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γ刀的全称是“γ射线立体定向放射治疗系统”．随着近十多年来计算机技术及ＣＴ、ＭＲＩ等先进成象技术的飞速发展，γ刀在临床中的应用也越来越广泛．而其中治疗规划方案的设计是一项非常庞杂的过程，均需涉及到大量的临床参数和计算，一般是由医生反复调试各参数后确定的，不仅费时，而且难以获得最佳结果．本文据此提出一种数学模型，并以该模型为基础，给出解决该问题的一种方法，即惩罚函数法，计算数据结果表明了这一方法的可行性．
The full name of γ knife is “γ-ray stereotactic radiotherapy system.” With the rapid development of computer technology and CT, MRI and other advanced imaging technologies in recent ten years, γ-knife has become more and more widely used in clinical practice. The design of the treatment planning program is a very complex process, involving a large number of clinical parameters and calculations, generally determined by the doctor after repeated testing of various parameters, not only time-consuming, and difficult to obtain the best results. Based on this model, a mathematical model is proposed. Based on this model, a method to solve this problem is given, namely, the penalty function method, and the calculation data shows the feasibility of this method.