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.     

Evaluation of blood flow velocity waveform in common carotid artery using multi-branched arterial segment model of human arteries

Arteriosclerosis is considered to be a major cause of cardiovascular diseases, which account for approximately 30% of the causes of death in the world. We have recently demonstrated a strong correlation between arteriosclerosis (arterial elasticity) and two characteristics: maximum systolic velocity (S1) and systolic second peak velocity (S2) of the common carotid artery flow velocity waveform (CCFVW). The CCFVW can be measured by using a small portable measuring device. However, there is currently no theoretical evidence supporting the causes of the relation between CCFVW and arterial elasticity, or the origin of the CCFVW characteristics. In this study, the arterial blood flow was simulated using a one-dimensional systemic arterial segments model of human artery in order to conduct a qualitative evaluation of the relationship between arterial elasticity and the characteristics of CCFVW. The simulation was carried out based on the discretized segments with the physical properties of a viscoelastic tube (the cross-sectional area at the proximal and terminal ends, the length, and the compliance per unit area of the tube (C_S)). The findings obtained through this study revealed that the simulated CCFVW had shape similar characteristics to that of the measured CCFVW. Moreover, when the compliance C_S of the model was decreased, the first peak of the simulated-CCFVW decreased and the second peak increased. Further, by separating the anterograde pulse wave and the reflected pulse wave, which form the CCFVW, we found that the decrease in the first peak of the simulated CCFVW was due to the arrival of a reflected pulse wave from the head after the common carotid artery toward the arrival of a anterograde pulse wave ejected directly from the heart and that the increase in the second peak resulted from the arrival of the peak of the reflected pulse wave from the thoracic aorta. These results establish that the CCFVW characteristics contribute to the assessment of arterial elasticity.     

A coupled hydrodynamic model of the cardiovascular and cerebrospinal fluid system

Coupling of the cardiovascular and cerebrospinal fluid (CSF) system is considered to be important to understand the pathophysiology of cerebrovascular and craniospinal disease and intrathecal drug delivery. A coupled cardiovascular and CSF system model was designed to examine the relation of spinal cord (SC) blood flow (SCBF) and CSF pulsations along the spinal subarachnoid space (SSS). A one-dimensional (1-D) cardiovascular tree model was constructed including a simplified SC arterial network. Connection between the cardiovascular and CSF system was accomplished by a transfer function based on in vivo measurements of CSF and cerebral blood flow. A 1-D tube model of the SSS was constructed based on in vivo measurements in the literature. Pressure and flow throughout the cardiovascular and CSF system were determined for different values of craniospinal compliance. SCBF results indicated that the cervical, thoracic, and lumbar SC each had a signature waveform shape. The cerebral blood flow to CSF transfer function reproduced an in vivo-like CSF flow waveform. The 1-D tube model of the SSS resulted in a distribution of CSF pressure and flow and a wave speed that were similar to those in vivo. The SCBF to CSF pulse delay was found to vary a great degree along the spine depending on craniospinal compliance and vascular anatomy. The properties and anatomy of the SC arterial network and SSS were found to have an important impact on pressure and flow and perivascular fluid movement to the SC. Overall, the coupled model provides predictions about the flow and pressure environment in the SC and SSS. More detailed measurements are needed to fully validate the model.     

A framework for incorporating 3D hyperelastic vascular wall models in 1D blood flow simulations

We present a novel framework for investigating the role of vascular structure on arterial haemodynamics in large vessels, with a special focus on the human common carotid artery (CCA). The analysis is carried out by adopting a three-dimensional (3D) derived, fibre-reinforced, hyperelastic structural model, which is coupled with an axisymmetric, reduced order model describing blood flow. The vessel transmural pressure and lumen area are related via a Holzapfel–Ogden type of law, and the residual stresses along the thickness and length of the vessel are also accounted for. After a structural characterization of the adopted hyperelastic model, we investigate the link underlying the vascular wall response and blood-flow dynamics by comparing the proposed framework results against a popular tube law. The comparison shows that the behaviour of the model can be captured by the simpler linear surrogate only if a representative value of compliance is applied. Sobol’s multi-variable sensitivity analysis is then carried out in order to identify the extent to which the structural parameters have an impact on the CCA haemodynamics. In this case, the local pulse wave velocity (PWV) is used as index for representing the arterial transmission capacity of blood pressure waveforms. The sensitivity analysis suggests that some geometrical factors, such as the stress-free inner radius and opening angle, play a major role on the system’s haemodynamics. Subsequently, we quantified the differences in haemodynamic variables obtained from different virtual CCAs, tube laws and flow conditions. Although each artery presents a distinct vascular response, the differences obtained across different flow regimes are not significant. As expected, the linear tube law is unable to accurately capture all the haemodynamic features characterizing the current model. The findings from the sensitivity analysis are further confirmed by investigating the axial stretching effect on the CCA fluid dynamics. This factor does not seem to alter the pressure and flow waveforms. On the contrary, it is shown that, for an axially stretched vessel, the vascular wall exhibits an attenuation in absolute distension and an increase in circumferential stress, corroborating the findings of previous studies. This analysis shows that the new model offers a good balance between computational complexity and physics captured, making it an ideal framework for studies aiming to investigate the profound link between vascular mechanobiology and blood flow.

