| Application | Key Mathematics Areas |
| Airflow patterns in the respiratory tract | computational geometry, three-dimensional grid generation, numerical solution of Navier-Stokes equations, visualization of numerical results | Regional uptake of inhaled materials by respiratory tract | numerical solution of transport equations, visualization of results | Transport and disposition of chemicals through the body | numerical solution of systems of ODEs and PDEs, reaction-diffusion equations, parameter estimation techniques, Monte Carlo simulations | Onset and progression of cancer and pre-malignant cells | birth-death processes, Markov chains, parameter estimation techniques, probability and statistics | Molecular and cellular mechanisms of toxicity | pattern recognition, numerical solution of systems of ODEs and PDEs |
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