An experimental study of pressure losses in pulsatile flows through rigid and pulsating stenosis

The time-dependent pressure curves of a pulsatile flow across rigid and pulsating stenoses were investigated experimentally in a laboratory simulator of the outflow tract of the heart right ventricle. The experiments were performed within the range of physiological conditions of frequency and flow rate. The experimental setup consisted of a closed flow system which was operated by a pulsatile pump, and a test chamber which enabled checking different modes of stenosis. Rigid constrictions were simulated by means of axisymmetric blunt-ended annular plugs with moderate-to-severe area reductions. The pulsating stenosis consisted of a short starling resistor device operated by a pulsating external pressure which was synchronized by the pulsatile flow. It was found that the shape of the time-dependent pressure curve upstream of the stenosis was different in the case of rigid stenosis than in the pulsating one. Potential clinical applications of the work may relate to diagnosis of the type of stenosis in the congenital heart disease known as Tetralogy of Fallot.     

Effects of pulmonary embolism on pulmonary vascular impedance in dogs and minipigs

Pigs have been reported to present with a stronger pulmonaryvascular reactivity than many other species, including dogs. Weinvestigated the pulmonary vascular impedance response to autologous blood clot embolic pulmonary hypertension in anesthetized and ventilated minipigs (n = 6) and dogs(n = 6). Before embolization, minipigs, compared with dogs, presented with higher mean pulmonary arterial pressure (Ppa; by an average of 9 mmHg), a steeper slope ofPpa-flow () relationships, and higher0-Hz impedance (Z₀) andfirst-harmonic impedance (Z₁),without significant differences in characteristic impedance (Zc), and alower ratio of pulsatile hydraulic power to total hydraulic power.Embolic pulmonary hypertension (mean Ppa: 40-55 mmHg) wasassociated with increased Z₀ andZ₁ in both species, but theminipigs had a steeper slope of Ppa/ plots and anincreased Zc. At identical and Ppa,minipigs still presented with higherZ₁ and Zc and a lower ratio ofpulsatile hydraulic power to total hydraulic power. The energytransmission ratio, defined as the hydraulic power in the measuredwaves divided by the hydraulic power in the forward waves, was betterpreserved after embolism in minipigs. No differences in wave reflection indexes were found before and after embolism. We conclude that minipigs, compared with dogs, present with a higher pulmonary vascularresistance and reactivity and adapt to embolic pulmonary hypertensionby an increased Zc without earlier wave reflection. These differencesallow for a reduced pulsatile component of hydraulic power and,therefore, a better energy transfer from the right ventricle to thepulmonary circulation.

     

Using hydraulic input impedance in determination of changes in the arteries of different calibre

In anaesthetised cats, the arterial input impedance in combination with seven-element lumped-parameter model was used to estimate the resistance change in arteries of different caliber. The results show that the method gives reasonable estimations of changes in hydraulic resistance of arterial vessels of different caliber. We found that the method of vascular input impedance permits to reveal and assess quantitatively local constrictions and dilations as well as hemodynamically insignificant stenosis of conduit arteries.     

In Vitro Model of Physiological and Pathological Blood Flow with Application to Investigations of Vascular Cell Remodeling

Vascular disease is a common cause of death within the United States. Herein, we present a method to examine the contribution of flow dynamics towards vascular disease pathologies. Unhealthy arteries often present with wall stiffening, scarring, or partial stenosis which may all affect fluid flow rates, and the magnitude of pulsatile flow, or pulsatility index. Replication of various flow conditions is the result of tuning a flow pressure damping chamber downstream of a blood pump. Introduction of air within a closed flow system allows for a compressible medium to absorb pulsatile pressure from the pump, and therefore vary the pulsatility index. The method described herein is simply reproduced, with highly controllable input, and easily measurable results. Some limitations are recreation of the complex physiological pulse waveform, which is only approximated by the system. Endothelial cells, smooth muscle cells, and fibroblasts are affected by the blood flow through the artery. The dynamic component of blood flow is determined by the cardiac output and arterial wall compliance. Vascular cell mechano-transduction of flow dynamics may trigger cytokine release and cross-talk between cell types within the artery. Co-culture of vascular cells is a more accurate picture reflecting cell-cell interaction on the blood vessel wall and vascular response to mechanical signaling. Contribution of flow dynamics, including the cell response to the dynamic and mean (or steady) components of flow, is therefore an important metric in determining disease pathology and treatment efficacy. Through introducing an in vitro co-culture model and pressure damping downstream of blood pump which produces simulated cardiac output, various arterial disease pathologies may be investigated.     

