Distribution of Flow in an Arteriovenous Fistula Using Reduced-Order Models.

The creation of a communication between an artery and a vein (arteriovenous fistula or AVF), to speed up the blood purification during hemodialysis of patients with renal insufficiency, induces significant rheological and mechanical modifications of the vascular network. In this study, we investigated the impact of the creation of an AVF with a zero-dimensional network model of the vascular system of an upper limb and a one-dimensional model around the anastomosis. We compared the simulated distribution of flow rate in this vascular system with Doppler ultrasound measurements. We studied three configurations: before the creation of the AVF, after the creation of the AVF, and after a focal reduction due to a hyper flow rate. The zero-dimensional model predicted the bounds of the diameter of the superficial vein that respects the flow constraints, assuming a high capillary resistance. We indeed highlighted the importance of knowing the capillary resistance as it is a decisive parameter in the models. We also found that the model reproduced the Doppler measurements of flow rate in every configuration and predicted the distribution of flow in cases where the Doppler was not available. The one-dimensional model allowed studying the impact of a venous constriction on the flow distribution, and the capillary resistance was still a crucial parameter.

Parameter estimation to study the immediate impact of aortic cross-clamping using reduced order models.

Aortic cross-clamping is a common strategy during vascular surgery, however, its instantaneous impact on hemodynamics is unknown. We, therefore, developed two numerical models to estimate the immediate impact of aortic clamping on the vascular properties. To assess the validity of the models, we recorded continuous invasive pressure signals during abdominal aneurysm repair surgery, immediately before and after clamping. The first model is a zero-dimensional (0D) three-element Windkessel model, which we coupled to a gradient-based parameter estimation algorithm to identify patient-specific parameters such as vascular resistance and compliance. We found a 10% increase in the total resistance and a 20% decrease in the total compliance after clamping. The second model is a nine-artery network corresponding to an average human body in which we solved the one-dimensional (1D) blood flow equations. With a similar parameter estimation method and using the results from the 0D model, we identified the resistance boundary conditions of the 1D network. Determining the patient-specific total resistance and the distribution of peripheral resistances through the parameter estimation process was sufficient for the 1D model to accurately reproduce the impact of clamping on the pressure waveform. Both models gave an accurate description of the pressure wave and had a high correlation (R2 > .95) with experimental blood pressure data.

Calculation of the aortic arch angles from three-dimensional reconstructions of computed tomography scans: Comparison between an automated program and visual assessment.

BACKGROUND: The curvature of the aortic arch is associated with the risk of endoleak formation after thoracic endovascular aortic repair (TEVAR). However, the adequate assessment of the angles of the aorta continues to represent a major difficulty. We developed a new program based on three-dimensional (3D) reconstructions of computed tomography (CT) scans to objectively identify the location of the aortic points of maximum curvature, and to automatically calculate the main aortic arch angles, comparing final values with visual assessment methods. METHODS: This is a cross-sectional validation study of a convenience sample of subjects with multislice CT angiography scans of the thoracic aorta from an institutional imaging database. The center lumen line (CLL) of the aorta was determined semi-automatically using Endosize software. The points of maximum curvature on the CLL were determined by two methods: visually by two physicians and through a custom program. RESULTS: The study enrolled 9 subjects: 4 with thoracic aneurysms and 5 with normal aortas. The inter-observer and inter-method correlation, agreement and reliability for each of the 3D spatial coordinates of the points of maximum curvature were appropriate. However, the aortic angles determined by visual assessment showed a very low to moderate correlation and reliability with those determined by our custom program. CONCLUSION: An automated custom program can reflect clinician's intuitive assessment of the location of points of maximum curvature and translate it into aortic angles with an apparently higher precision, reducing potential error and user time.

Linear and Nonlinear Viscoelastic Arterial Wall Models: Application on Animals.

This work deals with the viscoelasticity of the arterial wall and its influence on the pulse waves. We describe the viscoelasticity by a nonlinear Kelvin-Voigt model in which the coefficients are fitted using experimental time series of pressure and radius measured on a sheep's arterial network. We obtained a good agreement between the results of the nonlinear Kelvin-Voigt model and the experimental measurements. We found that the viscoelastic relaxation time-defined by the ratio between the viscoelastic coefficient and the Young's modulus-is nearly constant throughout the network. Therefore, as it is well known that smaller arteries are stiffer, the viscoelastic coefficient rises when approaching the peripheral sites to compensate the rise of the Young's modulus, resulting in a higher damping effect. We incorporated the fitted viscoelastic coefficients in a nonlinear 1D fluid model to compute the pulse waves in the network. The damping effect of viscoelasticity on the high-frequency waves is clear especially at the peripheral sites.

