Linear-quadratic Model Research Articles

Advanced autopilot design with extremum-seeking control for aircraft control

Abstract The aim of this research is to enhance adaptive autopilots for the effective management of aircraft systems, control maintenance, and the rejection of external disturbances. To achieve this objective, we propose the design of an autopilot integrated with the extremum-seeking control (ESC) algorithm. Although autopilots proficiently manage the lateral and longitudinal modes of aircraft control, they lack filtering or adaptive capabilities, thereby exposing the system to significant external threats. To mitigate these risks, the ESC method is employed. This adaptive approach can operate in a disturbance rejection manner by adjusting parameters for unknown inputs and restoring the system to its original controlled response. ESC represents a versatile control method suitable for effective application in simulations or experimental models. Through the incorporation of this method, the pitch attitude hold autopilot, altitude hold autopilot, and yaw autopilot acquire advanced disturbance rejection capabilities with adaptive ESC features. The novelty of the proposed method lies in providing advanced disturbance rejection properties to conventional autopilots, thereby rendering them innovative and superior disturbance rejection controllers. The newly developed autopilots are capable of eliminating severe disturbances from the system response, including ramp, sinusoidal, and step disturbances. The integration of autopilots with ESC offers significant advantages, such as superior disturbance rejection properties for the aircraft unmanned aerial vehicle (UAV) system. The proposed method successfully eliminates severe disturbances, as demonstrated in simulation results, surpassing previous methods in effectiveness. Furthermore, the Autopilot-ESC method enhances aircraft operation even under disturbances, minimizing energy consumption and ensuring stability and control. This novel method reduces operator workload and ensures reliable and efficient autonomous flight capabilities. Additionally, the adaptability of the Autopilot-ESC to changing environmental conditions make it well-suited in aircraft UAVs. This upgraded version of autopilot surpasses other robust controllers, such as Linear Quadratic Gaussian (LQG) regulator and Model Predictive Control (MPC), as it can effectively address ramp, sinusoidal, and step disturbances, which LQG and MPC cannot handle.

How quickly does FLASH need to be delivered? A theoretical study of radiolytic oxygen depletion kinetics in tissues

Purpose. Radiation delivered over ultra-short timescales (‘FLASH’ radiotherapy) leads to a reduction in normal tissue toxicities for a range of tissues in the preclinical setting. Experiments have shown this reduction occurs for total delivery times less than a ‘critical’ time that varies by two orders of magnitude between brain (∼0.3 s) and skin (⪆10 s), and three orders of magnitude across different bowel experiments, from ∼0.01 to ⪆(1–10) s. Understanding the factors responsible for this broad variation may be important for translation of FLASH into the clinic and understanding the mechanisms behind FLASH. Methods. Assuming radiolytic oxygen depletion (ROD) to be the primary driver of FLASH effects, oxygen diffusion, consumption, and ROD were evaluated numerically for simulated tissues with pseudorandom vasculatures for a range of radiation delivery times, capillary densities, and oxygen consumption rates (OCR’s). The resulting time-dependent oxygen partial pressure distribution histograms were used to estimate cell survival in these tissues using the linear quadratic model, modified to incorporate oxygen-enhancement ratio effects. Results. Independent of the capillary density, there was a substantial increase in predicted cell survival when the total delivery time was less than the capillary oxygen tension (mmHg) divided by the OCR (expressed in units of mmHg/s), setting the critical delivery time for FLASH in simulated tissues. Using literature OCR values for different normal tissues, the predicted range of critical delivery times agreed well with experimental values for skin and brain and, modifying our model to allow for fluctuating perfusion, bowel. Conclusions. The broad three-orders-of-magnitude variation in critical irradiation delivery times observed in in vivo preclinical experiments can be accounted for by the ROD hypothesis and differences in the OCR amongst simulated normal tissues. Characterization of these may help guide future experiments and open the door to optimized tissue-specific clinical protocols.

