Set Of Ordinary Differential Equations Research Articles

MHD boundary layer micropolar fluid flow over a stretching wedge surface: Thermophoresis and brownian motion effect

To investigate the consequence of thermophoresis and Brownian diffusion on convective boundary layer micropolar fluid flow over a stretching wedge-shaped surface. The effects of 
 non-dimensional parameters namely coupling constant parameter (0.01 ≤ B1 ≤ 0.05), magnetic parameter (1.0 ≤ M ≤ 15.0), Grashof number (0.3 ≤ Gr ≤ 0.9), modified Grashof number 
 (0.3 ≤ Gm ≤ 0.8), micropolar parameter (2.0 ≤ G2 ≤ 7.5), vortex viscosity constraint (0.02 ≤ G1 ≤ 0.2), Prandtl number (7.0 ≤ Pr ≤ 15.0), thermal radiation parameter (0.25 ≤ R ≤ 0.50), Brownian motion parameter (0.2 ≤ Nb ≤ 0.62), thermophoresis parameter (0.04 ≤ Nt ≤ 0.10), heat generation parameter (0.1 ≤ Q ≤ 0.5), Biot number (0.65 ≤ Bi ≤ 1.0), stretching parameter (0.2 ≤ A ≤ 0.5), Lewis number (3.0 ≤ Le ≤ 7.0), and chemical reaction parameter (0.2 ≤ K ≤ 0.7) on the steady MHD heat and mass transfer is investigated in the present study. The coupled non-linear partial differential equations are reduced into a set of non-linear ordinary differential equations employing similarity transformation. Furthermore, by using the Runge-Kutta method followed by the shooting technique, the transformed equations are solved. The main goal of this study is to investigate the numerical analysis of nanofluid flow within the boundary layer region with the effects of the microrotation parameter and velocity ratio parameter. The novelty of this paper is to propose a numerical method for solving third-order ordinary differential equations that include both linear and nonlinear terms. To understand the physical significance of this work, numerical analyses and tabular displays of the skin friction coefficient, Nusselt number, and Sherwood number are shown. The new approach of the present study contributes significantly to the understanding of numerical solutions to non-linear differential equations in fluid mechanics and micropolar fluid flow. Micropolar fluids are becoming even more of a focus due to the desire for engineering applications in various fields of medical, mechanical engineering, and chemical processing.

A semi-analytical rate-transient analysis model for fractured horizontal well in tight reservoirs under multiphase flow conditions

Abstract Rate-transient analysis (RTA) has been widely applied to extract reservoir/fracture properties using analytical and semi-analytical methods with simplifying assumptions. However, current RTA models may lead to misdiagnosis of flow regimes and incorrect estimates of reservoir/fracture information when complex fracture network, multiphase flow, and pressure-dependent properties occur in tight reservoirs simultaneously. A semi-analytical model is developed to account for multiphase flow, complex fracture network, and pressure-dependent properties. The technique uses the black oil formulation and butterfly model to determine three nonlinear partial differential equations (PDEs) that describe the flow of oil, gas, and water in the reservoir with complex fracture network. A modified Boltzmann variable considering the heterogeneity of complex fracture network is proposed to convert the fluid flow PDEs to a set of ordinary differential equations (ODEs) that can be solved through the Runge-Kutta method. A new rate-transient analysis workflow is also developed to improve flow regime identification (ID) and the accuracy for tight oil reservoirs with complex fracture network. It is applied to a synthetic case with equivalently modeled complex fracture network and multiphase flow. The estimated fracture properties are in excellent agreement with model inputs.

Inertial Parameter Identification for Closed-Loop Mechanisms: Adaptation of Linear Regression for Coordinate Partitioning

Abstract This study investigates the use of linear-regression-based identification in rigid multibody system applications. A multibody system model, originally described with differential-algebraic equations (DAE), is transformed into a set of ordinary differential equations using coordinate partitioning. This allows the identification framework (where the system is described with ordinary differential equations) to be applied to rigid multibody systems described with nonminimal coordinates. The methodology is demonstrated via numerical and experimental validation on a slider–crank mechanism. The results show that the presented methodology is capable of accurately identifying the system's inertial parameters even with a short motion trajectory used for training. The presented linear-regression-based identification approach opens new opportunities to develop more accurate multibody models. The resulting updated multibody models can be considered especially useful for state-estimation and the control of multibody systems.

