Lymphangion coordination minimally affects mean flow in lymphatic vessels

The lymphatic system returns interstitial fluid to the central venous circulation, in part, by the cyclical contraction of a series of "lymphangion pumps" in a lymphatic vessel. The dynamics of individual lymphangions have been well characterized in vitro; their frequencies and strengths of contraction are sensitive to both preload and afterload. However, lymphangion interaction within a lymphatic vessel has been poorly characterized because it is difficult to experimentally alter properties of individual lymphangions and because the afterload of one lymphangion is coupled to the preload of another. To determine the effects of lymphangion interaction on lymph flow, we adapted an existing mathematical model of a lymphangion (characterizing lymphangion contractility, lymph viscosity, and inertia) to create a new lymphatic vessel model consisting of several lymphangions in series. The lymphatic vessel model was validated with focused experiments on bovine mesenteric lymphatic vessels in vitro. The model was then used to predict changes in lymph flow with different time delays between onset of contraction of adjacent lymphangions (coordinated case) and with different relative lymphangion contraction frequencies (noncoordinated case). Coordination of contraction had little impact on mean flow. Furthermore, orthograde and retrograde propagations of contractile waves had similar effects on flow. Model results explain why neither retrograde propagation of contractile waves nor the lack of electrical continuity between lymphangions adversely impacts flow. Because lymphangion coordination minimally affects mean flow in lymphatic vessels, lymphangions have flexibility to independently adapt to local conditions.     

Contractions of the lymphangion under low filling conditions and the absence of stretching stimuli. The possibility of the sucking effect

Regulation of the function of the lymphatic pump is tightly connected to the degree of filling of the lymphangion. This mechanism is one of the principle ways that the lymphatics self-regulate lymph transport. But interpretation of the causes and consequences of this regulation is still far from perfect. The issue of whether automatism of electrical activity of the lymphatic smooth muscle cells or the distension of the cell membranes first causes depolarization, is a principal question which needs answering in order to understand the control of lymph transport. In our experiments with perfused isolated bovine mesenteric lymphangions, different values of lymph pressure were simulated. For this purpose, lowfrequency sinusoidal fluctuations of the input pressure were applied to lymphangions under conditions of regulated filling. A poor correlation was seen between lymph pressure fluctuations and lymphangion contractions, as well as between the rate of lymphangion filling and contractions. We observed stable spontaneous contractions of both bovine and rat mesenteric lymphangions at 0 cm of water intralymphatic pressure, and in the absence of distension stimuli (both radial and axial stretch). Under conditions of low filling, contractions of bovine lymphangions produced negative intralymphatic pressure and a suction effect. The automatism is an inherent feature of the lymphatic smooth muscle cells. Distension of the lymphangion modulates the electrical characteristics of the membranes and thus the contractile mechanisms in lymphangions.     

Intrinsic pump-conduit behavior of lymphangions

Lymphangions, segments of lymphatic vessels bounded by valves, have characteristics of both ventricles and arteries. They can act primarily like pumps when actively transporting lymph against a pressure gradient. They also can act as conduit vessels when passively transporting lymph down a pressure gradient. This duality has implications for clinical treatment of several types of edema, since the strategy to optimize lymph flow may depend on whether it is most beneficial for lymphangions to act as pumps or conduits. To address this duality, we employed a simple computational model of a contracting lymphangion, predicted the flows at both positive and negative axial pressure gradients, and validated the results with in vitro experiments on bovine mesenteric vessels. This model illustrates that contraction increases flow for normal axial pressure gradients. With edema, limb elevation, or external compression, however, the pressure gradient might reverse, and lymph may flow passively down a pressure gradient. In such cases, the valves may be forced open during the entire contraction cycle. The vessel thus acts as a conduit, and contraction has the effect of increasing resistance to passive flow, thus inhibiting flow rather than promoting it. This analysis may explain a possible physiological benefit of the observed flow-mediated inhibition of the lymphatic pump at high flow rates.     

