Linear-quadratic Equation Research Articles

A Random Parameter Model for Continuous-Time Mean-Variance Asset-Liability Management

We consider a continuous-time mean-variance asset-liability management problem in a market with random market parameters; that is, interest rate, appreciation rates, and volatility rates are considered to be stochastic processes. By using the theories of stochastic linear-quadratic (LQ) optimal control and backward stochastic differential equations (BSDEs), we tackle this problem and derive optimal investment strategies as well as the mean-variance efficient frontier analytically in terms of the solution of BSDEs. We find that the efficient frontier is still a parabola in a market with random parameters. Comparing with the existing results, we also find that the liability does not affect the feasibility of the mean-variance portfolio selection problem. However, in an incomplete market with random parameters, the liability can not be fully hedged.

Radiation exposure dose in human blood lymphocytes as assessed by the CBMN assay

Abstract The chances of accidental exposure are augmented as the application of ionizing radiation increases in various fields. Such accidental exposures may occur at nuclear power plants, laboratories, and hospitals. Cytogenetic assays have been used for estimating radiation dose in the situation of the accidents. The micronucleus assay has several advantages over the other cytogenetic methods as it is simple and fast. The present study aimed at investigation of the micronuclei fre-quencies in cytokinesis-block cells in human blood lymphocytes after γ-irradiation and at establishment of a standard dose response relationship. The samples of peripheral blood were obtained from 6 different donors aged between 24 and 30 years old. The bloods were irradiated in vitro with 0-5 Gy. A linear quadratic dose-response equation was obtained by scoring the micronuclei in binucleated cells; y = 27.87x 2 + 46.13x + 2.08 ( r 2 = 0.99). Irradiation caused a significant decrease in the nuclear division index. Necrotic and apoptotic cells increased in number after irradiation in a dose-dependent manner. In conclusion, the conventional cytokinesis-block micronucleus assay has proven to be the great technique in biological dosimetry. Dose-response calibration curve derived from CMBN assay could be used to estimate the exposure dose during a radiological emergency.

Z-score reference ranges for normal fetal heart sizes throughout pregnancy derived from fetal echocardiography.

To construct Z-score reference ranges for normal fetal heart sizes throughout pregnancy. This is a prospective cross-sectional investigation of 809 normal singleton fetuses from 11th week to term. Fetal transverse heart diameter (HD), heart length (HL), heart circumference (HC) and heart area (HA) were derived from two-dimensional echocardiography. The regression analyses of the mean (M) and the standard deviation (SD) for each parameter were calculated separately, using fetal somatic sizes as independent variables. A group of fetal heart diseases was assessed using these parameters. Strong correlations were found between fetal heart sizes and somatic sizes. Linear-cubic regression equations were each fitted to the models of the means of the heart sizes, whereas linear-quadratic equations were fitted to the models of the SDs. HD was the dependent variable that provided the highest correlation coefficient with all of the fetal sizes, followed by HL, HC and HA. All fetuses with Ebstein's anomaly and most with homozygous α-thalassemia-1 demonstrated Z-scores reflective of increased heart sizes. The calculation of Z-scores for heart sizes as a function of fetal somatic size is simple and may be useful for quantitative assessment of some cardiac diseases, particularly cardiomegaly caused by homozygous α-thalassemia-1.

P10 * CORRELATION BETWEEN BIOLOGICALLY EFFECTIVE DOSE (BED) AND LOCAL CONTROL OF BRAIN METASTASES POST STEREOTACTIC RADIOTHERAPY

INTRODUCTION: There is increasing interest in fractionated stereotactic radiotherapy (SRT) for brain metastases however the optimum model to compare regimens is not known. An overestimation of the biological effect of high dose per fraction radiotherapy by the linear quadratic (LQ) model has been demonstrated in in-vitro and in-vivo experiments. Several alternative models also exist. The purpose of this study was to determine if BED calculated with the linear quadratic cubic (LQC) equation resulted in a stronger correlation with 12 month local control following SRT (single or fractionated) than BED calculated with the LQ equation. METHOD: Series of SRT for brain metastasis were identified from a recent meta-analysis. BED for LQ was calculated using variable values of α/β (6,9,12,15 Gy). BED for LQC was calculated using variable values of α/β (6,9,12,15 Gy) and variable values for D1 (6,12,18,24 Gy). Correlation with 1 year local control was calculated using Pearson correlation statistic. RESULTS: No significant correlation with 1 year local control was seen when BED was calculated using the LQC equation and a D1 value of 12 Gy or less. Significant correlations were observed for all values of α/β tested for the LQ equation and values of D1 of 18 and 24 Gy for the LQC. The most significant correlations were seen with the LQ equation for α/β = 12 (p = 0.005) and with the LQC equation for α/β = 6, D1 = 24 (p = 0.009). CONCLUSION: There was no apparent advantage for the use of the LQC over the LQ equation within the data set examined and with the values for α/β and D1 employed. The LQ equation with with α/β = 12 seems the most appropriate model to use when assessing histologically heterogenous series of brain metastases treated with SRT.

