A Mathematical Treatment of Munch's Pressure-Flow Hypothesis of Phloem Translocation

The steady state solutions of two mathematical models are used to evaluate Münch's pressure-flow hypothesis of phloem translocation. The models assume a continuous active loading and unloading of translocate but differ in the site of loading and unloading and the route of water to the sieve tube. The dimensions of the translocation system taken are the average observed values for sugar beet and are intended to simulate translocation from a mature source leaf to an expanding sink leaf. The volume flow rate of solution along the sieve tube, water flow rate into the sieve tube, hydrostatic pressure, and concentration of sucrose in the sieve tube are obtained from a numerical computer solution of the models. The mass transfer rate, velocity of translocation, and osmotic and hydrostatic pressures are consistent with empirical findings. Owing to the resistance to water flow offered by the lateral membranes, the hydrostatic pressure generated by the osmotic pressure can be considerably less than would be predicted by the solute concentration. These models suggest that translocation at observed rates and velocities can be driven by a water potential difference between the sieve tube and surrounding tissue and are consistent with the pressure-flow hypothesis of translocation.     

Effect of angiotensin inhibition on the coronary artery lower pressure limit in anesthetized dogs

The renin-angiotensin system plays a critical role in regulating vasoconstriction and vasodilatation that can influence myocardial blood flow and its transmural distribution. We tested the hypothesis that angiotensin inhibition can induce a leftward shift of the coronary autoregulatory pressure-flow relation and preserve distribution of myocardial blood flow at lower coronary perfusion pressures. We established circumflex artery pressure-flow relations under baseline conditions and after intracoronary enalaprilat or losartan potassium. Thereafter, transmural myocardial blood flow was measured at baseline and at the lower coronary pressure limit (LPL). With enalaprilat, the LPL was shifted leftward from 48 +/- 6 mmHg at baseline to 43 +/- 3 mmHg (P = 0.026); with losartan, the LPL was shifted leftward from 48 +/- 10 mmHg at baseline to 41 +/- 5 mmHg (P = 0.027). The leftward shift occurred while cardiac hemodynamics and MVO2 were maintained at control levels. These results indicate that angiotensin inhibition extends the range of coronary autoregulation to lower LPL while preserving myocardial blood flow distribution, a physiologic effect that might explain the lower incidence of coronary events in treated patients.     

Pliometric activity of inspiratory muscles: maximal pressure-flow curves

We tested the hypothesis that inspiratory muscles, like other skeletal muscles, would exert greater force under pliometric conditions (being lengthened while active) than under isometric or miometric (active shortening) conditions. Maximal inspiratory pressure-flow curves of the respiratory system are analogous to the force-velocity curves for isolated muscle (Agostoni and Fenn, J. Appl. Physiol. 15:349-353, 1960). We measured esophageal pressure (Pes) and plethysmographic flow (V) at relaxation volume of the respiratory system in six trained subjects inspiring maximally through graded resistors (miometric), against a closed airway (isometric), and while constant expiratory flows were forced by a reduced pressure source at the airway opening (pliometric). Pes varied inversely with V and this trend continued into the pliometric range. In addition we found that the pressure-flow characteristics of the rib cage and of the abdomen are similar to those for the chest wall as a whole. The mechanical and energetic advantages of muscle activity under pliometric conditions may be available to some inspiratory muscles in both normal and pathological situations.     

Sieve-plate pores,open or occluded? A critical review

Abstract It is widely believed that there is a growing body of evidence that sieve plate pores in functioning phloem are open and quite free from obstruction. The arguments used to establish this idea are critically examined one by one and the conclusion is reached that it has very little foundation in published work. On the contrary, the view that sieve plate pores are delicately-occluded with P-protein in the angiosperms has much more evidence to substantiate it. Since ‘open’ and ‘occluded’ are physiologically defined this means that the pressure-flow hypothesis must be regarded as seriously in doubt.     

