Results
The present study was undertaken to determine the effect of proton SPE
radiation on peripheral blood cells using Yucatan minipigs as an experimental model
system. The WBC, lymphocyte, neutrophil, monocyte, eosinophil, RBC and platelet
count data (expressed as fraction of control) at different time points after
irradiation were compared to the respective baseline levels to evaluate the blood
cell count changes after irradiation. The blood cell count data were also fitted
using a linear-quadratic model to analyze the dose-response relationship for the
WBCs, lymphocytes, neutrophils, monocytes, eosinophils, RBCs and platelets. In the
irradiated Yucatan minipigs, the WBC count decreased within a day after irradiation
by 43.4, 57.4 and 59.3%, respectively, for the 5, 7.7 and 10 Gy radiation
dose groups ( Table 2 ). Between day 1 and day
4 after irradiation, the WBC count reached the lowest level, which was 54.2, 57.4
and 59.3% below the baseline level for the 5, 7.7 and 10 Gy radiation dose
groups. The WBC count recovered slowly thereafter. By day 30, the WBC count in the
irradiated animals was only 17.7%, 38.3% and 20.0% below the
baseline level for the 5, 7.7 and 10 Gy radiation dose groups. By day 90, the WBC
count recovered fully for the 5 Gy radiation dose group while remaining 18.7 and
33.5% below the baseline level for the 7.7 and 10 Gy radiation dose groups.
As for the dose-response relationships at different time points after the radiation
exposure, significant radiation dose responses for WBCs were observed in irradiated
animals on days 1, 4, 14, 30 and 90 after irradiation ( Fig. 2 ). The linear component of the dose-response curve slope was
0.103, 0.108, 0.084, 0.038 and 0.003, respectively, for days 1, 4, 14, 30 and 90
after irradiation. The steepest slope was observed on day 4 after irradiation. The
quadratic component of the dose-response curve slope was negligible (≤7.647
×10 −15 ) for all time points investigated.
Lymphocyte counts decreased significantly as early as 4 h after irradiation
for the 5, 7.7 and 10 Gy radiation dose groups ( Table 3 ). On day 1 after irradiation, the lymphocyte count reached the
lowest level, which was 73.0, 79.7 and 89.5% below the baseline level for
the 5, 7.7 and 10 Gy radiation dose groups, respectively. Lymphocyte counts
recovered slowly thereafter. By day 30, the lymphocyte count in the irradiated
animals was not more than 34.5% below the baseline level for the three
radiation dose groups. By day 90, the lymphocyte count recovered fully for the 5 Gy
radiation dose group and was not more than 19.5% below the baseline level
for the two higher radiation dose groups. For the dose-response relationships at
different time points after radiation exposure, significant radiation dose responses
for lymphocytes were observed in irradiated animals at 4 h and on days 1, 4 and 14
postirradiation ( Fig. 3 ). The dose responses on
days 30 and 90 were not statistically significant. The linear component of the
linear quadratic dose-response curve slope was 0.172, 0.236, 0.143, 0.108,
respectively, for 4 h and days 1, 4 and 14 after irradiation. The steepest slope was
observed on day 1 after irradiation. The quadratic component of the dose-response
curve slope was 0.002 for day 90 and negligible (≤ 1.030
×10 −18 ) for all other time points investigated.
Neutrophil counts increased by 8.7%, 79.8% and 26.3%
for the 5, 7.7 and 10 Gy radiation dose groups, respectively, at 4 h after
irradiation ( Table 4 ). Following the initial
increase, the neutrophil count decreased to 21.7–42.1% below
baseline for the three radiation dose groups on day 1 after irradiation. Between
days 4 and 14 postirradiation, the neutrophil counts were at their lowest levels of
60.4%, 52.5% and 52.1% below baseline, respectively, for the
5, 7.7 and 10 Gy dose groups. For the dose-response relationships at different time
points after irradiation, significant radiation dose responses for neutrophils were
observed in irradiated animals on days 1, 4, 14, 30 and 90 after irradiation ( Fig. 4 ). The linear component of the linear
quadratic dose-response curve slope was 0.054, 0.094, 0.076, 0.071 and 5.946
×10 −19 , respectively, for days 1, 4, 14, 30 and 90
after irradiation. The steepest slope was observed on day 4 after irradiation. The
quadratic component of the dose-response curve slope was 0.006 for day 90 and
negligible (≤ 1.005 ×10 −18 ) for all other time
points investigated.
