Vladimir Alexandrovich Marchenko

Dispersion estimates for one-dimensional Schrödinger and Klein-Gordon equations revisited

It is shown that for a one-dimensional Schrodinger operator with a potential whose first moment is integrable the elements of the scattering matrix are in the unital Wiener algebra of functions with integrable Fourier transforms. This is then used to derive dispersion estimates for solutions of the associated Schrodinger and Klein-Gordon equations. In particular, the additional decay conditions are removed in the case where a resonance is present at the edge of the continuous spectrum. Bibliography: 29 titles.

Respiratory activity generated by semi-isolated medullo-spinal preparation and recorded from the phrenic nerve of newborn rats

Inspiratory activity generated by superfusedin situ semi-isolated medullo-spinal preparations of newborn (one-day-old) and four- to five-day-old rats was recorded from then. phrenicus before and after transverse sectioning of the ventrolateral part of the medulla (VLPM) at different levels. Under similar experimental conditions, the frequency of inspiratory discharges (ID) and their integral intensity, reflecting the volume and temporal parameters of inspiration, are much lower in one-day-old rats, as compared with those in four- to five-day-old animals. Specific roles of different VLPM levels in respiration control in young rats are demonstrated. Transection of the VLPM below the most rostral VLPM portion, corresponding to theM chemosensitive zone, caused a significant increase in the ID frequency and a decrease in the ID integral intensity. Transection performed below the intermediate VLPM region, corresponding to theS chemosensitive zone, resulted in a significant decrease in both ID frequency and ID integral intensity, up to total ID blockade in 5 of 12 1-day-old preparations. This finding can be interpreted as an indication of morphofunctional immaturity of the respiratory network in the caudal VLPM regions in newborn animals. Comparative analysis of ID pattern showed that this activity in one-day-old rats is more or less gasping-like, while that in four- to five-day-old animals is eupnoe-like. The results allow us to conclude that the level of maturity of morphofunctional organization of medullary respiratory networks considerably differs in newborn and older animals. The mechanisms responsible for formation and control of respiratory activity in early postnatal period of rats are discussed.

Effect of nitric oxide on the respiratory activity generated under hypoxic conditions by medullo-spinal preparations from early postnatal rats

Experiments on superfusedin situ semi-isolated medullo-spinal preparations (SIMSP) of 3- to 4-day-old rats were carried out to study the effects of a blocker of nitric oxide synthase (NO synthase), methyl ester of NG-nitro-L-arginine (MENA), and an exogenic NO donor, nitroglycerin, on the respiratory activity. Inspiratory discharges (ID) were recorded from the phrenic nerve under superfusion of SIMSP with a standard saline and a solution saturated with anoxic isocapnic gas mixture. Under normal conditions, 3-min-long applications of 1.0 μM MENA evoked no significant changes in the parameters of inspiratory activity; yet 10.0 μM of this blocker evoked a significant drop in the amplitude and an increase in the ID frequency. Three-min-long applications of 1.0 μM nitroglycerin significantly decreased the ID frequency and somewhat increased their amplitude and integral intensity. Higher doses of nitroglycerin (10.0 μM) significantly increased the amplitude and integral intensity of ID and in a lesser extent lowered their frequency. Under conditions of 3-min-long hypoxia, 10-min-long preliminary superfusion of SIMSP with the 1.0 μM MENA-containing saline resulted in no significant changes of respiratory activity, as compared with the hypoxia effect in the norm. Applied before the hypoxic test, 10 μM MENA resulted in significant decreases in the amplitude and integral intensity of ID; concurrently their frequency became higher, as compared with the respective parameters measured at hypoxic testing of the intact preparations. Ten-min-long superfusion with 1.0 μM nitroglycerin-containing solution at subsequent hypoxic testing significantly increased the amplitude and integral intensity of ID and decreased their frequency; these shifts developed during the first half of exposure to the hypoxic solution. Increased (to 10 μM) nitroglycerin concentration resulted in less intensive shifts in the ID frequency within the first half of a hypoxic episode. In a part of the tests, the second half of exposure of SIMSP to the hypoxic solution was characterized by the appearance of low-amplitude short ID against the background of suppressed eupnea-like respiratory activity; we qualified such discharges as gasping discharges. The experimental data confirm the involvement, of NO in the central regulation of the frequency and amplitude parameters of inspiratory activity generated by SIMSP of early postnatal rats both under normoxic and hypoxic conditions. The role NO plays under hypoxic conditions in modifications of parameters of respiratory activity and in modulation of the functional, levels of the bulbar respiratory generator is discussed.

