Biomedical Engineering Reference
In-Depth Information
Tabl e 1 Main features of the description of the necrotic core ( N ) in some literature models
Dead cell
Necrotic core
Reaching
Mechanical
Model degradation
structure
steady state
aspects
[ 34 ]
First-order kinetics, Solid
Volume loss
Mono-phase model,
from N a
+
mitotic inhibitor
kinematic approach
production
mitotic inhibition
[ 48 ]
Absent
Solid
Phagocytosis of
Mono-phase model,
apoptotic cells
kinematic approach
[ 2 ]
Absent,
Solid
Proliferation
Mono-phase model,
mitotic inhibitor
blocked by
kinematic approach
production
mitotic inhibitors
diffusing from N
[ 62 ]
Immediate
Reservoir of
Volume loss
Two-phase model
from N b
diffusible
(one phase
“cellular material”
diffusible)
[ 41 ]
Immediate
Liquid at the
Volume loss
Two-fluid model,
from N c
steady state
momentum balance,
surface tension
(needed for
equilibrium)
[ 18 ]
Immediate
Reduced density
Volume loss
Two-fluid model,
from N c
of living cells
momentum balance,
surface tension
may be included
[ 12 ]
After a Gamma-
Solid
Volume loss
Multi-phase model,
from N a
distributed time
kinematic approach
[ 29 ]
After a fixed time
Includes a
Volume loss
Two-fluid model,
from N c
liquid core
kinematic approach
+ stress analysis,
solid shell surface tension
(needed for
equilibrium)
Volume loss: a Postulated b By diffusion c Supported by a fluid dynamical theory
within a
compartment characterized by a single diffusion coefficient. Moreover, NMR
imaging evidenced an intermediate zone between the viable rim and the centre of the
necrotic region, which still appears to have two diffusion compartments, although
the fraction of volume of the diffusion-restricted compartment was found lower than
the corresponding fraction in the viable rim.
The presence of an inner liquid core precludes, however, the possibility of
studying the spheroid on a pure kinematic basis, and requires the introduction of
a mechanical scheme. In the above cited papers, the two-fluid model was revisited
to investigate the spheroid steady state .
The main features of the necrotic core description in some literature models are
summarized in Table 1 .
 
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