Determination of volume of vortices in poststenotic pulsatile flow by ultrasonic Doppler power ratio and spectrum analysis

Based on the principle of ultrasonic Doppler flowmetry, a power ratio was derived from independent forward and reverse flow Doppler shift signals to measure a ratio of the volume of vortices to the total vessel volume in poststenotic separated flow. The ratio was also proportional to the ratio of the cross-sectional areas of vortices to the vessel lumen. In vitro pulsatile flow experiments were performed to test the methodology and to study flow separation and vortex shedding downstream from model stenoses. The averaged flow cross-sectional area ratio linearly correlated (r = 0.91) with the actual area reduction of the stenosis.     

In vitro hemodynamics and valve imaging in passive beating hearts

Due to their high complexity, surgical approaches to valve repair may benefit from the use of in vitro simulators both for training and for the investigation of those measures which can lead to better clinical results. In vitro tests are intrinsically more effective when all the anatomical substructures of the valvular complexes are preserved. In this work, a mock apparatus able to house an entire explanted porcine heart and subject it to pulsatile fluid-dynamic conditions was developed, in order to enable the hemodynamic analysis of simulated surgical procedures and the imaging of the valvular structures. The mock loop's hydrodynamic design was based on an ad-hoc defined lumped-parameter model. The left ventricle of an entire swine heart was dynamically pressurized by an external computer-controlled pulse duplicator. The ascending aorta was connected to a hydraulic circuit which simulated the input impedance of the systemic circulation; a reservoir passively filled the left atrium. Accesses for endoscopic imaging were located in the apex of the left ventricle and in the aortic root. The experimental pressure and flow tracings were comparable with the typical in vivo curves; a mean flow of 3.5±0.1l pm and a mean arterial pressure of 101±2 mmHg was obtained. High-quality echographic and endoscopic video recordings demonstrated the system's excellent potential in the observation of the cardiac structures dynamics. The proposed mock loop represents a suitable in vitro system for the testing of minimally-invasive cardiovascular devices and surgical procedures for heart valve repair.     

New methods for noninvasive and continuous determination of dynamic compliance of the carotid artery]

A new method for the noninvasive, continuous determination of the compliance of the carotid artery wall has been developed and, in an initial study, validated. Measurements of pulsatile changes in the diameter of the carotid artery are accomplished with the 4-electrode impedance method, and the intravascular blood pressure is measured using an applanation tonometer developed during this project. The method has been employed for measurements in 12 individuals with no vascular disease, and in one patient with carotid artery stenosis before, during and after successful dilatation. With the pressure-volume curves recorded during the cardiac cycle, it is possible to calculate dynamic compliance and the non-elastic deformation work. While initial results are very promising, further validation by a large-scale clinical study is required.     

A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree

Using a frequency-domain Womersley-type model, we previously simulated pulsatile blood flow throughout the coronary arterial tree. Although this model represents a good approximation for the smaller vessels, it does not take into account the nonlinear convective energy losses in larger vessels. Here, using Womersley's theory, we present a hybrid model that considers the nonlinear effects for the larger epicardial arteries while simulating the distal vessels (down to the 1st capillary segments) with the use of Womersley's Theory. The main trunk and primary branches were discretized and modeled with one-dimensional Navier-Stokes equations, while the smaller-diameter vessels were treated as Womersley-type vessels. Energy losses associated with vessel bifurcations were incorporated in the present analysis. The formulation enables prediction of impedance and pressure and pulsatile flow distribution throughout the entire coronary arterial tree down to the first capillary segments in the arrested, vasodilated state. We found that the nonlinear convective term is negligible and the loss of energy at a bifurcation is small in the larger epicardial vessels of an arrested heart. Furthermore, we found that the flow waves along the trunk or at the primary branches tend to scale (normalized with respect to their mean values) to a single curve, except for a small phase angle difference. Finally, the model predictions for the inlet pressure and flow waves are in excellent agreement with previously published experimental results. This hybrid one-dimensional/Womersley model is an efficient approach that captures the essence of the hemodynamics of a complex large-scale vascular network. The present model has numerous applications to understanding the dynamics of coronary circulation.     

