Probing the Depth of the Myocardium: Vasculature, Transit Time, and Perfusion Within the Left Ventricular Wall.

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.

A model of blood supply to the brain via the carotid arteries: Effects of obstructive vs. sclerotic changes.

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.

Reproduction Number and Asymptotic Stability for the Dynamics of a Honey Bee Colony with Continuous Age Structure.

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.

Age structure is critical to the population dynamics and survival of honeybee colonies.

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.

Baroreflex variability and "resetting": a new perspective.

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.

Neural control hierarchy of the heart has not evolved to deal with myocardial ischemia.

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.

Dynamic neural networking as a basis for plasticity in the control of heart rate.

A model is proposed in which the relationship between individual neurons within a neural network is dynamically changing to the effect of providing a measure of "plasticity" in the control of heart rate. The neural network on which the model is based consists of three populations of neurons residing in the central nervous system, the intrathoracic extracardiac nervous system, and the intrinsic cardiac nervous system. This hierarchy of neural centers is used to challenge the classical view that the control of heart rate, a key clinical index, resides entirely in central neuronal command (spinal cord, medulla oblongata, and higher centers). Our results indicate that dynamic networking allows for the possibility of an interplay among the three populations of neurons to the effect of altering the order of control of heart rate among them. This interplay among the three levels of control allows for different neural pathways for the control of heart rate to emerge under different blood flow demands or disease conditions and, as such, it has significant clinical implications because current understanding and treatment of heart rate anomalies are based largely on a single level of control and on neurons acting in unison as a single entity rather than individually within a (plastically) interconnected network.

Cardiac mechanoreceptor function implicated during premature ventricular contraction.

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.

Mechanical events within the arterial wall under the forces of pulsatile flow: a review.

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.

Adrenergic and myogenic regulation of viscoelasticity in the vascular bed of the human forearm.

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.

Coupled radial and longitudinal displacements and stresses within the arterial wall in pulsatile flow under tethered and free-wall conditions.

An analytical solution is presented of the governing equations for the coupled radial and longitudinal displacements and stresses within the finite thickness of the arterial wall in pulsatile flow. The results are used to examine the extent of coupling between the radial and longitudinal dynamics within the vessel wall, particularly when the wall is fully tethered. In the case of a free wall, it is found that the dynamics in the two directions are fairly decoupled from each other when the wavelength is at least of the order of 100 times the vessel radius. At 10 times the vessel radius, however, there is strong coupling between the two. These findings are consistent with expectations in the case of a free wall where the long-wave approximation has been applied in the past. In the case of a tethered wall, however, the results indicate that in general the long-wave approximation is strictly valid only when the combination of wall material and tethering allow the wave to be long.

Neural control of heart rate: the role of neuronal networking.

Neural control of heart rate, particularly its sympathetic component, is generally thought to reside primarily in the central nervous system, though accumulating evidence suggests that intrathoracic extracardiac and intrinsic cardiac ganglia are also involved. We propose an integrated model in which the control of heart rate is achieved via three neuronal "levels" representing three control centers instead of the conventional one. Most importantly, in this model control is effected through networking between neuronal populations within and among these layers. The results obtained indicate that networking serves to process demands for systemic blood flow before transducing them to cardiac motor neurons. This provides the heart with a measure of protection against the possibility of "overdrive" implied by the currently held centrally driven system. The results also show that localized networking instabilities can lead to sporadic low frequency oscillations that have the characteristics of the well-known Mayer waves. The sporadic nature of Mayer waves has been unexplained so far and is of particular interest in clinical diagnosis.

Pulse wave velocity as a diagnostic index: the pitfalls of tethering versus stiffening of the arterial wall.

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.

Myogenic activity in autoregulation during low frequency oscillations.

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 (~0.1Hz) 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 1.58s SD 0.69), a rise in heart rate at 2.64s (SD 0.98), a rise in cardiac output at 3.72s (SD 0.60), a peak in MSNA at 5.71s (SD 1.27) and, finally, a rise in TPR at 7.13s (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.

Mechanical events within the arterial wall: The dynamic context for elastin fatigue.