Numerical simulation for radiative hybrid nanofluid (TiO2+Fe3O4∕H2O) flow due to a non-uniform stretching sheet with variable permeability

Variable permeability plays a crucial role in various manufacturing and technical applications such as fixed-bed catalytic reactors, heat exchangers, and dying, among others. The primary focus of this paper is to investigate the impacts of variable permeability on hybrid nanofluid (HNF) flow due to nonlinear sheet stretching with thermal heat flux. The HNF is made up of a mixer of [Formula: see text] and [Formula: see text] nanoparticles and water serving as the base fluid. Using efficient similarity transformations, the flow-governing equations are converted into a set of ordinary differential equations, and the resulting system is computationally solved by using the MATLAB program (bvp4c). The impact of various physical variables on the fluid velocity and heat transfer characteristics is analyzed via graphs. It is found that as the permeability parameter rises, the velocity of the HNF diminishes while the temperature amplifies. The drag force coefficient declines with an intensification of the volume fraction of the [Formula: see text] nanoparticles. The HNF [Formula: see text] exhibits 0.45–0.75% increase in heat transfer rate when compared to a nanofluid [Formula: see text] for different values of heat source parameter. The current investigation is compared to the existing literature, revealing a good level of agreement.

Utilizing a third order difference scheme in numerical method of lines for solving the heat equation

Obtaining the numerical solution for partial differential equations (PDEs) is a fundamental task in computational mathematics and scientific computing. In this work, we propose a third order numerical method of lines (MOL) based on difference schemes for the efficient and accurate approximation of heat equation. The method combines the flexibility of MOL with the superior accuracy of higher order difference schemes. The proposed approach begins by discretizing the spatial domain, and then applies higher order difference schemes to approximate the spatial derivatives in the PDE. The MOL framework is utilized to transform the resultant set of ordinary differential equations to a system of algebraic equations, facilitating their solution through an appropriate numerical method of choice. We have utilized the Adams method for this purpose. We analyze the stability of the proposed method and establish conditions under which it yields accurate and reliable solutions. We present the theoretical foundations of the method and discuss its implementation. We also present numerical results that demonstrate the procedure’s precision and effectiveness. The results show that the method is able to achieve high accuracy with relatively few grid points, and the results are compared with those obtained by some existing numerical schemes accessible in the literature.

Structural and practical identifiability analysis in bioengineering: a beginner’s guide

Advancements in digital technology have brought modelling to the forefront in many disciplines from healthcare to architecture. Mathematical models, often represented using parametrised sets of ordinary differential equations, can be used to characterise different processes. To infer possible estimates for the unknown parameters, these models are usually calibrated using associated experimental data. Structural and practical identifiability analyses are a key component that should be assessed prior to parameter estimation. This is because identifiability analyses can provide insights as to whether or not a parameter can take on single, multiple, or even infinitely or countably many values which will ultimately have an impact on the reliability of the parameter estimates. Also, identifiability analyses can help to determine whether the data collected are sufficient or of good enough quality to truly estimate the parameters or if more data or even reparameterization of the model is necessary to proceed with the parameter estimation process. Thus, such analyses also provide an important role in terms of model design (structural identifiability analysis) and the collection of experimental data (practical identifiability analysis). Despite the popularity of using data to estimate the values of unknown parameters, structural and practical identifiability analyses of these models are often overlooked. Possible reasons for non-consideration of application of such analyses may be lack of awareness, accessibility, and usability issues, especially for more complicated models and methods of analysis. The aim of this study is to introduce and perform both structural and practical identifiability analyses in an accessible and informative manner via application to well established and commonly accepted bioengineering models. This will help to improve awareness of the importance of this stage of the modelling process and provide bioengineering researchers with an understanding of how to utilise the insights gained from such analyses in future model development.

