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Increasing evidence indicates that cerebrovascular compliance contributes to the dynamic regulation of cerebral blood flow but the mechanisms regulating cerebrovascular compliance in humans are unknown. This retrospective study investigated the impact of neural, endothelial, and myogenic mechanisms on the regulation of vascular compliance in the cerebral vascular bed compared with the forearm vascular bed. An index of vascular compliance (Ci) was assessed using a Windkessel model applied to blood pressure waveforms (finger photoplethysmography) and corresponding middle cerebral artery blood velocity or brachial artery blood velocity waveforms (Doppler ultrasound). Data were analyzed during a 5-min baseline period (10 waveforms) under control conditions and during distinct sympathetic blockade (experiment 1, phentolamine; 10 adults), cholinergic blockade (experiment 2, glycopyrrolate; 9 adults), and myogenic blockade (experiment 3, nicardipine; 14 adults). In experiment 1, phentolamine increased Ci similarly in the cerebral vascular bed (131 ± 135%) and forearm vascular bed (93 ± 75%; P = 0.45). In experiment 2, glycopyrrolate increased cerebrovascular Ci (72 ± 61%) and forearm vascular Ci (74 ± 64%) to a similar extent (P = 0.88). In experiment 3, nicardipine increased Ci but to a greater extent in the cerebral vascular bed (88 ± 88%) than forearm vascular bed (20 ± 45%; P = 0.01). Therefore, adrenergic, cholinergic, and myogenic mechanisms contribute to the regulation of cerebrovascular and forearm vascular compliance. However, myogenic mechanisms appear to exert more specific control over vascular compliance in the brain relative to the forearm.NEW & NOTEWORTHY Vascular compliance represents an important determinant in the dynamics and regulation of blood flow through a vascular bed. However, the mechanisms that regulate vascular compliance remain poorly understood. This study examined the impact of neural, endothelial, and myogenic mechanisms on cerebrovascular compliance compared with forearm vascular compliance. Distinct pharmacological blockade of α-adrenergic, endothelial muscarinic, and myogenic inputs altered cerebrovascular and forearm vascular compliance. These results further our understanding of vascular control and blood flow regulation in the brain.

NEW FINDINGS What is the central question of this study? Vascular compliance importantly contributes to the regulation of cerebral perfusion and complex mechanisms are known to influence compliance of a vascular bed: while vasodilatation mediates changes in vascular resistance, does it also affect compliance, particularly in the cerebral vasculature? What is the main finding and its importance? Cerebral vasodilatation, elicited by hypercapnia and sodium nitroglycerin administration, reduced cerebrovascular compliance by approximately 26% from baseline. This study provides new insight into mechanisms mediating cerebrovascular compliance. ABSTRACT Changes in vascular resistance and vascular compliance contribute to the regulation of cerebral perfusion. While changes in vascular resistance are known to be mediated by vasodilatation, the mechanisms contributing to changes in vascular compliance are complex. In particular, whether vasodilatation affects compliance of the vasculature within the cranium remains unknown. Therefore, the present study examined the impact of two vasodilatation pathways on cerebrovascular compliance in humans. Fifteen young, healthy adults (26 ± 5 years, seven females) completed two protocols: (i) sublingual sodium nitroglycerin (SNG; 0.4 mg) and (ii) hypercapnia (5-6% carbon dioxide gas mixture for 4 min). Blood pressure waveforms (finger photoplethysmography) and middle cerebral artery blood velocity waveforms (transcranial Doppler ultrasound) were input into a modified Windkessel model and an index of cerebrovascular compliance (Ci) was calculated. During the SNG protocol, Ci decreased 24 ± 17% from baseline ((5.0 ± 2.3) × 10-4 cm s-1 mmHg-1 ) to minute 10 ((3.6 ± 1.2) × 10-4 cm s-1 mmHg-1 ; P = 0.009). During the hypercapnia protocol, Ci decreased 28 ± 9% from baseline ((4.4 ± 1.9) × 10-4 cm s-1 mmHg-1 ) to minute 4 ((3.1 ± 1.4) × 10-4 cm s-1 mmHg-1 ; P