Simulation of a chain of collapsible contracting lymphangions with progressive valve closure

The aim of this investigation was to achieve the first step toward a comprehensive model of the lymphatic system. A numerical model has been constructed of a lymphatic vessel, consisting of a short series chain of contractile segments (lymphangions) and of intersegmental valves. The changing diameter of a segment governs the difference between the flows through inlet and outlet valves and is itself governed by a balance between transmural pressure and passive and active wall properties. The compliance of segments is maximal at intermediate diameters and decreases when the segments are subject to greatly positive or negative transmural pressure. Fluid flow is the result of time-varying active contraction causing diameter to reduce and is limited by segmental viscous and valvular resistance. The valves effect a smooth transition from low forward-flow resistance to high backflow resistance. Contraction occurs sequentially in successive lymphangions in the forward-flow direction. The behavior of chains of one to five lymphangions was investigated by means of pump function curves, with variation of valve opening parameters, maximum contractility, lymphangion size gradation, number of lymphangions, and phase delay between adjacent lymphangion contractions. The model was reasonably robust numerically, with mean flow-rate generally reducing as adverse pressure was increased. Sequential contraction was found to be much more efficient than synchronized contraction. At the highest adverse pressures, pumping failed by one of two mechanisms, depending on parameter settings: either mean leakback flow exceeded forward pumping or contraction failed to open the lymphangion outlet valve. Maximum pressure and maximum flow-rate were both sensitive to the contractile state; maximum pressure was also determined by the number of lymphangions in series. Maximum flow-rate was highly sensitive to the transmural pressure experienced by the most upstream lymphangions, suggesting that many feeding lymphatics would be needed to supply one downstream lymphangion chain pumping at optimal transmural pressure.     

Network Scale Modeling of Lymph Transport and Its Effective Pumping Parameters

The lymphatic system is an open-ended network of vessels that run in parallel to the blood circulation system. These vessels are present in almost all of the tissues of the body to remove excess fluid. Similar to blood vessels, lymphatic vessels are found in branched arrangements. Due to the complexity of experiments on lymphatic networks and the difficulty to control the important functional parameters in these setups, computational modeling becomes an effective and essential means of understanding lymphatic network pumping dynamics. Here we aimed to determine the effect of pumping coordination in branched network structures on the regulation of lymph flow. Lymphatic vessel networks were created by building upon our previous lumped-parameter model of lymphangions in series. In our network model, each vessel is itself divided into multiple lymphangions by lymphatic valves that help maintain forward flow. Vessel junctions are modeled by equating the pressures and balancing mass flows. Our results demonstrated that a 1.5 s rest-period between contractions optimizes the flow rate. A time delay between contractions of lymphangions at the junction of branches provided an advantage over synchronous pumping, but additional time delays within individual vessels only increased the flow rate for adverse pressure differences greater than 10.5 cmH₂O. Additionally, we quantified the pumping capability of the system under increasing levels of steady transmural pressure and outflow pressure for different network sizes. We observed that peak flow rates normally occurred under transmural pressures between 2 to 4 cmH₂O (for multiple pressure differences and network sizes). Networks with 10 lymphangions per vessel had the highest pumping capability under a wide range of adverse pressure differences. For favorable pressure differences, pumping was more efficient with fewer lymphangions. These findings are valuable for translating experimental measurements from the single lymphangion level to tissue and organ scales.     

