Personalized biventricular mechanics and sensitivity to model morphology

Figure D.1:. Double hill activation curves over one cardiac cycle for the atria (aLA/RA) and the ventricles (aLV/RV).

Figure E.1:. A: Fiber strain relative to the end-diastolic state (Eff,ED for the personalized 3D-0D BiV model, at three phases during the cardiac cycle. Strain is also plotted on BiV bullseye plots, using a standard 17 segment model for the LV [138] and a 15 segment model for the RV from [139]. B: Transmural variation of Eff and Eff,ED for the LV mid-cavity free wall region, composed of LV segments 10, 11, 12, and 7.

Figure 1:. Graphical abstract. We first develop a personalized model of biventricular (BiV) mechanics. This involves three major steps: 1) collecting patient data, including gated computed tomography angiography (CTA) images, electrocardiogram (ECG), and cuff blood pressure (BP); 2) constructing a multiscale model of BiV mechanics; and 3) personalizing the model to recapitulate the collected patient data. The personalized model is then evaluated in terms of agreement with image data and clinical metrics, as well as tissue stress and fiber strains. In the second part of this study, we compare the personalized BiV model with two simplified geometries: a truncated BiV model (t-BiV) and a left ventricle-only (LV) model, keeping all other model inputs identical. For these models, we also evaluate their sensitivity to plausible variations in boundary conditions and contractile strength. LDRBM: Laplace-Dirichlet Rule-Based method; VMS: variational multiscale; LA: left atrium; RA: right atrium; LV: left ventricle; RV: right ventricle; Sys: systemic, Pul: pulmonary, Art: arterial, Ven: venous.

Figure 2:. Phase-resolved ECG-gated CTA images were obtained at 10 time points over the cardiac cycle. Images are shown in the 4-chamber slice view, defined by a plane containing the apex, mitral valve center, and tricuspid valve center [95]. These images are automatically segmented using a deep-learning method [22] (white boundary in 4-chamber views and transparent 3D models). The method segments the blood pools of the LA, RA, and RV, as well as the myocardium of the LV. The trunks of the aorta and pulmonary arteries are also segmented. RRx% denotes the percentage of the cardiac cycle duration, starting at the R wave on an ECG. RR0% is approximately end-diastole, and RR40% is approximately end-systole.

Figure 3:. A-C: Three anatomical models are considered in this study: biventricle (BiV), biventricle truncated at the basal plane (t-BiV), and left ventricle (LV). The generated longitudinal fiber direction is also shown, colored by the transmural Laplace solution Φepi. D: Volume labels for the BiV mesh (shown here for the RR70% configuration). We partition the complete computational domain Ω into a myocardial domain Ωmyo and a valve ring domain Ωring, where we prescribe different material characteristics. E: Surface labels for the BiV mesh. We partition the complete domain boundary Γ=∂Ω into the epicardium Γepi, LV endocardium Γendo,LV, RV endocardium Γendo,RV, and valve rings Γvalve. We also label the apex Γapex⊂Γepi and generate cap surfaces for the LV and RV endocardia (Γcap,LV and Γcap,RV).

Figure 4:. The image-derived motion of BiV surface mesh over the cardiac cycle, denoted Γimg,RRi, i∈[0,10,…,90]. The deformation is obtained by morphing these models from the RR70% configuration using the motion predicted by MeshDeformNet. The color indicates the magnitude of displacement from the RR70% mesh.

Figure 5:. Multiscale BiV model setup. A: The BiV model is coupled to a closed-loop 0D circulation model (Section 2.3.3). B: A spatially varying Robin boundary condition (BC) is applied on the epicardium to model the mechanical support from the pericardium and surrounding thoracic anatomy (Section 2.3.4). C: An active stress formulation with a double Hill activation function is used to model myocardial contraction (Eq. (15)). Activation timing parameters are obtained directly from the collected ECG data (Appendix D).

Figure 6:. Visualization of various field quantities used to define the spatially varying stiffness for the epicardial Robin BC. A: Long-axis coordinate Ψlong. B: Left-to-right field Φ12r. C: Apicobasal scaling field sab, computed from Ψlong with α=5 and z0=0.7. D: Left-to-right scaling field s12r, computed from Φ12r with λr/l=0.1. E: spatially varying epicardial stiffness kepi, with kepimin=103Pa m−1 and kepimax=107Pam−1.

Figure 7:. The multiscale BiV model is tuned using a multistep personalization procedure. Step 1: We use a full 0D surrogate of the multiscale model (Figure 5A) to efficiently tune key circulation parameters (shown in gold). Step 2: Using the LV and RV diastolic pressure from the tuned full 0D surrogate, as well as image-derived diastolic mesh motion with landmark points (green), an iFEA algorithm is used to estimate the HO constitutive model parameters a, b, af and bf, as well as the reference configuration ΩX [111]. Step 3: To personalize the active myocardial behavior, we evaluate the multiscale BiV model over a range of active stress magnitudes τmax and choose the value that yields the best fit to the clinical data. iFEA: inverse finite element analysis; HO: Holzapfel-Ogden constitutive model

Figure 8:. Details on simulation inputs for models t-BiV and LV models. A: Myofiber directions are generated by interpolating the Laplace-Dirichlet solution fields, then generating fiber directions using the same parameters as for the BiV model (Section 2.2). B: The spatially varying epicardial BC is generated by interpolating the long-axis Ψlong and left-to-right coordinates Φ12r, then generating the spatially varying stiffness profile kepi using the same parameters as for the BiV model (Section 2.3.4). C: The reference configuration is generated by first computing the nodal displacements u from the RR70% configuration to the reference configuration for the BiV model (Section 2.4.2), then interpolating u onto t-BiV and LV models, and finally warping these models by this interpolated displacement field.

Figure 9:. Labeled surfaces on models t-BiV and LV. A: On t-BiV, the truncation introduces an artificial basal plane face Γbase. B: On LV, we divide the epicardial boundary into a septal portion Γepi,septum and a free wall portion Γepi,free.

Figure 10:. Results of the tuned full 0D circulation model. A-B: PV loops for LA, RA, LV, and RV. Colors indicate the phase of the cardiac cycle – atrial contraction (green), isovolumic contraction (yellow), ventricular ejection (red), isovolumic relaxation (purple), and ventricular passive filling (blue). C: (Left) Comparison between simulation outputs (orange) and scalar clinical targets (blue) for the studied patient. Error bars indicate the uncertainty in target patient values. (Right) RMS errors for the chamber volumes represent the average volume error across all imaged cardiac phases (RR0%, . . ., RR90%) and are computed using Eq. (25). V(⋅) quantities in mL and p(⋅) quantities are in mmHg. Percentage values above each bar indicate the percent relative error (Eqs. (23) and (24)).