Normal human pregnancy requires a dramatic increase in uteroplacental blood flow, which is achieved by a transformation in the geometry of uterine spiral arteries, a key element in this blood supply system. The transformation is mediated by trophoblast invasion directed at converting a portion of the spiral artery into an open funnel, thereby greatly reducing resistance to flow. The converted portion lies within the depth of the decidua and part of the myometrium. Insufficient depth of trophoblast invasion in early pregnancy predisposes to inadequate perfusion of the developing placenta and fetus and may lead to preeclampsia, fetal growth restriction, and preterm delivery, sometimes referred to as the "Great Obstetrical Syndromes." We examine the hemodynamic consequences of spiral artery transformation in human pregnancy and the relationship between the degree of transformation and the corresponding change in flow rate and resistance to flow. We identify two key variables in determining the hemodynamic change: the longitudinal converted fraction of the spiral artery and the relative downstream diameter of the open funnel. Our results indicate that there is a critical threshold in the value of the converted fraction required to achieve the marked increase in uteroplacental blood flow in normal pregnancy. This finding validates common clinical observations that the depth of trophoblast invasion reflects the "adequacy" of the increase in uteroplacental blood supply required in normal human pregnancy. Our results provide a quantitative measure of that adequacy and may serve as a future diagnostic marker for high-risk pregnancy.

The branching architecture of arterial trees traversing the thickness of the left ventricular wall is studied to determine the way in which adequate blood supply is provided to myocardial tissue at different depths within the wall thickness from arterial trees originating at the epicardial surface. The study is based on micro-CT images of tissue biopsies, coupled with a dedicated vascular tree analysis program. The results show that this combination of methodologies allows a more detailed and much more accurate exploration of the vasculature within the sampled tissue than is possible by histological means. The spatial density of the smallest resolvable "end" arterioles is found to be higher in the sub-endocardial region than in the sub-epicardial region, with vascular branching architecture consistent with a fractal structure. The concept of "transit time" is introduced as an approximate measure of the time it takes bulk flow to reach different regions of the myocardium. Our data suggest that a transit time differential is a major contributor to the equalization of transmural perfusion gradient against unequal distribution of "end' arteriolar density.

The carotid artery is one of the major supply routes of blood to the brain and a common site of vascular disease. Obstructive and sclerotic disorders within the carotid artery impact local blood flow patterns as well as overall impedance and blood supply to the brain. A lumped parameter model and an experimental in-vitro flow loop were used to study the effects of local stenosis and stiffness in the carotid artery based on a family of phantoms with different degrees of stenosis and compliance. The model also allows independent examination of the effects of downstream resistance and compliance. Mild to moderate stenosis was found to lead to minimal (∼1%) reduction in blood supply to the brain. Reduction in mean internal carotid artery (ICA) flow was statistically significant (p< 0.01) only above 70% stenosis. On the other hand, a three-fold increase in stiffness of the carotid artery, as might occur in aging, was found to lead to a modest yet statistically significant reduction (p< 0.01) in mean ICA flow. Effects of changing downstream resistance and compliance were examined. For a given pressure waveform, reduction in downstream compliance led to altered waveform shape and reduction in peak systolic flow rates where the mean flow rates were not altered. Increased downstream resistance resulted in drastic reduction in mean flow rates.

Mathieu functions of period $\pi$ or $2\pi$, also called elliptic cylinder functions, were introduced in 1868 by \'Emile Mathieu together with so-called modified Mathieu functions, in order to help understand the vibrations of an elastic membrane set in a fixed elliptical hoop. These functions still occur frequently in applications today: our interest, for instance, was stimulated by a problem of pulsatile blood flow in a blood vessel compressed into an elliptical cross-section. This paper surveys and recapitulates the historical development of the theory and methods of computation for Mathieu functions and modified Mathieu functions and identifies some gaps in current software capability, particularly to do with double eigenvalues of the Mathieu equation. We demonstrate how to compute Puiseux expansions of the Mathieu eigenvalues about such double eigenvalues, and give methods to compute the generalized eigenfunctions that arise there. In examining Mathieu's original contribution, we bring out that his use of anti-secularity predates that of Lindstedt. For interest, we also provide short biographies of some of the major mathematical researchers involved in the history of the Mathieu functions: \'Emile Mathieu, Sir Edmund Whittaker, Edward Ince, and Gertrude Blanch., Comment: 65 pages, 15 figures

Background The coiled geometry of spiral arteries in the human uteroplacental circulation is a hemodynamic enigma because of added length of a spiral artery compared with that of a straight artery, as well as added complexity of the flow within the vessel because of the coiling curvature. Methods We examined the geometric and hemodynamic characteristics of mathematically defined helical and spiral arteries and compared these with the corresponding characteristics of a straight artery traversing the same depth of tissue, with the aim of gaining some insight into the possible role of spiral geometry in uteroplacental perfusion. Results The results indicate that the added length of a spiral artery provides the uteroplacental circulation with a reserve of high resistance to flow. The effect of coiling geometry on the flow within the artery is the development of churning vortices in planes normal (perpendicular) to the main flow direction. Conclusions In the early stages of pregnancy the reserve of high resistance is intact, thus keeping blood supply low. As pregnancy progresses, the reserve is gradually purged by trophoblast invasion and transformation of the distal portion of the spiral artery into an open funnel, thus providing the required high blood supply. The development of churning vortices within the spiral artery support earlier suggestions in the literature that the “spurts” of maternal blood emerging from these arteries may play a role in shaping the anatomy of the villous trees among placental lobules.