A continuum model for pressure-flow relationship in human pulmonary circulation

A continuum model was introduced to analyze the pressure-flow relationship for steady flow in human pulmonary circulation. The continuum approach was based on the principles of continuum mechanics in conjunction with detailed measurement of vascular geometry, vascular elasticity and blood rheology. The pulmonary arteries and veins were considered as elastic tubes and the "fifth-power law" was used to describe the pressure-flow relationship. For pulmonary capillaries, the "sheet-flow" theory was employed and the pressure-flow relationship was represented by the "fourth-power law". In this paper, the pressure-flow relationship for the whole pulmonary circulation and the longitudinal pressure distribution along the streamlines were studied. Our computed data showed general agreement with the experimental data for the normal subjects and the patients with mitral stenosis and chronic bronchitis in the literature. In conclusion, our continuum model can be used to predict the changes of steady flow in human pulmonary circulation.     

Effect of aminophylline on hindlimb blood flow autoregulation during increased metabolism in dogs

The contribution of adenosine to hindlimb blood flow autoregulation during treadmill exercise or the administration of 2,4-dinitrophenol (DNP) was evaluated in 9 conscious dogs by determining hindlimb vascular bed pressure-flow relationships in the presence and absence of the adenosine receptor site antagonist, aminophylline. Hindlimb pressure-flow relationships were obtained by measuring blood flow during stepwise reductions in perfusion pressure produced with an occlusion cuff located distal to a flow probe on the external iliac artery. The efficiency of autoregulation was quantitated by calculating the closed-loop gain of flow regulation (Gc) at each pressure decrement utilizing the equation Gc = 1 - (% delta flow/% delta pressure). A Gc of one represents perfect autoregulation of flow, and a Gc of zero is indicative of a rigid system. During exercise, Gc averaged 0.44 +/- 0.07. Aminophylline reduced the Gc during exercise to -0.07 +/- 0.06 (P less than 0.05). During DNP administration, Gc averaged 0.54 +/- 0.09 and declined to -0.09 +/- 0.10 in the presence of aminophylline (P less than 0.05). These results support the hypothesis that adenosine is a primary mediator of hindlimb blood flow autoregulation during conditions that increase hindlimb metabolism.     

The structure of the phloem--still more questions than answers

Long-distance assimilate distribution in higher plants takes place in the enucleate sieve-tube system of the phloem. It is generally accepted that flow of assimilates is driven by an osmotically generated pressure differential, as proposed by Ernst Münch more than 80?years ago. In the period between 1960 and 1980, the pressure flow hypothesis was challenged when electron microscopic images suggested that sieve tubes contain obstructions that would prevent passive flow. This led to the proposal of alternative translocation mechanisms. However, most investigators came to the conclusion that obstructions in the sieve-tube path were due to preparation artifacts. New developments in bioimaging have vastly enhanced our ability to study the phloem. Unexpectedly, in vivo studies challenge the pressure-flow hypothesis once again. In this review we summarize current investigations of phloem structure and function and discuss their impact on our understanding of long-distance transport in the phloem.     

The state of the pores in functioning sieve plates

Summary Electron microscopy of Helianthus stem and Saxifraga sarmentosa stolon after first plunging the material into boiling water indicates that the natural condition of the sieve plate pores is to be plugged fairly compactly with slime substance. Electron microscopy of pre-wilted plants demonstrates the same thing. These and other arguments indicate that the slime-filled condition of the pores is not an artifact induced by enzyme action or turgor release, nor is it a consequence of rapid translocation of slime; it is the natural state. This conclusion, very damaging to the pressure-flow hypothesis, is favourable to the electroosmotic theory.     

A simple distensible vessel model for interpreting pulmonary vascular pressure-flow curves.

