Updated computer model results (in blue) for the three cases identified with stenosis.

<p>For comparison the results of the geometric uncertainty analysis without stenosis, and the results of Bode et al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0053615#pone.0053615-Bode1" target="_blank">[10]</a> are shown as well. The postoperative US flows are shown in green.</p

Overview of the computer model geometry and element types.

<p>Left: Schematic overview of the upper and lower arm generic geometries, divided into elements for the computer model. Inflow to the circulation was defined by a characteristic flow curve with an average flow of 5100 ml/min. At the end of the venous system (subclavian vein) a pressure of 10 mmHg was prescribed. The right panel shows a legend of the element types in the computer model and their (geometrical) parameters: radius (), wall thickness (), Young's modulus (), area (), length (), windkessel impedance (, calculated from radius), compliance (), and peripheral resistance (). The stenosis element was only used for the cases when the NCE-MRA was studied in detail and a stenosis was present.</p

Examples of patients in the non-overlapping group, who experienced thrombosis.

<p>The left pane shows orthogonal views on the site of interest, while the right pane displays an overlay between blood vessel segmentation (red) and a maximum intensity projection of the original data. (a). Patient #1, who had a mild narrowing (25%, see arrows) in a 5 cm long section of the blood vessel. The radius profile between start and end is given as well, including the start and end marks of the narrowing. (b). Patient #25, showing a 3.5 cm long severe (75%) stenosis, indicated by the white arrows. The yellow arrows indicate locations where no valid diameter measurement could be retrieved. These are also indicated in the graph of the radius. Begin and end of the stenosis region are shown in the radius plot as well.</p

Comparison of postoperative flow measurements (green) with computer model predictions based on geometric uncertainty analysis (orange) and full uncertainty analysis (red, data from Bode et al.

<p><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0053615#pone.0053615-Bode1" target="_blank">[<b>10</b>]</a><b>).</b> The error bars of the computer model indicate the 25th–75th percentile interval, while the error bars for the US flow measurements indicate the flow range that results from assuming a parabolic (lower value) or flat (upper value) velocity profile. Patients #8 and #24 were not simulated, because a non-standard surgical method was used. Patient #15 received a prosthetic PTFE graft, which could not be simulated, and patient #21 experienced thrombosis during surgery, which made postoperative flow results unavailable. Cases for which no overlap exists between the geometric uncertainty intervals of the computer model and postoperative flows are indicated with red circles (6/21). These were used for identification of geometry-related sources of error. (a). Patient #23 with thrombosis reported at one week post-surgery. A relevant section of the upper basilic vein is displayed with a significant (75%) stenosis, indicated by the arrows. (b). Patient #21, who experienced thrombosis during surgery. A relevant section of the lower arm artery (radial) is displayed. Average radius in this section was 0.71 mm, while US reported 1.12 mm. The surgical threshold for lower arm VA creation is at a radius of 1 mm <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0053615#pone.0053615-Tordoir4" target="_blank">[37]</a>.</p

Extraction of subclavian/axillary and brachial artery radius from the original data by three-phase line regression.

<p>The blue stars show the original radius values. Variable is the normalized position along the curve. The governing equations and the constants to be fitted (parameters: , , , and , transition points: and ) are shown as well. The red line demonstrates the result of the three-phase fitting, while the black circles indicate the fitted values at the vessel mapping locations of the US protocol.</p

Left arm vasculature divided into arterial, venous and anastomosis segments (middle).

<p>These segments locally describe the relation between pressure <i>p</i> and flow <i>q</i> via a lumped parameter approach (right), and consists of a resistor <i>R</i> (viscous resistance to blood flow), a resistor <i>R_L</i> (viscous resistance of blood flow to small side-branches), an inductor L (blood inertia) and a capacitor <i>C</i> (vascular compliance). The anastomosis is modeled with two nonlinear resistors <i>R_v</i> and <i>R_d</i>. The windkessels consist of two resistors, <i>Z_wk and R_wk</i> (together the peripheral resistance) and a capacitor C_wk (peripheral compliance). This figure is adapted from Huberts et al.</p

Patient-specific measurements performed in the context of the study.

<p>Patient-specific measurements performed in the context of the study.</p

The names of all vessels included in the computational domains.

<p>The names of all vessels included in the computational domains.</p

The predicted postoperative flows for a RCAVF, BCAVF and BBAVF configuration.

<p>The flows are presented as the median of all Monte Carlo simulations with their 25^th and 75^th percentile interval. In 4 patients postoperative brachial artery flow could not be simulated for all three AVF configurations because essential patient-specific data were missing due to thrombosis of the cephalic vein (patient #19, #23, and #25) or because the computations did not converge for all Monte Carlo simulations (patient #24). An asterix represents the fistula configuration chosen by the surgeon.</p

Schematic picture of the locations of the diameter measurements in the preoperative DUS examination (left).

<p>At the right a schematic picture of the postoperative flow determination is presented.</p