A fast computational model for circulatory dynamics: effects of left ventricle–aorta coupling

The course of diseases such as hypertension, systolic heart failure and heart failure with a preserved ejection fraction is affected by interactions between the left ventricle (LV) and the vasculature. To study these interactions, a computationally efficient, biophysically based mathematical model for the circulatory system is presented. In a four-chamber model of the heart, the LV is represented by a previously described low-order, wall volume-preserving model that includes torsion and base-to-apex and circumferential wall shortening and lengthening, and the other chambers are represented using spherical geometries. Active and passive myocardial mechanics of all four chambers are included. The cardiac model is coupled with a wave propagation model for the aorta and a closed lumped-parameter circulation model. Parameters for the normal heart and aorta are determined by fitting to experimental data. Changes in the timing and magnitude of pulse wave reflections by the aorta are demonstrated with changes in compliance and taper of the aorta as seen in aging (decreased compliance, increased diameter and length), and resulting effects on LV pressure–volume loops and LV fiber stress and sarcomere shortening are predicted. Effects of aging of the aorta combined with reduced LV contractile force (failing heart) are examined. In the failing heart, changes in aortic properties with aging affect stroke volume and sarcomere shortening without appreciable augmentation of aortic pressure, and the reflected pressure wave contributes an increased proportion of aortic pressure.

     

Determinants of LV diastolic function during atrial fibrillation: beat-to-beat analysis in acute dog experiments

Left ventricular (LV) diastolic function during atrial fibrillation (AF) remains poorly understood due to the complex interaction of factors and beat-to-beat variability. The purpose of the present study was to elucidate the physiological determinants of beat-to-beat changes in LV diastolic function during AF. The RR intervals preceding a given cardiac beat were measured from the right ventricular electrogram in 12 healthy open-chest mongrel dogs during AF. Doppler echocardiography and LV pressure and volume beat-to-beat analyses were performed. The LV filling time (FT) and early diastolic mitral inflow velocity-time integral (E(vti)) were measured using the pulsed Doppler method. The LV end-diastolic volume (EDV), peak systolic LV pressure (LVP), minimum value of the first derivative of LV pressure curve (dP/dt(min)), and the time constant of LV pressure decay (tau) were evaluated with the use of a conductance catheter for 100 consecutive cardiac cycles. Beat-to-beat analysis revealed a cascade of important causal relations. LV-FT showed a significant positive linear relationship with E(vti) (r = 0.87). Importantly, there was a significant positive linear relationship between the RR interval and LV-EDV in the same cardiac beat (r = 0.53). Consequently, there was a positive linear relationship between LV-EDV and subsequent peak systolic LVP (r = 0.82). Furthermore, there were significant positive linear and negative curvilinear relationships between peak systolic LVP and dP/dt(min) (r = 0.95) and tau (r = -0.85), respectively, in the same cardiac beat. In addition, there was a significant negative curvilinear relationship between dP/dt(min) and tau (r = -0.86). We have concluded that the determinants of LV diastolic function in individual beats during AF depend strongly on the peak systolic LVP. This suggests that the major benefit of slower ventricular rate appears related to lengthening of LV filling interval, promoting subsequent higher peak systolic LVP and greater LV relaxation.     

MRI and echocardiographic assessment of the diastolic dysfunction of normal aging: altered LV pressure decline or load?