First in vitro measurement of VHEE relative biological effectiveness (RBE) in lung and prostate cancer cells using the ARES linac at DESY

Very high energy electrons (VHEE) are a potential candidate for radiotherapy applications. This includes tumours in inhomogeneous regions such as lung and prostate cancers, due to the insensitivity of VHEE to inhomogeneities. This study explores how electrons in the VHEE range can be used to perform successful in vitro radiobiological studies. The ARES (accelerator research experiment at SINBAD) facility at DESY, Hamburg, Germany was used to deliver 154 MeV electrons to both prostate (PC3) and lung (A549) cancer cells in suspension. Dose was delivered to samples with repeatability and uniformity, quantified with Gafchromic film. Cell survival in response to VHEE was measured using the clonogenic assay to determine the biological effectiveness of VHEE in cancer cells for the first time using this method. Equivalent experiments were performed using 300 kVp X-rays, to enable VHEE irradiated cells to be compared with conventional photons. VHEE irradiated cancer cell survival was fitted to the linear quadratic (LQ) model (R2 = 0.96–0.97). The damage from VHEE and X-ray irradiated cells at doses between 1.41 and 6.33 Gy are comparable, suggesting similar relative biological effectiveness (RBE) between the two modalities. This suggests VHEE is as damaging as photon radiotherapy and therefore could be used to successfully damage cancer cells during radiotherapy. The RBE of VHEE was quantified as the relative doses required for 50% (D0.5) and 10% (D0.1) cell survival. Using these values, VHEE RBE was measured as 0.93 (D0.5) and 0.99 (D0.1) for A549 and 0.74 (D0.5) and 0.93 (D0.1) for PC3 cell lines respectively. For the first time, this study has shown that 154 MeV electrons can be used to effectively kill lung and prostate cancer cells, suggesting that VHEE would be a viable radiotherapy modality. Several studies have shown that VHEE has characteristics that would offer significant improvements over conventional photon radiotherapy for example, electrons are relatively easy to steer and can be used to deliver dose rapidly and with high efficiency. Studies have shown improved dose distribution with VHEE in treatment plans, in comparison to VMAT, indicating that VHEE can offer improved and safer treatment plans with reduced side effects. The biological response of cancer cells to VHEE has not been sufficiently studied as of yet, however this initial study provides some initial insights into cell damage. VHEE offers significant benefits over photon radiotherapy and therefore more studies are required to fully understand the biological effectiveness of VHEE.

Mathematical modeling of the synergistic interplay of radiotherapy and immunotherapy in anti-cancer treatments.

While radiotherapy has long been recognized for its ability to directly ablate cancer cells through necrosis or apoptosis, radiotherapy-induced abscopal effect suggests that its impact extends beyond local tumor destruction thanks to immune response. Cellular proliferation and necrosis have been extensively studied using mathematical models that simulate tumor growth, such as Gompertz law, and the radiation effects, such as the linear-quadratic model. However, the effectiveness of radiotherapy-induced immune responses may vary among patients due to individual differences in radiation sensitivity and other factors. We present a novel macroscopic approach designed to quantitatively analyze the intricate dynamics governing the interactions among the immune system, radiotherapy, and tumor progression. Building upon previous research demonstrating the synergistic effects of radiotherapy and immunotherapy in cancer treatment, we provide a comprehensive mathematical framework for understanding the underlying mechanisms driving these interactions. Our method leverages macroscopic observations and mathematical modeling to capture the overarching dynamics of this interplay, offering valuable insights for optimizing cancer treatment strategies. One shows that Gompertz law can describe therapy effects with two effective parameters. This result permits quantitative data analyses, which give useful indications for the disease progression and clinical decisions. Through validation against diverse data sets from the literature, we demonstrate the reliability and versatility of our approach in predicting the time evolution of the disease and assessing the potential efficacy of radiotherapy-immunotherapy combinations. This further supports the promising potential of the abscopal effect, suggesting that in select cases, depending on tumor size, it may confer full efficacy to radiotherapy.

Abstract PS16-09: Analysis of the Radiosensitivity Index/Genomic-Adjusted Radiation Dose (RSI-GARD) in Paired Pre- and Post-Treatment TNBC Samples: Implications for Biomarker-Guided Radiotherapy

