天麻素对动脉血管顺应性以及血流动力学的影响

本文旨在研究天麻素对动脉血管顺应性和血流动力学等的作用。采用改良风箱模型来计算动脉管的顺应性和血管中血流惯性。在静脉注射天麻素前后，分别记录和计算出狗的血压，心输出量，外周阻力，血流惯性以及中央和外周动脉血管的顺应性。结果表明天麻素具有降低血压和外周务管阻力，增加动脉血管中血流惯性，以及中央和外周动脉血管的顺应性等作用。因此，天麻素是一种有效的能够改善由血管顺应性下降所致的高血压－老年性高血压的中     

Simple and accurate way for estimating total and segmental arterial compliance: The pulse pressure method

We derived and tested a new, simple, and accurate method to estimate the compliance of the entire arterial tree and parts thereof. The method requires the measurements of pressure and flow and is based on fitting the pulse pressure (systolic minus diastolic pressure) predicted by the two-element windkessel model to the measured pulse pressure. We show that the two-element windkessel model accurately describes the modulus of the input impedance at low harmonics (0–4th) of the heart rate so that the gross features of the arterial pressure wave, including pulse pressure, are accounted for. The method was tested using a distributed nonlinear model of the human systemic arterial tree. Pressure and flow were calculated in the ascending aorta, thoracic aorta, common carotid, and iliac artery. In a linear version of the systemic model the estimated compliance was within 1% of the compliance at the first three locations. In the iliac artery an error of 7% was found. In a nonlinear version, we compared the estimates of compliance with the average compliance over the cardiac cycle and the compliance at the mean working pressure. At the first three locations we found the estimated and “actual” compliance to be within 12% of each other. In the iliac artery the error was larger. We also investigated an increase and decrease in heart rate, a decrease in wall elasticity and exercise conditions. In all cases the estimated total arterial compliance was within 10% of mean compliance. Thus, the errors result mainly from the nonlinearity of the arterial system. Segmental compliance can be obtained by subtraction of compliance determined at two locations.     

Fast Estimation of Arterial Vascular Parameters for Transient and Steady Beats with Application to Hemodynamic State under Variant Gravitational Conditions

Numerous parameter estimation techniques exist for characterizing the arterial system using electrical circuit analogs. These techniques are often limited by requiring steady-state beat conditions and can be computationally expensive. Therefore, a new method was developed to estimate arterial parameters during steady and transient beat conditions. A four-element electrical analog circuit was used to model the arterial system. The input impedance equations for this model were derived and reduced to their real and imaginary components. Next, the physiological input impedance was calculated by computing fast Fourier transforms of physiological aortic pressure (AoP) and aortic flow. The approach was to reduce the error between the calculated model impedance and the physiological arterial impedance using a Jacobian matrix technique which iteratively adjusted arterial parameter values. This technique also included algorithms for estimating physiological arterial parameters for nonsteady physiological AoP beats. The method was insensitive to initial parameter estimates and to small errors in the physiological impedance coefficients. When the estimation technique was applied to in vivo data containing steady and transient beats it reliably estimated Windkessel arterial parameters under a wide range of physiological conditions. Further, this method appears to be more computationally efficient compared to time-domain approaches. © 1999 Biomedical Engineering Society. PAC99: 8719Uv, 8710+e, 0230Qy     

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.     

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.     

Pulse Pressure Method and the Area Method for the Estimation of Total Arterial Compliance in Dogs: Sensitivity to Wave Reflection Intensity