Computer simulation of the geometry of the human bronchial tree

Some morphological features of the human bronchial tree were simulated by computergenerated trees. The trees were ordered by the methods of Horsfield and Strahler. Delta, the difference between the Horsfield orders of the two branches at a bifurcation, was determined by pseudorandom numbers generated according to a distribution of probabilities defined on input. By trial and error a distribution was found which resulted in trees being generated with average Strahler order branching ratios of 2.82, similar to a real bronchial tree. Branching angles and length ratio could also be defined on input. By varying these input parameters it was found that the form of the tree was quite sensitive to them, and that by a suitable choice the intrasegmental part of the bronchial tree could be simulated. It is concluded that branching ratio, length ratio, mean branching angles and distribution of delta are controlled within tight limits in the bronchial tree, and this may support the concept of optimal design.     

Blood Flow Characteristics and Tissue Nutrition in Apparently Ischaemic Feet

Blood flow in the apparently ischaemic feet of patients with atherosclerotic peripheral vascular disease was only weakly pulsatile but the volume of the resting total foot blood flow was higher than normal. No biochemical evidence of overall regional ischaemia or tissue anoxia was found to explain the aetiology of chronic nutritional skin lesions in these clinically ischaemic feet. The physiological effectiveness of a regional blood flow ultimately depends on its ability to perfuse the tissues, and in this respect it is suggested that pulse and pressure are more important than mere volume. It is further suggested that ischaemic or anoxic nutritional skin lesions develop in the presence of localized tissue perfusion failure and not from any overall regional blood flow insufficiency.     

Development of systemic arterial mechanical properties from infancy to adulthood interpreted by four-element windkessel models.

Aortic impedance data of infants, children and adults (age range 0.8-54 yr), previously reported by others, were interpreted by means of three alternative four-element windkessel models: W4P, W4S, and IVW. The W4P and W4S are derived from the three-element windkessel (W3) by connecting an inertance (L) in parallel or in series, respectively, with the aortic characteristic resistance (Rc). In the IVW, L is connected in series with a viscoelastic windkessel (VW). The W4S and IVW (same input impedance) fit the data best. The W4S, however, suffers from the assumption that Rc is part of total peripheral resistance (Rp). The IVW model offers a new paradigm for interpretation of resistive properties in terms of viscous (Rd) properties of vessel wall motion, distinguished from Rp. Results indicated that rapid reduction of Rd/Rp during early development is functional to modulation of decay time constant (taud) of pressure in diastole, such that normalization over heart period (taud/T) is independent of body size. Estimates of total arterial compliance (C) vs. age were fitted by a bell-shaped curve with a maximum at 33 yr. With body weight (BW) factored out by normalization, the C/BW data scattered about a bell-shaped curve centered at 66 mmHg. Inertance was significantly higher in pediatric patients than in adults, in accordance with a lower cross-sectional area of the vasculature, commensurate to a lower aortic flow. Changes of arterial properties appear functional to control the ratio of pulsatile power to active power and keep arterial efficiency as high as 97% in infants and children.     

Sequential venous anastomosis design to enhance patency of arterio-venous grafts for hemodialysis

Arterio-venous grafts (AVGs), the second best option as long-term vascular access for hemodialysis, face major issues of stenosis mainly due to development of intimal hyperplasia at the venous anastomosis which is linked to unfavorable hemodynamic conditions. We have investigated computationally the utility of a coupled sequential venous anastomotic design to replace conventional end-to-side (ETS) venous anastomosis, in order to improve the hemodynamic environment and consequently enhance the patency of AVGs. Two complete vascular access models with the conventional and the proposed venous anastomosis configurations were constructed. Three-dimensional, pulsatile blood flow through the models was simulated, and wall shear stress (WSS)-based hemodynamic parameters were calculated and compared between the two models. Simulation results demonstrated that the proposed anastomotic design provides: (i) a more uniform and smooth flow at the ETS anastomosis, without flow impingement and stagnation point on the artery bed and vortex formation in the heel region of the ETS anastomosis; (ii) more uniform distribution of WSS and substantially lower WSS gradients on the venous wall; and (iii) a spare route for the blood flow to the vein, to avoid re-operation in case of stenosis. The distinctive hemodynamic advantages observed in the proposed anastomotic design can enhance the patency of AVGs.     

