Biomedical Engineering Reference
In-Depth Information
single cell (a stem cell, for example), or it may be a complex structure
(nephrons in the kidney, for example).
Serial architecture
An organ or normal tissue
compartment has a serial
structure if the death or
inactivation of only one of
its FSUs is sufficient to
cause loss of function of the
tissue - i.e., to express the
endpoint in question. One
can imagine the prototypi-
cal serial structure as a chain
that will break if any one of
its links is broken - as
suggested in Figure 5.7. It is thought that the spinal cord, for example,
is a serial structure - although this has been questioned. The serial
model is also called the critical-element model.
Figure 5.7. Serial architecture: normal
tissue viewed as a chain which loses its
functionality (i.e., load-bearing capacity)
when even only one link is broken.
The central idea of mechanistic models of serial architecture is that
the NTCP of the normal tissue can be expressed in terms of the
probability of inactivating at least one of its constituent FSUs. The
relationship would then be:
N
FSU
(
)
(
(
)
)
(5.3)
∏
=
1
−
NTCP
=
1
−
P
d
i
i
1
where N
FSU
is the total number of FSUs, d
i
is the dose received by the
i
'th FSU (which is assumed to be small enough that the dose is
uniform throughout it), and P(d
i
) is the probability of inactivating an
i
equation (5.3) is very similar to the expression given above linking
TCP to the TCPs of the individual tumorlets. Here, however, it is the
probabilities of having no complications that are multiplicative.
Without going into the details of the models, I want to mention one
point that represents the critical difference between serial and parallel
FSU that receives a dose, d . It will immediately strike you that
architectures. Namely,
in a tissue with a serial architecture,
the
variation of NTCP with volume (with dose held constant) is, for small
NTCPs, a linear function of volume
. This implies, for example, that if
in a partial volume irradiation one doubles the volume irradiated, one
will double the NTCP - provided only that it is small compared to
100%.