In the irradiated animals, the lowest level of monocyte counts was observed
4 h after irradiation and was 62.3, 62.7 and 73.2% below the baseline values
for the 5, 7.7 and 10 Gy radiation groups, respectively ( Table 5 ). Due to the relatively large variation within
the treatment groups, the difference between different time points did not reach
statistical significance for any of the three radiation dose groups. The monocyte
count recovered slowly thereafter. On days 30 and 90, the monocyte count in the
irradiated animals was not more than 8.2% below the baseline level. For the
dose-response relationships at different time points after irradiation, significant
radiation dose responses for monocytes were observed at 4 h and on day 1 after
irradiation ( Fig. 5 ). The dose response was
marginally significant on day 14 postirradiation but was not statistically
significant on days 4, 30 and 90 postirradiation. The linear component of the linear
quadratic dose-response curve slope was 0.144 and 0.078, respectively, for 4 h and
day 1 postirradiation. The steepest slope was observed at 4 h postirradiation. The
quadratic component of the dose-response curve slope was 0.002 and 6.039
×10 −4 for days 1 and 30 after irradiation and was
negligible (≤ 1.428 ×10 −18 ) for all other time
points investigated.
Eosinophil counts in the irradiated animals decreased ≥24.2%
at 4 h postirradiation and reached the lowest levels between 4 h and day 14
postirradiation ( Table 5 ), which were 67.2,
73.5 and 75.5% below the baseline levels for the 5, 7.5 and 10 Gy radiation
dose groups, respectively. The eosinophil count recovered slowly after day 14, and
by day 90, the eosinophil count was fully recovered for the 5 Gy radiation dose
group but was still 33.5 and 62.6% below the baseline value for the 7.7 and
10 Gy radiation dose groups. For the dose-response relationships at different time
points post-irradiation, significant or nearly significant radiation dose responses
for eosinophils were observed in irradiated animals on days 1, 4, 14, 30 and 90
postirradiation ( Fig. 6 ). The linear component
of the linear quadratic dose-response curve slope was 0.141, 0.090, 0.147, 0.052 and
3.695 ×10 −17 , respectively, for days 1, 4, 14, 30 and 90
after irradiation. The steepest slope was reached on day 14 after irradiation. The
quadratic component of the dose-response curve slope was 0.005, 6.843
×10 −4 and 0.007 for days 4, 30 and 90 after
irradiation but was negligible (≤3.776 ×10 −18 )
for all other time points investigated.
In the irradiated animals, RBC or platelet counts did not show a significant
decrease at any of the time points investigated after proton-radiation exposure in
the 5, 7.7 or 10 Gy radiation dose groups and the dose responses of RBCs and
platelets were not statistically significant for any of the time points after
irradiation (data not shown).
Discussion
In the present study, changes in the counts of WBCs, lymphocytes,
neutrophils, monocytes, eosinophils, RBCs and platelets in response to proton SPE
irradiation at doses of 5, 7.7 and 10 Gy were evaluated in Yucatan minipigs. Among
the blood cell types evaluated, WBCs, lymphocytes, neutrophils, monocytes and
eosinophils declined substantially in at least the two highest radiation dose groups
within a day after irradiation. No significant decrease was observed for platelets
and RBCs after the proton irradiation at any time points after irradiation in any of
the three radiation dose groups. The lowest blood cell counts were observed at 4 h
after irradiation for monocytes, on day 1 for lymphocytes, on day 4 for WBCs,
between days 4–14 for neutrophils, and between 4 h and day 14 for
eosinophils. At the lowest levels of the blood cell counts, the WBCs, lymphocytes,
neutrophils, monocytes and eosinophils decreased by up to 59.1%,
89.5%, 60.4%, 73.2% and 75.5%, respectively, from
the respective baseline control values (preirradiation values). After the initial
decrease observed after irradiation, WBC, lymphocyte, neutrophil, monocyte and
eosinophil counts recovered slowly to levels that were not more than 38.3%,
34.5%, 47.8%, 8.2% and 44.8% below the respective
baseline control levels by day 30 postirradiation. By day 90 postirradiation, the
WBCs, lymphocytes, neutrophils, monocytes and eosinophils in the 5 Gy radiation dose
group had recovered to levels that were not more than 11.1% below their
respective baseline levels. However, for the two higher radiation dose groups (7.7
and 10 Gy), the levels of WBCs, lymphocytes, neutrophils and eosinophils were still
18.7%, 15.8%, 29.3% and 33.5% below the respective
baseline levels at day 90 postirradiation. Based on the magnitude of the decrease
and the time required to reach the lowest blood cell counts after irradiation,
lymphocytes appeared to be the most sensitive to SPE–like proton
irradiation.
