RL2. Modeling of Biological Systems & Health

Group Leader: Suárez Fernández, Antonio

Description:

The research work of RL2 focuses on the modeling and analysis of biological and health processes, in particular dynamics of living organisms, tumor growth and non-invasive diagnosis of diseases. Our strategy is to build differential models capturing the main characteristics of the biological processes. After studying their analytical properties, the differential model is modified on the feedback provided by the numerical simulations and the medical/biological advice. This allows us to describe the complex interactions present in tumor growth and provide insight to design novel therapies and optimize the current ones.
Our goal is to develop predictive models for the non-invasive diagnosis of diseases and the estimation of the evolution of infectious ones, based on the classification and regression analysis of a learning sample. We also develop pharmacokinetic models to analyze the variability of the pharmacological response depending on physiological characteristics of the patients. For this we develop statistical techniques based upon nonlinear mixed effects models.

Members:

Clara Grima Ruíz
Francisco Guillén González
Juan Vicente Gutiérrez Santacréu
Mª José Jiménez Rodríguez

Research portfolio:

Mathematics of human consciousness: theory, computation and clinical application
  • Mathematical techniques:
    A. Dynamical systems
    B. Geometrical and topological characterization of attractors of attractors
    C. Lotka-Volterra transform
    D. Informational structures for brain dynamics
  • Application sectors:
    Neuroscience, Psychology, Medical Sciences
Mathematical technology for better understanding of diseases and the control of therapies
  • Mathematical techniques:
    A. Partial differential equations
    B. Numerical Analysis
    C. Dynamical systems
    D. Machine learning techniques
    E. Complex statistical techniques
  • Application sectors:
    Ecology, Medicine, Neuroscience
Mathematical technology for the improvement of healthcare system
  • Mathematical techniques:
    A. Partial differential equations
    B. Numerical Analysis
    C. Dynamical systems
    D. Machine learning techniques
    E. Complex statistical techniques
  • Application sectors:
    Ecology, Medicine, Neuroscience
Long-time behavior of coupled systems with Navier-Stokes
  • Mathematical techniques:
    A. Theory of partial differential equations
    B. Mathematical modeling through conservation laws
  • Application sectors:
    Biology
Bioconvective flows
  • Mathematical techniques :
    A. Theory of partial differential equations
  • Application sectors:
    Biology
Chemotaxis models and Non-local models applied to Biology
  • Mathematical techniques :
    A. Theory of partial differential equations
    B. Bifurcation theory
    C. Sub-supersolutions methods
    D. Semigroup theory
  • Application sectors:
    Biology, Medicine
Numerical methods for Biological Models
  • Mathematical techniques :
    A. Partial Differential Equations
    B. Finite Element Methods
    C. Stabilization
    D. Discrete Maximum Principle
    E. Energy law
  • Application sectors:
    Biology, Pharmacy, Medicine
Computational topology and neural networks
  • Mathematical techniques :
    A. Computational topology
    B. Algebraic topology
    C. Machine learning.
    D. Deep learning.
    E. Topological data analysis
  • Application sectors:
    Technology
Topological analysis of biological data
  • Mathematical techniques :
    A. Topological data analysis
    B. Graph modelling
    C. Computational geometry
    D. Statistics
  • Application sectors:
    Pharmacology, Biomedicine
Theoretical and numerical analysis, and optimal control of biological problems related to the chemotaxis process
  • Mathematical techniques :
    A. Theory of partial differential equations
    B. Optimal control
    C. Numerical approximation using Finite Element Methods
    D. Numerical Analysis
  • Application sectors:
    Biology, Medicine
Theoretical and numerical analysis, and optimal control of biological problems. Identification of biologiccal parameters and comparision of therapies
  • Mathematical techniques :
    A. Theory of partial differential equations
    B. Optimal control
    C. Numerical approximation using Finite Element Methods (continuous and/or discontinuous)
    D. Numerical Analysis
  • Application sectors:
    Biology, Medicine
Biological and health systems
  • Mathematical techniques :
    A. Theory of Nonlinear Partial Differential Equations
    B. Nonlocal Transport terms. Fokker Planck and Porous media equations
    C. Solutions arising singularities. Blow-up in finite time
    D. Agent Based Models. Mean field equations. Random graphs
    E. Statistical Mechanics tools. Boltzmann Equation. Grazing limit.
    F. Markov Processes and Hydrodynamic limits
    G. Numerical simulations
    H. Some nonlocal diffusivities
  • Application sectors:
    Biological processes, epidemics , chemotaxis, population dynamics
Modeling and simulation of neuroendocrine processes
  • Mathematical techniques :
    A. Theory of Dynamical Systems and bifurcations
    B. Mathematical modelling through slow-fast systems
    C. Mathematical modelling through non-smooth systems
    D. Analysis of complex oscillations and ‘canard’ phenomena
    E. Numerical methods for stiff systems.
  • Application sectors:
    Biology, Health systems, Engineering

Related projects:

Related transfer: