Mathematical Model Of Response Research Articles

Clinical Validation of Mathematically Derived Early Tumor Dynamics for Solid Tumors in Response to Durvalumab.

Early prediction of response to immunotherapy may help guide patient management by identifying resistance to treatment and allowing adaptation of therapies. This analysis evaluated a mathematical model of response to immunotherapy that provides patient-specific prediction of outcome using the initial change in tumor size/burden from baseline to the first follow-up visit on standard imaging scans. We applied the model to 600 patients with advanced solid tumors who received durvalumab in Study 1108, a phase I/II trial, and compared outcome prediction performance versus size-based criteria with RECIST version 1.1 best overall response (BOR), baseline circulating tumor (ct)DNA level, and other clinical/pathologic predictors of immunotherapy response. In multiple solid tumors, the mathematical parameter representing net tumor growth rate at the first on-treatment computed tomography (CT) scan assessed around 6 weeks after starting durvalumab (α1) had a concordance index to predict overall survival (OS) of 0.66-0.77 on multivariate analyses. This measurement of early tumor dynamics significantly improved multivariate OS models that included standard RECIST v1.1 criteria, baseline ctDNA levels, and other clinical/pathologic factors in predicting OS. Furthermore, α1 was assessed consistently at the first on-treatment CT scan, whereas all traditional RECIST BOR groups were confirmed only after this time. These results support further exploring α1 as an integral biomarker of response to immunotherapy. This biomarker may be predictive of further benefit and can be assessed before RECIST response groups can be assigned, potentially providing an opportunity to personalize oncologic management.

Optimizing end milling parameters for custom 450 stainless steel using ant lion optimization and TOPSIS analysis

The current research examines the effectiveness of cryogenically treated (CT) tungsten carbide cutting inserts on Custom450 stainless steel using multi-objective soft computing approaches. The Taguchi-based L27 orthogonal array was employed in the experiments. During milling operations, cutting force, surface roughness, and cutting temperature were measured at different spindle speeds (rpm), feed rates (mm/min), and constant depths of cut (mm). The surface roughness and chip morphology of the Custom 450 stainless steel machined by cryo-treated (CT) and untreated (UT) cutting tool inserts were compared across various responses to cutting temperature and force. This paper also carried out multi-objective optimization, employing algorithm techniques such as Grasshopper Optimization Algorithm (GHO), Grey Wolf Optimization(GWO), Harmony Search Algorithm(HAS), and Ant line Optimization (ALO). The Multi-objective Taguchi approach and TOPSIS were first used to optimize the machining process parameters (spindle speed, feed rate, and cryogenic treatment) with different performance characteristics. Second, to relate the machining process parameters with the performance characteristics (cutting force, cutting temperature, and surface roughness), a mathematical model was developed using response surface analysis. The created mathematical response model was validated using ANOVA. The results showed that in IGD values of GHO, GWO, HSA and ALO module had 2.5765, 2.4706, 2.3647 and 2.5882 respectively, ALO has the best performance indicator. A Friedman’s test was also conducted, revealing higher resolution with the ALO method than with the HSA, GWO, and GHO methods. The results of the scanning test show that the ALO approach is workable.

Mathematical modeling for assessing the seismic response of buildings in Al Hoceima

The purpose of this paper is to apply structural dynamics principles to conduct a comprehensive mathematical analysis of how buildings respond to earthquakes, with a particular focus on the dynamic behavior of a reinforced concrete structure in the city of Al Hoceima, located in the north of Morocco, which is subjected to frequent seismic activity. Considering various parameters such as building configurations, materials, soil characteristics, and seismic conditions, we will build a mathematical model for response of structures to earthquakes and conduct numerical experiments using ETABS software on a typical building in this region with a G+2 house elevation.