Single-beat estimation of right ventricular end-systolic pressure-volume relationship

Assessment of right ventricular (RV) contractility from end-systolic pressure-volume relationships (ESPVR) is difficult due to problems in measuring RV instantaneous volume and to effects of changes in RV preload or afterload. We therefore investigated in anesthetized dogs whether RV ESPVR and contractility can be determined without measuring RV volume and without changing RV preload or afterload. The maximal RV pressure of isovolumic beats (P(max)) was predicted from isovolumic portions of RV pressure during ejecting beats and compared with P(max) measured during the first beat after pulmonary artery clamping. In RV pressure-volume loops obtained from RV pressure and integrated pulmonary arterial flow, end-systolic elastance (E(es)) was assessed as the slope of P(max)-derived ESPVR, pulmonary artery effective elastance (E(a)) as the slope of end-diastolic to end-systolic relation, and coupling efficiency as the E(es)-to-E(a) ratio (E(es)/E(a)). Predicted P(max) correlated with observed P(max) (r = 0.98 +/- 0.02). Dobutamine increased E(es) from 1.07 to 2.00 mmHg/ml and E(es)/E(a) from 1.64 to 2.49, and propranolol decreased E(es)/E(a) from 1.64 to 0.91 (all P < 0.05). After adrenergic blockade, preload reduction did not affect E(es), whereas hypoxia and arterial constriction markedly increased E(a) and somewhat increased E(es) due to the Anrep effect. Low preload did not affect E(es)/E(a) and high afterload decreased E(es)/E(a). In conclusion, in the right ventricle 1) P(max) can be calculated from normal beats, 2) P(max) can be used to determine ESPVR without change in load, and 3) P(max)-derived ESPVR can be used to assess ventricular contractility and ventricular-arterial coupling efficiency.     

Contraction of collecting lymphatics: organization of pressure-dependent rate for multiple lymphangions

The paper describes the extension of a previously developed model of pressure-dependent contraction rate to the case of multiple lymphangions. Mechanical factors are key modulators of active lymphatic pumping. As part of the evolution of our lumped-parameter model to match experimental findings, we have designed an algorithm whereby the time until the next contraction depends on lymphangion transmural pressure in the contraction just completed. The functional dependence of frequency on pressure is quantitatively matched to isobaric contraction experiments on isolated lymphatic segments. When each of several lymphangions is given this ability, a scheme for their coordination must be instituted to match the observed synchronization. Accordingly, and in line with an experiment on an isolated lymphatic vessel segment in which we measured contraction sequence and conduction delay, we took the fundamental principle to be that local timing can be overridden by signals to initiate contraction that start in adjacent lymphangions, conducted with a short delay. The scheme leads to retrograde conduction when the lymphangion chain is pumping against an adverse pressure difference, but antegrade conduction when contractions occur with no or a favourable pressure difference. Abolition of these conducted signals leads to chaotic variation of cycle-mean flow-rate from the chain, diastolic duration in each lymphangion, and inter-lymphangion delays. Chaotic rhythm is also seen under other circumstances. Because the model responds to increasing adverse pressure difference by increasing the repetition rate of contractions, it maintains time-average output flow-rate better than one with fixed repetition rate.     

Normal distribution of ventricular pressure-volume area of arrhythmic beats under atrial fibrillation in canine heart

We previously found the frequency distribution of the left ventricular (LV) effective afterload elastance (E(a)) of arrhythmic beats to be nonnormal or non-Gaussian in contrast to the normal distribution of the LV end-systolic elastance (E(max)) in canine in situ LVs during electrically induced atrial fibrillation (AF). These two mechanical variables determine the total mechanical energy [systolic pressure-volume area (PVA)] generated by LV contraction when the LV end-diastolic volume is given on a per-beat basis. PVA and E(max) are the two key determinants of the LV O(2) consumption per beat. In the present study, we analyzed the frequency distribution of PVA during AF by its chi(2), significance level, skewness, and kurtosis and compared them with those of other major cardiodynamic variables including E(a) and E(max). We assumed the volume intercept (V(0)) of the end-systolic pressure-volume relation needed for E(max) determination to be stable during arrhythmia. We found that PVA distributed much more normally than E(a) and slightly more so than E(max) during AF. We compared the chi(2), significance level, skewness, and kurtosis of all the complex terms of the PVA formula. We found that the complexity of the PVA formula attenuated the effect of the considerably nonnormal distribution of E(a) on the distribution of PVA along the central limit theorem. We conclude that mean (SD) of PVA can reliably characterize the distribution of PVA of arrhythmic beats during AF, at least in canine hearts.     

