The Integration of PDE Modeling, Machine Learning and Topology Analysis in MRIs Analysis

The Integration of PDE Modeling, Machine Learning and Topology Analysis in MRIs Analysis

The Integration of PDE Modeling, Machine Learning and Topology Analysis in MRIs Analysis

We propose an interdisciplinary effort targeted at the integration of partial differential equations modeling, topological data analysis and machine learning for tackling the challenges in the modeling,
recognition, shape recovery, and analysis for medical images. Due to the large shape variability, structure complexity, and restrictive scanning methods, the three-dimensional MRIs are still challenging
to analyze. In this proposed project, we will link the partial differential equation framework and the level set framework for implementing the image segmentation algorithm; besides, the topology
analysis approach will guide us in designing the novel topology feature preserving machine learning algorithm with applications in medical imaging. The initiative is well-aligned with the goal of the
current research in applications of machine learning in medical sciences, and our preliminary results will likely lead to future external funding in this field.

The main research goal of this proposal is to develop a new scheme for shape recognition, recovery, and analysis in medical images combining the machine learning methods from computer science and
the PDE methods from a mathematical perspective, along with topological considerations. Machine learning is a major driving force behind the current data science, while its full potential in unveiling
the shape variability, structure complexity, and etc. is yet to be reached. Due to the restrictive scanning method and limited image resolution, there is few quantitative or competitive deep learning
algorithm for analyzing the medical images. The driving force behind the current transition from qualitative and descriptive methods to quantitative, analytical and predictive approach is theoretical
modeling and computational algorithms, which have their roots in mathematics and computer science. Our project will first connect internal expertise in UGA in the related research areas and attempt to
underpin quantitative and predictive medical images applications.

One challenge for medical imaging analysis is to handle complex domains and variability shape, PIs from mathematics aspects will extend the PDEs framework together with the level set framework in
designing the fast and efficient numerical solver. The PDE modeling, numerical solver, stability, and accuracy analysis will be the fundamental research aspect from the applied math and topology aspect.
Hong recently proposed a novel deep neural network architecture for brain MRIs, which improves the performance of existing methods on brain extraction. Her previous successful work in brain tumor
segmentation will be leveraged in designing/comparing our new PDEs based algorithm. Besides, the other expertise from Epidemiology, Biostatistics, and Genetics will further add the machinery for
better understanding the complementary information and data set in the medical applications.

Team Lead

Lin Mu
Department of Mathematics

Team Members

Pengpeng Bi
Department of Genetics

Cuiyu He
Department of Mathematics

Yi Hong
Department of Computer Science

Weiwei Hu
Department of Mathematics

Changwei Li
Department of Epidemiology and Biostatistics

Weiwei Wu
Department of Mathematics