Elastoplastic solution for cylindrical cavity contraction in unsaturated soils

This paper develops an elastoplastic solution for cylindrical cavity contraction in unsaturated soils under constant suction conditions. The elastoplastic cavity contraction problem is formulated into a set of first-order ordinary differential equations by introducing a new auxiliary variable, which is solved as an initial value problem. The new solution is validated by comparison with numerical simulation results. Finally, parametric studies show that, as soil suction increases, the internal support pressure decreases faster with cavity contraction, the unloading-induced plastic zone becomes narrower, and the changes in effective stresses are smaller for a given tunnel convergence.

Entropy Generation and Thermal Radiation Impact on Magneto-Convective Flow of Heat-Generating Hybrid Nano-Liquid in a Non-Darcy Porous Medium with Non-Uniform Heat Flux

The principal objective of the study is to examine the impact of thermal radiation and entropy generation on the magnetohydrodynamic hybrid nano-fluid, Al2O3/H2O, flow in a Darcy–Forchheimer porous medium with variable heat flux when subjected to an electric field. Investigating the impact of thermal radiation and non-uniform heat flux on the hybrid nano-liquid magnetohydrodynamic flow in a non-Darcy porous environment produces novel and insightful findings. Thus, the goal of the current study is to investigate this. The non-linear governing equation can be viewed as a set of ordinary differential equations by applying the proper transformations. The resultant dimensionless model is numerically solved in Matlab using the bvp4c command. We obtain numerical results for the temperature and velocity distributions, skin friction, and local Nusselt number across a broad range of controlling parameters. We found a significant degree of agreement with other research that has been compared with the literature. The results show that an increase in the Reynolds and Brinckmann numbers corresponds to an increase in entropy production. Furthermore, a high electric field accelerates fluid velocity, whereas the unsteadiness parameter and the presence of a magnetic field slow it down. This study is beneficial to other researchers as well as technical applications in thermal science because it discusses the factors that lead to the working hybrid nano-liquid thermal enhancement.

Parametric optimisation for heat transfer through nanofluid impinging upon a Riga plate: the Taguchi method

The article presents a comprehensive analysis of the flow and heat transfer characteristics of the stagnation point flow of Casson nanofluid towards a Riga plate. The mathematical modelling of the problem is carried out by using Buongiorno's two-phase model for convective heat transport within nanofluids. The solution methodology includes the process of transforming the system of Partial Differential Equations (PDEs) into a set of Ordinary Differential Equations (ODEs) which then solved using a semi-analytical Optimal Homotopy Analysis Method (OHAM). The influence of various flow parameters on the skin friction coefficient ( C f x ) and Nusselt number is presented and analysed graphically. Furthermore, a parametric study for the optimisation of skin friction coefficient and Nusselt number ( N u x ) is performed using the Taguchi analysis along with ANOVA and the multivariate regression analysis. The parametric optimisation reveals that for skin friction coefficient, EMHD parameter is most significant term, whereas Prandtl number is found to be the parameter with the highest influence on the Nusselt number. The findings of the study may have bearings in engineering and industrial applications such as the thermal design of industrial equipment dealing with molten plastics and polymeric liquids.

Numerical treatment for double diffusion phenomenon with generalized heat flux effects in 3d nanomaterial flow over bi-directional stretched wall

Current study aims to numerically investigate the bi-directional flow of nanofluids in the presence of Cattaneo–Christov double diffusion for two heat sources, namely, prescribed surface temperature (PST) along with prescribed heat flux (PHF). The conventional mathematical model in partial differential equations (PDEs) of the system have been reduced into an equivalent set of ordinary differential equations (ODEs). The system dynamics in the form of approximate solutions of the ODEs is presented by Adams and Explicit Runge Kutta numerical solvers. For better understanding the influence of physical parameter of interest including Brownian movement parameter, thermophoresis parameter, concentration relaxation parameter, Schmidt number, Prandtl number, thermal relaxation parameter, temperature ratio parameter, stretching ratio parameter and Deborah number on temperature, as well as concentration profiles are presented exhaustively. Appropriateness of the scheme is ascertained through close resemblance of results for different state of the art counterparts with negligible error around 10–05 to 10–09.