We estimated total arterial compliance (C) in eight anesthetized mongrel dogs with (i) the area method (AM), (ii) the pulse pressure method (PPM), and (iii) the stroke volume-to-pulse pressure ratio (SV/PP). Average compliance was C__AM=1.11 ± 0.7 ml mm Hg¹ using AM; C_PPM=0.60 ± 0.31 ml mm Hg_-1 using PPM and C_SV/PP=0.87 ± 0.49 ml mm Hg^-1 using SV/PP. Mean aortic pressure was 64 ± 23 mm Hg. The overall agreement between C_AM and C_PPM was relatively poor (C_AM=0.15+1.61 C_PPM; r²=0.48), with a consistent overestimation of the area method with respect to the pulse pressure method. There was a significant correlation (r= -0.78) between the relative difference between PPM and AM, and the modulus of the first harmonic of the wave reflection coefficient || which was low in our dog population (0.37 ± 0.18). SV/PP overestimated PPM, but both methods were highly correlated (C_SV/PP=0.06+1.60 C_PPM; r²=0.97). C_SV/PP and C_AM were similar only for || > 0.4. The effect of isolated changes of || on PPM, AM, and SV/PP was studied using the linear wave separation technique. The area method appeared very sensitive to the wave reflection intensity. For low reflection coefficients, the diastolic wave profile was flattened and compliance was overestimated. PPM and SV/PP were relatively independent of || and remained even applicable for || = 0. We believe that the pulse pressure method is the most consistent method for the estimation of total arterial compliance in hemodynamic conditions characterized by a low wave reflection intensity. © 1999 Biomedical Engineering Society. PAC99: 8719Uv, 8719Hh     

Correlation Between Negative Near-Wall Shear Stress in Human Aorta and Various Stages of Congestive Heart Failure

The critical effect of advanced congestive heart failure is reduced blood flow in descending aorta resulting from mild to severe reduction in cardiac output, usually accompanying low ejection fraction. In these patients the heart tries to compensate by beating faster, but reduced blood flow combined with increased heart rate can lead to retrograde flow and negative shear stress along the vessel walls during each cardiac cycle. Our studies show that near-wall negative shear stress can result from an entire-retrograde flow at normal heart rates or a Womersley-type phase delayed near-wall retrograde flow at high heart rate and low ejection fraction conditions. In our experiments, a compliant aortic loop with appropriate pressure and flow instrumentation was used, running on either various aqueous glycerin solutions or property filtered, anticoagulated diluted bovine blood. The flow field was mapped using a General Electric Vingmed System 5 platform. The resulting images were analyzed with Caltech's digital ultrasound speckle image velocimetry technique. We showed the occurrence of near-wall retrograde flow under certain aortic flow rates and frequencies, charted via an empirical relationship between Reynolds and Womersley numbers. Also, we demonstrated a strong correlation between retrograde flow level and transition from preliminary to advanced congestive heart failure patients. © 2003 Biomedical Engineering Society. PAC2003: 8719Hh, 8719Rr, 8719Uv, 4380Qf, 8763Df     

On the Estimation of Total Arterial Compliance from Aortic Pulse Wave Velocity

Total arterial compliance (C _T) is a main determinant of cardiac afterload, left ventricular function and arterio-ventricular coupling. C _T is physiologically more relevant than regional aortic stiffness. However, direct, in vivo, non-invasive, measurement of C _T is not feasible. Several methods for indirect C _T estimation require simultaneous recording of aortic flow and pressure waves, limiting C _T assessment in clinical practice. In contrast, aortic pulse wave velocity (aPWV) measurement, which is considered as the ??gold standard?? method to assess arterial stiffness, is noninvasive and relatively easy. Our aim was to establish the relation between aPWV and C _T. In total, 1000 different hemodynamic cases were simulated, by altering heart rate, compliance, resistance and geometry using an accurate, distributed, nonlinear, one-dimensional model of the arterial tree. Based on Bramwell?CHill theory, the formula $ C_{\text{T}} = k \cdot {\text{aPWV}}^{ - 2} $ was found to accurately estimate C _T from aPWV. Coefficient k was determined both analytically and by fitting C _T vs. aPWV data. C _T estimation may provide an additional tool for cardiovascular risk (CV) assessment and better management of CV diseases. C _T could have greater impact in assessing elderly population or subjects with elevated arterial stiffness, where aPWV seem to have limited prognostic value. Further clinical studies should be performed to validate the formula in vivo.     

