Global sensitivity analysis of a model for venous valve dynamics.

Chronic venous disease is defined as dysfunction of the venous system caused by incompetent venous valves with or without a proximal venous obstruction. Assessing the severity of the disease is challenging, since venous function is determined by various interacting hemodynamic factors. Mathematical models can relate these factors using physical laws and can thereby aid understanding of venous (patho-)physiology. To eventually use a mathematical model to support clinical decision making, first the model sensitivity needs to be determined. Therefore, the aim of this study is to assess the sensitivity of the venous valve model outputs to the relevant input parameters. Using a 1D pulse wave propagation model of the tibial vein including a venous valve, valve dynamics under head up tilt are simulated. A variance-based sensitivity analysis is performed based on generalized polynomial chaos expansion. Taking a global approach, individual parameter importance on the valve dynamics as well as importance of their interactions is determined. For the output related to opening state of the valve, the opening/closing pressure drop (dpvalve,0) is found to be the most important parameter. The venous radius (rvein,0) is related to venous filling volume and is consequently most important for the output describing venous filling time. Finally, it is concluded that improved assessment of rvein,0 and dpvalve,0 is most rewarding when simulating valve dynamics, as this results in the largest reduction in output uncertainty. In practice, this could be achieved using ultrasound imaging of the veins and fluid structure interaction simulations to characterize detailed valve dynamics, respectively.

A 1D pulse wave propagation model of the hemodynamics of calf muscle pump function.

The calf muscle pump is a mechanism which increases venous return and thereby compensates for the fluid shift towards the lower body during standing. During a muscle contraction, the embedded deep veins collapse and venous return increases. In the subsequent relaxation phase, muscle perfusion increases due to increased perfusion pressure, as the proximal venous valves temporarily reduce the distal venous pressure (shielding). The superficial and deep veins are connected via perforators, which contain valves allowing flow in the superficial-to-deep direction. The aim of this study is to investigate and quantify the physiological mechanisms of the calf muscle pump, including the effect of venous valves, hydrostatic pressure, and the superficial venous system. Using a one-dimensional pulse wave propagation model, a muscle contraction is simulated by increasing the extravascular pressure in the deep venous segments. The hemodynamics are studied in three different configurations: a single artery-vein configuration with and without valves and a more detailed configuration including a superficial vein. Proximal venous valves increase effective venous return by 53% by preventing reflux. Furthermore, the proximal valves shielding function increases perfusion following contraction. Finally, the superficial system aids in maintaining the perfusion during the contraction phase and reduces the refilling time by 37%.

Non-invasive estimation of cardiovascular parameters using ballistocardiography.

Ballistocardiography is a non-invasive technique to estimate heart function and relative changes in cardiac output. The goal of this study was to establish the relationship between ballistocardiogram (BCG) parameters and changes in cardiovascular parameters. A group of 20 subjects performed three different exercises on a force plate. In this study, we have characterized the significant differences induced by static and dynamic squats, and controlled respiration exercises on BCG parameters such as IJ-amplitude and RJ-time. The dynamic squat exercise induced the largest changes in IJ-amplitude (107-123% higher) and the RJ-time (21-23% lower). Furthermore, the IJ-amplitude of the BCG signal was found to be positively related to the cardiac output.

Global sensitivity analysis of a wave propagation model for arm arteries.

Wave propagation models of blood flow and blood pressure in arteries play an important role in cardiovascular research. For application of these models in patient-specific simulations a number of model parameters, that are inherently subject to uncertainties, are required. The goal of this study is to identify with a global sensitivity analysis the model parameters that influence the output the most. The improvement of the measurement accuracy of these parameters has largest consequences for the output statistics. A patient specific model is set up for the major arteries of the arm. In a Monte-Carlo study, 10 model parameters and the input blood volume flow (BVF) waveform are varied randomly within their uncertainty ranges over 3000 runs. The sensitivity in the output for each system parameter was evaluated with the linear Pearson and ranked Spearman correlation coefficients. The results show that model parameter and input BVF uncertainties induce large variations in output variables and that most output variables are significantly influenced by more than one system parameter. Overall, the Young's modulus appears to have the largest influence and arterial length the smallest. Only small differences were obtained between Spearman's and Pearson's tests, suggesting that a high monotonic association given by Spearman's test is associated with a high linear corelation between the inputs and output parameters given by Pearson's test.

