An inverse approach to determining spatially varying arterial compliance using ultrasound imaging

Abstract

The mechanical properties of arteries are implicated in a wide variety of cardiovascular diseases, many of which are expected to involve a strong spatial variation in properties that can be depicted by diagnostic imaging. A pulse wave inverse problem (PWIP) is presented, which can produce spatially resolved estimates of vessel compliance from ultrasound measurements of the vessel wall displacements. The 1D equations governing pulse wave propagation in a flexible tube are parameterized by the spatially varying properties, discrete cosine transform components of the inlet pressure boundary conditions, viscous loss constant and a resistance outlet boundary condition. Gradient descent optimization is used to fit displacements from the model to the measured data by updating the model parameters. Inversion of simulated data showed that the PWIP can accurately recover the correct compliance distribution and inlet pressure under realistic conditions, even with severe simulated measurement noise. Silicone phantoms with known compliance contrast were imaged with a clinical ultrasound system .The PWIP produced spatially and quantitatively accurate maps of the phantom compliance compared to independent static property estimates, and the known locations of stiff inclusions (which were as small as 7mm). The PWIP is necessary for these phantom experiments as the spatiotemporal resolution, measurement noise and compliance contrast does not allow accurate tracking of the pulse wave velocity using traditional approaches (e.g. 50% upstroke markers). Results from simulated data suggest reflections generated from material interfaces may negatively affect wave velocity estimates, whereas these reflections are accounted for in the PWIP and do not cause problems.

In vivo repeatability of the pulse wave inverse problem in human carotid arteries

“…Previous studies have demonstrated that the PWIP can accurately imaging known compliance distributions in silicone phantoms (McGarry et al 2016). This in vivo investigation of the PWIP was promising, and demonstrated feasibility of applying the PWIP for in vivo human carotid compliance imaging.…”

“…Previous studies using conventional wavefront tracking have avoided the reflection by imaging further away from the bifurcation to ensure a single forward wave, and other methods have shown errors in PWV measured near reflections (Alastruey et al 2011, Borlotti et al 2014). In phantoms, the PWIP has been demonstrated to perform well in the presence of internally generated reflections due to inhomogeneities; as well as downstream reflections from the fittings (Mcgarry et al 2016). In this study, we expect that the PWIP BC applied at the bifurcation will reduce errors because major reflection sources are included in the model.…”

“…The PWIP is an inverse problem approach to recovering the unknown vessel properties, where parameters from a computational model are fitted to measured data using optimization methods (Mcgarry et al 2016). In this case, the computational model is the linearized partial differential equations governing 1-dimensional pulse wave propagation in heterogeneous flexible tubes (Fung et al 2013), $$k_p\frac{dP}{dt}+A_o\frac{du}{dx}=0$$ $$\frac{du}{dt}+\frac{1}{\rho }\frac{dP}{dx}+K_{R}u=0.$$…”

“…We have demonstrated a pulse wave inverse problem (PWIP), which accounts for reflections by fitting unknown parameters of a computational model of the governing 1D pulse wave equations to the measured data to compute spatially resolved estimates of the vessel compliance. The PWIP accurately computed the compliance distribution of heterogeneous phantoms with stiff inclusions as small as 7mm (Mcgarry et al 2016). This study aims to test in vivo feasibility and repeatability of the methodology in carotid arteries of healthy human subjects.…”

Detecting Regional Stiffness Changes in Aortic Aneurysmal Geometries Using Pressure-Normalized Strain

“…PWI has been validated in a series of FE modeling, vessel phantom and animal and human clinical feasibility studies (Apostolakis et al 2016; Cloonan et al 2014; Li et al 2013; Luo et al 2009; Shahmirzadi and Konofagou 2012). Although PWI can provide accurate measures of in vivo tissue stiffness, one of the greatest limitations of PWI is the degradation of the measurement second to pulse wave reflections at inclusion bodies and branch points, as well as variations in wall thickness, luminal radius and assumptions of tissue density (Apostolakis et al 2016; McGarry et al 2016; Shahmirzadi and Konofagou 2012). As with previous techniques, PWI is also limited in its assumption of simplistic axisymmetric homogenous geometries, which negatively bias results in complicated aneurysm geometries and locations of wave reflections.…”