Abstract Objectives: Adjuvant radiotherapy is an important component of curative treatment for triple-negative breast cancer (TNBC). While there are several accepted variations in nominal dose and fractionation, these regimens are generally felt to be radiobiologically equivalent. Molecular radiosensitivity biomarkers have the potential to allow tailoring of physical radiotherapy dose for individual patients. The Radiosensitivity Index (RSI)/Genomic-Adjusted Radiation Dose (GARD) is a gene expression signature that predicts intrinsic radiosensitivity across multiple malignancies, with initial studies demonstrating clinical utility of RSI-GARD in TNBC. Since most TNBC patients will receive neoadjuvant systemic therapy, we sought to understand how neoadjuvant therapy-induced molecular adaptations could alter intrinsic radiosensitivity and RSI-GARD. Methods: Total RNA was isolated from pre-treatment and paired surgical specimens (for patients with residual disease (RD)) from TNBC patients treated with chemotherapy on the NeoSTOP (NCT02413320) or chemoimmunotherapy on the NeoPACT (NCT03639948) neoadjuvant trials and was subjected to RNA exome sequencing. The RSI was calculated according to the published algorithm using normalized expression of the 10 genes in this signature (AR, JUN1, STAT1, PRKCB, RELA, ABL1, SUMO1, PAK2, HDAC1, and IRF1). The resulting RSI score was substituted as the surviving fraction (SF) using the linear quadratic model of radiation-induced cellular lethality assuming a fractional dose of 2.0 Gy and a constant β=0.05 Gy−2 to derive a patient-specific α, which is a coefficient modifying dose-dependent cellular lethality resulting from binary mis-repair of double-strand breaks (DSBs) arising from a single particle track. Results: Pre-treatment sequencing data were available for N=200 patients and the overall pathologic complete response (pCR) rate was 56.5%. Paired pre- and post-treatment sequencing data were available for N=58 patients (N=27 from NeoSTOP and N=31 from NeoPACT). One NeoPACT patient had a negative RSI, which led to an undefined α. Under the assumptions of the RSI-substituted LQ model, the median α/β ratio (reflecting sensitivity to fractionation) for all pre-treatment samples was 11.7 Gy. TNBC patients who achieved pCR had a significantly higher pre-treatment α (i.e., higher intrinsic radiosensitivity) compared to patients who had residual disease (P=0.04), and this trend was the same for patients treated with chemotherapy (P=0.31) or chemoimmunotherapy (P=0.05). Importantly, α did not change significantly between paired pre- and post-treatment samples (median change post- vs. pre-treatment=0.03 Gy−1 (range -0.25 to +0.24 Gy−1; P=0.26) in patients with RD, with no difference in subgroups treated with chemotherapy (P=0.99) or chemoimmunotherapy (P=0.10). Conclusions: We found that predicted intrinsic radiosensitivity using the RSI-GARD is associated with pathologic response to neoadjuvant systemic therapy, suggesting that this signature also predicts intrinsic chemosensitivity in TNBC patients. The modeled α/β ratio for all pre-treatment samples was 11.7 Gy, which is substantially higher than empirically determined α/β ratios in studies that were enriched for HR+/HER2- breast cancers. Globally, the RSI-GARD score was not impacted by neoadjuvant systemic therapy, with no significant change in the score in paired pre- and post-treatment samples. These results can inform future testing and implementation of RSI-GARD into prospective trials. Citation Format: Shane Stecklein, Julia White, Rachel Yoder, Joshua Staley, Zachary Schmitt, Anne O'Dea, Lauren Nye, Deepti Satelli, Gregory Crane, Rashna Madan, Maura O'Neil, Andrew Godwin, Harsh Pathak, Qamar Khan, Joyce O'Shaughnessy, Priyanka Sharma. Analysis of the Radiosensitivity Index/Genomic-Adjusted Radiation Dose (RSI-GARD) in Paired Pre- and Post-Treatment TNBC Samples: Implications for Biomarker-Guided Radiotherapy [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PS16-09.

Association between trajectories of the neighborhood social exposome and mental health in late adolescence: A FinnTwin12 cohort study

BackgroundAdolescent mental health problems impose a significant burden. Exploring evolving social environments could enhance comprehension of their impact on mental health. We aimed to depict the trajectories of the neighborhood social exposome from middle to late adolescence and assess the intricate relationship between them and late adolescent mental health. MethodsParticipants (n = 3965) from the FinnTwin12 cohort with completed questionnaires at age 17 were used. Nine mental health measures were assessed. The social exposome comprised 28 neighborhood social indicators. Trajectories of these indicators from ages 12 to 17 were summarized via latent growth curve modeling into growth factors, including baseline intercept. Mixture effects of all growth factors were assessed through quantile-based g-computation. Repeated generalized linear regressions identified significant growth factors. Sex stratification was performed. ResultsThe linear-quadratic model was the most optimal trajectory model. No mixture effect was detected. Regression models showed some growth factors saliently linked to the p-factor, internalizing problems, anxiety, hyperactivity, and aggression. The majority of them were baseline intercepts. Quadratic growth factors about mother tongues correlated with anxiety among sex-combined participants and males. The linear growth factor in the proportion of households of couples without children was associated with internalizing problems in females. LimitationsWe were limited to including only neighborhood-level social exposures, and the multilevel contextual exposome situation interfered with our assessment. ConclusionsTrajectories of the social neighborhood exposome modestly influenced late adolescent mental health. Tackling root causes of social inequalities through targeted programs for living conditions could improve adolescent mental health.

