RESEARCH

In my doctoral dissertation at the Indian Institute of Technology Delhi, India, I have primarily worked on developing a subject-specific in silico platform for neurosurgical simulations. The subject-specific model development requires generating subject-specific 3D anatomically correct geometrical models from raw MRI/CT scans, followed by determining unique material parameters from in vivo or in vitro methods. The integration of subject-specific information can then be used to set up and solve boundary value problems for the biomechanical assessment of surgical procedures. The clinical inference from these in silico models can then be used for per-surgical planning, intra-operative guidance, trauma prevention, or post-operative diagnosis. The whole work can be divided into the following projects:

• Development of an end-to-end pipeline for subject-specifc neurosurgical simulations utilizing Finite Element Method

• Development of scalable and efficient inverse finite element algorithms in MATLAB and Python for the in vivo mechanical characterization of soft tissue using Ultrasound and Magnetic Resonance Imaging (MRI) based quasi-static and dynamic elastography

• Developing a Python-based framework for differentiable finite element simulations tailored for inverse problems

• Application of a deep-learning based Wavelet Neural Operator (WNO) for solving the inverse problems of quasi-static and dynamic elastography  

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While at the Indian Institute of Technology Mandi, Himachal Pradesh, India, I primarily worked on the multiscale modeling of the nanostructure of the bone using a two-scale information passing approach coupled with asymptotic homogenization. The principal nanoscale constituents responsible for the formation of several hierarchical levels of bone are the organic phase (32-44% of bone volume), inorganic phase (33-43% of bone volume), and water (15-25% of bone volume). The distribution of these phases at both scales plays a crucial role in determining the mechanical behavior of bone. The basic building block of bone, Mineralized Collagen Fibril (MCF) was adopted as the coarse scale model while Microfibril (MF) as the fine scale model. The hierarchical structure of MCF consists of MF and Tropocollagen (TC) molecules at the fine scale. The structure-function relationship of MF was studied before using its properties at the next higher scale. The homogenized results from the MF scale were used as input to the MCF scale. The thesis involved the following projects:

• Multiscale modeling of the nanostructure of bone using an asymptotic homogenization approach coupled with Finite Element (FE) simulations

• Developelopment of a framework for generating representative volume elements taking into account the uncertainties in the geometric and material properties of different phases of MCF

• Determination of effective elastic properties of MCF using Monte Carlo simulations coupled with FE modeling

• Developed a computationally efficient statistical model predicting the strength of MCF 

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