Elimination of fast variables in stochastic nonlinear kinetics.

A reduced chemical scheme involving a small number of variables is often sufficient to account for the deterministic evolution of the concentration of the main species contributing to a reaction. However, its predictions are questionable in small systems used, for example in fluorescence correlation spectroscopy (FCS) or in explosive systems involving strong nonlinearities such as autocatalytic steps. We make precise dynamical criteria defining the validity domain of the quasi-steady-state approximation and the elimination of a fast concentration in deterministic dynamics. Designing two different three-variable models converging toward the same two-variable model, we show that the variances and covariance of the fluctuations of the slow variables are not correctly predicted using the two-variable model, even in the limit of a large system size. The more striking weaknesses of the reduced scheme are figured out in mesoscaled systems containing a small number of molecules. The results of two stochastic approaches are compared and the shortcomings of the Langevin equations with respect to the master equation are pointed out. We conclude that the description of the fluctuations and their coupling with nonlinearities of deterministic dynamics escape reduced chemical schemes.

Fisher-Kolmogorov-Petrovskii-Piskunov wave front as a sensor of perturbed diffusion in concentrated systems.

The sensitivity to perturbations of the Fisher and Kolmogorov, Petrovskii, Piskunov front is used to find a quantity revealing perturbations of diffusion in a concentrated solution of two chemical species with different diffusivities. The deterministic dynamics includes cross-diffusion terms due to the deviation from the dilution limit. The behaviors of the front speed, the shift between the concentration profiles of the two species, and the width of the reactive zone are investigated, both analytically and numerically. The shift between the two profiles turns out to be a well-adapted criterion presenting noticeable variations with the deviation from the dilution limit in a wide range of parameter values.

Study of lamina cribrosa depth and optic nerve in patients with spontaneous intracranial hypotension.

PURPOSE: The aim of this study is to analyze the lamina cribrosa depth and to study the optic nerve in patients with spontaneous intracranial hypotension. METHODS: A total of 10 eyes of the patients with spontaneous intracranial hypotension with unknown etiology (study group) and 10 eyes of healthy patients without any ophthalmological or neurological pathologies (control group) were included. The subjects were submitted to ophthalmological examination with the evaluation of visual acuity, spherical equivalent, applanation tonometry, pachymetry, axial length, retinography, computerized static perimetry (Humphrey 30-2 SITA-Standard), and OCT Spectralis with enhanced depth image, to calculate the depth of the anterior surface of the lamina cribrosa and to measure the nerve fiber layer thickness of the optic nerve. All of these parameters were compared between the two groups. RESULTS: Mean anterior surface of the lamina cribrosa depth was 447.96 ± 118.51 (313.30-632.0) µm for the spontaneous intracranial hypotension group and 292.56 ± 40.71 (247-387) µm for the control group, with a statistically significant difference between them (p = 0.001). The thickness of the nerve fiber layer did not differ significantly in the temporal (p = 0.94), nasal (p = 0.173), superior (p = 0.41), central (p = 0.36) or inferior (p = 0.5) sectors. Four eyes of patients with spontaneous intracranial hypotension showed a marked reduction in the temporal nerve fiber layer. Pachymetry (p = 0.16), axial length (p = 0.71), and intraocular pressure (p = 0.6) did not differ significantly between groups, whereas spherical equivalent (p = 0.03) was significantly different. Visual fields were normal in both groups. CONCLUSION: The translaminar gradient is determinant in the structure of the lamina cribrosa. Low intracranial pressure associated with a high translaminar gradient leads to an increased lamina cribrosa depth similar to that observed in glaucoma patients.

Comparative study of mydriasis in cataract surgery: topical versus Mydriasert versus intracameral mydriasis in cataract surgery.

PURPOSE: To compare the mydriatic efficacy and cardiovascular safety of the mydriatic options. METHODS: This was a prospective randomized analysis of 90 eyes submitted to senile cataract surgery. Group A (30 eyes) included topical mydriasis, group B (30 eyes) included mydriasis with the ophthalmic insert (Mydriasert), and group C (30 eyes) included intracameral mydriasis. Measures were mydriasis value before ophthalmic viscoelastic device (OVD) injection and at the end of surgery, blood pressure and heart rate, need for antihypertensive medication, and subjective iris stability. RESULTS: Before OVD injection and at the end of surgery, pupillary dilation was 8.1 and 7.0 mm in group A, 8.2 and 7.7 mm in group B, and 6.3 and 6.1 mm in group C, respectively. Mean surgery time was 8.3 min in group A, 8.1 min in group B, and 12.3 min in group C (p<0.05). The mean subjective iris stability score was 8.7/10 in group A, 9.3/10 in group B, and 6.1/10 in group C (p<0.05). Systolic blood pressure was greater than 180 mmHg in 9 (30%) patients in group A, 3 (10%) in group B, and 2 (6.6%) in group C. Antihypertensive medication was administered to 8 (26.6%) cases in group A, 2 (6.6%) in group B, and 0 (0%) in group C (p<0.05). CONCLUSIONS: The most effective mydriasis was obtained within the Mydriasert group, followed by the topical mydriasis group. From the cardiovascular point of view, intracameral mydriasis was the safest and topical mydriasis the least safe.