Estimation of distributed arterial mechanical properties using a wave propagation model in a reverse way.

To estimate arterial stiffness, different methods based either on distensibility, pulse wave velocity or a pressure-velocity loop, have been proposed. These methods can be employed to determine the arterial mechanical properties either locally or globally, e.g. averaged over an entire arterial segment. The aim of this study was to investigate the feasibility of a new method that estimates distributed arterial mechanical properties non-invasively. This new method is based on a wave propagation model and several independent ultrasound and pressure measurements. Model parameters (including arterial mechanical properties) are obtained from a reverse method in which differences between modeling results and measurements are minimized using a fitting procedure based on local sensitivity indices. This study evaluates the differences between in vivo measured and simulated blood pressure and volume flow waveforms at the brachial, radial and ulnar arteries of 6 volunteers. The estimated arterial Young's modulus range from 1.0 to 6.0MPa with an average of (3.8±1.7)MPa at the brachial artery and from 1.2 to 7.8MPa with an average of (4.8±2.2)MPa at the radial artery. A good match between measured and simulated waveforms and the realistic stiffness parameters indicate a good in vivo suitability.

Assessment of blood volume flow in slightly curved arteries from a single velocity profile.

Non-invasive estimation of arterial blood volume flow (BVF) has become a central issue in assessment of cardiovascular risk. Poiseuille and Womersley approaches are commonly used to assess the BVF from centerline velocity, but both methods neglect the influence of curvature. Based on the assumption that the velocity in curved tubes as function of the circumferential position for a given radial position can be approximated by a cosine, the BVF can also be estimated by averaging velocities at opposite radial positions, referred to as the cosine theta model (CTM). This study investigates the accuracy of BVF estimation in slightly curved arteries for BVF waveforms obtained in the brachial artery of 6 volunteers. Computational fluid dynamics simulations were used to compute the influence of curvature on velocity profiles. The BVF was then estimated from the simulation results with the CTM and methods based on Poiseuille, Womersley and using the center stream velocity and the velocity waveform at the position where the maximum velocity is observed, and compared to the prescribed BVF. The simulations show that the influence of curvature is strongest when the flow decelerates. For Poiseuille and Womersley, the time average BVF was underestimated by maximally 10.4% and 7.8% for a radius of curvature of 50 and 100 mm, respectively. The estimation error is lower for the CTM and equals 4.2% and 1.2% for a radius of curvature of 50 and 100mm, respectively. From this study, we can conclude that the velocity waveform at the position of the maximum rather than the center stream velocity waveform combined with the Womersley method should be chosen. The CTM improves current estimation techniques if in-vivo velocity distributions are available.

Model-based assessment of dynamic arterial blood volume flow from ultrasound measurements.

To assess in clinical practice arterial blood volume flow (BVF) from ultrasound measurements, the assumption is commonly made that the velocity profile can be approximated by a quasi-static Poiseuille model. However, pulsatile flow behaviour is more accurately described by a Womersley model. No clinical studies have addressed the consequences on the estimated dynamics of the BVF when Poiseuille rather than Womersley models are used. The aim of this study is to determine the influence of assumed Poiseuille profile instead of Womersley profile on the estimation and intrasubject variability of dynamical parameters of the BVF. For this purpose, a low number of volunteers sufficed. Brachial artery centerline velocity waveform and vessel diameter were measured with ultrasound within a small group of six volunteers. Within subjects, the intra- and inter-registration variability of BVF parameters estimates did not significantly differ. Poiseuille profiles compared to Womersley underestimates the maximum BVF by 19%, the maximum retrograde volume flow by 32% and the rise time by 18%. It can be concluded that when estimating in a straight vessel the dynamic properties of the BVF, Womersley profiles should preferably be chosen.