Institute of Mechanical Engineering Problems

Saint Petersburg, Russia

Institute of Mechanical Engineering Problems

Saint Petersburg, Russia

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Tosenberger A.,Institute des Hautes Etudes Scientifiques | Bessonov N.,Institute of Mechanical Engineering Problems | Volpert V.,Camille Jordan Institute
Journal of Mathematical Biology | Year: 2015

The paper is devoted to mathematical modelling of clot growth in blood flow. Great complexity of the hemostatic system dictates the need of usage of the mathematical models to understand its functioning in the normal and especially in pathological situations. In this work we investigate the interaction of blood flow, platelet aggregation and plasma coagulation. We develop a hybrid DPD–PDE model where dissipative particle dynamics (DPD) is used to model plasma flow and platelets, while the regulatory network of plasma coagulation is described by a system of partial differential equations. Modelling results confirm the potency of the scenario of clot growth where at the first stage of clot formation platelets form an aggregate due to weak inter-platelet connections and then due to their activation. This enables the formation of the fibrin net in the centre of the platelet aggregate where the flow velocity is significantly reduced. The fibrin net reinforces the clot and allows its further growth. When the clot becomes sufficiently large, it stops growing due to the narrowed vessel and the increase of flow shear rate at the surface of the clot. Its outer part is detached by the flow revealing the inner part covered by fibrin. This fibrin cap does not allow new platelets to attach at the high shear rate, and the clot stops growing. Dependence of the final clot size on wall shear rate and on other parameters is studied. © 2015 Springer-Verlag Berlin Heidelberg


PubMed | Institute of Mechanical Engineering Problems, Institute des Hautes Etudes Scientifiques and Camille Jordan Institute
Type: Journal Article | Journal: Journal of mathematical biology | Year: 2016

The paper is devoted to mathematical modelling of clot growth in blood flow. Great complexity of the hemostatic system dictates the need of usage of the mathematical models to understand its functioning in the normal and especially in pathological situations. In this work we investigate the interaction of blood flow, platelet aggregation and plasma coagulation. We develop a hybrid DPD-PDE model where dissipative particle dynamics (DPD) is used to model plasma flow and platelets, while the regulatory network of plasma coagulation is described by a system of partial differential equations. Modelling results confirm the potency of the scenario of clot growth where at the first stage of clot formation platelets form an aggregate due to weak inter-platelet connections and then due to their activation. This enables the formation of the fibrin net in the centre of the platelet aggregate where the flow velocity is significantly reduced. The fibrin net reinforces the clot and allows its further growth. When the clot becomes sufficiently large, it stops growing due to the narrowed vessel and the increase of flow shear rate at the surface of the clot. Its outer part is detached by the flow revealing the inner part covered by fibrin. This fibrin cap does not allow new platelets to attach at the high shear rate, and the clot stops growing. Dependence of the final clot size on wall shear rate and on other parameters is studied.


Cardone G.,University of Sannio | Durante T.,University of Salerno | Nazarov S.A.,Institute of Mechanical Engineering Problems
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik | Year: 2010

The problem about a body in a three dimensional infinite channel is considered in the framework of the theory of linear water-waves. The body has a rough surface characterized by a small parameter ε > 0 while the distance of the body to the water surface is also of order ε. Under a certain symmetry assumption, the accumulation effect for trapped mode frequencies is established, namely it is proved that, for any given d > 0 and integer N > 0, there exists a number ε (d, N) > 0 such that the problem has at least N eigenvalues in the interval (0, d) of the continuous spectrum in the case ε ∈ (0, ε (d, N)). The corresponding eigenfunctions decay exponentially at infinity, have finite energy, and imply trapped modes. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.


Gomez D.,University of Cantabria | Nazarov S.A.,Institute of Mechanical Engineering Problems | Perez E.,University of Cantabria
Networks and Heterogeneous Media | Year: 2011

We consider the Neumann spectral problem for a second order differential operator, with piecewise constants coefficients, in a domain Ωe{open} of R{double-struck}2. Here Ωe{open} is Ω ∪ ωe{open} ∪ Γ, where Ω is a fixed bounded domain with boundary Γ, ωe{open} is a curvilinear band of variable width O(e{open}), and Γ = Ω ∩ ωe{open}. The density and stiffness constants are of order O(e{open}-m-1) and O(e{open}-1 ) respectively in this band, while they are of order O(1) in Ω; m is a positive parameter and e{open} ε G (0, 1), e{open} → 0. Considering the range of the low, middle and high frequencies, we provide asymptotics for the eigenvalues and the corresponding eigenfunctions. For m > 2, we highlight the middle frequencies for which the corresponding eigenfunctions may be localized asymptotically in small neighborhoods of certain points of the boundary. © American Institute of Mathematical Sciences.