Measuring right ventricular function in the normal and hypertensive mouse hearts using admittance-derived pressure-volume loops

Mice are a widely used animal model for investigating cardiovascular disease. Novel technologies have been used to quantify left ventricular function in this species, but techniques appropriate for determining right ventricular (RV) function are less well demonstrated. Detecting RV dysfunction is critical to assessing the progression of pulmonary vascular diseases such as pulmonary hypertension. We used an admittance catheter to measure pressure-volume loops in anesthetized, open-chested mice before and during vena cava occlusion. Mice exposed to chronic hypoxia for 10 days, which causes hypoxia-induced pulmonary hypertension (HPH), were compared with control (CTL) mice. HPH resulted in a 27.9% increase in RV mass (P < 0.005), a 67.5% increase in RV systolic pressure (P < 0.005), and a 61.2% decrease in cardiac output (P < 0.05). Preload recruitable stroke work (PRSW) and slope of the maximum derivative of pressure (dP/dt(max))-end-diastolic volume (EDV) relationship increased with HPH (P < 0.05). Although HPH increased effective arterial elastance (E(a)) over fivefold (from 2.7 ± 1.2 to 16.4 ± 2.5 mmHg/μl), only a mild increase in the ventricular end-systolic elastance (E(es)) was observed. As a result, a dramatic decrease in the efficiency of ventricular-vascular coupling occurred (E(es)/E(a) decreased from 0.71 ± 0.27 to 0.35 ± 0.17; P < 0.005). Changes in cardiac reserve were evaluated by dobutamine infusion. In CTL mice, dobutamine significantly enhanced E(es) and dP/dt(max)-EDV but also increased E(a), causing a decrease in E(es)/E(a). In HPH mice, slight but nonsignificant decreases in E(es), PRSW, dP/dt(max)-EDV, and E(a) were observed. Thus 10 days of HPH resulted in RV hypertrophy, ventricular-vascular decoupling, and a mild decrease in RV contractile reserve. This study demonstrates the feasibility of obtaining RV pressure-volume measurements in mice. These measurements provide insight into ventricular-vascular interactions healthy and diseased states.     

Relation of effective arterial elastance to arterial system properties

Effective arterial elastance (E(a)), defined as the ratio of left ventricular (LV) end-systolic pressure and stroke volume, lumps the steady and pulsatile components of the arterial load in a concise way. Combined with E(max), the slope of the LV end-systolic pressure-volume relation, E(a)/E(max) has been used to assess heart-arterial coupling. A mathematical heart-arterial interaction model was used to study the effects of changes in peripheral resistance (R; 0.6-1.8 mmHg x ml(-1) x s) and total arterial compliance (C; 0.5-2.0 ml/mmHg) covering the human pathophysiological range. E(a), E(a)/E(max,) LV stroke work, and hydraulic power were calculated for all conditions. Multiple-linear regression analysis revealed a linear relation between E(a), R/T (where T is cycle length), and 1/C: E(a) = -0.13 + 1.02R/T + 0.31/C, indicating that R/T contributes about three times more to E(a) than arterial stiffness (1/C). It is demonstrated that different pathophysiological combinations of R and C may lead to the same E(a) and E(a)/E(max) but can result in differences of 10% in stroke work and 50% in maximal power.     

