Pulse Wave Propagation Model Research Articles

A 1D pulse wave propagation model of the hemodynamics of calf muscle pump function.

The calf muscle pump is a mechanism which increases venous return and thereby compensates for the fluid shift towards the lower body during standing. During a muscle contraction, the embedded deep veins collapse and venous return increases. In the subsequent relaxation phase, muscle perfusion increases due to increased perfusion pressure, as the proximal venous valves temporarily reduce the distal venous pressure (shielding). The superficial and deep veins are connected via perforators, which contain valves allowing flow in the superficial-to-deep direction. The aim of this study is to investigate and quantify the physiological mechanisms of the calf muscle pump, including the effect of venous valves, hydrostatic pressure, and the superficial venous system. Using a one-dimensional pulse wave propagation model, a muscle contraction is simulated by increasing the extravascular pressure in the deep venous segments. The hemodynamics are studied in three different configurations: a single artery–vein configuration with and without valves and a more detailed configuration including a superficial vein. Proximal venous valves increase effective venous return by 53% by preventing reflux. Furthermore, the proximal valves shielding function increases perfusion following contraction. Finally, the superficial system aids in maintaining the perfusion during the contraction phase and reduces the refilling time by 37%. © 2015 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons Ltd.

Applicability of the polynomial chaos expansion method for personalization of a cardiovascular pulse wave propagation model.

Patient-specific modeling requires model personalization, which can be achieved in an efficient manner by parameter fixing and parameter prioritization. An efficient variance-based method is using generalized polynomial chaos expansion (gPCE), but it has not been applied in the context of model personalization, nor has it ever been compared with standard variance-based methods for models with many parameters. In this work, we apply the gPCE method to a previously reported pulse wave propagation model and compare the conclusions for model personalization with that of a reference analysis performed with Saltelli's efficient Monte Carlo method. We furthermore differentiate two approaches for obtaining the expansion coefficients: one based on spectral projection (gPCE-P) and one based on least squares regression (gPCE-R). It was found that in general the gPCE yields similar conclusions as the reference analysis but at much lower cost, as long as the polynomial metamodel does not contain unnecessary high order terms. Furthermore, the gPCE-R approach generally yielded better results than gPCE-P. The weak performance of the gPCE-P can be attributed to the assessment of the expansion coefficients using the Smolyak algorithm, which might be hampered by the high number of model parameters and/or by possible non-smoothness in the output space.

Numerical modeling of the pulse wave propagation in large blood vessels based on liquid and wall interaction

The purpose of this article is to develop a non-linear, one-dimensional model of pulse wave propagation in the arterial cardiovascular system. The model includes partial differential equations resulting from the balance of mass and momentum for the fluid-filled area and the balance equation for the area of the wall and vessels. The considered mathematical model of pulse wave propagation in the thoracic aorta section takes into account the viscous dissipation of fluid energy, realistic values of parameters describing the physicochemical properties of blood and vessel wall. Boundary and initial conditions contain the appropriate information obtained from in vivo measurements. As a result of the numerical solution of the mass and momentum balance equations for the blood and the equilibrium equation for the arterial wall area, time- dependent deformation, respective velocity profiles and blood pressure were determined.

Numerical assessment of the stiffness index.

Elevated systemic vascular stiffness is associated with increased risk of cardiovascular disease. It has been suggested that the time difference between the two characteristic peaks of the digital volume pulse (DVP) measured at the finger using photoplethysmography is related to the stiffness of the arterial tree, and inversely proportional to the stiffness index (SI). However, the precise physical meaning of the SI and its relation to aortic pulse wave velocity (aPWV) is yet to be ascertained. In this study we investigated numerically the effect of changes in arterial wall stiffness, peripheral resistances, peripheral compliances or peripheral wave reflections on the SI and aPWV. The SI was calculated from the digital area waveform simulated using a nonlinear one-dimensional model of pulse wave propagation in a 75-artery network, which includes the larger arteries of the hand. Our results show that aPWV is affected by changes in aortic stiffness, but the SI is primarily affected by changes in the stiffness of all conduit vessels. Thus, the SI is not a direct substitute for aPWV. Moreover, our results suggest that peripheral reflections in the upper body delay the time of arrival of the first peak in the DVP. The second peak is predominantly caused by the impedance mismatch within the 75 arterial segments, rather than by peripheral reflections.

