Dynamic pressure-flow diagrams and impedance in experimental arterial stenosis and in stenotic atherosclerosis

Dynamic pressure-flow diagrams were generated by plotting instantaneous pulsatile pressure versus pulsatile flow measured 2 to 3 cm proximal to a graded arterial stenosis in the dog femoral artery. The slope of the major axis of the diagram was defined as the pulse impedance (Z _P).Z _p under steady-state and vasodilated conditions was linearly related to the large vessel impedance (Z _l) calculated independently as the average vascular input impedance modulus from 3 to 19 Hz, and linearly related to the hydraulic resistance of the stenosis. In a separate study,Z _p andZ _l each were shown to be greater in patients with severe femoral artery stenotic atherosclerosis than in control patents, and unchanged during vasodilation. In addition,Z _p andZ _l were reduced following femoral-to-popliteal bypass procedures. In summary, dynamic pressure-flow diagrams provide an easy-to-obtain index of the effective vascular hydraulic input impedance in stenotic arteries, and an index of the severity of distal arterial stenosis. This research has been supported in part by the North Carolina Heart Association (Grant-in-Aid 1974-75-A-62) and the Environmental Protection Agency, Chapel Hill, North Carolina.     

Influence of Vessel Distension and Myogenic Tone on Pulmonary Arterial Input Impedance. A Study using a Computer Model of Rabbit Lung

A computer model of the pulmonary arterial (PA) bed of rabbit lungs was designed in order to test experimental observations of changes in PA input impedance and pulsatile hydraulic power (cap.) during increased PA pressure. The computer model was based on a simple 3-component analog representation of single vessels (i.e. resistance, inertance and compliance). 16 generations of arterial vessels, from PA to 60 μm diameter, were combined to calculate PA input impedance. Input impedance was found to mimic closely that observed experimentally. Both venous pressure elevation and arteriolar constriction was found to reduce input impedance and Wp. By combining arteriolar constriction with increased myogenic tone of the larger arteries, Wp was found to show a minimum level at a certain PA pressure, dependent on the degree of arterial stiffening. Wp was found to follow changes in arterial volume and resistance during simulated vasoconstriction. Wp dissipation in arterial vessels was calculated to approx. 50% of total input Wp at physiological pressure conditions, and could be reduced by one half after PA pressure increase from 20 to 50 cm H₂O, despite a concurrent halving of arterial compliance. Arterial vessels smaller than 200 pm diameter were found to have negligible direct influence on PA input impedance.     

Influence of Moderate Vasoconstriction on the Wave Reflection Properties of the Pulmonary Arterial Bed

Increased transmural pressure in the pulmonary arterial bed may reduce vascular input impedance and reduce hydraulic power linked to pulsatile blood flow. Vascular impedance and pulsatile hydraulic power (Wp) levels of isolated perfused rabbit lungs were compared after similar rises of pulmonary arterial pressure (PAp), induced either by vasoconstriction or by left atrial pressure (LAp) elevation. Resulting Wp levels were significantly smaller after vasoconstriction than LAp elevation. Wp showed a minimum level at physiologic PAp (about 20 cm H₂O) irrespective of the cause of PAp elevation. Pressure pulse wave reflection coefficient (Γ) was calculated for control and test situations, and was found to be approximately doubled after vasoconstriction. Only minor changes in Γ were found after LAP elevation. Accordingly, moderate vasoconstriction (resulting PAp?20 cm H₂O) caused a backward traveling pressure wave of high amplitude, appearing in counter-phase to the forward pressure wave at the input site. The total pressure wave amplitude was thereby markedly lowered, resulting in a reduced Wp level. We assume that this effect of moderate vasoconstriction may be one reason for the existence of vascular smooth muscles in the pulmonary arteries.     

