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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” work flows, 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

This program has shared interest with the NIBIB Surgical Tools Program.


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-U01-EB016638-05 Multiscale Modeling of Facet Capsule Mechanobiology Victor Barocas University of Minnesota
5-R21-EB023051-02 New fractional calculus models of attenuation for shear wave elasticity imaging Robert Mcgough Michigan State University
1-R41-EB026358-01A1 Development and Validation of a Physical Anatomic Model for Surgical TrainingUsing 3D Printing Technology Jonathan Stone Simulated Inanimate Models, Llc
1-R43-EB027525-01 PostureCheck: A vision-based compensatory-posture-detection tool to enhance performance of the BURT® upper-extremity stroke-therapy device Alexandros Lioulemes Barrett Technology, Llc
5-R44-EB019802-02 Advanced virtual simulator for fundamentals of laparoscopic surgery training and credentialing Andinet Enquobahrie Kitware, Inc.
5-R21-EB020968-02 A new paradigm for aortic dissection: Mechanical mechanisms of delamination Jay Humphrey Yale University
1-R03-EB027444-01 Multi-scale modeling to predict and refine genotype-to-phenotype relationships in mammals Daniel Beard University of Michigan at Ann Arbor
1-R01-EB026955-01 Building analysis tools and a theory framework for inferring principles of neural computation from multi-scale organization in brain recordings Friedrich Sommer University of California Berkeley
1-R01-EB026953-01 Neuronal population dynamics within and across cortical areas Brent Doiron University of Pittsburgh at Pittsburgh