WALL SHEAR STRESSES IN A FLUID–STRUCTURE INTERACTION MODEL OF PULSE WAVE PROPAGATION

In our prior paper, a fluid–structure interaction model of pulse wave propagation, called the elastic tube model, has been developed. The focus of this paper is wall shear stress (WSS) in this model and the effects of different parameters, including rigid walls, wall thickness, and internal radius. The unsteady flow was assumed to be laminar, Newtonian and incompressible, and the vessel wall to be linear-elastic isotropic, and incompressible. A fluid–structure interaction scheme is constructed using a finite element method. The results demonstrate the elastic tube plays an important role in WSS distributions of wave propagation. It is shown that there is a time delay between the WSS waveforms at different locations in the elastic tube model while the time delay cannot be observed clearly in the rigid tube model. Compared with the elastic tube model, the increase of the wall thickness makes disturbed WSS distributions, however WSS values are increased greatly due to the decrease of the internal radius. The results indicate that the effects of different parameters on WSS distributions are significant. The proposed model gives valid results.

Computational model for estimating the short- and long-term cardiac response to arteriovenous fistula creation for hemodialysis

Creation of an arteriovenous fistula (AVF) for hemodialysis may result in cardiac failure due to dramatic increases in cardiac output. To investigate the quantitative relations between AVF flow, changes in cardiac output, myocardial stress and strain and resulting left ventricular adaptation, a computational model is developed. The model combines a one-dimensional pulse wave propagation model of the arterial network with a zero-dimensional one-fiber model of cardiac mechanics and includes adaptation rules to capture the effect of the baro-reflex and long-term structural remodelling of the left ventricle. Using generic vascular and cardiac parameters based on literature, simulations are done that illustrate the model's ability to quantitatively reproduce the clinically observed increase in brachial flow and cardiac output as well as occurence of eccentric hypertrophy. Patient-specific clinical data is needed to investigate the value of the computational model for personalized predictions.

A sensitivity analysis of a personalized pulse wave propagation model for arteriovenous fistula surgery. Part A: Identification of most influential model parameters

Previously, a pulse wave propagation model was developed that has potential in supporting decision-making in arteriovenous fistula (AVF) surgery for hemodialysis. To adapt the wave propagation model to personalized conditions, patient-specific input parameters should be available. In clinics, the number of measurable input parameters is limited which results in sparse datasets. In addition, patient data are compromised with uncertainty. These uncertain and incomplete input datasets will result in model output uncertainties. By means of a sensitivity analysis the propagation of input uncertainties into output uncertainty can be studied which can give directions for input measurement improvement. In this study, a computational framework has been developed to perform such a sensitivity analysis with a variance-based method and Monte Carlo simulations. The framework was used to determine the influential parameters of our pulse wave propagation model applied to AVF surgery, with respect to parameter prioritization and parameter fixing. With this we were able to determine the model parameters that have the largest influence on the predicted mean brachial flow and systolic radial artery pressure after AVF surgery. Of all 73 parameters 51 could be fixed within their measurement uncertainty interval without significantly influencing the output, while 16 parameters importantly influence the output uncertainty. Measurement accuracy improvement should thus focus on these 16 influential parameters. The most rewarding are measurement improvements of the following parameters: the mean aortic flow, the aortic windkessel resistance, the parameters associated with the smallest arterial or venous diameters of the AVF in- and outflow tract and the radial artery windkessel compliance.

A sensitivity analysis of a personalized pulse wave propagation model for arteriovenous fistula surgery. Part B: Identification of possible generic model parameters

Decision-making in vascular access surgery for hemodialysis can be supported by a pulse wave propagation model that is able to simulate pressure and flow changes induced by the creation of a vascular access. To personalize such a model, patient-specific input parameters should be chosen. However, the number of input parameters that can be measured in clinical routine is limited. Besides, patient data are compromised with uncertainty. Incomplete and uncertain input data will result in uncertainties in model predictions. In part A, we analyzed how the measurement uncertainty in the input propagates to the model output by means of a sensitivity analysis. Of all 73 input parameters, 16 parameters were identified to be worthwhile to measure more accurately and 51 could be fixed within their measurement uncertainty range, but these latter parameters still needed to be measured. Here, we present a methodology for assessing the model input parameters that can be taken constant and therefore do not need to be measured. In addition, a method to determine the value of this parameter is presented. For the pulse wave propagation model applied to vascular access surgery, six patient-specific datasets were analyzed and it was found that 47 out of 73 parameters can be fixed on a generic value. These model parameters are not important for personalization of the wave propagation model. Furthermore, we were able to determine a generic value for 37 of the 47 fixable model parameters.