A new framework is proposed for the interpretation of spontaneous cardiac baroreflex sensitivity data and the general concept of baroreflex resetting. The framework is used to explore baroreflex function along two separate lines of inquiry: one following a direct intervention in baroreflex function in individual subjects, another in a group of subjects where baroreflex function may have been compromised by coronary artery disease or aging. It is found that under baseline conditions the baroreflex is in a “free-floating” state in which the gain or “sensitivity” is highly variable, while under orthostatic stress or in the absence of or reduced vagal input the gain is more tightly controlled with an expected decline in sensitivity but a very large decline in the variability of that sensitivity. It is concluded that baroreflex “resetting” is better viewed not simply as a change in baroreflex sensitivity but rather as a change in the “focus” or “attention” of the baroreflex as expressed by an observed decline in the variability of the measured gain. The results do not support the interpretation of baroreflex “resetting” as a departure from or return to a universal “set point” as in homeostasis or open loop models.

The consequences of myocardial ischemia are examined from the standpoint of the neural control system of the heart, a hierarchy of three neuronal centers residing in central command, intrathoracic ganglia, and intrinsic cardiac ganglia. The basis of the investigation is the premise that while this hierarchical control system has evolved to deal with “normal” physiological circumstances, its response in the event of myocardial ischemia is unpredictable because the singular circumstances of this event are as yet not part of its evolutionary repertoire. The results indicate that the harmonious relationship between the three levels of control breaks down, because of a conflict between the priorities that they have evolved to deal with. Essentially, while the main priority in central command is blood demand, the priority at the intrathoracic and cardiac levels is heart rate. As a result of this breakdown, heart rate becomes less predictable and therefore less reliable as a diagnostic guide as to the traumatic state of the heart, which it is commonly used as such following an ischemic event. On the basis of these results it is proposed that under the singular conditions of myocardial ischemia a determination of neural control indexes in addition to cardiovascular indexes has the potential of enhancing clinical outcome.

Age structure is an important feature of the division of labour within honeybee colonies, but its effects on colony dynamics have rarely been explored. We present a model of a honeybee colony that incorporates this key feature, and use this model to explore the effects of both winter and disease on the fate of the colony. The model offers a novel explanation for the frequently observed phenomenon of ‘spring dwindle’, which emerges as a natural consequence of the age-structured dynamics. Furthermore, the results indicate that a model taking age structure into account markedly affects the predicted timing and severity of disease within a bee colony. The timing of the onset of disease with respect to the changing seasons may also have a substantial impact on the fate of a honeybee colony. Finally, simulations predict that an infection may persist in a honeybee colony over several years, with effects that compound over time. Thus, the ultimate collapse of the colony may be the result of events several years past.

In a premature ventricular contraction (PVC), a systolic blood pressure peak is missing during the affected cardiac cycle, leading to a prolonged reduction in blood pressure which is then followed by a large burst of sympathetic outflow. In a normal ventricular contraction, it is generally believed that peak carotid and aortic distensions associated with systolic pressure is the neural feedback that terminates sympathetic outflow through a baroreflex mechanism. Yet, the characteristically large sympathetic burst following a PVC is terminated without a systolic pressure and evidently without this mechanism. To address this anomaly, we examined the possible role of cardiac receptors in providing an alternative mechanism for the termination of sympathetic outflow in a PVC. For this purpose, recordings of electrocardiogram (ECG), arterial blood pressure (ABP), and muscle sympathetic neural activity (MSNA) were made in a human subject during repeated PVC episodes. The time intervals, or "latencies", from key events within the PVC to the peak of the associated MSNA burst were calculated and compared with the latency in a normal ventricular contraction which is associated with central baroreceptor function. It was found that the only event in a PVC that corresponds with a physiologically plausible latency is that which marks the end of ventricular filling. We conclude with the hypothesis that in the unique circumstances of a PVC, where the systolic pressure peak required to trigger arterial baroreceptors to terminate sympathetic outflow is absent, mechanoreceptors in the heart appear to "step in" to perform this sympathoinhibitory function.

