AbstractIn this paper we estimate and analyze the errors associated with the use of the discrete (fast) Fourier transformation for the numerical calculation of convo-lutions. We suggest and compare methods to reduce these errors without loosing the computational efficiency of the calculation scheme. A typical field of application of our findings is the calculation of aggregate loss distributions for, e.g., losses from insurance cases or operational risk losses in the finance industry.

Background Inspiratory activity is a prerequisite for successful application of patient triggered ventilation such as proportional assist ventilation (PAV). It has recently been reported that surfactant instillation increases the activity of slowly adapting pulmonary stretch receptors (PSRs) followed by a shorter inspiratory time (Sindelar et al, J Appl Physiol, 2005 [Epub ahead of print]). Changes in lung mechanics, as observed in preterm infants with respiratory distress syndrome and after surfactant treatment, might therefore influence the inspiratory activity when applying PAV early after surfactant treatment. Objective To investigate the regulation of breathing and ventilatory response in surfactant-depleted young cats during PAV and during continuous positive airway pressure (CPAP) early after surfactant instillation in relation to phrenic nerve activity (PNA) and the activity of PSRs. Methods Seven anesthetized, endotracheally intubated young cats were exposed to periods of CPAP and PAV with the same end-expiratory pressure (0.2–0.5 kPa) before and after lung lavage and after surfactant instillation. PAV was set to compensate for 75% of the lung elastic recoil. Results Tidal volume and respiratory rate were higher with lower PaCO 2 and higher PaO 2 during PAV than during CPAP both before and after surfactant instillation (p < 0.05; both conditions). As an indicator of breathing effort, esophageal deflection pressure and PNA were lower during PAV than during CPAP in both conditions (p < 0.02). Peak PSR activity was higher and occurred earlier during PAV than during CPAP (p < 0.01), and correlated linearly with PNA duration in all conditions studied (p < 0.001). The inspiratory time decreased as tidal volume increased when CPAP was changed to PAV, with the highest correlation observed after surfactant instillation (r = -0.769). No apneic periods could be observed. Conclusion PSR activity and the control of breathing are maintained during PAV in surfactant-depleted cats early after surfactant instillation, with a higher ventilatory response and a lower breathing effort than during CPAP.

We introduce a new topological sigma model, whose fields are bundle maps from the tangent bundle of a 2-dimensional world-sheet to a Dirac subbundle of an exact Courant algebroid over a target manifold. It generalizes simultaneously the (twisted) Poisson sigma model as well as the G/G-WZW model. The equations of motion are satisfied, iff the corresponding classical field is a Lie algebroid morphism. The Dirac Sigma Model has an inherently topological part as well as a kinetic term which uses a metric on worldsheet and target. The latter contribution serves as a kind of regulator for the theory, while at least classically the gauge invariant content turns out to be independent of any additional structure. In the (twisted) Poisson case one may drop the kinetic term altogether, obtaining the WZ-Poisson sigma model; in general, however, it is compulsory for establishing the morphism property.

The breathing pattern of preterm infants is immature and is associated with a variety of reflexes. In a patient on the ventilator these reflexes interfere with spontaneous breathing. A better understanding of the immature control of breathing could lead to further improvements in ventilatory techniques. This thesis concerns studies of pulmonary stretch receptor (PSR) and phrenic nerve activity as part of the regulation of breathing in an animal model.During assist/control ventilation with three different inspiratory pressure waveforms in animals with healthy lungs, squarewave pressure waveform strongly inhibits spontaneous inspiratory activity.During partial liquid ventilation (PLV) in animals with healthy lungs, all PSRs studied maintained their phasic character, with increased impulse frequency during inspiration. PSR activity was not higher during PLV than during gas ventilation (GV), indicating that there was no extensive stretching of the lung during PLV.During proportional assist ventilation (PAV) the applied airway pressure is servo-controlled proportionally to the ongoing breathing effort, thereby interacting with the activity of PSRs. Peak PSR activity was higher and occurred earlier during PAV than during CPAP. The regulation of breathing is maintained during PAV in surfactant-depleted animals before and early after surfactant instillation, with a higher ventilatory response and a lower breathing effort than during CPAP in both conditions.Both lung mechanics and gas exchange influence the regulation of breathing. Inhibition of inspiratory activity occurred at a lower arterial pH and a higher PaCO2 during PLV than during GV in animals with surfactant-depleted lungs, which might be related to recruitment of a larger number of pulmonary stretch receptors during PLV.In summary, selected aspects of the regulation of breathing were studied in an animal model with different ventilatory techniques under different lung conditions similar to those that can occur in infants.