Some Physical Properties of the Pulmonary Arterial Bed Deduced from Pulsatile Arterial Flow and Pressure

This study aimed to quantify changes of vascular compliance and resistance of the proximal and the peripheral pulmonary arterial vessels when vascular smooth muscle was stimulated. These above vascular characteristics were derived from registrations of pulsatile pressure and flow in the pulmonary artery (PA). An in situ cat lung preparation was used, with the right heart by-passed by a pulsatile blood pump. Vascular input impedance was derived from PA pulsatile pressure and flow recordings, and impedance characteristics were used for calculation of the variables of a simple lumped analog representation of the arterial bed. PA smooth muscle was stimulated by infusions of collagen suspension, by general hypoxia and by nor-adrenaline injections. Collagen caused 40% reduction of vascular compliance (C), no changes in proximal arterial resistance (Rl) and 18076 increase in peripheral vascular resistance (R2). Hypoxia caused 5096 reduced C, 20% increased R1 and 70% increased R2. Noradrenaline caused 20:6 reduced C and 30 % increased R1 and R2. These results, together with results derived from simulation of the observed impedance changes in a computer model of the lung arterial bed, indicated that collagen infusion elicited contraction of small and medium-sized arteries, with increased arterial volume as result of increased distending pressure. Hypoxia and noradrenaline, seemed both to cause contraction of the total arterial bed. This effect being most pronounced during hypoxia.     

Effect of compliance on a time-domain estimate of the characteristic impedance of the pulmonary artery during acute pulmonary hypertension

In 11 pigs under general endotracheal anaesthesia, the time-domain method of determining the pulmonary arterial input impedance was compared with the frequency-domain equivalent under normal conditions as well as acute pulmonary hypertension induced by glass microspheres. The time-domain methods of determining the pulmonary arterial compliance C and pulmonary vascular bed resistance R_p compared favourably with the frequency-domain equivalent (r=0·744, n=60, p<0·001 and r=0·906, n=60, p<0·001, respectively), even at mean pulmonary artery pressures (MPAP) of 35 mmHg and above. A consistent and everincreasing difference between characteristic impedance Z_o(ω), estimated by averaging input impedance modulus values over a selected frequency range, and its time domain equivalent R_o with increasing MPAP was shown to be the cause of the poor fit between the measured and remodelled pulmonary blood flow. By analysing a time-domain estimate of the pulmonary characteristic impedance R_o(C, R_p, t), it was demonstrated that the characteristic impedance was dependent on C. R_o is therefore not an accurate representation of the characteristic impedance, especially under conditions of acute pulmonary hypertension. R_o (C, R_p, t) should therefore be calculated instead.     

Use of Input Impedance to Determine Changes in the Resistance of Arterial Vessels at Different Levels in Feline Femoral Bed

In many studies, the functional state of vessels of different caliber was determined by fitting the lumped parameters of a mathematical model of the bed in order to fit the vascular input impedance (Z _in) data. However, reliability of the results obtained in such a way remains uncertain. In this study, we employed a mathematical model with seven lumped parameters and Z _in experimental data to analyze the distribution of resistance across the arterial bed of the hind limb in anesthetized cats, to test reliability of this distribution and to describe the process of ascending arterial dilation followed occlusion of iliac artery. The vascular bed was divided into three segments: large arteries, medium-sized arterial vessels and precapillary resistance vessels together with venous part of the bed. Based on the data of Z _in measured in a wide frequency range (from 0 to 150 Hz) we showed that pharmacologically induced constriction and dilation of the arterial microvessels were reflected in the model by the changes in the resistance of distal precapillary vessels only, whereas the local constriction or dilation of femoral and iliac arteries as well as artificial stenosis of the femoral artery resulted exclusively in the changes of the resistance describing the state of large arteries. Using the input impedance method we could demonstrate and quantitatively describe the process of ascending arterial dilation during the post-occlusion (reactive) hyperemia. All these results prove that the model of vascular bed with seven lumped elements used in combination with input hydraulic impedance data can be an effective tool permitted to quantitatively analyze the functional state of arterial vessels of different caliber and to describe the changes in resistance of arterial vessels during vascular reactions.     