Microcirculation impedance analysis in cat lung

An analysis of pulsatile microcirculation in cat lung, with special attention to the pulmonary microvascular impedance, is presented. A theoretical calculation is made on the basis of a complete set of experimental data on the morphology and elasticity of cat's pulmonary capillary sheets. The transfer matrix of the pulmonary microvascular impedance is obtained. The input impedance at the capillary entrance and exit are determined. The input impedance at the pulmonary arterial trunk is compared under various physiological conditions. It is shown that although the impact of pulmonary microcirculation on the relationship between the steady mean flow and pressure in the pulmonary arteries and veins is decisively large, the influence of the alveolar microcirculation on the input impedance at the pulmonary arterial trunk is small.     

Aortic wave dynamics and its influence on left ventricular workload

The pumping mechanism of the heart is pulsatile, so the heart generates pulsatile flow that enters into the compliant aorta in the form of pressure and flow waves. We hypothesized that there exists a specific heart rate at which the external left ventricular (LV) power is minimized. To test this hypothesis, we used a computational model to explore the effects of heart rate (HR) and aortic rigidity on left ventricular (LV) power requirement. While both mean and pulsatile parts of the pressure play an important role in LV power requirement elevation, at higher rigidities the effect of pulsatility becomes more dominant. For any given aortic rigidity, there exists an optimum HR that minimizes the LV power requirement at a given cardiac output. The optimum HR shifts to higher values as the aorta becomes more rigid. To conclude, there is an optimum condition for aortic waves that minimizes the LV pulsatile load and consequently the total LV workload.     

Gender differences in autonomic cardiovascular regulation: spectral, hormonal, and hemodynamic indexes.

The autonomic nervous system drives variability in heart rate, vascular tone, cardiac ejection, and arterial pressure, but gender differences in autonomic regulation of the latter three parameters are not well documented. In addition to mean values, we used spectral analysis to calculate variability in arterial pressure, heart rate (R-R interval, RRI), stroke volume, and total peripheral resistance (TPR) and measured circulating levels of catecholamines and pancreatic polypeptide in two groups of 25 +/- 1.2-yr-old, healthy men and healthy follicular-phase women (40 total subjects, 10 men and 10 women per group). Group 1 subjects were studied supine, before and after beta- and muscarinic autonomic blockades, administered singly and together on separate days of study. Group 2 subjects were studied supine and drug free with the additional measurement of skin perfusion. In the unblocked state, we found that circulating levels of epinephrine and total spectral power of stroke volume, TPR, and skin perfusion ranged from two to six times greater in men than in women. The difference (men > women) in spectral power of TPR was maintained after beta- and muscarinic blockades, suggesting that the greater oscillations of vascular resistance in men may be alpha-adrenergically mediated. Men exhibited muscarinic buffering of mean TPR whereas women exhibited beta-adrenergic buffering of mean TPR as well as TPR and heart rate oscillations. Women had a greater distribution of RRI power in the breathing frequency range and a less negative slope of ln RRI power vs. ln frequency, both indicators that parasympathetic stimuli were the dominant influence on women's heart rate variability. The results of our study suggest a predominance of sympathetic vascular regulation in men compared with a dominant parasympathetic influence on heart rate regulation in women.     

Pulsatile blood flow in the entire coronary arterial tree: theory and experiment

The pulsatility of coronary circulation can be accurately simulated on the basis of the measured branching pattern, vascular geometry, and material properties of the coronary vasculature. A Womersley-type mathematical model is developed to analyze pulsatile blood flow in diastole in the absence of vessel tone in the entire coronary arterial tree on the basis of previously measured morphometric data. The model incorporates a constitutive equation of pressure and cross-section area relation based on our previous experimental data. The formulation enables the prediction of the impedance, the pressure distribution, and the pulsatile flow distribution throughout the entire coronary arterial tree. The model is validated by experimental measurements in six diastolic arrested, vasodilated porcine hearts. The agreement between theory and experiment is excellent. Furthermore, the present pulse wave results at low frequency agree very well with previously published steady-state model. Finally, the phase angle of flow is seen to decrease along the trunk of the major coronary artery and primary branches toward the capillary vessels. This study represents the first, most extensive validated analysis of Womersley-type pulse wave transmission in the entire coronary arterial tree down to the first segment of capillaries. The present model will serve to quantitatively test various hypotheses in the coronary circulation under pulsatile flow conditions.     

