A 3D mathematical model of coupled stem cell-nutrient dynamics in myocardial regeneration therapy.

Stem cell therapy is a promising treatment for the regeneration of myocardial tissue injured by an ischemic event. Mathematical modeling of myocardial regeneration via stem cell therapy is a challenging task, since the mechanisms underlying the processes involved in the treatment are not yet fully understood. Many aspects must be accounted for, such as the spread of stem cells and nutrients, chemoattraction, cell proliferation, stages of cell maturation, differentiation, angiogenesis, stochastic effects, just to name a few. In this paper we propose a 3D mathematical model with a free boundary that aims to provide a qualitative description of some main aspects of the stem cell regenerative therapy in a simplified scenario. The paper mainly focuses on the description of the shrinking of the necrotic core during treatment. The stem cell and nutrients dynamics are described through coupled reaction-diffusion problems. Proliferation, chemoattraction, tissue regeneration and nutrient consumption are included in the model.

Short communication: placental collagen and premature rupture of fetal membranes.

Collagen content of 43 placentae from clinically normal females who went into labour spontaneously was determined by assaying hydroxyproline. In 23 cases the membranes ruptured before or at the beginning of labour, and in 20 cases the rupture was intrumentally provoked during the expulsive period. In the group with prematurely ruptured membranes, hydroxyproline concentration was 11.52 +/- 1.83 micrograms/mg lyophilized tissue, whereas in the other group concentration was 20.29 +/- 4.32 micrograms/mg tissue. These data disclose a much lower collagen placental content in the group with premature rupturing of the membranes.

The low hydroxyproline content of prematurely ruptured human fetal membranes.

Since collagen is one of the main factors responsible for the mechanical properties of soft tissue, we have determined the hydroxyproline content of the placental amnion, the free amnion and the chorion of 32 unruptured and 25 prematurely ruptured human fetal membranes. The hydroxyproline content of prematurely ruptured membranes was approximately 50% lower than in unruptured membranes. Hydroxyproline (microgram/mg lyophilized tissue), reported as mean +/- SD, was: 19.46 +/- 3.60 vs 37.53 +/- 8.93 for placental amnion; 16.97 +/- 3.93 vs 33.00 +/- 8.25 for free amnion, and 7.74 +/- 3.00 vs 13.23 +/- 3.95 for the chorion. This finding and the known decrease of hydroxyproline content of the amnion towards the end of gestation in normally evolving pregnancies suggest that an abnormally low collagen content may be the general cause of prematurely ruptured human fetal membranes.

Dynamics of mouse rod phototransduction and its sensitivity to variation of key parameters.

The deep understanding of the biochemical and biophysical basis of visual transduction, makes it ideal for systems-level analysis. A sensitivity analysis is presented for a self-consistent set of parameters involved in mouse phototransduction. The organising framework is a spatio-temporal mathematical model, which includes the geometry of the rod outer segment (ROS), the layered array of the discs, the incisures, the biochemistry of the activation/deactivation cascade and the biophysics of the diffusion of the second messengers in the cytoplasm and the closing of the cyclic guanosine monophosphate (cGMP) gated cationic channels. These modules include essentially all the relevant geometrical, biochemical and biophysical parameters. The parameters are selected from within experimental ranges, to obey basic first principles such as conservation of mass and energy fluxes. By means of the model they are compared to a large set of experimental data, providing a strikingly close match. Following isomerisation of a single rhodopsin R * (single photon response), the sensitivity analysis was carried out on the photo-response, measured both in terms of number of effector molecules produced, and photocurrent suppression, at peak time and the activation and recovery phases of the cascade. The current suppression is found to be very sensitive to variations of the catalytic activities, Hill's coefficients and hydrolysis rates and the geometry of the ROS, including size and shape of the incisures. The activated effector phosphodiesterase (PDE *) is very sensitive to variations of catalytic activity of G-protein activation and the average lifetimes of activated rhodopsin R * and PDE *; however, they are insensitive to geometry and variations of the transduction parameters. Thus the system is separated into two functional modules, activation/deactivation and transduction, each confined in different geometrical domains, communicating through the hydrolysis of cGMP by PDE *, and each sensitive to variations of parameters only in its own module.

Reduction of hydroxyproline content in the vessels of the human umbilical cord in premature rupture.

The hydroxyproline content of the amnion and the umbilical vessels obtained from cases in which the fetal membranes were instrumentally or prematurely ruptured was assayed. Hydroxyproline concentration (in micrograms/mg) in the latter group was 23.76, 16.79 and 17.86 in the amnion, artery and vein, whereas in the former the corresponding values were 42.20, 26.61 and 32.48. These results show that, in addition to a decrease in the amnion, hydroxyproline is lowered also in the umbilical vessels, suggesting that the reduction in the collagen in the fetal membranes is probably a particular manifestation of a general metabolic deficiency.

Very high collagen increase in placentae of smoking mothers.

In 55 placentae, collected at term from clinically normal pregnancies, hydroxyproline was assayed. Thirty were from mothers who smoke and 25 from nonsmokers. In placentae of smokers, hydroxyproline concentration was 42.77 +/- 8.77 micrograms/mg of tissue and in these of nonsmokers 22.52 +/- 7.46 micrograms/mg. Such high a difference discloses a large increment in placental collagen production in smokers, which may account for some of the noxious effects of tobacco on pregnancy.

PIP: Hydroxyproline was assayed in 55 placentae, collected at term from clinically normal pregnancies. 30 came from mothers who smoke and 25 from nonsmokers. In the placentae of smokers, hydroxyproline concentration was 42.77 +or- 8.77 mcg/mg of tissue and in those of nonsmokers, 22.52 +or- 7.46 mcg/mg. Such a high difference discloses a large increment in placental collagen production among smokers, which may account for some of the noxious effects of tobacco on pregnancy.

Mathematical model of the spatio-temporal dynamics of second messengers in visual transduction.

A model describing the role of transversal and longitudinal diffusion of cGMP and Ca(2+) in signaling in the rod outer segment of vertebrates is developed. Utilizing a novel notion of surface-volume reaction and the mathematical theories of homogenization and concentrated capacity, the diffusion of cGMP and Ca(2+) in the inter-disc spaces is shown to be reducible to a one-parameter family of diffusion processes taking place on a single rod cross section; whereas the diffusion in the outer shell is shown to be reducible to a diffusion on a cylindrical surface. Moreover, the exterior flux of the former serves as a source term for the latter, alleviating the assumption of a well-stirred cytosol. A previous model of visual transduction that assumes a well-stirred rod outer segment cytosol (and thus contains no spatial information) can be recovered from this model by imposing a "bulk" assumption. The model shows that upon activation of a single rhodopsin, cGMP changes are local, and exhibit both a longitudinal and a transversal component. Consequently, membrane current is also highly localized. The spatial spread of the single photon response along the longitudinal axis of the outer segment is predicted to be 3-5 microm, consistent with experimental data. This approach represents a tool to analyze point-wise signaling dynamics without requiring averaging over the entire cell by global Michaelis-Menten kinetics.