Multiple endemic equilibria in an environmentally-transmitted disease with three disease stages.

We construct, analyze and interpret a mathematical model for an environmental transmitted disease characterized for the existence of three disease stages: acute, severe and asymptomatic. Besides, we consider that severe and asymptomatic cases may present relapse between them. Transmission dynamics driven by the contact rates only occurs when a parameter R∗>1, as normally occur in directly-transmitted or vector-transmitted diseases, but it will not adequately correspond to a basic reproductive number as it depends on environmental parameters. In this case, the forward transcritical bifurcation that exists for R∗<1, becomes a backward bifurcation, producing multiple steady-states, a hysteresis effect and dependence on initial conditions. A threshold parameter for an epidemic outbreak, independent of R∗ is only the ratio of the external contamination inflow shedding rate to the environmental clearance rate. R∗ describes the strength of the transmission to infectious classes other than the I-(acute) type infections. The epidemic outbreak conditions and the structure of R∗ appearing in this model are both responsible for the existence of endemic states.

Mathematical analysis of FLASH effect models based on theoretical hypotheses.

OBJECTIVE: Clinical applications of FLASH radiotherapy require formulas to describe how the FLASH radiation features and other related factors determine the FLASH effect. Mathematical analysis of the models can connect the theoretical hypotheses with the radiobiological effect, which provides the foundation for establishing clinical application models. Moreover, experimental and clinical data can be used to explore the key factors through mathematical analysis. Approach: We abstract the complex models of the oxygen depletion hypothesis and radical recombination-antioxidants hypothesis into concise mathematical equations. The equations are solved to analyze how the radiation features and other factors influence the FLASH effect. Then we propose methodologies for determining the parameters in the models and utilizing the models to predict the FLASH effect. Main results: The formulas linking the physical, chemical and biological factors to the FLASH effect are obtained through mathematical derivation of the equation. The analysis indicates that the initial oxygen concentration, radiolytic oxygen consumption and oxygen recovery are key factors for the oxygen depletion hypothesis and that the level of antioxidants is the key factor for the radical recombination-antioxidants hypothesis. According to the model derivations and analysis, the methodologies for determining parameters and predicting the FLASH effect are proposed: the criteria for data filtration; the strategy of hybrid FLASH and conventional dose rate (CONV) irradiation to ensure the acquisition of effective experimental data across a wide dose range; pipelines of fitting parameters and predicting the FLASH effect. Significance: This study establishes the quantitative relationship between the FLASH effect and key factors. The derived formulas can be used to calculate the FLASH effect in future clinical FLASH radiotherapy. The proposed methodologies guide to obtain sufficient high-quality datasets and utilize them to predict FLASH effect. Furthermore, this study indicates the key factors of FLASH effect and offers clues to further explore the FLASH mechanism.

Modeling hepatitis A epidemiological profiles and estimating the pediatric vaccination threshold in the Russian Federation.

Background: To combat the hesitancy towards implementing a hepatitis A universal mass vaccination (UMV) strategy and to provide healthcare authorities with a comprehensive analysis of the potential outcomes and benefits of the implementation of such a vaccination program, we projected HAV seroprevalence and incidence rates in the total population of the Russian Federation and estimated the pediatric vaccination threshold required to achieve an incidence level of less than 1 case per 100,000 using a new mathematical model. Methods: A dynamic age-structured SEIRV (susceptible-exposed-infectious-recovered-vaccinated) compartmental model was developed and calibrated using demographic, seroprevalence, vaccination, and epidemiological data from different regions of the Russian Federation. This model was used to project various epidemiological measures. Results: The projected national average age at the midpoint of population immunity increases from 40 years old in 2020 to 50 years old in 2036 and is shifted even further to the age of 70 years in some regions of the country. An increase of varying magnitude in the incidence of symptomatic HAV infections is predicted for all study regions and for the Russian Federation as a whole between 2028 and 2032, if the HAV vaccination coverage level remains at the level of 2022. The national average vaccination coverage level required to achieve a symptomatic HAV incidence rate below 1 case per 100,000 by 2032 was calculated to be 69.8% if children aged 1-6 years are vaccinated following the implementation of a UMV program or 34.8% if immunization is expanded to children aged 1-17 years. Conclusion: The developed model provides insights into a further decline of herd immunity to HAV against the background of ongoing viral transmission. The current favorable situation regarding hepatitis A morbidity is projected to be replaced by an increase in incidence rates if vaccination coverage remains at the current levels. The obtained results support the introduction of a hepatitis A UMV strategy in the Russian Federation.

