Linear-quadratic Equation Research Articles

The Dose/Fractionation Debate in Limited-Stage Small Cell Lung Cancer.

To explore the most suitable dosage regimen for limited-stage small cell lung cancer (LS-SCLC) and provide references for clinical selection, strict inclusion criteria were applied, and studies were screened from Pubmed, Embase, and Web of Science. Subsequently, data on two-year overall survival rates and dosage regimens were collected, and scatter plots were constructed to provide a comprehensive perspective. The survival benefits of various dosage regimens were evaluated, and a linear quadratic equation was utilized to fit the relationship between the biologically effective dose (BED10) and the two-year overall survival rate. Among the five randomized controlled trials, the two-year overall survival rate of ConvTRT regimens with BED10 > 60 Gy (rough value) was only at or below the median of all ConvTRT regimens or all included study regimens, indicating that increasing the number and total dose of ConvTRT does not necessarily lead to better prognosis. In the exploration of HypoTRT regimens, there was a linear positive correlation between BED10 and the two-year overall survival rate (p < 0.0001), while the exploration of HyperTRT regimens was relatively limited, with the majority focused on the 45 Gy/30 F regimen. However, the current 45 Gy/30 F regimen is not sufficient to control LS-SCLC, resulting in a high local recurrence rate. High-dose ConvTRT regimens have long treatment durations and may induce tumor regrowth which may cause reduced efficacy. Under reasonable toxicity reactions, HyperTRT or HypoTRT with higher radiotherapy doses is recommended for treating LS-SCLC.

Effect of changing the radiation dose range on the in vitro cytogenetic dose response to gamma-rays

Purpose To examine the distortion of the linear quadratic (LQ) model of in vitro cytogenetic dose response over an extended range of γ-ray doses by analyzing the available literature data, and to establish the dose ranges, in which the LQ dose response curve (DRC) can be most accurately fitted for biological dosimetry. Materials and methods Data on yields of dicentrics (Dic) or dicentrics plus centric rings (Dic + CR) induced in vitro in human lymphocytes by acute γ-rays were extracted from 108 open sources. The overall dose response dataset in the dose range up to 50 Gy was fitted to a fractional-rational (FR) model, which included a ‘basic’ LQ function in the numerator, and a reduction factor dependent on the square of the dose in the denominator. Cytogenetic dose response data obtained at Grigoriev Institute for Medical Radiology, Kharkiv, Ukraine (GIMRO) in the range 0.1 − 20.3 Gy acute γ-rays were fitted to the LQ model with the progressive changing minimum or maximum radiation dose. Results The overall dose response, as expected, followed the LQ function in the dose range ≤5 Gy, but in the extended dose range appeared to be S-shaped, with intensive saturation and a plateau at doses ≥22 Gy. Coefficients of the ‘basic’ LQ equation in FR model were very close to many published DRCs; calculated asymptote was 17. Fitting of the GIMRO dataset to the LQ model with the shift of the dose range showed the increase in linear coefficient with the increment of either minimum or maximum radiation dose, while the decline of the quadratic coefficient was regulated mostly by the increase of the highest dose. The best goodness of fit, assessed by lower χ2 values, occurred for dose ranges 0.1 − 1.0 Gy; 0.5 − 5.9 Gy; 1.0 − 7.8 Gy; 2.0 − 9.6 Gy, 3.9 − 16.4 Gy and 5.9 − 20.3 Gy. The ‘see-saw’ effect in changes of LQ coefficients was confirmed by re-fitting datasets published by other laboratories. Conclusions The classical LQ model with fixed coefficients appears to have limited applicability for cytogenetic dosimetry at radiation doses >5 Gy due to the saturation of the dose response. Different response of the LQ coefficients to the changes of the dose range must be considered during the DRC construction. Proper selection of minimum and maximum dose in calibration experiments makes it possible to improve the goodness of fit of the LQ DRC.

