The use of quantitative medical imaging data to initialize and constrain mechanistic mathematical models of tumor growth has demonstrated a compelling strategy for predicting therapeutic response. More specifically, we have demonstrated a data-driven framework for prediction of residual tumor burden following neoadjuvant therapy in breast cancer that uses a biophysical mathematical model combining reaction-diffusion growth/therapy dynamics and biomechanical effects driven by early time point imaging data. Whereas early work had been based on a limited dimensionality reduction (two-dimensional planar modeling analysis) to simplify the numerical implementation, in this work, we extend our framework to a fully volumetric, three-dimensional biophysical mathematical modeling approach in which parameter estimates are generated by an inverse problem based on the adjoint state method for numerical efficiency. In an in silico performance study, we show accurate parameter estimation with error less than 3% as compared to ground truth. We apply the approach to patient data from a patient with pathological complete response and a patient with residual tumor burden and demonstrate technical feasibility and predictive potential with direct comparisons between imaging data observation and model predictions of tumor cellularity and volume. Comparisons to our previous two-dimensional modeling framework reflect enhanced model prediction of residual tumor burden through the inclusion of additional imaging slices of patient-specific data.

中文翻译：

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基于三维图像的机械建模预测乳腺癌对新辅助治疗的反应

使用定量医学成像数据来初始化和约束肿瘤生长的机械数学模型已经证明了预测治疗反应的引人注目的策略。更具体地说，我们已经展示了一个数据驱动的框架，用于预测乳腺癌新辅助治疗后的残留肿瘤负荷，该框架使用结合反应扩散生长/治疗动力学和由早期时间点成像数据驱动的生物力学效应的生物物理数学模型。早期的工作是基于有限的降维（二维平面建模分析）来简化数值实现，在这项工作中，我们将我们的框架扩展到完全体积的，三维生物物理数学建模方法，其中参数估计是通过基于数值效率的伴随状态方法的逆问题生成的。在计算机性能研究中，我们展示了准确的参数估计，与地面实况相比，误差小于 3%。我们将该方法应用于来自具有病理完全反应的患者和具有残留肿瘤负荷的患者的患者数据，并通过成像数据观察与肿瘤细胞结构和体积的模型预测之间的直接比较来证明技术可行性和预测潜力。与我们之前的二维建模框架的比较反映了通过包含患者特定数据的额外成像切片来增强对残余肿瘤负荷的模型预测。