Anharmonic analysis of arterial blood pressure and flow pulses

Fourier analysis is usually employed for the computation of blood flow in arteries. Although the orthogonality of Fourier eigenfunctions guarantees the accurate mathematical modeling of the blood pressure and flow waveforms, the physics behind this objective function is frequently missing. We propose a new method to account for the blood pressure and flow, single-cycle (systole-diastole) waveforms. It is based on the one dimensional hydrodynamic mass and momentum conservation equations for viscous flow. The similarity of the linear problem, under discussion, with related transmission line theory in electromagnetic wave propagation, permits expansion in anharmonic, non-separable eigenfunctions. In some cases one term in the expansion is adequate to fit the main peak of the observed waveforms. Analytical formulas are derived for the dependence of the pressure and flow main peaks on whole blood viscosity and distance from the heart, which interpret observations related to hypertension.     

Evaluation of a three point pressure method for the determination of arterial transmission characteristics

The mathematical expressions required to analyse wave transmission characteristics (frequency dependent phase velocity, attenuation, and reflection) in arteries, under in vivo conditions, are summarized. In addition, a three point pressure method, which theoretically permits experimental determination of the propagation constant (phase velocity and attenuation), was tested under in vitro conditions. It is found to be a potentially powerful tool for in vivo studies if used with the appropriate constraints.     

Simulations of the contractile cycle in cell migration using a bio-chemical-mechanical model

Cell migration relies on traction forces in order to propel a cell. Several computational models have been developed that help explain the trajectory that cells take during migration, but little attention has been placed on traction forces during this process. Here, we investigated the spatiotemporal dynamics of cell migration by using a bio-chemical-mechanical contractility model that incorporates the first steps of cell migration on an array of posts. In the model, formation of a new adhesion causes a reactivation of stress fibre assembly within a cell. The model was able to predict the spatial distribution of traction forces observed with previous experiments. Moreover, the model found that the strain energy exerted by the traction forces of a migrating cell underwent a cyclic relationship that rose with the formation of a new adhesion and fell with the release of an adhesion at its rear.     

Pulsatile pressure and flow in arterial stenoses simulated in a mathematical model

This paper presents the detailed pulsatile pressure and flow velocity patterns inside an axis symmetric stenosis model with 75% constriction. The pressure and velocities have been calculated by solving the Navier-Stokes equations by the finite element method, the velocity profile in a straight tube caused by a pulsating driving pressure has been calculated first and then used as a boundary condition for the stenosis calculations. The results of the mathematical simulations of the stenosis model have been obtained in terms of velocity vectors, streamlines and isobars at 16 different instances in time, each 15 degrees apart during a cardiac cycle. The calculated velocity field shows that a vortex is developed at the wall distal to the stenosis as the velocity decreases from the peak systolic value. At the site of the vortex, a local pressure minimum is found due to the conversion of pressure to kinetic energy. When the flow is reversed, the reversal occurs first along the wall, thus forcing the vortex toward the the centre of the tube. As the reverse flow velocity increases, a vortex is also developed at the proximal site of the stenosis.     

Simulations of a model for transmitter kinetics

The influence of the internal water balance on the phototactic behaviour in the walking female fly (Calliphora erythrocephala Meig.) was investigated. The phototactic reaction depends on the age of the flies and the duration of water withdrawal. In young blowflies with progressive dehydration, the strength of the light reaction varies considerably from fly to fly. From the 4th. day of life onwards up to day 21 the flies respond much more homogeneously and elicit a reproduceable temporal pattern of reaction (Figs. 2 and 3). All the following statements refer to the behaviour of 10-day-old, virgin females, which, under optimal humidity conditions, have been shown to be spontancously photonegative (Meyer, 1978). The phototactic reaction of progressively dehydrated flies depends in a characteristic manner on the illumination conditions during the intervals between tests. If the flies are kept in darkness during these intervals, the light reaction varies rhythmically, with a period of almost exactly 12 h (Figs. 4a and 5). Under the test conditions this rhythm is found not to vary with the time of day (Fig.4a), or with the length of the between-test intervals, for intervals up to 4h long (Fig. 6). If the flies are kept under illumination during the intervals between tests, the light reaction becomes arhythmical. After an initial maximum after 2–4h of dehydration, further photopositive responses are severely suppressed (Fig. 4b). When the ocelli are covered, the between-test illumination no longer influences the mean response to light. The arhythmic dehydrationtime vs. light-reaction curve in this case is characterised by a strong sustained enhancement of runs towards the light after 10h of dehydration (Fig. 7). A preliminary model of a possible control system for this moisture-dependent phototactic switching is presented, from which all essential results can be deduced. This system determines the phototactic turning direction from the ocelli afferences. These afferences act upon the central nervous system in two ways: directly and also indirectly via the internal water regulation.This work was supported by the DFG-(Me417/4)     

