The Julicher and Prost (1995) model of cooperative motion of molecular motors is discussed. Some inaccuracies in
original reasoning are corrected. Explicit analytical solution of model's equations is derived. Previously unexplored type
of cooperative motion (reverse motion in asymmetric potential in absence of external force) is described.
The mathematical model of clearing agent penetration at topical administration of the agent on skin surface has been
developed. Two-dimensional plane case has been considered. Skin was presented as multilayer medium with different
diffusion coefficients in each layer and boundary conditions between adjacent layers. Analytical solution of the boundary
problem has been obtained and approximation for large time interval has been derived.
Result of Monte Carlo simulations of skin optical clearing is presented. The model calculations were carried out with the
aim of studying of spectral response of skin under immersion liquids action and calculation of enhancement of light
penetration depth. In summary, we have shown that: 1) application of glucose, propylene glycol and glycerol produced
significant decreasing of light scattering in different skin layers; 2) maximal clearing effect will be obtained in case of
optical clearing of skin dermis, however, absorbed light fraction in skin dermis changed insignificantly, independently
from clearing agent and place it administration; 4) in contrast to it, the light absorbed fraction in skin adipose layer
increased significantly in case of optical clearing of skin dermis. It is very important because it can be used for
development of optical methods of obesity treatment.
The mathematical model of clearing agent diffusion after intradermal injection has been developed. Skin was presented
as multilayer medium, but one layer with proper boundary conditions is considered. Analytical solution of the boundary
problem for small and large time intervals is obtained.
Result of Monte Carlo simulations of skin optical clearing is presented. The model calculations were carried out with the aim of studying of spectral response of skin under immersion liquids action and calculation of enhancement of light penetration depth. In summary, we have shown that: 1) application of glucose, propylene glycol and glycerol produced significant decreasing of light scattering in different skin layers; 2) maximal clearing effect will be obtained in case of optical clearing of skin dermis, however, absorbed light fraction in skin dermis changed insignificantly, independently from clearing agent and place it administration; 4) in contrast to it, the light absorbed fraction in skin adipose layer increased significantly in case of optical clearing of skin dermis. It is very important because it can be used for development of optical methods of obesity treatment.
We present experimental results on optical properties of the human skin controlled by administration ofthe 40%-glucose
solution. In vivo reflectance spectra of the human skin were measured. Results of the experimental study of influence of
the 40%-glucose solution on reflectance spectra of the human skin are presented. A significant decrease of reflectance of
the human skin under action of the osmotic agent is demonstrated. The experiments show that administration of the
glucose solution allows for effective control of tissue optical characteristics, that makes skin more transparent, thereby
increasing the ability of light penetration through the tissue. Laser Doppler flowmetry has been used for study of skin
blood microcirculation under the action of the glucose solution. Results of the experiments demonstrated that at the
action of the glucose solution blood perfusion and blood concentration increase, however the mean blood velocity does
not change. The presented results can be used in developing functional imaging techniques, including OCT and
reflectance spectroscopy. A potential benefit of the optical clearing technique is the improvement of laser therapeutic
techniques that rely on sufficient light penetration to a target embedded in tissue.
Mathematical model of organelle transport by few molecular motors along filament is presented. Each motor is described as mechanochemical system, which consists of 3 elastically coupled Brownian particles and can be in different intrinsic states, jumping from one discrete filament bound site to other. Rigid or elastic coupling between motors and "cargo" are considered. Asymptotic analysis of organelle movement is performed and macroscopic parameters (average velocity and effective diffusion coefficient) are calculated.
Mathematical models construction of motor proteins dynamics at a transport of intracellular organelles is considered with taking into account the rheological properties of organelle membrane and cytoplasm. The possibility of extension of the existing idealized models of hard motors and a transported particle on the this general case is discussed.
In the report the mathematical model of melanosome transport along filaments in intact and UV-irradiated melanocytes is submitted. Processes at three levels are considered: dynamics of the single motor, transport of melanosome by ensemble of motors, and melanosomes distribution along microtubules. A single motor is considered as <<stochastic ratchet>>; modeling of transitions between internal states described by chemical kinetics equations allows to determine "force-velocity" dependence for motor. The ensemble of motors is described by system of equations for average motor velocities, and transported melanosome moves with average velocity, which in turn is determined by sum of force generated by each elastic-coupled motor (self-consistence problem). Distribution of melanosomes along a microtubule is described by system of equations for bidirectional motion of attached melanosome under coordinated action of "plus-end" and "minus-end" motors and free diffusion of unattached melanosomes. Influence of UV-radiation is resulted in change of number of each type motors simultaneously linked to one melanosome. It induces redistribution of melanosomes between centre and periphery of melanocyte.
