Sympathetic and parasympathetic nervous control of airway resistance in dog lungs

We studied autonomic nervous control of central (Rc), peripheral (Rp), and extremely peripheral (Rep) airway resistances using a combination of a retrograde catheter method and a pleural capsule method. Airflow through the pleural capsule enabled us to measure Rep, which mainly reflected the resistance of local bronchioles less than 0.6 mm in diameter. Rp of the airways less than about 2 mm in diameter was not negligibly small at any lung volume (VL). With vagi intact, Rc increased at high as well as low VL, whereas Rp and Rep increased sharply as VL decreased. Vagal stimulation increased Rp more markedly than Rc, and Rep least of all. Propranolol augmented total airway resistance (Rtot) two to four times as much as vagal stimulation, mainly because of increased Rp. Stimulation of stellate ganglia inhibited up to half the increase of Rtot elicited by vagal stimulation; most of the inhibition occurred in Rp, but little in Rc and Rep. Our data suggest that both sympathetic and parasympathetic control is more extensive for Rp than for Rc or Rep.     

Acute effects of cigarette smoke inhalation on peripheral airways in dogs

We studied the acute effects of the inhalation of cigarette smoke on the central and peripheral airways of 35 open-chested and tracheotomized dogs by the direct measurement of central (Rc) and peripheral (Rp) airway resistances. Rc was calculated by dividing the pressure difference between a tracheal catheter and a retrograde catheter by mouth flow, and Rp was obtained by dividing the pressure difference between the retrograde catheter and a pleural capsule by mouth flow. The pleural capsule was attached to the pleural surface for alveolar pressure measurement. Rc and Rp were measured by the 2-Hz forced oscillation method. With lung inhalation of the smoke of two-thirds of one cigarette in vagi intact dogs, Rp increased to 239% of the control value and Rc increased to 112%. After bilateral vagotomy, Rp increased to 143% and Rc increased to 104%. Propranolol did not influence the results. Hexamethonium and atropine both blocked these responses when vagi were intact. When the upper trachea, larynx, and nasopharynx, which were completely blocked by vagotomy, were exposed to the smoke of two-thirds of a cigarette, Rp increased to 155% and Rc increased to 144%. We thus conclude that cigarette smoke causes a major increase in Rp, mainly via the vagal reflex and partially via the stimulation of parasympathetic ganglia (probably nicotine), and a minor increase in Rc via vagal reflex.     

Dose-response curves of central and peripheral airways to nicotine injections in dogs

The dose-response curves of the central and peripheral airways to intravenously injected nicotine were studied in 55 anesthetized dogs. With intact vagi, nicotine caused a dose-dependent increase in central airway resistance (Rc) similar to the increase in peripheral airway resistance (Rp) at concentrations ranging from 4 to 64 micrograms/kg. However, the responses of both Rc and Rp fell progressively when sequential doses of nicotine greater than 256 micrograms/kg were administered. With intact vagi and the administration of propranolol, there was a greater increase in Rp than in Rc at a nicotine dose of 64 micrograms/kg (P less than 0.05). With vagotomy, the responsiveness of both central and peripheral airways to nicotine decreased with doses of nicotine less than 64 micrograms/kg, but with doses of nicotine greater than 256 micrograms/kg the suppressive effect of nicotine on both Rc and Rp was less than that seen with intact vagi. Under conditions in which the vagi were cut and atropine administered, the responsiveness of nicotine was even further depressed. Combinations either of atropine and chlorpheniramine or atropine and phenoxybenzamine also completely blocked reactions to nicotine. Additionally reactions to nicotine were completely blocked by hexamethonium. These results suggest that nicotine increases both Rc and Rp mainly through a vagal reflex and stimulation of the parasympathetic ganglia.     

