Page 118 - PRECONGRESS COURSE 01

Fractal Analysis of Sperm Trajectories
The fractal dimension (D):
Fractional dimension ‐ describes amount of space a line occupies on a plane1:
D = 1.0 for a straight line
D approaches 2 for a meandering line D can exceed 2 for a recursive line2
Calculation of D for sperm tracks2,3:
D = 1.12
D=
HA: D > 1.30, non‐HA: D < 1.20 (30 Hz and 60 Hz)3
D = 1.47
log (n) n = # track intervals
(log n) + log (d/L) d = max distance from origin
L = sum of all interval distances
1 Mandelbrot, The Fractal Geometry of Nature, 1977. 2 Katz and George, Bull Math Biol 47: 273, 1985
3 Mortimer et al, Hum Reprod 11: 1049, 1996
D = 2.45
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Hyperactivation assessment using D
 6240 tracks, each 1s @ 60Hz (IVOS II)
 SORT: VCL ≥ 150μm/s AND LIN ≤ 50% AND ALH ≥ 7μm  VCL&D = VCL ≥ 150μm/s AND D ≥ 1.20
100%
50%
0%
No agreement Both "not HA" Both "HA"
SORT vs D>1.30
SORT vs D>1.20
SORT vs VCL&D
Track Classification Criteria
Mortimer et al, Asian J Androl 17: 545, 2015
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Proportion