Poster - Thur Eve - 60: Clinical use of a 3D BED-based assessment tool for patient retreatment

A protocol was developed which enables the routine clinical use of a 3D biological equivalent dose (BED) plan sum for retreated patients. This protocol is used for patients who are to be retreated, where one of the plans is in a standard dose fractionation and the other is in a hypofractionated regime. A deformable registration is applied to the original dose map to the subsequent CT scan. An in-house program has been developed to sum the registered dose between original and subsequent dose plans. After the sum is accomplished, the 3D BED sum is converted to dose through a 3D voxel by voxel solution of the linear quadratic BED equation. The use of BED based 3D dose summation for replanned patients gives an improved picture of the overall dose distribution for situations where the daily dose is different in both plans. This tool allows a more thorough evaluation of the plan sum and provides an alternative to the worst case BED scenario using point maximum statistics, giving a potential for better PTV coverage.

Radiation biology in the context of changing patterns of radiotherapy.

The last decade has witnessed a revolution in the clinical application of high-dose "ablative" radiation therapy. Initially this approach was limited to the treatment of brain tumors, but more recently we have seen its successful extension to tumors outside the brain, e.g., for small lung nodules. These advances have been driven largely by improvements in image-guided inverse treatment planning that allow the dose per fraction to the tumor to be increased over the conventional 2 Gy dose while keeping the late normal tissue complications at an acceptable level by dose limitation. Despite initial concerns about excessive late complications, as might be expected based on dose extrapolations using the linear-quadratic equation, these approaches have shown considerable clinical promise. Our knowledge of the biological consequences of high-doses of ionizing radiation in normal and cancerous tissues has lagged behind these clinical advances. Our intent here is to survey recent experimental findings from the perspective of better understanding the biological effects of high-dose therapy and whether they are truly different from conventional doses. We will also consider the implications of this knowledge for further refining and improving these approaches on the basis of underlying mechanisms.

Outcomes and toxicity of SBRT for patients with unresectable pancreatic adenocarcinoma.

317 Background: To report updated outcomes and toxicity of stereotactic body radiotherapy (SBRT) for patients with unresectable pancreatic adenocarcinoma treated over the past 11 years from a single institution. Methods: One hundred and ninety-nine patients with primary, unresectable pancreatic adenocarcinoma were treated with SBRT at our institution from 2002 to 2013. One hundred and sixty-four had locally advanced disease, 12 had borderline resectable disease, 21 were medically inoperable, and 2 had resectable disease but refused surgery. Fifteen patients had metastases at the time of SBRT. Forty-six patients were treated with prior RT, 16 of whom were enrolled on a combined IMRT/SBRT trial. Most common treatment regimens were 25 Gy x 1 (51.3%), 6.6 Gy x 5 (25.6%), 6 Gy x 5 (15.0%). Fifty-seven patients had no prior/current chemo while 142 patients had prior/current chemo (134 had gemcitabine-based chemo). BED10 and BED3 were defined using the linear quadratic equation assuming an α/β of 10 and 3, respectively. Results: Median follow-up was 7.1 months (0.13-63.58). The 6- and 12-month cumulative incidence of local recurrence (CIR) were 7.93% (4.07-11.80%, 95% CI) and 12.48% (7.68-17.28%, 95% CI), respectively. Three patients converted to resection after SBRT. BED10 (median 87.5, range 19.5-97.5), prior RT, prior/current chemo, and tumor location did not predict for CIR. OS rates at 6 months and 12 months were 71.23% (65.02-78.0%, 95% CI) and 36.23% (29.54-44.4%, 95% CI), respectively. Median OS from date of diagnosis was 14.27 months (13.25-16.90 95% CI). Patients who received prior/current chemo had better OS (p=0.0035). There were 26 (13%) recorded GI ulcers/strictures/bleed (5 acute, 21 late) after treatment. BED3 (median 233.3, 30-233.3) predicted for these toxicities (OR 1.01, 1.00-1.01 95% CI, p=0.022), while age, prior RT, prior/current chemo, tumor location did not. Conclusions: SBRT for pancreatic adenocarcinoma is effective for local control with associated risk of toxicity. The risk of GI toxicity is correlated with BED3. Survival is associated with the use of chemotherapy. SBRT may be advantageous due to its good local control with shortened treatment duration that minimizes interruption in chemotherapy.