Changes in diastolic indexes during normal aging, including reduced early filling velocity (E), lengthened E deceleration time (DT), augmented late filling (A), and prolonged isovolumic relaxation time (IVRT), have been attributed to slower left ventricular (LV) pressure (LVP) decay. Indeed, this constellation of findings is often referred to as the "abnormal relaxation" pattern. However, LV filling is determined by the atrioventricular pressure gradient, which depends on both LVP decline and left atrial (LA) pressure (LAP). To assess the relative influence of LVP decline and LAP, we studied 122 normal subjects aged 21-92 yr by Doppler echocardiography and MRI. LVP decline was assessed by color M-mode (V(p)) and the LV untwisting rate. Early diastolic LAP was evaluated using pulmonary vein flow systolic fraction, pulmonary vein flow diastolic DT, color M-mode (E/V(p)), and tissue Doppler (E/E(m)). Linear regression showed the expected reduction of E, increase in A, and prolongation of IVRT and DT with advancing age. There was no relation of age to parameters reflecting the rate of LVP decline. However, older age was associated with reduced E/V(p) (P = 0.008) and increased pulmonary vein systolic fraction (P < 0.001), pulmonary vein DT (P = 0.0026), and E/E(m) (P < 0.0001), all suggesting reduced early LAP. Therefore, reduced early filling in older adults may be more closely related to a reduced early diastolic LAP than to slower LVP decline. This effect also explains the prolonged IVRT. We postulate that changes in LA active or passive properties may contribute to development of the abnormal relaxation pattern during the aging process.     

八肽胆囊收缩素对大鼠心功能的影响及受体机制

为探讨八肽胆囊收缩素 (CCK 8)对麻醉大鼠心功能的影响及受体机制 ,实验监测了左心室收缩压(LVP)、左心室收缩与舒张期内压变化的最大速率 (±LVdp/dtmax)、心率 (HR)和平均动脉压 (MAP)。结果如下 :小剂量CCK 8(0 4 μg/kg)可引起心动过速 ,MAP、LVP和±LVdp/dtmax轻度上升 ;中剂量CCK 8(4 μg/kg)和大剂量CCK 8(4 0 μg/kg)可引起心动过缓 ,MAP、LVP和±LVdp/dtmax显著增加 ;应用CCK 受体 (CCK R)拮抗剂丙谷胺 (1 0mg/kg)抑制以上变化 ;由逆转录 聚合酶链反应 (RT PCR)检测到心肌组织有CCK A受体 (CCK AR)和CCK B受体 (CCK BR)mRNA表达。以上结果提示 :CCK 8可激活心肌组织的CCK R ,引起剂量依赖性的心功能增加和心率改变。     

Muscle kinematics for minimal work of breathing.

A mathematical model was analyzed to obtain a quantitative and testable representation of the long-standing hypothesis that the respiratory muscles drive the chest wall along the trajectory for which the work of breathing is minimal. The respiratory system was modeled as a linear elastic system that can be expanded either by pressure applied at the airway opening (passive inflation) or by active forces in respiratory muscles (active inflation). The work of active expansion was calculated, and the distribution of muscle forces that produces a given lung expansion with minimal work was computed. The calculated expression for muscle force is complicated, but the corresponding kinematics of muscle shortening is simple: active inspiratory muscles shorten more during active inflation than during passive inflation, and the ratio of active to passive shortening is the same for all active muscles. In addition, the ratio of the minimal work done by respiratory muscles during active inflation to work required for passive inflation is the same as the ratio of active to passive muscle shortening. The minimal-work hypothesis was tested by measurement of the passive and active shortening of the internal intercostal muscles in the parasternal region of two interspaces in five supine anesthetized dogs. Fractional changes in muscle length were measured by sonomicrometry during passive inflation, during quiet breathing, and during forceful inspiratory efforts against a closed airway. Active muscle shortening during quiet breathing was, on average, 70% greater than passive shortening, but it was only weakly correlated with passive shortening. Active shortening inferred from the data for more forceful inspiratory efforts was approximately 40% greater than passive shortening and was highly correlated with passive shortening. These data support the hypothesis that, during forceful inspiratory efforts, muscle activation is coordinated so as to expand the chest wall with minimal work.     