A Frequency Domain Approach to Nonlinear and Structure Identification for Long Memory Systems: Application to Lung Mechanics

From the input–output point of view, many nonlinear biological systems display long memory characteristics which can become a critical issue using nonparametric time-domain kernel identification due to inevitable truncation of memory length. To avoid these limitations, we present an alternative approach in the frequency domain with application to lung mechanics. Generally, if the system is excited with a periodic wave form, the response will approach a steady state which dominates the long memory transients. Thus, we hypothesized that the kernels at discrete frequencies will not be significantly affected by memory truncation. To test this, we extended the frequency kernel analysis of Victor and Shapley (Biophys. J. 29:459–484, 1980) to a nonwhite input spectrum and developed a new structure test in the frequency domain to differentiate between Wiener and Hammerstein models. These techniques were applied to measured pressure–flow data of isolated lung lobes. The results showed that (1) the important nonlinearities in the pressure–flow relation are of second order, (2) the frequency kernels of the lobes were similar for flat and ventilatory-like input spectra, and (3) the structure test strongly suggested that the pressure–flow relationship during tidal-like excursions is consistent with a Wiener structure. © 1999 Biomedical Engineering Society. PAC99: 8719Uv, 8719Rr     

Intramyocardial Influences on Blood Flow Distributions in the Myocardial Wall

Flow velocity wave forms of coronary arterial inflow and venous outflow of myocardium are influenced by cardiac contraction and relaxation: arterial flow is exclusively diastolic; venous outflow is systolic. We first discuss the intramyocardial microvascular flow dynamics, then present some results of visualization of transmural microvessels by our needle-probe charge coupled device (CCD) microscope, along with an interpretation of the arteriolar and venular hemodynamics through a cardiac cycle. After describing a hierarchical system of coronary microvessels (small artery, arteriole, and capillary), we emphasize the importance of spatial heterogeneity of blood supply to myocardium with reference to a minimal vascular control unit (400 m). An understanding of mechanoenergetic interaction is fundamentally important to an understanding of intramyocardial coronary circulation, and the Physiome Project will provide powerful tools for understanding the integrated role of the intramyocardial microcirculation system. © 2000 Biomedical Engineering Society. PAC00: 8719Hh, 8719Ff, 8719Tt     

Non‐invasive assessment of cardiac output during exercise in healthy young humans: comparison between Modelflow method and Doppler echocardiography method

Aims: The Modelflow method can estimate cardiac output from arterial blood pressure waveforms using a three‐element model of aortic input impedance (aortic characteristic impedance, arterial compliance, and systemic vascular resistance). We tested the reliability of a non‐invasive cardiac output estimation during submaximal exercise using the Modelflow method from finger arterial pressure waveforms collected by Portapres in healthy young humans. Methods: The Doppler echocardiography method was used as a reference method. Sixteen healthy young subjects (nine males and seven females) performed a multi‐stage cycle ergometer exercise at an intensity corresponding to 70, 90, 110 and 130% of their individual ventilatory threshold for 2 min each. The simultaneous estimation of cardiac output (15 s averaged data) using the Modelflow and Doppler echocardiography methods was performed at rest and during exercise. Results and Conclusion: The Modelflow‐estimated cardiac output correlated significantly with the simultaneous estimates by the Doppler method in all subjects (r = 0.87, P < 0.0001) and the SE of estimation was 1.93 L min^?1. Correlation coefficients in each subject ranged from 0.91 to 0.98. Although the Modelflow method overestimated cardiac output, the errors between two estimates were not significantly different among the exercise levels. These results suggest that the Modelflow method using Portapres could provide a reliable estimation of the relative change in cardiac output non‐invasively and continuously during submaximal exercise in healthy young humans, at least in terms of the relative changes in cardiac output.     

