Biomedical Engineering Reference
In-Depth Information
a
b
20
( ,
)
t
+
t
r
ʸ
ʔ
ʸ
(°)
90
12
0
6
0
r
( , )
ʸ
t
20
15
t
+
ʔ
t
v
ʔ
t
( , )
t
ʸ
t
30
10
(°)
ʸ
240
280
320
360
0
0
c
0.2
v
ʔ
t
( , )
ʸ
t
210
330
0
ʸ
(°)
240
300
270
-0.2
Fig. 6.5
Estimation of the cell protrusion rate (Miyoshi and Adachi
2012
). (
a
) The distance,
r
(
ʸ
,
t
),
from the centroid of the outline to the outline edge is measured at the spatial sampling interval,
ʔ
ʸ
= 0.25°. (
b
) The displacement,
v
ʔ
t
(
ʸ
,
t
)
ʔ
t
(the
blue arrow
), of the cell periphery at angle
ʸ
from
time
t
to
t
+
t
) (the
brown line
),
and the distance,
r
(
ʸ
,
t
) (the
red line
). (
c
) The spatial change in the protrusion rate,
v
ʔ
t
(
ʸ
,
t
) =
(
r
(
ʸ
,
t
+
ʔ
t
is obtained from the difference between the distance,
r
(
ʸ
,
t
+
ʔ
t
(Adapted with permission from The Royal Society of Chemistry:
[Integrative Biology], copyright (2012))
ʔ
t
) −
r
(
ʸ
,
t
))/
ʔ
rates against space
ʸ
and time
t
. As seen in Fig.
6.6a
, the map of protrusion rates,
v
ʔ
t
(
ʸ
,
t
), calculated for a time interval on the order of 10 s,
t
= 11.35 s, shows that
the protruding region (red to yellow) and the retracting region (purple to blue) are
repeatedly located laterally along the cell boundary. The angle of the global protruding
region is approximately 60°. As indicated by the scale at the bottom of the map in
Fig.
6.6a
, the angle of 60° corresponds to an arc length of about 15-20
ʔ
ʼ
m. The
angle of the retracting region is also approximately 60° (15-20
m). We can recognize
that the global protruding regions and retracting regions travel along the cell boundary
at a constant speed. The speed is about one degree per second (a few hundred nano-
meters per second), as indicated by the white triangle in Fig.
6.6a
.
In Fig.
6.6b
, the protrusion rate,
v
ʔ
t
(
ʸ
,
t
), calculated at a time interval on the order
of 1 s,
ʼ
t
= 2.27 s, are plotted on an expanded ordinate scale, from 0 to 42 s, to
extract characteristics of cell peripheral activity at a local and short-time scale. The
map in the fi gure reveals that local active protruding domains (APDs) are embedded
in the global protruding region, as can be detected in Fig.
6.6a
. As seen in the
enlarged maps in Fig.
6.6d, e
, the angle of each APD is on the order of 10° (about
3
ʔ
m). The APDs travel in opposite directions laterally along the cell boundary at
about one degree per second (a few hundred nanometers per second).
In Fig.
6.6c
, the protrusion rates,
v
ʔ
t
(
ʸ
,
t
), calculated at a time interval on the
order of sub-seconds,
ʼ
t
= 0.45 s, are plotted on a more expanded ordinate scale,
from 0 to 8.4 s. In contrast to the results shown in Fig.
6.6a, b
, no coordinated
pattern in cell peripheral activity can be detected at the spatiotemporal scale in Fig.
6.6c
.
The apparent correlation pattern in the time domain
t
= 1, 2.5 and 4 s is considered
to be due to the image segmentation processes.
ʔ
