Partial Differential Equations

I specialize in the field of partial differential equations, particularly nonlinear partial differential equations. Specifically, my research focuses on advection-diffusion equation systems with a backdrop of biological phenomena, and I employ functional analytic methods for mathematical analysis. In the fiscal year 2015, my research was selected for the JST Strategic Basic Research Programs PRESTO, "Collaborative Research on Mathematics and Various Fields toward Solving Social Issues." Since then, I have collaborated with researchers from various fields such as medicine, medical engineering, physics, and numerical analysis, aiming to replicate and visualize phenomena through numerical simulations with the perspective of medical device development. With the initiation of the JST Strategic Basic Research Programs CREST in the year 2020, I have focused on constructing qualitative and quantitative mathematical models to describe observed phenomena, thereby advancing research with both mathematical analysis and mathematical model construction as twin pillars.

Development of a Fusion Technology of Mathematical Analysis and AI

Analysis for Estimating Vulnerable Sites in Cerebral Aneurysm Walls Due to the limited treatment options for cerebral vascular diseases such as subarachnoid hemorrhage, which are primarily confined to surgical procedures, many patients harbor concerns regarding the potential development of post-interventional sequelae. In our laboratory, we are developing a technology that enables the estimation of vulnerable sites in cerebral aneurysm walls without the need for surgical intervention, solely utilizing images obtained from "computed tomography (CT) scans/magnetic resonance imaging (MRI)" (hereinafter abbreviated as 4D-CTA/4D-MRA). In recent years, non-invasive observation methods utilizing 4D-CTA/4D-MRA have been established. However, conventional research in the medical field has yet to fully exploit the beneficial utilization of 4D-CTA/4D-MRA data for addressing the challenges in cerebral aneurysm treatment. In our laboratory, we propose a method for estimating the "aneurysm wall characteristics" without visual inspection by formulating the vascular wall micromotion of cerebral aneurysms based on 4D-CTA/4D-MRA data as a mathematical problem of differential equations.