Under the dynamic conditions of pulsatile flow, the forces exerted by the fluid on the vessel wall create considerable displacements and stresses within the thickness of the vessel wall. We review a series of analytical options for exploring the dynamics of the vessel wall, specifically displacements and stresses within the depth of the vessel wall, under a range of conditions including the degree of external tethering and the mechanical consistency of the wall material. It is shown that one of the most important effects of tethering is that of drastically restricting radial displacements of and within the vessel wall. This restriction in turn places limits on the length and speed of the propagating wave. Specifically, the wave speed is significantly reduced as a result of tethering. This has important consequences because the wave speed, or pulse wave velocity as it is referred to in the clinical setting, is used as an index of vascular stiffening in relation to aging or age related hypertension. It is found further that the extent of displacements and shear stresses within the vessel wall depend critically on the relative proportions of viscous and elastic content within the wall. In particular, loss of viscous consistency leads to higher shear stresses within the wall, thus putting higher loading on elastin and may ultimately lead to elastin fatigue. As elastin gradually fails, its load bearing function is presumably taken over by collagen which renders the vessel wall less elastic and more rigid as is observed in the aging process.

This study tested the hypothesis that the compliance (C) and viscoelasticity (K) of the forearm vascular bed are controlled by myogenic and/or α-adrenergic receptor (αAR) activation. Heart rate (HR) and waveforms of brachial artery blood pressure (Finometer) and forearm blood flow (Doppler ultrasound) were measured in baseline conditions and during infusion of noradrenaline (NA; αAR agonist), with and without phentolamine (αAR antagonist; n = 10; 6 men and 4 women). These baseline and αAR-agonist-based measures were repeated when the arm was positioned above or below the heart to modify the myogenic stimulus. A lumped Windkessel model was used to quantify the values of forearm C and K in each set of conditions. Baseline forearm C was inversely, and K directly, related to the myogenic load (P < 0.001). Compared with saline infusion, C was increased, but K was unaffected, with phentolanine, but only in the 'above' position. Compliance was reduced (P < 0.001) and K increased (P = 0.06) with NA infusion (main effects of NA) across arm positions; phentolamine minimized these NA-induced changes in C and K for both arm positions. Examination of conditions with and without NA infusion at similar forearm intravascular pressures indicated that the NA-induced changes in C and K were due largely to the concurrent changes in blood pressure. Therefore, within the range of arm positions used, it was concluded that vascular stiffness and vessel wall viscoelastic properties are acutely affected by myogenic stimuli. Additionally, forearm vascular compliance is sensitive to baseline levels of αAR activation when transmural pressure is low.

Pulse wave velocity (PWV) is often used as a clinical index of aging, vascular disease, or age related hypertension. This practice is based on the assumption that a higher wave speed indicates vascular stiffening. This assumption is well grounded in the physics of pulsatile flow of an incompressible fluid where it is fully established that a pulse wave travels faster in a tube of stiffer wall, the wave speed becoming infinite in the mathematical limit of a rigid wall. However, in this paper we point out that the physical principal of higher pulse wave velocity in a stiffer tube is strictly valid only when the wall is free from outside constraints, which in the physiological setting is present in the form of tethering of the vessel wall. The use of PWV as an index of arterial stiffening may thus lose its validity if tethering is involved. A solution of the problem of vessel wall mechanics as they arise from the physiological pulsatile flow problem is presented for the purpose of resolving this issue. The vessel wall is considered to have finite thickness with or without tethering and with a range of mechanical properties ranging from viscoelastic to stiff. The results show that, indeed, while the wave speed becomes infinite in the mathematical limit of a rigid free wall, the opposite actually happens if the vessel wall is tethered. Here the wave speed actually diminishes as the degree of tethering increases. This dichotomy in the effects of tethering versus stiffening of the arterial wall may clearly lead to error in the interpretation of PWV as an index of vessel wall stiffness. In particular, a normal value of PWV may lead to the conclusion that vessel wall stiffening is absent while this value may in fact have been lowered by tethering. In other words, the diagnostic test may lead to a false negative diagnosis. Our results indicate that the reason for which PWV is lower in a tethered wall compared with that in a free wall of the same stiffness is that the radial movements of the wall are greatly reduced by tethering. More precisely, the results show that PWV depends strongly on the ratio of radial to axial displacements and that this ratio is much lower in a tethered wall than it is in a free wall of the same stiffness.

