Functional origin of reflected pressure waves in a multibranched model of the human arterial system

1994 ◽  
Vol 267 (5) ◽  
pp. H1681-H1688 ◽  
Author(s):  
M. Karamanoglu ◽  
D. E. Gallagher ◽  
A. P. Avolio ◽  
M. F. O'Rourke
Keyword(s):  
Pressure Wave ◽  
Aortic Pressure ◽  
Lower Limbs ◽  
Arterial System ◽  
Pressure Waves ◽  
Upper Limbs ◽  
Arterial Tree ◽  
Wave Travel ◽  
Aortic Impedance

The effects of wave travel and wave reflection were simulated in a mathematical model of the whole arterial tree consisting of 142 uniform transmission line segments. The arterial model was partitioned into three separate segments: upper limbs, trunk, and lower limbs. Aging was simulated by increasing average pulse wave velocities of these segments (10.9–12.9, 8.0–11.7, and 9.0–11.3 m/s for upper limbs, trunk, and lower limbs, respectively). Reflection coefficients at the terminal elements were altered to simulate vasodilation (0.0) and vasoconstriction (0.95). The impedance patterns and spatial distribution of pressure waveforms generated by the model simulating aging and vasoconstriction were similar to in vivo measurements by other investigators. Reflected pressure waves from each segment reached the ascending aorta and contributed differently to the late systolic peak on the aortic pressure wave. Aging does not alter the origin of these reflected pressure waves in the trunk. Aortic impedance and pressure wave changes induced by simulation of dilation of splanchnic bed were similar to those observed experimentally with nitroglycerin.

Use of pulse pressure method for estimating total arterial compliance in vivo

1999 ◽  
Vol 276 (2) ◽  
pp. H424-H428 ◽  
Author(s):  
N. Stergiopulos ◽  
P. Segers ◽  
N. Westerhof
Keyword(s):  
Pulse Pressure ◽  
Diastolic Pressure ◽  
Arterial Compliance ◽  
Aortic Pressure ◽  
Lower Limbs ◽  
Pressure Method ◽  
Total Arterial Compliance ◽  
The Difference ◽  
Pulse Pressure Method

We determined total arterial compliance from pressure and flow in the ascending aorta of seven anesthetized dogs using the pulse pressure method (PPM) and the decay time method (DTM). Compliance was determined under control and during occlusion of the aorta at four different locations (iliac, renal, diaphragm, and proximal descending thoracic aorta). Compliance of PPM gave consistently lower values (0.893 ± 0.015) compared with the compliance of DTM (means ± SE; r = 0.989). The lower compliance estimates by the PPM can be attributed to the difference in mean pressures at which compliance is determined (mean pressure, 81.0 ± 3.6 mmHg; mean diastolic pressure, over which the DTM applies, 67.0 ± 3.6 mmHg). Total arterial compliance under control conditions was 0.169 ± 0.007 ml/mmHg. Compliance of the proximal aorta, obtained during occlusion of the proximal descending aorta, was 0.100 ± 0.007 ml/mmHg. Mean aortic pressure was 80.4 ± 3.6 mmHg during control and 102 ± 7.7 mmHg during proximal descending aortic occlusion. From these results and assuming that upper limbs and the head contribute as little as the lower limbs, we conclude that 60% of total arterial compliance resides in the proximal aorta. When we take into account the inverse relationship between pressure and compliance, the contribution of the proximal aorta to the total arterial compliance is even more significant.

In vivo adaptive responses of the aorta to hypertension and aging

1997 ◽  
Vol 273 (1) ◽  
pp. H96-H103 ◽  
Author(s):  
M. Sumitani ◽  
A. M. Cabral ◽  
L. C. Michelini ◽  
E. M. Krieger
Keyword(s):  
Blood Pressure ◽  
Aortic Distensibility ◽  
Aortic Pressure ◽  
Adaptive Responses ◽  
Arterial Tree ◽  
Stress Strain ◽  
Strain Relationship ◽  
Pressure Changes ◽  
Geometric Changes

