关键词: 球面覆盖模型, 多面体, 肿瘤, 凸多面角, 球冠

Abstract: A mathematical problem arising from the therapy of tumors was investigated．In the ultrasound-guided radio-frequency ablation to cure tumors‚the tumor is assumed to be sphere-like‚and the expendable size of the ablation electrode is assumed to be a small spheroid．Medical treatment requires that all the cells on the tumor surface be killed． The mathematical problem is how to utilize the sphere with a radius r to cover the spherical surface with a radius R （r ＜R）．In this paper‚the regular tetrahedron algorithm and the n-side regular prism algorithm were discussed‚according to the geometric properties of spheres and polyhedral angles and by using the method of stepwise covering．To solve the problem‚the pineapple-shaped algorithm and the spherical crown stepwise covering method were proposed‚ thus giving a minimal ablation placement algorithm which can be applied to the therapy of tumors．

Key words: spherical covering model, polyhedron, tumor, convex polyhedral angle, spherical crown