Involvement of NMDA receptors in the control of respiratory rhythm generated by medullo-spinal preparations of early postnatal rats

Effects of a non-competetive blocker of glutamate NMDA receptors, ketamine, on respiratory activity recorded from the phrenic nerve were studied in experiments on superfusedin situ semi-isolated medullo-spinal preparations (SIMSP) of 3− to 4-day-old rats. The experiments were carried out under conditions where the ventrolateral medullary region (VLM) was left intact, or its rostral portion (projectionally corresponding to the chemosensitiveM zone) was separated by transection. Three-min-long application of 1.0 μM ketamine evoked a slight increase in the duration of inspiratory discharges (ID) and a statistically significant increase in their frequency. After the rostral VLM had been separated, similar ketamine application resulted in significant increases in the duration, amplitude, and integral intensity of ID and some drop in their frequency. An increase to 10 μM ketamine concentration in the superfusing solution determined a significant rise of the ID duration, which indicates the possibility of inhibition of the mechanisms switching inspiration to expiration. Concurrently, the ID frequency significantly dropped, while their amplitude and integral intensity increased. After separation of the rostral VLM, the latter ketamine concentration ceased to increase the ID duration, and their frequency and amplitude significantly dropped. Application of ketamine in the concentration of 100 μM resulted in rather profound decreases of all measured ID parameters, and separation of the rostral VLM exerted no influence on the direction of the above modifications. Thus, we obtained evidence of the involvement of NMDA receptors of the VLM in the control of temporal and frequency-amplitude parameters of respiratory activity of early postnatal rats. Possible localization of NMDA receptors and mechanisms of their involvement in inspiration-expiration switching and tonic inhibitory control of respiratory rhythms are discussed.

Participation of the opioid- and serotonergic systems of the ventrolateral medullary regions in the control of respiratory activity in early postnatal rats

The effects of blockers of opioid and serotonin receptors (naloxone and methisergide, respectively) on the respiratory activity recorded from then. phrenicus of semi-isolated medullo-spinal preparations (SIMSP) were studied in newborn (1-day-old) and 4- to 5-day-old rats. The preparations were superfusedin situ, and inspiratory discharges (ID) were recorded before and after transverse sections of the ventrolateral medullary regions (VLMR) at different levels. Naloxone evoked an increase in the ID frequency in then. phrenicus both at the initial configuration of preparations and after successive transections of the VLMR between theM andS chemosensitive zones and between theS andL zones. The relative intensity of this effect was significantly higher in newborn rats than in 4- to 5-day-old ones. In contrast, methisergide made the ID frequency lower at all configurations of the SIMSP, and this effect was more intensive in 4- to 5-day-old animals. In the course of progressive separations of more rostral VLMR zones, the effects of naloxone and methisergide applications on the ID frequency became weaker. This allows us to suppose that in newborn rats the rostral VLMR portions provide more intensive opioidergic inhibitory control influences on the activity of respiratory networks than those in 4- to 5-day-old animals. At the same time, tonic activating influences from serotonergic VLMR neurons on the mechanisms generating respiratory rhythm are more intensive in 4- to 5-day-old animals than those in newborn ones. Thus, it can be supposed that the levels of maturation of the opioid- and serotonergic neurotransmitter systems, which provide tonic control of respiratory activity generated in the VLMR, are different in newborn and 4- to 5-day-old animals. The problems of how the opioid- and serotonergic mechanisms controlling respiratory rhythm generation are formed in the course of early stages of ontogenetic development are discussed.

Effects of hypoxia on the respiratory activity generated by semi-isolated medullo-spinal preparations of early postnatal rats

The effects of short- and long-lasting (2-min-long and up to 30-min-long) hypoxia episodes on the inspiratory activity (IA) recorded from then. phrenicus were tested in experiments on superfusedin situ semi-isolated medullo-spinal preparations (SIMSP) of newborn (the lst day of life) and 4- to 5-day-old rats. Hypoxia was provided by superfusion of the preparations with low-O2 solution. Short-lasting hypoxia evoked no significant modulation of the IA in preparations of newborn animals, while two-phase responses (an initial, up to 30 sec, increase in the frequency of inspiratory discharges, followed by their longer, up to 4 min, suppression) were observed in 4- to 5-day-old preparations. Long-lasting hypoxia suppressed activity in then. phrenicus of 1-day-old preparations, and this effect was replaced in five cases by the development of sporadic low-amplitude and short-lasting inspiratory discharges. These shortened discharges were qualified as gasps. The responses of 4- to 5-day-old SIMSP to long-lasting hypoxia episodes were more complex. An initial increase in the IA frequency lasted up to 30 sec, and in 4–6 min it was followed by complete suppression of the activity. In some of the SIMSP, permanent tonic activity appeared in then. phrenicus within the period of total absence of inspiratory discharges, which could be followed by generation of short low-amplitude gasping discharges. Against the background of gasping pattern, eupnoe-like discharges appeared in four preparations. Under control conditions, transerve section of the ventrolateral medullary regions (VLMR) at a middle level of then. hypoglossus root abolished respiratory activity in all studied SIMSP. Yet, in some of the SIMSP of both newborn and 4- to 5-day-old animals long-lasting hypoxia testing evoked weak tonic activity in then. phrenicus followed by the appearance of gasping discharges. After the transection of the VLMR at the caudal edge of then. hypoglossus root, long-lasting hypoxia evoked only weak tonic responses in some SIMSP of both age groups, and there were no phasic discharges in this case. The results of our experiments, first, show that the respiratory activity in newborn animals is more resistant to hypoxia than that in 4-to 5-day-old rats, and, second, they allow us to suppose that the gasp-generating medullary structures are localized in more caudal medullary regions. We discuss the questions of how the eupnoe-generating and gasp-generating medullary structures are formed in rats during their initial four to five postnatal days, and what specific features are typical of hypoxia-related respiratory responses in these animals.