RadPhysBio: A Radiobiological Database for the Prediction of Cell Survival upon Exposure to Ionizing Radiation.

Based on the need for radiobiological databases, in this work, we mined experimental ionizing radiation data of human cells treated with X-rays, γ-rays, carbon ions, protons and α-particles, by manually searching the relevant literature in PubMed from 1980 until 2024. In order to calculate normal and tumor cell survival α and β coefficients of the linear quadratic (LQ) established model, as well as the initial values of the double-strand breaks (DSBs) in DNA, we used WebPlotDigitizer and Python programming language. We also produced complex DNA damage results through the fast Monte Carlo code MCDS in order to complete any missing data. The calculated α/β values are in good agreement with those valued reported in the literature, where α shows a relatively good association with linear energy transfer (LET), but not β. In general, a positive correlation between DSBs and LET was observed as far as the experimental values are concerned. Furthermore, we developed a biophysical prediction model by using machine learning, which showed a good performance for α, while it underscored LET as the most important feature for its prediction. In this study, we designed and developed the novel radiobiological 'RadPhysBio' database for the prediction of irradiated cell survival (α and β coefficients of the LQ model). The incorporation of machine learning and repair models increases the applicability of our results and the spectrum of potential users.

Method for Determining Radioresistance of Cancer Cell Lines Based on Cluster Analysis of Clonogenic Cell Survival Data

Background: The outcome of radiation therapy, the duration and quality of life of cancer patients significantly depend on the radiosensitivity (RS) of a cancerous tumor, and the duration of the patient’s relapse-free period is largely determined by the degree of its radioresistance (RR). Today the results of molecular mechanism investigation of cancer radioresistance and the classification of cancer cells according to their radiophenotypes mostly contribute to improving prognosis methods of treatment outcomes and increasing effectiveness of radiation therapy. In this work, we developed a classification method of cancer cells according to their radiosensitivity using machine learning based on the data analysis of clonogenic cell survival under ionizing radiation. Material and methods: The method consists of clustering parameters of experimental dose-effect relationships, which were approximated using the equation of a linear-quadratic (LQ) model, which is used to evaluate RS of cancer cells in radiobiology. The training of the statistical model included published experimental dataset of 96 cancer cell lines, for which parameters a, b and their ratio a/b of the LQ model were determined. Classification of cancer cells according to their radiosensitivity was carried out based on principal component analysis (PCA) in the parameter space (a, a/b), k-means clustering and hierarchical clustering methods. Results: Application of the developed statistical model to a large dataset of cancer cells made it possible to reliably separate radiosensitive and radioresistant (RR) cells into two clusters according to the parameters a and a/b. Application of the model to cancer cells with acquired RR, in which RS was suppressed as a result of exposure to irradiation or hypoxia, allowed tracing the shift of parent cells’ parameters from the RS cluster to the RR cell cluster. To study the genetic mechanisms of radiosensitivity, we performed bioinformatic analysis of the mutation distribution in genes encoding proteins in the cellular signalling pathways of cancer cells, i.e. proliferation, apoptosis, repair of damaged DNA molecules and antioxidant defence cellular system. Conclusion: The developed statistical model of radiophenotypic classification of cancer cells based on their radiosensitivity can be used in the development of radiation therapy treatment plans taking into account radiosensitivity of patient’s tumour. The model may be also helpful in a joint analysis of the phenotypic and genotypic characteristics of cancer cells, aiming at the elucidation of the molecular and genetic mechanisms of radiosensitivity and development of biomarkers of radioresistance.

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.

Computational Approach for Spatially Fractionated Radiation Therapy (SFRT) and Immunological Response in Precision Radiation Therapy.