To investigate the dynamic behavior of the aorta of freely moving rats during the maintenance of hypertension, a longitudinal study was performed in renal hypertensive (Goldblatt 1 kidney, 1 clip) rats aged 3, 6, and 9 mo in which hypertension was maintained for 1, 3, and 6 mo, respectively. The pulsatile caliber of the thoracic aorta was measured (electrolytic strain gauge chronically implanted) simultaneously with aortic pressure under basal conditions and during transient changes of blood pressure. Aortic thickness was determined postmortem by morphometry. Establishment of hypertension (179 +/- 5 mmHg) by increasing the stress developed by the aorta caused increases in the resting values of caliber (20%), thickness (21%), and strain (95%); the maintenance of hypertension for a 6-mo period caused a further increase in thickness (58% vs. age-matched normotensive aortas) but not in aortic caliber and strain, the subsequent alterations of which were due only to growth/aging. Although different calibers, thicknesses, and dynamic strains were presented, the stress-strain relationship during transient blood pressure changes was similar for all hypertensive and normotensive groups with the exception of renal hypertensive rats aged 6 mo, which presented a steeper relationship (a large transitory increase in aortic distensibility was observed at that age). Dynamic adaptive responses of the aorta to hypertension compensate for geometric changes in such a way as to maintain a near-constant distensibility. It was concluded that, in contrast to the extrathoracic vessels, the adaptive responses of the aorta to hypertension were directed to maintain its compliance without changing the distensibility and stress-strain relationship, contributing to partially counterbalance the increased pressure and the decreased compliance of the more peripheral components of the arterial tree.

Estimation of total arterial compliance: an improved method and evaluation of current methods

1986 ◽  
Vol 251 (3) ◽  
pp. H588-H600 ◽  
Author(s):  
Z. Liu ◽  
K. P. Brin ◽  
F. C. Yin
Keyword(s):  
Diastolic Pressure ◽  
Arterial Compliance ◽  
Aortic Pressure ◽  
Arterial System ◽  
Windkessel Model ◽  
Total Arterial Compliance ◽  
Improved Methods ◽  
Mean Aortic Pressure

Determination of arterial compliance in vivo has long interested physiologists. Most current methods for estimating this parameter assume that compliance is constant, i.e., that arterial pressure-volume (P-V) relations are linear, and they also assume that diastolic aortic pressure decay is an exponential function of time. Both of these assumptions, however, are questionable. This study proposes improved methods of estimating compliance based on a Windkessel model of the arterial system but which utilize the area under the pressure tracing rather than the waveform itself. Formulations accounting for both linear and three hypothetical nonlinear arterial P-V relations (exponential, logarithmic, and parabolic) are presented. Data from patients with congestive heart failure and hypertension are used for illustration. Compliances assuming linear P-V relations are reasonably close to those assuming nonlinear P-V relations only at mean aortic pressure. At end-diastolic pressure the linear assumption underestimates and at peak systolic it overestimates the compliances obtained assuming nonlinear P-V relations. The simpler linear assumption still allows a first approximation to compliance, but we show that existing methods for obtaining compliance under this assumption have severe theoretical as well as practical shortcomings. Our proposed method avoids these shortcomings primarily because deviations from an exact exponential form of the pressure wave have less influence on these compliance estimates than currently used methods.

Determinants of stroke volume and systolic and diastolic aortic pressure

1996 ◽  
Vol 270 (6) ◽  
pp. H2050-H2059 ◽  
Author(s):  
N. Stergiopulos ◽  
J. J. Meister ◽  
N. Westerhof
Keyword(s):  
Stroke Volume ◽  
Venous Pressure ◽  
Analytical Form ◽  
Ventricular Volume ◽  
Aortic Pressure ◽  
Arterial System ◽  
Arterial Tree ◽  
Windkessel Model ◽  
Dimensionless Parameters ◽  
Analytical Expressions

We investigated how parameters describing the heart and the arterial system contribute to the systolic and diastolic pressures (Ps and Pd, respectively) and stroke volume (SV). We have described the heart by the varying-elastance model with six parameters and the systemic arterial tree by the three-element windkessel model, leading to a total of nine parameters. Application of dimensional analysis led to a total of six dimensionless parameters describing dimensionless Ps and Pd, i.e., pressures with respect to venous pressure (Ps/Pv and Pd/Pv). SV was normalized with respect to unloaded ventricular volume (Vd). Sensitivity analysis showed that Ps/Pv, Pd/Pv, and SV/Vd could be accurately described by four, three, and three dimensionless parameters, respectively. With this limited number of parameters, it was then possible to obtain empirical analytical expressions for Ps/Pv, Pd/Pv, and SV/Vd. The analytic predictions were tested against the model values and found to be as follows: Ps predicted = (1.0007 +/- 0.0062) Ps, r = 0.987; Pd predicted = (1.016 +/- 0.0085) Pd, r = 0.992; and SV predicted = (0.9987 +/- 0.0028) SV, r = 0.996. We conclude that aortic Ps, Pd, and SV can be accurately described by a limited number of parameters and that, for any condition of the heart and the arterial system, Ps, Pd, and SV can be presented in analytical form.