Estimation of the relative biological effectiveness (RBE) of the 177Lu − DOTA − iPSMA radiopharmaceutical

Relative biological effectiveness is a radiobiological parameter relevant in radiotherapy planning and useful in evaluating the physiological impact of radiation in different tissues. Targeted radionuclide therapy allows the selective and specific deposition of higher radiation doses in a noninvasive way and without collateral effects through the administration of radiopharmaceuticals. Lu−DOTA−177(hydrazinylnicotinoyl−Lys−(Nal)−NH−CO−NH−Glu) also called Lu−iPSMA177 is a third generation radiopharmaceutical composed by a peptide that recognizes the prostate-specific membrane antigen (PSMA), a membrane protein overexpressed in several types of cancer and that mediates the radiopharmaceutical's recognition of cancer cells. The present study reports radiobiological parameters of Lu−iPSMA177 and demonstrates the superiority of targeted radiopharmaceuticals over external radiotherapy treatment options in terms of their relative biological effectiveness. The relative biological effectiveness value of 1.020±0.003 for the LINAC, estimated by fitting the linear-quadratic model equation to the resulting survival curves, was like those of 1.25±0.04,1.060±0.005and1.00±0.04 obtained by an alternative method in relation to the mean lethal doses at 90, 80 or 60 survival percent respectively. While the relative biological effectiveness values of 5.65±0.13,4.72±0.27and2.87±0.19 estimated for Lu−iPSMA177 were significantly higher than those for the LINAC. The results confirm that the biological effect produced by the deposition of a radiation absorbed dose delivered by the LINAC can be induced with a quarter of that dose using Lu−iPSMA177 due to the energy distribution, dose-rate and energy fluence.

Biological dosimetry dose-response curves for residents living near nuclear power plants in South Korea.

The purpose of this study was to establish the dose-response curves for biological dosimetry of the Dong Nam Institute of Radiological and Medical Sciences to monitor radiation exposure of local residents in the vicinity of the nuclear power plant. The blood samples of five healthy volunteers were irradiated with gamma ray, and each sample was divided equally for analysis of chromosomal aberrations by Giemsa staining and three-color fluorescence in situ hybridization painting of the triplet (chromosomes #1, #2, and #4). The results of chromosomal aberrations followed the Poisson distribution in all individual and averaged data which include inter-individual variation in radiation susceptibility. Cytogenetics Dose Estimate Software version 5.2 was used to fit the dose-response curve and to determine the coefficients of linear-quadratic equations. The goodness of fit of the curves and statistical significance of fitted α and β-coefficients were confirmed in both Giemsa-based dicentric analysis and FISH-based translocation analysis. The coefficients calculated from the five-donor average data were almost identical in both of the analyses. We also present the results that the dose-response curve for dicentric chromosomes plus fragments could be more effective for dose estimation following low-dose radiation accidents.

Hypo-fractionated Gamma Knife Radiosurgery for Intra-cranial Pathologies: A Single-Center Prospective Analysis of Feasibility, Safety, Efficacy, and Complication Profile.

Single-session stereotactic radiosurgery (SRS) is a proven and effective treatment modality for various benign, malignant, and functional intra-cranial pathologies. In certain situations, single-fraction SRS is limited because of lesion size and location. Hypo-fractionated gamma knife radiosurgery (hfGKRS) is an alternative approach for such unconventional indications. To evaluate the feasibility, efficacy, safety, and complication profile of hfGKRS with evaluation of different fractionation schemes and dosing patterns. The authors prospectively evaluated 202 patients treated with frame-based hfGKRS over a 9-year period. GKRS was administered fractionated because of either a large volume (>14 cc) or an inability to spare neighboring organs at risk from permissible radiation in single-session GKRS. The inter-fraction interval was kept at 24 hours, and the dose calculation was performed with linear quadratic equations. Patients with more than 3 years of clinical and radiological follow-up were included in prospective analysis. At pre-decided follow-up criteria, treatment effects and side effects were documented on objective scales. A total of 169/202 patients met inclusion criteria. 41% patients received treatment in three fractions, whereas 59% received two-fraction GKRS. Two patients of giant cavernous sinus hemangiomas were treated with 5 Gy in the five-fraction regimen. In patients with more than 3 years of follow-up, the obliteration rate was 88% for complex arteriovenous malformations (AVMs) treated with hfGKRS because of eloquent locations, whereas it was 62% for Spetzler-Martin grade 4-5 AVMs. For non-AVM pathologies (meningiomas, schwannomas, pituitary adenomas, paragangliomas, hypothalamic hamartomas, etc.), the 5-year progression free survival was 95%. Tumor failure was noted in 0.05% patient population. Radiation necrosis developed in 8.1% patients, and radiation-induced brain edema developed in 12% patients. It was resistant to treatment in 4% patients. No patient developed radiation-induced malignancy. Hypo-fractionation did not provide any hearing improvement in giant vestibular schwannomas. hfGKRS is a valuable standalone treatment option for candidates unsuitable for single-session GKRS. The dosing parameters need to be tailored as per the pathology and neighboring structures. It provides comparable results to single-session GKRS with an acceptable safety and complication profile.

