Biomedical Engineering Reference
In-Depth Information
it is possible to finally conclude that
"
#
X
H
x
CM
/
1
T
1
v
CM
v
CM
a
volume
w
2
x
2
+
;
(4.20)
x
2
or, with another viewpoint,
X
H
x
CM
1
v
CM
a
volume
v
CM
w
2
x
2
:
/T
(4.21)
x
2
Some comments on the consequences of relation (4.13) are the following:
It is characteristic of an extremely viscous regime, such as the biological
environment where the individuals thus evolve under strong damping.
It is a definitive confirmation that discrete CPM objects move in order
to minimize the total energy. The modulus of the local velocity of
,
at any given time t, depends on the magnitude of the energy difference
due to the proposed spin flip, as well as on its intrinsic motility T
(t),
which, in our extended approach, is coherently a variable property of
each unit
.
Given that T
is now a property of each object
, different individuals
(or different individual subcompartments) may have different velocities
even if they experience the same energy gradient. A consequence is that
the one-to-one relationship between a MCS and the standard Boltzmann
temperature T characteristic of the basic CPM is lost.
Given that the energy functional H is the sum of the terms that rep-
resent multiple biological mechanisms with the same architecture, it is
straightforward to evaluate the contribution of each of them to the local
velocity of unit
. In fact, for any mechanism i, by equating all the
other terms to zero, we obtain
X
imechanism
/T
H
imechanism
x
CM
1
v
CM
a
volume
v
CM
w
2
x
2
:
x
2
(4.22)
In particular, it is possible to differentiate the contributions of either
short- or long-range mechanisms:
"
H
short range
+ H
long range
x
CM
#
P
x
2
w
2
x
2
v
CM
a
volume
v
CM
/T
(4.23)
the former of which includes, for example, adhesion and haptotaxis,
while the latter includes chemotaxis.
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