Leonid Yu. Kossovich

Free localized vibrations of a semi-infinite cylindrical shell

Free vibrations of a semi-infinite cylindrical shell, localized near the edge of the shell are investigated. The dynamic equations in the Kirchhoff-Love theory of shells are subjected to asymptotic analysis. Three types of localized vibrations, associated with bending, extensional, and super-low-frequency semi-membrane motions, are determined. A link between localized vibrations and Rayleigh-type bending and extensional waves, propagating along the edge, is established. Different boundary conditions on the edge are considered. It is shown that for bending and super-low-frequency vibrations the natural frequencies are real while for extensional vibrations they have asymptotically small imaginary parts. The latter corresponds to the radiation to infinity caused by coupling between extensional and bending modes.

Electrospun Chitosan Nanofiber Materials as Burn Dressing

Burn healing is one of the most important problems of modern surgery due to the high percentage of burns among other traumas, high lethality and disability after the treatment for burns of high surface area. Problem of the covering of large burned surfaces is still a challenge. In present study, a novel electrospun nanofibrous material is proposed as a new material for burn dressing. Versatility of electrospinning nanofiber manufacturing method allows developing various types of micro- and nanofiber materials from biocompatible and biodegradable polymers, including chitosan. Samples of chitosan nanofiber mats were created and tested as wound dressings for IIIa and IIIb degree burns. It is shown that chitosan nanofiber dressings provide effective absorbtion of exudate, ventilation of the wound, protection from infection and stimulate the process of skin tissue regeneration. Degradation of these materials prevents mechanical damage of wound during removing. The influence of thickness of materials on regenerative processes and degradation is studied. Mechanical properties of nanofiber mats are investigated.

Finite Element Model of the Patched Human Carotid

Introduction: The hemodynamic effects of carotid artery patching are not well known. Our objective was to develop a fluid-solid finite element model of the endarterectomized and patched carotid artery. Methods: Hyperelastic materials parameters were determined from studies of 8 cadaveric carotids. Blood flow characteristics were based on intraoperative data from a patient undergoing endarterectomy. Wall shear stress, cyclic strain and effective stress were computed as hemodynamic parameters with known association with endothelial injury, neointimal hyperplasia abd atherogenesis. Results: Low wall shear stress, high cyclic strain and high effective stress were identified diffusely in the carotid bulb, at the margins around the patch and in the flow divider. Conclusion: Endarterectomy and Polytetrafluoroethylene patching produce considerable abnormalities in the hemodynamics of the repaired carotid. Advanced mechanical modeling can be used to evaluate different carotid revascularization approaches to obtain optimized biomechanical and hemodynamic results for the care of patients with carotid bifurcation disease.

Analysis of the dispersion relation for an incompressible transversely isotropic elastic plate

SummaryThe dispersion relation associated with harmonic wave propagation in an incompressible, transversely isotropic elastic plate is derived. Such a material is characterized by only three material constants, contrasting with five in the corresponding compressible case. Motivated by a numerical investigation, asymptotic expansions, giving phase speed and frequency as functions of wave number, are derived in both the long and short wave regimes. These approximations, which owing to the constitutive simplifications are readily available, are shown to provide excellent agreement with the corresponding numerical solution. It is envisaged that the detailed investigation carried out in this paper will aid numerical inversion of the transform solutions often used in impact problems. Additionally, the asymptotic investigation provides the necessary basis for future studies to derive asymptotically approximate models to describe long and short wave motion.

Hybrid coarse-grained/atomistic model of “chitosan + carbon nanostructures” composites

We present a new hybrid molecular dynamics model of chitosan oligomers which is constructed specifically for studying chitosan + carbon nanostructures composites, their structure and mechanical properties. The model is derived for application within the modified molecular mechanics force field AMBER. Method of virtual sites mapping allowed to retain hexagonal rings of chitosan backbone. Mass and structural disposition of virtual atoms has been found as function of joined groups’ atoms masses and coordinates. Geometrical parameters (e.g., bond length, valence angles, torsional angles and van der Waals distances) were found using semi-empirical methods. Parameters of interaction within the AMBER force field were estimated according to structural and energy characteristics of chitosan dimers and oligomers. Model has successfully passed multilevel verification based on comparison of its behaviour with atomistic chitosan within the same force field. It appeared that the model reproduces structural and energy characteristics of chitosan and its composites with carbon nanostructures. Moreover, it allows estimation of their mechanical properties. Dynamical characteristics of composite components are also well reproduced.