The neutrophil counts at the 4 h time point were increased compared to
baseline values, followed by a reduction in counts by day 1 postirradiation. This
observed increase is believed to be a phase of granulocytosis where mature and early
precursor granulocytes are released from the bone marrow compartment ( 14 ). This process, called demargination of
granulocytes, is thought to be provoked by endogenous (or exogenous) epinephrine,
exercise or stress.
Due to technical limitations, the depth dose beam profiles for the simulated
electron SPE and proton SPE could not be perfectly matched and there were slight
variations in size between electron and proton SPE exposed animals. Previous results
for hematopoietic cell loss after irradiation have used homogeneous doses, so
knowing the exact target (i.e., marrow, circulating blood/lymphatic volume, etc.)
was perhaps not as relevant. This is a major issue in interpreting the results of
experiments in which inhomogeneous irradiation is delivered. We have previously
described the development and testing of a GEANT4 based Monte Carlo dose modeling
software tool that allows us to provide more accurate estimates for the dose to
specific organs. 2 Estimates of the median dose, mean dose and percentage
of organ volume receiving 2 Gy for an animal with a nominal 5 Gy skin dose are shown
in Table 1 . We have included organs of skin,
body (representing integral body dose), total lymphovascular volume (TLV, total body
without skin) and bone marrow (marrow cavities of skull, spine, ribs, pelvis and
proximal femur/humerus). This analysis demonstrates that the dose parameters for
these volumes are highly similar with a median difference of electron or proton dose
across all volumes of 5.6%. This is very close to the allowable variation
across the radiation field as delivered in clinical radiotherapy and is
approximately the allowable variation for human patients in prescribed vs. actual
dose (typically a 5% difference) and therefore is highly unlikely to be the
sole contributing factor behind any potential differences in hematopoietic responses
that might be observed between electron and proton SPE exposure in animals.
The effects of proton radiation on blood cell counts have been evaluated
previously in Rhesus monkeys exposed to 200 MeV protons at absorbed doses ranging
from 175 to 500 rads ( 11 ) or exposed to 146.8
MeV protons at doses ranging from 275 to 900 rads ( 10 ). At the first time point (day 3) after irradiation with 200 MeV
protons, the blood cell counts decreased by approximately 70% for WBCs and
by approximately 80% or more for lymphocytes, neutrophils and eosinophils
with the greatest initial depression in lymphocytes and the maximum level of
depression observed during the second and third weeks after irradiation. In
addition, the WBCs, lymphocytes, neutrophils, eosinophils and monocytes all
exhibited a similar general pattern of depression and recovery after proton
irradiation ( 11 ). The observations of the
monkey studies showing the radiation-induced decrease in WBC, lymphocyte and
neutrophil counts shortly after radiation exposure and the lymphocytes as the most
sensitive blood cell type are similar findings to our observations in the present
study utilizing the Yucatan minipig model. In Rhesus monkeys irradiated with 146.8
MeV protons, WBC and lymphocyte counts exhibited a dose-dependent decrease at the
first time point (day 3) after irradiation and reached the lowest level on day 8
postirradiation for lymphocytes, between days 8–11 for WBCs, and on day 11
for neutrophils ( 10 ). The radiation induced
reduction occurred earlier for lymphocytes than for WBCs in the Rhesus monkey, which
corresponds to the results reported here.
