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APRG Seminar

Title: Mathematics for Nanomedicine: From Accelerated acquisitions, Advance Image Processing, to Patient Specific Models
Speaker: Rahul Kumar (CIC biomaGUNE, San Sebastian, Spain)
Date: 10 April 2023
Time: 3 pm
Venue: Microsoft Teams (Online)

Nanomedicine is an offshoot of nanotechnology that involves many disciplines, including the manipulation and manufacturing of materials, imaging, diagnosis, monitoring, and treatment. An efficient iterative reconstruction algorithm,together with Total Variation (TV), and a good mathematical model, can be used to enhance the spatial resolution and predictive capabilities. In this webinar, I will start with our current results using integrated approach for predicting efficient biomarkers for Acute respiratory distress syndrome (ARDS) and then move to PDE based (Total variation flow) approach for Image denoising which can have promising applications in denoising medical images from different modalities. In principle, I will be discussing the below-mentioned topics and their important concepts in dealing with the main markers of cardiovascular diseases, specifically Pulmonary Hypertension.

1. 4D FlowMRI Data Assimilation: Integrated approach reveals new biomarkers for Experimental ARDS conditions. The purpose of this study is to characterize flow patterns and several other hemodynamic parameters (WSS, OSI, Helicity) using computational fluid dynamics model by combining imaging data from 4D-Flow MRI with hemodynamic pressure and flow waveforms from control and hypertensive subjects (related to acute respiratory distress syndrome). This work mainly concerns how to facilitate bench-bedside approach using integrated approach by combining CFD and AI.

2. An adaptive $C^0$ interior penalty discontinuous galerkin approximation of second order total variation problems. Singular nonlinear fourth order boundary value problems have significant applications in image processing and material science. We consider an adaptive $C^0$ Interior Penalty Discontinuous Galerkin (C0IPDG) method for the numerical solution of singular nonlinear fourth order boundary value problems arising from the minimization of functionals involving the second order total variation. The mesh adaptivity will be based on an aposteriori error estimator that can be derived by duality arguments. The fourth order elliptic equation reads as follows: \begin{align} u + \lambda \nabla \cdot \nabla \cdot \frac{D^2 u}{|D^2 w|} = & \ 0 \quad \mbox{in} \ Q := \Omega, \\ u = & \ 0 \quad \mbox{on} \ \Gamma,\\ n_{\Gamma} \cdot\frac{D^2 u} {n_{\Gamma}} = & \ 0 \quad \mbox{on} \ {\Gamma}. \end{align}

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 17 May 2024