Two-stage Purkinje network
We herein focus on the Purkinje network model proposed by Costabal et al. (23), which is generated by a fractal tree algorithm and was used to produce the LHHM Purkinje network. Its python code is freely available at https://github.com/fsahli/fractal-tree. The algorithm works by taking as input the model endocardium object, the coordinates of the Purkinje node of origin on the ventricular endocardium and the direction of propagation. Unique line elements are then automatically generated in an iterative tree branch-like pattern that are projected on the endocardium surface. The length, angle and curvature of the line elements are controllable. The complexity and superiority of this algorithm lies in its ability to project the network nodes on the irregular endocardium surface, including the protruding papillary muscles. The irregularities of the ventricular surface and the fact that the papillary muscles are known to be covered in Purkinje fibers have usually been overlooked by typical cardiac models unable to capture such complexity.
Even though there exists a notable level of variability from person to person in electrical activation sequences, experimental studies have highlighted certain similarities across human datasets. These studies include ex-vivo microelectrode recordings (27), in-vivo electromechanical wave imaging (28) and non-invasive electrocardiographic imaging (29). Based on these studies, Cardone-Noott, et al. (25) identified 7 root points in the ventricles from which excitation propagates; 4 in the left ventricle and 3 in the right ventricle. They tested the effect of the activation map on their heart-torso model ECGs by assuming the sites of earliest conduction to be the Purkinje-muscle junction sites and stimulating the endocardium there. Further configurations were done by varying passive tissue conductivities and tissue activation speed.
In this work we set off to take advantage of the LHHM and generate a Purkinje network with the primary aim of reproducing clinical ECGs of a healthy heart. The endocardium structure of the LHHM ventricles was extracted for use in the Purkinje generation. For each of the ventricles, we modified the Costabal et al. (23) fractal tree algorithm to generate a network that primarily ties to the endocardium at the root points of early activation before spreading to the remaining ventricular tissue. This was done for each ventricle by generating Purkinje fiber networks of limited size on the endocardium at these early activation sites indicated on Figure 1(a). We will refer to these disconnected Purkinje branches as stage 1. Stage 2 of the network was generated from the end of a single stage 1 branch in each ventricle to cover the remaining endocardium. It is possible to generate stage 2 from the end of each (rather than a single) stage 1 site but was deemed unnecessary to reach our objective of reproducing physiologically plausible ECGs. Through several trials and adjustments, the fractal tree algorithm parameters we used were a branch length of 6 mm, a branch angle of 0.3 rad, and a repulsion parameter of 0.1. The generated networks in the left and right ventricles shown in Figure 1(b) are then linked through the bundle of HIS which is directly connected to each branch in stage 1. The excitation of the atrioventricular (AV) node will thus travel through the bundle of HIS to activate the ventricular endocardium under the stage 1 branches, before propagating onward to the remaining tissue.
Integration into LHHM electrophysiology model
A major drawback to the pseudo-ECGs produced from the out-of-the-box (control) LHHM was an inverted T-wave that manifested in all six precordial leads. Since differences in repolarization across different regions of the ventricles are what contribute to the shape of the T-wave (30), changes in the repolarization rate of the Purkinje fibers translate to changes in the T-wave amplitude and direction. By reducing the refractoriness parameter, and in turn the repolarization, of the Purkinje fibers, the T-wave direction was corrected on the pseudo-ECGs of the precordial leads. This reduction is physiologically motivated by a closer inspection of the action potentials of the Purkinje fibers and the ventricular muscle in the control LHHM. By default, the ventricular muscle had been assigned a lower rate of repolarization than that of the Purkinje, when in fact the Purkinje fibers should have the lower rate of repolarization (31). A reduction we implemented to the refractoriness of the Purkinje fibers was thus only to correct their relative action potential durations (32), which resulted in the organ-level consequence of a corrected T-wave.
After adjusting the action potentials, our connected two-stage Purkinje network was then imported and integrated into the LHHM, as a replacement of the original Purkinje network. For the coupling between the Purkinje network and the ventricular myocardium to take effect, a node-to-node tie-condition (33) that connects the Purkinje line elements to the endocardial surfaces was implemented. The electric cardiac cycle was lastly adjusted from 500ms to 600ms to produce a pseudo-ECG more comparable to clinical ECGs than those of the control. The LHHM electric simulation was then run using the all other parameters and conditions as those of the control.
The out-of-the-box LHHM does not have a built-in method to generate pseudo-ECGs, which are approximations to the signal propagating off a patient’s body surface as a result of changing cardiac electrical potential. An actual ECG signal would be recorded via electrodes placed at specified distances from the heart, and would differ from one person to another. For an in-silico model of the heart that does not include the surrounding body, only approximate ECGs can be constructed, viz. a pseudo-ECG. Figure 2 marks approximate positions for six precordial leads, which we use to record the pseudo-ECG signals of our model, i.e. V1, V2, V3, V4, V5 and V6 (34), which are located where actual precordial leads would be anticipated.
We then utilize an open source software library, Chaste (Cancer, Heart and Soft Tissue Environment), which contains a broad set of numerical solvers and algorithms focused on biological modeling.(35) One such solver is its pseudo-ECG calculator which, by mean of Equation 1, calculates the extracellular potential Φe anticipated at electrode position ( x', y', z').
In Equation 1, is the diffusion coefficient, is the transmembrane potential and is the distance between the electrode and a point within the heart tissue, and integration is performed over the myocardial volume.(36) Hence, given the electrophysiological results produced by the LHHM solver, activation time maps can be generated and converted to an HDF5 file that are read by Chaste’s pseudo-ECG calculator. Moreover, the full mesh of the model is provided to Chaste in the form of an element file, a node file, and a face file, to complete the pseudo-ECG calculation.