Rheology of myocardium. The relation between force, velocity, sarcomere length and activation in rat cardiac muscle

The relations between force, shortening velocity and sarcomere length (F-V-SL) during cardiac contraction, underlie Starling's Law of the Heart. F-V-SL were investigated in isolated, intact and skinned trabeculae and myocytes from rat heart. SL and V were measured with laser diffraction techniques; F was measured with a silicon strain gauge. The "ascending" F-SL relation appeared to result from both length dependent sensitivity of the contractile system to activator calcium ions and the presence of restoring forces (Fr), residing in the collagen skeleton of the muscle. Fr increased exponentially with decreasing SL below slack length to 25% of maximal twitch force (Ft) at SL = 1.60 microns. V was inversely proportional to the load and attained a maximum at zero load (Vo). Vo increased with factors that increased F: [Ca++], SL, and time during the twitch. Vo reached a maximum and remained constant (13.5 microns/s) when F attained or exceeded 50% of its maximum value. Viscous force in the passive muscle increased with V to a maximum of 4% of Ft at V = 40 microns/s. The relation between Vo and these factors could be predicted by a model of contraction in which the measured visco-elastic properties of myocardium were incorporated, while the truly unloaded maximal velocity of sarcomere shortening was assumed to be independent of the level of activation of the contractile filaments. A model of the cardiac cycle which explains the relation between Frank's and Starling's laws is presented.     

Influence of viscosity on myocardium mechanical activity: a mathematical model

We have previously proposed and validated a mathematical model of myocardium contraction-relaxation cycle based on current knowledge of regulatory role of Ca2+ and cross-bridge kinetics in cardiac cell. That model did not include viscous elements. Here we propose a modification of the model, in which two viscous elements are added, one in parallel to the contractile element, and one more in parallel to the series elastic element. The modified model allowed us to simulate and explain some subtle experimental data on relaxation velocity in isotonic twitches and on a mismatch between the time course of sarcomere shortening/lengthening and the time course of active force generation in isometric twitches. Model results were compared with experimental data obtained from 28 rat LV papillary muscles contracting and relaxing against various loads. Additional model analysis suggested contribution of viscosity to main inotropic and lusitropic characteristics of myocardium performance.     

Effects of mechanical limitation of apical rotation on left ventricular relaxation and end-diastolic pressure

Left ventricular (LV) twist is thought to play an important role in cardiac function. However, how twist affects systolic or diastolic function is not understood in detail. We acquired apical and basal short-axis images of dogs undergoing open-chest procedures (n = 15) using a GE Vivid 7 at baseline and during the use of an apical suction device (Starfish) to limit apical rotation. We measured LV pressure and stroke volume using a micromanometer-tipped catheter and an ultrasonic flow probe, respectively. Peak radial strain, peak rotation, peak twist, peak systolic twisting rate (TR), peak untwisting rate during isovolumic relaxation period (UR(IVR)), and peak early diastolic untwisting rate after mitral valve opening (UR(E)) were determined using speckle tracking echocardiography. Immobilizing the apex with gentle suction significantly decreased apical rotation (-50 ± 27%) and slightly increased basal rotation, resulting in a significant decrease in twist. The time constant of LV relaxation (τ) was prolonged, and LV end-diastolic pressure increased. TR and UR(IVR) decreased. LV systolic pressure, peak positive and negative first derivative of LV pressure (±dP/dt), stroke volume, radial strain, and UR(E) were not changed. The correlation between τ and UR(IVR) (r = 0.63, P = 0.0006) was stronger than that between peak +dP/dt and TR (r = 0.46, P = 0.01). Diastolic function was impaired with reduced apical rotation and UR(IVR) when the apex of the heart was immobilized using an apical suction device.     

Wall stress misrepresents afterload in children and young adults with abnormal left ventricular geometry.