Abnormal open states patterns in the ATXN2 DNA sequence depends on the CAG repeats length.

Hereditary ataxias are one of the «anticipation diseases¼ types. Spinocerebral ataxia type 2 occurs when the number of CAG repeats in the coding region of the ATXN2 gene exceeds 34 or more. In healthy people, the CAG repeat region in the ATXN2 gene usually consists of 22-23 CAG trinucleotides. Mutations that increase the length of CAG repeats can cause severe neurodegenerative and neuromuscular disorders known as trinucleotide repeat expansion diseases. The mechanisms causing such diseases are associated with non-canonical configurations that can be formed in the CAG repeat region during replication, transcription or repair. This makes it relevant to study the zones of open states that arise in the region of CAG repeats under torque. The purpose of this work is to study, using mathematical modeling, zones of open states in the region of CAG repeats of the ATXN2 gene, caused by torque. It has been established that the torque effect on the 1st exon of the ATXN2 gene, in addition to the formation of open states in the promoter region, can lead to the formation of additional various sizes open states zones in the CAG repeats region. Moreover, the frequency of additional large zones genesis increases with increasing number of CAG repeats. The inverse of this frequency correlates with the dependence of the disease onset average age on the CAG repeats length. The obtained results will allow us to get closer to understanding the genetic mechanisms that cause trinucleotide repeat diseases.

An intelligent spraying system for weeds in wheat fields based on a dynamic model of droplets impacting wheat leaves.

Introduction: Targeted herbicide application refers to precise application of herbicides in weed-infested areas according to the location and density of farmland weeds. At present, targeted herbicide application in wheat fields generally faces problems including the low herbicide adhesion rate, leading to omission and excessive loss of herbicides. Methods: To solve these problems, changes in the impact force of herbicide and the weed leaves in the operation process of a spraying system were studied from the interaction between weeds and herbicides applied. A dynamic model of weed leaves was established. On this basis, the research indicated that the herbicide adhesion rate is highest under spraying pressure of 0.4 MPa and flow rate of 0.011 kg/s when the spray height is 300 mm. To study the dynamic deformation of weed leaves and the distribution of liquid herbicides in the external flow field under weed-herbicide interaction, a dynamic simulation model of herbicide application was built using the finite element method. Results and Discussion: The results show that when the spray height is 300 mm, the maximum weed leaf deformation index (LDI) is 0.43 and the velocity in the external flow field is 0 m/s under spraying pressure of 0.4 MPa and flow rate of 0.011 kg/s. This finding indicates that the herbicide is not splashed elsewhere and the turbulence intensity in the weed area is 2%, implying steady flow of the herbicide, most of which can be retained on weed leaves. Field test results of application quality of the herbicide show that the maximum LDI is 0.41 and the coverage of the herbicide in the sheltered area below the leaves is 19.02% when the spraying pressure is 0.4 MPa, flow rate is 0.011 kg/s, and spray height is 300 mm. This solves the problem of a low rate of utilization of herbicides because the herbicide passes through weed plants, and achieves the precision herbicide application in wheat fields.

Computational modeling of heart failure in microgravity transitions.

The space tourism industry is growing due to advances in rocket technology. Privatised space travel exposes non-professional astronauts with health profiles comprising underlying conditions to microgravity. Prior research has typically focused on the effects of microgravity on human physiology in healthy astronauts, and little is known how the effects of microgravity may play out in the pathophysiology of underlying medical conditions, such as heart failure. This study used an established, controlled lumped mathematical model of the cardiopulmonary system to simulate the effects of entry into microgravity in the setting of heart failure with both, reduced and preserved ejection fraction. We find that exposure to microgravity eventuates an increased cardiac output, and in patients with heart failure there is an unwanted increase in left atrial pressure, indicating an elevated risk for development of pulmonary oedema. This model gives insight into the risks of space flight for people with heart failure, and the impact this may have on mission success in space tourism.