A simple distensible vessel model was developed for the purpose of interpreting the vascular pressure-flow curve in the zone 3 lung. The model-governing equation has two parameters: R0, representing the hemodynamic resistance of the undistended pulmonary vascular bed, and alpha, representing the distensibility of the resistance vessels. To evaluate the model, the governing equation was used in a nonlinear regression analysis of the pressure-flow data from isolated dog lung lobes. The dependency of the estimates of the model parameters in response to changes in perfusate viscosity (hematocrit) was determined. The distensible vessel model provided reasonable fits to the data, and, as predicted, R0, but not alpha, was hematocrit dependent. On the other hand, the traditional linear ohmic-Starling resistor model fit to the same pressure-flow data generally provided fits approaching those of the distensibility model only if the pressure intercept (the mean "critical closing pressure") was allowed to increase with hematocrit. Because the ohmic-Starling resistor concept does not predict a hematocrit dependence of the critical closing pressure, this latter observation is evidence that the distensible vessel model offers an alternative conceptualization of the pulmonary circulation worthy of additional study with respect to the interpretation of experimental pressure-flow data.     

The pressure-flow relation for plasma in whole organ skeletal muscle and its experimental verification.

The whole-organ pressure-flow relation in resting rat skeletal muscle is examined for the flow of plasma. Due to the small size of the blood vessels in this organ, inertia and convective forces in the blood are negligible and viscous forces dominate. Direct measurements in the past have shown that skeletal muscle blood vessels are distensible. Theoretical formulations based on these measurements lead to a third order polynomial model for the pressure-flow relation. The purpose of the current study is to examine this relation experimentally in an isolated muscle organ. A high precision feedback controlled pump is used to perfuse artificial plasma into the vasodilated rat gracilis muscle. The results indicate that the pressure-flow curve in this tissue is nonlinear in the low flow region and almost linear at physiological flow rates, following closely the third order polynomial function. Vessel fixation with glutaraldehyde causes the curves to become linear at all pressures, indicating that vessel distention is the primary mechanism causing the nonlinearity. Furthermore, the resistance of the post-fixed tissue is determined by the pressure at which the fixative is perfused. At fixation pressures below 10 mmHg, the resistance is three times higher than in vessels fixed at normal physiological pressures. Dextran (229,000 Dalton) is used to obtain Newtonian perfusates at different viscosities. The pressure-flow relation is found to be linearly dependent on viscosity for all flow rates.(ABSTRACT TRUNCATED AT 250 WORDS)     

The pressure-flow relation in resting rat skeletal muscle perfused with pure erythrocyte suspensions

In spite of numerous investigations of erythrocyte rheology, there is limited information about the influence of erythrocyte suspensions on whole organ pressure-flow relationships. In this study, we present whole organ pressure-flow curves for resting vasodilated gracilis muscle of the rat, in which the microanatomy and vessel properties have been determined previously. For pure erythrocyte suspensions from donor rats, the organ resistance increases only mildly with perfusion time (less than a 5% shift over a one-hour perfusion time), while in contrast, erythrocyte suspensions containing leukocytes show an increases of resistance near 100% over a period of 25 min. Variation in pressure-flow curves in the muscle at the same arterial hematocrit between different rats is less than 15%. The pressure-flow relation for pure erythrocyte suspensions depends on hematocrit. Shear thinning is exhibited at high hematocrits, while Newtonian behavior is approached at arterial hematocrits below 15%. The whole organ apparent viscosity for pure erythrocyte suspensions (normalized by cell-free plasma resistance) is a non-linear function of hematocrit; at physiological pressures, it reaches values comparable to those of apparent viscosities measured in rotational viscometers or in in vitro tube flow (diameters greater than 0.8 mm). The apparent viscosities estimated from the whole organ experiments tend to be higher than those measured in straight tubes under in vitro conditions. The pressure-flow curves for pure erythrocyte suspensions are shifted towards lower pressures than the curves for mixed suspensions of erythrocytes at the same hematocrit and with leukocytes at physiological cell counts. These acute experiments show that pure erythrocyte suspensions yield highly reproducible resistances in the skeletal muscle microcirculation with dilated arterioles. Relative apparent viscosities measured in vivo are higher than those measured in straight glass tubes of comparable dimesions.     