Thermal proficiency of magnetized and radiative cross-ternary hybrid nanofluid flow induced by a vertical cylinder

Abstract The ternary hybrid nanofluid leads to a significant enhancement in thermal performance applications like heat transfer in automotive engines, solar thermal energy storage, aerospace, and electronic cooling. The present study investigates the thermal characteristics of a ternary hybrid magnetized and radiated cross nanofluid comprising Al2O3, TiO2, and Ag nanoparticles in water subjected to combined convection flow around a vertical cylinder. Furthermore, innovative effects of the magnetic field, absorber surface of the cylinder, non-linear thermal radiations, and effective thermophysical characteristics of ternary nanofluid are taken, and a new model for heat transport is successfully achieved. The governing equations in the form of partial differential equations (PDEs) are obtained through Navier–Stokes and heat equations by applying current assumptions. The system of PDEs is converted into a set of ordinary differential equations (ODEs) via a similarity variable. The built-in code bvp4c in Matlab software further exercises the dimensionless ODE equations numerically. Adding multiple nanoparticles and the magnetic field effect enhances the heat transfer rate in the ternary hybrid cross nanofluid. The Weissenberg number reduces the velocity, the radiation parameter increases heat transport, and the increased volume friction of nanoparticles enhances thermal conductivity and rapid heat transport.

Transformer oil‐based Casson ternary hybrid nanofluid flow configured by a porous rotating disk with hall current

AbstractThe present work examines the 3D, incompressible, magnetohydrodynamic, mixed convective, and Darcy‐Forchheimer Casson /transformer oil ternary hybrid nanofluid flow configured by a porous rotatory disk. This research work takes into account the influences of hall current, thermophoresis, heat absorption/generation, Brownian motion, joule heating, chemical reaction, thermal radiation, activation energy, and velocity slip condition. The administrative partial differential equations (PDEs) that expound the problem are modified into a set of ordinary differential equations (ODEs) by imposing a similarity conversion, which is further solved numerically by adapting the worthy bvp4c scheme. The velocity, thermal, and mass profiles are delineated through graphs, and the features of skin friction coefficient, heat, and mass transmission are also explicated thoroughly via tables. One significant observation of this research is that the Casson parameter weakens transversal velocity whereas a reverse tendency is noticed against the radial velocity. Our obtained outputs affirm that Casson ternary hybrid nanofluid has respectively 10.93 % and 8.86% higher heat deliverance rate when compared to Casson nanofluid and Casson hybrid nanofluid. Besides, the Casson ternary hybrid nanofluid has respectively 33.68 % and 27.52% higher mass deliverance rate when compared to the Casson nanofluid and Casson hybrid nanofluid. Also, the sturdy values of the Casson parameter lessen the skin friction coefficient. The inferences derived from our research may advantageously be used in rotating types of machinery, medical equipment, gas turbine rotators, etc.

A numerical analysis of the blood-based Casson hybrid nanofluid flow past a convectively heated surface embedded in a porous medium

Abstract The analysis of the fluid flow with the energy transfer across a stretching sheet has several applications in manufacturing developments such as wire drawing, hot rolling, metal extrusion, continuous casting, paper production, and glass fiber fabrication. The current examination presents the hybrid nanofluid flow past a convectively heated permeable sheet. The ferrous oxide (Fe3O4) and Gold (Au) nanoparticles have been dispersed in the blood. The significances of thermal radiation, inclined magnetic field, and space-dependent heat source have been observed in this work. The modeled equations are presented in the form of partial differential equations and reformed into the set of ordinary differential equations (ODEs) by using the similarity substitution. The Matlab built-in package (bvp4c) is employed to resolve the transform nonlinear set of ODEs. The significance of flow constraints versus the velocity and temperature profiles is demonstrated in the form of Figures and Tables. The numerical outcomes for the physical interest quantities are presented in tables. It has been perceived from the results that raising the angle of inclination from 0° to 90° reduces both the velocity and energy profile. The escalating values of Eckert number, constant heat source, and space-dependent heat source factor accelerate the temperature profile. The velocity and temperature distributions are very effective in the cases of hybrid nanofluid (Au–Fe3O4/blood) when compared to nanofluid (Au/blood). The skin friction and rate of heat transfer are very effective in the cases of hybrid nanofluid (Au–Fe3O4/blood) when compared to nanofluid (Au/blood).