Abstract P042: A genomic model to predict cellular radiosensitivity

Abstract Purpose: This group has previously worked on Radiosensitivity Index (RSI),1,2 which has been clinically validated in 1919 patients across multiple cohorts.3 The Linear Quadratic (LQ) model is a widely accepted model used to prescribe radiation dose and fractionation. We hypothesize that clonogenic data can be fitted to the linear quadratic equation to predict α and β based on gene expression. Here we introduce a novel genomic model (gLQ) developed in cell lines to estimate the α and β parameters in cell lines. Methods: We analyzed public data on 494 irradiated clonogenic cell lines,4 considering Survival Fraction (SF) at known radiation dosages (2-10 Gy, i.e., SF2 through SF10) and fractions to calculate “ground truth” α and β using RAD-ADAPT software.5 Ground truth α and β were aligned to publically available Affymetrix U133 2.0 plus microarray and RNA seq data. Normalization was performed by Robust Multi-array average and RSEM respectively. 90% of the 494 cell line data (n=444) was used to train the model, while 10% (n=50) was left untouched. To narrow the data on 18,468 genes for each cell line to a smaller set of representative genes, we used a combination of clustering analysis, feature selection using Max-min Markov Blanket, and evaluating the functionality of selected features as they relate to radiosensitivity and cancer.6 Limiting the genes used as inputs in the machine-trained regression improved model training time. Machine learning, specifically Bayesian Ridge Regression, was utilized to identify relationships between calculated α and β and the representative gene expression profile for each cell line. 598 genes were selected for the α model, and 1198 genes were selected for the β model. These models were then locked down and tested on the 50 untouched validation cell lines. Results: Calculated ground truth α and β had a strong fit (R2=0.94). The resulting trained, locked-down model predicted α and β values for the remaining unseen 10% of the cell lines as a separate validation cohort with R2 values of 0.8809 and 0.8175, respectively. Conclusions: This suggests that genomic data can be used to effectively predict cellular radiosensitivity.

Radiation Necrosis Risk in NSCLC Patients Receiving EGFR TKIs or ALK Inhibitors

<h3>Purpose/Objective(s)</h3> Epidermal growth factor receptor tyrosine kinase inhibitors (EGFR TKIs) and anaplastic lymphoma kinase (ALK) inhibitors have become commonplace in the treatment of locally advanced and metastatic NSCLC with activating mutations. The toxicity of stereotactic radiation therapy (SRT) when given concurrently with these drugs remains unclear. The purpose of this study was to determine the incidence of radiation necrosis (RN) in patients receiving these targeted therapies (TGT). <h3>Materials/Methods</h3> We retrospectively reviewed metastatic NSCLC patients who received EGFR TKI or ALK inhibitor at our institution. Patients with brain metastases treated with SRT with a minimum of 6 months post-SRT follow up were included for analysis, and demographic, oncologic, radiation and imaging records were reviewed. RN diagnosis was based upon the radiologist interpretation, radiation oncologist progress notes, or pathology reports after resection. Local recurrence was defined radiographically or histologically. Biologically effective dose was calculated using the linear quadratic equation using an α/β of 3 (BED3) and 10 (BED10). <h3>Results</h3> Thirty-nine patients with 161 treated brain lesions fit our inclusion criteria. Most patients were female (76.9%), with a median age of 60 (range 27-73), and were treated to a median of 3 (1-27) lesions per patient. EGFR TKI or ALK inhibitor was administered in the 2-week interval surrounding SRT (TGT+) for 116 of 161 lesions, and 28 of 116 (24.1%) developed evidence of RN (21 symptomatic, 18.1%). Among the 45 lesions where TKI or ALK inhibitor was not given in the 2-week interval surrounding SRT (TGT-), one case of RN (2.2%) was identified. Most symptomatic RN lesions (67%) resolved with therapy. Local control among TGT+ and TGT- lesions was 93.1% and 97.7% respectively (p=0.08). The odds for developing RN were higher for TGT+ than TGT- treatments (OR=14; 95%CI 1.8-106). In 19 out of 116 TGT+ lesions, TGT was either held during SRT or initiated within 2 weeks following SRT, and the RN rate was not lower than for SRT where TGT was administered concurrently (26.3% vs 23.7%, p=0.4). Among TGT+ lesions, there was no difference in number of TKIs received prior to, during, or after SRT for those with or without RN. There was no association of prescribed BED3 or BED10 with the development of RN. Lesions that developed RN were more likely to be treated with osimertinib than those without RN (46% vs 23%, p=0.02). <h3>Conclusion</h3> Patients receiving SRT with EGFR TKI or ALK therapy 2 weeks before or after SRT are at higher risk of RN. This risk does not appear to diminish when holding TGT during SRT or delaying TGT initiation until after SRT. Special attention should be given to patients receiving SRT with osimertinib therapy as our data suggest that they are at higher risk of developing RN. Future work will focus on identification of unique dosimetric and temporal factors that may be predictive of RN in patients taking these targeted agents.

