SIAM Journal on Applied Mathematics, Volume 81, Issue 2, Page 355-377, January 2021.
We present a shape-oriented data assimilation strategy suitable for front-tracking tumor growth problems. A general hyperbolic/elliptic tumor growth model is presented as well as the available observations corresponding to the location of the tumor front over time extracted from medical imaging as MRI or CT scans. We provide sufficient conditions allowing one to design a state observer by proving the convergence of the observer model to the target solution for exact parameters. In particular, the similarity measure chosen to compare observations and simulation of tumor contour is presented. A specific joint state-parameter correction with a Luenberger observer correcting the state and a reduced-order Kalman filter correcting the parameters is introduced and studied. We then illustrate and assess our proposed observer method with synthetic problems. Our numerical trials show that state estimation is very effective with the proposed Luenberger observer, but specific strategies are needed to accurately perform parameter estimation in a clinical context. We then propose strategies to deal with the fact that data is very sparse in time and that the initial distribution of the proliferation rate is unknown. The results on synthetic data are very promising, and work is ongoing to apply our strategy on clinical cases.

中文翻译：

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肿瘤生长模型的联合状态参数估计

SIAM应用数学杂志，第81卷，第2期，第355-377页，2021年1月。
我们提出了一种适合于前沿跟踪肿瘤生长问题的面向形状的数据同化策略。提出了一个一般的双曲线/椭圆形肿瘤生长模型，以及对应于从医学成像（如MRI或CT扫描）中提取的随着时间推移肿瘤前沿位置的可用观察结果。我们提供了充分的条件，允许人们通过证明观测器模型与目标解决方案的精确参数收敛，来设计状态观测器。特别是，提出了用于比较观察和模拟肿瘤轮廓的相似性度量。介绍并研究了一种特定的联合状态参数校正方法，其中包括用Luenberger观测器校正状态和使用降阶卡尔曼滤波器校正参数的方法。然后，我们说明和评估我们提出的带有综合问题的观察者方法。我们的数值试验表明，状态估计对于建议的Luenberger观测器非常有效，但是需要特定的策略才能在临床环境中准确地执行参数估计。然后，我们提出了应对数据时间稀疏且增殖率的初始分布未知的事实的策略。综合数据的结果非常有希望，并且正在进行将我们的策略应用于临床病例的工作。然后，我们提出了应对数据时间稀疏且增殖率的初始分布未知的事实的策略。综合数据的结果非常有希望，并且正在进行将我们的策略应用于临床病例的工作。然后，我们提出了应对数据时间稀疏且增殖率的初始分布未知的事实的策略。综合数据的结果非常有希望，并且正在进行将我们的策略应用于临床病例的工作。