Effects of hemodynamic edema formation on peripheral vs. central airway mechanics

The mechanisms governing increased central (Rc) and peripheral airway resistance (Rp) during hemodynamic edema formation were studied in anesthetized dogs. Rc and Rp were measured by forced oscillation at 1 Hz by use of a retrograde catheter to partition resistance and a pleural capsule to detect alveolar pressure. After elevation of left atrial pressure to 30 cmH2O by inflation of the left atrial balloon, Rc gradually increased an average of 60% above control in approximately 100 min. Vagotomy had a small influence on the change. On the other hand, Rp with vagus nerves intact increased triphasically: first, it increased transiently by 160% above the control value within 15-20 min before returning to near base line. It then increased gradually for approximately 40 min and finally rose sharply up to five times the control value after approximately 100 min. With vagi cut, the initial phase disappeared, but the second gradual and final rapid phases were not affected. Several sequential mechanisms of increased Rp can be proposed: 1) transient bronchoconstriction mediated by vagal reflex; 2) gradual formation of peribronchial edema; and 3) a sharp increase in airway fluid and formation of bronchial froth. In addition, narrowing of the airways by vascular engorgement may have contributed to the increase of Rp throughout all stages.     

Histamine-induced constriction of canine peripheral lung: an airway or tissue response?

We compared the histamine responsiveness of peripheral airways (less than 6.0 mm diam) and parenchymal tissues in eight anesthetized paralyzed open-chest mongrel dogs. We measured pressure in a peripheral bronchus by using an antegrade wedged catheter and pressure in the alveolar region subtended by the wedged bronchus by using an alveolar capsule. Sinusoidal volume oscillations at a frequency of 0.5 Hz were delivered by a linear motor pump into the segment through the wedged catheter. We calculated the resistance of the segment (Rseg) and partitioned Rseg into tissue viscance (i.e., proportional to the resistive pressure drop between the alveolus and the pleura) and peripheral airway resistance. Measurements were taken under baseline conditions and after delivery of increasing concentrations of aerosolized histamine (0.1 micrograms/ml to 100.0 mg/ml) into the segment. We found that the histamine responsiveness of the peripheral airways and lung tissues varied markedly within a given dog. In four of eight dogs the airways were more responsive to histamine, in three of eight the tissues were more responsive, and in one of eight the response was equivalent at the two sites. We conclude that in a given animal, there is marked heterogeneity in the histamine responsiveness of the peripheral airways and parenchymal tissues and that either may dominate responsiveness in the peripheral lung.     

Radiographic visualization of airway wall movement during oscillatory flow in dogs

It has been suggested that radial movement of the central airway walls during oscillatory flow might contribute to the increased frequency dependence of compliance seen in chronic obstructive pulmonary disease (COPD) (J. Appl. Physiol. 26: 670-677, 1969). Radial airway wall motion has also been invoked to explain the frequency-dependent decreases in the efficiency of gas exchange during low-volume high-frequency ventilation (HFV) in histamine-bronchoconstricted dogs and in patients with respiratory insufficiency. To test the possibility that airway wall motion increases with bronchoconstriction, we measured central airway diameters using cinebronchoradiography in anesthetized tracheostomized dogs during oscillatory HFV [50 and 100 ml tidal volume (VT) at frequencies (f) of 2, 6, and 12 Hz], under control conditions, during electrical stimulation of the vagi, and after exposure to histamine aerosol. Cineradiobronchograms from two dogs were evaluated quantitatively for tracheal diameter and for lengths and diameters of a number of major airways. Under control conditions, the diameter of the airways fluctuated 7-9% of the mean with VT of 50 ml and 9-18% with VT of 100 ml in the range of frequencies studied. Bronchoconstriction produced by aerosolized histamine increased radial airway wall movement to 10-47% with VT of 50 ml, and during vagal stimulation diameters changed 7-20% at VT of 50 ml. After histamine, the central airways displayed large diameter changes during HFV, whereas more peripheral airways were markedly constricted and did not change in diameter.(ABSTRACT TRUNCATED AT 250 WORDS)     

Location of flow-limiting segments via airway catheters near residual volume in humans

Previous studies have demonstrated sites of flow limitation in the central airways of dogs and humans. At low lung volumes, however, during a forced expiration, it is not clear whether flow-limiting segments (FLS) move into the lung periphery. Using intrabronchial lateral pressure catheters, we located FLS in human subjects at all lung volumes between functional residual capacity (FRC) and residual volume (RV). Three individuals with severe intracranial hemorrhage maintained on ventilators were studied. Partial maximal flow-volume curves were generated from 1 liter above FRC to RV by lowering downstream pressure and using the interrupter technique. Sites of FLS were defined as the most downstream points where lateral pressure did not change with driving pressure. FLS were found in all subjects in the central airways. In one subject, FLS moved from segmental bronchi to the first subsegmental bronchus as RV was approached but not beyond. In the other two subjects, FLS remained fixed in location at all measured lung volumes. At constant volume, multiple FLS were located, all in parallel, e.g., fixed in left upper, left lower, and right middle lobar bronchi. In conclusion, sites of flow limitation remain in the central airways as lung volume approaches RV. FLS may move peripherally within the central airways but not beyond proximal subsegmental bronchi.     