The dicrotic notch analyzed by a numerical model.

Divergent concepts on the origin of the dicrotic notch are widespread in medical literature and education. Since most medical textbooks explain the origin of the dicrotic notch as caused by the aortic valve closure itself, this is commonly transmitted in medical physiology courses. We present clinical data and numerical simulations to demonstrate that reflected pressure waves could participate as one of the causes of the dicrotic notch. Our experimental data from continuous arterial pressure measurements from adult patients undergoing vascular surgery suggest that isolated changes in peripheral vascular resistance using an intravenous bolus of phenylephrine (a selective alpha 1-receptor agonist and thus a potent vasoconstrictor) modify the dicrotic notch. We then explore the mechanisms behind this phenomenon by using a numerical model based on integrated axisymmetric Navier-Stokes equations to compute the hemodynamic flow. Our model illustrates clearly how modifications in peripheral artery resistance may result in changes in the amplitude of the dicrotic notch by modifying reflected pressure waves. We believe that this could be a useful tool in teaching medical physiology courses.

Fluid friction and wall viscosity of the 1D blood flow model.

We study the behavior of the pulse waves of water into a flexible tube for application to blood flow simulations. In pulse waves both fluid friction and wall viscosity are damping factors, and difficult to evaluate separately. In this paper, the coefficients of fluid friction and wall viscosity are estimated by fitting a nonlinear 1D flow model to experimental data. In the experimental setup, a distensible tube is connected to a piston pump at one end and closed at another end. The pressure and wall displacements are measured simultaneously. A good agreement between model predictions and experiments was achieved. For amplitude decrease, the effect of wall viscosity on the pulse wave has been shown as important as that of fluid viscosity.

Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model.

A reliable and fast numerical scheme is crucial for the 1D simulation of blood flow in compliant vessels. In this paper, a 1D blood flow model is incorporated with a Kelvin-Voigt viscoelastic arterial wall. This leads to a nonlinear hyperbolic-parabolic system, which is then solved with four numerical schemes, namely: MacCormack, Taylor-Galerkin, monotonic upwind scheme for conservation law and local discontinuous Galerkin. The numerical schemes are tested on a single vessel, a simple bifurcation and a network with 55 arteries. The numerical solutions are checked favorably against analytical, semi-analytical solutions or clinical observations. Among the numerical schemes, comparisons are made in four important aspects: accuracy, ability to capture shock-like phenomena, computational speed and implementation complexity. The suitable conditions for the application of each scheme are discussed.

Behaviour of silica nanoparticles in dermis-like cellularized collagen hydrogels.

A model of the fate of colloidal silica in the dermis was designed based on the diffusion of fluorescent silica nanoparticles through collagen hydrogels. The diffusion process was found to depend on particle size (10-200 nm) and surface charge, as well as on collagen concentration (1.5-5 mg mL-1). The presence of human dermal fibroblasts within the hydrogels also significantly impacted on the behaviour of the particles. In particular, the simultaneous monitoring of particulate and soluble forms of silica showed that both the hydrogel network and the cellular activity have a strong influence on the solubilization process of the silica particles, through a combination of surface sorption, uptake and intracellular dissolution. Interactions between silica and collagen in 3D environments also lower the cytotoxicity of 10 nm particles compared to traditional 2D cultures. The results emphasize the complexity of silica chemistry in living tissues and specifically indicate the need for further investigations of the in vivo behaviour of its soluble forms.

Identification methods for nonlinear stochastic systems.

Model identifications based on orbit tracking methods are here extended to stochastic differential equations. In the present approach, deterministic and statistical features are introduced via the time evolution of ensemble averages and variances. The aforementioned quantities are shown to follow deterministic equations, which are explicitly written within a linear as well as a weakly nonlinear approximation. Based on such equations and the observed time series, a cost function is defined. Its minimization by simulated annealing or backpropagation algorithms then yields a set of best-fit parameters. This procedure is successfully applied for various sampling time intervals, on a stochastic Lorenz system.