Parameters of discharges of respiratory neurons of the ventrolateral medullary regions in early postnatal rats

In experiments on superfusedin situ semi-isolated medullo-spinal preparations (SIMSP) of newborn (1st day of life) and 4- to 5-day-old rats, we studied the parameters of extracellularly recorded spike activity of respiratory neurons of the ventrolateral medullary regions (VLMR). In SIMSP of 4- to 5-day-old rats, the frequency of discharges of pre-inspiratory, inspiratory, and expiratory neurons is shown to be significantly higher, while the dispersion of its values is considerably lower, as compared with the corresponding values for newborn animals. In the majority of pre-inspiratory and inspiratory neurons of SIMSP of newborn rats, irregular low-frequency discharges are usually generated within the interinspiration phase. The relative intensity of suppression of discharges of pre-inspiratory and expiratory neurons within an inspiration phase is much lower in SIMSP of newborn rats, as compared with that in 4- to 5-day-old preparations. The activity of most pre-inspiratory neurons manifests a trend toward transformation from a two-phase pattern in newborn rats (with two frequency peaks, pre- and post-inspiratory) to a monophasic pattern (with one pre-inspiratory frequency peak) typical of 4- to 5-day-old animals. The effects of electrical stimulation of the site of localization of pre-inspiratory neurons showed that in SIMSP of both age groups of rats an inspiratory response could be evoked in then. phrenicus only in the case when stimulation was applied within the second half of an interinspiratory phase. Therefore, it can be supposed that the respiratory network in newborn animals is to a considerable extent immature in the morphofunctional aspect. It seems probable that in early postnatal rats pre-inspiratory neurons are involved in the medullary mechanisms foron-off switching of the inspiratory and expiratory phases.

Об уточнении дисперсионных оценок для одномерных уравнений Шрeдингера и Клейна - Гордона@@@

We show that for a one-dimensional Schrodinger operator with a potential whose first moment is integrable the scattering matrix is in the unital Wiener algebra of functions with integrable Fourier transforms. Then we use this to derive dispersion estimates for solutions of the associated Schrodinger and Klein-Gordon equations. In particular, we remove the additional decay conditions in the case where a resonance is present at the edge of the continuous spectrum.

Pacemaker properties of respiratory neurons of the ventrolateral medullary regions in early postnatal rats

Spike activity of respiratory neurons of the ventrolateral medullary regions was studied under conditions of blocking of synaptic transmission. The experiments were carried out on superfusedin situ semi-isolated medullo-spinal preparations (SIMSP) of newborn (1st day of life) and 4- to 5-day-old rats. Part of the pre-inspiratory and (to a somewhat lesser extent) expiratory neurons of newborn rats appeared most resistive to superfusion of preparations with a low-Ca2+ (0.2 mM) and Mg2+-rich (5.0 mM) solution. Spike activity in some neurons of these groups was preserved up to 40 and 25 min, respectively, after mass inspiratory discharges in then. phrenicus had disappeared. Similar neurons in 4- to 5-day-old SIMSP were less resistive. Inspiratory neurons in animals of both age groups demonstrated no pacemaker properties. Coagulation of the regions where pre-inspiratory neurons are localized (the retrofacial zone) did not evoke irreversible blockade of respiratory rhythm in all SIMSP of 4- to-5-day-old rats and in most SIMSP of newborn animals. At the same time, coagulation of the zone where inspiratory neurons are concentrated (the pre-Bötzinger complex) resulted in the blockade of respiratory rhythm in all SIMSP, with no exceptions.