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Background: Predicting biological responses to mixed radiation types is of considerable importance when combining radiation therapies that use multiple radiation types and delivery regimens. These may include the use of both low‐ and high‐linear energy transfer (LET) radiations. A number of theoretical models have been developed to address this issue. However, model predictions do not consistently match published experimental data for mixed radiation exposures. Furthermore, the models are often computationally intensive. Accordingly, there is a need for efficient analytical models that can predict responses to mixtures of low‐ and high‐LET radiations. Additionally, a general formalism to calculate equieffective dose (EQDX) for mixed radiations is needed. Purpose: To develop a computationally efficient analytical model that can predict responses to complex mixtures of low‐ and high‐LET radiations as a function of either absorbed dose or EQDX. Methods: The Zaider‐Rossi model (ZRM) was modified by replacing the geometric mean of the quadratic coefficients in the interaction term with the arithmetic mean. This modified ZRM model (mZRM) was then further generalized to any number of radiation types and its validity was tested against published experimental observations. Comparisons between the predictions of the ZRM and mZRM, and other models, were made using two and three radiation types. In addition, a generalized formalism for calculating EQDX for mixed radiations was developed within the context of mZRM and validated with published experimental results. Results: The predictions of biological responses to mixed‐LET radiations calculated with the mZRM are in better agreement with experimental observations than ZRM, especially when high‐ and low‐LET radiations are mixed. In these situations, the ZRM overestimated the surviving fraction. Furthermore, the EQDX calculated with mZRM are in better agreement with experimental observations. Conclusion: The mZRM is a computationally efficient model that can be used to predict biological response to mixed radiations that have low‐ and high‐LET characteristics. Importantly, interaction terms are retained in the calculation of EQDX for mixed radiation exposures within the mZRM framework. The mZRM has application in a wide range of radiation therapies, including radiopharmaceutical therapy. [ABSTRACT FROM AUTHOR]

Cervical cancer remains a pressing global health concern, necessitating advanced therapeutic strategies. Radiotherapy, a fundamental treatment modality, has faced challenges such as targeted dose deposition and radiation exposure to healthy tissues, limiting optimal outcomes. To address these hurdles, nanomaterials, specifically gold nanoparticles (AuNPs), have emerged as a promising avenue. This study delves into the realm of cervical cancer radiotherapy through the meticulous exploration of AuNPs' impact. Utilizing ex vivo experiments involving cell lines, this research dissected intricate radiobiological interactions. Detailed scrutiny of cell survival curves, dose enhancement factors (DEFs), and apoptosis in both cancer and normal cervical cells revealed profound insights. The outcomes showcased the substantial enhancement of radiation responses in cancer cells following AuNP treatment, resulting in heightened cell death and apoptotic levels. Significantly, the most pronounced effects were observed 24 h post-irradiation, emphasizing the pivotal role of timing in AuNPs' efficacy. Importantly, AuNPs exhibited targeted precision, selectively impacting cancer cells while preserving normal cells. This study illuminates the potential of AuNPs as potent radiosensitizers in cervical cancer therapy, offering a tailored and efficient approach. Through meticulous ex vivo experimentation, this research expands our comprehension of the complex dynamics between AuNPs and cells, laying the foundation for their optimized clinical utilization. [ABSTRACT FROM AUTHOR]

The linear quadratic (LQ) model has been the dominant tool in preclinical radiobiological modeling of cell survival as a function of dose. However, as a second‐order polynomial approximation, it suffers from two well‐known pitfalls: nonmonotonic behavior and poor extrapolation. This study examined the raw data of 253 sets of photons and 943 sets of the ion beam from the Particle Irradiation Data Ensemble (PIDE) project to understand how often the LQ model could result in a negative β, which would give unrealistic predictions. Additionally, the predictive performance of the LQ model, the power model, and the linear model's predictive performance was studied using leave‐one‐out cross‐validation (LOOCV) and twofold cross‐validation. It was found that, when fitted to the LQ model, 7.5% of the photon and 29.8% of the ion beam dose–response data would result in negative β, compared to 0.77% and 2.0%, respectively, reported in published works. The LQ model performed poorly in LOOCV compared to the alternative power model, and performed the worst among the three models in twofold cross‐validation. The LQ model leads to unrealistic parameters, which are vastly under‐reported in published studies, and performs poorly in standard cross‐validation tests. Therefore, the LQ model is not a valid predictive dose–response model for cell survival. Alternative models need to be investigated. [ABSTRACT FROM AUTHOR]

