ICANCER RESEARCH(SLJPPL.)55. 581ls-5816s, December 1, 19951
Reconciliation
of Tumor Dose Response to External Beam Radiotherapy versus
Radioimmunotherapy
with 131lodine-labeled Antibody for a
Colon Cancer Model1
Peter L. Roberson2 and Donald J. Buchsbaum
Department of Radiation Oncology. University of Michigan, Ann Arbor, Michigan 48109-0010
Birmingham, Birmingham, Alabama 35233-6832 [D. J. B.]
Abstract
[P. L RI, and Department
Materials
of Radiation Oncology, University of Alabama at
and Methods
Activity Density Reconstruction. Athymic nude mice bearing LS174T
Reported doses of external beam radiotherapy and radioimmuno
therapy (RIT) to produce equivalent therapeutic effects are inconsistent, human colon cancer xenografts were treated with i.p. injections of 300 pCi
with many proposed causes. Calculations ofeffective dose were performed ‘311-labeled17-lA monoclonal antibody. The tumors were resected and see
for the case of LS174T human colon cancer xenografts, where a @°Cotioned. Serial-section radiographs were converted to activity density distribu
tions using gelatin calibration standards and a laser densitometer. The activity
single fraction exposure (6 Gy) was matched with ‘31I-labeled
17-lA
monoclonal antibody therapy (300 pCi injection, 19 ±2 Gy using the density distributions were aligned to reconstruct the 3D tumor activity density
distribution. Detailed procedure descriptions appear elsewhere (4—6).
Medical Internal Radiation Dose uniform isotropic model). Measured
Tumor Model. Tumorsaveragedapproximately1 cm in diameter(range,
three-dimensional dose-rate distributions were used to form a time-de
0.5—1.7cm). Tumor growth delay for a 300 pCi 17-lA monoclonal antibody
pendent description of the dose-rate nonuniformity. Included in the cal
injection 1UT was found to correspond to a single @°Co
EBRT exposure of 6
culation of RIT effective dose was energy loss, dose nonuniformity, dose
Gy (3). The dose calculated using the uniform isotropic model described by the
rate dependence, hypoxic fraction, and cell proliferation. The calculations
Medical Internal Radiation Dose formalism (7), assuming total absorption,
assumed the linear quadratic model for cell survival with a
0.3 Gy',
a/li 15 to 25 Gy, and p 0.46 h'@ The biologicallyeffective dose for resulted in a calculated dose of 19 ±2 Gy for RIT. The contribution in the
components was negligible (<2%) and was not included.
the single fraction @°Co
exposure was 7.4 to 8.4 Gy. Estimates of dose mouse due to the ‘y
The contribution from the (3component due to other organs was also negligible
efficiency factors consecutively applied to the BIT dose estimate were: (a)
because of the tumor location (hind flank) and the average range of the ‘@‘I
@3
energy loss external to the tumor (xO.85); (b) effect ofdose nonuniformity
particles (—‘0.4
mm). The calculational uncertainty was derived from the
on cell survival (xO.65); and (c) effect of correlation of dose nonunifor
experimental variations in tumor uptake measurements (3). Improved dose and
mity with cell proliferation
rate (x 1.08). The resulting
effective dose for
RIT was 11.4 Gy for tumor regrowth. This analysis substantially recon
ciles external beam radiotherapy/kIT dose-response results for this tumor
model
to within
experimental
uncertainties.
Introduction
Comparisons
effective dose claculations
Dosimetry
of therapeutic
effects
and doses
of EBRT3
and RIT
have been reported by many groups. Recent reviews discuss the
inconsistency of the results and list many possible causes for the
discrepancies (1, 2). The relative efficiency of tumor growth delay
ranged between factors of 0.3 to 3. Potential causes noted were: (a)
dose nonuniformity; (b) dose-rate effects; (c) RJ.T preferentially tar
geting rapidly proliferating cells; (d) enhanced reoxygenation with
RIT; (e) cell geometric effect; (f) cell cycle redistribution with
accumulation in the radiosensitive G2 phase; and (e) RIT contribution
to increased tumor vascular permeability. Because these factors prob
ably affect each EBRTIRIT experimental model differently, it is
useful to investigate the effects for each model independently. Here
we address athymic nude mice bearing LS 174T human colon cancer
xenografts treated with i.p. ‘31I-labeled17-lA monoclonal antibody
(3).