     

Exercise reduces arterial pressure augmentation through vasodilation of muscular arteries in humans

Exercise markedly influences pulse wave morphology, but the mechanism is unknown. We investigated whether effects of exercise on the arterial pulse result from alterations in stroke volume or pulse wave velocity (PWV)/large artery stiffness or reduction of pressure wave reflection. Healthy subjects (n = 25) performed bicycle ergometry. with workload increasing from 25 to 150 W for 12 min. Digital arterial pressure waveforms were recorded using a servo-controlled finger cuff. Radial arterial pressure waveforms and carotid-femoral PWV were determined by applanation tonometry. Stroke volume was measured by echocardiography, and brachial and femoral artery blood flows and diameters were measured by ultrasound. Digital waveforms were recorded continuously. Other measurements were made before and after exercise. Exercise markedly reduced late systolic and diastolic augmentation of the peripheral pressure pulse. At 15 min into recovery, stroke volume and PWV were similar to baseline values, but changes in pulse wave morphology persisted. Late systolic augmentation index (radial pulse) was reduced from 54 +/- 3.9% at baseline to 42 +/- 3.7% (P < 0.01), and diastolic augmentation index (radial pulse) was reduced from 37 +/- 1.8% to 25 +/- 2.9% (P < 0.001). These changes were accompanied by an increase in femoral blood flow (from 409 +/- 44 to 773 +/- 48 ml/min, P < 0.05) and an increase in femoral artery diameter (from 8.2 +/- 0.4 to 8.6 +/- 0.4 mm, P < 0.05). In conclusion, exercise dilates muscular arteries and reduces arterial pressure augmentation, an effect that will enhance ventricular-vascular coupling and reduce load on the left ventricle.     

Effect of Isovolemic,Isothermic Hemodialysis on Cerebral Perfusion and Vascular Stiffness Using Contrast Computed Tomography and Pulse Wave Velocity

Background

Patients undergoing hemodialysis treatment have a six-fold increased risk for stroke relative to the general population. However, the effect of hemodialysis on cerebral blood flow is poorly studied and confounding factors like blood pressure and ultrafiltration as well as temperature changes have rarely been accounted for. The aim of our study was to use state-of-the-art technology to evaluate the effect of a single dialysis session on cerebral perfusion as well as on vascular stiffness.

Methods

Chronic hemodialysis patients (7 male/3 female, mean age 58 years) were recruited. Cerebral blood flow and arterial pulse wave velocity were measured before and immediately after a hemodialysis session. To exclude effects of volume changes we kept ultrafiltration to a minimum, allowing no change in body weight. Isothermic conditions were maintained by using the GENIUS single-pass batch-dialysis system with a high-flux polysulfone dialyser. Cerebral blood flow was measured by contrast-enhanced computed tomography. Pulse wave velocity was measured using the SphygmoCor (AtCor Medical, USA) device by a single operator.

Results

This study shows for the first time that isovolemic, isothermic hemodialysis neither affected blood pressure or heart rate, nor total or regional cerebral perfusion. There was also no change in pulse wave velocity.

Conclusions

Mechanisms other than the dialysis procedure itself might be causative for the high incidence of ischemic strokes in this patient population. Moreover, the sole removal of uremic toxins does not lead to short-term effects on vascular stiffness, underlying the importance of volume control in this patient population.     