Vagal control of central and peripheral pulmonary resistance in developing piglets

To study the postnatal maturation of vagal control of airway muscle tone, we determined the effects of vagotomy and supramaximal vagal stimulation on the resistance of the respiratory system in eight newborn and seven 6-wk-old piglets. Because the lung periphery has distinctive responses to cholinergic agonists and a lower density of vagal fibers and cholinergic receptors than the central airways, we partitioned the respiratory resistance of the piglets between central airways (Rc) and peripheral airways and lung tissue (Rp) with bronchial catheters inserted in a retrograde manner. The piglets were anesthetized with alpha-chloralose and ventilated with positive airway pressure. Vagotomy did not change Rc or Rp in either the newborn or the 6-wk-old piglets. Vagal stimulation, on the other hand, increased both Rc (median increase 53% in the newborn and 72% in the 6-wk-old piglets) and Rp (54 and 42%, respectively). At all states of vagal tone, Rp increased as the lungs were inflated, suggesting a large contribution of tissue viscoelasticity to this resistance. Our results demonstrate that vagal bronchomotor tone is absent during mechanical ventilation with positive pressure in the developing piglet. However, vagal innervation of both central airways and tissue contractile elements is functionally competent at the time of birth in this species.     

Low-frequency respiratory system resistance in the normal dog during mechanical ventilation

The low-frequency resistances of the respiratory system, lung, and chest wall were investigated in four anesthetized paralyzed dogs mechanically ventilated at various frequencies between 0.08 and 0.83 Hz. The resistances were calculated by three different methods: 1) as the real part of the complex impedance obtained from regular ventilation data, 2) as the effective resistance of a two-compartment model fitted to the same data, and 3) as the resistance of a single-compartment model fitted to data obtained during sinusoidal ventilation at various frequencies. Alveolar pressures were measured by a closed-chest alveolar capsule technique and afforded a direct measure of airways resistance. All three resistance estimates were very similar and decreased markedly with frequency between 0 and 1 Hz. The real part of lung impedance at the higher frequencies investigated (around 5 Hz) closely approximated airways resistance, as predicted by the eight-parameter viscoelastic model of respiratory mechanics proposed by Bates et al. (J. Appl. Physiol. 67:2276-2285, 1989).     

Analysis of bronchial mechanics and density dependence of maximal expiratory flow

The computational model for expiratory flow in humans of Lambert and associates (J. Appl. Physiol. Respirat. Environ. Exercise Physiol. 52: 44-56, 1982) was used to investigate the effect of bronchial constrictions in three airway zones on the density dependence of maximal expiratory flow. It was found that constriction of the peripheral airways (less than 2 mm diam) reduced density dependence and increased the volume of isoflow. Constriction of the larger intraparenchymal airways resulted in increased density dependence at low lung volumes and essentially normal values at other volumes. The volume of isoflow was reduced. Extraparenchymal (but intrathoracic) airway constriction caused no change in the volume of isoflow but caused increased density dependence at the higher lung volumes. It was shown that in these model simulations the addition of extraparenchymal constriction to intraparenchymal constriction causes essentially no changes in density dependence. An increased volume of isoflow and significantly decreased density dependence at 50 and 25% vital capacity were produced by simulated constrictions only in the peripheral airways.     

Effect of lung volume on interrupter resistance in cats challenged with methacholine

