Algorithms of the calculation for Conduction velocity
The calculation for the conduction velocity can be selected at [View]-[Display Window for PeakTime Vector] on the main menu of BV_Analyzer, and the algorithms are described below. In general, the conduction velocity is calculated and displayed after some processing; the first derivative, the detection of activation time point (PeakTime), the calculation of conduction velocity vector on all directions on each pixel, the calculation of synthesized vector oneach pixel, the display of the conduction velocity vectors.
(1) The detection of the peak time
The
peak time point of each pixel can be detected as the frame number, after the
set of the frame range at [Start] & [End] in [Time & Movie Control] on
[Control] tab page. The PeakTime is set as Tpk (x,
y). The maximum negative value in
the set range is detected as PeakTime because BV_Analyzer inverts the wave display in default setting,
and the polarity of real data value is inverted.
(2)
The
calculation of a vector
The
all basic vectors in four directions on each pixel (V1, V2, V3 and V4) are
calculated.
V1 = Tpk(x,y-1) - Tpk(x,y+1)
V2 = Tpk(x+1,y) - Tpk(x-1,y)
V3 = Tpk(x+1,y-1) - Tpk(x-1,y+1)
V4 = Tpk(x+1,y+1) - Tpk(x-1,y-1)
(3) The synthesis of vectors
The
conduction velocity is calculated from V1, V2, V3 and V4. The zero angles is
on right direction on x axis. The angle is set as Ang(x,
y) and the speed is set as VV(x, y).
Vx = V1 + V3/√2 +V4/√2
Vy = V2 + V3/√2 -V4/√2
VV = √（ Vx*Vx + Vy*Vy
)
Ang=
asin(VyVV)
(4) The display of the conduction velocity
(vectors)
Ang(x, y) and VV(x, y) are shown on the background
image. The arrows are colored in
four colors according to those direction so that the
direction of arrows can be recognized easily.
0 - 90’ : Green
90-180’ : Yellow
0 - ( -90’) : Blue
(-90) -( -180’) : Red
・The set
of activation time point on the peak, or
on 50% of amplitude of upstroke of the wave
When
[Peak] is selected, the peak time point on each pixel is set as the activation
time point. When [50% of Min-Max] is selected, the minimum
and maximum values in the set range are detected, and the 50% point is set as Tpk(x, y).
・Zooming
of Image
The
size of image can be set on 3X, 5X, or 7X.
・Length of
vector
[Length] sets the maximum length of vectors on the image.
・Interval
of vector
[Space] sets the interval between vectors.
When the number is “1”, vectors on all pixels are displayed.
・Threshold
of vector display
[Threshold] may reduce the noise of vectors. The peak value under the threshold is
ignored as “0”. Be careful that
this threshold is connected to [Gain] on [Control] tab page. Dpk(x, y) is
difference value from reference value of the activation time point.
V1 = Tpk(x,y-1) - Tpk(x,y+1)
If Dpk(x, y-1) or Dpk(x, y+1) is less than
Threshold, V1=0
V2 = Tpk(x+1,y)
- Tpk(x-1,y)
If Dpk(x+1, y)
or Dpk(x-1, y) is less than Threshold, V2=0
V3 = Tpk(x+1,y-1)
- Tpk(x-1,y+1)
if Dpk(x+1, y-1) or Dpk(x-1,
y+1) is less than Threshold, V3=0
V4 = Tpk(x+1,y+1)
- Tpk(x-1,y-1)
If Dpk(x+1, y+1) or Dpk(x-1,
y-1) is less than Threshold, V4=0
・Limitation
of conduction velocity
The unit is number of frames. The
unnatural value of the conduction velocity is appears sometimes. The difference of frame (time point)
should be in reasonable range. This
function ignores the conduction velocity which is more than set difference of
frames.
V1 = Tpk(x,y-1) - Tpk(x,y+1)
If V1 > Limit, V1=0
V2 = Tpk(x+1,y)
- Tpk(x-1,y)
If V2 > Limit, V2=0
V3 = Tpk(x+1,y-1)
- Tpk(x-1,y+1)
If V3 > Limit , V3=0
V4 = Tpk(x+1,y+1)
- Tpk(x-1,y-1)
If V4 > Limit , V4=0
・Export of
conduction velocity data[Export
CSV]
[Export
CSV] exports the frame number (activation time point), the amplitude of the
vector and the angle of vector, of all pixels in CSV file format.
[Export
BMP] exports the displayed image in BMP format.