Effects of oscillation on the arteries measured by arterial impedance during left ventricular assistance

Oscillating blood flow has effects on the arteries similar to the effects of pulsatile blood flow at lower frequencies. Alternating-current theory is useful to study the pulse in the circulatory system. Arterial impedance is a good index to estimate the frequency characteristics of the artery. In this study, total vascular resistance and arterial impedance were studied in animal experiments during left ventricular assistance. A centrifugal pump was used for comparison with a VFP (vibrating-flow pump). Left ventricular assistance was performed in animal experiments using goats. Total vascular resistance and arterial impedance were studied to estimate the frequency characteristics of the artery. Total vascular resistance during steady flow assistance decreased compared with that during nonassistance. Arterial walls were extended by the blood flow assistance at steady flow. The resistance during oscillating blood flow was different at each driving frequency, showing the frequency dependency, or pulse effect, of the arterial system under nonsteady flow. Arterial impedance was also studied during oscillating blood flow and showed a slight increase at a driving frequency of 25 or 30 Hz. These fluctuations in impedance are influenced by the reflection of the pulse. Arterial impedance should be taken into consideration when analyzing pulsatile blood flow because the pulse reflection may have some effects on the arterial wall. Some variation of blood pressure and blood flow might be necessary for stable support with artificial circulatory assistance.     

Analytical relationship between arterial input impedance and the three-element Windkessel series resistance

The recently proposed energy-balance method for estimating the series resistance of the three-element Windkessel model is reformulated in the frequency domain. New mathematical expressions are analytically derived, involving Fourier harmonics of pulsatile arterial pressure and flow. It is shown that the series resistance of the arterial three-element Windkessel model can be expressed as a weighted sum of the arterial input impedance moduli.     

The correlation of cardiac mass with arterial haemodynamics of resistive and capacitive load in rats with normotension and established hypertension

In hypertensive animals and humans, cardiac hypertrophy may occur as a consequence of an external load on the heart. Several studies have suggested that the non-pulsatile components of arterial haemodynamics, such as arterial pressure and vascular resistance, do not adequately represent the ventricular afterload and are not well correlated with the degree of cardiac hypertrophy (CH). The present study was undertaken to analyse the correlation between the degree of CH and various haemodynamic parameters in the spontaneously hypertensive rat (SHR) with established hypertension. A total of 36 SHRs (6–8 months) with a tail-cuff pressure above 190 mm Hg were used. Control data were obtained from 32 age-matched normotensive Wistar Kyoto rats (WKY). Animals were anaesthetized with pentobarbitone sodium (40 mg/kg i.p.) and artificially ventilated with a respirator. A Millar catheter with a high-fidelity pressure sensor was used to record the aortic pressure and an electromagnetic flow transducer to monitor the aortic flow. The pressure and flow signals were subjected to Fourier transformation for the analysis of the arterial impedance spectrum. The left ventricular weight-to-body weight ratio (LVW/BW) was taken as a measure of the degree of CH. The measured haemodynamic parameters in these anaesthetized, open-chest SHRs were systolic pressure (SP) (mean ± SE) 172±4 mm Hg, diastolic pressure (DP), 120±3 mm Hg, pulse pressure (PP) 52±2 mm Hg, peripheral resistance (R _p) 344,032±8,012 dyne · s · cm^–5, characteristic impedance (Z_c) 6,442±313 dyne · s · cm^–5, the impedance modulus at the first harmonic (Z1) 26,611±1,061 dyne · s · cm^–5, mean arterial compliance (C _m) 0.87 ±0.04 l/mm Hg and LVW/BW 3.092±0.026 mg/g. These parameters were significantly greater than the corresponding values in WKY, except that C _m was much decreased. In SHR, the LVW/BW was not significantly correlated with the SP, DP, R _p and steady external power. In contrast, the degree of CH was positively correlated with Z_c (r=0.66, P<0.001), Z1 (r=0.62, P<0.001) and pulsatile external work (r=0.41, P<0.05). It was also positively correlated with the backward pressure wave (r=0.42, P<0.05) and negatively correlated with C _m (r=-0.72, P<0.01). Such correlations of LVW/BW with pulsatile haemodynamics were not found in the normotensive WKY. The results indicate that the degree of cardiac hypertrophy in hypertensive rats, with a high blood pressure and increased stiffness of the arterial tree, is more closely related to pulsatile arterial haemodynamics than to the nonpulsatile components.     