To examine the effects of changes in lung volume on the magnitude of maximal bronchoconstriction, seven anesthetized, paralyzed, tracheostomized cats were challenged with aerosolized methacholine (MCh) and respiratory system resistance (Rss) was measured at different lung volumes using the interrupter technique. Analysis of the pressure changes following end-inspiratory interruptions allowed us to partition Rss into two quantities with the units of resistance, one (Rinit) corresponding to the resistance of the airways and the other (Rdif) reflecting the viscoelastic properties of the tissues of the respiratory system as well as gas redistribution following interruption of flow. Rinit and Rdif were used to construct concentration-response curves to MCh. Lung volume was increased by the application of 5, 10, and 15 cmH2O of positive end-expiratory pressure. The curve for Rinit reached a plateau in all cats, demonstrating a limit to the degree of MCh-induced bronchoconstriction. The mean value of Rinit (cmH2O.ml-1.s) for the group under control conditions was 0.011 and rose to 0.058 after maximal bronchoconstriction; the volume at which the flow was interrupted was 11.5 +/- 0.5 (SE) ml/kg above functional residual capacity (FRC). It then fell progressively to 0.029 at 21.2 +/- 0.8 ml/kg above FRC, 0.007 at 35.9 +/- 1.3 ml/kg above FRC, and 0.005 at 52.0 +/- 1.8 ml/kg above FRC. Cutting either the sympathetic or parasympathetic branches of the vagi had no significant effect on the lung volume-induced changes in MCh-induced bronchoconstriction.(ABSTRACT TRUNCATED AT 250 WORDS)     

Tracking variations in airway caliber by using total respiratory vs. airway resistance in healthy and asthmatic subjects.

An index of airway caliber can be tracked in near-real time by measuring airway resistance (Raw) as indicated by lung resistance at 8 Hz. These measurements require the placing of an esophageal balloon. The objective of this study was to establish whether total respiratory system resistance (Rrs) could be used rather than Raw to track airway caliber, thereby not requiring an esophageal balloon. Rrs includes the resistance of the chest wall (Rcw). We used a recursive least squares approach to track Raw and Rrs at 8 Hz in seven healthy and seven asthmatic subjects during tidal breathing and a deep inspiration (DI). In both subject groups, Rrs was significantly higher than Raw during tidal breathing at baseline and postchallenge. However, at total lung capacity, Raw and Rrs became equivalent. Measured with this approach, Rcw appears volume dependent, having a magnitude of 0.5-1.0 cmH2O. l-1. s during tidal breathing and decreasing to zero at total lung capacity. When resistances are converted to an effective diameter, Rrs data overestimate the increase in diameter during a DI. Simulation studies suggest that the decrease in apparent Rcw during a DI is a consequence of airway opening flow underestimating chest wall flow at increased lung volume. We conclude that the volume dependence of Rcw can bias the presumed net change in airway caliber during tidal breathing and a DI but would not distort assessment of maximum airway dilation.     

Configuration of maximum expiratory flow-volume curve: model experiments with physiological implications

A two-compartment mechanical model of the lungs was constructed with two parallel peripheral and collapsible bronchi in series with one central and collapsible trachea. Maximal expiratory flow-volume (MEFV) curves similar to those obtained in most dogs and in some humans could be produced: a peak followed by a gently sloping plateau ending in a knee, where flow suddenly fell to a much smaller value approaching zero rather slowly over the last 25 to 50% of the expired vital capacity. It was shown that flow before the knee was limited in the trachea, and after the knee it was limited in the bronchi. Two patterns of changes in the configuration of the MEFV curve could be observed. Pattern of changes affecting the central airway, at a given volume, maximal flow during the first part of the expiration (i.e., before the knee) is decreased; the knee occurs at a lower lung volume; the flow at the beginning of the knee is decreased. This pattern was observed with the following interventions: decreased cross-sectional area of the trachea (partial obstruction); decreased axial tension of the trachea; and, increased frictional loss between the trachea and the bronchi. Pattern of changes affecting the airways in the periphery: the knee occurs at a higher lung volume; at a given volume, flow after the knee becomes smaller; the absolute flow at the start of the knee is almost unchanged. This pattern was observed with the following interventions: decreased cross-sectional area of the peripheral airways (partial obstruction); increased frictional loss upstream to the peripheral airways; and, decreased elastic recoil pressure.(ABSTRACT TRUNCATED AT 250 WORDS)     