Wall stress, although commonly used as an index of afterload, fails to take into account forces generated within the wall of the left ventricle (LV) that oppose systolic fiber shortening. Wall stress may, therefore, misrepresent fiber stress, the force resisting fiber shortening, particularly in the presence of an abnormal LV thickness-to-dimension ratio (h/D). M-mode LV echocardiograms were obtained from 207 patients with a wide range of values for LV mass and/or h/D. Diagnoses were valvar aortic stenosis, coarctation repair, anthracycline treated, and severe aortic and/or mitral regurgitation. End-systolic wall stress (WS(es)) and fiber stress (FS(es)) were expressed as age-corrected Z scores relative to a normal population. The difference between WS(es) and FS(es) was extreme when h/D was elevated or reduced [WS(es) Z score - FS(es) Z score = 0.14 x (h/D)(-1.47) - 2.13; r = 0.78, P < 0.001], with WS(es) underestimating FS(es) when h/D was increased and overestimating FS(es) when h/D was decreased. Analyses of myocardial mechanics based on wall stress have limited validity in patients with abnormal ventricular geometry.     

Titin-induced force enhancement and force depression: A ‘sticky-spring’ mechanism in muscle contractions?

The sliding filament and crossbridge theories do not suffice to explain a number of muscle experiments. For example, from the entire muscle to myofibrils, predictions of these theories were shown to underestimate the force output during and after active tissue stretch. The converse applies to active tissue shortening.In addition to the crossbridge cycle, we propose that another molecular mechanism is effective in sarcomere force generation. We suggest that, when due to activation, myosin binding sites are available on actin, the giant protein titin's PEVK region attaches itself to the actin filament at those sites. As a result, the molecular spring length is dramatically reduced. This leads to increased passive force when the sarcomere is stretched and to decreased or even negative passive force when the sarcomere shortens. Moreover, during shortening, the proposed mechanism interferes with active-force production by inhibiting crossbridges.Incorporation of a simple ‘sticky-spring’ mechanism model into a Hill-type model of sarcomere dynamics offers explanations for several force-enhancement and force-depression effects. For example, the increase of the sarcomere force compared to the force predicted solely by the sliding filament and crossbridge theories depends on the stretch amplitude and on the working range. The same applies to the decrease of sarcomere force during and after shortening. Using only literature data for its parameterization, the model predicts forces similar to experimental results.     

Internal viscoelastic loading in cat papillary muscle.

The passive mechanical properties of myocardium were defined by measuring force responses to rapid length ramps applied to unstimulated cat papillary muscles. The immediate force changes following these ramps recovered partially to their initial value, suggesting a series combination of viscous element and spring. Because the stretched muscle can bear force at rest, the viscous element must be in parallel with an additional spring. The instantaneous extension-force curves measured at different lengths were nonlinear, and could be made to superimpose by a simple horizontal shift. This finding suggests that the same spring was being measured at each length, and that this spring was in series with both the viscous element and its parallel spring (Voigt configuration), so that the parallel spring is held nearly rigid by the viscous element during rapid steps. The series spring in the passive muscle could account for most of the series elastic recoil in the active muscle, suggesting that the same spring is in series with both the contractile elements and the viscous element. It is postulated that the viscous element might be coupled to the contractile elements by a compliance, so that the load imposed on the contractile elements by the passive structures is viscoelastic rather than purely viscous. Such a viscoelastic load would give the muscle a length-independent, early diastolic restoring force. The possibility is discussed that the length-independent restoring force would allow some of the energy liberated during active shortening to be stored and released during relaxation.     

心钠素前体分子内调控对心肌Na^＋—K^＋—ATP酶的作用

目的：研究利钾尿肽及心钠素前体分子内调控作用对心肌Ｎａ＋Ｋ＋ＡＴＰ酶的作用。方法：将大鼠心肌匀浆后,分别加入利钾尿肽、心钠素以及利钾尿肽＋心钠素,用比色法测定Ｎａ＋Ｋ＋ＡＴＰ酶活性。将大鼠心脏悬挂于Ｌａｎｇｅｎｄｏｒｆ灌流装置,分别以利钾尿肽、心钠素、利钾尿肽＋心钠素为灌流液,灌注心脏,用四道生理仪观测左心室内压、左心室收缩最大速率,左心室舒张最大速率,心率及冠脉流量。结果：心钠素虽然对Ｎａ＋Ｋ＋ＡＴＰ酶有抑制作用（抑制率２６．２％）,但是,与对照无显著性差异（Ｐ＞０．０５）。利钾尿肽显著抑制酶的活性（抑制率４６．５％,Ｐ＜０．０１）这种抑制作用可被心钠素抵消（抑制率１７．６％,Ｐ＞０．０５）。利钾尿肽可以增加左心室收缩和舒张最大速率以及左室内压,而这种强心作用可因心钠素的加入而消失或减弱。结论：利钾尿肽可以抑制心肌Ｎａ＋Ｋ＋ＡＴＰ酶的活性,产生强心作用,心钠素可以抵消以上作用。     