The field of precision radiation therapy has seen remarkable advancements in both experimental and computational methods. Recent literature has introduced various approaches such as Spatially Fractionated Radiation Therapy (SFRT). This unconventional treatment, demanding high-precision radiotherapy, has shown promising clinical outcomes. A comprehensive computational scheme for SFRT, extrapolated from a case report, is proposed. This framework exhibits exceptional flexibility, accommodating diverse initial conditions (shape, inhomogeneity, etc.) and enabling specific choices for sub-volume selection with administrated higher radiation doses. The approach integrates the standard linear quadratic model and, significantly, considers the activation of the immune system due to radiotherapy. This activation enhances the immune response in comparison to the untreated case. We delve into the distinct roles of the native immune system, immune activation by radiation, and post-radiotherapy immunotherapy, discussing their implications for either complete recovery or disease regrowth.

A random sampling method for radiobiological modeling

Various radiobiological models have been proposed to describe the clonogenic cell survival after radiation. Least square model fitting to match experimental survival data can be tedious and sometimes difficult for complex models with multiple parameters. In this work, a random sampling method is developed to optimize the model parameters automatically to achieve best fitting with the experimental data. A computer program is developed to read the experimental data and to calculate the cell survival fractions based on a given mathematical model. Model parameters are randomly sampled, and the model predictions are compared with the experimental data. The mean square error (MSE) is used as an objective function to drive the iterative process. The goodness-of-fit of the linear quadratic (LQ), multitarget (MT), universal survival curves (USC) and multimode (MM) model was compared between the new method and previous studies for melanoma and non–small-cell lung cancer (NSCLC) cell lines. Good fitting was obtained for the MM model with the NSCLC data (MSE = 0.0005), which was better than the fits to the LQ, MT and USC models (MSE = 0.0019, 0.0082, 0.0024, respectively). The parameters used for the LQ, MT and USC models were α = 0.33Gy, α/β = 10Gy, D0 = 1.25Gy, n = 4.22 and DT = 6.2Gy. The parameters for the MM model (n = 4) were D1 = 3.0Gy, D2 = 8.27Gy, and D3 = 2.93Gy and D4 = 10.6Gy. It is concluded that the random sampling method provides a useful tool for the parameterization of radiobiological models for radiation research and clinical applications.

Shape of radiation dose response relationship for ischaemic heart disease mortality and its interpretation: analysis of the national registry for radiation workers (NRRW) cohort

Statistically significant increases in ischemic heart disease (IHD) mortality with cumulative occupational external radiation dose were observed in the National Registry for Radiation Workers (NRRW) cohort. There were 174 541 subjects in the NRRW cohort. The start of follow up was 1955, and the end of the follow-up for each worker was chosen as the earliest date of death or emigration, their 85th birthday or 31 December 2011. The dose-response relationship showed a downward curvature at a higher dose level >0.4 Sv with the overall shape of the dose-response relationship best described by a linear-quadratic model. The smaller risk at dose >0.4 Sv appears to be primarily associated with workers who started employment at a younger age (<30 years old) and those who were employed for more than 30 years. We modelled the dose response by age-at-first exposure. For the age-at-first exposure of 30+ years old, a linear dose-response was the best fit. For age-at-first exposure <30 years old, there was no evidence of excess risk of IHD mortality for radiation doses below 0.1 Sv or above 0.4 Sv, excess risk was only observed for doses between 0.1–0.4 Sv. For this age-at-first exposure group, it was also found that the doses they received when they were less than 35 years old or greater than 50 years old did not contribute to any increased IHD risk.

Ultrasensitive Response Explains the Benefit of Combination Chemotherapy Despite Drug Antagonism.

Most aggressive lymphomas are treated with combination chemotherapy, commonly as multiple cycles of concurrent drug administration. Concurrent administration is in theory optimal when combination therapies have synergistic (more than additive) drug interactions. We investigated pharmacodynamic interactions in the standard 4-drug "CHOP" regimen in peripheral T-cell lymphoma (PTCL) cell lines and found that CHOP consistently exhibits antagonism and not synergy. We tested whether staggered treatment schedules could improve tumor cell kill by avoiding antagonism, using in vitro models of concurrent or staggered treatments. Surprisingly, we observed that tumor cell kill is maximized by concurrent drug administration despite antagonistic drug-drug interactions. We propose that an ultrasensitive dose response, as described in radiology by the linear-quadratic (LQ) model, can reconcile these seemingly contradictory experimental observations. The LQ model describes the relationship between cell survival and dose, and in radiology has identified scenarios favoring hypofractionated radiotherapy-the administration of fewer large doses rather than multiple smaller doses. Specifically, hypofractionated treatment can be favored when cells require an accumulation of DNA damage, rather than a "single hit," to die. By adapting the LQ model to combination chemotherapy and accounting for tumor heterogeneity, we find that tumor cell kill is maximized by concurrent administration of multiple drugs, even when chemotherapies have antagonistic interactions. Thus, our study identifies a new mechanism by which combination chemotherapy can be clinically beneficial that is not contingent on positive drug-drug interactions.