Abstract Background This work addresses a basic inconsistency in the way dose is accumulated in radiotherapy when predicting the biological effect based on the linear quadratic model (LQM). To overcome this inconsistency, we introduce and evaluate the concept of the total biological dose, bEQDd. Methods Daily computed tomography imaging of nine patients treated for prostate carcinoma with intensity-modulated radiotherapy was used to compute the delivered deformed dose on the basis of deformable image registration (DIR). We compared conventional dose accumulation (DA) with the newly introduced bEQDd, a new method of accumulating biological dose that considers each fraction dose and tissue radiobiology. We investigated the impact of the applied fractionation scheme (conventional/hypofractionated), uncertainties induced by the DIR and by the assigned α/β-value. Results bEQDd was systematically higher than the conventionally accumulated dose with difference hot spots of 3.3–4.9 Gy detected in six out of nine patients in regions of high dose gradient in the bladder and rectum. For hypofractionation, differences are up to 8.4 Gy. The difference amplitude was found to be in a similar range to worst-case uncertainties induced by DIR and was higher than that induced by α/β. Conclusion Using bEQDd for dose accumulation overcomes a potential systematic inaccuracy in biological effect prediction based on accumulated dose. Highest impact is found for serial-type late responding organs at risk in dose gradient regions and for hypofractionation. Although hot spot differences are in the order of several Gray, in dose-volume parameters there is little difference compared with using conventional or biological DA. However, when local dose information is used, e.g. dose surface maps, difference hot spots can potentially change outcomes of dose-response modelling and adaptive treatment strategies.

In this paper, we propose a mean-field game model for the price formation of a commodity whose production is subjected to random fluctuations. The model generalizes existing deterministic price formation models. Agents seek to minimize their average cost by choosing their trading rates with a price that is characterized by a balance between supply and demand. The supply and the price processes are assumed to follow stochastic differential equations. Here, we show that, for linear dynamics and quadratic costs, the optimal trading rates are determined in feedback form. Hence, the price arises as the solution to a stochastic differential equation, whose coefficients depend on the solution of a system of ordinary differential equations.

Simple Summary: ThermoBrachyTherapy, a combination therapy where radiation and heat are simultaneously applied using needle-shaped applicators from within the target, is a potentially very effective treatment for prostate cancer. When radiation and thermal therapies are applied, the dose coverage of each treatment is preplanned without considering the combined effect of the two dose distributions. In this study, we propose a method to automatically plan the thermal dose in such a treatment, based on the combined effect with the radiation. Furthermore, we apply the method on 10 patients and compare the treatment to a brachytherapy-only treatment plan. In this way, we show that, with properly optimized ThermoBrachyTherapy, we can provide equivalent combined dose coverages to the prostate, while reducing the dose delivered to critical organs surrounding the prostate, which might translate to reduced toxicity of the treatment. In high-dose-rate brachytherapy (HDR-BT) for prostate cancer treatment, interstitial hyperthermia (IHT) is applied to sensitize the tumor to the radiation (RT) dose, aiming at a more efficient treatment. Simultaneous application of HDR-BT and IHT is anticipated to provide maximum radiosensitization of the tumor. With this rationale, the ThermoBrachyTherapy applicators have been designed and developed, enabling simultaneous irradiation and heating. In this research, we present a method to optimize the three-dimensional temperature distribution for simultaneous HDR-BT and IHT based on the resulting equivalent physical dose (EQDphys) of the combined treatment. First, the temperature resulting from each electrode is precomputed. Then, for a given set of electrode settings and a precomputed radiation dose, the EQDphys is calculated based on the temperature-dependent linear-quadratic model. Finally, the optimum set of electrode settings is found through an optimization algorithm. The method is applied on implant geometries and anatomical data of 10 previously irradiated patients, using reported thermoradiobiological parameters and physical doses. We found that an equal equivalent dose coverage of the target can be achieved with a physical RT dose reduction of 20% together with a significantly lower EQDphys to the organs at risk (p-value < 0.001), even in the least favorable scenarios. As a result, simultaneous ThermoBrachyTherapy could lead to a relevant therapeutic benefit for patients with prostate cancer. [ABSTRACT FROM AUTHOR]

Based on Hurwicz model of uncertain optimal control model with jump, in this paper, a Hurwicz model of uncertain linear quadratic optimal control with jump is proposed. Then, the necessary and sufficient condition for the existence of optimal control is obtained. Finally, an example is given to illustrate usefulness of the proposed model. [ABSTRACT FROM AUTHOR]