Attenuation of left ventricular dysfunction by an ACE inhibitor after myocardial infarction in a kininogen-deficient rat model

Bradykinin (BK) coronary outflow and left ventricular (LV) performance of kininogen-deficient Brown Norway Katholiek (BNK) rats and Brown Norway Hannover (BNH) controls were investigated. We analyzed whether the angiotensin-converting enzyme (ACE) inhibitor ramipril is able to attenuate LV dysfunction after induction of myocardial infarction (MI) in this animal model. Ex vivo, the basal BK content in the coronary outflow of buffer-perfused, isolated hearts was measured by specific radioimmunoassay. In vivo, left ventricular pressure (LVP), the maximal rate of LVP increase, LV end-diastolic pressure, the maximal rate of LVP decrease and heart rate were determined using a tip catheter 3 weeks after induction of MI. Compared to BNK rats, basal BK outflow was increased 30-fold in controls (p<0.01). In vivo, we found no significant differences between sham-ligated BNK and BNH rats in basal LV function. After MI, the impairment of LV function was significantly worse in BNK rats when compared to BNH rats. ACE inhibition significantly attenuated this LV dysfunction in both groups, when compared to untreated animals. Reduced basal BK level resulting from kininogen deficiency has no effect on basal LV function, but remains to be a risk factor for the ischemic heart. However, ACE inhibition is sufficient to improve LV function despite kininogen deficiency.     

Impaired subendocardial contractile myofiber function in asymptomatic aged humans, as detected using MRI

With aging, structural and functional changes occur in the myocardium without obvious impairment of systolic left ventricular (LV) function. Transmural differences in myocardial vulnerability for these changes may result in increase of transmural inhomogeneity in contractile myofiber function. Subendocardial fibrosis and impairment of subendocardial perfusion due to hypertension might change the transmural distribution of contractile myofiber function. The ratio of LV torsion to endocardial circumferential shortening (torsion-to-shortening ratio; TSR) during systole reflects the transmural distribution of contractile myofiber function. We investigated whether the transmural distribution of systolic contractile myofiber function changes with age. Magnetic resonance tissue tagging was performed to derive LV torsion and endocardial circumferential shortening. TSR was quantified in asymptomatic young [age 23.2 (SD 2.6) yr, n = 15] and aged volunteers [age 68.8 (SD 4.4) yr, n = 16]. TSR and its standard deviation were significantly elevated in the aged group [0.47 (SD 0.12) aged vs. 0.34 (SD 0.05) young; P = 0.0004]. In the aged group, blood pressure and the ratio of LV wall mass to end-diastolic volume were mildly elevated but could not be correlated to the increase in TSR. There were no significant differences in other indexes of systolic LV function such as end-systolic volume and ejection fraction. The elevated systolic TSR in the asymptomatic aged subjects suggests that aging is associated with local loss of contractile myofiber function in the subendocardium relative to the subepicardium potentially caused by subclinical pathological incidents.     