Intravascular pressure and diameter profile of the utero-ovarian resistance artery network: estrous cycle-dependent modulation of resistance artery tone

Blood flow to the ovary varies dramatically in both magnitude and distribution throughout the estrous cycle to meet the hormonal and metabolic demands of the ovarian parenchyma as it cyclically develops and regresses. Several vascular components appear to be critical to vascular regulation of the ovary. As a first step in resolving the role of the resistance arteries and their paired veins in regulating ovarian blood flow and transvascular exchange, we characterized the architecture and intravascular pressure profile of the utero-ovarian resistance artery network in an in vivo preparation of the ovary of the anesthetized Golden hamster. We also investigated estrous cycle-dependent changes in resistance artery tone. The right ovary and the cranial aspect of the uterus in 26 female hamsters were exposed for microcirculatory observations. Estrous-cycle phase was determined in each animal before experimentation. The utero-ovarian vascular architecture was determined and resistance artery diameters were measured in each animal by video microscopy. Servo-null intravascular pressure measurements were made throughout the uteroovarian arterial network in 11 of the animals. Architectural data showed a complex anastomotic network jointly supplying the uterus and ovary. Resistance arteries showed a high degree of coiling and close apposition to veins, maximizing countercurrent-exchange capabilities. Arterial pressure dropped below 60% of systemic arterial pressure before the arteries entered the ovary. Both the ovarian artery and the uterine artery, which jointly feed the ovary, showed cycle day-dependent changes in diameter. Arterial diameters were smallest on the day following ovulation, during the brief luteal phase of the hamster. The data show that resistance arteries comprise a critical part of a complex network designed for intimate local communication and control and suggest that these arteries may play an important role in regulating ovarian blood flow in an estrous cycle-specific manner.     

Ventricular-arterial coupling in a rat model of reduced arterial compliance provoked by hypervitaminosis D and nicotine

The vitamin D(3) and nicotine (VDN) model is one of isolated systolic hypertension (ISH) in which arterial calcification raises arterial stiffness and vascular impedance. The effects of VDN treatment on arterial and cardiac hemodynamics have been investigated; however, a complete analysis of ventricular-arterial interaction is lacking. Wistar rats were treated with VDN (VDN group, n = 9), and a control group (n = 10) was included without the VDN. At week 8, invasive indexes of cardiac function were obtained using a conductance catheter. Simultaneously, aortic pressure and flow were measured to derive vascular impedance and characterize ventricular-vascular interaction. VDN caused significant increases in systolic (138 +/- 6 vs. 116 +/- 13 mmHg, P < 0.01) and pulse (42 +/- 10 vs. 26 +/- 4 mmHg, P < 0.01) pressures with respect to control. Total arterial compliance decreased (0.12 +/- 0.08 vs. 0.21 +/- 0.04 ml/mmHg in control, P < 0.05), and pulse wave velocity increased significantly (8.8 +/- 2.5 vs. 5.1 +/- 2.0 m/s in control, P < 0.05). The arterial elastance and end-systolic elastance rose significantly in the VDN group (P < 0.05). Wave reflection was augmented in the VDN group, as reflected by the increase in the wave reflection coefficient (0.63 +/- 0.06 vs. 0.52 +/- 0.05 in control, P < 0.05) and the amplitude of the reflected pressure wave (13.3 +/- 3.1 vs. 8.4 +/- 1.0 mmHg in control, P < 0.05). We studied ventricular-arterial coupling in a VDN-induced rat model of reduced arterial compliance. The VDN treatment led to development of ISH and provoked alterations in cardiac function, arterial impedance, arterial function, and ventricular-arterial interaction, which in many aspects are similar to effects of an aged and stiffened arterial tree.     

Inlet boundary conditions for blood flow simulations in truncated arterial networks

In the context of patient-specific cardiovascular applications, hemodynamics models (going from 3D to 0D) are often limited to a part of the arterial tree. This restriction implies the set up of artificial interfaces with the remaining parts of the cardiovascular system. In particular, the inlet boundary condition is crucial: it supplies the impulsion to the system and receives the reflected backward waves created by the distal network. Some aspects of this boundary condition need to be properly defined such as the treatment of backward waves (reflected or absorbed) and the value of the imposed hemodynamic wave (total or forward component). Most authors prescribe as inlet boundary condition (BC) the total measured variable (pressure, velocity or flow rate) in a reflective way. We show that with this type of inlet boundary condition, the model does not produce physiological waveforms. We suggest instead to prescribe only the forward component of the prescribed variable in an absorbing way. In this way, the computed reflected waves superpose with the prescribed forward waves to produce the total wave at the inlet. In this work, different inlet boundary conditions are implemented and compared for a 1D blood flow model. We test our boundary conditions on a truncated arterial model presented in the literature as well as on a patient-specific lower-limb model of a femoral bypass. We show that with this new boundary condition, a much better fitting is observed on the shape and intensity of the simulated pressure and velocity waves.     

