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

Tube law parametrization using in vitro data for one-dimensional blood flow in arteries and veins: TUBE LAW PARAMETRIZATION IN ARTERIES AND VEINS

The deformability of blood vessels in one-dimensional blood flow models is typically described through a pressure-area relation, known as the tube law. The most used tube laws take into account the elastic and viscous components of the tension of the vessel wall. Accurately parametrizing the tube laws is vital for replicating pressure and flow wave propagation phenomena. Here, we present a novel mathematical-property-preserving approach for the estimation of the parameters of the elastic and viscoelastic tube laws. Our goal was to estimate the parameters by using ovine and human in vitro data, while constraining them to meet prescribed mathematical properties. Results show that both elastic and viscoelastic tube laws accurately describe experimental pressure-area data concerning both quantitative and qualitative aspects. Additionally, the viscoelastic tube law can provide a qualitative explanation for the observed hysteresis cycles. The two models were evaluated using two approaches: (i) allowing all parameters to freely vary within their respective ranges and (ii) fixing some of the parameters. The former approach was found to be the most suitable for reproducing pressure-area curves.

Signatures of obstructions and expansions in the arterial frequency response

BACKGROUND AND OBJECTIVE

The blood pressure and flow waveforms carry valuable information about the condition of the cardiovascular system and a patient's health. Waveform analysis in health and pathological conditions can be performed in the time or frequency domains; the information to be emphasised defines the use of either domain. However, physicians are more familiar with the time domain, and the changes in the waveforms due to cardiovascular diseases and ageing are better characterised in such domain. On the other hand, the analysis of the vascular and geometrical variables determining the signatures in the frequency response of local vascular anomalies, such as aneurysms and stenoses, has not been thoroughly explored. This paper aims to characterise the signatures of obstructions (stenoses) and expansions (aneurysms) in the frequency response of tapered arteries.

METHODS

The first step in our methodology was to incorporate the viscous response of the arterial wall into a one-dimensional elastic formulation that solves the governing equations in the frequency domain. As a second step, we imposed a volumetric flow excitation in arteries simulating the aorta with increasing geometry complexity: from straight to tapered arteries with local expansions or obstructions; and we assessed the frequency response.

RESULTS

We found that the obstructions and expansions cause characteristic signatures in an artery's frequency response that are distinguishable from a health condition. The signatures of obstruction and expansions differ; the obstructions increase the magnitude of fundamental frequency and work as a close boundary condition. On the other hand, the expansions diminish the fundamental frequency and work as an open boundary condition. Furthermore, such signatures correlate to the distance between the artery's inlet and the anomaly's starting point and have the potential to pinpoint abnormalities non-invasively.

CONCLUSIONS

We found that the obstructions and expansions cause characteristic signatures in an artery's frequency response that have the potential to detect and follow up on the development of vascular abnormalities. For the latter purpose, constant monitoring may be required; despite this not being a common clinical practice, the new wearable technology offers the possibility of continuous monitoring of biophysical markers such as the pressure waveform.

Verification of the coupled-momentum method with Womersley's Deformable Wall analytical solution

In this paper, we perform a verification study of the Coupled-Momentum Method (CMM), a 3D fluid-structure interaction (FSI) model which uses a thin linear elastic membrane and linear kinematics to describe the mechanical behavior of the vessel wall. The verification of this model is done using Womersley's deformable wall analytical solution for pulsatile flow in a semi-infinite cylindrical vessel. This solution is, under certain premises, the analytical solution of the CMM and can thus be used for model verification. For the numerical solution, we employ an impedance boundary condition to define a reflection-free outflow boundary condition and thus mimic the physics of the analytical solution, which is defined on a semi-infinite domain. We first provide a rigorous derivation of Womersley's deformable wall theory via scale analysis. We then illustrate different characteristics of the analytical solution such as space-time wave periodicity and attenuation. Finally, we present the verification tests comparing the CMM with Womersley's theory.