Lower body negative pressure (LBNP) was applied in eight human subjects to trigger low frequency oscillations in order to study the nature of functional coupling between the hemodynamic and autonomic nervous systems, with particular focus on how the myogenic response fits within this coupling. To this end muscle sympathetic nerve activity (MSNA), mean arterial pressure (MAP), heart rate (HR), cardiac output (CO), and total peripheral resistance (TPR) were measured at baseline and during LBNP and were then examined in both the time and frequency domains. At the height of low frequency oscillations (~ 0.1 Hz) there was a strong coupling between all the five indices, marked by perfect alignment of their oscillatory frequencies. Results in the time domain show that a fall in MAP is followed by a fall in TPR at 1.58 s SD 0.69), a rise in heart rate at 2.64 s (SD 0.98), a rise in cardiac output at 3.72 s (SD 0.60), a peak in MSNA at 5.71 s (SD 1.27) and, finally, a rise in TPR at 7.13 s (SD 1.02). A possible interpretation of the latter is that a drop in MAP first triggers a drop in TPR via a myogenic response before the expected rise in TPR via a rise in MSNA. In other words, following a drop in arterial pressure, myogenic response controls vessel diameter before this control is taken over by MSNA. These findings provide a possible resolution of a longstanding conceptual argument against attributing a significant role for the myogenic response in blood flow autoregulation.

In the field of fluid flow within the human body, focus has been placed on the transportation of blood in the systemic circulation since the discovery of that system; but, other fluids and fluid flow phenomena pervade the body. Some of the most fascinating fluid flow phenomena within the human body involve fluids other than blood and a service other than transport—the lymphatic and pulmonary systems are two striking examples. While transport is still involved in both cases, this is not the only service which they provide and blood is not the only fluid involved. In both systems, filtration, extraction, enrichment, and in general some “treatment” of the fluid itself is the primary function. The study of the systemic circulation has also been conventionally limited to treating the system as if it were an open-loop system governed by the laws of fluid mechanics alone, independent of physiological controls and regulations. This implies that system failures can be explained fully in terms of the laws of fluid mechanics, which of course is not the case. In this paper we examine the clinical implications of these issues and of the special biofluid mechanics issues involved in the lymphatic and pulmonary systems.

The dynamics of blood supply to a vascular bed depend on lumped mechanical properties of that bed, namely the compliance (C), resistance (R), viscoelasticity (K), and inertance (L). While the study of regulatory mechanisms has so far placed the emphasis largely on R, it is not known how the remaining properties contribute collectively to the play of dynamics in vasomotor control. To examine this question and to establish some benchmark values of these properties, simultaneous measurements of pressure and flow waveforms in the vascular bed of the forearm were obtained from three groups: young healthy individuals, older hypertensives with controlled blood pressure, and older hypertensives with uncontrolled blood pressure. The values of R and C were found to vary within a wide range in each of the three groups to the extent that neither R nor C could be used independently as an indicator of health or age of the subjects tested. However, higher level dynamic properties of the bed, such as the time constants and damping index, which depend on combinations of C,K, and L, and which may reflect measures of the dynamic responsiveness or “sluggishness” of the system, were found to be maintained over a wide range of pulse pressures. These findings support a hypothesis that the pulsatile dynamics of blood supply to a vascular bed are adapted to the individual baseline values of R and C in different subjects with the effect of optimizing the level of dynamic responsiveness to changes in pressure or flow, and that this dynamic property of the vascular bed may be a protected and/or regulated property.

A system of partial differential equations is derived as a model for the dynamics of a honey bee colony with a continuous age distribution, and the system is then extended to include the effects of a simplified infectious disease. In the disease-free case, we analytically derive the equilibrium age distribution within the colony and propose a novel approach for determining the global asymptotic stability of a reduced model. Furthermore, we present a method for determining the basic reproduction number [Formula: see text] of the infection; the method can be applied to other age-structured disease models with interacting susceptible classes. The results of asymptotic stability indicate that a honey bee colony suffering losses will recover naturally so long as the cause of the losses is removed before the colony collapses. Our expression for [Formula: see text] has potential uses in the tracking and control of an infectious disease within a bee colony.