Synchrony of sarcomeric movement regulates left ventricular pump function in the in vivo beating mouse heart

Sarcomeric contraction in cardiomyocytes serves as the basis for the heart’s pump functions. It has generally been considered that in cardiac muscle as well as in skeletal muscle, sarcomeres equally contribute to myofibrillar dynamics in myocytes at varying loads by producing similar levels of active and passive force. In the present study, we expressed α-actinin–AcGFP in Z-disks to analyze dynamic behaviors of sequentially connected individual sarcomeres along a myofibril in a left ventricular (LV) myocyte of the in vivo beating mouse heart. To quantify the magnitude of the contribution of individual sarcomeres to myofibrillar dynamics, we introduced the novel parameter “contribution index” (CI) to measure the synchrony in movements between a sarcomere and a myofibril (from −1 [complete asynchrony] to 1 [complete synchrony]). First, CI varied markedly between sarcomeres, with an average value of ∼0.3 during normal systole. Second, when the movements between adjacent sarcomeres were asynchronous (CI < 0), a sarcomere and the ones next to the adjacent sarcomeres and farther away moved in synchrony (CI > 0) along a myofibril. Third, when difference in LV pressure in diastole and systole (ΔLVP) was lowered to <10 mm Hg, diastolic sarcomere length increased. Under depressed conditions, the movements between adjacent sarcomeres were in marked asynchrony (CI, −0.3 to −0.4), and, as a result, average CI was linearly decreased in association with a decrease in ΔLVP. These findings suggest that in the left ventricle of the in vivo beating mouse heart, (1) sarcomeres heterogeneously contribute to myofibrillar dynamics due to an imbalance of active and passive force between neighboring sarcomeres, (2) the force imbalance is pronounced under depressed conditions coupled with a marked increase in passive force and the ensuing tug-of-war between sarcomeres, and (3) sarcomere synchrony via the distal intersarcomere interaction regulates the heart''s pump function in coordination with myofibrillar contractility.     

Respiratory changes in parasternal intercostal intramuscular pressure

In an attempt to obtain insight in the forces developed by the parasternal intercostal muscles during breathing, changes in parasternal intramuscular pressure (PIP) were measured in 14 supine anesthetized dogs using a microtransducer method. In six animals, during bilateral parasternal stimulation a linear relationship between contractile force exerted on the rib and PIP was demonstrated (r greater than 0.95). In eight animals, during quiet active inspiration, substantial (55 +/- 11.5 cmH2O) PIP was developed. During inspiratory resistive loading and airway occlusion the inspiratory rise in PIP increased in proportion to the inspiratory fall in pleural pressure (r = 0.82). Phrenicotomy and vagotomy resulted in an increase in the inspiratory rise in PIP of 21% and 99%, respectively. During passive deflation, when the parasternal intercostals were passively lengthened, large rises (320 +/- 221 cmH2O) in intramuscular pressure were observed. During passive inflation intramuscular pressure remained constant or even decreased slightly (-8 +/- 25 cmH2O) as expected on the basis of the passive shortening of the muscles. PIP thus invariably increased when tension increased either actively or passively. From PIP it is clear that the parasternals exert significant forces on the ribs during respiratory maneuvers.     

Differences between mouse and rat myocardial contractile responsiveness to calcium

Genetically altered mice have become an increasingly important tool for the study of mechanisms of cardiac function, and therefore it is vital to characterize the basic contractile properties of the mouse heart. As a first approach to this goal, we first optimized perfusion conditions and characterized the effect of incremental left ventricular balloon inflation on end-diastolic, systolic and developed pressures in the isovolumically-contracting mouse heart. Under constant loading conditions, we determined developed pressure in response to changing perfusate calcium (1.25, 2.5, 3.75 and 5.0 mM) and perfusate temperature (30 and 37 degrees C). We then compared the intrinsic inotropic responsiveness to changes in extracellular calcium of left ventricular myocardium from mouse to that from the rat. In the baseline state (1.25 mM extracellular calcium; [Ca2+]o), both isometric contraction duration and normalized active force at the peak of the active force-length relationship (Lmax) were less in mouse than in rat myocardium. Under isotonic conditions, temporal parameters of shortening and the relative shortening were less in mouse vs rat myocardium. Increasing [Ca2+]o from 1.25 to 2.5 mM markedly increased active isometric force and rate of force development (+dF/dt) in the mouse. However, rat myocardium responded to a lesser extent. Under isotonic conditions, peak shortening and the rate of shortening also increased to a greater extent in mouse relative to rat myocardium. Increasing the bath calcium concentration to 5.0 mM increased isometric force and +dF/dt further in the rat but not the mouse, suggesting that two species operate at different points on the force vs [Ca2+]o relationship. We conclude that mouse myocardium exhibits increased sensitivity to changes in [Ca2+]o within the physiologic range in comparison to rat. These differences do not appear to be due to differences in loading conditions. The data suggest that differences in inotropic responsiveness to calcium may reflect intrinsic differences in myocardial calcium sensitivity between species.     