Background: This work addresses a basic inconsistency in the way dose is accumulated in radiotherapy when predicting the biological effect based on the linear quadratic model (LQM). To overcome this inconsistency, we introduce and evaluate the concept of the total biological dose, bEQDd.Methods: Daily computed tomography imaging of nine patients treated for prostate carcinoma with intensity-modulated radiotherapy was used to compute the delivered deformed dose on the basis of deformable image registration (DIR). We compared conventional dose accumulation (DA) with the newly introduced bEQDd, a new method of accumulating biological dose that considers each fraction dose and tissue radiobiology. We investigated the impact of the applied fractionation scheme (conventional/hypofractionated), uncertainties induced by the DIR and by the assigned α/β-value.Results: bEQDd was systematically higher than the conventionally accumulated dose with difference hot spots of 3.3-4.9 Gy detected in six out of nine patients in regions of high dose gradient in the bladder and rectum. For hypofractionation, differences are up to 8.4 Gy. The difference amplitude was found to be in a similar range to worst-case uncertainties induced by DIR and was higher than that induced by α/β.Conclusion: Using bEQDd for dose accumulation overcomes a potential systematic inaccuracy in biological effect prediction based on accumulated dose. Highest impact is found for serial-type late responding organs at risk in dose gradient regions and for hypofractionation. Although hot spot differences are in the order of several Gray, in dose-volume parameters there is little difference compared with using conventional or biological DA. However, when local dose information is used, e.g. dose surface maps, difference hot spots can potentially change outcomes of dose-response modelling and adaptive treatment strategies. [ABSTRACT FROM AUTHOR]

Effective radiation treatment (RT) for recurrent nasopharyngeal cancers (NPC), featuring an intrinsic hypoxic sub-volume, remains a clinical challenge. Lack of disease‐specific in-vitro models of NPC, together with difficulties in establishing patient derived xenograft (PDX) models, have further hindered development of personalized therapeutic options. Herein, we established two NPC organoid lines from recurrent NPC PDX models and further characterized and compared these models with original patient tumors using RNA sequencing analysis. Organoids were cultured in hypoxic conditions to examine the effects of hypoxia and radioresistance. These models were then utilized to determine the radiobiological parameters, such as α/β ratio and oxygen enhancement ratio (OER), characteristic to radiosensitive normoxic and radioresistant hypoxic NPC, using simple dose-survival data analytic tools. The results were further validated in-vitro and in-vivo, to determine the optimal boost dose and fractionation regimen required to achieve effective NPC tumor regression. Despite the differences in tumor microenvironment due to the lack of human stroma, RNA sequencing analysis revealed good correlation of NPC PDX and organoid models with patient tumors. Additionally, the established models also mimicked inter-tumoral heterogeneity. Hypoxic NPC organoids were highly radioresistant and had high α/β ratio compared to its normoxic counterparts. In-vitro and in-vivo fractionation studies showed that hypoxic NPC was less sensitive to RT fractionation scheme and required a large bolus dose or 1.4 times of the fractionated dose that was effective against normoxic cells in order to compensate for oxygen deficiency. This study is the first direct experimental evidence to predict optimal RT boost dose required to cause sufficient damage to recurrent hypoxic NPC tumor cells, which can be further used to develop dose-painting algorithms in clinical practice.

Effective radiation treatment (RT) for recurrent nasopharyngeal cancers (NPC), featuring an intrinsic hypoxic sub-volume, remains a clinical challenge. Lack of disease‐specific in-vitro models of NPC, together with difficulties in establishing patient derived xenograft (PDX) models, have further hindered development of personalized therapeutic options. Herein, we established two NPC organoid lines from recurrent NPC PDX models and further characterized and compared these models with original patient tumors using RNA sequencing analysis. Organoids were cultured in hypoxic conditions to examine the effects of hypoxia and radioresistance. These models were then utilized to determine the radiobiological parameters, such as α/β ratio and oxygen enhancement ratio (OER), characteristic to radiosensitive normoxic and radioresistant hypoxic NPC, using simple dose-survival data analytic tools. The results were further validated in-vitro and in-vivo , to determine the optimal boost dose and fractionation regimen required to achieve effective NPC tumor regression. Despite the differences in tumor microenvironment due to the lack of human stroma, RNA sequencing analysis revealed good correlation of NPC PDX and organoid models with patient tumors. Additionally, the established models also mimicked inter-tumoral heterogeneity. Hypoxic NPC organoids were highly radioresistant and had high α/β ratio compared to its normoxic counterparts. In-vitro and in-vivo fractionation studies showed that hypoxic NPC was less sensitive to RT fractionation scheme and required a large bolus dose or 1.4 times of the fractionated dose that was effective against normoxic cells in order to compensate for oxygen deficiency. This study is the first direct experimental evidence to predict optimal RT boost dose required to cause sufficient damage to recurrent hypoxic NPC tumor cells, which can be further used to develop dose-painting algorithms in clinical practice. [ABSTRACT FROM AUTHOR]

