Biomedical subjects

K Y Volokh

Publications and source records attributed to K Y Volokh.

8 recordsLinked to original sources

PubMed2006

Stresses in growing soft tissues.

Biochemical processes of tissue growth lead to production of new proteins, cells, and other material particles at the microscopic level. At the macroscopic level, growth is marked by the change of the tissue shape and mass. In addition, the appearance of the new material particles is generally accompanied by deformation and, consequently, stresses in the surrounding material. Built upon a microscopic toy-tissue model mimicking the mechanical processes of mass supply, a simple phenomenological theory of tissue growth is used in the present work for explaining residual stresses in arteries and studying stresses around growing solid tumors/multicell spheroids. It is shown, in particular, that the uniform volumetric growth can lead to accumulation of residual stresses in arteries because of the material anisotropy. This can be a complementary source of residual stresses in arteries as compared to the stresses induced by non-uniform tissue growth. It is argued that the quantitative assessment of the residual stresses based on in vitro experiments may not be reliable because of the essential stress redistribution in the tissue samples under the cutting process. Concerning the problem of tumor growth, it is shown that the multicell spheroid or tumor evolution depends on elastic properties of surrounding tissues. In good qualitative agreement with the experimental in vitro observations on growing multicell spheroids, numerical simulations confirm that stiff hosting tissues can inhibit tumor growth.

Animals↗

PubMed2006

Prediction of femoral head collapse in osteonecrosis.

The femoral head deteriorates in osteonecrosis. As a consequence of that, the cortical shell of the femoral head can buckle into the cancellous bone supporting it. In order to examine the buckling scenario we performed numerical analysis of a realistic femoral head model. The analysis included a solution of the hip contact problem, which provided the contact pressure distribution, and subsequent buckling simulation based on the given contact pressure. The contact problem was solved iteratively by approximating the cartilage by a discrete set of unilateral linear springs. The buckling calculations were based on a finite element mesh with brick elements for the cancellous bone and shell elements for the cortical shell. Results of 144 simulations for a variety of geometrical, material, and loading parameters strengthen the buckling scenario. They, particularly, show that the normal cancellous bone serves as a strong supporting foundation for the cortical shell and prevents it from buckling. However, under the development of osteonecrosis the deteriorating cancellous bone is unable to prevent the cortical shell from buckling and the critical pressure decreases with the decreasing Young modulus of the cancellous bone. The local buckling of the cortical shell seems to be the driving force of the progressive fracturing of the femoral head leading to its entire collapse. The buckling analysis provides an additional criterion of the femoral head collapse, the critical contact pressure. The buckling scenario also suggests a new argument in speculating on the femoral head reinforcement. If the entire collapse of the femoral head starts with the buckling of the cortical shell then it is reasonable to place the reinforcement as close to the cortical shell as possible.

Computer Simulation↗

PubMed2006

Compressibility of arterial wall in ring-cutting experiments.

It is common practice in the arterial wall modeling to assume material incompressibility. This assumption is driven by the observation of the global volume preservation of the artery specimens in some mechanical loading experiments. The global volume preservation, however, does not necessarily imply the local volume preservation - incompressibility. In this work, we suggest to use the arterial ring- cutting experiments for the assessment of the local incompressibility assumption. The idea is to track the local stretches of the marked segments of the arterial ring after the stress-relieving cut. In the particular case of the rabbit thoracic artery, considered in this work, the following criteria for radial stretches come from preliminary analysis. If after the radial cut the marked segments shorten at the inner surface of the wall and lengthen at the outer surface while remaining unchanged in the middle of the wall then material is locally incompressible. If, however, the marked segments remain unchanged at the surfaces while lengthening in the middle of the wall then the material is locally compressible. Any other scenario would be an indication of the improper modeling assumptions, i.e. residual stresses are not relieved or material constants are inaccurate etc. It is believed that the proposed approach can be successfully implemented in experiments shedding new light on the arterial incompressibility issue.

Animals↗

PubMed2005

Growth, anisotropy, and residual stresses in arteries.