Prostate Cancer and the Hypofractionation Hypothesis

Prostate Cancer and the Hypofractionation Hypothesis

Abstract 439: Mathematical modeling of cellular dose-response for radiation and radiation-drug combinations including cell cycle effects.

Abstract Thirty-six in vitro radiation dose-response data sets having 7 or more points, covering a variety of cell lines, were used to test four proposed models as alternatives to the linear-quadratic equation: the single-mechanism lognormal, the two-mechanism lognormal, the single-mechanism Hill and the two-mechanism Hill. All four models are forms of our general “damage model,” developed originally for drug dose-response. The lognormal models relate survival to damage using the cumulative lognormal density function, whereas the Hill models use a Hill equation. The models were ranked according to the Akaike Information Criterion, with the single-mechanism lognormal performing the best overall. A subset of the data showing 2-mechanism behavior was identified using the F-test method; for this subset, the two-mechanism lognormal model was superior. The lognormal model is therefore proposed as an alternative to the linear-quadratic. The lognormal damage model is then extended to the case of radiochemotherapy using the concept of additive damage, which we previously developed for drugs with two mechanisms, and then applied to combination exposure. Previously, it was found that fixed-schedule, varying-dose exposures to drug and radiation could be described by the additive damage model. Here, the case of varying schedule is considered, for gemcitabine, which showed schedule-dependent radiosensitization in studies by Pauwels et al (2003, 2009). Cell cycle effects are included through a kinetic equation describing the evolution of the population distribution over the cell cycle. In contrast to some previous models where discrete phases of the cell cycle are treated as compartments, here the distribution is a continuous density function. Gemcitabine is assumed to cause a block at a single point, with dose-dependent duration. The cell cycle phase population density distribution then enters into the radiation damage term. The model thus includes radiation-drug interaction in two ways: through additive damage and through cell cycle effects. The case of fractionated doses of gemcitabine alone is also considered. Overall, the model provides a framework for understanding the complex effects of schedule and dose, as well as a method to potentially predict combination or fractionated dose-response from knowledge of a drug's perturbations to the cell cycle phase distribution. It is expected that these models will have application in preclinical optimization of combination therapy, as well as in computational simulation of anticancer therapy. Citation Format: Katherine S. Williams, Ardith W. El-Kareh, Timothy W. Secomb. Mathematical modeling of cellular dose-response for radiation and radiation-drug combinations including cell cycle effects. [abstract]. In: Proceedings of the 104th Annual Meeting of the American Association for Cancer Research; 2013 Apr 6-10; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2013;73(8 Suppl):Abstract nr 439. doi:10.1158/1538-7445.AM2013-439

Theoretical implications of incorporating relative biological effectiveness into radiobiological equivalence relationships

Earlier radiobiological equivalence relationships as derived for low-linear energy transfer (LET) radiations are revisited in the light of newer radiobiological models that incorporate an allowance for relative biological effectiveness (RBE). Linear-quadratic (LQ) radiobiological equations for calculating biologically effective dose at both low- and high-LET radiations are used to derive new conditions of equivalence between a variety of radiation delivery techniques. The theoretical implications are discussed. The original (pre-LQ) concept of equivalence between fractionated and continuous radiotherapy schedules, in which the same physical dose is delivered in each schedule, inherently assumed that low-LET radiation would be used in both schedules. LQ-based equivalence relationships that allow for RBE and are derived assuming equal total physical dose between schedules are shown to be valid only in limited circumstances. Removing the constraint of equality of total physical dose allows the identification of more general (and more practical) relationships. If the respective schedules under consideration for equivalence both involve radiations of identical LET, then the original equivalence relationships remain valid. However, if the compared schedules involve radiations of differing LET, then new (and more restrictive) equivalence relationships are found to apply. Theoretically derived equivalence relationships based on the LQ model provide a framework for the design and intercomparison of a wide range of clinical techniques including those involving high- and/or low-LET radiations. They also provide a means of testing for the validity of variously assumed tissue repair kinetics.

