Biomedical Engineering Reference
In-Depth Information
hundred within a tumor of at least 10
10
cells (Tepper, 1981) - or if
there were a distribution of sensitivities among patients. As the
former was judged unlikely, assumption (3) was invoked, and
experimental data concerning the observed distribution of cell
sensitivities supported this understanding. Recently, there is a sug-
gestion that the number of clonogenic cells may be much smaller
than was previously thought (Chen
et al
., 2006; Huff
et al
., 2006).
Under the above assumptions, one readily comes up with a
mathematical prescription for estimating TCP under conditions of
non-uniform irradiation. The basic approach is as follows:
1.
One divides the tumor up into tumorlets, which are sub-
volumes (the i'th of which has a volume v
i
) small enough that
the dose (d
i
) is essentially uniform within each one.
2.
A dose-response model for the entire tumor of a given
radiosensitivity, uniformly irradiated, is represented by a
sigmoid curve whose slope,
γ
50
,
4
and the dose needed to
achieve 50% TCP, D
50
, are based on clinical experience.
3.
The dose-response for a tumorlet of volume v
i
is deduced from
that for the entire tumor (of volume V) through the relationship
v
[
]
.
This relationship is a very general one, based on Poison
statistics and the assumption that tumor control is obtained
when no viable cells remain.
4.
The TCP for the whole tumor of a given patient is taken to be
the product of the TCPs for each tumorlet. i.e.,
i
TCP(d
,
v
)
=
TCP(d
,
V)
V
i
i
i
n
∏
=
TCP
=
TCP(d
,
v
)
⋅
TCP(d
,
v
)
⋅
TCP(d
,
v
)
⋅
⋅
⋅
=
TCP(d
,
v
)
1
1
2
2
3
3
i
i
i
1
5.
Lastly, to get the TCP for a patient population, the individual's
TCP is averaged over the presumed Gaussian distribution of
the radiosensitivities of the patient population. That distribu-
tion can be arrived at by fitting the results for a uniformly
irradiated tumor to the observed slope of clinical data.
4
The symbol
γ
P
represents the slope of a dose-response curve at a level of
response probability of P. It is expressed as the increase in response
probability divided by percentage increase in dose. At 50% response
probability, the slope is written as
γ
50
.