ARID1A deficiency as a biomarker for sensitivity to radiation and ATR inhibition (232)

<b>Objectives:</b> <i>ARID1A,</i> which encodes a protein that participates in the SWI/SNF chromatin remodeling complex, is frequently mutated in ovarian and endometrial malignancies. The emergence of the role of <i>ARID1A</i> in gynecologic cancer progression reveals potential implications for therapeutic targets. Our primary purpose was to investigate <i>ARID1A</i> deficiency as a potential biomarker conferring sensitivity to ionizing radiation and ATR inhibitors. <b>Methods:</b> Paired isogenic cell lines ES2 and HCT116 were used containing wild-type <i>ARID1A</i> or homozygous loss of function <i>ARID1A</i> mutations. Ionizing radiation doses were delivered using Precision X-ray 320-kV orthovoltage unit at a dose rate of 2 Gy/45 seconds. Cytotoxicity assays were performed to evaluate cell survival following various doses of ATR inhibitor AZD6738. Clonogenic survival assays were performed with or without 50 nM of AZD6738 one hour prior to radiation at doses of 0, 1, 2, 4, or 6 Gy. Survival curves were generated and compared using the linear quadratic equation on GraphPad Prism. gH2AX foci formation following radiation at 5 Gy was observed using immunofluorescence (IF) and Western blot. IF images were analyzed using ImageJ. Cell cycle distribution following radiation at 5 Gy was performed using flow cytometry, and analysis was performed using FlowJo software. <b>Results:</b> <i>ARID1A</i>-deficient cells exhibited greater sensitivity to radiation alone compared to wild-type cells as measured by clonogenic survival and demonstrated a diminished DNA damage response following radiation compared to wild-type cells, as measured by gH2AX foci formation by IF and Western blot. <i>ARID1A</i>-deficient cells exhibited an impaired G2/M cell cycle checkpoint following radiation, as exhibited by diminished arrest at G2/M compared to wild-type cells. <i>ARID1A</i>-deficient cells demonstrated sensitization to AZD6738 alone compared to wild-type cells by cytotoxicity assay. Preliminary results suggest that <i>ARID1A-</i>deficient cells have greater sensitization to AZD6738 treatment prior to radiation compared to radiation alone. Further evaluation of combinatorial strategies is in progress. <b>Conclusions:</b> Our <i>in vitro</i> findings confirm that <i>ARID1A</i>-deficiency confers sensitivity to radiation and ATR inhibition, suggesting a biologically informed treatment strategy for <i>ARID1A</i>-deficient malignancies. Further work regarding dosing and timing of combination treatment will be explored in the future.

