Vaidya V G, Alexandro F J
Int J Biomed Comput. 1982 Jan;13(1):19-36. doi: 10.1016/0020-7101(82)90048-4.
A number of mathematical models for tumor growth have been proposed in the past to increase the understanding of the tumor growth process. This study evaluates the exponential, the Gompertz, the Bertalanffy and the logistic models. The data used for the evaluation of the models consists of: the untreated primary carcinoma of the human lung, and induced sarcoma in mice. The non-linear regression method was used for the analysis of the data. The logistic equation gave the best fit in the cases of all seven patients. However, the Bertalanffy equation was the best in seven out of 10 cases of mice. The models were also judged by comparing the percentage error in predicting the volume of a tumor.
过去已经提出了许多肿瘤生长的数学模型，以增进对肿瘤生长过程的理解。本研究评估了指数模型、冈珀茨模型、贝塔朗菲模型和逻辑斯蒂模型。用于模型评估的数据包括：人类原发性肺癌未经治疗的病例，以及小鼠诱发肉瘤的病例。采用非线性回归方法对数据进行分析。在所有7例患者的病例中，逻辑斯蒂方程拟合效果最佳。然而，在10例小鼠病例中，有7例贝塔朗菲方程拟合效果最佳。还通过比较预测肿瘤体积的百分比误差来评判这些模型。
