Despite the remarkable advances in cancer diagnosis, treatment, and management that have occurred over the past decade, malignant tumors remain a major public health problem. Further progress in combating cancer may be enabled by personalizing the delivery of therapies according to the predicted response for each individual patient. The design of personalized therapies requires patient-specific information integrated into an appropriate mathematical model of tumor response. A fundamental barrier to realizing this paradigm is the current lack of a rigorous, yet practical, mathematical theory of tumor initiation, development, invasion, and response to therapy. In this review, we begin by providing an overview of different approaches to modeling tumor growth and treatment, including mechanistic as well as data-driven models based on ``big data" and artificial intelligence. Next, we present illustrative examples of mathematical models manifesting their utility and discussing the limitations of stand-alone mechanistic and data-driven models. We further discuss the potential of mechanistic models for not only predicting, but also optimizing response to therapy on a patient-specific basis. We then discuss current efforts and future possibilities to integrate mechanistic and data-driven models. We conclude by proposing five fundamental challenges that must be addressed to fully realize personalized care for cancer patients driven by computational models.

翻译：尽管在过去十年中，癌症诊断、治疗与管理取得了显著进展，恶性肿瘤仍然是重大公共健康问题。通过根据每位患者的预测反应个性化制定治疗方案，可能进一步推动抗癌斗争。个性化治疗的设计需要将患者特异性信息整合到适当的肿瘤反应数学模型中。实现这一范式的基本障碍在于目前缺乏关于肿瘤起始、发展、侵袭及治疗反应的严谨而实用的数学理论。在本综述中，我们首先概述了肿瘤生长与治疗建模的不同方法，包括基于“大数据”和人工智能的机制模型及数据驱动模型。接着，我们通过实例展示数学模型的实用性，并讨论独立机制模型与数据驱动模型的局限性。我们进一步探讨了机制模型在患者特异性基础上不仅预测、还能优化治疗反应的潜力。然后，我们讨论了当前整合机制模型与数据驱动模型的努力及未来可能性。最后，我们提出五个必须解决的基本挑战，以全面实现由计算模型驱动的癌症患者个性化治疗。