Abstract DEB2-2: Con - One Week of Whole Breast RT is the New Standard of Care

Abstract The dual role of breast irradiation post lumpectomy for conservative treatment is to yield local cancer control comparable to that achieved with mastectomy while maintaining a sensate and cosmetically acceptable breast. Through application of a linear quadratic equation that characterizes the radiobiological relationship of total dose and dose per fraction to predict efficacy as well as tissue specific toxicity, breast radiation that is equally effective can be delivered with fewer treatments. This has allowed standard post lumpectomy breast radiation to be reduced to 15 -16 treatments from 25-28 with similar efficacy and toxicity confirmed in multiple clinical trials. The recent Fast Forward trial (Lancet 2020; 395: 1613-26) has now further advanced the application of this radiobiological model evaluating breast irradiation delivered in 5 treatments. This resulted in non-inferior recurrence events compared to 15-treatment breast irradiation. When using fewer treatments of larger radiation dose, small changes can result in significant toxicity effects. For example, with 1 Gy difference between 26 Gy and 27 Gy total dose treatment arms on the Fast Forward trial, significantly higher rates of breast adverse outcomes were seen. Additional experience with the 5-fraction breast irradiation is needed prior to its replacing the current 15-16 treatment standard. Citation Format: J White. Con - One Week of Whole Breast RT is the New Standard of Care [abstract]. In: Proceedings of the 2021 San Antonio Breast Cancer Symposium; 2021 Dec 7-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2022;82(4 Suppl):Abstract nr DEB2-2.

A simulation approach to predict the calibration curve of low LET radiations for biological dosimetry using the Geant4-DNA toolkit

Ionizing radiation is extensively utilized in various applications; however, it can lead to significant harm to living systems. In this regard, the radiation absorbed dose is usually evaluated by performing biological dosimetry and physical reconstruction of exposure scenarios. But, this is costly, time-consuming, and maybe impractical for a biodosimetry lab to perform biological dosimetry. This study aimed to assess the applicability and reliability of the Geant4-DNA toolkit as a simulation approach to construct a reliable dose-response curve for biodosimetry purposes as an appropriate substitution for experimental measurements. In this matter, the total number of double-strand breaks (DSBs), due to different doses of low LET radiation qualities on DNA molecules, was calculated and converted to the values of dicentric chromosomes using a mechanistic model of cellular response. Then, the number of dicentric chromosomes induced by 200 kVp X-rays were modified by using a semi-empirical scaling factor for compensating the restriction of simulation code to consider what can happen in a real cell. Next, the trend of dicentrics for 137Cs and 60Co were calculated and modified by the above scaling factor. Finally, the dose-response curves for these gamma sources compared to several published experiments. The suggested calibration curves for 137Cs and 60Co followed a linear quadratic equation: Ydic = 0.0054 (± 0.0133) - 0.0089 (± 0.0212) × D + 0.0568 (± 0.0051) × D2 and Ydic = 0.0052 (± 0.0128) - 0.00568 (± 0.0203) × D + 0.0525 (± 0.0049) × D2 respectively. They revealed a satisfactory agreement with the experimental data reported by others. The Geant4 program developed in this work could provide an appropriate tool for predicting the dose-response (calibration) curve for biodosimetry purposes.

Optimization of wind power generation benefit with considering the partial system information

This paper aims to solve the coupled problem of wind turbine modeling and wind power generation benefit analysis. The salient features of the proposed method are as follows: First, the model of wind power generation benefit is obtained, and the task is formulated as an optimization problem of a linear quadratic (LQ) optimal equation in terms of wind power generation benefit. Second, the controller is designed with considering the partial system information and solved based on the Forward and Backward Stochastic Differential Equations (FBSDEs) and adjoint equations. Numerical simulations are adopted to verify the proposed optimization method for partial information and full information cases, respectively.

EQD2 Dose Accumulation Based on Deformable Image Registration of HR-CTV, Bladder, Rectum and Bowel for Combined External-Beam Radiotherapy and Brachytherapy for Cervical Cancer

