Biomedical Engineering Reference
In-Depth Information
a
sgn(
)
v
∆
t
M
INUS
P
LUS
´
sgn(
)
v
∆
t
p
lus
m
inus
Pp-d1
Pp-d2
Pp-d3 Pp-d4
v
∆
t
( , )
0.2
v
∆
t
( ,
)
= < >
θ
t
Φ
θ
t
0.2
0
0.0
´
v
∆
t
( , )
θ
t
-0.2
=
v
∆
t
( , ) -
v
∆
t
( , )
θ
t
θ
t
-0.2
0
360
120
240
Angle, (°)
θ
b
c
100
Pm
Pp
1.0
Pp-d4
n=2209
n=2063
80
Pp-d2
0.5
60
Pp-d1
0
40
-0.08 -0.04
0
0.04
0.08
-0.5
Pp-d3
v
j
min
v
i
max
´
´
(
µ
m/sec)
(
µ
m/sec)
-1.0
100
Mp
Mm
0.00
0.10
0.20
n=2220
n=1979
80
Relative
´
v
∆
t
protrusion rate,
60
(
µ
m/sec)
40
-0.08 -0.04
0
0.04
0.08
v
j
min
v
i
max
´
´
(
µ
m/sec)
(
µ
m/sec)
Retracting
Protruding
Local
Fig. 7.5
Relationship between cell peripheral
ac
tivity and cell peripheral shape (Miyoshi and
Adachi
2012
). (
a
) The averaged protrusion rate,
v
(
)
=
(
)
(the
grey line
) is esti-
mated for ʦ = 120ﾰ and subtracted from
v
ʔ
t
to acquire the relative protrusion rate,
v
ʔt
ƹ (the
orange
line
), with the spatial variat
io
n at the scale on the order of 10ﾰ. At the top, the regions
w
ith global
protruding movement sgn(
v
D t
) > 0 and those with global retracting movement sgn(
v
D
) < 0 are
indicated by the
light red
and
light blue shaded rectangles
, respectively. The relative protruding
domains with sgn(
v
ʔt
ƹ) > 0 and the relative retracting domains with sgn(
v
ʔt
ƹ) < 0 are indicated by the
red
and
blue
bars, respectively. The domains indicated as Pp-d1, -d2, -d3 and -d4 are the r
e
presen-
tative protruding domains (sgn(
v
ʔt
ƹ) > 0) relative to the global protruding movement (sgn(
v
D
) > 0)
that are used to make the scatter plot in (
b
). (
b
) The scatter plots of the relative protrusion rate,
v
ʔt
ƹ,
and the curvature,
ʺ
ʔs
, in Pp-d1, -d2, -d3 and -d4 in (
a
). The lines of best fit are estimated using the
method of least squares. (
c
) The relationships between
v
ʔt
ƹ and
ʺ
ʔs
in Pp (
top right
), Pm (
top left
),
Mp (
bottom right
) and Mm (
bottom left
) domains. At the right, the percentage of the domains
representing a negative correlation between
v
ʔt
ƹ and
ʺ
ʔs
is plotted against
v
i
ƹ
max
which is a measure
of the magnitude of the relative protruding activity for Pp and Mp domains. At the left, the percentage
of the domains representing a negative correlation between
v
ʔt
ƹ and
ʺ
ʔs
is plotted against
v
j
ƹ
min
which is a measure of the magnitude of the relative retracting activity for Pm and Mm domains.
The
dotted lines
indicate 50 %. The analysis is based on the data as used for the analysis in Fig.
7.2
,
Society of Chemistry: [Integrative Biology], copyright (2012))
q
,
t
v
q
,
t
D
t
D
t
F