3D activity density distributions were determined, each specific to
the time of tumor resection. Since for the present model the activity
distribution was time dependent (4), we used activity distributions
from 22 tumors resected at 5 time points after injection to construct a
mathematical description of spatial and temporal dependencies.
used the wealth of information available for this
model, including the biodistribution data (3), 3D reconstructions of the activity
densities at several time points (4—6),and a summation scheme for deriving
total dose distributions while approximately retaining the pattern of time
dependent uptake heterogeneity (8).
Model.
Activity density distributions
for 22 tumors covering
five time points after injection were reconstructed. Three-dimensional dose
rate distributions were calculated for each tumor. Since each tumor had a
unique geometrical shape, the dose-rate distributions were not directly aver
aged or summed.
The predominant data characteristic was high tumor surface uptake at early
times and a slow movement of the activity toward the center at later times (5,
8). The main features
of the data were retained
by averaging/summing
surface
or central dose rates separately. This was performed by expressing each tumor
as a function of fractional radius. Each of 30 radial segments was defined as
a constant fraction of the distance from the tumor center of mass to the tumor
surface. The activity or dose-rate distribution for each segment was expressed
as a histogram, normalized to reflect a spherical tumor with 1 cm diameter. For
each time point, the histograms for each fractional radius were averaged to
obtain a single representative dose-rate distribution. The result was five dis
tributions with 30 histograms each, representing the dose-rate distribution
characteristic of each radial increment. The averaged dose-rate distributions for
days 1 and 4 after injection of 300 pCi of ‘@‘I
are shown in Fig. 1.
The spatially and temporally varying description of the dose rate used the
measured tumor uptake curve (Fig. 2) and the associated radially dependent
dose-rate distributions. The tumor uptake curve (Fig. 2) averaged previously
reported whole organ measurements (3) and the whole organ measurements for
the activity-reconstructedtumors. An exponential extrapolation was performed
for times beyond day 10. To ensure data consistency, the averaged dose-rate
distribution for each time point was renormalized to reflect the activity of the
decay corrected tumor uptake curve. The portion of the uptake curve assigned
to each measured spatial distribution was determined according to the number
‘
Presented
at the “Fifth
Conference
on Radioimmunodetection
andRadioimmuno of tumors used to form the average. For example, the averaged distribution
therapy of Cancer,―October 6—8, 1994, Princeton, NJ. Supported by National Cancer
representing 4 days after injection and 7 tumors was assigned a larger time
Institute Grant RO1CA44173.
interval of the tumor uptake curve compared to the distribution representing 3
‘
To whomrequestsfor reprintsshouldbe addressed,
at Departmentof Radiation
days after injection and 2 tumors. The averaged data represented an idealized
Oncology, University of Michigan, Ann Arbor, MI 48109-0010.
history of a representative tumor.
3 The abbreviations
used are: EBRT,
extemal
beam radiotherapy;
RIT, radioimmuno
therapy; 3D, three-dimensional.
The tumor model description included a prescription for summing dose rates
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RECONCILIATION
OF TUMOR DOSE RESPONSE
TO EBRT vs.
q)
Fig. I. Radial dependence
of dose rate for 300
pci injectionof ‘3'I-labeled
17-IAmonoclonalan
tibody in LSI74T xenografts. Plotted are histograms
for each of 30 radial increments (tumor center = 0;
tumor surface = 30; for a 10-mm diameter tumor,
each radial increment represented 0. 167 mm). Each
histogram represents the number of cubic voxels
experiencing dose rates within a radial interval
(dose-rate volume histograms). Voxel dimensions
were 0.2 or 0.25 mm on a side. A and B, I and 4 days
after injection, respectively. Data for 3, 7, and 10
days after injection are not shown.
