Parameter subset reduction for patient-specific modelling of arrhythmogenic cardiomyopathy-related mutation carriers in the CircAdapt model

Abstract

Arrhythmogenic cardiomyopathy (AC) is an inherited cardiac disease, clinically characterized by life-threatening ventricular arrhythmias and progressive cardiac dysfunction. Patient-specific computational models could help understand the disease progression and may help in clinical decision-making. We propose an inverse modelling approach using the CircAdapt model to estimate patient-specific regional abnormalities in tissue properties in AC subjects. However, the number of parameters (n = 110) and their complex interactions make personalized parameter estimation challenging. The goal of this study is to develop a framework for parameter reduction and estimation combining Morris screening, quasi-Monte Carlo (qMC) simulations and particle swarm optimization (PSO). This framework identifies the best subset of tissue properties based on clinical measurements allowing patient-specific identification of right ventricular tissue abnormalities. We applied this framework on 15 AC genotype-positive subjects with varying degrees of myocardial disease. Cohort studies have shown that atypical regional right ventricular (RV) deformation patterns reveal an early-stage AC disease. The CircAdapt model of cardiovascular mechanics and haemodynamics has already demonstrated its ability to capture typical deformation patterns of AC subjects. We, therefore, use clinically measured cardiac deformation patterns to estimate model parameters describing myocardial disease substrates underlying these AC-related RV deformation abnormalities. Morris screening reduced the subset to 48 parameters. qMC and PSO further reduced the subset to a final selection of 16 parameters, including regional tissue contractility, passive stiffness, activation delay and wall reference area. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Keywords: CircAdapt; Morris screening method; arrhythmogenic cardiomyopathy; parameter subset reduction; particle swarm optimization; quasi-Monte Carlo.

Figure 1.

Visualization of the two-step approach. In the first step, sensitivity analysis (SA) is performed using the MSM, which is applied iteratively on the CircAdapt model. Based on the elementary effect, a parameter selection is done. The final SA subset is used in qMC. Using the best estimations for each patient from qMC as a starting point, PSO is applied. Based on PSO results, the previous reduction is validated. Using the diaphony, the subset is further reduced. (Online version in colour.)

Figure 2.

(a) Strain indices for one strain curve as used in the MSM. The same indices are included for the three RVfw segments, as well the LVfw and IVS segment. The indices are time to 10%, 50% and 90% shortening (1,2,3), pre-stretch (4), systolic strain (5), post-systolic strain (6) and peak strain (7). The verticle dashed line indicates closure of the pulmonary valve. (b) An area is used to calculate the fit error. The area is defined from onset of QRS to 50% relaxation (the white dot with the vertical line) of the global RVfw strain (thick dashed line) and is calculated for all three RVfw segments, as well the LVfw and IVS segment. For the actual fit error, the area for all three RVfw segments, LVfw segment and IVS segment is included. (Online version in colour.)

Figure 3.

Minimum summed squared error (E_ss) after qMC (a) and after PSO (b) of the subsets, where parX indicates the number of parameters included. Green lines indicate subjects in the concealed stage, the light and dark red lines indicate subjects in the electrical and structural stage. Black–white lines show the average summed squared error of all subjects including standard deviation. (Online version in colour.)

Figure 4.

Example fits from PSO of par53 (left), par23 (middle) and par16 (right) of the best fit ((a); subject 12) and worst fit ((b); subject 14) of subjects with abnormal strain. For subject 12, the summed squared error was 8.2, 13 and 17 for par53, par23 and par16, respectively. For subject 14, the summed squared error was 14, 30 and 37, respectively. (Online version in colour.)

Figure 5.

Normalized estimations resulting from qMC and PSO of subject 12 (a) and subject 14 (b) of the subset with 53, 26, 23 and 16 parameters (par53, par26, par23 and par16, respectively). Included parameters are indicated by the yellow bars. The best 100 simulations from qMC are shown in grey, the global optimum from PSO is shown in the thick black–white line. (Online version in colour.)