The linear-quadratic (LQ) model represents a simple and robust approximation for many mechanistically-motivated models of radiation effects. We believe its tendency to overestimate cell killing at high doses derives from the usual assumption that radiogenic lesions are distributed according to Poisson statistics. In that context, we investigated the effects of overdispersed lesion distributions, such as might occur from considerations of microdosimetric energy deposition patterns, differences in DNA damage complexities and repair pathways, and/or heterogeneity of cell responses to radiation. Such overdispersion has the potential to reduce dose response curvature at high doses, while still retaining LQ dose dependence in terms of the number of mean lethal lesions per cell. Here we analyze several irradiated mammalian cell and yeast survival data sets, using the LQ model with Poisson errors, two LQ model variants with customized negative binomial (NB) error distributions, the Padé-linear-quadratic, and Two-component models. We compared the performances of all models on each data set by information-theoretic analysis, and assessed the ability of each to predict survival at high doses, based on fits to low/intermediate doses. Changing the error distribution, while keeping the LQ dose dependence for the mean, enables the NB LQ model variants to outperform the standard LQ model, often providing better fits to experimental data than alternative models. The NB error distribution approach maintains the core mechanistic assumptions of the LQ formalism, while providing superior estimates of cell survival following high doses used in radiotherapy. Importantly, it could also be useful in improving the predictions of low dose/dose rate effects that are of major concern to the field of radiation protection. [ABSTRACT FROM AUTHOR]

This article deals with the combined production and maintenance plans for a manufacturing system satisfying a random demand. We first establish an optimal production plan which minimises the average total inventory and production cost. Second, using this optimal production plan, and taking into account the deterioration of the machine according to its production rate, we derive an optimal maintenance schedule which minimises the maintenance cost. A numerical example illustrates the proposed approach, this analytical approach, based on a stochastic optimisation model and using the operational age concept, reveals the significant influence of the production rate on the deterioration of the manufacturing system and consequently on the integrated production/maintenance policy. [ABSTRACT FROM AUTHOR]

Aim: This study is designed to investigate the superiority and applicability of the model among the linear-quadratic (LQ), linear-quadratic-linear (LQ-L) and universal-survival-curve (USC) models by fitting published radiation cell survival data of lung cancer cell lines. Materials and Method: The radiation cell survival data for small cell (SC) and non-small cell (NSC) lung cancer cell lines were obtained from published reports, and were used to determine the LQ and cell survival curve parameters, which ultimately were used in the curve fitting of the LQ, LQ-L and USC models. Results: The results of this study demonstrate that the LQ-L(Dt-mt) model, compared with the LQ and USC models, provides best fit with smooth and gradual transition to the linear portion of the curve at transition dose Dt-mt, where the LQ model loses its validity, and the LQ-L(Dt-2α/β) and USC(Dt-mt) models do not transition smoothly to the linear portion of the survival curve. Conclusion: The LQ-L(Dt-mt) model is able to fit wide variety of cell survival data over a very wide dose range, and retains the strength of the LQ model in the low-dose range.

While multisession dose fractionated Gamma Knife radiosurgery (DFGKS) is common, its use has never been described for jugular paragangliomas (JP), which are notoriously difficult to treat. To define efficacy, safety, and complication profile of DFGKS in 2 or 3 consecutive sessions for the treatment of a cohort of 10 cases of JP. Between 2012 and 2017, 10 patients with JP were treated with DFGKS in 2 or 3 sessions, because it was not safe to treat the lesion in a single session because of the large volume or proximity to organs at risk. The small to medium-sized JP are treated with 16–22 Gy radiation, but the large-volume JP were treated with 23–25 Gy radiation dose. The Leksell G frame was kept in situ during the whole procedure. The tumor volumes on pretreatment and posttreatment imaging were compared, using the Leksell Gamma Plan treatment plan software to assess tumor progression. The patients were regularly evaluated for their clinical outcome with radiologic correlation. The mean radiologic follow-up was 39 months (range, 12–78 months). The mean marginal dose for 3 fractions and 2 fractions was 7.64 Gy at 50% and 11.2 Gy at 50%, respectively. The mean tumor size was 29.9 cm3 (range, 9.95–47.63 cm3) at treatment and 21.9 cm3 (range, 8.83–37.5 cm3) at follow-up (suggestive of 26.7% reduction). Tumor control was achieved in all patients (100%). Of 110 potential neurologic problems (signs/symptoms) evaluated (11 in each patient), 56 (50.9%) were present preoperatively. Of them, 27 (48.2%) improved and 29 (51.8%) stabilized after treatment. There were 2 new-onset neurologic problems (of 110, 1.8%) attributable to treatment (new-onset headache and spinal accessory paresis). No patient had any permanent neurologic deterioration. DFGKS for large-volume JP leads to acceptable progression-free survival, tumor control rate, and symptomatic improvement. It may be preferred to surgery or fractionated radiotherapy given its better safety, efficacy, and complication profile. [ABSTRACT FROM AUTHOR]