Cardone G.,University of Sannio | Nazarov S.A.,Institute of Mechanical Engineering Problems | Piatnitski A.L.,Narvik University College | Piatnitski A.L.,RAS Lebedev Physical Institute
Zeitschrift fur Angewandte Mathematik und Physik | Year: 2011

The aim of the paper is to compare the asymptotic behavior of solutions of two boundary value problems for an elliptic equation posed in a thin periodically perforated plate. In the first problem, we impose homogeneous Dirichlet boundary condition only at the exterior lateral boundary of the plate, while at the remaining part of the boundary Neumann condition is assigned. In the second problem, Dirichlet condition is also imposed at the surface of one of the holes. Although in these two cases, the homogenized problem is the same, the asymptotic behavior of solutions is rather different. In particular, the presence of perturbation in the boundary condition in the second problem results in logarithmic rate of convergence, while for non-perturbed problem the rate of convergence is of power-law type. © 2010 Springer Basel AG.


Nazarov S.A.,Institute of Mechanical Engineering Problems | Sokolowski J.,University of Lorraine
Latin American Journal of Solids and Structures | Year: 2011

The three-dimensional spectral elasticity problem is studied in an anisotropic and inhomogeneous solid with small defects, i.e., inclusions, voids, and microcracks. Asymptotics of eigenfrequencies and the corresponding elastic eigenmodes are constructed and justified. New technicalities of the asymptotic analysis are related to variable coefficients of differential operators, vectorial setting of the problem, and usage of intrinsic integral characteristics of defects. The asymptotic formulae are developed in a form convenient for application in shape optimization and inverse problems.


Nazarov S.A.,Institute of Mechanical Engineering Problems | Specovius-Neugebauer M.,University of Kassel
Archive for Rational Mechanics and Analysis | Year: 2011

Starting with a plane anisotropic homogeneous elasticity problem in a domain with an interior crack, we develop a mathematical frame where nonlinear effects in the tip zones like crack kinking or plastic zones can be modeled in an enlarged state space with the help of additional conditions at the crack tips. Using generalized Green's formulae, we show that the solutions to these problems turn out to minimize energy functionals which contain terms additional to the classical elastic energy and work of external forces. They can be interpreted as performed work and energy stored in the crack tips. Within the theory of matched asymptotic expansions, the general type of these energy functionals can be characterized in a form applicable to mechanical problems. © 2011 Springer-Verlag.


Nazarov S.A.,Institute of Mechanical Engineering Problems | Slutskij A.S.,Institute of Mechanical Engineering Problems | Sweers G.H.,University of Cologne | Sweers G.H.,Technical University of Delft
Journal of Elasticity | Year: 2012

Asymptotically optimal Korn inequalities are derived for a composite material that consists of two families of stiff rods surrounded by a homogeneous soft material. The composite plate is fixed through the protruding stiff rods only. The asymptotic behaviour is shown to be crucially different for families of connected rods and for those where the rods are isolated. © 2010 Springer Science+Business Media B.V.


PubMed | Institute of Mechanical Engineering Problems, Camille Jordan Institute and Joseph Fourier University
Type: Journal Article | Journal: Acta biotheoretica | Year: 2016

We propose to study the wound healing in Zebrafish by using firstly a differential approach for modelling morphogens diffusion and cell chemotactic motion, and secondly a hybrid model of tissue regeneration, where cells are considered as individual objects and molecular concentrations are described by partial differential equations.


PubMed | Institute of Mechanical Engineering Problems, French Institute of Health and Medical Research, Camille Jordan Institute, Unite Of Biostatistique Et Devaluation Des Therapeutiques Center Leon Berard and 5 more.
Type: | Journal: Mathematical medicine and biology : a journal of the IMA | Year: 2017

T lymphoblastic lymphoma (T-LBL) is a rare type of lymphoma with a good prognosis with a remission rate of 85%. Patients can be completely cured or can relapse during or after a 2-year treatment. Relapses usually occur early after the remission of the acute phase. The median time of relapse is equal to 1 year, after the occurrence of complete remission (range 0.2-5.9 years) (Uyttebroeck et al., 2008). It can be assumed that patients may be treated longer than necessary with undue toxicity.The aim of our model was to investigate whether the duration of the maintenance therapy could be reduced without increasing the risk of relapses and to determine the minimum treatment duration that could be tested in a future clinical trial.We developed a mathematical model of virtual patients with T-LBL in order to obtain a proportion of virtual relapses close to the one observed in the real population of patients from the EuroLB database. Our simulations reproduced a 2-year follow-up required to study the onset of the disease, the treatment of the acute phase and the maintenance treatment phase.

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