RESULTS

1
Cluster model analysis of late rectal
bleedingafter IMRT of prostate cancer a
case-control study Susan L. Tucker1, Ph.D., Ming
Zhang1, Ph.D., Lei Dong2, Ph.D., Radhe Mohan2,
Ph.D., Deborah Kuban3, M.D., and Howard D.
Thames1, Ph.D.
RESULTS Fig. 4 shows the distribution of maximum
cluster sizes calculated by numerical simulation
for two case-control pairs using one choice of
parameter values b1 and b2. On the left, the
expected (mean) maximum cluster size is larger
for the case than for the control on the right
it is smaller.
BACKGROUND Some dose-volume analyses have
suggested that late rectal toxicity after
radiotherapy is a consequence of high-dose (gt 60
Gy) exposure to portions of the rectal wall
(1,2), while others have suggested that much
lower doses (30-40 Gy) may be more relevant
(3,4). Such discrepancies might be explained in
part by data analyses based on quantities derived
from the dose-volume histogram (DVH). The DVH has
the limitation that it does not retain spatial
information regarding dose, e.g. what portions of
the organ receive what dose, and whether the
high-dose region is a single contiguous volume or
consists of two or more spatially separated
sub-volumes. Cluster models (5) are designed to
capture this spatial information. Here we present
the results of a case-control study of late
rectal bleeding after IMRT of prostate cancer to
demonstrate that cluster models carry information
beyond that captured by the DVH (6). MATERIALS
AND METHODS Patients Rectal dose-surface
histograms (DSHs) were calculated as described
elsewhere (4) for patients with localized
prostate cancer receiving IMRT at The University
of Texas M.D. Anderson Cancer Center (UTMDACC)
from January 2000 to November 2001, excluding
patients with diabetes mellitus or a history of
rectal hemorrhoids. Patients received 42
fractions of 1.8 Gy per fraction (total dose 75.6
Gy), and had no hormone therapy. Plans were
designed using a commercial system (Corvus, North
American Scientific, Chatsworth, CA) and patients
were treated with either a serial tomotherapy
device (Peacock, North American Scientific,
Chatsworth, CA) or the step-and-shoot MLC (Varian
Medical Systems, Palo Alto, CA). All patients had
ultrasonic prostate localization (BAT, North
American Scientific, Chatsworth, CA) prior to
each treatment. 9 patients (cases) experienced
grade gt 2 late rectal bleeding, where toxicity
was scored using a modified RTOG scale (7). 54
patients (controls) had at least 3 years of
follow-up and no late rectal bleeding. Each case
was matched with the control whose absolute
cumulative DSH had the smallest mean-squared
difference from the DSH of the case, assessed at
doses ranging from 0 to 100 Gy in increments of
0.1 Gy (Fig. 1). This retrospective paired
case-control study (N 9), was approved by the
Institutional Review Board of the UTMDACC.
MATERIALS AND METHODS (continued) Rectal surface
dose-map arrays The rectal surface of each
patient (9 cases 9 controls) was represented as
a 2-dimensional grid of squares by dividing the
rectal contour on each slice of the planning CT
scan into 72 approximately even intervals around
the circumference (Fig. 2). Additional CT slices
were interpolated as necessary to produce
approximately square voxels in the dose-map
array. The dose to each voxel was interpolated
from the treatment-planning dose distribution.
Fig. 2 LeftContour points defining the outer
rectal surface as entered by the attending
physician on a slice of the planning CT.
RightInterpolated points dividing the rectal
circumference into 72 intervals of approximately
equal length.
Fig. 4 Distributions of maximum cluster size
obtained by numerical simulation for two
case-control pairs using parameter values b1 3
and b2 0.03 Gy-1.
The maximum observed consistency of the cluster
model with data was 8/9. All parameter pairs for
which the consistency reached 8/9 correspond to
D50 values (i.e., values of D for which p(D)
50 in Eq. 1) in the range 27 - 43 Gy.
Cluster models A 2-dimensional (2-D) cluster
model (6) was used to study the spatial
distribution of damaged voxels in the dose-map
array after exposure to radiation. The
probability of damaging a voxel exposed to dose
D was modeled as p(D) 1/(1 exp(b1 b2 (a/b
x)D)) (Eq. 1) where x
dose per fraction D/42 and the bis are
unknown parameters. The a/b ratio from the
linear-quadratic model was assumed to be 5.4 Gy,
based on a recent estimate for late rectal
toxicity (8). For each of 800 choices (b1,b2) of
model parameters, numerical simulations were
performed to calculate the distribution of
maximum cluster sizes on each rectal surface.
2-connectivity (5) was used to compute maximum
cluster size (Fig. 3). For each parameter pair
(b1,b2), consistency of the cluster model with
the data was quantified by the fraction of
case-control pairs for which the expected maximum
cluster size was larger for the case (a patient
with grade gt 2 late rectal bleeding) than for the
matched control (a patient without late rectal
bleeding but having the same rectal DSH c.f.
Fig. 1).
CONCLUSIONS 1. Parameter values for the
local-damage function (Eq. 1) were found for
which a 2-D cluster model of the rectal surface
is highly consistent (8/9) with the occurrence of
grade gt 2 late rectal bleeding data from a paired
case-control study. Specifically, in 8 of 9
matched pairs, the expected maximum cluster size
was larger for the case (bleeder) than for the
matched control (non-bleeder with same rectal
DSH). 2. This demonstrates that a 2-D cluster
model successfully carries spatial information
about the dose distribution that is not retained
in the DSH of the rectal surface
. 3. Interestingly, the results of the study
suggest that intermediate doses (30-40 Gy)
rather than high doses (gt 60 Gy) are most
significantly associated with the type of damage
to rectal wall that is manifested as grade gt 2
late rectal bleeding.
SELECTED REFERENCES 1. Benk et al. IJROBP
199326551-557. 2. Storey et al. IJROBP
200048635-642. 3. Skwarchuk et al. IJROBP
200047103-113. 4. Tucker et al. IJROBP
2004601589-1601. 5. Thames et al. IJROBP
2004591491-1504. 6. Tucker et al. IJROBP 2005
submitted. 7. Pollack et al. IJROBP
2002531097-1105. 8. Brenner, IJROBP 2004
601013-1015.
Fig. 3 Illustration of 2-connectivity. After
irradiation, 6 squares in the 4X4 grid on the
left have been damaged (black squares), as have 5
squares on the right. The maximum cluster size is
1 on the right (1 cluster of spatially contiguous
damaged voxels made up of black 2X2 blocks) and 0
on the right (no group of spatially contiguous
black squares contains a black 2X2 block).
Fig. 1 Cumulative DSH curves for the 9 pairs of
matched cases and controls