Nasal and oral airway pressure-flow relationships.

We examined the inspiratory and expiratory pressure-flow relationships of both the oral and nasal airways before and after exercise in normal upright subjects. With the use of a partitioned facemask, nasal resistance was measured using posterior rhinomanometry, and oral resistance was measured by recording transoral pressure during oral breathing. Both the nasal and oral pressure-flow relationships for inspiration and expiration were curvilinear and were well described by a power function of the form delta P = aVb (where P is pressure, V is flow, a and b are constants) (r2 = 0.96 +/- 0.01). The exponent b describes the curvilinearity of the pressure-flow curve and can be used to infer the flow regimen. At rest, the inspiratory nasal and oral curves suggested a similar degree of turbulence (b = 1.77 +/- 0.06 and 1.83 +/- 0.04, respectively). However, inspiratory flow regimens were inferred to be more turbulent than those during expiration both before and after exercise. After exercise, decreases in inspiratory nasal resistance at low flows were associated with a change in flow regimen from fully turbulent to orifice flow over the entire flow range. Thus the application of a power function to nasal and oral pressure-flow data permits representation of the whole relationship and allows insight into the nature of the flow regimens.     

Functional contribution of P2Y1 receptors to the control of coronary blood flow

Activation of ADP-sensitive P2Y(1) receptors has been proposed as an integral step in the putative "nucleotide axis" regulating coronary blood flow. However, the specific mechanism(s) and overall contribution of P2Y(1) receptors to the control of coronary blood flow have not been clearly defined. Using vertically integrative studies in isolated coronary arterioles and open-chest anesthetized dogs, we examined the hypothesis that P2Y(1) receptors induce coronary vasodilation via an endothelium-dependent mechanism and contribute to coronary pressure-flow autoregulation and/or ischemic coronary vasodilation. Immunohistochemistry revealed P2Y(1) receptor expression in coronary arteriolar endothelial and vascular smooth muscle cells. The ADP analog 2-methylthio-ADP induced arteriolar dilation in vitro and in vivo that was abolished by the selective P2Y(1) antagonist MRS-2179 and the nitric oxide synthase inhibitor N(G)-nitro-l-arginine methyl ester. MRS-2179 did not alter baseline coronary flow in vivo but significantly attenuated coronary vasodilation to ATP in vitro and in vivo and the nonhydrolyzable ATP analog ATPγS in vitro. Coronary blood flow responses to alterations in coronary perfusion pressure (40-100 mmHg) or to a brief 15-s coronary artery occlusion were unaffected by MRS-2179. Our data reveal that P2Y(1) receptors are functionally expressed in the coronary circulation and that activation produces coronary vasodilation via an endothelium/nitric oxide-dependent mechanism. Although these receptors represent a critical component of purinergic coronary vasodilation, our findings indicate that P2Y(1) receptor activation is not required for coronary pressure-flow autoregulation or reactive hyperemia.     

The effect of nitrogen on the movement of tracers down the stolon of Saxifraga sarmentosa,with some observations on the influence of light

Summary The movement of applied ¹³⁷Cs and of naturally-assimilated ¹⁴C down the long stolon of Saxifraga is strongly inhibited by confining a length of 10 to 30 cm of the stolon in an atmosphere of nitrogen. The inhibition is reversible, normal transport being restored after less then 4 h when the stolon is returned to air from 5 h in nitrogen. Callose formation does not seem to be involved. There is evidence that local darkness has a similar adverse effect on phloem transport.These findings are considered antagonistic to the pressure-flow hypothesis, but favourable to the active mass-flow theories.This work formed part of that submitted for the degree of Ph.D. of the University of London.     