<h3>Purpose/Objective(s)</h3> Evaluate the accuracy of DVH parameter summation between brachytherapy (BT) and external-beam radiotherapy (EBRT) for cervical cancer, by comparing deformable image registration (DIR) EQD2 dose accumulation. DVH summation of dosimetric parameters can overestimate cumulative organ at risk (OAR) doses due to daily variations in relative OAR position. <h3>Materials/Methods</h3> Ten patients were studied. Nine out of 10 patients received BT+EBRT. All women were treated with intracavitary tandem and ring BT. In phase I, CT simulation images from each BT fraction were rigidly fused with first fraction BT images, (BT1) focusing on the applicator and uterus. Hybrid-based DIR was then conducted using MIM software. Contours used for DIR were CTV_HR, bladder, rectum and bowel space. For phase II, EBRT and BT1 utero-cervix contours were rigidly fused, followed by contour-based DIR using utero-cervix, bladder and rectum. Each BT fraction and sum EBRT dose was accumulated onto BT1 and converted to EQD2 (Gy) via the linear quadratic equation with a/b of 10 for tumor and 3 for OARs. The absolute dose differences were reported for D0.1cc, D1cc and D2cc (OARs) and D90% (CTV_HR). The dice similarity coefficient (DSC) of all contours was reported. For phase I, the D2cc isodose level and OAR overlap structure was assessed for each BT fraction and the initial and deformed D2cc reported. The mean distance-to-agreement (MDA) and DSC of D2cc were reported for DIR accuracy assessment. <h3>Results</h3> For phase I, average DSC values for CTV_HR, bladder, rectum and bowel were 0.84 ± 0.07, 0.86 ± 0.08, 0.82 ± 0.05, 0.81 ± 0.07 and average DSC of initial vs. deformed D2cc were 0.88 ± 0.02, 0.89 ± 0.02, 0.88 ± 0.03 respectively. Average D2cc MDA values were 0.28 ± 0.04, 0.29 ± 0.05, 0.33 ± 0.06 for the bladder, rectum and bowel, respectively with absolute D2cc differences in Gy of 0.04 ± 0.04, 0.01 ± 0.01, and 0.03 ± 0.03. For CTV_HR, absolute D90 difference in EQD2 was 2.69 ± 1.98 Gy. For bladder, rectum and bowel, absolute EQD2 differences in Gy for D0.1cc were 5.57 ± 3.73, 2.78 ± 2.27, 5.10 ± 2.70 respectively. For D1cc, values in Gy were 3.27 ± 1.80, 1.62 ± 1.04, and 4.20 ± 2.51. For D2cc, 2.42 ± 0.80 Gy, 1.16 ± 0.72 Gy, and 2.83 ± 2.23 Gy. For phase II, average DSC values for utero-cervix, bladder and rectum were 0.82 ± 0.12, 0.80 ± 0.08, and 0.82 ± 0.17 respectively. Average absolute EQD2 difference in Gy for CTV_HR D90 was 7.43 ± 3.10 and 12.87 ± 6.84 and 6.02 ± 4.80 respectively for bladder and rectum D0.1cc. For D1cc and D2cc, absolute EQD2 differences in Gy were 10.46 ± 5.10 and 8.10 ± 4.48 respectively for bladder and 3.84 ± 2.95 and 3.21 ± 2.17 for rectum. <h3>Conclusion</h3> Arithmetic DVH addition over-estimated OAR D2cc in 7 of 10 patients. D2cc overestimation of bladder occurred in 6 of 9 patients and 7 of 9 patients for rectum. Our results show good estimation of accumulated dose with DVH parameter addition for both BT only and BT + EBRT.

Analysis of Reachable Workspace for Spatial Three-Cable Under-Constrained Suspended Cable-Driven Parallel Robots

Abstract The workspace is an important reference for designs of cable-driven parallel robots (CDPRs). Most current researches focus on calculating the workspace of redundant CDPRs. However, few literature study the workspaces of under-constrained CDPRs. In this paper, the static equilibrium reachable workspaces (SERWs) of spatial 3-cable under-constrained CDPRs are solved numerically since expressions describing workspace boundaries cannot be obtained in closed forms. The steps to solve the SERWs are as follows. First, expressions that describe the SERWs and their boundaries are proposed. Next, these expressions are instantiated through a novel anchor points model composed of linear equations, quadratic equations, and tension limits in cables. Then, based on the reformulated linearization technique (RLT), the constraints system is transformed into a system containing only linear equality constraints and linear inequality constraints. Finally, the framework of the branch-and-prune (BP) algorithm is adopted to solve this system. The effect of the algorithm is verified by two examples. One is searching the SERWs boundaries of a special three-cable-driven parallel robot (CDPR) whose anchor points layouts both on the moving platform (MP) and on the base are equilateral triangles, followed by a method to extract the SERW boundary where cables do not interfere with each other. The other is searching the SERWs boundaries of a general three-cable CDPR with randomly selected geometry arrangement. The presented method in this paper is universal for calculating the SERWs of spatial three-cable CDPRs with arbitrary geometry parameters.