0
5...
q)
over time. Dose rates for each radial increment were summed over time
assuming the approximation of maximum heterogeneity. That is, the partial
volume with the highest dose rates were summed, the partial volume with the
next highest dose rates were summed, etc. (8). This procedure was equivalent
to monotonically spreading the dose rates over spherical shells and summing
the shells by aligning the highest dose rate points for each sphere.
The present approach to the dosimetric model was designed to be consistent
Effective Dose. The effective dose was defined as the uniform absorbed
dose required to produce the same fractional cell survival (5), assuming a
linear dose response:
with the Medical Internal Radiation Dose formalism. The calculations for the
distribution:
D,ff
1/cs ln (S)
(A)
where a is the linear dose-response coefficient. For a spatially varying dose
uniform isotropic model used the area under the tumor uptake curve to
calculate the integral of activity-time. The present model used the same uptake
curve,
with the time-dependent
dose-rate
nonuniformity
S=
as supplemental
@Jexp [-aD(@)] d3r
information.
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(B)
RECONCILIATIONOF TUMOR DOSE RESPONSE TO EBRT vs. PiT
Regions with well-nourished cells at the outer rim and in internal pockets
gradually
changed
to regions
containing
greater
fractions
of hypoxic
cells and
finally necrotic cells as the distance from the high vascular density increased.
At any given tumor radius, oxic, hypoxic, and necrotic cells may coexist,
separated by as little as 200 @.sm
(14).
Asimplemodelwasusedtorelatedensityofvesselstorelativefraction
ofoxic,
hypoxic, and necrotic cells. Local vessels were assumed parallel with uniform,
equidistant spacing (similar to Krogh's cylinder model of oxygen transport; Ref.
15). As the spacing
between
vessels
increased,
the probability
of hypoxic
cells
increasedfrom an initialvalueofzero, reacheda maximum,and then decreasedas
necrosis predominated(Fig. 3). Sharp divisions between cell oxygenationstates,
with 150 and 180 pm from the nearest vessel separating the oxic/hypoxic and the
hypoxic/necrotic boundaries, respectively, were assumed (14).
The fraction of necrotic tissue increased with tumor size. For the nominal
tumor size of 1 cm diameter (0.5 g mass), the fraction of necrotic tissue was
taken to be the average observed value (30%). The vascular density was
closely associated with the initial antibody uptake. The average measured
activity density distribution at 1 day after injection was assumed proportional
Time (days)
to the vascular density distribution. The hypoxic and necrotic fractions as a
Fig. 2. Blood and tumor uptake for ‘311-labeled17-lA monoclonal antibody in athymic
nude mice bearing LS174T xenografts following i.p. injection. Shown are the measured
values and spline fit used to interpolate between measured values. %!D/g, percentage of
injected dose/gram.
where the integral is performed over the volume V and D(@)is the spatially
@
varying dose distribution.
was also expressed as:
De@ D X RE
(C)
function of radius were calculated by folding the fractional volume function
with the vascular density function. The constant of proportionality was ad
justed to yield a 0.30 fractional necrotic volume. The calculation resulted in a
net hypoxic fractional volume of 0. 10. The cell oxygenation status curves as a
function of radius are shown in Fig. 4.
