Vladimir Kotev

Dynamic properties of a delayed protein cross talk model.

In this paper we investigate how the inclusion of time delay alters the dynamical properties of the Jacob-Monod model, describing the control of the beta-galactosidase synthesis by the lac repressor protein in E. coli. The consequences of a time delay on the dynamics of this system are analysed using Hopfs theorem and Lyapunov-Andronovs theory applied to the original mathematical model and to an approximated version. Our analytical calculations predict that time delay acts as a key bifurcation parameter. This is confirmed by numerical simulations. A critical value of time delay, which depends on the values of the model parameters, is analytically established. Around this critical value, the properties of the system change drastically, allowing under certain conditions the emergence of stable limit cycles, that is self-sustained oscillations. In addition, the features of the end product repression play an essential role in the characterisation of these limit cycles: if cooperativity is considered in the end product repression, time delay higher than the mentioned critical value induce differentiated responses during the oscillations, provoking cycles of all-or-nothing response in the concentration of the species.

Design and performance study of an orthopaedic surgery robotized module for automatic bone drilling

Many orthopaedic operations involve drilling and tapping before the insertion of screws into a bone. This drilling is usually performed manually, thus introducing many problems. These include attaining a specific drilling accuracy, preventing blood vessels from breaking, and minimizing drill oscillations that would widen the hole. Bone overheating is the most important problem. To avoid such problems and reduce the subjective factor, automated drilling is recommended.

Computer and Mathematical Modelling of the Female Human Body: Determination of Mass-inertial Characteristics in Basic Body Positions.

The aim of the current article is: 1) to present 16-segmental biomechanical model of the female human body generated within a SolidWorks medium. 2) to determine the mass-inertial characteristics of the human body of the average Bulgarian female on the basis of the model. These parameters are needed in order to design wearable or rehabilitation robots and devices properly; 3) to verify the model via comparing its results for the segments of the body with analytical results from our previous investigation of these segments; 4) to predict the inertial properties of a human body in various body positions. The comparison performed between our model results and data reported in literature gives us confidence that this model could be reliably used to calculate these characteristics at random postures of the body.

Determination of Mass-Inertial Characteristics of the Human Body in Basic Body Positions: Computer and Mathematical Modelling

The aim of the current article is: 1) to determine the mass-inertial characteristics of the human body of the Bulgarian male on the basis of 16-segmental biomechanical model generated within a SolidWorks medium. They are needed in order to design wearable or rehabilitation robots and devices properly; 2) to verify the model via analytical results from our previous investigation; 3) to predict the inertial properties of a human body in various body positions. The comparison performed between our model results and data reported in literature gives us confidence that this model could be used to calculate these characteristics at random postures of the body.

An Evolution Equation of Blood Flow in a Dilated Artery

In this study we derive an evolution equation for propagation of nonlinear waves in a blood-filled artery with a local dilatation (an idealized aneurysm) in a long–wave approximation. The equation is a version of the perturbed Korteweg-deVries-Burgers equation with variable coefficients. Exact travelling-wave solution of this equation is obtained by the modified method of simplest equation where the differential equation of Riccati is used as simplest equation. A numerical example of the obtained exact solution is presented and discussed from the point of view of arterial disease mechanics.

Robotized System for Bone Drilling and Cutting in Orthopedic Surgery

Bone drilling and cutting manipulations are widespread in the orthopedic surgery. In free hand performance of them some errors such as an inaccurate penetration and dilate of bone hole, overheating, harm soft tissues could be occurring. The goal of this study is to design and develop control concept for a bone drilling and cutting robotized system. The proposed orthopedic system consists of two executive modules for drilling and cutting and common control panel. The control algorithms and programs for drilling have done and given in the paper. We are developing the control algorithms for cutting manipulation.