Background. The aim of this study was to use various theoretical methods derived from the Linear Quadratic (LQ) model to calculate the effects of number of subfractions, time intervals between subfractions, dose per subfraction, and overall fraction time on the cells’ survival. Comparison of the results with experimental outcomes of melanoma and breast adenocarcinoma cells was also performed. Finally, the best matched method with experimental outcomes is introduced as the most accurate method in predicting the cell response.

Background. The aim of the study was to investigate whether biologically effective dose (BED) based on linearquadratic model can be used to estimate spinal cord tolerance dose in spine stereotactic body radiation therapy (SBRT) delivered in 4 or more fractions.

Abstract Glioblastoma contains self-renewing, tumorigenic cancer stem-like cells that contribute to tumor initiation and therapeutic resistance. The aim of this research was to estimate and compare the effectiveness ratio (α/β) of stem-like cells and differentiated glioma cells derived from the U87MG glioblastoma cell line. Cell survival experiments were obtained in a dose range of 0–20 Gy (13.52 ± 0.09 Gy/h) as a hyperfractionationated accelerated radiotherapy scheme. Biochemical characterization of the post-irradiated cells was performed by flow cytometry analysis and the percentage of stem-like cells that resisted irradiation was determined by the CD133 expression. Results showed that U87MG stem-like cells are highly proliferative and more radioresistant than the U87MG adherent group (with a lesser stem-like character), this in association with the calculated α/β ratio of 17 and 14.1, respectively. Highlights • Glioma stem-like cells are highly proliferative and radioresistant. • The effectiveness ratio (α/β) value of U87MG stem-like cells is 17. • The effectiveness ratio (α/β) value of differentiated U87MG cells is 14.1. [ABSTRACT FROM AUTHOR]

Most preclinical studies examining the radiobiology of brachytherapy have focused on dose rate effects. Scarcer data are available on other major parameters of therapeutic index, such as cell cycle distribution, repopulation or reoxygenation. The linear quadratic model describes the effect of radiotherapy in terms of normal tissue or tumour response. It allows some comparisons between various irradiation schemes. This model should be applied cautiously for brachytherapy, because it relies on cell death analysis only, and therefore partially reflects the biological effects of an irradiation. Moreover, the linear quadratic model validity has not been demonstrated for very high doses per fraction. A more thorough analysis of mechanisms involved in radiation response is required to better understand the true effect of brachytherapy on normal tissue. The modulation of immune response is one promising strategy to be tested with brachytherapy. A translational approach applied to brachytherapy should lead to design trials testing pharmacological agents modulating radiation response, in order to improve not only local control, but also decrease the risk of distant failure. Here we review the radiobiology of brachytherapy, from the historical view based on linear quadratic model to recent perspectives for biological optimization. [ABSTRACT FROM AUTHOR]

Combined radiotherapy (RT) and hyperthermia (HT) treatments may improve treatment outcome by heat induced radio-sensitisation. We propose an empirical cell survival model (AlphaR model) to describe this multimodality therapy. The model is motivated by the observation that heat induced radio-sensitisation may be explained by a reduction in the DNA damage repair capacity of heated cells. We assume that this repair is only possible up to a threshold level above which survival will decrease exponentially with dose. Experimental cell survival data from two cell lines (HCT116, Cal27) were considered along with that taken from the literature (baby hamster kidney [BHK] and Chinese hamster ovary cells [CHO]) for HT and combined RT-HT. The AlphaR model was used to study the dependence of clonogenic survival on treatment temperature, and thermal dose R2 ≥ 0.95 for all fits). For HT survival curves (0-80 CEM43 at 43.5-57 °C), the number of free fit AlphaR model parameters could be reduced to two. Both parameters increased exponentially with temperature. We derived the relative biological effectiveness (RBE) or HT treatments at different temperatures, to provide an alternative description of thermal dose, based on our AlphaR model. For combined RT-HT, our analysis is restricted to the linear quadratic arm of the model. We show that, for the range used (20-80 CEM43, 0-12 Gy), thermal dose is a valid indicator of heat induced radio-sensitisation, and that the model parameters can be described as a function thereof. Overall, the proposed model provides a flexible framework for describing cell survival curves, and may contribute to better quantification of heat induced radio-sensitisation, and thermal dose in general. [ABSTRACT FROM AUTHOR]