The radiation dose-responses were determined for each blood cell type at
each time point after radiation exposure. From the data represented in the
dose-response curves, the steepest slope of the dose-response curve was observed 4 h
postirradiation for monocytes, on day 1 postirradiation for lymphocytes, on day 4
postirradiation for WBCs and neutrophils and on day 14 postirradiation for
eosinophils, which coincide with the timing of the lowest blood cell counts for the
respective cell types. There are several mathematical models that can be used to
establish the dose-response relationship between radiation dose and cell survival,
with the linear-quadratic model being the most widely used. The linear-quadratic
model assumes that there are two components to cell killing by radiation, with one
proportional to radiation dose and the other proportional to the square of the
radiation dose ( 15 ). A survival curve derived
from the linear-quadratic model is not constrained as a straight log-linear line and
therefore the slope can vary with the radiation dose, providing final slopes that
differ even at the low-radiation dose range, in which a shoulder is prominent in
standard survival curves. The shape of a linear quadratic survival curve is
determined by a linear component and a quadratic component, which determines the
extent of curvature of the survival curve on a log-scale. In the present studies,
the survival curves were fitted using the linear quadratic equation. The quadratic
component of the survival curves was negligible in most cases, with only a few
exceptions. These results indicate that the dose-response relationship for blood
cell counts in the Yucatan minipig after proton irradiation is essentially linear on
a log scale and the linear-quadratic model is suitable in most situations for
accurate description of the dose-response relationship for the blood cell counts in
the proton irradiated Yucatan minipig.
Taken together, proton SPE radiation exposure in the Yucatan minipig results
in a dose-response reduction in peripheral blood cell counts, contributing to the
hematopoietic injury observed during the ARS. The data presented here indicate
significant acute effects of proton radiation to the hematopoietic compartment, as
well as potential late-radiation effects since blood cell counts did not recover by
day 90 postirradiation in the 7.7 and 10 Gy dose groups, as they were observed to do
in the 5 Gy dose group. Lastly, the Yucatan minipig serves as a suitable porcine
model alternative to the nonhuman primate model when evaluating the hematopoietic
effects of space radiation.
Introduction
Exposure to space radiation in a major solar particle event (SPE) may place
astronauts at significant risk for acute radiation sickness (ARS), skin injury
and/or a compromised immune defense. Unpredictable, highly energetic SPEs originate
from magnetically disturbed regions of the sun, which sporadically emit bursts of
energetic charged particles ( 1 , 2 ). Normally, large SPEs occur only once or twice in a
solar cycle; however, during the 22nd solar cycle, four comparable extremely large
SPEs occurred in a 4 month period. The types of radiation emitted during SPEs are
predominately protons ( 3 ).
The high skin doses that would occur during exposure to SPE radiation result
from the relatively low energy of most of the SPE protons, which have limited
penetrating ability in tissue. Thus, exposure to SPE radiation results in an
inhomogeneous total-body dose distribution, with considerably higher doses delivered
to the skin and subcutaneous tissues than those delivered to internal organs, as
described by Cengel et al . ( 4 ). The doses that could have been received by astronauts during large SPEs
have been estimated by modeling 3 large historic SPEs ( 5 ). During extravehicular activity (EVA), skin doses are
estimated to be as high as 32 Gy and in the blood-forming organs (BFO), 1.4 Gy.
Inside the spacecraft, the doses are estimated to be ∼3 Gy to the skin and
0.5 Gy to the BFO ( 5 ). From the modeling of
past SPEs, it has been concluded that the probable radiation environment of
astronauts will lead to the following doses during EVA: >5 Gy to the skin
and the maximum deep dose is estimated at 2 Gy (F. Cucinotta, NASA-Space Radiation
Program Element, http://www.nasa.gov/exploration/humanresearch/elements/research_info_element-srpe.html ).
The National Aeronautics and Space Administration (NASA) has determined that the
likelihood of acute risks during internal vehicle activity (IVA) is very small;
however, there are scenarios during lunar, trans-lunar or Mars EVAs in which ARS may
occur.
ARS represents a constellation of clinical toxicities that varies both
qualitatively and quantitatively with radiation dose, dose rate, quality and
individual radiation sensitivity ( 3 ). The
stages of the ARS include the prodromal stage (nausea, vomiting and diarrhea), the
latent stage, the manifest illness stage and the recovery or death stage. The
prodromal phase occurs within a few hours post-exposure, with a latency time
inversely correlated with dose. There are three classic ARS syndromes that can lead
to death; these are the hematopoietic syndrome, the gastrointestinal syndrome and
the cerebrovascular syndrome. Symptoms of the cerebrovascular syndrome include
severe nausea and emesis, diarrhea, loss of consciousness, convulsive seizures, and
coma. The mechanisms involved in the cerebrovascular syndrome are unclear. Both the
hematopoietic and gastrointestinal syndromes are thought to result from the cell
killing effects of radiation in the stem cells of critical self-renewing tissues.