利用硅胶管流动腔系统模拟动脉脉动血流切应力和周向应力环境

目的选择硅胶管流动腔的前、后负荷,模拟生理脉动流条件下动脉内皮细胞所承受的切应力和周向应力环境。方法利用在体脉动血流切应力和周向应力波形,在求得硅胶管流动腔几何和力学特性的情况下,反向求解硅胶管流动腔内径、压力和流量波形;根据所求得的压力和流量波形,确定出硅胶管流动腔的后负荷(即输入阻抗)条件;利用冯忠刚等提出的三弹性腔九元件集中参数模型模拟该后负荷,并求出各元件参数。结果三弹性腔九元件集中参数模型模拟出的输入阻抗模和幅角与目标输入阻抗模和幅角能较好的吻合。结论该方法为选择合适的硅胶管流动腔前、后负荷,构建能较真实再现动脉脉动血流切应力和周向应力环境的硅胶管流动腔系统提供了一定的理论依据。     

Physiological and fluid-dynamic investigations of the transthoracic impedance plethysmography method for measuring cardiac output. Part II—Analysis of the transthoracic impedance wave by perfusing dogs

By perfusing the aorta and the pulmonary artery of dogs with a controlled sinusoidal or pulsatile flow, the source of the transthoracic impedance variation and the relationship between the actual blood volume flow and the stroke volume value calculated by Kubicek's impedance method s.v._z were investigated. The results are as follows: (a) the main component of the transthoracic impedance waveform from which the s.v._z value is calculated originates from the systemic blood flow rather than from the pulmonary blood flow; (b) not the absolute but the relative value of the stroke volume can be calculated by Kubicek's equation; and (c) the s.v._z value is greatly affected by the hydraulic frequency of the actual sinusoidal blood flow.     

Pressure-flow relationships of the canine iliac periphery and systemic hemodynamics: Effects of sodiumnitroprusside and adenosine

It has been reported that sodiumnitroprusside (SNP) decreases mean systemic pressure and simultaneously increases pressure pulse amplification towards the iliac periphery (Kenner and van Zwieten 1982). This unexpected finding was suggested to be due to a decrease in iliac peripheral resistance but an increase in iliac differential resistance. In order to investigate this apparent contradiction, the iliac periphery was hemodynamically isolated from the rest of the circulation and perfused with the dog's own blood by means of a pump. Perfusion pressure (P) and flow (F), femoral venous pressure (P_v), systemic pressure (P_s) and cardiac output (CO) were measured. Steady state pressure-flow relations of the isolated bed were obtained during control and during various i.v. infusion rates of SNP and adenosine (ADS) and were found to be straight (meanr=0.99). Their slope (P/F) was defined as differential resistance (R_d). Peripheral resistance (R_p) of the iliac bed was defined as R_p=(P-P_v)/F, calculated at the flow value where perfusion pressure equalled the prevailing systemic pressure. Total peripheral resistance (TPR) was defined as TPR=P_s/CO. The changes of R_d, R_p, P_s, CO and TPR with respect to control show that during low SNP infusion rates R_d and R_p were both increased while TPR was decreased. During all infusion rates of SNP CO did not change while P_s decreased. During low infusion rates of adenosine CO increased while P_s, R_d and R_p did not change and TPR decreased. During high infusion rates of ADS CO decreased again, R_d, R_p and P_s decreased, and TPR remained constant but at a decreased level.It is concluded that: (1) the suggestion of Kenner and van Zwieten is not supported, since SNP (as well as ADS) affects iliac peripheral and iliac differential resistance in a similar way; (2) SNP (as well as ADS) affects iliac peripheral resistance and total peripheral resistance in a differentiated way, and even in an opposite way during low infusion rates of SNP; (3) it is this opposite effect that explains the paradoxical observations of Kenner and van Zwieten; (4) for comparable reductions of TPR, CO is better maintained during infusion of SNP, while P_s is better maintained during infusion of ADS.     