A Predictive Study of Congenital Heart Disease and Need for Care

For long-term planning in the delivery of health care, prevalence data are essential for budget estimates in terms both of distribution and training of manpower and fiscal responsibility. From incidence figures, from the knowledge of the natural history of congenital heart disease and from predicted population estimates it is possible to construct a model that reflects the prevalence of congenital heart disease. This has been done for the state of California; the methods used and the data gathered should prove useful nationally.It is estimated that there were in 1975 in California 17,531 children under 21 years of age with congenital heart disease; 24 percent of these had ventricular septal defects and 23 percent had pulmonary stenosis, 11 percent had atrial septal defects and 9 percent had aortic stenosis; the other forms of congenital heart disease constituted the remaining 33 percent. Based on these estimates it is then possible to plan the medical resources necessary for optimal care.     

Characterization of the Isolated,Ventilated, and Instrumented Mouse Lung Perfused with Pulsatile Flow

The isolated, ventilated and instrumented mouse lung preparation allows steady and pulsatile pulmonary vascular pressure-flow relationships to be measured with independent control over pulmonary arterial flow rate, flow rate waveform, airway pressure and left atrial pressure. Pulmonary vascular resistance is calculated based on multi-point, steady pressure-flow curves; pulmonary vascular impedance is calculated from pulsatile pressure-flow curves obtained at a range of frequencies. As now recognized clinically, impedance is a superior measure of right ventricular afterload than resistance because it includes the effects of vascular compliance, which are not negligible, especially in the pulmonary circulation. Three important metrics of impedance - the zero hertz impedance Z₀, the characteristic impedance Z_C, and the index of wave reflection R_W - provide insight into distal arterial cross-sectional area available for flow, proximal arterial stiffness and the upstream-downstream impedance mismatch, respectively. All results obtained in isolated, ventilated and perfused lungs are independent of sympathetic nervous system tone, volume status and the effects of anesthesia. We have used this technique to quantify the impact of pulmonary emboli and chronic hypoxia on resistance and impedance, and to differentiate between sites of action (i.e., proximal vs. distal) of vasoactive agents and disease using the pressure dependency of Z_C. Furthermore, when these techniques are used with the lungs of genetically engineered strains of mice, the effects of molecular-level defects on pulmonary vascular structure and function can be determined.Download video file.^{(61M, mov)}     

High frequency characteristics of the arterial system

Pressure, flow and diameter were measured in the abdominal aorta of five anesthetized dogs during normal heart beats and heart beats with a superimposed impulse (generated by rapidly injecting a small volume of saline into the system). From Fourier analysis it was found that the impulse enhanced the amplitudes of the higher harmonics so that frequencies up to 80 Hz could be studied. Both the input impedance and apparent phase velocity above 20 Hz were independent of frequency and their average values were designated as characteristic impedance and true phase velocity. Average characteristic impedance for all five animals was 2.0 +/- 0.1 X 10(8) Nsm-5 and average phase velocity was 8.3 +/- 0.6 ms-1. Phase velocities calculated from characteristic impedance (1.76-2.39 X 10(8) Nsm-5) and from the slope of the pressure-diameter relation (0.102-0.25 X 10(-8) Nm-3) were similar to the true phase velocity as defined above (6.79-9.85 ms-1). It may be concluded that the input impedance converges to characteristic impedance and apparent phase velocity converges to phase velocity for high frequencies.     

Simulation of coronary artery revascularization

Simulation of the commonly constructed geometries of aorto-coronary bypass anastomoses was carried out using especially fabricated distensible tubes and a pulsatile pump. The system pressure was maintained between 80 and 120 mmHg. The total mean flow was set at 250 ml min-1 (Reynolds number of 200) and the pulsatile frequency was varied from 0 to 2 Hz. A water-glycerine mixture having a density and viscosity similar to that of blood was used throughout. A 16 mm film of the front of black dye injected proximal to the anastomosis was made as the dye approached and passed through the anastomosis. Anastomotic geometries consisted of: end to side, parallel, 45 degree angle, and 90 degree angle. Stenoses, located in the tube representing the coronary artery, were simulated using a bevelled insert which represented an 80-85% area reduction. Flow visualization revealed that distensible tubes gave more realistic flow patterns than rigid tubes, a result particularly evident when a stenosis was present. Pulsatile flow demonstrated considerably more mixing than steady flow. The use of pulsatile flow in distensible tubing with a partial stenosis showed retrograde flow through the stenosis which was not evident for either steady flow or for flow in rigid tubing. The flow at the anastomatic site of the graft having an angle of 0 degrees showed a jetting action with a zone of recirculating fluid being present whereas for a 90 degree graft a distinct helical flow was formed distal to the anastomosis.