To understand the mechanisms behind improved oxygenation after intratracheal surfactant instillation, the immediate and late effects on lung volume and compliance of the respiratory system (CRS) were analysed. Infants received modified porcine surfactant (Curosurf) or modified bovine surfactant (Alveofact). Measurements of functional residual capacity (FRC) and CRS were successfully performed in 90 ventilated preterm infants (birth weight 1264±435 g; gestational age 28.2±2.5 weeks) with severe respiratory distress syndrome. FRC and CRS were measured during mechanical ventilation prior to and 1, 3, 6, 24, 48, 72, 96, 120 and 168 h after surfactant replacement. Oxygenation rapidly improved. FRC increased significantly from 7.64±1.58 ml/kg to 15.35±3.27 ml/kg ( P <0.01) at 1 h after surfactant instillation. CRS remained virtually unchanged during the first hours after surfactant replacement and a concomitant decrease in specific compliance was seen. Conclusion: the changes in lung function following surfactant treatment can only be explained by initial stabilisation of already aerated alveoli followed by recruitment of new gas exchange units as mechanisms involved in mediating the effect of surfactant on gas exchange. However, since no significant correlation between changes in functional residual capacity and improvement in arterial-to-alveolar oxygen tension ratio was seen, other effects of surfactant must be considered. These include local and/or systemic changes in haemodynamics.

During proportional assist ventilation (PAV), the ventilator pressure is servocontrolled throughout each spontaneous inspiration such that it instantaneously increases in proportion to the airflow (resistive unloading mode), or inspired volume (elastic unloading mode), or both (combined unloading mode). The PAV pressure changes are generated in a closed-loop feedback circuitry commonly using a pneumotachographic signal. In neonates, however, a pneumotachograph increases dead space ventilation, and its signal may include a substantial endotracheal tube leak component. We hypothesized that respiratory inductive plethysmography (RIP) can replace pneumotachography to drive the ventilator during PAV without untoward effects on ventilation or respiratory gas exchange. Ten piglets and five rabbits were supported for 10-min (normal lungs) or 20-min (meconium injured lungs) periods by each of the three PAV modes. In each mode, three test periods were applied in random order with the ventilator driven by the pneumotachograph signal, or the RIP abdominal band signal, or the RIP sum signal of rib cage and abdomen. Interchanging the three input signals did not affect the regularity of spontaneous breathing, and gas exchange was achieved with similar peak and mean airway pressures (ANOVA). However, the RIP sum signal worked adequately only when the relative gains of rib cage and abdominal band signal were calibrated. We conclude that an RIP abdominal band signal can be used to generate PAV, avoiding increased dead space and endotracheal tube leak problems.

Positive end expiratory pressure is routinely used when ventilating preterm infants. Elevation of PEEP increases lung. volume, as does surfactant treatment. The purpose of this study was to investigate the effect of various levels of PEEP within the range of 0.2 to 0.4 kPa on lung volume, compliance and gas exchange. We measured functional residual capacity, compliance of the respiratory system and arterial blood gases in 20 infants (median birth weight 1240 g, range 660-1690 g; median gestational age 28 weeks, range 24-32 weeks; postnatal age 3-4 days). The infants were studied at 72 hours after their last dose of natural surfactant. At this time the patients were routinely nursed at 0.3 kPa of PEEP, the PEEP level was lowered to 0.2 kPa or raised to 0.4 kPa in random order. The PEEP level was then changed to the third level 0.4 kPa or 0.2 kPa. Each new setting was maintained for 20 min before FRC, compliance and blood gases were measured. FRC was assessed using SF6 washout technique. Increasing PEEP from 0.2 to 0.3 to 0.4 kPa resulted in increases in FRC (p < 0.01) and oxygenation (ns) in all infants. In 16 infants compliance decreased and paCO(2) increased with elevation of PEEP. Only in 4 infants compliance increased and CO2 fell.Conclusion: In the majority of our infants reduction of PEEP from 0.4 to 0.2 kPa resulted in increases in compliance and CO2 reduction. Our results might suggest that relatively low levels of PEEP < 0.3 kPa may be appropriate at 72 hours after surfactant replacement. Furthermore, these results underline the importance of PEEP test in clinical practice.