A lumped parameter model of mechanically mediated acute and long-term adaptations of contractility and geometry in lymphatics for characterization of lymphedema

A primary purpose of the lymphatic system is to transport fluid from peripheral tissues to the central venous system in order to maintain tissue–fluid balance. Failure to perform this task results in lymphedema marked by swelling of the affected limb as well as geometric remodeling and reduced contractility of the affected lymphatic vessels. The mechanical environment has been implicated in the regulation of lymphatic contractility, but it is unknown how changes in the mechanical environment are related to loss of contractile function and remodeling of the tissue. The purpose of this paper was to introduce a new theoretical framework for acute and long-term adaptations of lymphatic vessels to changes in mechanical loading. This theoretical framework combines a simplified version of a published lumped parameter model for lymphangion function and lymph transport, a published microstructurally motivated constitutive model for the active and passive mechanical behavior of isolated rat thoracic ducts, and novel models for acute mechanically mediated vasoreactive adaptations and long-term volumetric growth to simulate changes in muscle contractility and geometry of a single isolated rat thoracic duct in response to a sustained elevation in afterload. The illustrative examples highlight the potential role of the mechanical environment in the acute maintenance of contractility and long-term geometric remodeling, presumably aimed at meeting fluid flow demands while also maintaining mechanical homeostasis. Results demonstrate that contractility may adapt in response to shear stress to meet fluid flow demands and show that pressure-induced long-term geometric remodeling may attenuate these adaptations and reduce fluid flow. The modeling framework and illustrative simulations help suggest relevant experiments that are necessary to accurately quantify and predict the acute and long-term adaptations of lymphangions to altered mechanical loading.     

ENOS,ET-1 and ETB-R immunoreactivities in the porcine mesometrial lymphatics during the estrous cycle

Abstract: Immunohistochemical localization and distribution of nitric oxide synthase (eNOS), endothelin (ET-1) and endothelin beta receptor (ETB-R) were investigated in precollector and collector lymph vessels in the broad ligament of the uterus during different phases of the estrous cycle in pigs. The polyclonal antibody for ET-1 and ETB-R and monoclonal antibody for eNOS isoform were used to perform observations on the light microscopic level. Immunoreactivities to ET-1, ETB-R and eNOS were observed in the endothelium of precollector and collector lymphangions but not in smooth muscle cells of the lymphatics examined. The staining for eNOS in the endothelial cells of all studied lymphatic vessels was stronger comparing to ET-1 and ETB-R. During the estrous cycle, only eNOS showed the correlation with the particular phases of the estrous cycle. The differences between ET-1 and ETB-R immunoreactivities were very slight and rather independent of the size or type of the lymphatic lymphangions and estrous cycle. The highest immunoreactivity level for eNOS was displayed by collector lymphangions with widened lumen in the follicular phase comparing to the precollector ones. During the luteal phase, a slight decrease in the reaction intensity was observed. The immunoreactivities for ET-1 in the endothelium of the studied vessels was not comparable with the presence or with the reactivity level of ETB-R. Optically stronger immunoreaction for ETB-R was observed in the cytoplasm of collector lymphangions in the follicular phase. eNOS, ET-1 and ETB-R were also present in the cytoplasm of the lymphatic valves. These results suggest that ET-1 and eNOS can play a role in the mechanisms regulating the vascular contractile activity, promoting lymph flow during the estrous cycle in the porcine broad ligament.     

Systolic elastance and resistance in the regulation of cardiac pumping function in early streptozotocin-diabetic rats