Empirical model for dynamic force-length behavior of airway smooth muscle.

An empirical mathematical model that describes the relation between force and length for dynamic loading of maximally activated airway smooth muscle is described. The model consists of three first-order, ordinary differential equations: one for muscle shortening, one for lengthening, and a third that describes the evolution of an internal variable that depends on muscle history. The model fits data on the dynamic force-length behavior of maximally activated trachealis muscle for a range of amplitudes and rates of shortening and lengthening. The muscle model is incorporated into a model for an intact airway tethered to the surrounding parenchyma. As an example of its use, the model airway is subjected to the loading that occurs during a deep breath. After the breath, the rate of muscle shortening is determined by the interaction between muscle dynamics and the elastic load that is imposed by interdependence forces.     

Effects of smooth muscle activation on axial mechanical properties of excised canine bronchi.

This study tested the hypothesis that airway smooth muscle (ASM) activation produces an airway active axial force (AAAF). Bronchi (n = 10) immersed in a tissue bath containing 95% O2-5% CO2-equilibrated Krebs solution were subjected to passive axial lengthening and shortening at 0-20 cmH2O of transmural pressure. ASM was relaxed with isoproterenol and activated with methacholine. Axial tensile (epsilonx), transverse compressive (epsilony), and shear strains (epsilonxy) were computed from the displacements of four markers placed onto the specimen's surface. The AAAF was estimated by subtracting the control axial force (AF) values at a given epsilonx from those obtained after methacholine. epsilonx-AF relationships were curvilinear, with maximum epsilonx being approached at approximately 15 g of AF. The epsilony decreased during bronchial lengthening. Cholinergic stimulation produced 1) a decrease of both epsilonx and epsilony at a given AF relative to control, indicating ASM shortening, and 2) an AAAF that increased with increasing epsilonx and transmural pressure. A portion of the work of expanding the lungs is required to lengthen the airways; therefore, an AAAF would increase lung elastance and recoil.     

The effects of muscle stretching and shortening on isometric forces on the descending limb of the force-length relationship

The purpose of this study was to examine the effects of stretching and shortening on the isometric forces at different lengths on the descending limb of the force-length relationship. Cat soleus (N = 10) was stretched and shortened by various amounts on the descending limb of the force-length relationship, and the steady-state forces following these dynamic contractions were compared to the isometric forces at the corresponding muscle lengths. We found a shift of the force-length relationship to greater force values following muscle stretching, and to smaller force values following muscle shortening. Shifts in both directions critically depended on the magnitude of stretching/shortening and the final muscle length. We confirm recent findings that the steady-state isometric force following some stretch conditions clearly exceeded the maximal isometric forces at optimum muscle length, and that force enhancement was associated with an increase in the passive force, i.e., a passive force enhancement. When the passive force enhancement was subtracted from the total force enhancement, forces following stretch were always equal to or smaller than the isometric force at optimum muscle length. Together, these findings led to the conclusions: (a). that force enhancement is composed of an "active and a "passive" component; (b). that the "passive" component of force enhancement allows for forces greater than the maximal isometric forces at the muscle's optimum length; and (c). that force enhancement and force depression are critically affected by muscle length and stretch/shortening amplitude.