Comparative analysis and evolution of civilian versus combatant mortality ratios in Israel-Gaza conflicts, 2008-2023.

Background: There is a need for statistical methodologies that scrutinize civilian casualties in conflicts, evaluating the degree to which the conduct of war affects civilians and breaches the laws of war. Employing an epidemiological method, this study introduced, developed, and applied a novel approach for investigating mortality of civilians versus combatants in conflicts. Methods: A deterministic mathematical model, structured by age and sex, was developed to describe the process of conflict-related deaths among both combatants and civilians. The model was calibrated using demographic and conflict-related data from different Israel-Gaza conflicts. To quantify the extent of the impact on civilians and determine whether they are the primary focus of a conflict, a statistical metric, the index of killing civilians, along with associated criteria, was devised. Results: The model-estimated proportion of deaths in Gaza categorized as combatants was 62.1% (95% uncertainty interval (UI): 57.6-66.2%), 51.1% (95% UI: 47.1-54.9%), and 12.7% (95% UI: 9.7-15.4%) in the 2008-2009, 2014, and 2023 Israel-Gaza conflicts, respectively. The index of killing civilians was 0.61 (95% UI: 0.51-0.74), 0.96 (95% UI: 0.82-1.12), and 7.01 (95% UI: 5.50-9.29) in the 2008-2009, 2014, and 2023 conflicts, respectively. These index values indicate strong evidence for civilians being an object of war in the 2008-2009 and 2014 conflicts, but combatants were still identified as the primary focus of the conflict. In the 2023 conflict, there is robust evidence for civilians being an object of war, with civilians identified as the primary focus of the conflict. Conclusion: Findings imply a progressive shift in Israel's rules of engagement over time, with a trend towards higher acceptance of casualties among civilians. The 2023 conflict stands apart from preceding Israel-Gaza conflicts, with civilians identified as the primary focus of the conflict.

Modeling the CD8＋ T cell immune response to influenza infection in adult and aged mice.

The CD8＋ T cell response is the main determinant of viral clearance during influenza infection. However, influenza viral dynamics and the respective immune responses are affected by the host's age. To investigate age-related differences in the CD8＋ T cell immune response dynamics, we propose an 16 ordinary differential equation models of existing experimental data. These data consist of viral titer and CD8＋ T cell counts collected periodically over a period of 19 days from adult and aged mice infected with influenza A/Puerto Rico/8/34 (H1N1). We use the corrected Akaike Information Criterion to identify the models which best represent the considered data. Our model selection process indicates differences in mechanisms which reduce the CD8＋ T cell response: linear downregulation is favored for adult mice, while baseline exponential decay is favored for aged mice. Parameter fitting of the top ranked models suggests that the aged population has reduced CD8＋ T cell proliferation compared to the adult population. More experimental work is needed to determine the specific immunological features through which age might cause these differences. A better understanding of the immunological mechanisms by which aging leads to discrepant CD8＋ T cell dynamics may inform future treatment strategies.

Learning from the COVID-19 pandemic: A systematic review of mathematical vaccine prioritization models.

As the world becomes ever more connected, the chance of pandemics increases as well. The recent COVID-19 pandemic and the concurrent global mass vaccine roll-out provides an ideal setting to learn from and refine our understanding of infectious disease models for better future preparedness. In this review, we systematically analyze and categorize mathematical models that have been developed to design optimal vaccine prioritization strategies of an initially limited vaccine. As older individuals are disproportionately affected by COVID-19, the focus is on models that take age explicitly into account. The lower mobility and activity level of older individuals gives rise to non-trivial trade-offs. Secondary research questions concern the optimal time interval between vaccine doses and spatial vaccine distribution. This review showcases the effect of various modeling assumptions on model outcomes. A solid understanding of these relationships yields better infectious disease models and thus public health decisions during the next pandemic.