We determined the roles of maximal systolic elastance (E(max)) and theoretical maximum flow ((max)) in the regulation of cardiac pumping function in early streptozotocin (STZ)-diabetic rats. Physically, E(max) can reflect the intrinsic contractility of the myocardium as an intact heart, and (max) has an inverse relation to the systolic resistance of the left ventricle. Rats given STZ 65 mg/kg i.v. (n = 17) were divided into two groups, 1 week and 4 weeks after induction of diabetes, and compared with untreated age-matched controls (n = 15). Left ventricular (LV) pressure and ascending aortic flow signals were recorded to calculate E(max) and (max), using the elastance-resistance model. After 1 or 4 weeks, STZ-diabetic animals show an increase in effective LV end-diastolic volume (V(eed)), no significant change in peak isovolumic pressure (P(iso)(max)), and a decline in effective arterial volume elastance (E(a)). The maximal systolic elastance E(max) is reduced from 751.5 +/- 23.1 mmHg/ml in controls to 514.1 +/- 22.4 mmHg/ml in 1- and 538.4 +/- 33.8 mmHg/ml in 4-week diabetic rats. Since E(max) equals P(iso)(max)/V(eed), an increase in V(eed) with unaltered P(iso)(max) may primarily act to diminish E(max) so that the intrinsic contractility of the diabetic heart is impaired. By contrast, STZ-diabetic rats have higher theoretical maximum flow (max) (40.9 +/- 2.8 ml/s in 1- and 44.5 +/- 3.8 ml/s in 4-week diabetic rats) than do controls (30.7 +/- 1.7 ml/s). There exists an inverse relation between (max) and E(a) when a linear regression of (max) on E(a) is performed over all animals studied (r = 0.65, p < 0.01). The enhanced (max) is indicative of the decline in systolic resistance of the diabetic rat heart. The opposing effects of enhanced (max) and reduced E(max) may negate each other, and then the cardiac pumping function of the early STZ-diabetic rat heart could be preserved before cardiac failure occurs.     

Pressure-volume-based single-beat estimations cannot predict left ventricular contractility in vivo

The end-systolic pressure-volume relationship is regarded as a useful index for assessing the contractile state of the heart. However, the need for preload alterations has been a serious limitation to its clinical applications, and there have been numerous attempts to develop a method for calculating contractility based on one single pressure-volume loop. We have evaluated four of these methods. Pressure-volume data were obtained by combined pressure and conductance catheters in 37 pigs. All four methods were applied to 88 steady-state pressure-volume files, including eight files sampled during dopamine infusions. Estimates of single-beat contractility (elastance) were compared with preload-varied multiple-beat elastance [E(es(MB))]. All methods had a low average bias (-0.3 to 0.5 mmHg/ml) but limits of agreement (+/-2 SD) were unacceptably high (+/-2.6 to +/-3.8 mmHg/ml). In the dopamine group, E(es(MB)) showed an increase of 1.7 +/- 0.8 mmHg/ml (mean +/- SD) compared with baseline (P < 0.001). None of the single-beat methods predicted this increase in contractility. It is therefore doubtful whether any of the methods allow for single-beat assessment of contractility.     

A multiscale sliding filament model of lymphatic muscle pumping

The lymphatics maintain fluid balance by returning interstitial fluid to veins via contraction/compression of vessel segments with check valves. Disruption of lymphatic pumping can result in a condition called lymphedema with interstitial fluid accumulation. Lymphedema treatments are often ineffective, which is partially attributable to insufficient understanding of specialized lymphatic muscle lining the vessels. This muscle exhibits cardiac-like phasic contractions and smooth muscle-like tonic contractions to generate and regulate flow. To understand the relationship between this sub-cellular contractile machinery and organ-level pumping, we have developed a multiscale computational model of phasic and tonic contractions in lymphatic muscle and coupled it to a lymphangion pumping model. Our model uses the sliding filament model (Huxley in Prog Biophys Biophys Chem 7:255–318, 1957) and its adaptation for smooth muscle (Mijailovich in Biophys J 79(5):2667–2681, 2000). Multiple structural arrangements of contractile components and viscoelastic elements were trialed but only one provided physiologic results. We then coupled this model with our previous lumped parameter model of the lymphangion to relate results to experiments. We show that the model produces similar pressure, diameter, and flow tracings to experiments on rat mesenteric lymphatics. This model provides the first estimates of lymphatic muscle contraction energetics and the ability to assess the potential effects of sub-cellular level phenomena such as calcium oscillations on lymphangion outflow. The maximum efficiency value predicted (40%) is at the upper end of estimates for other muscle types. Spontaneous calcium oscillations during diastole were found to increase outflow up to approximately 50% in the range of frequencies and amplitudes tested.

