Fig 1.
A A cohort of 10 LA meshes with epicardial adipose tissue (EAT) was generated from the end-diastolic (ED) frame of a gated contrast-enhanced CT image-set. B Using image registration, the ED LA mesh was deformed over cardiac cycle, with maximum deformation at end-systolic (ES). Plots show the endocardial volume and surface displacement transients derived from feature tracking motion models. C The loading conditions applied in our LA modelling framework and the simulation set-up with boundary conditions applied. A estimated pressure profile was applied to LA endocardium. Patient-specific image-derived mitral valve (MV) displacement was applied to the MV annulus in simulation model. D Description of how Gaussian process emulators (GPEs) were used to speed up computation time. E-G Summary of the fitting methods used in this study.
Table 1.
Simulator input parameters with the input ranges explored during our analysis.
Table 2.
Patient cohort demographics.
Fig 2.
Images show the anterior view of the cohort of 10 meshes generated using the pipeline described in Methods. * indicates patients with AF.
Fig 3.
Regional heterogeneity in LA displacement.
Plots show regional endocardial surface displacements transients derived from the feature tracking motion models for a representative case (A) and the distribution of the regional ES displacements across the cohort (B). Each marker symbol corresponds to one of the 10 patients. Significance was determined using a paired t-test with the Bonferroni correction for multiple comparisons applied. *** indicates a p-value < 0.001. **** indicates a p-value < 0.0001.
Fig 4.
Effect of anatomical features on observed LA displacement.
Plots show how regional averages of end-systolic (ES) displacement vary with regionally averaged LA wall thickness (A) and regional EAT volume (B). Each marker symbol corresponds to one of the 10 patients.
Fig 5.
Global sensitivity analysis results.
A Heatmap of the total effect of the parameters (x-axis) on the outputs (y-axis). B Barplot of the maximum total effect of each parameter over all outputs. The parameters are ranked from most to least important. The coloured bars represent the total sensitivity up to 90%.
Fig 6.
The panels show the global and regional displacements as well as the volumes obtained from the initial simulator dataset. The dashed black line indicates the LA behaviour derived from the CT image set. The solid circles indicate the time of ventricular end-systole (ES). The LA reservoir, conduit and booster pump phases were identified from the volume transient. Our simulations focused on passive LA function, hence only the reservoir and conduit phase were simulated.
Fig 7.
(A) High-dimensional input parameter space reduction during HM. (B) Changes in the simulator outputs for each wave of history matching. The solid horizontal lines indicate the value of the output feature at ventricular end-systole (ES) estimated from the CT images. The shaded areas a represent 95% confidence interval on the observed output feature values. For dregion, the standard deviation is estimated from feature tracking and for ESV, the standard deviation is assumed to be ±5% EDV.
Fig 8.
Plots showing the parameter distributions for a representative patient estimated using MCMC. Each tile represents a projection of the Markov chain samples. We implemented an ensemble sampler of 18 parallel walkers of 100 000 steps. A burn-in period of 10 000 steps and a thinning frequency of 10 was used. For each parameter, the MAP estimate is indicated by the blue line. The histograms along the diagonal display the posterior distributions for each parameter individually. The off-diagonal panels show the 2D distributions as contour plots where the contours are drawn at levels containing 11.8%, 39.3%, 67.5% and 86.4% of the samples.
Fig 9.
The panels show the global and regional displacements as well as the volumes obtained when the simulator was evaluated using the MAP dataset. The dashed black line indicates the LA behaviour derived from the CT image set and the shaded box represents 95% confidence interval on the target value.
Fig 10.
Regionally calibrated stiffness parameters.
(A) Box plots showing the distribution of calibrated stiffness parameters per region across the 10-patient cohort. Each marker symbol corresponds to one of the 10 patients. (B) Plots show how regional averages of end-systolic (ES) displacement vary with regional stiffness.
Table 3.
Summary of verification study results for input parameters.
The table lists each simulator input parameter with its target value and the corresponding uncertainty and accuracy metrics under two observation noise scenarios: baseline noise and high noise. For each noise condition, we report the 95% confidence interval (CI) of the posterior distribution, whether the target value lies within this interval, and the distance of the MAP estimate from the target.
Fig 11.
MCMC calibration using synthetic data for case 01.
The MAP estimates returned by MCMC at the lowest and higest level of noise are indicated by the purple and blues lines respectively. The target input values are shown in black. The histograms along the diagonal display the posterior distributions for each parameter individually. The off-diagonal panels show the 2D distributions as contour plots where the contours are drawn at levels containing 11.8%, 39.3%, 67.5% and 86.4% of the samples.
Fig 12.
The panels show the global and regional displacements as well as the volumes obtained when the simulator was evaluated using the MAP estimate derived from three model set-ups: (i) model includes patient-specific LA wall thickness and regionally varying stiffness parameters; (ii) model includes patient-specific LA wall thickness and a single global stiffness parameter; (iii) model includes uniform LA wall thickness and regionally varying stiffness parameters. The dashed black line indicates the LA behaviour derived from the CT image set and the shaded box represents 95% confidence interval on the target value.