The Effects of Space and Terrestrial Weather Factors on Arterial Stiffness and Endothelial Function in Humans

A differential evolution algorithm was used to detect the biotropic influence of geomagnetic activity on several parameters of human vascular tone. Studies of the characteristics of vascular tone in healthy volunteers showed that arterial stiffness and endothelial function, as well as blood pressure and heart rate, depend on the geomagnetic and, in most cases, weather conditions. The pulse wave velocity (PWV) was measured to characterize the arterial stiffness and was found to be the most sensitive to the effects of space weather parameters. The strength of the effect of geomagnetic activity was for the first time observed to depend on the configuration of terrestrial weather parameters. A linear correlation between the K index of geomagnetic activity and PWV was estimated at r =–0.44 (p = 0.0003), although the relationship was detectable exclusively in the case of certain terrestrial weather parameters. Endothelial dysfunction and the pulse-rate response to variations in geomagnetic activity implicated nitrogen monoxide in body adaptation to variations in geomagnetic activity.

     

Computational model for simulation of vascular adaptation following vascular access surgery in haemodialysis patients

An important number of surgical procedures for creation of vascular access (VA) in haemodialysis patients still results in non-adequate increase in blood flow (non-maturation). The rise in blood flow in arteriovenous shunts depends on vascular remodelling. Computational tools to predict the outcome of VA surgery would be important in this clinical context. The aim of our investigation was then to develop a 0D/1D computational model of arm vasculature able to simulate vessel wall remodelling and related changes in blood flow. We assumed that blood vessel remodelling is driven by peak wall shear stress. The model was calibrated with previously reported values of radial artery diameter and blood flow after end-to-end distal fistula creation. Good agreement was obtained between predicted changes in VA flow and in arterial diameter after surgery and corresponding measured values. The use of this computational model may allow accurate vascular surgery planning and ameliorate VA surgery outcomes.     

A novel,FFT-based one-dimensional blood flow solution method for arterial network

In the present work, we propose an FFT-based method for solving blood flow equations in an arterial network with variable properties and geometrical changes. An essential advantage of this approach is in correctly accounting for the vessel skin friction through the use of Womersley solution. To incorporate nonlinear effects, a novel approximation method is proposed to enable calculation of nonlinear corrections. Unlike similar methods available in the literature, the set of algebraic equations required for every harmonic is constructed automatically. The result is a generalized, robust and fast method to accurately capture the increasing pulse wave velocity downstream as well as steepening of the pulse front. The proposed method is shown to be appropriate for incorporating correct convection and diffusion coefficients. We show that the proposed method is fast and accurate and it can be an effective tool for 1D modelling of blood flow in human arterial networks.

     

Tuning of pulmonary arterial circulation evidenced by MR phase mapping in healthy volunteers.

Magnetic resonance (MR) phase mapping was used to noninvasively assess both blood flow and cross-sectional area (CSA) in the main pulmonary artery (MPA) of 12 healthy volunteers. Flow and CSA patterns exhibited two positive peaks: high systolic and small diastolic. This finding can be explained using a simple "distributed" theoretical model that takes into account the role of a reflected pressure wave from pulmonary vascular impedance in generating a diastolic flow. The mean reflection coefficient of pressure wave, MPA input impedance, and pulmonary vascular impedance were assessed. We verified, in this series, that pressure wave velocity appears to be age-dependent. MR phase mapping has been used to observe the tuning (resonance) of the right cardiovascular system at rest under physiological conditions. MR phase mapping could be used to assess pathological modifications of the tuning that occurs in cases of pulmonary arterial hypertension.     

Numerical assessment of time-domain methods for the estimation of local arterial pulse wave speed

A local estimation of pulse wave speed c, an important predictor of cardiovascular events, can be obtained at arterial locations where simultaneous measurements of blood pressure (P) and velocity (U), arterial diameter (D) and U, flow rate (Q) and cross-sectional area (A), or P and D are available, using the PU-loop, sum-of-squares (∑(2)), lnDU-loop, QA-loop or new D(2)P-loop methods. Here, these methods were applied to estimate c from numerically generated P, U, D, Q and A waveforms using a visco-elastic one-dimensional model of the 55 larger human systemic arteries in normal conditions. Theoretical c were calculated from the parameters of the model. Estimates of c given by the loop methods were closer to theoretical values and more uniform within each arterial segment than those obtained using the ∑(2). The smaller differences between estimates and theoretical values were obtained using the D(2)P-loop method, with root-mean-square errors (RMSE) smaller than 0.18 ms(-1), followed by averaging the two c given by the PU- and lnDU-loops (RMSE <2.99 ms(-1)). In general, the errors of the PU-, lnDU- and QA-loops decreased at locations where visco-elastic effects were small and nearby junctions were well-matched for forward-travelling waves. The ∑(2) performed better at proximal locations.     

