Uncertainty Quantification of Cardiac Properties | 87 defined from the onset of the QRS complex until 100ms after peak strain of the segment with longest shortening phase. To account for dependencies in strain, we included weighted dimensionless errors based on strain (e2 ϵ, seg)), strain rate (e 2 ˙ϵ, seg)), and inter-segmental strain differences (e 2 Δϵinter). Errors in EF (e2 EF), EDV (e 2 EDV) and RVD (e 2 RVD) were assumed independent, resulting in the Χ2 to be the sum of all individual weighted dimensionless errors e2: Χ2 = ∑ seg∈segments (e2 ϵ, seg +e 2 ˙ϵ, seg)+ ∑ inter∈interseg e2 Δϵinter + ∑ m∈(EF, EDV, RVD) e2 m . (7) Standard deviations used to normalize each individual term were manually estimated a priori to meet differences between the inter- and intraobserver datasets. Standard deviations used to normalize EF, EDV, and RVD were set a priori in consultation with clinical partners. RV tissue properties To relate our simulations to clinical measures, four RV tissue properties were investigated, namely contractility, activation delay, compliance, and myocardial work. Segmental contractility was defined as the maximum rate of active stress rise, which can be seen as the equivalent of the maximum rate of ventricular systolic pressure rise (dP/dtmax) on a local tissue level. Segmental wall compliance was defined as the slope of the end-diastolic myofibre stress-strain relationship at time before first ventricular activation and can be interpreted as the regional equivalent of the slope of the global end-diastolic pressure-volume relation. Myocardial work density was defined as the area within the stress-strain loop and can be interpreted as the regional equivalent of global stroke work. Simulation protocol Uncertainty Quantification of Real Patient datasets Nine clinical datasets in which the echocardiographic images were analysed twice by two independent observers were included to test reproducibility, leading to 36 datasets. For each individual dataset, parameters were estimated three times resulting in 108 estimations in total. Since no ground truth exists for estimated model parameters, only the reproducibility of estimations was evaluated. Three kinds of reproducibility were investigated, namely computational reproducibility, reproducibility including interobserver variability, and reproducibility including intraobserver variability. First, computational reproducibility was defined as the reproducibility of the exact same clinical dataset and quantified by the mutual information (MI) between two model parameter estimations. The same protocol was repeated three times with a different random seed. To calculate the MI, two distributions were discretized into 100 bins. The MI was then defined as the overlap divided by the union of the distributions. Secondly, reproducibility including interobserver variability was tested on the nine patient datasets, whereby a second blinded observer performed deformation imaging analysis on the same echocardiographic loops as the first observer. It was defined as MI between two estimated model parameter distributions from two datasets observed by the two different observers. Finally, reproducibility including intraobserver variability was quantified similarly from two different datasets, whereby the observer performed the deformation analysis again after at least two weeks, blinded to previous results. The median MI with 95% confidence interval (CI) 5
RkJQdWJsaXNoZXIy MTk4NDMw