A predictionof the outcome of radiationtherapy with dose may be described
using fractional cell survival. Presumably, the hypoxic cells are more difficult to
sterilize and may be described with different parameters (aHj3@,)such that:
rtH
where D is the physical absorbed dose and RE is the relative effectiveness
factor. Using the linear quadratic model, the RE for a single fraction of EBRT
cs0/OER
(G.l)
(aH/13,@)(ao/f30)*OER
(0.2)
was (9):
RE = 1 + D/(a/13)
(D)
where a/@are the linear and quadratic dose-response coefficients. The relative
effectiveness
factor
@
for RIT was taken from Millar
(10):
where OER is the oxygen enhancement ratio, H represents hypoxic, and 0
representsoxic. The above equationsfor the hypoxic fractionmove the cell
loss versus dose-curve relative to the oxic fraction by multiplying the dose axis
by the OER. The surviving fraction was recalculated using:
t) = exp
( 2 J R(@,tI)[ _f@t@
R(@,t@)e@t_t')dt?]dt'/(a/13)
—a0 J
R(@,t')dt' . RE0(@,t)
(H.l)
SH(@,
t) = exP(_aH . L R(@,t')dt' . REH(@,
t))
(H.2)
REO@,t)=1+I
(E)
\s@
@
where R(?, t) is the local dose rate as a function of time, ,.t is the cell repair
constant, t' and ‘
are time integration variables, and the relative effective
nessfactor is space-time dependent. Then, the fractional cell survival is:
@
S(t) =
f
exp (_@
@f R(@, t')dt'RE(@,
t))d3r
S(t) = @?
f@
SN(@,
t) = 0
(H.3)
t) . F0(P)+ SH(@,
t) . FH(@)]
d3r
(H.4)
(F)
where the RECr,t) values were calculated for each radius and time by per
forming
the indicated
integrals
over the dose rates,
R(@, t). The 3D spacial
dependence of R(@,t) was represented by the histograms at each radius,
configured for a 1-cm diameter tumor. These integrals (or sums) were per
formed assuming the approximation of maximum heterogeneity, as if the
maximum to minimum dose rates were similarly spread from maximum to
minimum in the spherical tumor at all time points.
E
C
Correlation with Cell Proliferation Rate. The antibodydelivery route
(circulating blood) produces a natural correlation of the activity density with
C
.‘@
tumor cell oxygenation and cell proliferation rate, since the blood delivers both
oxygen and the radiolabeled antibodies. Monoclonal antibody targeting of
antigen sites in tumor has been observed to be highly correlated with vascular
density (11, 12). This implies a correlation of absorbed dose with cell prolif
eration rate. Because the vasculature is primarily concentrated at the tumor
periphery, along with interior pockets in some tumors (13), rapid cell prolif
eration and maximum dose rates are near the surface or, less frequently, in
small interior volumes.
1E-06
Relative
1E-05
Vascular
1E-04
Density
For tumors of the size studied (—1 cm diameter), there were partial volumes
Fig. 3. Fractional oxic, hypoxic, and necrotic volumes as a function of vascular density.
of necrosis, estimated from our data to range between 10 to 40% of the tumor Calculations assumed uniform equidistant spacing of vessels with 150 and 180 @sm
volume and consistent with reported values for the LS l74T cell line (13). distances to hypoxic and necrotic cells, respectively.
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RECONCILIATIONOF TUMOR DOSE RESPONSE TO EBRT vs. RIT
‘5
relative magnitudes. RE (Eq. D) for a single fraction EBRT varied
from 1.24 to 1.40, depending on the a/f3 ratio. The effective dose for
EBRT was 7.4 to 8.4 Gy. For RIT, the fraction of energy retained
5?
E
0.6
inside
C
0.4
C
V
0.2
Hypoxic
1@
=
@
‘p
10
15
of the tumor
was calculated
by comparing
the average
tumor
dose to the dose assuming the uniform isotropic model. The average
fraction of energy retained was 0.85. The effective dose calculated
using the surviving fraction of cells (Eq. B) was 0.65 times the
average dose. The effect of cell status (Eq. H.4 with RE = 1.0) was
negligible. The effect of dose rate (Eq. F) using a = 0.3 Gy ‘,
a/3
20
2:5
30
35
Radial Increment
Fig. 4. Fractional oxic, hypoxic, and necrotic volumes as a function of tumor radial
increment. Fractional volumes as a function of vascular density were convolved with the
tumor vascular density distribution. assumed equal to the measured antibody uptake, 1day
after injection.
15 or
25
Gy,
and
@.t=
0.46
h
â€w̃as
small
(2—4%).
The
inclusion
of cell oxygenation status (Eq. H.4) to the dose-rate calculation
produced a negligible change. The calculated effective dose was
to 10.8 Gy.