SELECTING THE OPTIMAL LOCATION FOR AVF CREATION: THE LIFELINE FOR HEMODIALYSIS PATIENTS

A vascular access facilitates the high blood flow needed for hemodialysis and is therefore crucial for successful treatment of patients suffering from endstage renal disease. Preferably, a vascular access is created by surgically connecting an artery and vein in the arm (arteriovenous fistula, AVF). The optimal location (upper or lower arm) is selected by the vascular surgeon based on extensive preoperative diagnostics. Nevertheless, flow-related complications still occur in up to 30% of all cases [Allon, 2003]. Previously, a pulse wave propagation model was developed that has potential to support decision-making in AVF surgery. In this study, the model’s feasibility for personalized AVF surgery planning is examined.

IMPROVING PERSONALIZATION OF A 1D WAVE PROPAGATION MODEL APPLIED FOR AVF SURGERY

An arteriovenous fistula (AVF) is used as vascular access in hemodialysis. A previously developed patient-specific pulse wave propagation model [Huberts, 2011] might be useful to improve selection of the optimal AVF location (upper or lower arm) by predicting postoperative flow. However, personalizing the model parameters is difficult due to the limitations of measurement modalities, the large uncertainties in clinical measurements and the burden on the patient that should be minimized, resulting in sparse datasets. Therefore, it would be beneficial to identify the model parameters that are essential in the flow prediction and should thus be measured for each patient. Hence, the aim of this study was to identify the (non-) influential model parameters of the pulse wave propagation model applied to AVF surgery.

EXPERIMENTAL VALIDATION OF A 1D WAVE PROPAGATION MODEL FOR HEMODYNAMICS AFTER AVF SURGERY

An arteriovenous fistula (AVF) is a surgically created connection between an artery and vein in the arm, made for connecting hemodialysis patients to an artificial kidney [Tordoir, 2003]. Previously, a pulse wave propagation model was developed [Huberts, 2011] that has potential in supporting decision-making in AVF surgery by predicting mean postoperative flow. The model was able to select the same AVF configuration as an experienced vascular surgeon (> 1000 AVFs created) in 9/10 patients. Although the model might already be of clinical use, model improvements can be made since the predicted flow differed in 4/10 patients with flow measured after surgery. Differences can result either from inaccurate postoperative flow measurements, inaccurate model input, neglecting adaptation and/or an incomplete physical description of the pulse wave propagation after AVF surgery. To examine if the physical description is complete the model should be validated with an experimental setup. Moreover, the experimental setup gives the possibility to validate the pressure and flow waveforms which are required when adaptation laws will be incorporated in the model. Therefore, the aim of this study was to validate the pulse wave propagation model with an experimental setup mimicking AVF surgery.

Experimental validation of a pulse wave propagation model for predicting hemodynamics after vascular access surgery

Hemodialysis patients require a vascular access that is, preferably, surgically created by connecting an artery and vein in the arm, i.e. an arteriovenous fistula (AVF). The site for AVF creation is chosen by the surgeon based on preoperative diagnostics, but AVFs are still compromised by flow-associated complications. Previously, it was shown that a computational 1D-model is able to describe pressure and flow after AVF surgery. However, predicted flows differed from measurements in 4/10 patients. Differences can be attributed to inaccuracies in Doppler measurements and input data, to neglecting physiological mechanisms or to an incomplete physical description of the pulse wave propagation after AVF surgery. The physical description can be checked by validating against an experimental setup consisting of silicone tubes mimicking the aorta and arm vasculature both before and after AVF surgery, which is the aim of the current study. In such an analysis, the output uncertainty resulting from measurement uncertainty in model input should be quantified. The computational model was fed by geometrical and mechanical properties collected from the setup. Pressure and flow waveforms were simulated and compared with experimental waveforms. The precision of the simulations was determined by performing a Monte Carlo study. It was concluded that the computational model was able to simulate mean pressures and flows accurately, whereas simulated waveforms were less attenuated than experimental ones, likely resulting from neglecting viscoelasticity. Furthermore, it was found that in the analysis output uncertainties, resulting from input uncertainties, cannot be neglected and should thus be considered.