Dose-effect relationships of 12C6+ ions-induced dicentric plus ring chromosomes, micronucleus and nucleoplasmic bridges in human lymphocytes in vitro

Purpose The objective of this research was to explore the dose-effect relationships of dicentric plus ring (dic + r), micronucleus (MN) and nucleoplasmic bridges (NPB) induced by carbon ions in human lymphocytes. Materials and methods Venous blood samples were collected from three healthy donors. 12C6+ ions beam was used to irradiate the blood samples at the energy of 330 MeV and linear energy transfer (LET) of 50 keV/μm with a dose rate of 1 Gy/min in the spread-out Bragg peak. The irradiated doses were 0 (sham irradiation), 1, 2, 3, 4, 5 and 6 Gy. Dic + r chromosomes aberrations were scored in metaphases. The cytokinesis-block micronucleus cytome (CBMN) was conducted to analyze MN and NPB. The maximum low-dose relative biological effectiveness (RBEM) values of the induction of dic + r, MN and NPB in human lymphocytes for 12C6+ ions irradiation was calculated relative to 60Co γ-rays. Results The frequencies of dic + r, MN and NPB showed significantly increases in a dose-depended manner after exposure to 12C6+ ions. The distributions of dic + r and MN exhibited overdispersion, while the distribution of NPB agreed with Poisson distribution at all doses. Linear-quadratic equations were established based on the frequencies of dic + r and MN. The dose-response curves of NPB frequencies followed a linear model. The derived RBEM values for dic + r, MN and NPB in human lymphocytes irradiated with 12C6+ ions were 8.07 ± 2.73, 2.69 ± 0.20 and 4.00 ± 2.69 in comparison with 60Co γ-rays. Conclusion The dose-response curves of carbon ions-induced dic + r, MN and NPB were constructed. These results could be helpful to improve radiation risk assessment and dose estimation after exposed to carbon ions irradiation.

Reduced order modelling of nonlinear cross-diffusion systems

In this work, we present reduced-order models (ROMs) for a nonlinear cross-diffusion problem from population dynamics, the Shigesada-Kawasaki-Teramoto (SKT) equation with Lotka-Volterra kinetics. The formation of the patterns of the SKT equation consists of a fast transient phase and a long stationary phase. Reduced order solutions are computed by separating the time into two time-intervals. In numerical experiments, we show for one- and two-dimensional SKT equations with pattern formation, the reduced-order solutions obtained in the time-windowed form, i.e., principal decomposition framework, are more accurate than the global proper orthogonal decomposition solutions obtained in the whole time interval. The finite-difference discretization of the SKT equation in space results in a system of linear-quadratic ordinary differential equations. The ROMs have the same linear-quadratic structure as the full order model. Using the linear-quadratic structure of the ROMs, the computation of the reduced-order solutions is further accelerated by the use of proper orthogonal decomposition in a tensorial framework so that the computations in the reduced system are independent of the full-order solutions. Furthermore, the prediction capabilities of the ROMs are illustrated for one- and two-dimensional patterns. Finally, we show that the entropy is decreasing by the reduced solutions, which is important for the global existence of solutions to the nonlinear cross-diffusion equations such as the SKT equation.

Explicit Symplectic-Precise Iteration Algorithms for Linear Quadratic Regulator and Matrix Differential Riccati Equation

Efficient, robust and precise algorithms for linear quadratic regulator (LQR) and matrix differential Riccati equation (MDRE) are essential in optimal control. However, there are lack of good algorithms for time-varying LQR problem because of the difficulty of solving the nonlinear time-varying MDRE. In this paper, we proved that the n-th order LQR problem is equivalent to n parallel 1-dim Hamiltonian systems and proposed the explicit symplectic-precise iteration method (SPIM) for solving LQR and MDRE. The explicit symplectic-precise iteration algorithms (ESPIA) designed with SPIM have three typical merits: firstly, there are no accumulative errors in the sense of long-term time which inherits from symplectic difference scheme; secondly the stiffness problem due to the inverse of matrix is avoided by the precise iteration method; and finally the algorithmic structure of ESPIA is simple and no extra assumptions are required. Systematic analysis shows that the time complexity of the symplectic algorithms for the n-th order LQR and MDRE is <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) where k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> is the iteration times specified by the time duration. Numerical examples and simulations are provided to validate the performance of the ESPIA.