Comparative study of viscoelastic arterial wall models in nonlinear one-dimensional finite element simulations of blood flow

It is well known that blood vessels exhibit viscoelastic properties, which are modeled in the literature with different mathematical forms and experimental bases. The wide range of existing viscoelastic wall models may produce significantly different blood flow, pressure, and vessel deformation solutions in cardiovascular simulations. In this paper, we present a novel comparative study of two different viscoelastic wall models in nonlinear one-dimensional (1D) simulations of blood flow. The viscoelastic models are from papers by Holenstein et al. in 1980 (model V1) and Valdez-Jasso et al. in 2009 (model V2). The static elastic or zero-frequency responses of both models are chosen to be identical. The nonlinear 1D blood flow equations incorporating wall viscoelasticity are solved using a space-time finite element method and the implementation is verified with the Method of Manufactured Solutions. Simulation results using models V1, V2 and the common static elastic model are compared in three application examples: (i) wave propagation study in an idealized vessel with reflection-free outflow boundary condition; (ii) carotid artery model with nonperiodic boundary conditions; and (iii) subject-specific abdominal aorta model under rest and simulated lower limb exercise conditions. In the wave propagation study the damping and wave speed were largest for model V2 and lowest for the elastic model. In the carotid and abdominal aorta studies the most significant differences between wall models were observed in the hysteresis (pressure-area) loops, which were larger for V2 than V1, indicating that V2 is a more dissipative model. The cross-sectional area oscillations over the cardiac cycle were smaller for the viscoelastic models compared to the elastic model. In the abdominal aorta study, differences between constitutive models were more pronounced under exercise conditions than at rest. Inlet pressure pulse for model V1 was larger than the pulse for V2 and the elastic model in the exercise case. In this paper, we have successfully implemented and verified two viscoelastic wall models in a nonlinear 1D finite element blood flow solver and analyzed differences between these models in various idealized and physiological simulations, including exercise. The computational model of blood flow presented here can be utilized in further studies of the cardiovascular system incorporating viscoelastic wall properties.     

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

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

Aortic and Carotid Arterial Stiffness and Epigenetic Regulator Gene Expression Changes Precede Blood Pressure Rise in Stroke-Prone Dahl Salt-Sensitive Hypertensive Rats

Multiple clinical studies show that arterial stiffness, measured as pulse wave velocity (PWV), precedes hypertension and is an independent predictor of hypertension end organ diseases including stroke, cardiovascular disease and chronic kidney disease. Risk factor studies for arterial stiffness implicate age, hypertension and sodium. However, causal mechanisms linking risk factor to arterial stiffness remain to be elucidated. Here, we studied the causal relationship of arterial stiffness and hypertension in the Na-induced, stroke-prone Dahl salt-sensitive (S) hypertensive rat model, and analyzed putative molecular mechanisms. Stroke-prone and non-stroke-prone male and female rats were studied at 3- and 6-weeks of age for arterial stiffness (PWV, strain), blood pressure, vessel wall histology, and gene expression changes. Studies showed that increased left carotid and aortic arterial stiffness preceded hypertension, pulse pressure widening, and structural wall changes at the 6-week time-point. Instead, differential gene induction was detected implicating molecular-functional changes in extracellular matrix (ECM) structural constituents, modifiers, cell adhesion, and matricellular proteins, as well as in endothelial function, apoptosis balance, and epigenetic regulators. Immunostaining testing histone modifiers Ep300, HDAC3, and PRMT5 levels confirmed carotid artery-upregulation in all three layers: endothelial, smooth muscle and adventitial cells. Our study recapitulates observations in humans that given salt-sensitivity, increased Na-intake induced arterial stiffness before hypertension, increased pulse pressure, and structural vessel wall changes. Differential gene expression changes associated with arterial stiffness suggest a molecular mechanism linking sodium to full-vessel wall response affecting gene-networks involved in vascular ECM structure-function, apoptosis balance, and epigenetic regulation.     

