Dr. Bharat B Tripathi completed his Ph.D. in Mechanical Engineering (2015) at the Institut d’Alembert, Sorbonne University (Paris VI). His doctoral research pioneered the use of Discontinuous Galerkin methods for nonlinear acoustic shock waves, with applications ranging from sonic boom prediction to therapeutic ultrasound. His prior academic achievements include an M.Sc. in Applied Statistics and Informatics (2012) from the Indian Institute of Technology Bombay and a B.Sc. (Hons.) in Statistics (2010) from Banaras Hindu University, where he was awarded the University Gold Medal.

Following his Ph.D, he conducted postdoctoral and faculty-level research (2016-2020) at the University of North Carolina at Chapel Hill, where the focus was the computational modelling of nonlinear shear shock waves in brain tissue within the context of traumatic brain injury.

Dr. Tripathi, a Lecturer (Above the Bar) in Applied Mathematics at the University of Galway since September 2020 leads Tripathi Lab where his research in predictive computational modelling of nonlinear wave–brain interactions for injury mechanics and non-invasive neurological therapies continues.

Tripathi Lab develops and applies advanced mathematical models and high-performance numerical simulations to explore nonlinear wave and dynamical phenomena in biological systems, with a core focus on understanding and protecting the human brain. Our work bridges continuum mechanics, nonlinear dynamics, and computational neuroscience across multiple spatial and temporal scales.

1. Wave-Tissue Interaction and Brain Mechanics

   We study the complex interactions between high-intensity mechanical and acoustic waves and soft biological tissues, particularly neural tissue. This involves applying principles from nonlinear conservation laws, acoustic and shear shock wave theory, and viscoelastic electrodynamics to capture the intricate, nonlinear response of the brain to dynamic loads.

2. Biomedical Applications

   Our theoretical work is driven by critical applications in brain health and medical technology:

   • Traumatic Brain Injury (TBI): Modelling the initiation and propagation of mechanical waves and shocks during impact events to predict tissue damage and long-term neurophysiological consequences.
   • Therapeutic Ultrasound: Designing and optimizing non-invasive ultrasound modalities, including High-Intensity Focused Ultrasound (HIFU) for ablation, histotripsy for tissue fractionation, and emerging techniques for neuromodulation and temporary blood–brain barrier disruption.

3. Computational and Theoretical Methods

   We develop cutting-edge computational tools necessary for high-fidelity, large-scale simulations:

   • Numerical Methods: Development and analysis of robust, high-order numerical methods, including Discontinuous Galerkin finite element methods and high-resolution finite volume/difference schemes.
   • Computational Neuroscience: Addressing problems in nonlinear dynamical systems, including network-level neurodynamics and the multiscale coupling of mechanical waves with neural responses.
   • Advanced Computing: Employing uncertainty quantification (UQ) to rigorously account for biological variability and using machine learning techniques to accelerate model calibration and enable efficient, predictive simulations.

• Nonlinear Dynamical Systems (MP491)
• Fluid mechanics (MP365)
• Mathematical Methods II (MP346)
• Methods in Mathematical Physics II (MP232)
• Mathematical Physics I (MP345)

Nonlinear shear wave characterisation of clots

• Role - Principal Investigator (Academic Mentor)

• Funder - MSCA-CURAM Co-fund, MedDevDoc #: 101126640

Neural Operators for Predicting Brain Deformations in Concussions

• Project Acronym - DigiBrain

• Role - Principal Investigator (Academic Mentor)

• Funder - Research Ireland#: GOIPG/2025/7514

• Project link - DigiBrain - University of Galway

Machine Learning for Predicting Brain Deformation in Concussions using Head

• Project Acronym - DigiBrain

• Role - Principal Investigator (Individual Award)

• Funder - SFI#: 22/NCF/FD/11007.

• Project link - DigiBrain - University of Galway

Modelling Shear Shock Waves in the Brain with Machine Learning

• Project Acronym - DiscoSoft

• Role - Principal Investigator (Academic Mentor)

• Funder - IRC#: GOIPD/2023/1552

• Project link - DiscoSoft - University of Galway

Artificial Intelligence for Diagnostic Predictors of Aortic Disorders

• Project Acronym - AIDA

• Role - Collaborator with budget

• Funder - CURAM-Insight-Artivion

• Project link - AIDA - University of Galway

Adaptive Information Refinement Modeling of Nonlinear Shear Wave Propagation in Biological Tissue

• Role - Co-Investigator

• Funder - NSF#: DMS-1903174

Acoustic Radiation Force Impulse (ARFI) Imaging of Cardiac Tissue

• Role - Co-Investigator

• Funder - NIH#: 5R37HL096023