A pulse wave propagation model to support decision-making in vascular access planning in the clinic

AbstractThe preferred vascular access for hemodialysis is an autologous arteriovenous fistula (AVF) in the arm: a surgically created connection between an artery and vein. The surgeon selects the AVF location based on experience and preoperative diagnostics. However, 20–50% of all lower arm AVFs are hampered by a too low access flow, whereas complications associated with too high flows are observed in 20% of all upper arm AVFs. We hypothesize that a pulse wave propagation model fed by patient-specific data has the ability to assist the surgeon in selecting the optimal AVF configuration by predicting direct postoperative flow. Previously, a 1D wave propagation model (spectral elements) was developed in which an approximated velocity profile was assumed based on boundary layer theory. In this study, we derived a distributed lumped parameter implementation of the pulse wave propagation model. The elements of the electrical analog for a segment are based on the approximated velocity profiles and dependent on the Womersley number. We present the application of the lumped parameter pulse wave propagation model to vascular access surgery and show how a patient-specific model is able to predict the hemodynamical impact of AVF creation and might assist in vascular access planning.The lumped parameter pulse wave propagation model was able to select the same AVF configuration as an experienced surgeon in nine out of ten patients. In addition, in six out of ten patients predicted postoperative flows were in the same order of magnitude as measured postoperative flows. Future research should quantify uncertainty in model predictions and measurements.

An Elaborated Multi-Branched Model of Human Arteries

Blood pressure pulse wave is propagated from heart to peripheral blood vessels with changing its waveform according to characteristics of pass way. Dynamic characteristics of total arteries have been investigated by wave equation on multi-branched arterial model. Some diseases, such as an abdominal aortic aneurysm, can be predicted by using the relation between the pulse waveform and arterial stiffness. The aim of this research is to propose a new method to detect such diseases based on the pulse wave propagation model on an arterial tree. In this paper, influences of tissue surrounding an artery, model of peripheral arteries and elasticity of arteries are investigated to elaborate a multi-branched arterial model of human body.

B47 脈波伝播の計測による動脈病変推定法の提案(生体計測・評価II)

Blood pressure pulse waves are propagated from the heart to peripheral with changing their shapes according to characteristics of pass way. A characteristic of total arteries can be detected from pulse waves as an arterial stiffness. Some diseases, like an abdominal aortic aneurysm, can be predicted if some deformed pulse waveform of specific arteries are detected. The aim of this research is to propose new method to detect such diseases. A pulse wave propagation model based on an arterial tree can help to analyze the cause of deformed pulse waveform. In this paper, the propagation of pulse wave characteristics is theoretically analyzed and new method to detect the diseases is proposed and verified in the simulation.

Separation of the reservoir and wave pressure and velocity from measurements at an arbitrary location in arteries

Previous studies based on measurements made in the ascending aorta have demonstrated that it can be useful to separate the arterial pressure P into a reservoir pressure P* generated by the windkessel effect and a wave pressure p generated by the arterial waves: P = P*+p. The separation in these studies was relatively straightforward since the flow into the arterial system was measured. In this study the idea is extended to measurements of pressure and velocity at sites distal to the aortic root where flow into the arterial system is not known. P* is calculated from P at an arbitrary location in a large artery by fitting the pressure fall-off in diastole to an exponential function and assuming that p is proportional to the flow into the arterial system. A local reservoir velocity U* that is proportional to P* is also defined. The separation algorithm is applied to in vivo human and canine data and to numerical data generated using a one-dimensional model of pulse wave propagation in the larger conduit arteries. The results show that the proposed algorithm is reasonably robust, allowing for the separation of the measured pressure and velocity into reservoir and wave pressures and velocities. Application to data measured simultaneously in the aorta of the dog shows that the reservoir pressure is fairly uniform along the aorta, a test of self-consistency of the assumptions leading to the algorithm. Application to data generated with a validated numerical model indicates that the parameters derived by fitting the pressure data are close to the known values which were used to generate the numerical data. Finally, application to data measured in the human thoracic aorta indicates the potential usefulness of the separation.