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# A for-loop is all you need. For solving the inverse problem in the case of personalized tumor growth modeling

*Proceedings of the 2nd Machine Learning for Health symposium*, PMLR 193:566-577, 2022.

#### Abstract

Solving the inverse problem is the key step in evaluating the capacity of a physical model to describe real phenomena. In medical image computing, it aligns with the classical theme of image-based model personalization. Traditionally, a solution to the problem is obtained by performing either sampling or variational inference based methods. Both approaches aim to identify a set of free physical model parameters that results in a simulation best matching an empirical observation. When applied to brain tumor modeling, one of the instances of image-based model personalization in medical image computing, the overarching drawback of the methods is the time complexity of finding such a set. In a clinical setting with limited time between imaging and diagnosis or even intervention, this time complexity may prove critical. As the history of quantitative science is the history of compression (Schmidhuber and Fridman, 2018), we align in this paper with the historical tendency and propose a method compressing complex traditional strategies for solving an inverse problem into a simple database query task. We evaluated different ways of performing the database query task assessing the trade-off between accuracy and execution time. On the exemplary task of brain tumor growth modeling, we prove that the proposed method achieves one order speed-up compared to existing approaches for solving the inverse problem. The resulting compute time offers critical means for relying on more complex and, hence, realistic models, for integrating image preprocessing and inverse modeling even deeper, or for implementing the current model into a clinical workflow. The code is available at https://github.com/IvanEz/for-loop-tumor.