Table 1.

List of conduction velocity techniques and their advantages and disadvantages. Suitability of the methods to different data modalities and any restrictions on the type of data are also noted.

Method	Advantages	Disadvantages	Suitability and requirements
Triangulation [4,62,100–102]	Local score, examine regional heterogeneities, any arrangement of points, uses actual LATs	Sensitive to error in LAT, difficult to automate	Clinical,$3\ge d\ge 20\mathrm{mm}$, LAT differences $>3$ ms
Finite difference [42,40]	Local score, examine regional heterogeneities, easy to implement, uses actual LATs	Sensitive to noise / missing data, Fails if times are identical, Requires regular grid	Optical mapping, Multielectrode arrays, 4 points, sufficient temporal resolution to avoid adjacent equal activation times
Polynomial surface [1,2,85,106,40]	Any arrangement of points, robust to noise, allows missing data points, residual to assess quality of fit	May require more points than available, requires choice of $\mathrm{\Delta }X,\mathrm{\Delta }T$	Optical mapping, Multielectrode arrays, 3D: linear (4 points), quadratic (10 points), cubic (20 points), more points needed for complicated rhythms
Cosine-fit [82,108,83,109]	Measure of curvature and distance to focal source, any arrangement of points, robust to noise, residual to assess quality of fit	Single macroscopic wavefront only, one vector per catheter	Clinical, no colliding wavefronts
Vector loops [3,110,111]	Does not require LAT assignment	Requires specific catheter	Clinical, 2 orthogonal pairs of bipoles
Radial basis [112,114]	Multiple wavefronts, use to find LATs anywhere on surface, no assumption on arrangement and spacing, high res. velocity field (div, curl)	Computationally demanding	Clinical, any arrangement
Isopotential lines [116]	Accurate wavefront curvature estimation, robust to spatial noise	Requires measurements of membrane potential, requires high resolution, LATs do not always coincide with isopotential lines	Optical mapping, high resolution
Arbitrary scalar fields [117]	Extends CV calculation from isopotential lines to use other variables	Requires measurement of another scalar field	Scalar field (e.g. activation time, electrical potential, phase)
Time delays [86]	Uses neighbouring location information, can deal with incorrect LATs, local score, Any arrangement of points	Assumption of plane wave locally	Clinical
Analytic expressions [118]	Velocity and curvature from 4/5 points, low density data, simple to apply	Points must lie on a square, radius of curvature must be large, requires accurate LATs	Optical mapping, multielectrode arrays, points on a square
Maximum likelihood [119]	Statistical approach, tolerant of LAT measurement errors	Requires grid of recording points	Multielectrode arrays, equally spaced grid of points