Abstract 7374: Mathematical modeling of targeted radionuclide therapy and CAR-T cell immunotherapy for maximizing therapeutic efficacy in multiple myeloma

Abstract Background: Resistance of cancer cells to monotherapies has led to the development of sequential or combination therapy regimens. However, dosing and scheduling of these therapies is challenging due to the numerous dosing and scheduling combinations that can be given. Mathematical models are thus critical tools for addressing this challenge as multiple therapy combinations can be tested in silico to finalize a patient-specific therapeutic regimen in vivo. Here we develop a mathematical framework for combining targeted radiation therapy (TRT) with Chimeric Antigen Receptor (CAR)-T cell immunotherapy and demonstrate the use of in silico techniques to schedule these therapies for maximizing survival. Methods: In the mathematical framework tumor growth is assumed to be exponential and the effect of radiation on both tumor cells and CAR-T cells is modeled using the linear-quadratic model of cell survival to radiation. A predator-prey model is used to characterize the dynamics of tumor and CAR-T cells. Using a preclinical disseminated mouse model of multiple myeloma (MM1S), we evaluate tumor response to 200 nCi of 225Ac-DOTA-Daratumumab (TRT) and 1 million cells of CS1 CAR-T cell therapy both as monotherapies as well as in combination. Tumor burden tracked using bioluminescence imaging from six groups of mice is used to calibrate model parameters: (a) No treatment. (b) Day 7 TRT. (c) Day 7 CAR-T cell therapy. (d) Day 7 TRT + Day 18 CAR-T cell therapy. (e) Day 7 TRT + Day 25 CAR-T cell therapy. (f) Day 7 TRT + Day 32 CAR-T cell therapy. Response to therapy is evaluated using progression-free survival (PFS), overall survival (OS) and time to minimum tumor burden (tmin), all of which are calculated using the predicted in silico tumor burden dynamics and the tumor burden at the start of first therapy. We evaluate these response metrics for various dosing and scheduling regimens. Results: Therapy intervals that were too short or too long are shown to be detrimental for therapeutic efficacy. TRT too close to CAR-T cell therapy results in radiation related CAR-T cell killing, while the interval being too long results in tumor regrowth, negatively impacting tumor control and survival. If a single dose is split into multiple doses, the splitting is advantageous only if the first therapy delivered can produce a significant benefit as a monotherapy. Based on the model parameters we estimate the minimum required TRT activity and CAR-T cell dose to demonstrate an improvement in PFS. Conclusions: The proposed model demonstrates the impact of different dosing and scheduling regimens of TRT and CAR-T therapy on survival metrics. It is a potent tool for translating preclinical results to the clinic and eventually tailor therapy regimens for patients. Citation Format: Vikram Adhikarla, Dennis Awuah, Enrico Caserta, Megan Minnix, Maxim Kuznetsov, Amrita Krishnan, Jeffrey Y. Wong, John E. Shively, Xiuli Wang, Flavia Pichiorri, Russell C. Rockne. Mathematical modeling of targeted radionuclide therapy and CAR-T cell immunotherapy for maximizing therapeutic efficacy in multiple myeloma [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 7374.

A generalisation of the method of regression calibration and comparison with Bayesian and frequentist model averaging methods