Process optimization for enhancing interconnect performance of large-size BGA component during vibration loading

A series of problems such as failure solder at SnAgCu large-size BGA component and Pb-rich phase at SnPb component are always found during mixed lead-free/tin-lead assembly. In order to give a better reflow process window of assembled printed circuit board, process optimization was carried out to satisfy a favourable reflow time for all the components. Numerical simulation according to the Box-Behnken design method was carried out to monitor the effective reflow time of mixed lead-free/tin-lead and tin-lead components, and a mathematical response model between the effective reflow time and the process curve was developed by multivariate quadratic regression analysis. An optimal reflow process curve was established by simulated annealing algorithm. According to the optimal process parameter, numerical simulation was carried out to observe the temperature distribution and residual stress, and the experimental researches including the vibration test and micro structure analysis were conducted on the mixed lead-free/tin-lead assembled component to monitor the dynamic resistance and deformation and characterize the reaction product at the interface. It is shown that the corner BGA component still suffers from both a higher residual stress (about 32 MPa) after reflow process and a larger deformation (about 64 μm) at the first order modality during random vibration test. However, a continuous intermetallic compound layer with the thickness of 1.2–1.5 μm containing the reaction products Ni3Sn4 and (Au,Ni)Sn4 is well generated, and no cracks and voids are observed.

Performance evaluation of Cu-W-Si green P/M composite electrode for surface modification of P20+Ni steel using electrical discharge machine

The current experimental research is being carried out to investigate the correlation between the process parameter of the electrical discharge machine (EDM) with the composite electrode (Cu-W-Si) produced through the process of powder metallurgy (P/M). The experiments on P20+Ni die steel were planned and performed using the rotatable second-order central composite design (CCD). The mathematical response model was obtained through response surface methodology. MRR, TWR and SR have been studied on the significance of compaction pressure (Cp), peak current (Ip), pulse-on time (Ton) and duty cycle (τ). ANOVA was conducted to investigate the contribution percentage of the parameters. The optimal set of process parameters was obtained using a multi-objective optimisation technique called 'composite desirability'. The predicted results of responses were confirmed with the experimental results. The reasonable agreements between predicted and experimental results of MRR and TWR have been obtained with error lying within 5.19% and −3.33% respectively.

Influence Analysis of Factors Related to the Clod Heaping Quantity of Subsoilers

In order to increase the performance of three working parts of this machine at the same time, it needs to increase its operating speed, 1MG11-200type compound paddy tiller consists of the mounted compound structure arranged the subsoiler with cutting edge at the front part and rotary-tiller without power in the middle part and curved tooth-beam harrow in the rear part, this be able to plough and harrow and level at a time. As operating speed increases in clay loam, the clod heaping occurs in the space of subsoilers, even fill up in the spaces. Therefore, during the working, it is one of important matter to found the optimum operating speed and subsoiler’s interval without clod heaping. In a field study conducted at MiGok co-op farm, Sariwon, Democratic People’s Republic of Korea, were tested for clod heaping quantity on different operating speed and subsoiler’s intervals for clay loam. Mathematical response model was built on clod heaping quantity relative to operating speed and subsoiler’s interval to found the operating levels without clod heaping. It was found that the subsoiler, while working in clay loam, should have operating speed 6.2km/h, subsoiler’s side interval 0.5m and subsoiler’s front-rear interval 0.46m for optimum level without clod heaping.

About Realizations of Compatible Control Impacts on the Object in the Man—Machine Systems

We consider the problems of implementing control actions on the object in the ergatic system man—machine, combined through the control body of the human-machine interface apparatus, in order to effectively distribute the control functions between the human operator and the system’s control automat. Peculiarities of technical realization of operating influences on object ergatic system using the apparatus combines new type of control, through a management body of which is communication between a human operator and automatic system. The principle of construction of joint control devices is shown with the help of pictorial models of discrete and continuous operation devices that have an Electromechanical drive device that reacts to signals from the control machine due to the movement of the control body. The devices provide for the possibility of moving the control body and the muscular effort of the human operator. For the verbal model of actions and responses of the human operator and the machine, adopted in engineering psychology, mathematical models of joint control of the object of the ergatic system, describing the movements of the control body, are developed. The mathematical model of the response of the controlled object of the system is represented by a normal system of ordinary differential equations. As a result of composition of models of actions and reactions for the system man—machine obtained a finite set of incomplete representations of the elementary movements depicting point in the state space, which is constructed for controlled movement of an object in a sequence of elementary movements. Virtual discrete control signals corresponding to specific positions of the control bodies of the joint control devices of the human-machine interface of the system, which are used for sequential transitions from one elementary movement to another, are determined. The results of approbation of joint traffic control of vessels using a mathematical model of actions and responses in full-scale experiments with increased requirements for safety and accuracy of movement are presented. Conclusions are formulated about the effectiveness of the use of Sov-local management in transport ergatic systems man—machine. It is shown that in this case, the advantages of management partners are most used and combined.