Pulsatile pressure and flow in an arterial aneurysm simulated in a mathematical model

The pressure and flow patterns within arterial aneurysms are little known. In the present work the equations describing pulsatile flow, the Navier-Stokes equations, are solved numerically using the finite element method with a computer. The solutions of the Navier-Stokes equations are obtained at 24 points in time during the cardiac cycle. At selected instants in time, the solutions are presented as velocity vectors, streamlines and isobars. The results demonstrate a vortex formation during most of the cycle. The pressure within the aneurysm is nearly constant. At the downstream end of the expansion,high pressure gradients are found.     

Effects of transmural pressure and wall shear stress on LDL accumulation in the arterial wall: a numerical study using a multilayered model

The accumulation of low-density lipoprotein (LDL) is recognized as one of the main contributors in atherogenesis. Mathematical models have been constructed to simulate mass transport in large arteries and the consequent lipid accumulation in the arterial wall. The objective of this study was to investigate the influences of wall shear stress and transmural pressure on LDL accumulation in the arterial wall by a multilayered, coupled lumen-wall model. The model employs the Navier-Stokes equations and Darcy's Law for fluid dynamics, convection-diffusion-reaction equations for mass balance, and Kedem-Katchalsky equations for interfacial coupling. To determine physiologically realistic model parameters, an optimization approach that searches optimal parameters based on experimental data was developed. Two sets of model parameters corresponding to different transmural pressures were found by the optimization approach using experimental data in the literature. Furthermore, a shear-dependent hydraulic conductivity relation reported previously was adopted. The integrated multilayered model was applied to an axisymmetric stenosis simulating an idealized, mildly stenosed coronary artery. The results show that low wall shear stress leads to focal LDL accumulation by weakening the convective clearance effect of transmural flow, whereas high transmural pressure, associated with hypertension, leads to global elevation of LDL concentration in the arterial wall by facilitating the passage of LDL through wall layers.     

Examination of elastic non-uniformity in the arterial system using a hydraulic model

Pressure wave propagation has been examined in a model artery with spatially varying compliance. Although results were affected by viscous losses, appropriate allowance for such losses produced agreement between experimental findings and predictions of linear wave transmission theory. Particularly, the ability of non-uniformity of the tube wall to generate amplification of the pressure wave was confirmed. However, extrapolation to the physiological situation suggests that reflections from discrete sites in peripheral beds have a greater effect on pressure wave propagation than does elastic non-uniformity of major vessels. A theoretical analysis has demonstrated that the effects of elastic non-uniformity can be interpreted as the integrated effects of infinitesimal reflections from each progressive increment in wall stiffness.     

Numerical investigation of the physical model of a high-power electromagnetic wave in a magnetically insulated transmission line

An efficient numerical code for simulating the propagation of a high-power electromagnetic pulse in a vacuum transmission line is required to study the physical phenomena occurring in such a line, to analyze the operation of present-day megavolt generators at an ∼10-TW power level, and to design such new devices. The main physical theoretical principles are presented, and the stability of flows in the near-threshold region at the boundary of the regime of magnetic self-insulation is investigated based on one-dimensional telegraph equations with electron losses. Numerical (difference) methods—specifically, a method of characteristics and a finite-difference scheme—are described and their properties and effectiveness are compared by analyzing the high-frequency modes.     

Estimating absolute aortic pressure using MRI and a one-dimensional model

Aortic blood pressure is a strong indicator to cardiovascular diseases and morbidity. Clinically, pressure measurements are done by inserting a catheter in the aorta. However, imaging techniques have been used to avoid the invasive procedure of catheterization. In this paper, we combined MRI measurements to a one-dimensional model in order to simulate blood flow in an aortic segment. Absolute pressure was estimated in the aorta by using MRI measured flow as boundary conditions and MRI measured compliance as a pressure law for solving the model. Model computed pressure was compared to catheter measured pressure in an aortic phantom. Furthermore, aortic pressure was estimated in vivo in three healthy volunteers.     