The Influence of Pulmonary Blood Flow Rate on Vascular Input Impedance and Hydraulic Power in the Sympathetically and Noradrenaline Stimulated Cat Lung

This study was designed to evaluate the influence of sympathetic nerve stimulation (NS) and α-adrenergic receptor stimulation (αS) on the pulmonary vascular input impedance and hydraulic power output of the right heart during variations of cardiac output (CO). An open chest cat preparation was used and pulsatile pressure and flow in the pulmonary artery were measured by high frequency response transducers. Calculations showed that vascular resistance (VR) was inversely dependent on CO, hut input impedance of the unstimulated lung was not influenced by CO variations. NS or αS increased VR and input impedance significantly, and the relation pulsatile hydraulic power/total hydraulic power (W_p/W_t) increased 40%, indicating that such stimulation has larger relative influence on impedance than on resistance. The reduction of arterial compliance during NS (maximal stimulus) was calculated to be 60%, independent of CO. Input impedance during NS or αS was reduced by CO elevations, probably because the concomitant distension of the arterial bed reduced arterial resistance and inertance. The ratio W_p/CO, which expresses the fraction of pulsatile hydraulic power lost per ml mean arterial flow, was found to be flow dependent both in control and stimulated conditions: W_p/CO was positively correlated to CO in control condition and weakly negatively correlated to CO during stimulation. At high CO the arterial vessels could he stimulated and stiffened without much extra load on the right heart.     

Model-based assessment of cardiovascular health from noninvasive measurements

Cardiovascular health is currently assessed through a variety of hemodynamic parameters, many of which can only be determined by invasive measurement often requiring hospitalization. A noninvasive method of evaluating several of these parameters such as systemic vascular resistance (SVR), maximum left ventricular elasticity E__LV end diastolic volume V _ED and cardiac output, is presented. The method has three elements: (1) a distributed model of the human cardiovascular system (Ozawa [et_al.], Ann. Biomed. Eng. 29:284–297, 2001) to generate a solution library that spans the anticipated range of parameter values, (2) a method for establishing the multidimensional relationship between features computed from the arterial blood pressure and/or flow traces (e.g., mean arterial pressure, pulse amplitude, mean flow velocity) and the critical hemodynamic parameters, and (3) a parameter estimation method that yields the best fit between measured and computed data. Sensitivity analyses were used to determine the critical parameters, and the influence of fixed model parameters. Using computer-generated brachial pressure and velocity profiles (which can be measured noninvasively), the error associated with this method was found to be less than 3% for SVR, and less than 10% for E _LV and V _ED Simulations were also performed to test the ability of the approach to predict changes in SVR and E _LV from an initial base line state. © 2002 Biomedical Engineering Society. PAC2002: 8719Hh, 8719Uv     

Extracellular Measurement of Anisotropic Bidomain Myocardial Conductivities. I. Theoretical Analysis

The passive electrical properties of cardiac tissue, such as the intracellular and interstitial conductivities along the longitudinal and transverse axes, have not been often measured because intracellular electrodes are usually needed for these measurements. In this paper, we present a theoretical analysis of two myocardial models developed to estimate these properties by analyzing potentials recorded with a pair of extracellular electrodes while injecting alternating current between another pair of electrodes. First, the cardiac tissue is represented by a standard bidomain model which includes a membrane capacitance; second, this model is modified by adding an intracellular capacitance representing the intercalated disks. Numerical solutions are computed with a fast Fourier transform algorithm without constraining the anisotropy ratios of the interstitial and intracellular domains. We systematically investigate the effects of changes in the bidomain parameters on the voltage-to-current ratio curves. We also demonstrate how the bidomain parameters can be theoretically estimated by fitting, with a modified Shor's r algorithm, the simulated potentials along the longitudinal and transverse axes for different frequencies between 10 and 10000 Hz. An important finding is that the interelectrode distance must be similar to the myocardial space constant so as to obtain frequency dependent measurements. © 2001 Biomedical Engineering Society. PAC01: 8719Nn, 8719Hh, 8716Uv, 0230Uu, 8716Ac     

Spectral indices of human cerebral blood flow control: responses to augmented blood pressure oscillations