Study of surface integrity and effect of process parameters in wire electrical discharge turning of Ti-6Al-4V

Wire electrical discharge turning set-up has been developed by modifying the conventional five axes CNC WEDM machine. The main objective of this setup is to achieve cylindrical forms on hard to cut materials. This work focuses on the study of effect of input process parameters like pulse on-time, pulse off time, gap voltage, spindle rotational speed on output responses like surface roughness, material removal rate and wire wear ratio. A mathematical model of responses has been developed using response surface methodology and the optimal value of process parameters has been obtained by desirability function. Surface morphology studies of the machined surface and the worn-out wire has also been elaborated by FE-SEM images. The results show that with an increase in machining parameters value except pulse-on time, all the desired machining outcome decreases. Surface roughness, material removal rate and wire wear ratio have been found in the range of 1.99 μm – 1.37 μm, 7.55 – 13.66 mm3/min and 0.05–0.08, respectively. The formation of thick recast layer over the machined surface has also been discussed. The reduction in wire dimension has been calculated by optical microscopy and its morphology has been discussed by FE-SEM images.

A Model of Indirect Cell Death Caused by Tumor Vascular Damage after High-Dose Radiotherapy.

There is increasing evidence that high doses of radiotherapy, like those delivered in stereotactic body radiotherapy (SBRT), trigger indirect mechanisms of cell death. Such effect seems to be two-fold. High doses may trigger an immune response and may cause vascular damage, leading to cell starvation and death. Development of mathematical response models, including indirect death, may help clinicians to design SBRT optimal schedules. Despite increasing experimental literature on indirect tumor cell death caused by vascular damage, efforts on modeling this effect have been limited. In this work, we present a biomathematical model of this effect. In our model, tumor oxygenation is obtained by solving the reaction-diffusion equation; radiotherapy kills tumor cells according to the linear-quadratic model, and also endothelial cells (EC), which can trigger loss of functionality of capillaries. Capillary death will affect tumor oxygenation, driving nearby tumor cells into severe hypoxia. Capillaries can recover functionality due to EC proliferation. Tumor cells entering a predetermined severe hypoxia status die according to a hypoxia-death model. This model fits recently published experimental data showing the effect of vascular damage on surviving fractions. It fits surviving fraction curves and qualitatively reproduces experimental values of percentages of functional capillaries 48 hours postirradiation, and hypoxic cells pre- and 48 hours postirradiation. This model is useful for exploring aspects of tumor and EC response to radiotherapy and constitutes a stepping stone toward modeling indirect tumor cell death caused by vascular damage and accounting for this effect during SBRT planning. SIGNIFICANCE: A novel biomathematical model of indirect tumor cell death caused by vascular radiation damage could potentially help clinicians interpret experimental data and design better radiotherapy schedules.

Effect of Machining Parameters on Tool Wear and Surface Roughness In Dry and Wet Machining of Aisi 316 Austenitic Stainless Steel by Taguchi Method

Stainless steels are widely used to manufacture mechanical components due to excellent mechanical properties. Machining is considered as one of the most critical manufacturing processes in mechanical industry to produce desired shapes and dimensional accuracy of the components. It also affects the performance of the components in its functional requirement. This paper deals with the optimization of cutting parameters in machining operation for AISI 316 austenitic steel with dry and wet environment conditions. The chosen machining parameters in this research are cutting speed, feed rate, and depth of cut as input variables, whereas the response factors are surface roughness and wear rate. Taguchi method with the L9 orthogonal array was used to analyze the process parameters based in dry and wet machining conditions. The Taguchi approach provides the best setting with lower values of surface roughness and wear rate. The regression analysis is performed to obtain a mathematical model of responses in terms of the process parameter. The composite regression optimization gives best setting for dry condition (cutting speed 173 rpm, feed 0.25 mm/rev, and 0.87 mm of the depth of cut) and for wet condition (cutting speed 173 rpm, feed 0.3 mm/rev, and 0.57 mm of the depth of cut). The results show that surface roughness and wear rate are lower in the wet environment than the dry environment.