Unraveling host-pathogen dynamics in a murine Model of septic peritonitis induced by vancomycin-resistant Enterococcus faecium.

Vancomycin-resistant Enterococcus faecium (E. faecium) infection is associated with higher mortality rates. Previous studies have emphasized the importance of innate immune cells and signalling pathways in clearing E. faecium, but a comprehensive analysis of host-pathogen interactions is lacking. Here, we investigated the interplay of host and E. faecium in a murine model of septic peritonitis. Following injection with a sublethal dose, we observed significantly increased murine sepsis score and histological score, decreased weight and bacterial burden, neutrophils and macrophages infiltration, and comprehensive activation of cytokine-mediated signalling pathway. In mice receiving a lethal dose, hypothermia significantly improved survival, reduced bacterial burden, cytokines, and CD86 expression of MHC-II+ recruited macrophages compared to the normothermia group. A mathematical model constructed by observational data from 80 animals, recapitulated the host-pathogen interplay, and further verified the benefits of hypothermia. These findings indicate that E. faecium triggers a severe activation of cytokine-mediated signalling pathway, and hypothermia can improve outcomes by reducing bacterial burden and inflammation.

Fluid shear stress-induced changes in megalin trafficking enhance endocytic capacity in proximal tubule cells.

Proximal tubule (PT) cells maintain a high-capacity apical endocytic pathway to recover essentially all proteins that escape the glomerular filtration barrier. The multi ligand receptors megalin and cubilin play pivotal roles in the endocytic uptake of normally filtered proteins in PT cells but also contribute to the uptake of nephrotoxic drugs, including aminoglycosides. We previously demonstrated that opossum kidney (OK) cells cultured under continuous fluid shear stress (FSS) are superior to cells cultured under static conditions in recapitulating essential functional properties of PT cells in vivo. To identify drivers of the high-capacity, efficient endocytic pathway in the PT, we compared FSS-cultured OK cells with less endocytically active static-cultured OK cells. Megalin and cubilin expression are increased, and endocytic uptake of albumin in FSS-cultured cells is > 5-fold higher compared with cells cultured under static conditions. To understand how differences in receptor expression, distribution, and trafficking rates contribute to increased uptake, we used biochemical, morphological, and mathematical modeling approaches to compare megalin traffic in FSS- versus static-cultured OK cells. Our model predicts that culturing cells under FSS increases the rates of all steps in megalin trafficking. Importantly, the model explains why, despite seemingly counterintuitive observations (a reduced fraction of megalin at the cell surface, higher colocalization with lysosomes, and a shorter half-life of surface-tagged megalin in FSS-cultured cells), uptake of albumin is dramatically increased compared with static-grown cells. We also show that FSS-cultured OK cells more accurately exhibit the mechanisms that mediate uptake of nephrotoxic drugs in vivo compared with static-grown cells. This culture model thus provides a useful platform to understand drug uptake mechanisms, with implications for developing interventions in nephrotoxic injury prevention.

Role of informal sector to combat unemployment in developing economy: A modeling study.

In developing countries, informal sector is the primary job provider for a significant portion of the workforce. This study aims to analyze how jobs in the informal sector affect the unemployment dynamics of developing nations. To achieve this goal, we formulate a nonlinear mathematical model by categorizing the considered workforce into three distinct classes: unemployed, employed, and self-employed, and include a separate dynamic variable to represent vacancies within the informal sector. The proposed model is analyzed using the qualitative theory of dynamical systems. A threshold quantity known as the reproduction number is derived and using this, one can compute the job generation rate necessary to stabilize the system. It is observed that variations in the reproduction number lead to qualitative changes, such as transcritical (forward or backward) and saddle-node bifurcations in the formulated system. Moreover, we propose an optimal control problem to determine an optimal strategy for government policy implementation in enhancing the employment rate of unemployed individuals and promoting the self-employment of informal employees inside the informal sector. Further, the analytical findings are validated numerically. The obtained results suggest that promoting the self-employment of informal employees for job generation effectively reduces unemployment.