The destruction of hematopoietic progenitor cells ultimately results in reduced
numbers of mature, circulating blood cells. Lymphopenia has been used in the past as
an indicator of the systemic effects of radiation exposure, as lymphocytes are known
to be the most sensitive blood cell type to radiation. Lymphocytes mediate the
adaptive immune response, and they have a life span of weeks to years. Neutrophil
granulocytes are the most abundant phagocyte (other circulating phagocytes include
eosinophils and monocytes), and they are the first line of defense in the body.
Encompassing 50–60% of the circulating white blood cells (WBCs) in
humans, these cells have a short life span and are constantly being renewed.
Neutropenia commonly occurs in patients receiving chemotherapy or radiation therapy
and may result in infections, fever and impairment of immune system mechanisms.
While wound healing is suppressed in the space environment ( 6 ), platelet count depression contributes to bleeding
caused by hemorrhage. For the gastrointestinal syndrome, the destruction of stem
cells in the gut leads to a depopulation of the epithelial lining of the
gastrointestinal tract. The symptoms resulting from the loss of the epithelial
lining include diarrhea, emaciation and dehydration. For astronauts, it is not
expected that the doses received will be sufficiently high to result in death from
the gastrointestinal or cerebrovascular syndrome, but the doses received may be
sufficient to cause hematopoietic cell loss, immune system dysfunction and symptoms
of the ARS such as vomiting. If such ARS symptoms do occur in astronauts, it is
expected that they would be accompanied by skin damage, due to high skin doses from
SPEs, which can lead to burns.
A combined U.S. Air Force (USAF)/NASA project was conducted from
1963–1969, to measure the biological effects of space radiation (with
varying energies of proton radiation) and calculate the relative biological
effectiveness (RBE) values using approximately 2,000 primates ( 7 ). Late radiation effects included leukemia ( 8 ) and endometriosis ( 9 ). The authors suggest that the occurrence of radiation
induced endometriosis is a systemic rather than local disease, with deficiencies in
the immune system as likely contributors; however, immune parameters were not
reported. The acute effects after whole-body proton, γ or X irradiation at
energies and doses found in the space environment, were measured. During these
studies, ARS symptoms reported include malaise with depression ( 10 ), loss of appetite and diarrhea ( 10 , 11 ). Blood
samples were taken from Rhesus monkeys within days post-irradiation to evaluate the
hematopoietic tissue injury. A dose-dependent reduction in circulating WBC counts
after proton or γ irradiation, with a greater depression in the
proton-irradiated animals, was reported ( 11 ).
A dose-rate effect on proton-radiation induced acute mortality was also reported
( 10 ).
As the studies reported here were designed to mimic EVA conditions for
astronauts during a large SPE, it was decided that the skin doses to be used would
range from 5–10 Gy. The SPE exposures delivered at the James M. Slater, M.D.
Proton Treatment and Research Center were created to match the electron irradiations
(used as the control radiation modality) described by Cengel et al .
( 4 ).
In the current study, we investigated SPE-like proton radiation on peripheral
blood cell counts as early as 4 h postirradiation to 90 days postirradiation in a
porcine model utilizing the Yucatan minipig. The Yucatan minipig was used in our
previous study investigating electron radiation induced skin toxicity ( 12 ). In the current study, Yucatan minipigs
were exposed to proton radiation to characterize the time and dose response of
radiation induced changes in the hematopoietic system. The data presented here are
similar to the data from the large-scale primate study, suggesting that the Yucatan
minipig may be an alternative to the nonhuman primate in radiobiology research and a
suitable large animal model to study the physiological symptoms associated with
ARS.
Materials|Methods
Yucatan minipigs aged 8–10 weeks were purchased from Sinclair
BioResources (Auxvasse, MO). Animals were acclimated for 7 days in the Loma
Linda University Medical Center (LLUMC) animal facility, and were housed
individually, given water ad libitum and fed standard
mini-piglet chow twice daily. The animal care and treatment procedures were
approved by the Institutional Animal Care and Use Committee of the LLUMC and the
University of Pennsylvania.
Upon acclimation, the animals were randomly assigned to 4 groups with 3
animals per group and exposed to proton radiation at doses of 0
(sham-irradiation control), 5.0, 7.7 and 10.0 Gy. Animals were evaluated once
daily for at least 90 days after irradiation.
