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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2025, Vol. 42 ›› Issue (4): 619-631.doi: 10.3969/j.issn.1005-3085.2025.04.002cstr: 32411.14.cjem.CN61-1269/O1.2025.04.002

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多种肿瘤生长的数据拟合与预测

王晶囡,   胥  丽   

  1. 哈尔滨理工大学理学院，哈尔滨  150080
  • 收稿日期:2022-11-30 接受日期:2023-05-22 出版日期:2025-08-15 发布日期:2025-10-15
  • 基金资助:
    国家自然科学基金 (11801122)；黑龙江省自然科学基金 (LH2022E084).

Data Fitting and Prediction of Multiple Tumor Growths

WANG Jingnan,   XU Li   

  1. School of Science, Harbin University of Science and Technology, Harbin 150080
  • Received:2022-11-30 Accepted:2023-05-22 Online:2025-08-15 Published:2025-10-15
  • Supported by:
    The National Natural Science Foundation of China (11801122); the Natural Science Foundation of Heilongjiang Province (LH2022E084).

摘要：

运用最小二乘法和 SPSS 22.0 分别得到了在肿瘤最大环境容纳量已知和未知情况时的三类常见的肿瘤生长模型的参数估计公式。通过参数估计式和已有数据，得到 8 种癌症的生长率，并利用 Matlab 进行了数据拟合。将肿瘤细胞生长初期数据的前四分之三作为拟合所用数据，将后四分之一实验数据作为预测所用数据，进一步评估了拟合效果，确定了各种肿瘤生长所符合的最佳数学模型。按肿瘤生长模型的特点和拟合效果，以及肿瘤所处部位的具体功能，将 8 种不同部位的癌症细胞的生长情况进行了数学归类。理论研究与数值拟合为进一步研究免疫抗肿瘤生长的机理与免疫细胞抑制肿瘤生长模型的改进提供了一定的理论参考。

关键词: 肿瘤生长模型, 最小二乘方法, 数据拟合, 一元线性回归, SPSS软件

Abstract:

The least square method and SPSS 22.0 are used to obtain three common parameter estimation formulas of the tumor growth model whether the maximum environmental capacity of tumor cells is known or unknown. Through the parameter estimation formula and the published data, the growth rates of 8 different types of cancers are calculated. The original data are fitted through Matlab. Furthermore, the fitting effect is verified by taking the first three quarters of the initial data of tumor cell growths as the fitting data and by taking the last quarter of the experimental data as the prediction data. The optimal mathematical models for describing various tumor growths are determined. According to the characteristics and the fitting effects of tumor growths, as well as the function characteristics of the organs where tumors are located, the growth situations of 8 types of cancer cells in different organs are classified from a mathematical perspective. Further, this study provides a theoretical reference for further research on the anti-tumor
immunity mechanism and the improvement of mathematical models for immune cells inhibiting tumor growths.

Key words: tumor growth model, least square method, data fitting, univariate linear regression, SPSS software

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