Effect of Laser Welding Parameters on Weld Bowing Distortion of Thin Plates

AbstractWeld bowing distortions are detrimental to the assembly process, where laser process parameters such as laser power, welding speed, defocusing distance and gas flow rate play a significant role in determining the weld bowing distortion. Herein, weld bowing distortions in 1-mm-thick AA5052 aluminum were measured by the digital image correlation technique following laser welding. Two mathematical response models were developed to predict the laser weld bowing distortion according to the central composite rotatable design method. The optimized process parameters for minimum bowing distortion were obtained, and the influence of the laser process parameters on the weld bowing distortions was found.

Modeling and Optimizing the Synthesis of Urea-formaldehyde Fertilizers and Analyses of Factors Affecting these Processes

Previous research into the synthesis of urea-formaldehyde fertilizers was mostly based on orthogonal experimental designs or single factor tests; this led to low precision for synthesis and relatively large ranges of parameters for these processes. To obtain mathematical response models for the synthesis of urea-formaldehyde fertilizers with different nitrogen release properties, a central composite design (CCD) of response surface methodology was used in our research to examine the effects of different reaction times, temperatures, and molar ratios on nitrogen insoluble in either hot or cold water. Our results showed that nitrogen insoluble in cold or hot water from urea-formaldehyde fertilizers were mainly affected by urea: formaldehyde molar ratios. Also, quadratic polynomial mathematical models were established for urea-formaldehyde. According to the models, the optimal process parameters which maximize cold-water-insoluble nitrogen and minimize hot-water-insoluble nitrogen for the synthesis of urea formaldehyde were as follows urea: formaldehyde molar ratio was 1.33, reaction temperature was 43.5 °C, and reaction time was 1.64 h. Under these conditions, the content of cold-water-insoluble nitrogen was 22.14%, and hot-water-insoluble nitrogen was 9.87%. The model could be an effective tool for predicting properties of urea-formaldehyde slow release fertilizers if the experimental conditions were held within the design limits.

Mathematical Models of Cell Response Following Heating.

The cells of the cardiovascular system can experience temperature excesses of a few degrees during a diseased state or of tens of degrees during a thermal therapy treatment. These raised temperatures may be acute or of long duration. The multiple cell lines that compose each tissue then react, in approximate order of increasing thermal insult, by expressing heat shock proteins, undergoing apoptosis, or suffering necrosis. Mathematical models of the response of cells could aid in planning and designing thermal therapies. The multi-factor nature of the cell response makes it challenging to develop such models. The models most used clinically are mathematically simple and based on the response of representative tissues. The model that might provide the most fundamental understanding of the biochemical response of cells requires many parameters, some of which are difficult to measure. None of the semi-empirical models that provide improved prediction of cell fate have been widely accepted to plan therapies. There remain great opportunities for developing mathematical models cell response.

Process optimization and performance evaluation on laser beam welding of austenitic/martensitic dissimilar materials

Laser beam welding of austenitic/martensitic dissimilar combination is used in a precision electromechanical product for function design. In order to achieve the better mechanical performance and physical performance of welding joints, process optimization was first carried out according to the Box-Behnken design method, and mathematical response models of weld depth and peak temperature value at special point were developed by multivariate quadratic/linear regression analysis. An optimal group of welding process parameters is obtained. Then, mechanical performance was evaluated by micro-structure analysis, non-destructive test, and uniaxial tensile test, and the influence of cooling style after laser beam welding process was discussed on hardness distribution and fracture force. It is shown that a rapid cooling style can avoid the crack occurrence at the heat-affected zone of austenitic stainless steel and enhance fracture force of weld joint. However, the hardness distribution is not even, and it has the highest value at the heat-affected zone of martensitic stainless steel and the lowest value at the heat-affected zone of austenitic stainless steel. However, the welding joint has a better mechanical performance under the condition of low temperature.