Probabilistic analysis of linear-quadratic logistic-type models with hybrid uncertainties via probability density functions

&lt;abstract&gt;&lt;p&gt;We provide a full stochastic description, via the first probability density function, of the solution of linear-quadratic logistic-type differential equation whose parameters involve both continuous and discrete random variables with arbitrary distributions. For the sake of generality, the initial condition is assumed to be a random variable too. We use the Dirac delta function to unify the treatment of hybrid (discrete-continuous) uncertainty. Under general hypotheses, we also compute the density of time until a certain value (usually representing the population) of the linear-quadratic logistic model is reached. The theoretical results are illustrated by means of several examples, including an application to modelling the number of users of Spotify using real data. We apply the Principle Maximum Entropy to assign plausible distributions to model parameters.&lt;/p&gt;&lt;/abstract&gt;

Nonconvex lifted unbalanced branch flow model: Derivation, implementation and experiments

This paper develops a novel nonconvex formulation of the unbalanced power flow equations. This formulation extends the lifted nonconvex ‘DistFlow’ a.k.a. balanced branch flow model formulation to the unbalanced case. The feasible set is characterized by linear and nonconvex quadratic equations in matrix variables. It is shown that this formulation is equivalent to previously published rank-constrained semidefinite programming formulations. The formulation is implemented and compared numerically with rectangular and polar versions of the nonlinear AC unbalanced optimal power flow problem.

The 4Rs in radiation therapy

It has been realized that the 4Rs (repair, repopulation, redistribution, and reoxygenation) would affect the result of cell irradiation, and thus radiation treatment. The 4Rs each occurs at different dose rates, usually very low dose rates. Depending on the dose rate used for treatment, the corresponding R should be included in the linear－quadratic equation (LQ) and biological effective dose (BED) calculation. For low dose rate brachytherapy(LDR) especially permanent implant, all the 4Rs should be included in LQ for BED calculation. The 4Rs, especially repair and repopulation, play a critical role in dose fractionation. Various dose fractionation schemes such as hyperfractionation and hypofractionation are determined in consideration of the 4Rs. Stereotactic radiation therapy uses hypofractionation with high fractional doses and combine with high accuracy target localization techniques to achieve high local control rates compared to conventional dose fractionation schemes. The 4Rs have been taken into account for LDR and permanent implant. Recently, LQ for permanent implant brachytherapy has been modified to include all the 4Rs for gynecological malignancy 131Cs permanent implants. Including the 4Rs in radiation therapy has significantly improved the effectiveness and efficiency of radiation therapy for cancer treatment. Key words: Repair; Repopulation; Redistribution; Reoxygenation; Linear quadratic equation

Quantitative Estimation of the Equivalent Radiation Dose Escalation using Radiofrequency Hyperthermia in Mouse Xenograft Models of Human Lung Cancer

Hyperthermia is a potent radiosensitizer, and its effect varies according to the different types of cancer cells. In the present study, the radiosensitizing effect of hyperthermia on lung cancer cell lines A549 and NCI-H1299 was determined based on the equivalent radiation dose escalation. In vitro cell experiments were conducted using lung cancer cell lines A549 and NCI-H1299 to determine thermal radiosensitivity. In vivo experiments were conducted using mouse heterotopic xenograft models to determine the treatment response and increase in the temperature of tumors using a 13.56 MHz radiofrequency (RF) hyperthermia device. Using the α and β values of the linear–quadratic equations of cell survival curves, numerical simulations were performed to calculate the equivalent radiation dose escalations. The dielectric properties of tumors were measured, and their effect on the calculated equivalent radiation dose was analyzed. Hyperthermia increased the equivalent radiation dose of lung cancer xenografts and a higher escalation was found in NCI-H1299 cells compared with that observed in A549 cells. An underestimation of the calculated equivalent radiation dose was observed when the dielectric property of the tumor was varied. This study may contribute to the effective planning of thermoradiotherapy in clinics.