A simple phenomenological theory of tissue growth is used in order to demonstrate that volumetric growth combined with material anisotropy can lead to accumulation of residual stresses in arteries. The theory is applied to growth of a cylindrical blood vessel with the anisotropy moduli derived from experiments. It is shown that bending resultants are developed in the ring cross-section of the artery. These resultants may cause the ring opening or closing after cutting the artery in vitro as it is observed in experiments. It is emphasized that the mode of the arterial ring opening is affected by the parameters of anisotropy.

Animals↗

PubMed2005

On Eulerian constitutive equations for modeling growth and residual stresses in arteries.

Recently Volokh and Lev (2005) argued that residual stresses could appear in growing arteries because of the arterial anisotropy. This conclusion emerged from a continuum mechanics theory of growth of soft biological tissues proposed by the authors. This theory included Lagrangian constitutive equations, which were formulated directly with respect to the reference configuration. Alternatively, it is possible to formulate Eulerian constitutive equations with respect to the current configuration and to 'pull them back' to the reference configuration. Such possibility is examined in the present work. The Eulerian formulation of the constitutive equations is used for a study of arterial growth. It is shown, particularly, that bending resultants are developed in the ring cross-section of the artery. These resultants may cause the ring opening or closing after cutting the artery in vitro as it is observed in experiments. It is remarkable that the results of the present study, based on the Eulerian constitutive equations, are very similar to the results of Volokh and Lev (2005), based on the Lagrangian constitutive equations. This strengthens the authors' argument that anisotropy is a possible reason for accumulation of residual stresses in arteries. This argument appears to be invariant with respect to the mathematical description.

Arteries↗

PubMed2004

Mathematical framework for modeling tissue growth.

A phenomenological continuum mechanics framework for modeling growth of living tissues is proposed. Tissue is considered as an open system where mass is not conserved. The momentum balance is completed with the full-scale mass balance. Constitutive equations define simple growing materials. 'Thermoelastic' formulation of a simple growing material is specified. Within this framework traction free growth of a cylinder is considered. It is shown that the theory accommodates the case where stresses are not generated in uniform volumetric growth. It is also found that surface growth corresponds to a boundary layer solution of the governing equations.

Animals↗

PubMed2004

A simple phenomenological theory of tissue growth.

A simple phenomenological framework for modeling growth of living tissues is proposed. Growth is defined as a change of mass and configuration of the tissue. Tissue is considered as an open system where mass conservation is violated and the full-scale mass balance is applied. A possible structure of constitutive equations is discussed with reference to simple growing materials. 'Thermoelastic' formulation of the simple growing material is specified. Within this framework traction free growth of cylindrical and spherical bodies is examined. It is shown that the theory accommodates the case where stresses are not generated in uniform volumetric growth. It is also found that surface growth corresponds to a boundary layer solution of the governing equations. This finding proves the ability of continuum mechanics to describe surface growth. The latter is contrary to the usual use of purely kinematical theories, which do not involve balance and constitutive equations, for treating surface growth.

Biomechanical Phenomena↗

PubMed2000

Tensegrity architecture explains linear stiffening and predicts softening of living cells.

The problem of theoretical explanation of the experimentally observed linear stiffening of living cells is addressed. This explanation is based on Ingber's assumption that the cell cytoskeleton, which enjoys tensegrity architecture with compressed microtubules that provide tension to the microfilaments, affects the mechanical behavior of the living cell. Moreover, it is shown that the consideration of the extreme flexibility of microtubules and the unilateral response of microfilaments is crucial for the understanding of the living cell overall behavior. Formal nonlinear structural analysis of the cell cytoskeleton under external mechanical loads is performed. For this purpose, a general computer model for tensegrity assemblies with unilateral microfilaments and buckled microtubules is developed and applied to the theoretical analysis of the mechanical response of 2D and 3D examples of tensegrity cells mimicking the behavior of real living cells. Results of the computer simulations explain the experimentally observed cell stiffening. Moreover, the theoretical results predict the possible existence of a transient softening behavior of cells, a phenomenon, which has not been observed in experiments yet.

Biomechanical Phenomena↗