In vivo validation of a one-dimensional finite-element method for predicting blood flow in cardiovascular bypass grafts.
ABSTRACT Current practice in vascular surgery utilizes only diagnostic and empirical data to plan treatments and does not enable quantitative a priori prediction of the outcomes of interventions. We have previously described a new approach to vascular surgery planning based on solving the governing equations of blood flow in patient-specific models. A one-dimensional finite-element method was used to simulate blood flow in eight porcine thoraco-thoraco aortic bypass models. The predicted flow rate was compared to in vivo data obtained using cine phase-contrast magnet resonance imaging. The mean absolute difference between computed and measured flow distribution in the stenosed aorta was found to be 4.2% with the maximum difference of 10.6% anda minimum difference of 0.4%. Furthermore, the sensitivity of the flow rate and distribution with respect to stenosis and branch losses were quantified.
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ABSTRACT: The mechanisms underlying the shape of pulse waves in the systemic arterial network are studied using the time-domain, one-dimensional (1-D) equations of blood flow in compliant vessels. The pulse waveform at an arbitrary location in the network is initially separated into a peripheral component that depends on the cardiac output, total compliance and total peripheral resistance of the network, and a conduit component governed by reflections at the junctions of the large conduit arteries and at the aortic valve. The dynamics of the conduit component are then analysed using a new algorithm that describes all the waves generated in the linear 1-D model network by a single wavefront starting at the root. This algorithm allows one to systematically follow all the waves arriving at the measuring site and identify all the reflection sites that these waves have visited. Application of this method to the pulse waves simulated using a 1-D model of the largest 55 systemic arteries in the human demonstrates that peripheral components make a larger contribution to aortic pressure waveforms than do the conduit components. Conduit components are closely related to the outflow from the left ventricle in early systole. Later in the cardiac cycle, they are the result of reflections at the arterial junctions and aortic valve. The number of reflected waves increases approximately as 3 m , with m being the number of reflection sites encountered. The pressure changes associated with these waves can be positive or negative but their absolute values tend to decrease exponentially. As a result, wave activity is minimal during late diastole, when the peripheral components of pressure and the flow are dominant, and aortic pressures tend to a space-independent value determined by the cardiac output, total compliance and total peripheral resistance. The results also suggest that pulse-wave propagation is the mechanism by which the arterial system reaches the mean pressure dictated by the cardiac output and total resistance that is required to perfuse the microcirculation. The total compliance determines the rate at which this pressure is restored when the system has departed from its equilibrium state of steady oscillation. This study provides valuable information on identifying and measuring the parameters and pathways of the arterial network that have the largest effect on the simulated pulse waveforms.Journal of Engineering Mathematics 04/2009; 64(4):331-351. · 0.86 Impact Factor
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ABSTRACT: Zero-dimensional (lumped parameter) and one dimensional models, based on simplified representations of the components of the cardiovascular system, can contribute strongly to our understanding of circulatory physiology. Zero-D models provide a concise way to evaluate the haemodynamic interactions among the cardiovascular organs, whilst one-D (distributed parameter) models add the facility to represent efficiently the effects of pulse wave transmission in the arterial network at greatly reduced computational expense compared to higher dimensional computational fluid dynamics studies. There is extensive literature on both types of models. The purpose of this review article is to summarise published 0D and 1D models of the cardiovascular system, to explore their limitations and range of application, and to provide an indication of the physiological phenomena that can be included in these representations. The review on 0D models collects together in one place a description of the range of models that have been used to describe the various characteristics of cardiovascular response, together with the factors that influence it. Such models generally feature the major components of the system, such as the heart, the heart valves and the vasculature. The models are categorised in terms of the features of the system that they are able to represent, their complexity and range of application: representations of effects including pressure-dependent vessel properties, interaction between the heart chambers, neuro-regulation and auto-regulation are explored. The examination on 1D models covers various methods for the assembly, discretisation and solution of the governing equations, in conjunction with a report of the definition and treatment of boundary conditions. Increasingly, 0D and 1D models are used in multi-scale models, in which their primary role is to provide boundary conditions for sophisticate, and often patient-specific, 2D and 3D models, and this application is also addressed. As an example of 0D cardiovascular modelling, a small selection of simple models have been represented in the CellML mark-up language and uploaded to the CellML model repository http://models.cellml.org/. They are freely available to the research and education communities. Each published cardiovascular model has merit for particular applications. This review categorises 0D and 1D models, highlights their advantages and disadvantages, and thus provides guidance on the selection of models to assist various cardiovascular modelling studies. It also identifies directions for further development, as well as current challenges in the wider use of these models including service to represent boundary conditions for local 3D models and translation to clinical application.BioMedical Engineering OnLine 01/2011; 10:33. · 1.40 Impact Factor
Article: A pulse wave propagation model to support decision-making in vascular access planning in the clinic.[show abstract] [hide abstract]
ABSTRACT: The 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.Medical Engineering & Physics 08/2011; 34(2):233-48. · 1.62 Impact Factor