Excitation wave propagation within narrow pathways: Geometric configurations facilitating unidirectional block and reentry

Model of reentrant ventricular tachycardia based on infarct border zone geometry predicts reentrant circuit features as determined by activation mapping

“…Near the isthmus entrance, the wavefront is concave [16][17][18] in the XY plane due to convergence of the two bifurcated portions of the double-loop wavefront (denoted as transparent sheets labeled 1-3). Concave curvature also occurs along the thickness axis (Z-axis) due to diminishing IBZ thickness during propagation toward the plateau (wavefronts A-C).…”

“…Previous studies have also suggested the important role of geometrical variations and structural discontinuities on wavefront propagation and on the constancy of reentrant circuit location during ventricular tachycardia [16][17][18]22,[27][28] . The combined effect of all factors on reentrant ventricular tachycardia conduction: geometry, ionic and gap junctional properties, and anisotropy, can be determined using a heterogeneous ion channel bidomain model 25 .…”

“…We would expect anisotropy to increase the probability of longitudinal isthmus alignment because the higher resistance of ~1kΩcm 24 that would be encountered laterally as the wavefront expands in the XY direction at an isthmus entrance or exit point would lessen the overall impedance mismatch and thereby increase the likelihood of propagation [16][17][18] . We would anticipate a decreased probability of transverse isthmus alignment due to the lowered resistance of ~500Ωcm 24 encountered laterally at entrance-exit points, thus increasing the overall impedance mismatch and the likelihood of block [16][17][18] . For this reason, we would anticipate that transverse alignment would only be supported when the isthmus is wide with gradual thickness change at entrance-exit points so that three-dimensional convex wavefront curvature is reduced, the subject of future research.…”

A mathematical model of the unidirectional block caused by the pulmonary veins for anatomically induced atrial reentry

“…With the microscopic causes of reentry being recapitulated at a macroscopic level, most causes of PV re-entry can be translated as the macroscopic components of the reentry mechanism, known as the leading-circle model, as empirically first observed in the early 1900s by MacWilliam [18], Mayer [19] and Mines [20] and developed furthermore since then [3,[21][22][23]. As illustrated in Fig.…”

“…In eikonal Eq. (22), being originally derived in π e , we extend the curved surface π e in the neighborhood of each point in the following way: consider a curved surface as a two-dimensional submanifold embedded in three-dimensional Euclidean space z i . The function ψ(y 1 , y 2 ) can be extended to a function ψ(z 1 , z 2 , z 3 ) in a tubular neighborhood of the surface where the directional derivative of ψ along the surface normal is zero.…”