It is well known that the optimal control of a linear quadratic model is characterized by the solution of a Riccati differential equation. In many cases, the corresponding Riccati differential equation cannot be solved exactly such that the optimal feedback control may be a complex time-oriented function. In this article, a parametric optimal control problem of an uncertain linear quadratic model under an optimistic value criterion is considered for simplifying the expression of optimal control. Based on the equation of optimality for the uncertain optimal control problem, an approximation method is presented to solve it. As an application, a two-spool turbofan engine optimal control problem is given to show the utility of the proposed model and the efficiency of the presented approximation method. [ABSTRACT FROM AUTHOR]

Aim: This study is designed to investigate the superiority and applicability of the model among the linear-quadratic (LQ), linear-quadraticlinear (LQ-L) and universal-survival-curve (USC) models by fitting published radiation cell survival data of lung cancer cell lines. Materials and Method: The radiation cell survival data for small cell (SC) and non-small cell (NSC) lung cancer cell lines were obtained from published reports, and were used to determine the LQ and cell survival curve parameters, which ultimately were used in the curve fitting of the LQ, LQ-L and USC models. Results: The results of this study demonstrate that the LQ-L(Dt-mt) model, compared with the LQ and USC models, provides best fit with smooth and gradual transition to the linear portion of the curve at transition dose Dt-mt, where the LQ model loses its validity, and the LQ-L(Dt-2α/β) and USC(Dt-mt) models do not transition smoothly to the linear portion of the survival curve. Conclusion: The LQ-L(Dt-mt) model is able to fit wide variety of cell survival data over a very wide dose range, and retains the strength of the LQ model in the low-dose range. [ABSTRACT FROM AUTHOR]

Context: Prior research over the past few decades has shown that the hypofractionated external beam radiation therapy could be a valuable method with an outstanding potential to treat the prostate cancer. The alpha-beta ratio (α/β) is an indication of the fractionation sensitivity of a particular cell type. Values of α/β ≥ 10 Gy are responsible for early-responding normal tissues and most tumors, while values of α/β <5 Gy are for late-responding normal tissues. The α/β ratio could be raised by either a local tumor control increase or a decrease of normal tissue late effects through the application of an unconventional fractionation schedules. Evidence Acquisition: This review article aimed to investigation the details of radiobiological and clinical trials which are reported to highlight the characteristics of hypofractionation for the prostate cancer treatment based on the investigation of clinical results from hypofractionated treatments. Results: With the sufficient radiobiological and physiological research studies, it may be claimed that if α/β value for prostate cancer is less than the adjacent surrounding organs at risk and by applying fewer and larger fractions; a better therapeutic ratio can be achieved for the patient. Conclusions: Radiobiological modeling can play a major role in the design of new protocols. Also, one should be aware that in modeling the hypofractionated treatment, normal tissue iso-effects are significantly important and some assumptions needed to be made regarding α/β values for the critical normal tissue complication endpoint. [ABSTRACT FROM AUTHOR]

We propose a Bayesian hierarchical model applicable to the calibration of the linear-quadratic model of radiation dose–response. Experimental data used in model calibration were taken from a clonogenic survival assay conducted on human breast cancer cells (MDA-MB-231) across a range of radiation doses (0–6 Gy). Employing Markov-chain Monte Carlo methods, we calibrated the proposed Bayesian hierarchical model, computed posterior distributions for the model parameters and survival fraction dose–response probability densities. Key contributions include the proposal of a model that incorporates multiple sources of inter- and intra-experiment variability commonly neglected in the standard frequentist approach and its subsequent application to in vitro experimental data. [ABSTRACT FROM AUTHOR]

The combination of radiotherapy modalities with external bundles and systemic radiotherapy (CIERT) could be a reliable alternative for patients with multiple lesions or those where treatment planning maybe difficult because organ(s)-at-risk (OARs) constraints. Radiobiological models should have the capacity for predicting the biological irradiation response considering the differences in the temporal pattern of dose delivering in both modalities. Two CIERT scenarios were studied: sequential combination in which one modality is executed following the other one and concurrent combination when both modalities are running simultaneously. Expressions are provided for calculation of the dose-response magnitudes Tumor Control Probability (TCP) and Normal Tissue Complication Probability (NTCP). General results on radiobiological modeling using the linear-quadratic (LQ) model are also discussed. Inter-subject variation of radiosensitivity and volume irradiation effect in CIERT are studied. OARs should be under control during the planning in concurrent CIERT treatment as the administered activity is increased. The formulation presented here may be used for biological evaluation of prescriptions and biological treatment planning of CIERT schemes in clinical situation. [ABSTRACT FROM AUTHOR]