For the proton radiation exposures (referred to as proton SPE), a custom
designed double scattering system was developed and built to allow for the
delivery of 50-cm diameter radiation field with a radiation flatness of
3.5% or better. This system was installed on one of the research
beam-lines available at LLUMC and was tuned to deliver approximately 5 Gy/h. A
clinical modulator wheel was used to create a fully modulated 155 MeV/n proton
beam, while radiation dose was prescribed at a depth of 1.1 cm in water along
the central beam axis. A 2 stage bolus at the level of the animal chamber and
beam weighting allowed for the creation of a custom depth dose profile to match
the combined 6 + 12 MeV electron beam (referred to electron SPE)
described by Cengel et al . ( 4 ), which itself was developed to mimic the dose profile of an SPE.
This setup delivered a maximum proton range of 5.0 cm (approximately 80 MeV) at
the entrance of the animal cage and a distribution of proton energies below 80
MeV (due to the beam modulation), which is reflective of the space environment
where the maximum proton energy is accompanied by a significant number of lower
energy protons. Characterization of the proton beam was completed using
radiographic film, radiochromic film and ionization chambers. Figure 1 shows the dose distribution profile of the
proton SPE beam developed at LLUMC (dashed line), measured using Gafchromic film
(EDR-2) verified with a plane parallel ionization chamber, and the electron SPE
beam profile (solid line), measured with a plane parallel ionization chamber
(PPC40, IBA-Dosimetry) in a plastic water phantom. Field flatness was
established using radiochromic film at both the external and internal surface of
the minipig cage. The dose at the prescription point was calibrated using an
Exradin T1 ionization chamber. Animals were irradiated to 5.0, 7.7 and 10.0 Gy
per side with the animal cage rotated at 50% dose delivery per side.
Dose delivery was verified with TLD dosimeters that were attached to the
animal.
A Geant4 based Monte Carlo dose modeling software tool was utilized to
estimate dose to specific organs and a completed description will be published
separately. Estimates of the median dose, mean dose and percentage of organ
volume receiving 2 Gy for an animal with a nominal 5 Gy skin dose are shown in
Table 1 . We have included organs of
skin, body (representing integral body dose), total lymphovascular volume (TLV)
and bone marrow (marrow cavities of skull, spine, ribs, pelvis and proximal
femur/humerus). TLV is essentially the entirety of the body that receives blood
or lymphatic flow and is defined as “from the dermis inward”,
i.e., almost the whole body, but without the part of the skin that has no
vessels.
At 4 h and 1, 4, 14, 30 and 90 days after radiation exposure,
whole-blood samples were collected from each anesthetized animal (cranial vena
cava) and placed into a lavender top collection tube containing EDTA and kept at
ambient temperature during preparation for transport. Samples were then
transported at 4°C to Antech Diagnostics (Irvine, CA) and analyzed using
a Bayer Advia 120 Hematology Analyzer (using the porcine specific profile)
within 24 h of the blood sample collection. It has been previously determined
that the blood cell counts are stable and reliable when comparing blood cell
counts analyzed immediately after collection or within/up to 24 h after
collection ( 13 ).
The mean counts of WBCs, lymphocytes, neutrophils, monocytes,
eosinophils, red blood cells (RBCs) and platelets of all animals before
irradiation were calculated and used as the baseline control values for the
respective blood cell types (n = 12). For each animal at each time point
after irradiation, the count of each blood cell type was divided by the
respective baseline control value and the result was expressed as fractions of
control for all further analyses. The blood cell count at each time point for
each dose group consists of 3 data points (n = 3), except for the
baseline control value (obtained prior to radiation exposure), or 0 Gy dose
group, which consists of 12 data points (n = 12). The blood cell count
data for animals irradiated with 0 (sham radiation control), 5.0, 7.7 and 10.0
Gy of proton radiation were compared by one-way ANOVA followed by
Tukey's test using SigmaPlot software (Version 12) to evaluate the blood
cell count changes at different time points after irradiation.
The relationship between radiation dose and counts of each blood cell
type was determined for each time point after irradiation by fitting the data to
a linear-quadratic model ( y =
e – aD – bD2 )
using SigmaPlot graphics software (SPSS Inc., Chicago, IL), in which
D is the radiation dose and y is the blood
cell count expressed as a fraction of control.
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