The deflection of a carbon composite carbon nanotube / graphene using molecular dynamics simulation

For the first time, the dependence of the bending force on the transverse displacement of atoms in the center of the composite material consisting of graphene and parallel oriented zigzag nanotubes was studied. Mathematical modeling of the action of the needle of the atomic force microscope was carried out using the single-layer armchair carbon nanotube. Armchair nanotubes are convenient for using them as a needle of an atomic force microscope, because their edges are not sharpened (unlike zigzag tubes). Consequently, armchair nanotubes will cause minimal damage upon contact with the investigation object. The geometric parameters of the composite was revealed under the action of the bending force of 6μN.

Method of active contour for segmentation of bone systems on bitmap images

It is developed within a method of the active contours the approach, which is allowing to realize separation of a contour of a object of the image in case of its segmentation. This approach exceeds a parametric method on speed, but also does not concede to it on decision accuracy. The approach is offered within this operation will allow to realize allotment of a contour with high accuracy of the image and quicker than a parametric method of the active contours.

Usage of CT data in biomechanical research

Object of study: The investigation is focused on development of personalized medicine. The determination of mechanical properties of bone tissues based on in vivo data was considered. Methods: CT, MRI, natural experiments on versatile test machine Instron 5944, numerical experiments using Python programs. Results: The medical diagnostics methods, which allows determination of mechanical properties of bone tissues based on in vivo data. The series of experiments to define the values of mechanical parameters of bone tissues. For one and the same sample, computed tomography (CT), magnetic resonance imaging (MRI), ultrasonic investigations and mechanical experiments on single-column test machine Instron 5944 were carried out. The computer program for comparison of CT and MRI images was created. The grayscale values in the same points of the samples were determined on both CT and MRI images. The Haunsfield grayscale values were used to determine rigidity (Young module) and tensile strength of the samples. The obtained data was compared to natural experiments results for verification.

Patient-specific modeling of human cardiovascular system elements

Object of study: The research is aimed at development of personalized medical treatment. Algorithm was developed for patient-specific surgical interventions of the cardiovascular system pathologies. Methods: Geometrical models of the biological objects and initial and boundary conditions were realized by medical diagnostic data of the specific patient. Mechanical and histomorphological parameters were obtained with the help mechanical experiments on universal testing machine. Computer modeling of the studied processes was conducted with the help of the finite element method. Results: Results of the numerical simulation allowed evaluating the physiological processes in the studied object in normal state, in presence of different pathologies and after different types of surgical procedures.

Patient-specific system for prognosis of surgical treatment outcomes of human cardiovascular system

Object of study: Improvement of life quality of patients with high stroke risk ia the main goal for development of system for patient-specific modeling of cardiovascular system. This work is dedicated at increase of safety outcomes for surgical treatment of brain blood supply alterations. The objects of study are common carotid artery, internal and external carotid arteries and bulb. Methods: We estimated mechanical properties of carotid arteries tissues and patching materials utilized at angioplasty. We studied angioarchitecture features of arteries. We developed and clinically adapted computer biomechanical models, which are characterized by geometrical, physical and mechanical similarity with carotid artery in norm and with pathology (atherosclerosis, pathological tortuosity, and their combination). Results: Collaboration of practicing cardiovascular surgeons and specialists in the area of Mathematics and Mechanics allowed to successfully conduct finite-element modeling of surgical treatment taking into account various features of operation techniques and patching materials for a specific patient. Numerical experiment allowed to reveal factors leading to brain blood supply decrease and atherosclerosis development. Modeling of carotid artery reconstruction surgery for a specific patient on the basis of the constructed biomechanical model demonstrated the possibility of its application in clinical practice at approximation of numerical experiment to the real conditions.