Simulating transmission and control of Taenia solium infections using a Reed-Frost stochastic model

The transmission dynamics of the human-pig zoonotic cestode Taenia solium are explored with both deterministic and stochastic versions of a modified Reed-Frost model. This model, originally developed for microparasitic infections (i.e. bacteria, viruses and protozoa), assumes that random contacts occur between hosts and that hosts can be either susceptible, infected or 'recovered and presumed immune'. Transmission between humans and pigs is modelled as susceptible roaming pigs scavenging on human faeces infected with T. solium eggs. Transmission from pigs to humans is modelled as susceptible humans eating under-cooked pork meat harbouring T. solium metacestodes. Deterministic models of each scenario were first run, followed by stochastic versions of the models to assess the likelihood of infection elimination in the small population modelled. The effects of three groups of interventions were investigated using the model: (i) interventions affecting the transmission parameters such as use of latrines, meat inspection, and cooking habits; (ii) routine interventions including rapid detection and treatment of human carriers or pig vaccination; and (iii) treatment interventions of either humans or pigs. It is concluded that mass-treatment can result in a short term dramatic reduction in prevalence, whereas interventions targeting interruption of the life cycle lead to long-term reduction in prevalence.     

Resonance in a mathematical model of baroreflex control: arterial blood pressure waves accompanying postural stress

A mathematical model of the arterial baroreflex was developed and used to assess the stability of the reflex and its potential role in producing the low-frequency arterial blood pressure oscillations called Mayer waves that are commonly seen in humans and animals in response to decreased central blood volume. The model consists of an arrangement of discrete-time filters derived from published physiological studies, which is reduced to a numerical expression for the baroreflex open-loop frequency response. Model stability was assessed for two states: normal and decreased central blood volume. The state of decreased central blood volume was simulated by decreasing baroreflex parasympathetic heart rate gain and by increasing baroreflex sympathetic vaso/venomotor gains as occurs with the unloading of cardiopulmonary baroreceptors. For the normal state, the feedback system was stable by the Nyquist criterion (gain margin = 0.6), but in the hypovolemic state, the gain margin was small (0.07), and the closed-loop frequency response exhibited a sharp peak (gain of 11) at 0.07 Hz, the same frequency as that observed for arterial pressure fluctuations in a group of healthy standing subjects. These findings support the theory that stresses affecting central blood volume, including upright posture, can reduce the stability of the normally stable arterial baroreflex feedback, leading to resonance and low-frequency blood pressure waves.     

One-dimensional model for propagation of a pressure wave in a model of the human arterial network: comparison of theoretical and experimental results

Pulse wave evaluation is an effective method for arteriosclerosis screening. In a previous study, we verified that pulse waveforms change markedly due to arterial stiffness. However, a pulse wave consists of two components, the incident wave and multireflected waves. Clarification of the complicated propagation of these waves is necessary to gain an understanding of the nature of pulse waves in vivo. In this study, we built a one-dimensional theoretical model of a pressure wave propagating in a flexible tube. To evaluate the applicability of the model, we compared theoretical estimations with measured data obtained from basic tube models and a simple arterial model. We constructed different viscoelastic tube set-ups: two straight tubes; one tube connected to two tubes of different elasticity; a single bifurcation tube; and a simple arterial network with four bifurcations. Soft polyurethane tubes were used and the configuration was based on a realistic human arterial network. The tensile modulus of the material was similar to the elasticity of arteries. A pulsatile flow with ejection time 0.3 s was applied using a controlled pump. Inner pressure waves and flow velocity were then measured using a pressure sensor and an ultrasonic diagnostic system. We formulated a 1D model derived from the Navier-Stokes equations and a continuity equation to characterize pressure propagation in flexible tubes. The theoretical model includes nonlinearity and attenuation terms due to the tube wall, and flow viscosity derived from a steady Hagen-Poiseuille profile. Under the same configuration as for experiments, the governing equations were computed using the MacCormack scheme. The theoretical pressure waves for each case showed a good fit to the experimental waves. The square sum of residuals (difference between theoretical and experimental wave-forms) for each case was <10.0%. A possible explanation for the increase in the square sum of residuals is the approximation error for flow viscosity. However, the comparatively small values prove the validity of the approach and indicate the usefulness of the model for understanding pressure propagation in the human arterial network.     

慢性动脉血压调节与原发性高血压病——Ⅰ.慢性动脉血压调节

机体在不同条件下维持动脉血压恒定的机理是不相同的。目前认为,长时程或慢性血压调节的关键器官是肾脏,这种调节与机体的水盐平衡有密切的关系。动脉血压的升高可以导致肾脏排尿量（或排钠量）的升高,即动脉血压与肾脏的排尿量（或排钠量）呈明显的正相关关系,称之为“压力-利尿作用”。当血容量升高时,通过肾脏的压力-利尿作用,可以排出过多的容量,维持动脉血压的恒定。只有在肾脏功能受到损伤的条件下,高血容量才可能引起高血压。