It is postulated that the outcomes in treating breast cancer with intraoperative radiotherapy ( IORT) would be affected by the residual cancer cell distribution within the tumor bed. The three-dimensional (3D) radiation doses of Intrabeam TM ( IB) IORT with a 4-cm spherical applicator at the energy of 50 and 40 kV were calculated. The modified linear quadratic model ( MLQ) was used to estimate the radiobiological responses of the cancer cells and interspersed normal tissues with various radiosensitivities. By comparing the average survival fraction of normal tissues in IB- IORT and uniform dose treatment for the same level of cancer cell killing, the therapeutic ratios ( TRs) were derived. The equivalent uniform dose ( EUD) was found to increase with the prescription dose and decrease with the cancer cell infiltrating distance. For 50 kV beam at the 20 Gy prescription dose, the EUDs are 18.03, 16.49 and 13.56, 11. 29, and 9.28 Gy respectively, for 1.5, 3.0, 6.0, 9, and 15.0 mm of the cancer cell infiltrating distance into surrounding tissue. The dose rate of 50 kV is at least 1.87× higher than that of 40 kV beam. The EUDs of 50 kV beam are up to 15% higher than that of the 40 kV beam. The TR increases with the prescription dose, but decreases with the distance of cancer cell infiltration distance. Average TRs of 50 kV beam are up to 30% larger than that of 40 kV beam. In conclusion, IB- IORT can provide a possible therapeutic advantage on sparing more normal tissue compared with the External Beam IORT ( EB- IORT) for shallowly populated unicentric breast lesion. Our data suggest that IB- IORT dose size should be adjusted based on the individual patient's cancer cell infiltrating distance for delivering an effective dose, one dose-fits-all regimen may have undertreated some patients with large cancer infiltrating distance. [ABSTRACT FROM AUTHOR]

Background: To evaluate the feasibility, safety and efficacy of dose fractionated gamma knife radiosurgery (DFGKRS) on a daily schedule beyond the linear quadratic (LQ) model, for large volume arteriovenous malformations (AVMs).Material and Methods: Between 2012-16, 14 patients of large AVMs (median volume 26.5 cc) unsuitable for surgery or embolization were treated in 2-3 of DFGKRS sessions. The Leksell G frame was kept in situ during the whole procedure. 86% (n = 12) patients had radiologic evidence of bleed, and 43% (n = 6) had presented with a history of seizures. 57% (n = 8) patients received a daily treatment for 3 days and 43% (n = 6) were on an alternate day (2 fractions) regimen. The marginal dose was split into 2 or 3 fractions of the ideal prescription dose of a single fraction of 23-25 Gy.Results: The median follow up period was 35.6 months (8-57 months). In the three-fraction scheme, the marginal dose ranged from 8.9-11.5 Gy, while in the two-fraction scheme, the marginal dose ranged from 11.3-15 Gy at 50% per fraction. Headache (43%, n = 6) was the most common early postoperative complication, which was controlled with short course steroids. Follow up evaluation of at least three years was achieved in seven patients, who have shown complete nidus obliteration in 43% patients while the obliteration has been in the range of 50-99% in rest of the patients. Overall, there was a 67.8% reduction in the AVM volume at 3 years. Nidus obliteration at 3 years showed a significant rank order correlation with the cumulative prescription dose (p 0.95, P value 0.01), with attainment of near-total (more than 95%) obliteration rates beyond 29 Gy of the cumulative prescription dose. No patient receiving a cumulative prescription dose of less than 31 Gy had any severe adverse reaction. In co-variate adjusted ordinal regression, only the cumulative prescription dose had a significant correlation with common terminology criteria for adverse events (CTCAE) severity (P value 0.04), independent of age, AVM volume, number of fractions and volume of brain receiving atleast 8 Gy of radiation.Conclusion: DFGKRS is feasible for large AVMs with a fair nidus obliteration rate and acceptable toxicity. Cumulative prescription dose seems to be the most significant independent predictor for outcome following DFGKRS with 29-30 Gy resulting in a fair nidus obliteration with least adverse events. [ABSTRACT FROM AUTHOR]