Renal handling of albumin in rats with early stage diabetes: A theoretical analysis.

In early diabetic nephropathy (DN), recent studies have shown that albuminuria stems mostly from alterations in tubular function rather than from glomerular damage. Several factors in DN, including hyperfiltration, hypertrophy and reduced abundance of the albumin receptors megalin and cubilin, affect albumin endocytosis in the proximal tubule (PT). To assess their respective contribution, we developed a model of albumin handling in the rat PT that couples the transport of albumin to that of water and solutes. Our simulations suggest that, under basal conditions, ∼75% of albumin is retrieved in the S1 segment. The model predicts negligible uptake in S3, as observed experimentally. It also accurately predicts the impact of acute hyperglycaemia on urinary albumin excretion. Simulations reproduce observed increases in albumin excretion in early DN by considering the combined effects of increased glomerular filtration rate (GFR), osmotic diuresis, hypertrophy, and megalin and cubilin downregulation, without stipulating changes in glomerular permselectivity. The results indicate that in isolation, glucose-elicited osmotic diuresis and glucose transporter upregulation raise albumin excretion only slightly. Enlargement of PT diameter not only augments uptake via surface area expansion, but also reduces fluid velocity and thus shear stress-induced stimulation of endocytosis. Overall, our model predicts that downregulation of megalin and cubilin and hyperfiltration both contribute significantly to increasing albumin excretion in rats with early-stage diabetes. The results also suggest that acute sodium-glucose cotransporter 2 inhibition lowers albumin excretion only if GFR decreases sufficiently, and that angiotensin II receptor blockers mitigate urinary albumin loss in early DN in large part by upregulating albumin receptor abundance. KEY POINTS: The urinary excretion of albumin is increased in early diabetic nephropathy (DN). It is difficult to experimentally disentangle the multiple factors that affect the renal handling of albumin in DN. We developed a mathematical model of albumin transport in the rat proximal tubule (PT) to examine the impact of elevated plasma glucose, hyperfiltration, PT hypertrophy and reduced abundance of albumin receptors on albumin uptake and excretion in DN. Our model predicts that glucose-elicited osmotic diuresis per se raises albumin excretion only slightly. Conversely, increases in PT diameter and length favour reduced albumin excretion. Our results suggest that downregulation of the receptors megalin and cubilin in PT cells and hyperfiltration both contribute significantly to increasing albumin excretion in DN. The model helps to better understand the mechanisms underlying urinary loss of albumin in early-stage diabetes, and the impact of specific treatments thereupon.

HIV incidence before and during the COVID-19 pandemic in Japan.

At the end of 2022, a total of 20,003 diagnoses of human immunodeficiency virus (HIV) infection and 8,983 cases of acquired immunodeficiency syndrome (AIDS) among Japanese nationals, and 3,860 HIV diagnoses and 1,575 AIDS cases among foreign residents, had been notified to the government in Japan. This study updates the estimate of HIV incidence, including during the COVID-19 pandemic. It aimed to reconstruct the incidence of HIV and understand how the disruption caused by COVID-19 affected the epidemiology of HIV. Using a median incubation period of 10.0 years, the number of undiagnosed HIV infections was estimated to be 3,209 (95% confidence interval (CI): 2,642, 3,710) at the end of 2022. This figure has declined steadily over the past 10 years. Assuming that the median incubation period was 10.0 years, the proportion of diagnosed HIV infections, including surviving AIDS cases, was 89.3% (95% CI: 87.8%, 91.0%). When AIDS cases were excluded, the proportion was 86.2% (95% CI: 84.3%, 88.3%). During the COVID-19 pandemic, the estimated annual diagnosis rate was slightly lower than during earlier time intervals, at around 16.5% (95% CI: 14.9%, 18.1%). Japan may already have achieved diagnostic coverage of 90%, given its 9% increment in the diagnosed proportion during the past 5 years. The incidence of HIV infection continued to decrease even during the COVID-19 pandemic from 2020 to 2022, and the annual rate of diagnosis decreased slightly to 16.5%. Monitoring the recovery of diagnosis along with the effective reproduction number is vital in the future.

