Mathematical modeling in biomedicine
Mathematical modeling in biomedicine

Development and research of blood clotting models and description of thrombin production in normal and pathological (hemophilia) cases; comparison with experimental data. The study of spatial models of blood clotting based on reaction-diffusion equations. The study of the rate of thrombosis, considered as a reaction-diffusion wave. The study of blood clotting in the stream (veins, arteries), determination conditions for normal growth of the clot and excessive growth leading to the development of thrombosis.

The study of mathematical models of cancer growth, taking into account angiogenesis; determination of optimal protocols for drug administration, taking into account the interaction of chemotherapy and angiogenesis. The study of hematological cancers, including multiple myeloma. The study of mutations of malignant cells and the emergence of resistant clones. The study of the interaction of cancer with the body's immune system and the determination of various modes of tumor growth.

Development and study of mathematical models of the immune response to viral infection taking into account mutations of viruses. Determination of the conditions and dynamics of the evolution of viruses. Construction and calibration of mathematical models of various extent of specification for a compact description of key processes of regulation of the immune response, taking into account the structure of lymphoid organs. Investigation of integrative mathematical models of the immune system response to HIV infection on the criterion of controllability and the structure of reachable sets.

List of key publications on the project:

  • V. Volpert.  Existence of reaction-diffusion waves  in a model of  immune response. MJOM
  • Nikolai Bessonov, Gennady Bocharov, Andreas Meyerhans, Vladimir Popov, Vitaly Volpert. Nonlocal reaction-diffusion model of viral evolution: emergence of virus strains. Mathematics.
  • Anne Beuter, Anne Balossier, François Vassal, Simone Hemm, Vitaly Volpert. Closed-loop stimulation for post-stroke aphasia: Towards model-guided neuromodulation. Biological Cybernetics (Q2)
  • Tarik Touaoula, Nor Frioui, Nicolay Bessonov, Vitaly Volpert. Dynamics of solutions of a reaction-diffusion equation with delayed inhibition. Discrete and continuous dynamical systems – S (Q2)
  • N. Ratto, M. Marion, V. Volpert. Existence of pulses for a reaction-diffusion system of blood coagulation.  Topological methods in nonlinear analysis (Q2)
  • Anass Bouchnita, Vitaly Volpert, Mark J. Koury, Andreas Hellande. A multiscale model to design therapeutic strategies that overcome drug resistance to TKIs in multiple myeloma. Mathematical biosciences (Q2)
  • Gennady Bocharov, Vitaly Volpert, Burkhard Ludewig and Andreas Meyerhans. Editorial: Mathematical Modeling of the Immune System in Homeostasis, Infection and Disease. Frontiers Immunology (Q1)
  • Kalyan Manna, Vitaly Volpert, Malay Banerjee. Dynamics of a Diffusive Two-Prey-One-Predator Model with Nonlocal -Specific Competition for Both the Prey Species. Mathematics (Q1)
  • N. Bessonov, G. Bocharov, C. Leon, V. Popov, V. Volpert. Genotype dependent virus distribution and competition of virus strains. MATHEMATICS AND MECHANICS OF COMPLEX SYSTEMS (Q2)
  • M. Banerjee, N. Mukherjee, V. Volpert. Prey-predator model with nonlocal and global consumption in the prey dynamics. Discrete and continuous dynamical systems – S (Q2)
  • D. Sen, S. Petrovskii, S. Ghorai, M. Banerjee. Rich Bifurcation Structure of Prey–Predator Model Induced by the Allee Effect in the Growth of Generalist Predator.  International Journal of Bifurcation and Chaos. (Q1)
  • Sergei Petrovskii, Weam Alharbi, Abdulqader Alhomairi, Andrew Morozov. Modelling Population Dynamics of Social Protests in Time and Space: The Reaction-Diffusion Approach. Mathematics  (Q1)
  • Andrew Morozov, Karen Abbott, Kim Cuddington, Tessa Francis, Gabriel Gellner, Alan Hastings, Ying-Cheng Laig, Sergei Petrovskii, Katherine Scranton, Mary Lou Zeeman. Long transients in ecology: Theory and applications. Physics of life reviews (Q1)
Project goals
  • Mathematical modelling in biology and medicine in three priority directions: cardiovascular system, oncological diseases, the immune response and infectious diseases.
Project leader All participants
Vitalii Volpert

Vitalii Volpert

Doctor of Sciences, professor
Project results
Blood coagulation - analysis
Formation of blood clot in response to the vessel damage is triggered by the complex network of biochemical reactions of the coagulation cascade. The process of clot growth can be modeled as a traveling wave solution of the bistable reaction–diffusion system. The critical value of the initial condition which leads to convergence of the solution to the traveling wave corresponds to the pulse solution of the corresponding stationary problem. In the current study we prove the existence of the pulse solution for the stationary problem in the model of the main reactions of the blood coagulation cascade using the Leray–Schauder method.
Blood coagulation – modelling
The mechanics of platelet initial adhesion due to interactions between GPIb receptor with von Willebrand factor (vWf) multimers is essential for thrombus growth and the regulation of this process. Multimeric structure of vWf is known to make adhesion sensitive to the hydrodynamic conditions, providing intensive platelet aggregation in bulk fluid for high shear rates. But it is still unclear how it affects the dynamics of platelet motion near vessel walls and efficiency of their adhesion to surfaces. Our goal is to resolve the principal issues in the mechanics of platelet initial attachment via GPIb-vWf bonds in near-wall flow conditions: when the platelet tends to roll or slide and how this dynamics depends on the size, conformation and adhesive properties of the vWf multimers. We employ a 3D computer model based on a combination of the Lattice Boltzmann method with mesoscopic particle dynamics for explicit simulation of vWf-mediated blood platelet adhesion in shear flow. Our results reveal the link between the mechanics of platelet initial adhesion and the physico-chemical properties of vWf multimers. This has implications in further theoretical investigation of thrombus growth dynamics, as well as the interpretation of in vitro experimental data.
Application area
  • The results obtained in the course of the project have applications in oncology, immunology, and the field of cardiovascular diseases.