     

Pressure-volume properties of the upper airway of rabbits

In 10 anesthetized rabbits the upper airway cephalad of the vocal cords was isolated from the distal airway and sealed. Static deflation pressure-volume data were recorded from the isolated upper airway. The relationship between pressure and volume in the upper airway was a straight line; the correlation coefficient (r) ranged from 0.97 to 1.00. The following quantities were derived from the data: the pressure-volume ratio (upper airway elastance, cmH2O/ml), the pressure in the airway at airway closure (closing pressure, cmH2O), and the airway volume at zero airway pressure (reserve volume, ml). Mean upper airway elastance was 8.13 +/- 1.45 [95% confidence intervals (CI)] cmH2O/ml, closing pressure was -6.93 +/- 1.53 (95% CI) cmH2O, and reserve volume was 0.74 +/- 0.15 (95% CI) ml. There was no significant correlation between elastance and closing pressure (r = 0.47, P greater than 0.1), but closing pressure and reserve volume were significantly correlated (r = 0.77, P less than 0.01). Pressure-volume data recorded from newly dead animals exhibited the same linear relationship between pressure and volume observed in living animals. It is concluded that the pressure-volume properties of the isolated upper airway of the rabbit can be expressed as a single value for airway elastance, that estimation of pressure-volume properties over part of the volume range is representative of the whole volume range, and that pressure-volume properties are determined by passive elastic properties of the airway tissues. It appears that the resistance of the upper airway to collapse by negative intraluminal pressure is more dependent on the initial size of the airway than on its elastance.     

Noninvasive quantitative imaging of lymph function in mice

BACKGROUND: Whereas functional lymph imaging in rodents is imperative for drug discovery of lymph therapeutics, noninvasive imaging of propulsive lymph function in rodents has not been reported previously. Herein, we present a noninvasive and rapid approach to measure lymphatic function in a rodent model using a near-infrared (NIR) dye to minimize background autofluorescence and maximize tissue penetration. METHODS AND RESULTS: Mice were dynamically imaged following intradermal (i.d.) injection of 2 to 10 microL of 1.3 mM of indocyanine green (IC-Green) into the tail and the limb. Our results demonstrate the ability to image the IC-Green trafficking from the lymph plexus, through lymph vessels and lymphangions, to the ischial nodes in the tail, and to the axillary nodes in the limb. Our results show that lymph flow velocity from the propelled IC-Green "packet" in the lymph vessels in the tail ranged from 1.3 to 3.9 mm/s and the fluorescence intensity peaks repeated on an average of every 51.3 +/- 17.4 seconds in five animals. While pulsatile lymph flow was detected in the deep lymph vessels, lymph propulsion was not visualized in the superficial lymphatic network in the tail. In axillary lymphatic imaging, propulsive lymph flow was also detected. The intensity profile shows that the lymph flow velocity ranged from 0.28 to 1.35 mm/s at a frequency ranging from 0.72 to 11.1 pulses per minute in five animals. CONCLUSIONS: Our study demonstrates the ability to noninvasively and quantitatively image propulsive lymph flow, which could provide a new method to investigate lymph function and its change in response to potential therapeutics.     