The semi-phenomenological model of epidermal cell dynamics is submitted. The model takes into account three types of basal layer keratinocytes (stem, transient amplifying, terminally differentiated), distribution of first two types cells on mitotic cycle stages and resting states, keratinocytes-lymphocytes interactions that provide a positive feedback loop, influence of more differentiated cells on their progenitors that provide a negative feedback loop. Simplified model are developed and its stationary solutions are received. The opportunity of interpretation of some received modes as corresponding to various stages of psoriasis is discussed. Influence of UV-radiation on transitions between various modes of epidermis functioning is qualitatively analyzed.
Cascade of reactions of cAMP-dependent signaling pathway in melanocytes is investigated by mathematical modeling. Model takes into account (alpha) -melanocyte stimulating hormone binding to melanocortin-1 receptor, adenylate cyclase activation by G-protein, increase of the intracellular cAMP concentration, PKA activation by cAMP, CREB phosphorylation by PKA, microphthalmia gene expression, microphthalmia binding to tyrosinase gene promoter, increase of tyrosinase synthesis. Positive and negative feedback loops of this system are analyzed.
In the paper the mathematical model of UV-induced PKC activation is presented. Phosphorylation of membrane receptors, activation of phospholipases and phospholipids turnover, diacylglycerol, inositol trisphosphate and arachidonic acid production, calcium releasing are taken into account.
Tyrosinase is the key enzyme of melanogenesis with unusual enzyme kinetics. Protein kinase C plays an important role in regulating of tyrosinase activity. In the paper the mathematical model of PKC-DAG-dependent signal transduction pathway for UV-radiation is presented.
KEYWORDS: Absorption, Photons, Mathematical modeling, Scattering, Skin, Optical properties, Monte Carlo methods, Tissue optics, Solar radiation models, Data modeling
In the work the mathematical model of melanogenesis is presented that allows to predict a qualitative change of epidermis absorption and scattering under UV-irradiation. Epidermal sublayers and inhomogeneous melanin distribution are taken into account.
Experimental study and computer modeling were used to investigate the optical properties of melanin in the skin and skin-like phantoms. To investigate light scattering by melanosomes in skin we made skin-like phantoms on the base of gelatin with different content of melanin particles. Spectra of total transmittance and diffuse reflectance of the phantoms were obtained in the wavelength range from 400 to 800 nm. Absorption and reduced scattering coefficients of melanin were calculated. Mie theory was used to estimate the optical properties of melanin particles. Wavelength dependence of refractive indices of eumelanin particles (isolated and purified from the ink of the cuttlefish Sepia officinalis) and synthetic melanin particles was estimated.
'Me1anin screen" effect, i.e. the increase of epiderinal absorption due to UV-induced melanogenesis leads to decrease of effective doses of UVA-radiation at subsequent photochemotherapy sessions. In the work the mathematical model of melanogenesis. induced by sequence of UVA-radiation "pulses" ,is developed. Processes on cellular, subcellular and molecular levels are described. The structure of equations allows to split the problem and to consider differential equations system at given intensity, to calculate a melanin distribution and absorption coefficient, to define a new value of intensity etc. The melanin content in basal and upper layers is defined. The time and dose dependencies of epidermal absorption coefficient are determined. Thus using the presented model it is possible to inspect a modification of modes during PUVAtherapy.
The mathematical model of processes in UV-irradiated furocoumarin-sensitized epidermis is presented taking into account the mutual influence of keratinocytes and melanocytes populations. The model describes epidermis as a hierarchical structure on tissue (keratinocytes-melanocytes cooperation, melanin screen formation), cellular (proliferation and differentiation, transitions between subpopulations), subcellular (cell movement on mitotic cycle, generation, maturing and migration of melanosomes), and molecular (melanin synthesis, processes of DNA damage and repair, molecular signal transduction) levels.
In the work the mathematical model is presented which describes the processes in the epidermis sensitized by the furocoumarins under UVA-radiation. The model describes the processes at three levels: molecular (the photochemical transformations of the psoralen molecules and their reactions with the DNA-molecules), cellular (proliferation, differentiation and repairing of injuries), and tissue (humoral regulation, space-time cell dynamics in the epidermis). The results of the numerical simulations of both the latent period and psoriasis manifestation are given. The therapeutical effect of the UV-radiation is considered in the framework of the model.
Some biophysical and mathematical aspects of development of a computer model of low- intensity laser radiation influence on the dynamics of the x-irradiated bone marrow tissue hemopoiesis are discussed.
In this work the mathematical model presented describes the processes in the epidermis sensitized by the furocoumarins under UVA-radiation of pulse laser.
Some biophysical and mathematical aspects of development of computer model of low-intensity laser radiation influence of the dynamics of the X-irradiated bone marrow tissue hemopoiesis are discussed.
The mathematical model is presented of low-intensity laser radiation influence on the dynamics of the X-irradiated bone marrow tissue erythropoiesis. The process of recovering in postradiation stage of the cells of erythroid series has been investigated for various parameters of laser emission.
The mathematical model is presented of low-intensity laser radiation influence on the dynamics of the X-irradiated bone marrow tissue erythropoiesis. The process of recovering in postradiation stage of the cells of erythroid series has been investigated for various parameters of laser emission.
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