Numerical and graphical simulation of the non-linear fractional dynamical system of bone mineralization.

The objective of the present study was to improve our understanding of the complex biological process of bone mineralization by performing mathematical modeling with the Caputo-Fabrizio fractional operator. To obtain a better understanding of Komarova's bone mineralization process, we have thoroughly examined the boundedness, existence, and uniqueness of solutions and stability analysis within this framework. To determine how model parameters affect the behavior of the system, sensitivity analysis was carried out. Furthermore, the fractional Adams-Bashforth method has been used to carry out numerical and graphical simulations. Our work is significant owing to its comparison of fractional- and integer-order models, which provides novel insight into the effectiveness of fractional operators in representing the complex dynamics of bone mineralization.

Pharmacological studies and pharmacokinetic modelling to support the development of interventions targeting ecological reservoirs of Lyme disease.

The development of interventions targeting reservoirs of Borrelia burgdorferi sensu stricto with acaricide to reduce the density of infected ticks faces numerous challenges imposed by ecological and operational limits. In this study, the pharmacokinetics, efficacy and toxicology of fluralaner were investigated in Mus musculus and Peromyscus leucopus mice, the main reservoir of B. burgdorferi in North America. Fluralaner showed rapid distribution and elimination, leading to fast plasma concentration (Cp) depletion in the first hours after administration followed by a slow elimination rate for several weeks, resulting in a long terminal half-life. Efficacy fell below 100% while Cp (± standard deviation) decreased from 196 ± 54 to 119 ± 62 ng/mL. These experimental results were then used in simulations of fluralaner treatment for a duration equivalent to the active period of Ixodes scapularis larvae and nymphs. Simulations showed that doses as low as 10 mg/kg have the potential to protect P. leucopus against infestation for a full I. scapularis active season if administered at least once every 7 days. This study shows that investigating the pharmacology of candidate acaricides in combination with pharmacokinetic simulations can provide important information to support the development of effective interventions targeting ecological reservoirs of Lyme disease. It therefore represents a critical step that may help surpass limits inherent to the development of these interventions.

A Lumped-Parameter Model of the Cardiovascular System Response for Evaluating Automated Fluid Resuscitation Systems.

Physiological closed-loop controlled (PCLC) medical devices, such as those designed for blood pressure regulation, can be tested for safety and efficacy in real-world clinical settings. However, relying solely on limited animal and clinical studies may not capture the diverse range of physiological conditions. Credible mathematical models can complement these studies by allowing the testing of the device against simulated patient scenarios. This research involves the development and validation of a low-order lumped-parameter mathematical model of the cardiovascular system's response to fluid perturbation. The model takes rates of hemorrhage and fluid infusion as inputs and provides hematocrit and blood volume, heart rate, stroke volume, cardiac output and mean arterial blood pressure as outputs. The model was calibrated using data from 27 sheep subjects, and its predictive capability was evaluated through a leave-one-out cross-validation procedure, followed by independent validation using 12 swine subjects. Our findings showed small model calibration error against the training dataset, with the normalized root-mean-square error (NRMSE) less than 10% across all variables. The mathematical model and virtual patient cohort generation tool demonstrated a high level of predictive capability and successfully generated a sufficient number of subjects that closely resembled the test dataset. The average NRMSE for the best virtual subject, across two distinct samples of virtual subjects, was below 12.7% and 11.9% for the leave-one-out cross-validation and independent validation dataset. These findings suggest that the model and virtual cohort generator are suitable for simulating patient populations under fluid perturbation, indicating their potential value in PCLC medical device evaluation.

A Model for the Coexistence of Competing Mechanisms for Ca 2 + Oscillations in T-lymphocytes.