Thoracoabdominal asynchrony (TAA) and chest wall distortion (CWD) are commonly seen in preterm infants secondary to a highly compliant rib cage and poor compensation of distorting forces by inspiratory rib cage muscles. Continuous positive airway pressure (CPAP) reduces TAA and CWD by stenting the chest wall. We hypothesized that application of positive airway pressure only during inspiration and in proportion to an infant's inspiratory effort should have a similar but more pronounced effect than CPAP alone. A ventilator providing airway pressure changes in proportion to flow and volume generated by an infant (proportional assist ventilation) was used to unload the respiratory pump during inspiration. Ten preterm infants were studied [birth weight, 745 (635–1175) g; gestational age, 26.5 (24–31) wk; postnatal age 3 (1–7) d; medium (range)]. TAA and CWD were determined by respiratory inductive plethysmography. TAA was expressed as the phase angle between the rib cage and abdominal motion and CWD as the total compartmental displacement ratio. In addition, we measured tidal volume with a pneumotachograph and esophageal and airway pressure deflections with pressure transducers. Measurements were obtained during alternating periods of CPAP and two different degrees of support (Gain 1 = 1.09 ± 0.68, Gain 2 = 1.84 ± 0.84 cm H 2 O/mL) that were provided by a proportional assist ventilator. Phase angle and the total compartmental displacement ratio decreased with increasing gain compared with CPAP alone. Peak airway pressure increased from 0.6 to 3.8 to 7.6 cm H 2 O above positive end-expiratory pressure (PEEP) with CPAP, Gain 1, and Gain 2, respectively, as tidal volume increased from 2.8 to 4.1 to 4.7 mL/kg. Esophageal pressure changes decreased only little with increasing gain. Chest wall excursion increased and abdominal movement decreased, indicating a redistribution of tidal volume between chest and abdomen. We conclude that proportional assist ventilation reduces TAA and CWD by generating a small increase in airway pressure that occurs in synchrony and in proportion to each inspiratory effort.

Objective. A dead space free method based on simultaneous ventilatory measurements in the inspiratory and expiratory limb of the ventilator circuit was compared to the conventional endotracheal method where the flow is measured between ETT and Y-Piece. The aim of our study was to find out how the arrangement of this setup affects the measuring accuracy of 1) the ventilatory and 2) the lung mechanical parameters by means of a computer simulation. Method. The system consisting of ventilator tubes and lung was described in state space and the flow signals of endotracheal method, of dead space free method and the pressure at the Y-piece were simulated in the time domain. To investigate the influence of the position of the pneumotachographs (PNTs) in the ventilator circuit on measuring accuracy, the distance d0 of the PNT from the Y-piece was varied between 0 and 900mm. The respiratory compliance C, resistance R and inertance I were calculated by least square method using the simulated flow and pressure signals of both methods. Results. Compared to the endotracheal method, with increasing d0 the tidal volume measured with the deadspace free method rose linearly, depending on the ratio between the compliance of the ventilator tubes to the respiratory compliance. The differences of C and R for both methods were acceptable (< 10%) if the distance between each PNT and the y-piece didn’t exceed 200mm and the shorter d0 the higher the measuring accuracy. The inertance could not be measured by this method with satisfactory accuracy if d0 was higher than 100 mm. Inconclusion, the dead space free method can be used for accurate ventilatory measurements during mechanical ventilation. However, for lung mechanic measurements in very low birth weight infants the position of the PNTs must be as short as possible.

Different modes of assisted ventilation were investigated in cats before and after lung lavage and after instillation of surfactant. The activity of single units of slowly adapting pulmonary stretc ...

In volatility estimations of fixed income instruments the mapping of cash flows to the anchor points of the yield curve plays a crucial role. The author argues in favor of a modification of the traditional approaches

