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A profound analysis of pressure and flow wave propagation in cardiovascular systems is the key in noninvasive assessment of hemodynamic parameters. Pulse transit time (PTT), which closely relates to the physical properties of the cardiovascular system, can be linked to variations of blood pressure and stroke volume to provide information for patient-specific clinical diagnostics. In this work, we present mathematical and numerical tools, capable of accurately predicting the PTT, local pulse wave velocity, vessel compliance, and pressure/flow waveforms, in a viscous hyperelastic cardiovascular network. A new one-dimensional framework, entitled cardiovascular flow analysis (CardioFAN), is presented to describe the pulsatile fluid-structure interaction in the hyperelastic arteries, where pertaining hyperbolic equations are solved using a high-resolution total variation diminishing Lax-Wendroff method. The computational algorithm is validated against well-known numerical, in vitro and in vivo data for networks of main human arteries with 55, 37 and 26 segments, respectively. PTT prediction is improved by accounting for hyperelastic nonlinear waves between two arbitrary sections of the arterial tree. Consequently, arterial compliance assignments at each segment are improved in a personalized model of the human aorta and supra-aortic branches with 26 segments, where prior in vivo data were available for comparison. This resulted in a 1.5% improvement in overall predictions of the waveforms, or average relative errors of 5.5% in predicting flow, luminal area and pressure waveforms compared to prior in vivo measurements. The open source software, CardioFAN, can be calibrated for arbitrary patient-specific vascular networks to conduct noninvasive diagnostics.

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Reduced fluid-structure interaction models are the key component of hemodynamic simulation. In this work, a multi-purpose computational model applicable to specific physiological components such as arterial, venous and cerebrospinal fluid circulatory systems has been developed based on the Hamilton's variational principle. This model encompasses a viscous Newtonian fluid structure interaction (FSI) framework for the large compliant bifurcated arterial networks and its subsystems. This approach provides the groundworks for a correct formulation of reduced FSI models with an account for arbitrary non-linear viscoelastic properties of a compliant vascular tree. The hyperbolic properties of the derived mathematical model are analyzed and used to construct the Lax-Wendroff finite volume numerical scheme, with second order accuracy in time and space. The computational algorithm is validated against well-known numerical and in vitro experimental data reported in the literature for the case of human arterial trees, comprising 55 and 37 main arterial vessels. Utilizing the physics based nonlinear constitutive framework, this model can be adequately tested, calibrated and applied for patient-specific clinical diagnosis and prediction.

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PURPOSE: The current 1-dimensional fluid structure interaction model (FSI) for understanding cerebrospinal fluid (CSF) circulation requires pulsatility as a precondition and has not been applied to patients with continuous-flow left ventricular assist devices (CF-LVAD) where pulsatility is chronically reduced. Our study aims to characterize the behavior of CSF pressure and flow in patients with CF-LVADs using a computational FSI model. METHODS: Utilizing the computational FSI model, CSF production in choroid plexuses of the 4 ventricles was specified as a boundary condition for the model. The other source of production from capillary ultrafiltrate spaces was accounted for by the mass conservation equation. The primary CSF absorption sites (i.e., arachnoid granulations) were treated as the outlet boundary conditions. We established a low pulse wave to represent patients with a CF-LVAD. RESULTS: From the model, low pulse conditions resulted in a reduction in CSF pressure amplitude and velocity though the overall flow rate was unchanged. CONCLUSIONS: The existing FSI model is not a suitable representation of CSF flow in CF-LVAD patients. More studies are needed to elucidate the role of pulsatility in CSF flow and the compensatory changes in CSF production and absorption that occur in patients with CF-LVADs in whom pulsatility is diminished.

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Hypertension is a significant worldwide health issue. Continuous blood pressure monitoring is important for early detection of hypertension, and for improving treatment efficacy and compliance. Pulse wave velocity (PWV) has the potential to allow for a continuous blood pressure monitoring device; however published studies demonstrate significant variability in this correlation. In a recently presented physics-based mathematical model of PWV, flow velocity is additive to the classic pressure wave as estimated by arterial material properties, suggesting flow velocity correction may be important for cuff-less non-invasive blood pressure measures. The present study examined the impact of systolic flow correction of a measured PWV on blood pressure prediction accuracy using data from two published in vivo studies. Both studies examined the relationship between PWV and blood pressure under pharmacological manipulation, one in mongrel dogs and the other in healthy adult males. Systolic flow correction of the measured PWV improves the R2 correlation to blood pressure from 0.51 to 0.75 for the mongrel dog study, and 0.05 to 0.70 for the human subjects study. The results support the hypothesis that systolic flow correction is an essential element of non-invasive, cuff-less blood pressure estimation based on PWV measures.

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Pulse wave velocity (PWV) quantification commonly serves as a highly robust prognostic parameter being used in a preventative cardiovascular therapy. Being dependent on arterial elastance, it can serve as a marker of cardiovascular risk. Since it is influenced by a blood pressure (BP), the pertaining theory can lay the foundation in developing a technique for noninvasive blood pressure measurement. Previous studies have reported application of PWV, measured noninvasively, for both the estimation of arterial compliance and blood pressure, based on simplified physical or statistical models. A new theoretical model for pulse wave propagation in a compliant arterial segment is presented within the framework of pseudo-elastic deformation of biological tissue undergoing finite deformation. An essential ingredient is the dependence of results on nonlinear aspects of the model: convective fluid phenomena, hyperelastic constitutive relation, large deformation and a longitudinal pre-stress load. An exact analytical solution for PWV is presented as a function of pressure, flow and pseudo-elastic orthotropic parameters. Results from our model are compared with published in-vivo PWV measurements under diverse physiological conditions. Contributions of each of the nonlinearities are analyzed. It was found that the totally nonlinear model achieves the best match with the experimental data. To retrieve individual vascular information of a patient, the inverse problem of hemodynamics is presented, calculating local orthotropic hyperelastic properties of the arterial wall. The proposed technique can be used for non-invasive assessment of arterial elastance, and blood pressure using direct measurement of PWV, with account of hyperelastic orthotropic properties.

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Pressure wave velocity (PWV) is commonly used as a clinical marker of vascular elasticity. Recent studies have increased clinical interest in also analyzing the impact of heart rate, blood pressure, and left ventricular ejection time on PWV. In this article we focus on the development of a theoretical one-dimensional model and validation via direct measurement of the impact of ejection time and peak pressure on PWV using an in vitro hemodynamic simulator. A simple nonlinear traveling wave model was developed for a compliant thin-walled elastic tube filled with an incompressible fluid. This model accounts for the convective fluid phenomena, elastic vessel deformation, radial motion, and inertia of the wall. An exact analytical solution for PWV is presented which incorporates peak pressure, ejection time, ejection volume, and modulus of elasticity. To assess arterial compliance, the solution is introduced in an alternative form, explicitly determining compliance of the wall as a function of the other variables. The model predicts PWV in good agreement with the measured values with a maximum difference of 3.0%. The results indicate an inverse quadratic relationship ([Formula: see text]) between ejection time and PWV, with ejection time dominating the PWV shifts (12%) over those observed with changes in peak pressure (2%). Our modeling and validation results both explain and support the emerging evidence that, both in clinical practice and clinical research, cardiac systolic function related variables should be regularly taken into account when interpreting arterial function indices, namely PWV.

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