For many cancer sites low-dose risks are not known and must be extrapolated from those observed in groups exposed at much higher levels of dose. Measurement error can substantially alter the dose–response shape and hence the extrapolated risk. Even in studies with direct measurement of low-dose exposures measurement error could be substantial in relation to the size of the dose estimates and thereby distort population risk estimates. Recently, there has been considerable attention paid to methods of dealing with shared errors, which are common in many datasets, and particularly important in occupational and environmental settings. In this paper we test Bayesian model averaging (BMA) and frequentist model averaging (FMA) methods, the first of these similar to the so-called Bayesian two-dimensional Monte Carlo (2DMC) method, and both fairly recently proposed, against a very newly proposed modification of the regression calibration method, the extended regression calibration (ERC) method, which is particularly suited to studies in which there is a substantial amount of shared error, and in which there may also be curvature in the true dose response. The quasi-2DMC with BMA method performs well when a linear model is assumed, but very poorly when a linear-quadratic model is assumed, with coverage probabilities both for the linear and quadratic dose coefficients that are under 5% when the magnitude of shared Berkson error is large (50%). For the linear model the bias is generally under 10%. However, using a linear-quadratic model it produces substantially biased (by a factor of 10) estimates of both the linear and quadratic coefficients, with the linear coefficient overestimated and the quadratic coefficient underestimated. FMA performs as well as quasi-2DMC with BMA when a linear model is assumed, and generally much better with a linear-quadratic model, although the coverage probability for the quadratic coefficient is uniformly too high. However both linear and quadratic coefficients have pronounced upward bias, particularly when Berkson error is large. By comparison ERC yields coverage probabilities that are too low when shared and unshared Berkson errors are both large (50%), although otherwise it performs well, and coverage is generally better than the quasi-2DMC with BMA or FMA methods, particularly for the linear-quadratic model. The bias of the predicted relative risk at a variety of doses is generally smallest for ERC, and largest for the quasi-2DMC with BMA and FMA methods (apart from unadjusted regression), with standard regression calibration and Monte Carlo maximum likelihood exhibiting bias in predicted relative risk generally somewhat intermediate between ERC and the other two methods. In general ERC performs best in the scenarios presented, and should be the method of choice in situations where there may be substantial shared error, or suspected curvature in the dose response.

Theoretical evaluation of the impact of diverse treatment conditions by calculation of the tumor control probability (TCP) of simulated cervical cancer Hyperthermia-Radiotherapy (HT-RT) treatments in-silico

Introduction Hyperthermia (HT) induces various cellular biological processes, such as repair impairment and direct HT cell killing. In this context, in-silico biophysical models that translate deviations in the treatment conditions into clinical outcome variations may be used to study the extent of such processes and their influence on combined hyperthermia plus radiotherapy (HT + RT) treatments under varying conditions. Methods An extended linear-quadratic model calibrated for SiHa and HeLa cell lines (cervical cancer) was used to theoretically study the impact of varying HT treatment conditions on radiosensitization and direct HT cell killing effect. Simulated patients were generated to compute the Tumor Control Probability (TCP) under different HT conditions (number of HT sessions, temperature and time interval), which were randomly selected within margins based on reported patient data. Results Under the studied conditions, model-based simulations suggested a treatment improvement with a total CEM43 thermal dose of approximately 10 min. Additionally, for a given thermal dose, TCP increased with the number of HT sessions. Furthermore, in the simulations, we showed that the TCP dependence on the temperature/time interval is more correlated with the mean value than with the minimum/maximum value and that comparing the treatment outcome with the mean temperature can be an excellent strategy for studying the time interval effect. Conclusion The use of thermoradiobiological models allows us to theoretically study the impact of varying thermal conditions on HT + RT treatment outcomes. This approach can be used to optimize HT treatments, design clinical trials, and interpret patient data.

Utility of realistic microscopy-based cell models in simulation studies of nanoparticle-enhanced photon radiotherapy

To enhance the effect of radiation on the tumor without increasing the dose to the patient, the combination of high-Z nanoparticles with radiotherapy has been proposed. In this work, we investigate the effects of the physical parameters of nanoparticles (NPs) on the Dose Enhancement Factor (DEF), and on the Sensitive Enhancement Ratio (SER) by applying a version of the Linear Quadratic Model. A method for constructing voxelized realistic cell geometries in Monte Carlo simulations from confocal microscopy images was developed and applied to Gliobastoma Multiforme cell lines (U87 and U373). The comparison of simulations with realistic geometry and spherical geometry shows that there is significant impact on the survival curves obtained for the same irradiation conditions. Using this model, the DEF and the SER are determined as a function of the concentration, size and distribution of gold nanoparticles within the cell. For small NPs, d AuNP = 10 nm, no clear trend in the DEF and SER was observed when the number of NPs within the cell increases. Experimentally, the variable number of NPs measured inside the U373 cells (ranging between 1.48 × 105 and 1.19 × 106) also did not influence much the observed cell survival upon irradiation of the cells with a Co-60 source. The same lack of trend is obtained when the Au content in the cell is kept constant, 0.897 mg/g, but the size of the NPs is changed. However, if the number of NPs is kept constant (7.91 × 105) and the size changes, there is a critical diameter above which the dose effect increases significantly. Using the realistic geometries, it was verified that the key parameter for the DEF and the SER enhancement is the volume fraction of Au in the cell, with NP size being a more important parameter than the number of NPs.

