Discrete-time stimulation of the oscillatory and excitable forms of a FitzHugh-Nagumo model applied to the pulsatile release of luteinizing hormone releasing hormone

A model for the pulsatile release of luteinizing hormone releasing hormone (LHRH) can be reduced to a FitzHugh-Nagumo model subject to regular and quasiregular (i.e., with slight random variation in the interstimulus interval), discrete-time stimulation. The relationship of output pulse frequency (OPF) to stimulus frequency is compared between the excitable and oscillatory forms of the model and discussed in the context of results from other pulse-driven model systems. Some examples of the changes in OPF caused by quasiregular and purely Poissonian stimuli are given for the excitable case. The unstimulated system frequently interacts with the stimulation in such a complex manner that the OPF bears little resemblance to the frequency of stimulation or of the unstimulated system. Furthermore, the inability of the oscillatory form of the model to allow complete suppression of output pulses for moderate stimulation frequencies suggests that the LHRH system can be more appropriately described by the excitable form of the model. (c) 1995 American Institute of Physics.     

EBIT trapping program

The LLNL electron beam ion trap provides the world's only source of stationary highly charged ions up to bare U. This unique capability makes many new atomic and nuclear physics experiments possible.     

A Pitzer Model for Lead Oxide Solubilities in the Presence of Borate to High Ionic Strength

In this study, a hydrolysis model for lead, applicable to high ionic strength, is developed based on lead oxide solubilities as a function of ionic strength. Solubility measurements on lead oxide, α-PbO (tetragonal, red), mineral name litharge, as a function of ionic strength were conducted in NaClO₄ solutions up to I?=?0.45 mol·kg^?1, in NaCl solutions up to I?=?5.0 mol·kg^?1, and in Na₂SO₄ solutions up to I?=?5.4 mol·kg^?1, at room temperature (22.5?±?0.5 °C). The lead hydroxyl species considered in this work include the following,

$$ {\text{PbO}}\left( {\text{cr}} \right) \, + {\text{ 2H}}^{ + } \rightleftharpoons {\text{Pb}}^{ 2+ } + {\text{ H}}_{ 2} {\text{O}}\left( {\text{l}} \right) $$

(1)

$$ {\text{Pb}}^{ 2+ } + {\text{ H}}_{ 2} {\text{O}}\left( {\text{l}} \right) \rightleftharpoons {\text{PbOH}}^{ + } + {\text{ H}}^{ + } $$

(2)

$$ {\text{Pb}}^{ 2+ } + {\text{ 2H}}_{ 2} {\text{O}}\left( {\text{l}} \right) \rightleftharpoons {\text{Pb}}\left( {\text{OH}} \right)_{ 2} \left( {\text{aq}} \right) \, + {\text{ 2H}}^{ + } $$

(3)

$$ {\text{Pb}}^{ 2+ } + {\text{ 3H}}_{ 2} {\text{O}}\left( {\text{l}} \right) \rightleftharpoons {\text{Pb(OH}})_{3}^{ - } + 3{\text{H}}^{ + } $$

(4)

The equilibrium constants for Reactions (1) and (2) were taken from literature. The equilibrium constants in base 10 logarithmic units for Reactions (3) and (4) are determined in this study as ? 17.05?±?0.10 (2σ) and ? 27.99?±?0.15 (2σ), respectively, with a set of Pitzer parameters describing the interactions with Na⁺, Cl^?, and \( {\text{SO}}_{4}^{2 - } .\) In combination with the parameters from literature including those that have already been published by our group, the solution chemistry of lead in a number of media including NaCl, MgCl₂, NaHCO₃, Na₂CO₃, Na₂SO₄, NaClO₄, and their mixtures, can be accurately described in a wide range of ionic strengths.