The current view of neurogenic vasomotor control in skeletal muscle is based largely on changes in vascular bed resistance. The purpose of this study was to determine to what extent vascular bed compliance may also play a role in this regulation. For this purpose, pressure waveforms (Millar and Finometer) and flow waveforms (Doppler ultrasound) were measured simultaneously in the brachial artery of seven healthy individuals during physiological manoeuvres which were expected to produce non-neurogenic changes in resistance (wrist-cuff occlusion; n= 5) or compliance (arm elevation; n= 6) of the forearm vascular bed. Vascular resistance (R) was calculated from the average flow and pressure values. A lumped Windkessel model was used to obtain vascular bed compliance (C) from these concurrently measured waveforms. Compared with baseline (3.81 ± 1.59 ml min−1 mmHg−1), wrist occlusion increased R (65 ± 75%; P < 0.05) with minimal change in C (−15 ± 16%; n.s.). Compared with the arm in neutral position (0.0075 ± 0.003 ml mmHg−1), elevation of the arm above heart level produced a 86 ± 41% increase in C (P < 0.05) with little change in R (−5 ± 11%). In addition, neurogenic changes were assessed during lower body negative pressure (LBNP) and a cold pressor test (CPT; n= 7). Lower body negative pressure induced a 29 ± 24% increase in R and a 26 ± 12% decrease in C (both P < 0.05). The CPT induced no consistent change in R but a 22 ± 7% reduction in C (P < 0.05). It was concluded that vascular bed compliance is an independent variable which should be considered along with vascular bed resistance in the mechanics of vasomotor regulation in skeletal muscle.

Flow in tubes is one of the most common physical phenomena, indeed one of the most common physical tools, in biology.

The oscillatory pressure drops used in all previous chapters have been of a particularly simple form, namely that of a trigonometric sine or cosine function. These simple waveforms have specific properties that make them particularly useful for the study of oscillatory systems, but the ultimate aim in pulsatile blood flow is to examine the dynamics of such systems under oscillatory pressure drops of more general forms, in particular the forms of pressure waves generated by the heart. In what follows, and for reasons to become clear shortly, we shall refer to these generically as “composite” wave forms.

With the grounds laid in Sect. 1.7, we are now in a position to apply the laws of motion at every point within a body of fluid. The equations of motion obtained in this way can be thought of as point equations in the sense that they do not govern the motion of the fluid body as a whole but the motion of individual material points (fluid elements) within that body.

The pressure difference across the two ends of a tube provides only the force needed to drive the flow through the tube. In order to maintain the flow it is necessary to maintain this driving force, and to do so requires a source of continuous energy, a power source.

It seems reasonable to think of blood vessels as “tubes” because the physical principles of flow in tubes is at the core of how blood is conveyed within the body. Indeed, the study of these principles has been the declared theme of this book, and “flow in tubes” has been the language we used so far and the language we will continue to use. Yet, paradoxically, it would be a gross error to think of the arterial tree as only a system of branching tubes, a system of passive conduits.

In this study vasa vasorum in the walls of porcine coronary arteries were examined, using three-dimensional (3D) micro-CT scanning techniques. These techniques leave the 3D structure of the vasa vasorum tree intact and thus provide a much more direct view of this structure than is possible from conventional histological sections. The study demonstrates-for the first time, we believe-both the different types and the fine architecture of these vasa vasorum. Furthermore, with the use of automated tree analysis software, it was possible to obtain quantitative geometrical data on the 3D structure of vasa vasorum trees that have not previously been available. The results indicate that despite the restrictive topology of the space in which they are present, the branching architecture of the vasa vasorum trees, which we surveyed, is surprisingly similar to that of vasculature in general. The volume of vessel wall tissue perfused or drained by a vasa vasorum tree was found to correlate well with the cross-sectional area of the root segment of the vasa vasorum tree, and the luminal surface area corresponding to this volume was found to be comparable with the surface area of an early atherosclerotic lesion. This is consistent with earlier findings that the ligation or removal of vasa vasorum leads to atherogenesis.

The carotid artery is one of the major supply routes of blood to the brain. Currently, it is unknown what impact local changes within the carotid artery have on global circulation and specifically on the pressure and flow relationship in the common carotid artery (CCA) to the internal carotid artery (ICA) and eventually into the cerebral circulation. We used a lumped parameter model matched to an in vitro flow loop to study the effects of local stenosis and stiffness changes in the carotid artery, together with a family of carotid artery phantoms incorporating a progressively increasing stenosis or varying compliance. We found that in general local stenosis had minimal impact on blood supply to the brain, up to a certain threshold. Statistically significant changes were seen in the mean ICA flow beyond a 70 (p

A combination of experimental, theoretical, and imaging methodologies is used to examine the hierarchical structure and function of intramyocardial arteriolar trees in porcine hearts to provide a window onto a region of myocardial microvasculature which has been difficult to fully explore so far. A total of 66 microvascular trees from 6 isolated myocardial specimens were analyzed, with a cumulative number of 2438 arteriolar branches greater than or equal to 40 μm lumen diameter. The distribution of flow rates within each tree was derived from an assumed power law relationship for that tree between the diameter of vessel segments and flow rates that are consistent with that power law and subject to conservation of mass along hierarchical structure of the tree. The results indicate that the power law index increases at levels of arteriolar vasculature closer to the capillary level, consistent with a concomitant decrease in shear stress acting on endothelial tissue. These results resolve a long standing predicament which could not be resolved previously because of lack of data about the 3D, interconnected, arterioles. In the context of myocardial perfusion, the results indicate that the coefficient of variation of flow rate in pre-capillary distal arterioles is high, suggesting that heterogeneity of flow rate in these arterioles is not entirely random but may be due at least in part to active control.