Modelling of pulsatile blood flow in arterial trees of retinal vasculature

The paper presents a numerical investigation of the pulsatile blood flow in the detailed arterial vasculatures of a mouse retina using the mathematical model based on frequency domain incorporating an appropriate outlet boundary impedance at the end of the terminal vessels of the arterial trees. The viscosity in the vessels was evaluated considering the Fahraeus-Lindqvist effect, the plasma skimming effect and in vivo viscosity effect in the microcirculation. Comparative studies of the pulsatile circulation were carried out for cases of rigid vessels, constant viscosity, zero and non-zero outlet boundary impedances. In addition, the dependence of the oscillating input impedance at the inlet of the arterial trees on angular frequencies of the oscillation and vessel elasticises was also studied. The study shows that the pressure wave continues in the pre-capillary vessels throughout the retina. In elastic vessels, the amplitude of oscillatory velocity and wall shear stress in larger vessels and in vessels at the periphery region of the retina is amplified. The pulsatile blood flow is significantly influenced by the outlet boundary (or load) impedance which simulates the effect of the capillary and venous vasculatures. The oscillating input impedance at the inlet of the arterial trees is also found to be dependent on the angular frequency and the Young modulus of the vessel segment. Insights into the potential variations of the dynamic responses of the system under retinal pathological condition of arteriosclerosis may be inferred from the findings of the present study.     

Sensitivity and afterload independence of zero-load aortic flow

The computed zero-load flow is the expected aortic flow when the aortic pressure is zero, thus eliminating the effect of afterload on ventricular ejection. Zero-load flow was computed in 15 anesthetized dogs (sodium pentobarbital 25 mg/kg, iv) by studying the response of left-ventricular pressure or aortic pressure, and aortic flow to the change in aortic input impedance induced by partial snare occlusion of the aorta. The waveform and peak value of zero-load flow were computed from a theoretical model of the left ventricle and verified by measurements of aortic flow in the first beat after transection of the aorta. To study the sensitivity, changes of zero-load flow were computed under the enhanced inotropic state produced by isoproterenol (0.1 μg/kg/min), and under the depressed contractile state induced by propranolol (0.15 mg/kg). Administration of isoproterenol resulted in an increase in the peak zero-load flow by 143.9% (p<0.001), compared with a 50.6% increase (p<0.05) in peakdp/dt. The difference of the variations was statistically significant in a pairedt test. After injection of propranolol, peak zero-load flow decreased by 32.0% (p<0.005). Afterload independence of zero-load flow was studied by computing zero-load flow before and after increasing arterial pressure by partial aortic occlusion or injection of 5 mg methoxamine. After injection of methoxamine in denervated dogs, the peak zero-load flow increased by 11.2% (N.S.), while input resistance increased by 153% (p<0.025). The peak zero-load flow decreased by 8% (N.S.) after partial aortic occlusion, while cardiac output decreased by 26.7% (p<0.001). These results may suggest that the computed peak zero-load flow is an afterload independent index of the pumping capability of the left ventricle in the intact heart.     

Design of an artificial lung compliance chamber for pulmonary replacement

Matching the impedance of an artificial lung for pulmonary replacement to native pulmonary impedance is important in preventing right ventricular dysfunction. A lumped-parameter theoretical model and bench-top experiments were used to investigate the effect of a prototype compliance chamber on input impedance. The bench-top simulation consisted of a pulsatile flow generator, a prototype compliance chamber, and a low resistance artificial lung connected in series. Effective compliance was varied using pneumatic compression. The theoretical model considered a similar circuit with resistors before and after a compliance element. The bundle flow pulsatility (flow amplitude divided by average flow) and input impedance were calculated in the theoretical and experimental models. More compliance and lower upstream resistance result in lower bundle flow pulsatility and reduced first harmonic impedance. Matching the time scale of the circuit to the period of pulsatile flow also reduces impedance. The bench-top circuit demonstrated an optimal chamber pressure at which first harmonic impedance is reduced by 80%. The prototype compliance chamber in series with the artificial lung more closely matches native pulmonary impedance. The lumped-parameter model and the bench-top simulation will aid in the design and testing of compliance chamber modifications to improve its efficiency.     

Evaluation of the theory of cardiac-output computation from transthoracic impedance plethysmogram

To analyse the limit of the stimation of stroke volume by thoracic impedance plethysmography (SV_z), we considered an elastic tube forced with a trapezoidal flow input as a model of the aorta, and, based on Kubicek's equation, the volume input (SV_a) was related to its impedance change via the model system parameters such as elasticity, fiuid inertia, peripheral resistance, total impedance across the tube and the rise and fall time of the input. SV_z is equal to SV_a only when the inflow is a square wave. The ratio SV_z/SV_a decreases with increasing input rise time, while it increases with increasing fall time, if the maximum flow rate and ejection time of the inflow are held constant. SV_z hardly changes in association with changes in elasticity, fluid inertia, peripheral resistance or total impedance. A part of the results, the relationship between SV_z, transthoracic total impedance and aortic flow waveform, was also demonstrated in dogs.     