Subendocardial and subepicardial pressure-flow relations in the rat heart in diastolic and systolic arrest

Ischemic heart disease is more apparent in the subendocardial than in subepicardial layers. We investigated coronary pressure-flow relations in layers of the isolated rat left ventricle, using 15 microm microspheres during diastolic and systolic arrest in the vasodilated coronary circulation. A special cannula allowed for selective determination of left main stem pressure-flow relations. Arterio-venous shunt flow was derived from microspheres in the venous effluent. We quantitatively investigated the pressure-flow relations in diastolic arrest (n=8), systolic arrest at normal contractility (n=8) and low contractility (n=6). In all three groups normal and large ventricular volume was studied. In diastolic arrest, at a perfusion pressure of 90 mmHg, subendocardial flow is larger than subepicardial flow, i.e., the endo/epi ratio is approximately 1.2. In systolic arrest the endo/epi ratio is approximately 0.3, and subendocardial flow and subepicardial flow are approximately 12% and approximately 55% of their values during diastolic arrest. The endo/epi ratio in diastolic arrest decreases with increasing perfusion pressure, while in systole the ratio increases. The slope of the pressure-flow relations, i.e., inverse of resistance, changes by a factor of approximately 5.3 in the subendocardium and by a factor approximately 2.2 in the subepicardium from diastole to systole. Lowering contractility affects subendocardial flow more than subepicardial flow, but both contractility and ventricular volume changes have only a limited effect on both subendocardial and subepicardial flow. The resistance (inverse of slope) of the total left main stem pressure-flow relation changes by a factor of approximately 3.4 from diastolic to systolic arrest. The zero-flow pressure increases from diastole to systole. Thus, coronary perfusion flow in diastolic arrest is larger than systolic arrest, with the largest difference in the subendocardium, as a result of layer dependent increases in vascular resistance and intercept pressure. Shunt flow is larger in diastolic than in systolic arrest, and increases with perfusion pressure. We conclude that changes in contractility and ventricular volume have a smaller effect on pressure-flow relations than diastolic-systolic differences. A synthesis of models accounting for the effect of cardiac contraction on perfusion is suggested.     

Upper airway response to electrical stimulation of the genioglossus in obstructive sleep apnea.

Contraction of the genioglossus (GG) has been shown to improve upper airway patency. In the present study, we evaluated responses in upper airway pressure-flow relationships during sleep to electrical stimulation (ES) of the GG in patients with obstructive sleep apnea. Five patients with chronically implanted hypoglossal nerve (HG) electrodes and nine patients with fine-wire electrodes inserted into the GG were studied. Airflow was measured at multiple levels of nasal pressure, and upper airway collapsibility was defined by the nasal pressure below which airflow ceased ["critical" pressure (Pcrit)]. ES shifted the pressure-flow relationships toward higher flow levels in all patients over the entire range of nasal pressure applied. Pcrit decreased similarly during both HG-ES and GG-ES (deltaPcrit was 3.98 +/- 2.31 and 3.18 +/- 1.70 cmH2O, respectively) without a significant change in upstream resistance. The site of collapse (velo- vs. oropharynx) did not influence the response to GG-ES. Moreover, ES-induced reductions in the apnea-hypopnea index of the HG-ES patients were associated with substantial decreases in Pcrit. Our findings imply that responses in apnea severity to HG-ES can be predicted by characterizing the patient's baseline pressure-flow relationships and response to GG-ES.     

Hypoxic pulmonary vasoconstriction during steady and pulsatile flow in ferrets

We examined the effects of hypoxia and pulsatile flow on the pressure-flow relationships in the isolated perfused lungs of Fitch ferrets. When perfused by autologous blood from a pump providing a steady flow of 60 ml/min, the mean pulmonary arterial pressure rose from 14.6 to 31.3 Torr when alveolar PO2 was reduced from 122 to 46 Torr. This hypoxic pressor response was characterized by a 10.1-Torr increase in the pressure-axis intercept of the extrapolated pressure-flow curves and an increase in the slope of these curves from 130 to 240 Torr X l-1 X min. With pulsatile perfusion from a piston-type pump, mean pulmonary arterial pressure increased from 17.5 to 36.3 Torr at the same mean flow. This hypoxic pressor response was also characterized by increases in the intercept pressure and slope of the pressure-flow curves. When airway pressure was raised during hypoxia, the intercept pressure increased further to 25 +/- 1 Torr with a further increase in vascular resistance to 360 Torr X l-1 X min. Thus, in contrast to the dog lung, in the ferret lung pulsatile perfusion does not result in lower perfusion pressures during hypoxia when compared with similar mean levels of steady flow. Since the effects of high airway pressure and hypoxia are additive, they appear to act at or near the same site in elevating perfusion pressure.     