While anterior/posterior chest x‐rays (CXR) are routinely performed to estimate lung volume (LV) and adjust ventilator settings, the precise measurement of LV requires additional sophistication. In 31 infants ventilated because of surfactant deficiency (n = (23), bronchopulmonary dysplasia (n = 7), or pulmonary hypoplasia (n = 1) with either intermittent positive pressure (n = 18) or high frequency oscillation (n = 13) gestational age 23–39 weeks (median 26 weeks); birthweight 550–2780 g (median 840 g); age at measurement 1–91 days (median 6 days); weight at study time (WST) 675–3000 g (median 938 g), we investigated whether LV, as measured by the sulfur hexafluoride (SF6) washout technique, could by estimated from CXR by: (1) the sum (A+B) of the right (A) and left (B) lung fields areas; 2) the product (LxW) of the distances from the right apex to the right costophrenic angle (L) and between both costophrenic angles (W); (3) the diaphragm position relative to the posterior parts of the ribs (DP); and (4) the lung radiolucency (RL, grades 0–4). Correlations between A+B (r = 0.44) or LxW (r = 0.37) and LV were poor, but improved when A+B, LxW, and LV were normalized to WST: (A+B)/WST vs. LV/WST (r = 0.74), and LxW/WST vs. LV/WST (r = 0.67). DP (r = 0.13) and RL (Spearman's rho = 0.17) did not correlate with LV/WST. A multiple linear regression analysis led to the following best‐fit equation: LV/WST = 2.58 (A+B)/WST − 5.47 DP + 42.2 (r = 0.83). We concluded that an estimate of LV from CXR lacked sufficient accuracy. DP and RL did not correlate with LV measured by SF6 washout. Pediatr Pulmonol. 1998; 26:265–272. © 1998 Wiley‐Liss, Inc.

Measurement of mean lung volume (MLV) in high-frequency oscillatory ventilation (HFO) may be useful for optimizing the high lung volume strategy, but has not been available until now. We have measured MLV by means of the sulfur hexafluoride (SF6) washout method in 13 premature infants ventilated with HFO because of respiratory distress syndrome (gestational age, 23 to 31 wk [median, 25 + 6/7 wk]; birthweight, 630 to 1,140 g [790 g]; age at measurement, 2 to 10 d [4 d]; weight, 675 to 1,250 g [850 g]). To evaluate the relationship between MLV and mean airway pressure (MAP), the latter was systematically varied between the measurements. With clinically selected MAP, MLV was between 23.3 and 41.9 ml/kg (median, 33.5 ml/kg) and was strongly dependent on MAP in each patient; linear regression analyses resulted in slope factors between 1.0 and 6.9 ml/cm H2O/kg (median, 2.83 ml/cm H2O/kg), with correlation coefficients between 0.77 and 0.99 (median, 0.94). Stabilization of MLV after modification of MAP took 2 to 25 min (median, 9 min). We conclude that the selection of MAP on a clinical basis leads to a wide range of different MLVs. Despite the strong dependence of MLV on MAP, the prediction of MLV solely based on MAP was impossible because of large patient to patient variability of linear regressions. Alveolar recruitment and derecruitment may take up to 25 min after MAP changes.

Compared with conventional modes of patient-initiated mechanical ventilation, respiratory mechanical unloading aims at improving the match between ventilator pressure profiles and the specific derangements in lung mechanics. This may reduce lung barotrauma. The ventilator pressure increases either in proportion to the volume or to the flow of spontaneous breathing (elastic or resistive unloading), thereby selectively decreasing elastic or resistive work of breathing. The clinician sets a gain of increase in pressure per unit of volume or flow. In an attempt to develop criteria for selecting an appropriate gain, we investigated the effects of unloading using increasing gains that either partially compensated or overcompensated lung elastance or resistance. We studied spontaneously breathing, anesthetized, and tracheotomized rabbits. Compared with continuous positive airway pressure, respiratory unloading decreased the electromyographic activity of the diaphragm and increased minute ventilation in normal (n = 5) and surfactant-depleted (n = 6) animals when the gain was partially compensating. Fluctuations in systemic blood pressure associated with breathing decreased. The end-expiratory lung volume remained unchanged. Overcompensation of lung elastic recoil during elastic unloading with an excessive gain caused large tidal volumes associated with a cyclic decrease in blood pressure. Overcompensation of resistance induced oscillations. Complete inhibition of spontaneous breathing occurred with a further increase in gain. We conclude that respiratory unloading with an appropriate gain enhances the effect of diaphragmatic muscle activity on ventilation. A stable breathing pattern ensues whenever a regular spontaneous effort is present. However, excessive gain causes large tidal volumes during elastic unloading or oscillations during resistive unloading.