Electrical impedance plethysmography: Its use in studying the cerebral circulation of the rabbit

Electrical impedance plethysmography (EIP) is a noninvasive method that may be useful for both the continuous and serial measurement of changes in pulsatile cerebral blood volume and perhaps cerebral blood flow (CBF). It has not been well validated by comparison with other methods. To attempt to validate the EIP technique, the relationship between the peak amplitude of the transcranial, cardiac-synchronous impedance waveform (dZ_p) and cerebral blood flow measured by the radiolabelled microsphere technique (CBF_rlm) and laser Doppler spectroscopy (CBF_rds) was studied in rabbits. CBF was altered by inducing hypertension using metaraminol, hypotension by controlled haemorrhage or hypocarbia by hyperventilation. Twenty-three comparisons between dZ_p and CBF_ids and 19 comparisons with CBF_rim were made in eight rabbits. The percentage change between each measurement using the three techniques in each animal was calculated. Using pooled data from all the animals, the linear regression equations were dZ_p=0.5 CBF_rim+33 (r=0.38, p=0.22, SE=79) and dZ_p=0.84 CBF_ids+19.6 (r=0.46, p=0.09, SE=72). It is concluded that, in the anaesthetised rabbit, when large changes in CBF are induced by the manoeuvres described above, changes in dZ_p correlate very weakly with changes in either cortical or global CBF, and are influenced by other factors such as pulsatile intracranial blood volume.     

Does pulsatile and sustained neck pressure or neck suction produce differential cardiovascular and sympathetic responses in humans?

Although square-wave sustained and R wave-triggered pulsatile stimuli have been used to assess carotid baroreflex (CBR) function in humans, it remains unclear whether these different stimulus protocols elicit comparable responses and whether CBR responses adapt during prolonged stimulation. Thus, we measured muscle sympathetic nerve activity (MSNA), heart rate (HR) and mean arterial pressure (MAP) in response to +30 Torr neck pressure (NP) and -30 Torr neck suction (NS) delivered for 20 s either as a sustained or pulsatile stimulus. CBR-mediated changes in MSNA, HR and MAP were similar with sustained and pulsatile stimuli. The time course of MSNA and HR responses identified that significant changes occurred during the initial 5 s and were better maintained over 20 s with NP than with NS. Changes in MAP exhibited a slower onset with the peak increase during NP occurring at 10 s (sustained, 7 +/- 1 mmHg; pulsatile, 7 +/- 1 mmHg; P > 0.05) and the nadir during NS occurring at 20 s (sustained, -7 +/- 1 mmHg; pulsatile, -9 +/- 2 mmHg; P > 0.05). These data demonstrate that sustained and pulsatile NP and NS produce comparable CBR-mediated responses. Furthermore, despite MSNA and HR returning towards baseline during NS, CBR-mediated changes in MAP are well maintained over 20 s of NS and NP.     

A hybrid mock circulatory system: development and testing of an electro-hydraulic impedance simulator

Mock circulatory systems are used to test mechanical assist devices and for training and research purposes; when compared to numerical models, however, they are not flexible enough and rather expensive. The concept of merging numerical and physical models, resulting in a hybrid one, is applied here to represent the input impedance of the systemic arterial tree, by a conventional windkessel model built out of an electro-hydraulic (E-H) impedance simulator added to a hydraulic section. This model is inserted into an open loop circuit, completed by another hybrid model representing the ventricular function. The E-H impedance simulator is essentially an electrically controlled flow source (a gear pump). Referring to the windkessel model, it is used to simulate the peripheral resistance and the hydraulic compliance, creating the desired input impedance. The data reported describe the characterisation of the E-H impedance simulator and demonstrate its behaviour when it is connected to a hybrid ventricular model. Experiments were performed under different hemodynamic conditions, including the presence of a left ventricular assist device (LVAD).