Comparative analysis of aortic impedance and wave reflection in ferrets and dogs

2002 ◽  
Vol 282 (1) ◽  
pp. H244-H255 ◽  
Author(s):  
R. Burattini ◽  
K. B. Campbell
Keyword(s):  
Animal Species ◽  
Wave Reflection ◽  
Pulse Wave ◽  
Aortic Pressure ◽  
The Body ◽  
Frequency Range ◽  
Wave Travel ◽  
Arterial Model ◽  
Aortic Impedance ◽  
The Difference

Our modified version of the T-tube arterial model (consisting of two parallel, loss-free transmission paths terminating in lumped loads of complex and frequency-dependent nature) was applied to experimental measurements of ascending aortic pressure and of ascending and descending aortic flows taken from dogs and ferrets. Our aim was to provide quantitative evaluation of the aortic pressure and flow pulse wave components as they relate to the distribution of arterial properties and relate to wave travel and reflection in mammalians of consistently different size and shape. Estimated effective lengths (distances to effective reflection sites) of the head-end ( d h) and body-end ( d b) transmission paths were ∼12 and 30 cm, respectively, in the dog and 6.5 and 13 cm, respectively, in the ferret. These lengths and distributions of estimated arterial properties were consistent with the difference in the body size and with the more central location of the heart in the ferret's body than it is in the dog's body. In both animal species the ascending aortic pressure and flow waves could be interpreted in terms of forward and reflected components arising from the two distinct effective reflection sites, although the higher d h/ d b ratio in the ferret determined the presence of one broad, indistinct minimum in the modulus of ascending aortic impedance in the frequency range from 0 to 10 Hz, rather than two distinct minima as observed in the dog.

Exaggerated wave reflection in the kangaroo simulates arterial counterpulsation

1984 ◽  
Vol 246 (2) ◽  
pp. R267-R270
Author(s):  
A. P. Avolio ◽  
W. W. Nichols ◽  
M. F. O'Rourke
Keyword(s):  
Pressure Wave ◽  
Wave Reflection ◽  
Diastolic Pressure ◽  
Systolic Pressure ◽  
Peripheral Circulation ◽  
Aortic Pressure ◽  
Pulse Contour ◽  
Aortic Impedance ◽  
Intra Aortic Balloon Counterpulsation ◽  
Balloon Counterpulsation

The ascending aortic pressure wave in kangaroos is quite different from that seen in other experimental animals and in humans, despite an ascending aortic flow wave that is virtually identical. The diastolic pressure surge in the ascending aortic pressure wave of kangaroos is very prominent--so much so that peak diastolic pressure is often greater than peak systolic pressure, with the pressure wave resembling that recorded in humans during intra-aortic balloon counterpulsation. Ascending aortic impedance patterns in kangaroos indicate the presence of a single functionally discrete reflecting site in the peripheral circulation, with high reflection coefficient. All findings--of pulse contour and impedance patterns--are explicable on the basis of arterial anatomy and body shape. Wave reflection from the distant, large, and vascular lower body appears to dominate the effects of wave reflection from the short, small, and less vascular head and forelimb system.

Beat-to-beat estimation of peripheral resistance and arterial compliance during pressure transients

1987 ◽  
Vol 252 (6) ◽  
pp. H1275-H1283 ◽  
Author(s):  
G. P. Toorop ◽  
N. Westerhof ◽  
G. Elzinga
Keyword(s):  
Heart Rate ◽  
Arterial Compliance ◽  
Peripheral Resistance ◽  
Estimation Method ◽  
Aortic Pressure ◽  
Autonomous Nervous System ◽  
Mean Flow ◽  
Arterial Tree ◽  
Total Arterial Compliance

We have used a computer-based parameter estimation method to obtain peripheral resistance, total arterial compliance, and characteristic resistance from the measurement of aortic pressure and flow in the open-thorax cat, assuming the three-element windkessel as a model of the systemic arterial tree. The method can be applied on a beat-to-beat basis in the steady state and in transients. We have validated this method by analyzing nonsteady-state data obtained from an electrical analog with fixed values of the resistances and compliance and by showing that the values obtained by this procedure were within 5% of the fixed values of the circuit. Changes in total peripheral resistance and arterial compliance were studied before, during, and after acute heart rate changes in five open-thorax cats with blocked autonomous nervous system. As expected, the peripheral resistance, estimated during the heart rate transient [3.93 +/- 0.94 (SE) kPa X ml-1 X s] was the same as before the transient (3.53 +/- 0.83 kPa X ml-1 X s); total arterial compliances were also identical (0.28 +/- 0.04 vs. 0.27 +/- 0.03 ml/kPa). In six cats without nervous blockade we obtained similar results. Calculation of peripheral resistance during transients from the mean pressure-to-mean flow ratio, i.e., without correction for arterial compliance, suggested changes in resistance values of less than or equal to 57%, which shows that correction is necessary. The findings indicate that peripheral resistance and total arterial compliance can be estimated in vivo on a beat-to-beat basis, even during hemodynamic transients.