Simulation of Pulmonay Damages Induced by Inhaled CL2 on the Bronchial Tree

We have measured the change of lung mechanical parameters on isolated rabbit lungs exposed to chlorine gas (Cl{in2}). Experimental results show parallel increase in elastance and resistance of impaired lungs. We tried to determine whether this may be explained by a reduction of the ventilated areas in the lung, consecutive to closure of some airways. We have then tried to simulate these experimental results by studying the effects of various airways occlusions imposed on two concurrent models (symmetrical and dissymmetrical) of the tracheo-bronchial tree. For each model, we successively evaluated the resistance of the normal lung, simulated a partial peripheral airways occlusion and estimated the induced changes in total resistance. Analytical expressions of the "occluded lung" elastance and resistance have been found for the symmetrical model but not for the dissymmetrical model (a graphical approach is proposed). With the symmetrical model, simulated results are comparable to experimental ones when the occlusion level is proximal. Whatever the dissymmetry level (δ) of the fractal tree model, we could not simulate the expected increase in resistance with the observed increase in elastance. We conclude that either the occlusion is non homogeneous or the lung impairment is not only a reduction in ventilated areas. This revised version was published online in June 2006 with corrections to the Cover Date.     

Frequency characteristics of airway and tissue impedances in respiratory diseases

We measured the frequency characteristics (at 10-40 Hz) of airway (Za) and tissue (Zt) impedances in cases of chronic obstructive pulmonary disease [asthmatic bronchitis (AB), chronic pulmonary emphysema (CPE)] and interstitial pneumonitis (IP) by use of an improved random noise oscillation and body box method. The results were then compared with those obtained for normal subjects. The real part of Za was markedly elevated in patients with AB but only slightly elevated in those with CPE. To interpret these data we used an electromechanical analogue including serial inhomogeneity with shunt impedance. From this model we concluded that AB causes both the central and peripheral airway resistances to increase, while CPE brings about a rise mainly in peripheral resistance. In IP patients, only the imaginary part of Zt decreased, which might reflect the decrease in both lung and chest wall compliance. In CPE patients, but not in AB patients, the real part of Zt fell. These data were consistent with the assumption that the decrease in mass per unit volume of lung tissue and hyperinflation of the chest wall in CPE patients might lower the tissue resistances.     

Trachea and lung dimensions in nonsmoking twins: morphological and functional studies

To compare genetic and environmental factors that determine lung function and dimensions, chest radiographs and pulmonary function were measured in 17 pairs of nonsmoking twin adolescent boys (12 monozygotic pairs and 5 dizygotic pairs). Genetic factors dominated in tracheal width and lung dimensions (height, width, and apicofissural and fissurodiaphragmatic distances) at residual volume. Genetic factors also affected forced vital capacity, functional residual capacity, forced expiratory volume in 1 s, maximum expiratory flow at 25% vital capacity, and maximum flow at 50% vital capacity-to-forced vital capacity ratio. Peak expiratory flow correlated with tracheal width at residual volume. Age correlated with lung dimensions (width and depth) but not with tracheal width. These results indicate that genetic factors determine the dimensions and function of central airways, peripheral airways, and lung parenchyma in adolescent males. The effects of genetic factors on some functional measurements (airway resistance, closing volume-to-vital capacity ratio, and phase III in single-breath N2 washout) may be masked because of poor reproducibility of the tests.     

Localized compliance of small airways in excised rat lungs using microfocal X-ray computed tomography.

Airway compliance is a key factor in understanding lung mechanics and is used as a clinical diagnostic index. Understanding such mechanics in small airways physiologically and clinically is critical. We have determined the "morphometric change" and "localized compliance" of small airways under "near"-physiological conditions; namely, the airways were embedded in parenchyma without dehydration and fixation. Previously, we developed a two-step method to visualize small airways in detail by staining the lung tissue with a radiopaque solution and then visualizing the tissue with a cone-beam microfocal X-ray computed tomography system (Sera et al. J Biomech 36: 1587-1594, 2003). In this study, we used this technique to analyze changes in diameter and length of the same small airways ( approximately 150 microm ID) and then evaluated the localized compliance as a function of airway generation (Z). For smaller (<300-microm-diameter) airways, diameter was 36% larger at end-tidal inspiration and 89% larger at total lung capacity; length was 18% larger at end-tidal inspiration and 43% larger at total lung capacity than at functional residual capacity. Diameter, especially at smaller airways, did not behave linearly with V(1/3) (where V is volume). With increasing lung pressure, diameter changed dramatically at a particular pressure and length changed approximately linearly during inflation and deflation. Percentage of airway volume for smaller airways did not behave linearly with that of lung volume. Smaller airways were generally more compliant than larger airways with increasing Z and exhibited hysteresis in their diameter behavior. Airways at higher Z deformed at a lower pressure than those at lower Z. These results indicated that smaller airways did not behave homogeneously.     

