Computational Modeling of Canine Ventricular Fiber Orientation

The LDRB algorithm was tested in a MRI-based computational model of the structurally normal canine ventricles. The geometry and DTI-derived fiber orientation of the model were constructed using the methods of Vadakkumpadan et al.^{34 (link)} applied to MRI and DTI data collected by Helm et al.^{16 (link)} To generate the same model but with LDRB fiber orientation, the input functions in Eqs. (1)–(4) were optimized so that the mean angle between the LDRB and DTI-derived fiber orientations was minimal. The optimal values for the input parameters α_endo, α_epi, β_endo and β_epi of the LDRB algorithm were determined by varying each parameter in the range of ±90° in intervals of 5°, then choosing the parameter combination that produced the smallest mean angle (θ_mean) between the LDRB and DTI vectors (F  S  T) calculated over the total number of elements in Ω(N_elem). Since fiber orientation is bi-directional, θ_mean was calculated as
$${\theta }_{\text{mean}}({\overrightarrow{x}}_i)=\frac{1}{N_{\text{elem}}}\ast {\displaystyle \sum _{i=0}^{N_{\text{elem}}}}{\text{cos}}^{-1}\left(\right|\frac{{\overrightarrow{x}}_i^{\text{LDRB}}·{\overrightarrow{x}}_i^{\text{DTI}}}{\Vert {\overrightarrow{x}}_i^{\text{LDRB}}\Vert \Vert {\overrightarrow{x}}_i^{\text{DTI}}\Vert }\left|\right),$$
$$\overrightarrow{x}=[F,S,T]$$
Membrane kinetics in this model of the canine ventricles were described by the Greenstein–Winslow myocyte model.^{12 (link)} Orthotropic tissue conductivities of 0.5 (S/m) along F, 0.3 (S/m) along T, and 0.16 (S/m) along S were assigned to produce conduction velocities within the range of 20–80 cm/s as observed in experiments.^{8 (link)} Monodomain simulations were performed with the model of the canine ventricles using the Cardiac Arrhythmia Research Package^{37 (link)} (CardioSolv LLC) running on 16 compute nodes, each with four Dual Core AMD Opteron processors (Model 2222) and 8GB of memory. All simulations were executed with a 10 µs time step.