The structure of the double layer on the boundary between solid and liquid phases is described by various models, of which the Stern-Gouy-Chapman model is still commonly accepted. Generally, the solid phase is charged, which also causes the distribution of the electric charge in the adjacent diffuse layer in the liquid phase. We propose a new mathematical model of electromigration considering the high deviation from electroneutrality in the diffuse layer of the double layer when the liquid phase is composed of solution of weak multivalent electrolytes of any valence and of any complexity. The mathematical model joins together the Poisson equation, the continuity equation for electric charge, the mass continuity equations, and the modified G-function. The model is able to calculate the volume charge density, electric potential, and concentration profiles of all ionic forms of all electrolytes in the diffuse part of the double layer, which consequently enables to calculate conductivity, pH, and deviation from electroneutrality. The model can easily be implemented into the numerical simulation software such as Comsol. Its outcome is demonstrated by the numerical simulation of the double layer composed of a charged silica surface and an adjacent liquid solution composed of weak multivalent electrolytes. The validity of the model is not limited only to the diffuse part of the double layer but is valid for electromigration of electrolytes in general.

• Klíčová slova
• Double layer, Electric charge, Electromigration, Electroneutrality, Poisson equation,
• MeSH
• elektrická vodivost MeSH
• elektrolyty * MeSH
• ionty MeSH
• roztoky MeSH
• teoretické modely * MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH
• Názvy látek
• elektrolyty * MeSH
• ionty MeSH
• roztoky MeSH

The previously developed mathematical model of CD4+ lymphocyte dynamics in HIV infection incorporated a homeostatic mechanism regulating production of both CD4+ and CD8+ lymphocytes. The model simulated the CD4+ lymphocyte dynamics well, but simulation of CD8+ lymphocyte values was not satisfactory, because simulated numbers of these cells increased even at later stages of infection, when no further increase was observed in infected individuals. Modifications of the model were attempted to obtain better simulation results assuming the influence of HIV infection on CD8+ lymphocyte maturation. Satisfactory results were obtained, if the influx of immature CD4+ and CD8+ lymphocytes was constrained by HIV infection. This modified version was then used for simulation of the anti-CD8 antibody administration effect in HIV-infected persons.

• MeSH
• CD8-pozitivní T-lymfocyty imunologie   MeSH
• HIV infekce imunologie   MeSH
• lidé MeSH
• matematické výpočty počítačové * MeSH
• modely imunologické * MeSH
• Check Tag
• lidé MeSH
• Publikační typ
• časopisecké články MeSH

• MeSH
• klasické podmiňování * MeSH
• matematika MeSH
• ptáci MeSH
• teoretické modely * MeSH
• zvířata MeSH
• Check Tag
• zvířata MeSH
• Publikační typ
• časopisecké články MeSH

• MeSH
• chřipka lidská epidemiologie   MeSH
• epidemický výskyt choroby * MeSH
• lidé MeSH
• teoretické modely * MeSH
• Check Tag
• lidé MeSH
• Publikační typ
• anglický abstrakt MeSH
• časopisecké články MeSH

Plants can adjust their competitive traits for acquiring resources in response to the relatedness of their neighbours. Recently, it has been found that plants can alter their investment in traits of attracting pollinators based on kin-interaction. We build a mathematical model to study the optimal floral display to attract pollinators in a patch with kin structure. We show that when plants can attract pollinators to a whole patch through the magnet effect, the floral display should increase with the increasing relatedness of the plants in the patch. Our model also indicates that increasing investment into attracting pollinators is a form of altruism, reducing a plant's own seed production but increasing the contribution of other plants to its fitness. We also predict that seed production should increase with increasing relatedness in the patch. Our model provides the explicit conditions when resource allocation to attract pollinators in response to neighbour relatedness can be favoured by kin selection, and a possible mechanism for the plants to deal with the consequent loss of pollinator diversity and abundance.

• Klíčová slova
• Altruism, Cooperation, Magnet effect, Optimal allocation, Pollinator attraction,
• MeSH
• květy * MeSH
• opylení * MeSH
• rostliny MeSH
• semena rostlinná MeSH
• teoretické modely MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH

PURPOSE: In 2010, approximately 14.9 million babies (11.1%) were born preterm. Because preterm infants suffer from an immature thermoregulatory system they have difficulty maintaining their core body temperature at a constant level. Therefore, it is essential to maintain their temperature at, ideally, around 37°C. For this, mathematical models can provide detailed insight into heat transfer processes and body-environment interactions for clinical applications. METHODS: A new multi-node mathematical model of the thermoregulatory system of newborn infants is presented. It comprises seven compartments, one spherical and six cylindrical, which represent the head, thorax, abdomen, arms and legs, respectively. The model is customizable, i.e. it meets individual characteristics of the neonate (e.g. gestational age, postnatal age, weight and length) which play an important role in heat transfer mechanisms. The model was validated during thermal neutrality and in a transient thermal environment. RESULTS: During thermal neutrality the model accurately predicted skin and core temperatures. The difference in mean core temperature between measurements and simulations averaged 0.25±0.21°C and that of skin temperature averaged 0.36±0.36°C. During transient thermal conditions, our approach simulated the thermoregulatory dynamics/responses. Here, for all infants, the mean absolute error between core temperatures averaged 0.12±0.11°C and that of skin temperatures hovered around 0.30°C. CONCLUSIONS: The mathematical model appears able to predict core and skin temperatures during thermal neutrality and in case of a transient thermal conditions.