We set out to fully examine the frequency domain relationship between arterial pressure and cerebral blood flow. Oscillatory lower body negative pressure (OLBNP) was used to create consistent blood pressure oscillations of varying frequency and amplitude to rigorously test for a frequency- and/or amplitude-dependent relationship between arterial pressure and cerebral flow. We also examined the predictions from OLBNP data for the cerebral flow response to the stepwise drop in pressure subsequent to deflation of ischaemic thigh cuffs. We measured spectral powers, cross-spectral coherence, and transfer function gains and phases in arterial pressure and cerebral flow during three amplitudes (0, 20, and 40 mmHg) and three frequencies (0.10, 0.05, and 0.03 Hz) of OLBNP in nine healthy young volunteers. Pressure fluctuations were directly related to OLBNP amplitude and inversely to OLBNP frequency. Although cerebral flow oscillations were increased, they did not demonstrate the same frequency dependence seen in pressure oscillations. The overall pattern of the pressure–flow relation was of decreasing coherence and gain and increasing phase with decreasing frequency, characteristic of a high-pass filter. Coherence between pressure and flow was increased at all frequencies by OLBNP, but was still significantly lower at frequencies below 0.07 Hz despite the augmented pressure input. In addition, predictions of thigh cuff data from spectral estimates were extremely inconsistent and highly variable, suggesting that cerebral autoregulation is a frequency-dependent mechanism that may not be fully characterized by linear methods.     

Arterial Wall Adaptation under Elevated Longitudinal Stretch in Organ Culture

Arteries in vivo are subjected to large longitudinal stretch which may change significantly due to vascular disease and surgery. However, little is known about the effect of longitudinal stretch on vascular function and wall remodeling, although the effects of tensile and shear stress from blood pressure and flow have been well documented. To study the effect of longitudinal stretch on vascular function and wall remodeling, porcine carotid arteries were longitudinally stretched 20% more than in vivo for 5 days while being maintained in an ex vivo organ culture system under conditions of pulsatile flow at physiologic pressure. Vessel viability was demonstrated by strong vasomotor responses to norepinephrine (NE, 10^-6M), carbachol (10^-6M), and sodium nitroprusside (10^-5M), as well as by dense staining for mitochondrial activity and a low occurrence of cell necrosis. Cell proliferation was examined by incorporation of bromodeoxyuridine (BrdU). Results showed that arteries maintain normal structure and viability after 5 days in organ culture. Both the stretched and control arteries demonstrated significant contractile responses. For example, both stretched and control arteries showed approximately 10% diameter contraction in response to NE. Stretched arteries contained 8% BrdU-positive cells compared to 5% in controls (p < 0.05). These results indicate that longitudinal stretch promotes cell proliferation in arteries while maintaining arterial function. © 2003 Biomedical Engineering Society. PAC2003: 8719Rr, 8717Ee, 8719Uv     

Role of the mechanical properties of tracheobronchial airways in determining the respiratory resistance time course

A physiologically based simulation model of breathing mechanics was considered in an attempt to interpret and explain the time course of input respiratory resistance during the breathing cycle, observed in recent studies on ventilated patients. The model assumes a flow-dependent Rohrer resistance for the upper extrathoracic airways and volume-dependent resistance and elastance for the intermediate airways. A volume-dependent resistance describes the dissipative pressure loss in the lower airways, and two constant elastances represent lung and chest wall elasticity. Simulated mouth flow and pressure signals obtained in a variety of well-controlled conditions were used to analyze total respiratory resistance and elastance estimated by an on-line algorithm based on a time-varying parameter model. These estimates were compared with those provided by classical estimation algorithms based on time-invariant models with two, three, and four parameters. The results show that the four-parameter model is difficult to identify, while the three-parameter one offers no substantial advantage for estimating input resistance with respect to the more simple two-parameter model. In contrast, the time-varying approach provides good on-line estimates of the simulated end-expiration and end-inspiration resistances. These values provide further information of potential clinical utility, with respect to time-invariant models. For example, the results show that the difference between the end-expiration and end-inspiration resistance increases when obstructions shift from the upper to the lower airways. The similarity of the results obtained with measured and simulated data indicates that, in spite of its simplicity, the simulation model describes important physiological mechanisms underlying changes in respiratory input resistance, specifically the mechanical properties of intermediate airways. © 2001 Biomedical Engineering Society. PAC01: 8719Uv, 8719Rr     

