Mathematical Modeling, Simulation and Analysis

This program supports the development of novel mathematical modeling, simulation and analysis tools that can be broadly applied across a wide spectrum of diagnostic, therapeutic, imaging, and interventional applications.

Mathematical Modeling

Emphasis is on engineering solutions for theory-driven, physics-based, physiologically realistic, virtual representations of biomedical systems, with a particular weight on multiscale modeling. NIBIB interests include, but are not limited to:

  • multiscale modeling methodologies to bridge spatial and temporal scales
  • predictive modeling frameworks to facilitate the formation of testable hypothesis
  • non-standard methodologies that address modeling challenges, such as, uncertainty quantification, modularity, sparse data, scaling of species models, etc.
  • methods to address model credibility, reproducibility, and reuse by the biomedical community

This program supports the Interagency Modeling and Analysis Group (IMAG) and the Multiscale Modeling Consortium.


Emphasis is on engineering, mathematical, statistical and computational approaches for emulating system dynamics and processes implicated in biomedical applications, with a particular weight on medical simulator design and development to reduce medical errors and increase patient safety.  NIBIB interests include, but are not limited to:

  • virtual coaches incorporating artificial intelligence for performance training in medical procedures and workflows to provide real-time feedback to the end-user
  • simulation interfaces to facilitate dissemination and use of virtual environments for end-users
  • realistic representations of anatomy, tissue, instrument, tactile feedback, and collision dynamics
  • simulator designs that focus on complicated or rare procedures, or rare adverse events
  • simulators that replicate “real life” workflows, including planning, warm-up exercises, and rehearsal leading up to the actual procedure
  • portable, easy-to-use simulators for skilled practitioners in rural and low-resource settings


Emphasis is on theoretical, mathematical, statistical and engineering approaches to interpret the behavioral of complex biomedical data and its dynamics, with a particular weight on paradigm-shifting methodologies and software interfaces.  NIBIB interests include, but are not limited to:

  • intelligent control systems approaches of medical devices and hardware systems
  • novel methods to extract fundamental dynamical (mechanistic) features and patterns from large nonlinear, spatio-temporal datasets for real-time data analysis
  • novel implementations of dynamic versions of principal component analysis
  • tools to address data dimensionality, data fusion, and data assimilation methods to combine heterogeneous data and link sparse data with mechanisms
  • formal statistical inference frameworks to conduct network connectivity and causal-inference analyses from different types of biomedical data

The NIH BRAIN Initiative supports many projects in this program.

Applications proposing to use, rather than develop Mathematical Modeling, Simulation and Analysis tools should be referred to another institute.

Grant Number Project Title Principal Investigator Institution
5-R01-EB018965-04 Automated patient specific artery modeling using ultrasound virtual histology Melissa Young Mayo Clinic Rochester
5-R01-EB025703-03 CRCNS: Microimaging/modeling of retinal responses measured with laser magnetometer Igor Savukov New Mexico Consortium, Inc.
5-R03-EB026837-02 Disturbed stress-mediated remodeling of the lens capsule after cataract surgery determines implanted accommodative intraocular lens efficacy Ryan Pedrigi University of Nebraska Lincoln
5-R03-EB026036-02 Development of a Multi-scale Mathematical Model for Chip-based Chromatography Hui Zhao University of Nevada Las Vegas
5-U01-EB021956-04 Multiscale Modeling of the Mammalian Circadian Clock: The Role of GABA Signaling Michael Henson University of Massachusetts Amherst
5-U01-EB021921-04 Multiscale models of neural population control in spinal cord Terence Sanger University of Southern California
2-T32-EB009403-11 Integrated Interdisciplinary, inter-university PhD Program Computational Biology (T32) James Faeder University of Pittsburgh at Pittsburgh
5-R03-EB027444-02 Multi-scale modeling to predict and refine genotype-to-phenotype relationships in mammals Daniel Beard University of Michigan at Ann Arbor
5-R01-EB021293-04 Uncovering mechanical mechanisms of traumatic axonal injury Vivek Shenoy University of Pennsylvania
5-R01-EB018302-04 Enabling reliable cardiovascular simulations via uncertainty quantification Alison Marsden Stanford University