Additional insight can be gained by including cell proliferation
to the relatively long exposure times for RIT. The dose, fractional
survival, and effective dose are time dependent, as illustrated in
also
10.6
5. The average
and
dose initially
increased
rapidly,
then more slowly,
due
cell
Fig.
finally exponentially approached the maximum dose value. The frac
Table IproliferationCell
Parameters used for effective dose calculatio,,s ip,cluding cell
Table 2 RIT versus EBRTdose estimatesCorrectionDose
and effectivedose
GyUniform
compositionParametersa/Il
= 25
= 15 Gya/(3
daysHypoxicfNecroticO(@
Oxica
td
dose,factorGyEBRTUniform
or effective
= 0.3 Gy'
= 0.3 Gy'
3.Odaysa
td
3.4
.006.0Doseabsorbed doseI
= 0.26
@
au
= 0.26 Gy'
Gy'
0. 13 Gy
0. 13 Gy
I@H 0.0043 Gy@
‘d
Ratea
0.3 Gy ‘
, a/13 = 15 Gy
7.4―RITUniform
a
0.3 Gy', a/Il = 25 GyI
I-@H 0.0026 Gy@
3.0 daysa0
td
3.4
days
isotropic modelI
2.13D
where F1Cr)is the fraction of cells at position r of type i and N represents necrotic
regions.
The surviving
fractions
of oxic, hypoxic,
and necrotic
.40
I .248.4―
.001
8.8 ±
distribution0.8516.0(energy
dose
loss)Dose
cells were calcu
lated separatelyand then summedto yield the total survivingfraction.An oxygen
nonuniformity
enhancement ratio of 2.0 for low-dose rate irradiation (14) was used.
(a
Gy')0.6510.4―with
0.3
Cell proliferation was represented by exponential cell growth of the well
oxygenated cell population (16).
status1.0010.5―Dose
cell
ratea/@
@
S0(@, t) = exp
—a
R(1:, t')dt'
Gy1.0410.8―a/fi
15
.0210.7―a/f3
25 GyI
(I)
. REØ(@,t) + At
status1.0010.8―a/Il
15 Gy with cell
.0010.6―Proliferationa/Il
25 Gy with cell statusI
where A is the cell proliferation constant. The tumor doubling time, td, equals
(1n2)/A. The hypoxic
@
fraction
was assumed
dormant
with no reoxygenation.
(4.5)―a/fJ
15 Gy0.99
(4.8)―a/13
25 Gy0.97
(0.52)11.4(5.6)―a/IJT=:
15Gy withcell status1.05
25 Gy with cell statusI
Parameter Determination. Typicalparametersused for the presentmodel
were a = 0.3 (9, 10), a/@3 15 to 25 (17, 18),and
0.46 h ‘
(9, 10). Since
the primary purpose of the present work was to compare EBRT to RIT
effective dose calculations, parameters used for each were kept consistent.
Buchsbaum
et a!. (3) quoted
the regrowth
time delay
to LS174T
a Effective
tumor
b Values
(0.42)―10.7
(0.45)10.5
in parentheses
represent
endpoint
for
tumor
doubling to be 15 ±3 days (300 pCi ‘@‘l17- 1A) and 15 ±1 day (6 Gy @°Co).
Doubling time estimates taken from unirradiated or irradiated tumor growth
curves near the I-cm tumor diameter size were —4days. This implies a time
shorter
due to lesser
fractions
of hypoxic/necrotic
cure
probability.
20
to regrowth of I 1 days. The doubling time during earlier stages of regrowth
was presumably
1.4 (5.9)―
.08 (0.56)1
dose.
is
tissues.
Given a = 0.3 Gy ‘
and a regrowth time of 11 days for 6 Gy @°Co
exposure,
@
10
the implied mean doubling time was td = (ln 2)/A = 3.4 days (a/f3 = 25 Gy)
or 3.0 days (ts/f3= 15Gy). These values are similar to the doubling time of 3.3
days measured by Leith et a!. (19) for LSI74T. The same values of a/@3and td
were used for the EBRT and RIT calculations. Small adjustments in the
parameters had a minimal effect on the EBRTIRIT comparison.