Corrections to “Riccati Equations on Noncommutative Banach Algebras"

This paper contains corrections to [R. Curtain, SIAM J. Control Optim., 49 (2011), pp. 2542--2557]. While all claims remain valid, and the proof for the linear quadratic Riccati equations is correct, this proof does not cover the positive-real and bounded-real Riccati equations. Here a correct proof is given for these cases.

Abstract 3962: Mathematical models for cellular pharmacodynamics of fractionated radiation and radiochemotherapy

Abstract Cellular response to radiation is generally described by the linear-quadratic equation, but the extension to complicated fractionated schedules, and to combined exposure with chemotherapeutic drugs is not well-established. Mathematical models for cellular response are needed for predictive quantitative modeling of treatment. Here, such models are formulated using the previously developed concepts of peak damage models and additive damage, which in prior studies proved successful in describing cellular pharmacodynamics of single-agent and combination chemotherapy. The exponential form of the linear-quadratic equation is replaced by Hill or cumulative lognormal functions of the peak value over time of a quantity termed “cellular damage.” Damage is a saturating function of radiation dose. Cell survival depends on whether the peak value of cellular damage ever exceeds a threshold value during treatment. This model is tested for a range of data sets for single-dose radiation, and compares favorably with the linear-quadratic. In one data set (Park et al 2008) the dose range was sufficiently wide to show the significant overestimation of cell kill by the linear-quadratic model at high doses; the Hill/lognormal formulation behaves more satisfactorily in this limit. The model is then extended to the case of fractionated radiation through the assumption that damage decays between treatments according to first-order kinetics, and damage from different cycles is additive. The model gives a satisfactory fit to literature data with multiple fractionation schedules for the same drug and cell line. Finally, the principle of additive damage is applied to model cellular response to radiochemotherapy, with damage as a linear superposition of terms from radiation and drug. Overall, the peak cellular damage model with additive damage was found to fit in vitro dose-response data well, and provides a tool for understanding and predicting response as schedule and dose are varied in combination treatments. It is expected that these models will have application in assessment of preclinical cellular pharmacodynamics data, as well as computational simulations of treatment response. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 103rd Annual Meeting of the American Association for Cancer Research; 2012 Mar 31-Apr 4; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2012;72(8 Suppl):Abstract nr 3962. doi:1538-7445.AM2012-3962

Abstract 3447: Tetrac (tetraiidothyroacetic acid) decreases in vitro x-ray survival of a human medullary thyroid cancer cell line under oxic and hypoxic conditions

Abstract In 2009 we showed that 2 µM tetrac given for 1 hour at 37oC prior to 250 kVP x-irradiation sensitized GL261 murine brain tumor cells. Radiosensitization was accomplished by increasing the alpha component in the linear-quadratic equation of cell survival (Cell Cycle, 8:2586-91). In 2011, we showed that tetrac also sensitized U87MG human brain tumor cells to 250 kVp x-rays (Cell Cycle, 10: 352-57). Again radiosensitization was accomplished by an increase in the αx-ray component. Tetrac also inhibited the repair of DNA double strand breaks in U87MG cells. However, tetrac which binds to the αvβ3 integrin receptor and inhibitssignaling from the αvβ3 receptor, penetrates the cell and has a thyromimetic effect which offsets radiosensitization. In this regard, we synthesized a nanoparticle tetrac formulation termed Nano-T. Nano-T also binds to the αvβ3 receptor but does notpenetrate the cell. Nano-T causes radiosensitization in vitro in H522 lung cancer cells, producing an added benefit compared to tetrac. We have also shown that daily treatment of in vivo human-MTC (h-MTC) solid tumors in mice with Nano-T for 20 days produced significant growth inhibition. It is our intent to combine Nano-T with ionizing radiation in vivo, and we have begun by studying the effects of tetrac on h-MTC cells in vitro. These h-MTC cells are show an in vitro cell culture doubling time of 96.2 hours and a clonogenicity of 3.16%. We irradiated cells in exponential growth with 250 kVp X-rays. Below we give the LQ survival parameters, and the surviving fraction at 2 Gy (SF2). Table 1. Initial Results of 250 kVp Single Dose X-irradiation on h-MTC CellsIn Vitro without and with Tetrac ≤ α SF2 Tetrac Oxygen (Gy-1 x 10-1) (Gy-2 x 10-2) Enhancment Enhancement Factor Factor Without Tetrac Oxic Cells - 0.033 0.0256 0.901 2.55 Hypoxic Cells 0.030 0.0023 0.922 With Tetrac Oxic Cells 0.472 0.0495 0.330 2.84 2.60 Hypoxic Cells 0.013 0.0256 0.803 2.84 First, h-MTC cells irradiated as oxic or hypoxic, exponentially growing cells are very radioresistant suggesting a large capacity to repair radiation damage. Second, tetrac sensitized both oxic and hypoxic h-MTC cells. These characteristics speak to our proposed Nano-T in treatment of h-MTC tumors in vivo. Nano-T should increase the radiosensitivity of both oxic and hypoxic cells and should also decrease the repair of radiation damage in conventional fractionated radiation therapy. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 103rd Annual Meeting of the American Association for Cancer Research; 2012 Mar 31-Apr 4; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2012;72(8 Suppl):Abstract nr 3447. doi:1538-7445.AM2012-3447