Effects of lung volume, bronchoconstriction, and cigarette smoke on morphometric airway dimensions

To examine the role of airway wall thickening in the bronchial hyperresponsiveness observed after exposure to cigarette smoke, we compared the airway dimensions of guinea pigs exposed to smoke (n = 7) or air (n = 7). After exposure the animals were anesthetized with urethan, pulmonary resistance was measured, and the lungs were removed, distended with Formalin, and fixed near functional residual capacity. The effects of lung inflation and bronchoconstriction on airway dimensions were studied separately by distending and fixing lungs with Formalin at total lung capacity (TLC) (n = 3), 50% TLC (n = 3), and 25% TLC (n = 3) or near residual volume after bronchoconstriction (n = 3). On transverse sections of extraparenchymal and intraparenchymal airways the following dimensions were measured: the internal area (Ai) and internal perimeter (Pi), defined by the epithelium, and the external area (Ae) and external perimeter (Pe), defined by the outer border of smooth muscle. Airway wall area (WA) was then calculated, WA = Ae - Ai. Ai, Pe, and Ae decreased with decreasing lung volume and after bronchoconstriction. However, WA and Pi did not change significantly with lung volume or after bronchoconstriction. After cigarette smoke exposure airway resistance was increased (P less than 0.05); however, there was no difference in WA between the smoke- and air-exposed groups when the airways were matched by Pi. We conclude that Pi and WA are constant despite changes in lung volume and smooth muscle tone and that airway hyperresponsiveness induced by cigarette smoke is not mediated by increased airway wall thickness.     

Airway closure on imaging relates to airway hyperresponsiveness and peripheral airway disease in asthma

The regional pattern and extent of airway closure measured by three-dimensional ventilation imaging may relate to airway hyperresponsiveness (AHR) and peripheral airways disease in asthmatic subjects. We hypothesized that asthmatic airways are predisposed to closure during bronchoconstriction in the presence of ventilation heterogeneity and AHR. Fourteen asthmatic subjects (6 women) underwent combined ventilation single photon emission computed tomography/computed tomography scans before and after methacholine challenge. Regional airway closure was determined by complete loss of ventilation following methacholine challenge. Peripheral airway disease was measured by multiple-breath nitrogen washout from which S(cond) (index of peripheral conductive airway abnormality) was derived. Relationships between airway closure and lung function were examined by multiple-linear regression. Forced expiratory volume in 1 s was 87.5 ± 15.8% predicted, and seven subjects had AHR. Methacholine challenge decreased forced expiratory volume in 1 s by 23 ± 5% and increased nonventilated volume from 16 ± 4 to 29 ± 13% of computed tomography lung volume. The increase in airway closure measured by nonventilated volume correlated independently with both S(cond) (partial R(2) = 0.22) and with AHR (partial R(2) = 0.38). The extent of airway closure induced by methacholine inhalation in asthmatic subjects is greater with increasing peripheral airways disease, as measured by ventilation heterogeneity, and with worse AHR.     

Tissue and airway impedance of excised normal, senile, and emphysematous lungs.

We partitioned pulmonary resistance (RL) in excised normal, senile, and emphysematous human lungs at various distending pressures; peripheral resistance (Rp) was measured by means of retrograde catheters and lung tissue resistance (Rti) by means of pleural capsules. By subtracting Rp from RL and Rti from Rp, we obtained, respectively, central (Rcaw) and peripheral (Rpaw) airway resistance. We determined also lung volumes, the elastic recoil pressure-volume curve, and the forced expiratory volume in 1 s-to-vital capacity ratio (FEV1/VC). The functional data were related to morphometry: mean linear intercept (Lm), diameter (d), and density (n/cm2) of membranous bronchioles. In the three groups of lungs, Rti demonstrates a marked negative frequency dependence and increases with transplumonary pressure. In emphysematous lungs, the increase of RL is mainly due to an increase of Rpaw; in addition, Rcaw and Rti are higher than normal. In the group of senile lungs, airway resistances are within normal range, but Rti is slightly increased. FEV1/VC is related to Rpaw and elastic recoil pressure; Rpaw is related to d and n/cm2, and Rti is related to dynamic elastance and to Lm.