Peripheral vascular decoupling in porcine endotoxic shock

Cardiac output measurement from arterial pressure waveforms presumes a defined relationship between the arterial pulse pressure (PP), vascular compliance (C), and resistance (R). Cardiac output estimates degrade if these assumptions are incorrect. We hypothesized that sepsis would differentially alter central and peripheral vasomotor tone, decoupling the usual pressure wave propagation from central to peripheral sites. We assessed arterial input impedance (Z), C, and R from central and peripheral arterial pressures, and aortic blood flow in an anesthetized porcine model (n = 19) of fluid resuscitated endotoxic shock induced by endotoxin infusion (7 μg·kg?1·h?1 increased to 14 and 20 μg·kg?1·h?1 every 10 min and stopped when mean arterial pressure <40 mmHg or Sv(O?) < 45%). Aortic, femoral, and radial artery pressures and aortic and radial artery flows were measured. Z was calculated by FFT of flow and pressure data. R and C were derived using a two-element Windkessel model. Arterial PP increased from aortic to femoral and radial sites. During stable endotoxemia with fluid resuscitation, aortic and radial blood flows returned to or exceeded baseline while mean arterial pressure remained similarly decreased at all three sites. However, aortic PP exceeded both femoral and radial arterial PP. Although Z, R, and C derived from aortic and radial pressure and aortic flow were similar during baseline, Z increases and C decreases when derived from aortic pressure whereas Z decreases and C increases when derived from radial pressure, while R decreased similarly with both pressure signals. This central-to-peripheral vascular tone decoupling, as quantified by the difference in calculated Z and C from aortic and radial artery pressure, may explain the decreasing precision of peripheral arterial pressure profile algorithms in assessing cardiac output in septic shock patients and suggests that different algorithms taking this vascular decoupling into account may be necessary to improve their precision in this patient population.     

Analysis of blood flow in the entire coronary arterial tree

A hemodynamic analysis of coronary blood flow must be based on the measured branching pattern and vascular geometry of the coronary vasculature. We recently developed a computer reconstruction of the entire coronary arterial tree of the porcine heart based on previously measured morphometric data. In the present study, we carried out an analysis of blood flow distribution through a network of millions of vessels that includes the entire coronary arterial tree down to the first capillary branch. The pressure and flow are computed throughout the coronary arterial tree based on conservation of mass and momentum and appropriate pressure boundary conditions. We found a power law relationship between the diameter and flow of each vessel branch. The exponent is approximately 2.2, which deviates from Murray's prediction of 3.0. Furthermore, we found the total arterial equivalent resistance to be 0.93, 0.77, and 1.28 mmHg.ml(-1).s(-1).g(-1) for the right coronary artery, left anterior descending coronary artery, and left circumflex artery, respectively. The significance of the present study is that it yields a predictive model that incorporates some of the factors controlling coronary blood flow. The model of normal hearts will serve as a physiological reference state. Pathological states can then be studied in relation to changes in model parameters that alter coronary perfusion.     

Model-based cardiovascular disease diagnosis: a preliminary in-silico study

In this study, we developed and examined the feasibility of a model-based system identification approach to cardiovascular disease diagnosis. The basic premise of the approach is that it may be possible to diagnose cardiovascular disease from disease-induced alterations in the arterial mechanical properties manifested in the proximal and distal arterial blood pressure waveforms. It first individualizes the lumped-parameter model of wave propagation and reflection in the artery using the measurement of proximal and distal arterial blood pressure waveforms. Then, it employs a diagnosis logic, in the form of disease-specific patterns in model parameters, referred as \(\alpha , \beta \) and pulse transit time. The longitudinal change in these parameters is used to diagnose the presence of peripheral artery disease and arterial stiffening. We illustrated the feasibility of the proposed approach by testing it in a full-scale in-silico arterial tree simulation. The results showed that the approach exhibited superior sensitivity to ankle-brachial index and convenience to carotid-femoral pulse wave velocity: The model parameters \(\alpha \) and \(\beta \) responded with up to 100 and 40 % changes to peripheral artery disease with up to 50 % arterial blockage whereas the change in ankle-brachial index was \({<}5\,\%\); the same parameters responded with up to 300 and 40 % changes to up to 100 % arterial stiffening while pulse transit time changed by up to 24 %. Together with the development of more convenient techniques for the measurement of arterial blood pressure waveforms, the proposed approach may evolve into a viable alternative to the state-of-the-art techniques for cardiovascular disease diagnosis.