• Klíčová slova
• Bioheat model, Computer simulation, Physiological processes, Premature infants, Thermoregulation,
• MeSH
• biologické modely * MeSH
• gestační stáří MeSH
• lidé MeSH
• novorozenec fyziologie   MeSH
• počítačová simulace MeSH
• předčasný porod patofyziologie   MeSH
• tepelná vodivost MeSH
• teplota kůže MeSH
• teplota MeSH
• termoregulace * MeSH
• vysoká teplota MeSH
• životní prostředí MeSH
• Check Tag
• lidé MeSH
• novorozenec fyziologie   MeSH
• Publikační typ
• časopisecké články MeSH

A mathematical model of peripheral blood stem cell harvests was developed, taking two new parameters R (number of recruited cells/minute) and E(f) (efficiency of collection) into consideration in addition to concentrations and collected amounts of cells. This model was tested on 241 harvest procedures in cancer patients (chemotherapy+G-CSF stimulation), donors of allogeneic PBSC, and platelet donors, using different collection procedures, with a Cobe Spectra Cell separator. The relationships between preapheresis concentrations, R, E(f) and harvested amounts of cells were complex, and different for different harvest procedures and populations of donors. However, invariably, recruitment played an important role and contributed significantly to the final harvest in all types of cells studied. For example, for the patient group, mean recruitment was 1.3 x 10(6) CD34+ cells/min and the amount of recruited cells corresponded to 65% of all collected cells. Recruitment was significantly influenced by pretreatment with chemo-therapy and/or radiotherapy. The mean recruitment values for the subgroups with limited, moderate, and extensive pretreatment were 1.65 x 10(6), 0.87 x 10(6), and 0.32 x 10(6) CD34+ cells released per minute, respectively. The finding of a quick and massive recruitment phenomenon may stimulate further research into hematopoiesis in order to maximize harvested cells.

• MeSH
• hematopoéza MeSH
• kinetika MeSH
• lidé MeSH
• mobilizace hematopoetických kmenových buněk * MeSH
• počet buněk MeSH
• separace buněk metody   MeSH
• separace krevních složek MeSH
• teoretické modely * MeSH
• Check Tag
• lidé MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH

Simul 5 Complex is a one-dimensional dynamic simulation software designed for electrophoresis, and it is based on a numerical solution of the governing equations, which include electromigration, diffusion and acid-base equilibria. A new mathematical model has been derived and implemented that extends the simulation capabilities of the program by complexation equilibria. The simulation can be set up with any number of constituents (analytes), which are complexed by one complex-forming agent (ligand). The complexation stoichiometry is 1:1, which is typical for systems containing cyclodextrins as the ligand. Both the analytes and the ligand can have multiple dissociation states. Simul 5 Complex with the complexation mode runs under Windows and can be freely downloaded from our web page http://natur.cuni.cz/gas. The article has two separate parts. Here, the mathematical model is derived and tested by simulating the published results obtained by several methods used for the determination of complexation equilibrium constants: affinity capillary electrophoresis, vacancy affinity capillary electrophoresis, Hummel-Dreyer method, vacancy peak method, frontal analysis, and frontal analysis continuous capillary electrophoresis. In the second part of the paper, the agreement of the simulated and the experimental data is shown and discussed.

• MeSH
• cyklodextriny MeSH
• elektroforéza kapilární * MeSH
• počítačová simulace MeSH
• stereoizomerie MeSH
• teoretické modely * MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH
• Názvy látek
• cyklodextriny MeSH

BACKGROUND: The acidity of human body fluids, expressed by the pH, is physiologically regulated in a narrow range, which is required for the proper function of cellular metabolism. Acid-base disorders are common especially in intensive care, and the acid-base status is one of the vital clinical signs for the patient management. Because acid-base balance is connected to many bodily processes and regulations, complex mathematical models are needed to get insight into the mixed disorders and to act accordingly. The goal of this study is to develop a full-blood acid-base model, designed to be further integrated into more complex human physiology models. RESULTS: We have developed computationally simple and robust full-blood model, yet thorough enough to cover most of the common pathologies. Thanks to its simplicity and usage of Modelica language, it is suitable to be embedded within more elaborate systems. We achieved the simplification by a combination of behavioral Siggaard-Andersen's traditional approach for erythrocyte modeling and the mechanistic Stewart's physicochemical approach for plasma modeling. The resulting model is capable of providing variations in arterial pCO2, base excess, strong ion difference, hematocrit, plasma protein, phosphates and hemodilution/hemoconcentration, but insensitive to DPG and CO concentrations. CONCLUSIONS: This study presents a straightforward unification of Siggaard-Andersen's and Stewart's acid-base models. The resulting full-blood acid-base model is designed to be a core part of a complex dynamic whole-body acid-base and gas transfer model.

• Klíčová slova
• Acid-base modeling, Behavioral acid-base, Modelica, Physicochemical acid-base, Physiolibrary, Physiology, Siggaard-Andersen,
• MeSH
• acidobazická rovnováha * fyziologie   MeSH
• biologické modely * MeSH
• chemické modely * MeSH
• koncentrace vodíkových iontů MeSH
• lidé MeSH
• poruchy acidobazické rovnováhy diagnóza   epidemiologie   patofyziologie   MeSH
• teoretické modely * MeSH
• Check Tag
• lidé MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH

• MeSH
• akční potenciály MeSH
• matematika MeSH
• neurony fyziologie   MeSH
• teoretické modely MeSH
• Publikační typ
• časopisecké články MeSH