Mathematical models for response to amino acids: estimating the response of broiler chickens to branched-chain amino acids using support vector regression and neural network models

Support vector regression (SVR) and neural network (NN) models were used to predict average daily gain (ADG), feed efficiency (FE), and feed intake (FI) of broiler chickens during the starter period. Input variables for construction of the models were levels of dietary protein and branched-chain amino acids (BCAA; valine, isoleucine, and leucine). Starting with 241 lines, the SVR and NN models were trained using 120 data lines and the remainder (n = 121) was used as the testing set. The SVR models were developed using different kernel functions including: linear, polynomial (second and third order), radial basis function (RBF), and sigmoidal. In order to evaluate the SVR models, their performance was compared to that of multilayer perceptron (MLP)- and RBF-type NN models. Results indicated that MLP-type NN models were the most accurate in predicting the investigated output variables (R 2 for ADG in training and testing = 0.81 and 0.81; FE = 0.87 and 0.87; FI = 0.68 and 0.62). Among the different SVR kernels, best performance was achieved with the RBF (R 2 for ADG in training and testing = 0.76 and 0.76; FE = 0.85 and 0.87; FI = 0.46 and 0.48) and polynomial (third order) function (R 2 for ADG in training and testing = 0.77 and 0.77; FE = 0.85 and 0.87; FI = 0.46 and 0.39), whose prediction ability was better than that of the RBF-type NN (R 2 for ADG in training and testing = 0.75 and 0.75; FE = 0.82 and 0.82; FI = 0.41 and 0.39) models. Sigmoidal SVR models provided the poorest prediction. The work demonstrates that, through proper selection of kernel functions and corresponding parameters, SVR models can be considered as an alternative to NN models in predicting the response of broiler chickens to protein and BCAA. This type of model should also be applicable in poultry and other areas of animal nutrition.

Development of Bacillus subtilis Mutants for Overproduction of Protease

Proteases are widely used in leather processing, silk industry, diary meat processing, and preparation of organic fertilizer as well as for the liberation of silver from recycled X-ray films. Ultraviolet radiation mutagenesis of Bacillus subtilis IBL-04 was carried out for hyper producing strain development. Mutants of Bacillus subtilis were isolated and screened for selection of hyper producing mutant. Production of protease by the selected mutant BS-90 (treated for 90 min) was optimized by varying pH, temperature, and inoculum size and fermentation time simultaneously in Response Surface Method (RSM) under Central Composite Design (CCD). The mathematical response model is considered to be reliable with an R2 value of 0.9842. The adjusted R2 value was 0.9695 suggesting a significant model by determining the close relationship to the actual R2 value. Predicted R2 value shown in this model was 0.9133. The Pred R-Squared of 0.9133 is close as to the Adj R-Squared of 0.9695 as expected. The ratio of 22.60 attained in this model represents an adequate signal. The calculated C.V was 3.25 which indicate the good level of model precision and reliability. The maximum enzyme activity was 95.89 (IU/mL) at optimum conditions pH 8, Temperature 50°C, Inoculum size 2.5 mL and fermentation time 72 h. These characteristics render its potential use in detergent industries for detergent formulation.

Development the Adjusted Mathematical Model of Responses in the Nondestructive Testing Defectiveness Method Based on the Mechanoelectrical Transformations.

The improving version the responses mathematical model when using the method of mechanoelectrical transformations for nondestructive testing of defects in composite dielectric materials was examined. The refinement is conditioned by necessity of account of the frequency-dependent attenuation. For this has been used spectral approach: decomposition of excitation pulse in range and the formation of the amount each attenuate spectral component with the sample pulse response.

