traversing the binary tree down from the root node to the corresponding leaf node. As a drawback, the memory savings come at the cost of more frequent memory access, which might slow down simulations in which memory access constitutes a substantial fraction of the execution time. Methods to generate and efficiently store in memory a binary tree geometry, and an example implementation in a GPU-accelerated Monte Carlo code for X-ray imaging virtual clinical trials, are presented. Results of a simulation of mammography and tomosynthesis imaging with a computational breast phantom voxelized at 50 μm show that the implemented binary tree geometry can achieve a 50-fold reduction of memory use, with a 4.7% increase in simulation time.

I. Introduction

Computational human phantoms are an essential tool to study the performance of medical devices in silico. The most common data format used to describe computational phantoms is a voxelized geometry. In this geometric model the composition of the object or patient is discretized into a uniform 3-D grid with equal size elements (voxels). Using a large number of tiny voxels, the intricate shape of the anatomic structures can be described with very high spatial resolution. Some voxelized phantoms, such as those directly generated by tomographic reconstruction of medical scans, have variability in the value of each voxel due to subvoxel tissue structures and noise inherent to the image acquisition process. However, the phantoms most commonly used in computer simulations are typically preprocessed using a manual or automatic segmentation algorithm that assigns the voxels into a small number of tissue types or organs. The use of a uniform grid with a segmented phantom is inefficient because large numbers of adjacent voxels correspond to the same organ and are composed of the same tissue.