Finding interpretable biomechanical models can provide insight into the functionality of organs with regard to physiology and disease. However, identifying broadly applicable dynamical models for in vivo tissue remains challenging. In this proof of concept study we propose a reconstruction framework for data-driven discovery of dynamical models from experimentally obtained undersampled MRI spectral data. The method makes use of the previously developed spectro-dynamic framework which allows for reconstruction of displacement fields at high spatial and temporal resolution required for model identification. The proposed framework combines this method with data-driven discovery of interpretable models using Sparse Identification of Non-linear Dynamics (SINDy). The design of the reconstruction algorithm is such that a symbiotic relation between the reconstruction of the displacement fields and the model identification is created. Our method does not rely on periodicity of the motion. It is successfully validated using spectral data of a dynamic phantom gathered on a clinical MRI scanner. The dynamic phantom is programmed to perform motion adhering to 5 different (non-linear) ordinary differential equations. The proposed framework performed better than a 2-step approach where the displacement fields were first reconstructed from the undersampled data without any information on the model, followed by data-driven discovery of the model using the reconstructed displacement fields. This study serves as a first step in the direction of data-driven discovery of in vivo models.

翻译：寻找可解释的生物力学模型能够为理解器官在生理与病理状态下的功能机制提供重要见解。然而，针对活体组织建立具有广泛适用性的动力学模型仍面临挑战。在本概念验证研究中，我们提出了一种重建框架，用于从实验获取的欠采样MRI谱数据中数据驱动地发现动力学模型。该方法利用了先前开发的谱-动力学框架，该框架能够重建模型辨识所需的高时空分辨率位移场。所提出的框架将此方法与基于稀疏非线性动力学辨识（SINDy）的可解释模型数据驱动发现相结合。重建算法的设计旨在建立位移场重建与模型辨识之间的共生关系。我们的方法不依赖于运动的周期性。通过使用临床MRI扫描仪采集的动态体模谱数据，该方法得到了成功验证。该动态体模被编程执行符合5种不同（非线性）常微分方程的运动。与先从未知模型信息条件下从欠采样数据重建位移场、再基于重建位移场数据驱动发现模型的两步法相比，所提出的框架表现出更优性能。本研究为活体模型的数据驱动发现迈出了第一步。