Source localization of reaction-diffusion models for brain tumors

We propose a mathematically well-founded approach for locating the source (initial state) of density functions evolved within a nonlinear reaction-diffusion model. The reconstruction of the initial source is an ill-posed inverse problem since the solution is highly unstable with respect to measurement noise. To address this instability problem, we introduce a regularization procedure based on the nonlinear Landweber method for the stable determination of the source location. This amounts to solving a sequence of well-posed forward reaction-diffusion problems. The developed framework is general, and as a special instance we consider the problem of source localization of brain tumors. We show numerically that the source of the initial densities of tumor cells are reconstructed well on both imaging data consisting of simple and complex geometric structures.

Introducing a pilot data collection model for real-time evaluation of data redundancy

In order to reduce serious health incidents, individuals with high risks need to be identified as early as possible so that effective intervention and preventive care can be provided. This requires regular and efficient assessments of risk within communities that are the first point of contacts for individuals. Clinical Decision Support Systems CDSSs have been developed to help with the task of risk assessment, however such systems and their underpinning classification models are tailored towards those with clinical expertise. Communities where regular risk assessments are required lack such expertise. This paper presents the continuation of GRiST research team efforts to disseminate clinical expertise to communities. Based on our earlier published findings, this paper introduces the framework and skeleton for a data collection and risk classification model that evaluates data redundancy in real-time, detects the risk-informative data and guides the risk assessors towards collecting those data. By doing so, it enables non-experts within the communities to conduct reliable Mental Health risk triage.