A one-dimensional mathematical model of collecting lymphatics coupled with an electro-fluid-mechanical contraction model and valve dynamics

We propose a one-dimensional model for collecting lymphatics coupled with a novel Electro-Fluid-Mechanical Contraction (EFMC) model for dynamical contractions, based on a modified FitzHugh–Nagumo model for action potentials. The one-dimensional model for a deformable lymphatic vessel is a nonlinear system of hyperbolic Partial Differential Equations (PDEs). The EFMC model combines the electrical activity of lymphangions (action potentials) with fluid-mechanical feedback (circumferential stretch of the lymphatic wall and wall shear stress) and lymphatic vessel wall contractions. The EFMC model is governed by four Ordinary Differential Equations (ODEs) and phenomenologically relies on: (1) environmental calcium influx, (2) stretch-activated calcium influx, and (3) contraction inhibitions induced by wall shear stresses. We carried out a stability analysis of the stationary state of the EFMC model. Contractions turn out to be triggered by the instability of the stationary state. Overall, the EFMC model allows emulating the influence of pressure and wall shear stress on the frequency of contractions observed experimentally. Lymphatic valves are modelled by extending an existing lumped-parameter model for blood vessels. Modern numerical methods are employed for the one-dimensional model (PDEs), for the EFMC model and valve dynamics (ODEs). Adopting the geometrical structure of collecting lymphatics from rat mesentery, we apply the full mathematical model to a carefully selected suite of test problems inspired by experiments. We analysed several indices of a single lymphangion for a wide range of upstream and downstream pressure combinations which included both favourable and adverse pressure gradients. The most influential model parameters were identified by performing two sensitivity analyses for favourable and adverse pressure gradients.     

Global cardiac function: mechano-energetico-informatics

This review on the global cardiac function covers cardiac mechanics, energetics, and informatics that I have developed with my collaborators over the last 30 years in Japan and USA. We first established E(max) (end-systolic maximum elastance or pressure/volume ratio) as a new index of ventricular contractility using canine hearts. We then expanded the E(max) concept to PVA (systolic pressure-volume area consisting of external mechanical work and mechanical potential energy) as an innovative measure of total mechanical energy of ventricular contraction and discovered it to be a reliable determinant of ventricular energetics or O(2) consumption (V(O(2))). We have discovered that E(max) shifts the V(O(2))-PVA relation and the E(max) dependency (O(2) cost of E(max)) varies among different pathophysiological hearts. We also searched for the basis of E(max) in crossbridge behavior information contained in an X-ray diffraction of papillary muscle. Recently, we established a new integrative analysis to estimate total Ca(2+) recruited for excitation-contraction coupling in a beating heart using the E(max)-PVA-V(O(2)) information. These global, mechano-energetico-informatic approaches seem to facilitate better understanding of cardiac function, as required in the present post-genomic era when more physiomic knowledge is required not only in cardiac function but also in all other physiologic functions.     

Heart failure attenuates muscle metaboreflex control of ventricular contractility during dynamic exercise

Underperfusion of active skeletal muscle elicits a reflex pressor response termed the muscle metaboreflex (MMR). In normal dogs during mild exercise, MMR activation causes large increases in cardiac output (CO) and mean arterial pressure (MAP); however, in heart failure (HF) although MAP increases, the rise in CO is virtually abolished, which may be due to an impaired ability to increase left ventricular contractility (LVC). The objective of the present study was to determine whether the increases in LVC seen with MMR activation during dynamic exercise in normal animals are abolished in HF. Conscious dogs were chronically instrumented to measure CO, MAP, and left ventricular (LV) pressure and volume. LVC was calculated from pressure-volume loop analysis [LV maximal elastance (E(max)) and preload-recruitable stroke work (PRSW)] at rest and during mild and moderate exercise under free-flow conditions and with MMR activation (via partial occlusion of hindlimb blood flow) before and after rapid ventricular pacing-induced HF. In control experiments, MMR activation at both workloads [mild exercise (3.2 km/h) and moderate exercise (6.4 km/h at 10% grade)] significantly increased CO, E(max), and PRSW. In contrast, after HF was induced, CO, E(max), and PRSW were significantly lower at rest. Although CO increased significantly from rest to exercise, E(max) and PRSW did not change. In addition, MMR activation caused no significant change in CO, E(max), or PRSW at either workload. We conclude that MMR causes large increases in LVC in normal animals but that this ability is abolished in HF.