Characterization of pharyngeal resistance during sleep in a spectrum of sleep-disordered breathing.

Aims of the study were 1) to compare Hudgel's hyperbolic with Rohrer's polynomial model in describing the pressure-flow relationship, 2) to use this pressure-flow relationship to describe these resistances and to evaluate the effects of sleep stages on pharyngeal resistances, and 3) to compare these resistances to the pressure-to-flow ratio (DeltaP/V). We studied 12 patients: three with upper airway resistance syndrome (UARS), four with obstructive sleep hypopnea syndrome (OSHS), three with obstructive sleep apnea syndrome (OSAS), and two with simple snoring (SS). Transpharyngeal pressures were calculated between choanae and epiglottis. Flow was measured by use of a pneumotachometer. The pressure-flow relationship was established by using nonlinear regression and was appreciated by the Pearson's square (r(2)). Mean resistance at peak pressure (Rmax) was calculated according to the hyperbolic model during stable respiration. In 78% of the cases, the value of r(2) was greater when the hyperbolic model was used. We demonstrated that Rmax was in excellent agreement with P/V. UARS patients exhibited higher awake mean Rmax than normal subjects and other subgroups and a larger increase from wakefulness to slow-wave sleep than subjects with OSAS, OSHS, and SS. Analysis of breath-by-breath changes in Rmax was also a sensitive method to detect episodes of high resistance during sleep.     

Flow and volume dependence of expiratory resistance in anesthetized cats

In five anesthetized paralyzed cats, mechanically ventilated with tidal volumes of 36-48 ml, the isovolume pressure-flow relationships of the lung and respiratory system were studied. The expiratory pressure was altered between 3 and -12 cmH2O for single tidal expirations. Isovolume pressure-flow plots for three lung volumes showed that the resistive pressure-flow relationships were curvilinear in all cases, fitting Rohrer's equation: P = K1V + K2V2, where P is the resistive pressure loss, K1 and K2 are Rohrer's coefficients, and V is flow. Values of K1 and K2 declined with lung inflation, consistent with the volume dependence of pulmonary (RL) and respiratory system resistances (Rrs). During lung deflation against atmospheric pressure, RL and Rrs tended to remain constant through most of expiration, resulting in a nearly linear volume-flow relationship. In the presence of a fixed respiratory system elastance, the shape of the volume-flow profile depended on the balance between the volume and the flow dependence of RL and Rrs. However, the flow dependence of RL and Rrs indicates that their measured values will be affected by all factors that modify expiratory flow, e.g., respiratory system elastance, equipment resistance, and the presence of respiratory muscle activity.     

A state space model of local energy exchange and circulatory control

Based on the assumption that the maintenance of the energy content of the living tissue was the goal of the control, a generalized model of the regulation of local circulation was developed. The goodness of the model realised on a microcomputer was verified by the good fits of simulation with various physiological reactions obtained in animal experiments that were performed in cats anaesthetized with alpha-chloralose (50 mg/kg, i.v.). The reactions were elicited by tilting the animal (45 degrees head up) and by obstructing hindlimb blood flow by means of inflation of a pressure cuff. The appropriateness of energetic considerations of the hypothesis and the properness of the construction of the model was confirmed also by the similarity of the simulated static and dynamic pressure-flow and flow-temperature characteristics, respectively, with those obtained in animal experiments reported in the literature. The performance of the model suggests that the well-known regulatory phenomena of the local circulation are the results of a set point-free control system.