Chromosomal aberrations in the bone marrow cells of mice induced by accelerated 12C 6+ ions

The whole bodies of 6-week-old male Kun-Ming mice were exposed to different doses of 12C 6+ ions or X-rays. Chromosomal aberrations of the bone marrow (gaps, terminal deletions and breaks, fragments, inter-chromosomal fusions and sister-chromatid union) were scored in metaphase 9 h after exposure, corresponding to cells exposed in the G 2-phase of the first mitosis cycle. Dose–response relationships for the frequency of chromosomal aberrations were plotted both by linear and linear-quadratic equations. The data showed that there was a dose-related increase in the frequency of chromosomal aberrations in all treated groups compared to controls. Linear-quadratic equations were a good fit for both radiation types. The compound theory of dual radiation action was applied to decipher the bigger curvature ( D 2) of the dose–response curves of X-rays compared to those of 12C 6+ ions. Different distributions of the five types of aberrations and different degrees of homogeneity were found between 12C 6+ ion and X-ray irradiation and the possible underlying mechanism for these phenomena were analyzed according to the differences in the spatial energy deposition of both types of radiation.

Dose-Fractionation Sensitivity of Prostate Cancer Deduced From Radiotherapy Outcomes of 5,969 Patients in Seven International Institutional Datasets: α/β = 1.4 (0.9–2.2) Gy

There are reports of a high sensitivity of prostate cancer to radiotherapy dose fractionation, and this has prompted several trials of hypofractionation schedules. It remains unclear whether hypofractionation will provide a significant therapeutic benefit in the treatment of prostate cancer, and whether there are different fractionation sensitivities for different stages of disease. In order to address this, multiple primary datasets have been collected for analysis. Seven datasets were assembled from institutions worldwide. A total of 5969 patients were treated using external beams with or without androgen deprivation (AD). Standard fractionation (1.8-2.0 Gy per fraction) was used for 40% of the patients, and hypofractionation (2.5-6.7 Gy per fraction) for the remainder. The overall treatment time ranged from 1 to 8 weeks. Low-risk patients comprised 23% of the total, intermediate-risk 44%, and high-risk 33%. Direct analysis of the primary data for tumor control at 5 years was undertaken, using the Phoenix criterion of biochemical relapse-free survival, in order to calculate values in the linear-quadratic equation of k (natural log of the effective target cell number), α (dose-response slope using very low doses per fraction), and the ratio α/β that characterizes dose-fractionation sensitivity. There was no significant difference between the α/β value for the three risk groups, and the value of α/β for the pooled data was 1.4 (95% CI = 0.9-2.2) Gy. Androgen deprivation improved the bNED outcome index by about 5% for all risk groups, but did not affect the α/β value. The overall α/β value was consistently low, unaffected by AD deprivation, and lower than the appropriate values for late normal-tissue morbidity. Hence the fractionation sensitivity differential (tumor/normal tissue) favors the use of hypofractionated radiotherapy schedules for all risk groups, which is also very beneficial logistically in limited-resource settings.

The Educational Kuznets Curve: A Case of Nepal

Education is among the basic human needs and one of the components of well being in the modern world. Equal distribution of education is of great interest in public policy analysis. Spending in education represents substantial share of government revenue. The inequality in educational distribution represents large welfare loss. The purposes of this article are three folds. First, it calculates average years of schooling. Second, it estimates educational inequality in terms of standard deviation of schooling. Third, it examines the Educational Kuznets Curve in case of Nepal and answers the question: does it fit? This is quantitative study based on the secondary data collected and published by Central Bureau of Statistics. The study finds that the average years of schooling are increasing over the census years. It stood at 0.125 years in 1952 for all population and 0.245 and 0.019 respectively for males and females. The same data for all population, males and females for the year 2001are 4.385, 5.119, and3.083 years respectively. The data on standard deviation of schooling show that they are all in increasing trend from the census year 1952 to Census Year 2001.With the help of econometric test of both linear and nonlinear quadratic equations, this study concludes that the Educational Kuznets Curves does not exist in Nepal due to very low average years of schooling.