In recent few decades, linear quadratic optimal control problems have achieved great improvements in theoretical and practical perspectives. For a linear quadratic optimal control problem, it is well known that the optimal feedback control is characterized by the solution of a Riccati differential equation, which cannot be solved exactly in many cases, and sometimes the optimal feedback control will be a complex time-oriented function. In this paper, we introduce a parametric optimal control problem of uncertain linear quadratic model and propose an approximation method to solve it for simplifying the expression of optimal control. A theorem is given to ensure the solvability of optimal parameter. Besides, the analytical expressions of optimal control and optimal value are derived by using the proposed approximation method. Finally, an inventory-promotion problem is dealt with to illustrate the efficiency of the results and the practicability of the model. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an approximate model and propose a piecewise optimisation method to simplify the expression of optimal control for an uncertain linear quadratic optimal control problem. First, we consider an optimal control problem of uncertain linear quadratic model under optimistic value criterion. Based on the equation of optimality, we deduce an analytic expression of optimal control. Then, we study an approximate model with control parameter and propose a piecewise optimisation method for solving the optimal parameter of such an approximate model. As an application, a four-wheel steering vehicle optimal control problem is given to show the utility of the proposed approximate model and the efficiency of the proposed piecewise optimisation method. [ABSTRACT FROM AUTHOR]

We present a comprehensive software program, RAD-ADAPT, for the quantitative analysis of clonogenic assays in radiation biology. Two commonly used models for clonogenic assay analysis, the linear-quadratic model and single-hit multi-target model, are included in the software. RAD-ADAPT uses maximum likelihood estimation method to obtain parameter estimates with the assumption that cell colony count data follow a Poisson distribution. The program has an intuitive interface, generates model prediction plots, tabulates model parameter estimates, and allows automatic statistical comparison of parameters between different groups. The RAD-ADAPT interface is written using the statistical software R and the underlying computations are accomplished by the ADAPT software system for pharmacokinetic/pharmacodynamic systems analysis. The use of RAD-ADAPT is demonstrated using an example that examines the impact of pharmacologic ATM and ATR kinase inhibition on human lung cancer cell line A549 after ionizing radiation. [ABSTRACT FROM AUTHOR]

Purpose:To provide a rule for the agreement or disagreement of the Poisson approximation (PA) and the Zaider-Minerbo formula (ZM) on the ranking of treatment alternatives in terms of tumor control probability (TCP) in the linear quadratic model. Materials and methods:A general criterion involving a critical cell birth rate was formally derived. For demonstration, the criterion was applied to a distinct radiobiological model of fast growing head and neck tumors and a respective range of 22 conventional and nonconventional head and neck schedules. Results:There is a critical cell birth rate bcritbelow which PA and ZM agree on which one out of two alternative treatment schemes with single-cell survival curves S′(t) and S′′(t) offers better TCP: For cell birth rates b above this critical cell birth rate, PA and ZM disagree if and only if b >bcrit> 0. In case of the exemplary head and neck schedules, out of 231 possible combinations, only 16 or 7% were found where PA and ZM disagreed. In all 231 cases the prediction of the criterion was numerically confirmed, and cell birth rates at crossovers between schedules matched the calculated critical cell birth rates. Conclusions:TCP estimated by PA and ZM almost never numerically coincide. Still, in many cases both formulas at least agree about which one out of two alternative fractionation schemes offers better TCP. In case of fast growing tumors featuring a high cell birth rate, however, ZM may suggest a re-evaluation of treatment options. [ABSTRACT FROM PUBLISHER]

Toxicological tests are experiments that show the effects of a toxic on organisms, ecosystems, etc. This study focuses on tests in the aquatic environment, in which the test involving Ceriodaphnia Dubia organism stands out. The literature indicates that in two out of every three experiments carried out with this organism, there is hormesis. This study applies optimal experimental design theory to a linear quadratic model with a Poisson distribution for the response, in order to obtain designs that allow efficient detection and characterization of hormesis. To this end, a variety of utility functions are used, including the dose for the zero equivalent point, the area under the curve, the dose at which maximum response is reached or the dose at which there is a given relative inhibition with respect to the control or the maximum. A study of cross efficiencies of the calculated designs shows the importance of correctly defining the goal of the experiment, in order to obtain the most appropriate design. • Theory of optimal experimental design is applied to the Ceriodaphnia Dubia test focused on the hormetic effect. • Linear quadratic model with Poisson distribution is considered. • c -and L -optimal designs are computed for estimating the utility functions which characterize the hormesis. • KL -optimal designs are computed for detecting the hormesis. [ABSTRACT FROM AUTHOR]