With the inclusion of the hypoxic/necrotic volumes, an average value of
0
a=0.3
Gy was
retained.
The
a0and
rtH
values
were
determined
using
the
-5
relative volumes of oxic (60%), hypoxic (10%), and necrotic (30%) cells.
Parameters
used for the cell proliferation
calculations
are given in Table
1.
Time, d
Results
Estimated doses and effective doses are given in Table 2. Correc
tion factors are applied sequentially to allow a comparison of their
Fig. 5. Time dependence of dose, effective dose, and fractional cell survival (S). The
calculations used the spatial average of the cumulated dose [D(@,t)J, the time-dependent
expression for S (Eq. I), and D@1@
(time-dependent version of Eq. A).
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RECONCILIATIONOF TUMOR DOSE RESPONSE TO EBRT vs. RIT
tional cell survival decreased to near zero and rebounded. The effec
tive dose initially
@
rose more rapidly
than the average
dose, then less
rapidly, and reached a peak value before cell proliferation predomi
nated. A negative
represented an increased number of tumor cells
compared to those initially present (at t = 0).
The fractional cell survival is replotted on a log scale in Fig. 6 and
compared to the corresponding curve for EBRT. For the parameters
that reproduce the tumor regrowth curve for EBRT (i.e., tumor re
growth in 11 days), the RIT curve predicted regrowth in 15 days. To
match the RIT curve to the experimental results (dashed curve), the
effective dose must be divided by a factor of I .44. If the useful
effective dose up to the time for regrowth only was included, the
effective dose was 11.4 Gy (see values used in Table 2). The ratios
small, since the half-time for repair (1.5 h) was small compared to the
effective half-life of the radioactivity.
Preferential Targeting of Rapidly Proliferating Cells. This
mechanism implies an advantage derived from correlating the larger
doses with the highest cell proliferation rate. The present model does
show this effect but is limited to less than 10% of the effective dose
for the regrowth end point.
As pointed out above, there are several ways of expressing the
dose effect of proliferation. Assuming a uniform cell status, the
between
the low- and high-dose
EBRT and RIT effective
doses were 1.54 (a/j3 = 15 Gy) or
I.36 (a/@3= 25 Gy). These ratios are in approximate agreement with
@
the 1.44 factor noted above.
The effective dose for tumor cure probability (fractional cell sur
vival curve minimum and effective dose curve maximum) is consid
erably less than the effective dose for tumor regrowth delay and are
listed in brackets in Table 2 (5.6—5.9Gy). This difference is due to the
choice of end point. There was a smaller time interval (and less
physical dose deposited) to the cell survival curve minimum than to
the tumor regrowth point.
The EBRT/RIT comparison of effective doses for regrowth was
7.4—8.4
@
Dose Rate. Dose-rate corrections are dependent on the a/j3 ratio
and the repair constant (p.). Dose rates for the present model were low
Gy
EBRT
versus
1 1.4 Gy
RIT
(36
to 54%
difference).
Given the experimental uncertainty in the tumor uptake curve
(1 1%) and the uncertainty of matching tumor growth delay curves
for EBRT versus RIT (—20%), these effective dose values are
consistent. This analysis appears to reconcile EBRT/RIT results to
within experimental uncertainties.
Discussion
The proposed causes for the discrepancy of EBRT/XRT efficacy
will be discussed below.
Dose Nonuniformity. For a uniform dose deposition, tumor con
trol is made more difficult with a heterogeneous cell response. Like
wise, tumor control is more difficult with a nonuniform dose deposi
tion compared to a uniform dose for the same average value. This may
be illustrated by noting that the functional form describing cell sur
vival is not linear in dose but exponential. The average of an expo
nential function of a variable is less than the average of the variable.
Differences between the effective dose and the average physical dose
are dependent on the magnitude of the nonuniformity and can be
large. Here we calculate an efficiency factor of 0.65.