Ca 2 + is a ubiquitous signaling mechanism across different cell types. In T-cells, it is associated with cytokine production and immune function. Benson et al. have shown the coexistence of competing Ca 2 + oscillations during antigen stimulation of T-cell receptors, depending on the presence of extracellular Ca 2 + influx through the Ca 2 + release-activated Ca 2 + channel (Benson in J Biol Chem 29:105310, 2023). In this paper, we construct a mathematical model consisting of five ordinary differential equations and analyze the relationship between the competing oscillatory mechanisms.. We perform bifurcation analysis on two versions of our model, corresponding to the two oscillatory types, to find the defining characteristics of these two families.

Optimized microwave-assisted azadirachtin extraction using response surface methodology.

The neem tree (Azadirachta indica A. Juss) is grown mainly for shade, fuel, and numerous non-timber forest products using its leaves, fruit, and bark. It produces an essential oil that is used as a source for obtaining bioinsecticides, with a broad spectrum of action in agricultural production. Its bioinsecticidal activity is due to the presence of triterpenes, such as azadirachtin, a product in continued growth of the global biopesticide market. Optimal conditions for neem oil extraction using response surface methodology (RSM) and microwave-assisted extraction (MAE) methods have been defined. However, the extraction conditions for these methods tend to consume high volumes of organic solvent and long extraction times. The aim of the present study is to determine the optimal conditions for the extraction of azadirachtin from neem seeds in a hydroalcoholic medium using MAE and RSM with a Box-Behnken design (BBD). A BBD was applied to evaluate the effects of the factors, magnetron voltage (X1), extraction time (X2), and pH of the extraction medium (X3), on the yield of the azadirachtin extraction process. The effect of each variable on the extraction yield was studied independently, considering the pure coefficients (linear and quadratic) on the three levels that were studied in the experiments. Moreover, the study experiments were conducted in triplicate, data were presented as mean and standard deviation, homogeneity of variances was estimated using Levene's test, and a two-way ANOVA with Tukey's post hoc analysis was performed to identify the experimental conditions that allowed us to find the highest extraction yield and to analyze whether the response surface model adequately described our data. The most significant effects of the model correspond to quadratic and interaction effects (p < 0.0001); the quadratic terms voltage (X1), extraction time (X2), and pH (X3); and the interaction effects between voltage-pH (X1*X3) and time-pH (X2*X3), which had a significant influence on the model. Moreover, a canonical analysis was performed. The optimal conditions were as follows: 69.22 V, 6.89 min, and a pH value of 4.35, coinciding with the zones shown in the contour plots. Furthermore, the response obtained at the optimal conditions was 37.5 µg of azadirachtin per gram of pretreated seed.

Assessing tumor volumetric reduction with consideration for setup errors based on mathematical tumor model and microdosimetric kinetic model in single-isocenter VMAT for brain metastases.

The volumetric reduction rate (VRR) was evaluated with consideration for six degrees-of-freedom (6DoF) patient setup errors based on a mathematical tumor model in single-isocenter volumetric modulated arc therapy (SI-VMAT) for brain metastases. Simulated gross tumor volumes (GTV) of 1.0 cm and dose distribution were created (27 Gy/3 fractions). The distance between the GTV center and isocenter (d) was set at 0-10 cm. The GTV was translated within 0-1.0 mm (Trans) and rotated within 0-1.0° (Rot) in the three axis directions using affine transformation. The tumor growth volume was calculated using a multicomponent mathematical model (MCTM), and lethal effects of irradiation and repair from damage during irradiation were calculated by a microdosimetric kinetic model (MKM) for non-small cell lung cancer (NSCLC) A549 and NCI-H460 (H460) cells. The VRRs were calculated 5 days after the end of irradiation using the physical dose to the GTV for varying d and 6DoF setup errors. The tolerance value of VRR, the GTV volume reduction rate, was set at 5%, based on the pre-irradiation GTV volume. With the exception of the only one A549 condition where (Trans, Rot) = (1.0 mm, 1.0°) was repeated for 3 fractions, all conditions met all the tolerance VRR values for A549 and H460 cells with varying d from 0 to 10 cm. Evaluation based on the mathematical tumor model suggested that if the 6DoF setup errors at each irradiation could be kept within 1.0 mm and 1.0°, there would be little effect on tumor volume regardless of the distance from the isocenter in SI-VMAT.