Simulating re-reflections of arterial pressure waves at the aortic valve using difference equations

2020 ◽  
Vol 234 (11) ◽  
pp. 1243-1252 ◽  
Author(s):  
Bernhard Hametner ◽  
Hannah Kastinger ◽  
Siegfried Wassertheurer
Keyword(s):  
Blood Pressure ◽  
Aortic Valve ◽  
Reflection Coefficient ◽  
Difference Equation ◽  
Arterial Pressure ◽  
Aortic Pressure ◽  
Equation Model ◽  
Arterial System ◽  
Pressure Curve ◽  
Pressure Waves

Re-reflections of arterial pressure waves at the aortic valve and their influence on aortic wave shape are only poorly understood so far. Therefore, the aim of this work is to establish a model enabling the simulation of re-reflection and to test its properties. A mathematical difference equation model is used for the simulations. In this model, the aortic blood pressure is split into its forward and backward components which are calculated separately. The respective equations include reflection percentages representing reflections throughout the arterial system and a reflection coefficient at the aortic valve. While the distal reflections are fixed, different scenarios for the reflection coefficient at the valve are simulated. The results show that the model is capable to provide physiological pressure curves only if re-reflections are assumed to be present during the whole cardiac cycle. The sensitivity analysis on the reflection coefficient at the aortic valve shows various effects of re-reflections on the modelled blood pressure curve. Higher levels of the reflection coefficient lead to higher systolic and diastolic pressure values. The augmentation index is notably influenced by the systolic level of the reflection coefficient. This difference equation model gives an adequate possibility to simulate aortic pressure incorporating re-reflections at the site of the aortic valve. Since a strong dependence of the aortic pressure wave on the choice of the reflection coefficient have been found, this indicates that re-reflections should be incorporated into models of wave transmission. Furthermore, re-reflections may also be considered in methods of arterial pulse wave analysis.

A CARDIOVASCULAR SIMULATOR WITH ELASTIC ARTERIAL TREE FOR PULSE WAVE STUDIES

2015 ◽  
Vol 15 (06) ◽  
pp. 1540045 ◽  
Author(s):  
JU-YEON LEE ◽  
MIN JANG ◽  
SIWOO LEE ◽  
HEEJUNG KANG ◽  
SANG-HOON SHIN
Keyword(s):  
Pulse Wave ◽  
Physical Phenomenon ◽  
Ascending Aorta ◽  
Arterial System ◽  
Pressure Waves ◽  
Arterial Tree ◽  
Quantitative Indices ◽  
Cardiovascular Simulator ◽  
Measured Pressure ◽  
Good Agreement

Blood pressure is an important factor in cardiovascular diseases, and it is impossible to precisely reproduce the physical phenomenon of the arteries by using conventional simulators with modeling blood vessels as air-filled chambers. The purpose of this study was to develop a cardiovascular simulator that replicates the human arterial system. The vessel part was manufactured with silicon which has similar stiffness and arterial tree structure. To evaluate the validity of the developed simulator, the pressure and flow were analyzed in the ascending aorta and radial artery. Measured pressure waves and input impedance of the ascending aorta were compared with clinical data using quantitative indices. The generated pulse by the developed simulator showed a good agreement with the physiological characteristics of the arterial system in the human body.

A square-pulse flow method for measuring characteristics of the arterial bed

1976 ◽  
Vol 40 (3) ◽  
pp. 425-433 ◽  
Author(s):  
M. G. Bottomley ◽  
G. W. Mainwood
Keyword(s):  
Arterial Compliance ◽  
Peripheral Resistance ◽  
Mean Value ◽  
Pressure Response ◽  
Arterial System ◽  
Response Curves ◽  
Arterial Tree ◽  
Pulse Flow ◽  
Critical Closing Pressure ◽  
Closing Pressure

A device was designed to provide a “square” pulse of blood flow into the arterial system. Pulses were injected into the carotid artery of the rabbit during transient cardiac arrest. Analysis of pressure response curves generated by the flow provides information as to the state of the arterial tree. With certain assumptions it is possible to estimate from these curves lumped values of peripheral resistance, critical closing pressure, and arterial compliance. In a series of 12 rabbits the mean value of peripheral resistance was found to be 0.21 +/- 0.7 mmHg-ml-1-min and critical closing pressure was estimated to be 23.6 +/- 3.8 mmHg. This method gives two possible values for arterial compliance 0.036 +/- 0.010 and 0.055 +/- 0.010 ml-mm-1 based, respectively, on the rise and decay curves of the pressure response. The theory and limitations of the method are discussed. The use of the method is illustrated in following the response to increased PCO2 and hemorrhage.

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