Reverse geometric modeling for pre-form shape of prolate ellipsoid before hydro-forming

In order to form the needed prolate ellipsoidal shell with higher dimension accuracy, it is essential to develop an optimal pre-form shape before hydro-forming. A group of numerical simulation according to the optimal Latin hypercube design (Opt LHD) was first conducted on the combined prolate ellipsoidal shells, and the mathematical response models of axis lengths were developed. And then based on the adaptive simulated annealing algorithm, the reverse geometric modeling process was carried out and the possible pre-form shapes were given. Finally, an experimental verification was conducted to evaluate the reverse geometric modeling process, and the comparison between reverse design and experimental data was mainly discussed. It is shown that the dimension deviation between experiment and reverse design is less than 1 %. It is also experimentally proved that the needed prolate ellipsoidal shell can be formed by reversely designing an optimal pre-form shell.

Abstract B2-38: Learning the dynamic response to Ras-ERK signaling with paired reporters

Abstract To characterize key cell signaling pathways in cancer, we employ a modular strategy to examine how signals propagate between two members in a pathway, using paired time series measurements in live cells. The two pathway members chosen bracket a sub-network for which we measure input and output signals. In this study, we characterize models for the response of FRA1 (Fos related antigen 1) to ERK (extracelluar regulated kinase) activity. Mathematical response models are constrained by the paired signal data to produce a predictive module for the ERK-to-FRA1 sub-network, complementing existing modeling efforts as a building block for complete models. Background: Many mutations in cancer impair cellular information processing by hyperactivating signaling pathways associated with proliferation and migration. However, targeted inhibitors for hyperactivated elements have not yielded consistent responses, and acquired resistance hinders their use in therapy. Cell signaling can be a complex dynamic process [1], the detailed understanding of which will support development of new research directions and clinical therapies. The Ras-ERK signaling pathway regulates cell proliferation and migration, and is often mutated in cancer. ERK activity (the nominal pathway output) regulates major drivers of cell decision making, such as the transcription factor FRA1 which is involved in migration and invasion [2]. FRA1 is observed being regulated by ERK at three levels: (1) transcription via ERK-dependent phosphorylation of transcription factors; (2) translation via promotion of mTORC1 (mammalian target of rapamycin complex 1), and (3) stability via ERK-dependent phosphorylation of a c-terminal destabilization motif. The interplay of multiple regulation points in this feed-forward manner may lead to complex responses, including behavior as a ‘persistence detector’ for ERK activity, where only long term activity produces strong responses because short pulses fail to stabilize the protein. Experimental method: To make paired measurements, we generate a cell line expressing both a fluorescent reporter for ERK activity, and a fluorescent FRA1 fusion protein on the genomic locus. Cells are treated with varied levels of extracellular ligands and therapeutic drugs to elicit varied ERK responses, and time series images taken for up to 72 hours. Segmentation and particle tracking yield individual cell time courses over the length of the experiment. Modeling: Models of the FRA1 response to ERK activity are considered at several levels of abstraction to evaluate the complexity of the response against a mechanistic model. The most parsimonious model, that which satisfies data with the least complexity, can then predict FRA1 levels based on ERK activity, with minimal bias from overfitting. Fitting individual cell time courses produces the distribution of cell responses over populations. Conclusions: The characterized response models demonstrate the predictive capacity for FRA1 from ERK activity, revealing that the responsiveness to ERK varies from cell to cell. Over the cell populations observed, the models capture the distribution of the response. These models augment the existing body of work describing the ERK activity resulting from receptor stimulation, and may be further combined with future modular models toward a predictive global model.

Pre-form design for hydro-forming process of combined ellipsoidal shells by response surface methodology

In order to obtain a reasonable pre-form shell design for the needed sound ellipsoidal shell, a research has been conducted on variation of axis lengths during hydro-forming process of the combined ellipsoidal shell with double generating lines. Numerical simulation was carried out for parametric study of the pre-form shells with different structural parameters according to the Box-Behnken design method, and a mathematical response model between axis lengths and structural parameters was developed by multivariate quadratic regression analysis. Experiments were then carried out for hydro-forming process of the combined ellipsoidal shells with double generating lines. The deformation of the shell shape was separately reported, and the variation of axis lengths was recorded. Subsequently, comparative analysis of axis lengths between experimental data and predicted data coming from mathematical response model was deeply discussed. The comparison results show that the variation of axis lengths can be well predicted by the mathematical response model, which indicates that the needed ellipsoidal shell can be easily obtained by the optimization design of pre-form shell.