(<10 cGy/h average). As expected (9, 10), dose-rate corrections were
Doff decreased
5
10
15
20
25
Time, d
Fig. 6. Fractional cell survival for EBRT versus RIT. ----. the RIT dose that matched
the experimental tumor regrowth. The EBRT curve assumed exponential regrowth. The
RIT curve was the time-dependent Dc,, curve of Fig. 5. a/(3 = 25 Gy.
it tended
to increase
rate regions.
When
the difference
between
cell oxygenation
status
was included, increased dose rates and cell losses in the most
rapidly proliferating regions increased the DCIf rate 5—8%.How
ever, the greatest effect was on the Deff for tumor cure potential
curve maximum). Deff decreased by approximately a factor of
two by changing the end point. This loss in effect was due to the
dose rate used to offset the effect of cell proliferation rate early in
treatment and that portion was entirely discounted when the cell
proliferation rate predominated (after the curve maximum). These
estimates of the decrease in Doff due to cell proliferation are
consistent with those presented by O'Donoghue (16). Note that the
effect of preferential targeting of rapidly proliferating cells (with
status included) increased
by —24% using tumor cure poten
tial as the end point.
Enhanced Reoxygenation with RIT. A reoxygenation half-time
of less than —5 days could affect fractional cell kill efficiency.
However, for the present model, the impact on the effective dose
calculation would be small because the surviving hypoxic and oxic
fractions are approximately the same magnitude. This effect may be
greater with a more aggressive therapy (i.e., higher doses) and/or a
more resistant cell line, where the probability of cure is limited
primarily
by the initially
hypoxic
clonogenic
cell population.
Cell Geometric Effect. The cell geometriceffect was discussed by
Humm and Cobb (20). The cell nucleus is assumed to be the target,
and the activity is assumed to predominantly reside on the cell surface.
This effect for the present tumor model is negligible (<2%) due to the
relatively long range of the ‘@
‘I
13particles. If a large fraction of the
activity remained unbound in the interstitial spaces, as is the case here,
this effect would be even more diluted (closer to unity).
Cell Cycle Redistribution (G2Block). Repairandrepopulationby
surviving
0
because
tumor
cells may be an important
effect
for low-dose-rate
radiation treatments, such as Rif. Mitchell et a!. (21) demonstrated
the correlation between the dose-rate that inhibited growth and the
length of mitotic delay after acute radiation. Dillehay et a!. (22)
documented the rise of the G2+M phase under continuous low
dose-rate radiation and obtained increased cell kill when methylxan
thines were used for cell cycle redistribution (unblocking the 02
phase). The enhanced cell killing observed by unblocking the 02
phase provides evidence that 02 blocking effects may be significant.
For a 6 cOy/h dose rate delivered for 3 days, unblocking increased log
cell kill relative to control samples by factors of 1.2 to 1.8 in a
hepatoma cell line. This implies a dose efficiency factor of approxi
mately 0.7 for continuous low-dose-rate irradiation due to the G2
block effect in a radioresistant cell line. The magnitude of this effect
will vary with cell type. Since the LS l74T cell line is radiosensitive
and the dose rates for the present case were low (<10 cOy/h), this
effect was expected to be minimal (18).
RIT
Contribution
to Tumor
Vascular
Permeability.
The RIT
contribution to increased tumor vascular permeability is included in
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RECONCILIA11ON
OF TUMOR DOSE RESPONSE
the measured data, both the tumor uptake curves and the 3D activity
reconstructions.
Uncertainty
Analysis. Primary sources of calculational uncer
tainty are: (a) use of the linear-quadratic model (Eq. F) or the
time-dependent linear-quadratic model (Eq. I) and the uncertainty in
References
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58l6s
Downloaded from cancerres.aacrjournals.org on June 14, 2017. © 1995 American Association for Cancer Research.
Reconciliation of Tumor Dose Response to External Beam
Radiotherapy versus Radioimmunotherapy with 131
Iodine-labeled Antibody for a Colon Cancer Model
Peter L. Roberson and Donald J. Buchsbaum
Cancer Res 1995;55:5811s-5816s.
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