Change in arterial stiffness is generally considered a risk factor for cardiovascular disease and, in various ways, has been associated with hypertension, diabetes, hyperlipidemia, atherosclerosis, and heart failure, likely because of altered dynamics of the wall and of the fluid-wall interplay in pulsatile flow. We present a comprehensive analytical study of longitudinal displacements and stresses within the thickness of the vessel wall induced by pulsatile flow at different times within the cardiac cycle, using the fractional derivative model which has been found to provide a good descriptor of the rheological material's response to frequency. The results indicate that the extent of displacement and shear stress within the depth of the vessel wall depend critically on the degree to which the wall is tethered to surrounding tissue and on the mechanical consistency of the wall material, particularly 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 and, 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 indeed observed in the aging process. It is thus concluded that loss of viscous content within the vessel wall, whether by disease or aging, may be a prelude to elastin fatigue and elastin failure within the vessel wall.

Arterial wall tethering as a distant boundary condition.

A standing difficulty in the problem of blood vessel tethering has been that only one of the two required boundary conditions can be fully specified, namely, that at the inner (endothelial) wall surface. The other, at the outer layer of the vessel wall, is not known except in the limiting case where the wall is fully tethered such that its outer layer is prevented from any displacement. In all other cases, where the wall is either free or partially tethered, a direct boundary condition is not available. We present a method of determining this missing boundary condition by considering the limiting case of a semi-infinite wall. The result makes it possible to define the degree of tethering imposed by surrounding tissue more accurately in terms of the displacement of the outer layer of the vessel wall, rather than in terms of equivalent added mass which has been done in the past. This new approach makes it possible for the first time to describe the effect of partial tethering in its full range, from zero to full tethering. The results indicate that high tethering leads to high stresses and low displacements within the vessel wall, while low tethering leads to low stresses and high displacements. Since both extremes would be damaging to wall tissue, particularly elastin, this suggest that moderate tethering would be optimum in the physiological setting.

Solutions of the Maxwell viscoelastic equations for displacement and stress distributions within the arterial wall.

Mechanical events within the thickness of the vessel wall caused by pulsatile blood flow are considered, with focus on axial dynamics of the wall, driven by the oscillatory drag force exerted by the fluid on the endothelial layer of the wall. It is shown that the focus on the axial direction makes it possible to derive simplified equations of motion which, combined with a viscoelastic model of the wall material, makes it possible in turn to obtain solutions in closed form for the displacement and stress of material elements within the wall. The viscoelastic model allows a study of the dynamics of the wall with different ratios of viscosity to elasticity of the wall material, to mimic changes in the properties of the arterial wall caused by disease or aging. It is found that when the wall is highly viscous the displacements and stresses caused by the flow are confined to a thin layer close to the inner boundary of the wall, while as the wall material becomes less viscous and more rigid the displacements and stresses spread deeper into the thickness of the wall to affect most of its elements.

Role of vascular bed compliance in vasomotor control in human skeletal muscle.

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.

Mechanism of smart baroreception in the aortic arch.

A mechanism is proposed by which the patch of baroreceptors along the inner curvature of the arch of the aorta can sense hemodynamic events occurring downstream from the aortic arch, in the periphery of the arterial tree. Based on a solution of equations governing the elastic movements of the aortic wall, it is shown that the pressure distribution along the patch of baroreceptors has the same functional form as the distribution of strain along the patch. The significance of these findings are discussed, particularly as they relate to the possibility of a neuromechanical basis of essential hypertension.

"Smart" baroreception along the aortic arch, with reference to essential hypertension.

Beat-to-beat regulation of heart rate is dependent upon sensing of local stretching or local "disortion" by aortic baroreceptors. Distortions of the aortic wall are due mainly to left ventricular output and to reflected waves arising from the arterial tree. Distortions are generally believed to be useful in cardiac control since stretch receptors or aortic baroreceptors embedded in the adventitia of the aortic wall, transduce the distortions to cardiovascular neural reflex pathways responsible for beat-to-beat regulation of heart rate. Aortic neuroanatomy studies have also found a continuous strip of mechanosensory neurites spread along the aortic inner arch. Although their purpose is now unknown, such a combined sensing capacity would allow measurement of the space and time dependence of inner arch wall distortions due, among other things, to traveling waves associated with pulsatile flow in an elastic tube. We call this sensing capability--"smart baroreception." In this paper we use an arterial tree model to show that the cumulative effects of wave reflections, from many sites far downstream, have a surprisingly pronounced effect on the pressure distribution in the root segment of the tree. By this mechanism global hemodynamics can be focused by wave reflections back to the aortic arch, where they can rapidly impact cardiac control via smart baroreception. Such sensing is likely important to maintain efficient heart function. However, alterations in the arterial tree due to aging and other natural processes can lead in such a system to altered cardiac control and essential hypertension.