Impaired pulmonary mechanics can cause chest wall distortion (CWD) so that work of breathing is dissipated in deforming the rib cage. We hypothesized that respiratory mechanical unloading as a technique of assisted mechanical ventilation would reduce CWD in animals with injured lungs. We studied five piglets and five adult rabbits to test across different ages and chest configurations. As a result of intratracheal meconium instillation, lung compliance decreased from 21 (median; range 17-35) to 9.5 (6.7-14) mL/kPa/kg in rabbits and from 26 (18-31) to 7.9 (4.9-11) in piglets. Airway resistance increased from 5.0 (4.6-6.1) to 6.9 (5.8-7.9) kPa/L/s in rabbits only. Respiratory inductive plethysmography was used to measure the phase shift between the rib cage and abdominal compartment movements and the total compartmental displacement ratio. We aimed at unloading at least three-fourths of lung elastance in all animals and 2.0 kPa/L/s of resistance in rabbits. Elastic unloading decreased the phase shift in all but one animal. It reduced the total compartmental displacement ratio from 1.27 (1.14-3.73) to 1.16 (1.02-1.82) in piglets and from 1.77 (1.45-5.24) to 1.37 (1.11-4.78) in rabbits. The inspiratory rib cage expansion increased, whereas abdominal expansion did not. The tidal esophageal pressure deflection decreased. Tidal volume increased, whereas respiratory rate remained unaffected so that the partial pressure of arterial CO2 decreased. Resistive unloading as an adjunct to elastic unloading further reduced CWD and induced a more rapid, shallower breathing. We conclude that respiratory unloading as a mechanical support to spontaneous breathing reduces CWD. We speculate that the decrease in CWD increases ventilatory efficiency for a given diaphragmatic effort.

In mechanical ventilation of preterm infants, positive endexpiratory pressure (PEEP) is widely used to prevent alveolar collapse, maintain functional residual capacity (FRC) and improve oxygenation. Prolongation of inspiratory time (ti) and increase of peak inspiratory pressure (PIP) are also used for this purpose. We investigated the effect of variations of PEEP, PIP and ti on FRC in ten infants with hyaline membrane disease and onset of bronchopulmonary dysplasia (BPD, n= 7), pulmonary hypertension (n= 1), pulmonary hypoplasia (n= 1) or severe BPD (n= 1) (gestational age 24–39 weeks, median 26 weeks; birth weight 590–2960 g, 785 g; chronological age 7–84 days, 19 days; weight 689–4650 g, 1185 g). FRC, measured using the sulphur hexafluoride washout technique, was between 6.2 and 48.3 ml/kg (median 21.5 ml/kg). PEEP was changed stepwise 2–5 times in each patient (median 3) and mean airway pressure (MAP) was modified independently of PEEP by changing PIP 0–2 times (median 1) and ti 0–2 times (median 2). Changes of FRC correlated well with modifications of PEEP in each patient (r= 0.90, range 0.71–0.99). The slope factors of linear correlations had a median value of 2.94 ml/cm H2O per kg, which was significantly different from zero (P < 0.01) and significantly higher than the slope factors of linear correlations between FRC and MAP after modifications of PIP or ti (P < 0.01). The latter two were statistically not different from zero. The quotients ΔFRC/ΔMAP were significantly higher after adjustments of PEEP than after adjustments of PIP or ti (P < 0.01). The time lag between the change of PEEP and the stabilization of FRC on a new level ranged from 2 to 14 min (median 5).

During assisted mechanical ventilation with respiratory unloading, the applied airway pressure follows quasi-instantaneously the infant's pattern of spontaneous breathing. This allows the infant to fully control the amplitude and timing of each breath. The ventilator receives the flow signal of spontaneous breathing as input and quasi-instantaneously provides an airway pressure output in proportion to the volume signal and/or the airflow signal of spontaneous breathing. With elastic unloading, the airway pressure increases during inspiration in proportion to the volume signal to oppose lung elastic recoil pressure. During resistive unloading, the airway pressure increases above baseline (PEEP) in proportion to inspiratory airflow. This decreases resistive work of breathing. The clinician adjusts the gain of the assist (the ratios of airway pressure per unit of volume and/or airflow) to tailor the pressure waveforms to the type (restrictive and/or obstructive) and degree of lung disease.

While a.p. chest x-rays (CXR) are routinely performed in all preterm neonates requiring mechanical ventilation, the measurement of lung volume (LV) requires sophisticated devices. We have investigated the accuracy of two published methods for estimating LV from CXR measurements (planimetry of the lung fields and the length by width product) and two items often used in clinical practice (diaphragm position and lung transparency).

Respiratory Mechanical Unloading Decreases Thoraco-Abdominal Asynchrony and Chest Wall Distortion In Very Low Birth Weight Preterm Infants. † 1552