We propose a model that combines the dynamics of the spread of disease within a bee colony with the underlying demographic dynamics of the colony to determine the ultimate fate of the colony under different scenarios. The model suggests that key factors in the survival or collapse of a honey bee colony in the face of an infection are the rate of transmission of the infection and the disease-induced death rate. An increase in the disease-induced death rate, which can be thought of as an increase in the severity of the disease, may actually help the colony overcome the disease and survive through winter. By contrast, an increase in the transmission rate, which means that bees are being infected at an earlier age, has a drastic deleterious effect. Another important finding relates to the timing of infection in relation to the onset of winter, indicating that in a time interval of approximately 20 days before the onset of winter the colony is most affected by the onset of infection. The results suggest further that the age of recruitment of hive bees to foraging duties is a good early marker for the survival or collapse of a honey bee colony in the face of infection, which is consistent with experimental evidence but the model provides insight into the underlying mechanisms. The most important result of the study is a clear distinction between an exposure of the honey bee colony to an environmental hazard such as pesticides or insecticides, or an exposure to an infectious disease. The results indicate unequivocally that in the scenarios that we have examined, and perhaps more generally, an infectious disease is far more hazardous to the survival of a bee colony than an environmental hazard that causes an equal death rate in foraging bees.

We tested the hypotheses that smoking-induced changes in vascular mechanics would be detected earlier in the lumped properties of peripheral vascular beds, which include the properties of microvasculature, than in the local properties of central conduits, and that such changes are reversible with lifestyle changes that include smoking cessation and exercise. Vascular measures were made in 53 young (18–40 years) female smokers and 25 age-matched non-smokers. Twenty-two of the smokers were tested before and after a 14-week smoking cessation program and, of these, 13 were tested again after 52 weeks of smoking cessation. Compared with non-smokers, lumped forearm vascular bed compliance (C: mL/mm Hg) was lower, while lumped viscoelasticity (K: mm Hg/(mL·min)) and resistance (R: mm Hg/(mL·min)) were higher in the smoker group. Neither the carotid-to-toe pulse wave velocity nor local carotid artery elasticity indices were different between groups. Compared with non-smokers, brachial artery distensibility was less, and other markers of stiffness higher, in the smoker group. At 14 and 52 weeks of smoking cessation, forearm vascular R was reduced and C was increased while K was unchanged. The changes in C and R occurred while maintaining a constant R×C value, which represents a dynamic time constant. Thus, early changes in K were observed in the forearm vascular bed of smokers, which were not reflected in the local properties of central conduit vessels. Forearm C, but not K, was reversed following smoking cessation, a finding that may represent a persistent effect of smoking on the intercellular matrix of the vessel wall.

A definition for the fractal dimension of a vascular tree is proposed based on the hemodynamic function of the tree and in terms of two key branching parameters: the asymmetry ratio of arterial bifurcations and the power law exponent governing the relation between vessel diameter and flow. Data from the cardiovascular system, which generally exhibit considerable scatter in the values of these two parameters, are found to produce the same degree of scatter in the value of the fractal dimension. When this scatter is explored for a multifractal pattern, however, it is found that the required collapse onto a single curve is achieved in terms of the coarse Hölder exponent. Thus, the presence of multifractility is confirmed, and the legitimacy of the defined dimension is affirmed in the sense of the theoretical Hausdorff limit in as much as this limit can be reached with experimental data.

Vagal nerve stimulation in cardiac therapy involves delivering electrical current to the vagal sympathetic complex in patients experiencing heart failure. The therapy has shown promise but the mechanisms by which any benefit accrues is not understood. In this paper we model the response to increased levels of stimulation of individual components of the vagal sympathetic complex as a differential activation of each component in the control of heart rate. The model provides insight beyond what is available in the animal experiment in as much as allowing the simultaneous assessment of neuronal activity throughout the cardiac neural axis. The results indicate that there is sensitivity of the neural network to low level subthreshold stimulation. This leads us to propose that the chronic effects of vagal nerve stimulation therapy lie within the indirect pathways that target intrinsic cardiac local circuit neurons because they have the capacity for plasticity.