Influence of central and peripheral changes on the hydraulic input impedance of the systemic arterial tree

The input impedance of the systemic arterial tree of the dog has been computed by Fourier analysis. It was shown that a distance between pressure and flow transducers of less than 2 cm results in appreciable errors which manifest themselves mainly in the phase of the input impedance. The input impedance for controls, occlusions at various locations in the aorta, and an increase and decrease of peripheral resistance were studied. For the same experiments, the total arterial compliance was calculated from the peripheral resistance of the diastolic aortic-pressure curve. The characterstic impedance of the ascending aorta was also estimated. The impedance in the control situation may be modelled by means of a 3-element Windkessel consisting of a peripheral resistance and (total) arterial compliance, together with a resistance equal to the characteristic impedance of the aorta. The occlusions of the aorta show that blockage at (and beyond) the trifurcation do not result in a detectable change in input impedance, except for a slight increase of the peripheral resistance. The more proximal an aortic occlusion, the more effect it has on the pattern of the input impedance. When the aorta is occluded at the diphragm, or higher, the single (uniform) tube appears to be a much better model than the Windkessel. Occlusion of one or both carotid arteries increases the mean pressure; consequently not only the peripheral resistance increases but also the total arterial compliance decreases. The Windkessel with increased peripheral resitance and decreased compliance is again a good model. After a sudden release of occlusion of the aorta, the arterial system has a low peripheral resistance and may also be modelled by the Windkessel.     

Arterial pulsatility improvement in a feedback-controlled continuous flow left ventricular assist device: An ex-vivo experimental study

Continuous flow left ventricular assist devices (CF-LVADs) reduce arterial pulsatility, which may cause long-term complications in the cardiovascular system. The aim of this study is to improve the pulsatility by driving a CF-LVAD at a varying speed, synchronous with the cardiac cycle in an ex-vivo experiment. A Micromed DeBakey pump was used as CF-LVAD. The heart was paced at 140 bpm to obtain a constant cardiac cycle for each heartbeat. First, the CF-LVAD was operated at a constant speed. At varying-speed CF-LVAD assistance, the pump was driven such that the same mean pump output was generated. For synchronization purposes, an algorithm was developed to trigger the CF-LVAD each heartbeat. The pump flow rate was selected as the control variable and a reference model was used for regulating the CF-LVAD speed. Continuous and varying-speed CF-LVAD assistance provided the same mean arterial pressure and flow rate, while the index of pulsatility doubled in both arterial pressure and pump flow rate signals under pulsatile pump speed support. This study shows the possibility of improving the pulsatility in CF-LVAD support by regulating pump speed over a cardiac cycle without compromising the overall level of support.     

Staged Growth of Optimized Arterial Model Trees

There is a marked difference in the structure of the arterial tree between epi- and endocardial layers of the human heart. To model these structural variations, we developed an extension to the computational method of constrained constructive optimization (CCO). Within the framework of CCO, a model tree is represented as a dichotomously branching network of straight cylindrical tubes, with flow conditions governed by Poiseuille's law. The tree is grown by successively adding new terminal segments from randomly selected points within the perfusion volume while optimizing the geometric location and topological site of each new connection with respect to minimum intravascular volume. The proposed method of staged growth guides the generation of new terminal sites by means of an additional time-dependent boundary condition, thereby inducing a sequence of domains of vascular growth within the given perfusion volume. Model trees generated in this way are very similar to reality in their visual appearance and predict diameter ratios of parent and daughter segments, the distribution of symmetry, the transmural distribution of flow, the volume of large arteries, as well as the ratio of small arterial volume in subendocardial and subepicardial layers in good agreement with experimental data. From this study we conclude that the method of CCO combined with staged growth reproduces many characteristics of the different arterial branching patterns in the subendocardium and the subepicardium, which could not be obtained by applying the principle of minimum volume alone. © 2000 Biomedical Engineering Society. PAC00: 8719Uv, 8719Hh, 4760+i