A fast strong coupling algorithm for the partitioned fluid–structure interaction simulation of BMHVs

The numerical simulation of Bileaflet Mechanical Heart Valves (BMHVs) has gained strong interest in the last years, as a design and optimisation tool. In this paper, a strong coupling algorithm for the partitioned fluidstructure interaction simulation of a BMHV is presented. The convergence of the coupling iterations between the flow solver and the leaflet motion solver is accelerated by using the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet accelerations. This Jacobian is numerically calculated from the coupling iterations. An error analysis is done to derive a criterion for the selection of useable coupling iterations. The algorithm is successfully tested for two 3D cases of a BMHV and a comparison is made with existing coupling schemes. It is observed that the developed coupling scheme outperforms these existing schemes in needed coupling iterations per time step and CPU time

A strong FSI coupling scheme for simulating BMHV dynamics: study of wall shear stress on the valve leaflets

One of the major challenges in the design of Bileaflet Mechanical Heart Valves (BMHVs) is reduction of the blood damage generated by non-physiological blood flow. Numerical simulations provide relevant insights into the (fluid) dynamics of the BMHV and are used for design optimization. In this paper, a strong coupling algorithm for the partitioned fluid-structure interaction (FSI) simulation of a BMHV is presented. The convergence of the coupling iterations between the flow solver and the leaflet motion solver is accelerated by using a numerically calculated Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet accelerations. The developed algorithm is used to simulate the dynamics of a 3D BMHV in three different geometries, allowing an analysis of the solution process. Moreover, the leaflet kinematics and the general flow field are discussed, with special focus on the shear stresses on the valve leaflets

Serum BAFF levels during follow-up in the KTS-1-2008 and KTS-2-2010 trials.

<p>Panel A: Serum BAFF levels at baseline and at 3, 6, and 8-months follow-up in the placebo arm of the KTS-1-2008 trial, relative to baseline levels (n = 13). Panel B: Serum BAFF levels at baseline, and at 3, 6, and 8-months follow-up in the rituximab arm of the randomized KTS-1-2008 trial, relative to baseline levels (n = 14). Panel C: Serum BAFF levels at baseline and at 3, 6, and 10-months follow-up in the open-label KTS-2-2010 rituximab maintenance trial, relative to baseline levels (n = 22). Panel D: Serum APRIL levels at baseline, and at 3 and 8-months follow-up in the placebo arm of the KTS-1-2008 trial, relative to baseline levels (n = 12). Panel E: Serum APRIL levels at baseline, and at 3 and 8-months follow-up in the rituximab arm of the KTS-1-2008 trial, relative to baseline levels (n = 13). P-values from Repeated measures One-way ANOVA with Dunnett’s test for adjusted p-values for individual comparisons of the different time points to baseline. Error bars denote mean and 95% CI.</p

Serum BAFF levels at baseline.

<p>Panel A: Baseline serum BAFF levels (pg/mL) in 70 ME/CFS patients and in 56 healthy controls. Serum samples before treatment in the KTS-1-2008 and KTS-2-2010 trials (n = 38), and in addition 32 samples from ME/CFS patients fulfilling Canadian diagnostic criteria, were included. Panel B: Baseline APRIL serum concentrations (ng/mL), in ME/CFS patients included in KTS-1-2008 study (n = 28) and in healthy controls (n = 22). P-values from unpaired t-test (equal variances not assumed). Error bars denote mean and 95% confidence intervals (CI).</p

Lymphocyte subsets during follow-up in the KTS-1-2008 and KTS-2-2010 trials.

<p>Panels A-D: Lymphocyte subsets among patients included in the randomized KTS-1-2008 study, in the rituximab group (red) and the placebo group (black), determined by flowcytometry and shown as million cells per liter at baseline (0 months), and at 1, 2, 3, 4, 6, 8, 10, and 12 months follow-up (n = 30). Panel A: CD3+ T-cells, panel B: CD4+ T helper cells, panel C: CD8+ cytotoxic T-cells, panel D: CD56+/16+ NK-cells. For 29 patients, data on lymphocyte populations were missing for 16 out of 261 (6.1%) time points. For General linear model (GLM) for repeated measures these were replaced by interpolation between preceding and succeeding values. The missing values were not replaced in the plots. Panels E-J: T-cell activation markers among patients included in the KTS-1-2008 trial, at baseline and through 12-months follow-up, and shown as percentage of the CD4+ T helper cell population, as determined by flowcytometry. Panel E: Regulatory T-cells, panel F: CD69+ cells, panel G: CD154+ cells, panel H: CD278+ (ICOS) cells, panel I: HLA-DR+ cells. Panel J shows the percentage of HLA-DR+ cells among the CD8+ cytotoxic T-cells. For 29 patients, data on T-regulatory cells and T-cell activation parameters were missing for 30 out of 261 (11.5%) time points. For GLM, missing values were replaced by interpolation between the preceding and succeeding analyses (not replaced in the plots). Panels K-O: Lymphocyte subsets among patients in the KTS-2-2010 study receiving rituximab maintenance therapy, determined by flowcytometry and shown as million cells per liter at baseline (0 months), and 3, 6, 12, 15, 20, and 24-months follow-up. Responders to B-cell depletion therapy are shown in red and non-responders in blue. Panel K: Ratio of CD4+/CD8+ T-cells, panel L: CD3+T- cells, panel M: CD4+ T helper cells, panel N: CD8+ cytotoxic T-cells, panel O: CD56/16+ NK-cells. In three patients, data on lymphocyte subpopulations for at least three time points were missing, these three were omitted leaving 23 patients for GLM analyses to assess the interaction between time and response group. In these 23 patients, 15/161 (9.3%) data were missing; these were replaced by interpolation between preceding and succeeding values (not replaced in the plots). Analyses for interaction between time and intervention group, i.e. assessing for difference in course of the variables over time, between the rituximab and placebo groups (panels A-J), or between responders and nonresponders to rituximab maintenance treatment (panels K-O), were performed using GLM for repeated measures. Error bars denote 95% confidence intervals (CI) for the mean values. The dotted lines indicate lower and upper normal reference values as established at Haukeland University Hospital.</p

Serum immunoglobulin levels during 24-months follow-up, in KTS-2-2010 trial.

<p>Immunoglobulin levels in serum during 24 months follow-up, for patients included in the KTS-2-2010 trial with rituximab maintenance therapy, and shown as grams per liter (g/L). In panels A, B and C are shown serum levels for IgG, IgA, and IgM, respectively, with corresponding values at baseline and at 24-months, for each of 23 patients included in KTS-2-2010. P-values from paired t-tests. Panel D: Baseline levels of serum IgG (g/L), shown for patients with subsequent clinical response to B-cell depletion therapy during follow-up, or patients with no response. P-value from unpaired Mann-Whitney U test. The dotted lines indicate normal reference values as established by Haukeland University Hospital.</p