Microvasculature associated with the sciatic nerve was examined using high-resolution micro-CT scanning in one group of rats and surgical exploration in another. The results indicate that blood supply to the sciatic nerve is an "open-ended" system in which the vessels run longitudinally within the epineurium and connect with external vasculature primarily at junction points. Although the range of vasculature found extended down to 4-5 μ, only a few isolated vessels of this size were found, with no capillary "mesh" as such, possibly because of the close proximity of the intrinsic vessel to nerve fibers within the epineurium. While the study did not include direct measurements of flow or nerve function, the "open-ended" pattern of vasculature found has important implications regarding the relationship between the two. Specifically, the nerve is less vulnerable to a severe or complete disruption in blood supply than it would be under a close-ended system such as that of the heart or brain, where a severe disruption can occur with the obstruction of only a single vessel. Indeed, the pattern of vasculature found, subject to further study of vasculature at the capillary level, suggests that flow within the intrinsic vessels may be in either direction, depending on circumstances, somewhat like flow within the circle of Willis in the cerebral circulation.

© 2016 The Authors. Physiological Reports published by Wiley Periodicals, Inc. on behalf of the American Physiological Society and The Physiological Society. Interval sprint exercise performed on a manually propelled treadmill, where the hands grip the handle bars, engages lower and upper limb skeletal muscle, but little is known regarding the effects of this exercise modality on the upper limb vasculature. We tested the hypotheses that an acute bout of sprint exercise and 6 weeks of training induces brachial artery (BA) and forearm vascular remodeling, favoring a more compliant system. Before and following a single bout of exercise as well as 6 weeks of training three types of vascular properties/methodologies were examined in healthy men: (1) stiffness of the entire upper limb vascular system (pulse wave velocity (PWV); (2) local stiffness of the BA; and (3) properties of the entire forearm vascular bed (determined by a modified lumped parameter Windkessel model). Following sprint exercise, PWV declined (P < 0.01), indices of BA stiffness did not change (P ≥ 0.10), and forearm vascular bed compliance increased and inertance and viscoelasticity decreased (P ≤ 0.03). Following manually propelled treadmill training, PWV remained unchanged (P = 0.31), indices of BA stiffness increased (P ≤ 0.05) and forearm vascular bed viscoelasticity declined (P = 0.02), but resistance, compliance, and inertance remained unchanged (P ≥ 0.10) compared with pretraining values. Sprint exercise induced a more compliant forearm vascular bed, without altering indices of BA stiffness. These effects were transient, as following training the forearm vascular bed was not more compliant and indices of BA stiffness increased. On the basis of these data, we conclude that adaptations to acute and chronic sprint exercise on a manually propelled treadmill are not uniform along the arterial tree in upper limb.

Local hemodynamics in a bypass loop model with dimensions typical of those in the human coronary circulation are studied, particularly with regards to the effects of wave reflections. While in a single vessel of such dimensions and a single source of wave reflections the effects would be insignificant, in a bypass loop the combination of a narrowed vessel with a converging junction and several reflection sites may produce wave reflections with significant effects on the pressure and flow distributions within the vessels forming the loop. Calculations to test this possibility were performed, based on D'Alembert's solutions of the wave equation and with a proposed matching scheme to deal with the converging junction. The results indicate that there are very large wave reflection effects at a frequency of 10 Hz, smaller but significant effects at 5 Hz, and some insignificant effects at 1 Hz. The results also indicate that partial flow cut-off may occur within the loop under some singular circumstances, whereby certain harmonic components of the incident wave are totally reflected. In the clinical setting these effects would detract from the efficiency of the bypass as a conduit, to a degree dependent on the degree of occlusion of the bypassed vessel. The choice of a larger diameter for the bypass appears to diminish this dependence and is thus on the whole favorable despite the contribution it makes to impedance mismatch at the junction.

We tested the hypothesis that changes in the arteriolar branching architecture contributed to increased running capacity of rats subjected to two-way artificial selection for intrinsic aerobic endurance treadmill running capacity resulting in strains of low-capacity and high-capacity endurance rats. Hearts and gastrocnemius muscles were harvested from each strain, and the microvasculature's branching geometry measured from micro-CT images. The vascular branching geometry of the hearts and skeletal muscle from the high capacity was indistinguishable from low-capacity rats. Our hypothesis was not supported. Neither remodeling nor an increase in arteriolar microvasculature branching appears to play a role in the enhanced performance of the high capacity rats. We are led to speculate that endothelial tolerance for shear stress and/or increased coupling of myocardial muscle fiber metabolic-to-contractile function is increased in the high-capacity runner strain to the effect of allowing either higher flow rate per unit volume of muscle or more efficient use of oxygen and nutrients in the high-capacity endurance rats.