Mechanistic formulation of a lineal‐quadratic‐linear (LQL) model: Split‐dose experiments and exponentially decaying sources

In recent years, several models were proposed that modify the standard linear-quadratic (LQ) model to make the predicted survival curve linear at high doses. Most of these models are purely phenomenological and can only be applied in the particular case of acute doses per fraction. The authors consider a mechanistic formulation of a linear-quadratic-linear (LQL) model in the case of split-dose experiments and exponentially decaying sources. This model provides a comprehensive description of radiation response for arbitrary dose rate and fractionation with only one additional parameter. The authors use a compartmental formulation of the LQL model from the literature. They analytically solve the model's differential equations for the case of a split-dose experiment and for an exponentially decaying source. They compare the solutions of the survival fraction with the standard LQ equations and with the lethal-potentially lethal (LPL) model. In the case of the split-dose experiment, the LQL model predicts a recovery ratio as a function of dose per fraction that deviates from the square law of the standard LQ. The survival fraction as a function of time between fractions follows a similar exponential law as the LQ but adds a multiplicative factor to the LQ parameter beta. The LQL solution for the split-dose experiment is very close to the LPL prediction. For the decaying source, the differences between the LQL and the LQ solutions are negligible when the half-life of the source is much larger than the characteristic repair time, which is the clinically relevant case. The compartmental formulation of the LQL model can be used for arbitrary dose rates and provides a comprehensive description of dose response. When the survival fraction for acute doses is linear for high dose, a deviation of the square law formula of the recovery ratio for split doses is also predicted.

The Hug–Kellerer equation as the universal cell survival curve

The Hug–Kellerer (H-K) equation is one of the earliest proposed radiation cell survival curves. We examine this equation in view of the recent perceived need for a universal cell survival curve which would be applicable to single radiation fractions at high doses. We derive relationships between the three parameters of the H-K equation and the parameters α and β of the linear-quadratic equation. Using these relationships we show how the H-K equation can be used to determine single-fraction doses which are equivalent in theory to the dose in a conventional multi-fraction course of radiation therapy.

Stereotactic Body Radiotherapy for Primary Management of Early-Stage, Low- to Intermediate-Risk Prostate Cancer: Report of the American Society for Therapeutic Radiology and Oncology Emerging Technology Committee

Stereotactic Body Radiotherapy for Primary Management of Early-Stage, Low- to Intermediate-Risk Prostate Cancer: Report of the American Society for Therapeutic Radiology and Oncology Emerging Technology Committee

ESTABLISHMENT OF AN X-RAY STANDARD CALIBRATION CURVE BY CONVENTIONAL DICENTRIC ANALYSIS AS PREREQUISITE FOR ACCURATE RADIATION DOSE ASSESSMENT

The dicentric assay was established to carry out cytogenetic biodosimetry after suspected radiation overexposure, including a comprehensive documentation system to record the processing of the specimen, all data, results, and stored information. As an essential prerequisite for retrospective radiation dose assessment, a dose-response curve for dicentric induction by in vitro x-ray irradiation of peripheral blood samples was produced. The accelerating potential was 240 kV (maximum photon energy: 240 keV). A total of 8,377 first-division metaphases of four healthy volunteers were analyzed after exposure to doses ranging from 0.2 to 4.0 Gy at a dose rate of 1.0 Gy min. The background level of aberrations at 0-dose was determined by the analysis of 14,522 first-division metaphases obtained from unirradiated blood samples of 10 healthy volunteers. The dose-response relationship follows a linear-quadratic equation, Y = c + alphaD + betaD, with the coefficients c = 0.0005 +/- 0.0002, alpha = 0.043 +/- 0.006, and beta = 0.063 +/- 0.004. The technical competence and the quality of the calibration curve were assessed by determination of the dose prediction accuracy in an in vitro experiment simulating whole-body exposures within a range of 0.2 to 2.0 Gy. Dose estimations were derived by scoring up to 500-1,000 metaphase spreads or more (full estimation mode) and by evaluating only 50 metaphase spreads (triage mode) per subject. The triage mode was applied by performing manifold evaluations of the full estimation data in order to test the robustness of the curve for triage purposes and to assess possible variations among the estimated doses referring to a single exposure and preparation.