Path Tracking Control with Constraint on Tire Slip Angles under Low-Friction Road Conditions

This paper presents a method to design a path tracking controller with a constraint on tire slip angles under low-friction road conditions. On a low-friction road surface, a lateral tire force is easily saturated and decreases as a tire slip angle increases by a large steering angle. Under this situation, a path tracking controller cannot achieve its maximum performance. To cope with this problem, it is necessary to limit tire slip angles to a value where the maximum lateral tire force is achieved. The most commonly used controllers for path tracking, linear quadratic regulator (LQR) and model predictive control (MPC), are adopted as a controller design methodology. The control inputs of LQR and MPC are front and rear steering angles and control yaw moment, which have been widely used for path tracking. The constraint derived from tire slip angles is imposed on the steering angles of LQR and MPC. To fully verify the performance of the path tracking controller with the constraint on tire slip angles, a simulation is conducted on vehicle simulation software. From the simulation results, it is shown that the path tracking controller with the constraint on tire slip angles presented in this paper is quite effective for path tracking on low-friction road surface.

Impact of radiation therapy on healthy and cancerous cell dynamics: a Mathematical analysis

This study proposes a novel therapeutic model for cancer treatment with radiation therapy by analyzing the interactions among cancer, immune and healthy cells through a system of three ordinary differential equations. In this model, the natural influx rate of mature immune cells is assumed constant and is denoted by, a. The overall effect of radiation therapy on cancer cells is represented by a parameter, s; which is the surviving fraction of cells as determined by the Linear Quadratic (LQ) model. Conditions for the stability of equilibria in the interaction model modified to include the surviving fraction, are systematically established in terms of the dose and model parameters. Numerical simulations are performed in Wolfram MATHEMATICA software, investigating a spectrum of initial cell population values irradiated with 60Co γ -ray Low-LET radiation and High-LET 165 keV / μ m Ni-ion radiation to facilitate improved visualization and in-depth analysis. By analyzing the model, this study identifies threshold values for the absorbed dose D for particular values of the model and radiation parameters for both High Linear Energy Transfer (high-LET) and Low Linear Energy Transfer (low-LET) radiations that ensure either eradication or minimization of cancer cells from a patient’s body, providing valuable insights for designing effective cancer treatments.

Biological treatment evaluation in thermoradiotherapy: application in cervical cancer patients.

Hyperthermia treatment quality is usually evaluated by thermal (dose) parameters, though hyperthermic radiosensitization effects are also influenced by the time interval between the two modalities. This work applies biological modelling for clinical treatment evaluation of cervical cancer patients treated with radiotherapy plus hyperthermia by calculating the equivalent radiation dose (EQDRT, i.e., the dose needed for the same effect with radiation alone). Subsequent analyses evaluate the impact of logistics. Biological treatment evaluation was performed for 58patients treated with 23-28fractions of 1.8-2 Gy plus 4-5 weekly hyperthermia sessions. Measured temperatures (T50) and recorded time intervals between the radiotherapy and hyperthermia sessions were used to calculate the EQDRT using an extended linear quadratic (LQ) model with hyperthermic LQ parameters based on extensive experimental data. Next, the impact of a30-min time interval (optimized logistics) as well as a4‑h time interval (suboptimal logistics) was evaluated. Median average measured T50 and recorded time intervals were 41.2 °C (range 39.7-42.5 °C) and 79 min (range 34-125 min), respectively, resulting in amedian total dose enhancement (D50) of 5.5 Gy (interquartile range [IQR] 4.0-6.6 Gy). For 30-min time intervals, the enhancement would increase by ~30% to 7.1 Gy (IQR 5.5-8.1 Gy; p < 0.001). In case of 4‑h time intervals, an ~ 40% decrease in dose enhancement could be expected: 3.2 Gy (IQR 2.3-3.8 Gy; p < 0.001). Normal tissue enhancement was negligible (< 0.3 Gy), even for short time intervals. Biological treatment evaluation is auseful addition to standard thermal (dose) evaluation of hyperthermia treatments. Optimizing logistics to shorten time intervals seems worthwhile to improve treatment efficacy.