Activation energy with binary chemical reaction of convective radiative magnetized nanofluid flow with viscous dissipation and pressure gradient

ABSTRACT The present investigation deals with the study of activation energy with the binary chemical reaction on magnetohydrodynamic convective radiative heat and mass transfer of nanofluid flow with internal heat source/sink, viscous dissipation, pressure gradient force, and suction effects. The basic equations of conservation of momentum, energy, and mass diffusion are brought to a set of ordinary differential equations (nonlinear) using suitable similarity transformations, and these are then solved using the Homotopy Perturbation Method (HPM). The validity of the present results is established by comparing them with those obtained by the Runge-Kutta-Fehlberg method (RKFM). The results reveal that the temperature distribution increases with raising the value of the thermal radiation parameter. It is found that the concentration distribution increases by increasing the values of the activation energy parameter. In contrast, the reverse effect is observed by enhancing the chemical reaction parameter, Schmidt number, and pressure gradient parameter. Further, the skin-friction coefficient and Nusselt number decrement by enhancing the value of the Hartmann number, whereas the reverse trend is found by enhancing the pressure gradient and suction parameter values. Also, the Sherwood number retards with an enhancement in the Hartmann number, whereas it rises by increasing the pressure gradient and suction parameters.

Influences of blowing and internal heating processes on steady MHD mixed convective boundary layer flows of radiating titanium dioxide‐ethylene glycol nanofluids

AbstractThe present analysis intends predominantly to explore the multiple behaviors of radiating ethylene glycol‐based titanium dioxide nanofluids during their steady boundary layer flows near a vertical permeable surface under the prominent impacts of uniform blowing and nonuniform internal heating processes. By incorporating the dynamical contribution of Lorentz and buoyancy forces in the momentum equation and adopting the single‐phase nanofluid approach along with the constitutive equations of the second‐grade rheological model and Corcione's correlations, the governing partial differential equations and their appropriate boundary conditions are derived mathematically based on the boundary layer theory and other admissible physical approximations. After several simplifications, the aforesaid differential formulation is converted into a set of ordinary differential equations and realistic boundary conditions, which are solved thereafter numerically using GDQ's‐NT method. Moreover, it is demonstrated that the strengthening in the blowing and internal heating processes has a boosting effect on the velocity and temperature profiles. However, the other influencing parameters show dissimilar dynamical and thermal trends. Furthermore, it is witnessed that the mixed convective heat transfer, the viscoelasticity trend of the nanofluidic medium, and the nanoparticles’ loading exhibit an enhancing impression on the surface heat transfer rate.

Numerical investigation on MHD non-Newtonian pulsating Fe 3 O 4-blood nanofluid flow through vertical channel with nonlinear thermal radiation, entropy generation, and Joule heating

The main aim of the present investigation is to examine the effect of nonlinear thermal radiation, slip, and Joule heating on MHD Pulsatile flow of third-grade ferro-nanofluid via vertical channel with entropy generation. The significance of this study is that it has plenty of physiological applications like cancer treatment, vitamin injections, dialysis, heart–lung machines during surgeries and industrial applications like filtration, pharmaceutical fluid production, and dispensing cosmetic/glue emulsions with no contamination. Furthermore, the ferro-nanoliquid model is the best model for numerous bio/industrial fluids. Therefore, this study explores the entropy analysis of pulsating third-grade ferro-nanoliquid flow between two parallel vertical walls under an applied magnetic field. Blood is taken as a base fluid (third grade), and iron oxide is used as nanoparticles. The governed nonlinear partial differential equations (PDEs) are nondimensionalized, and then the perturbation technique is employed to attain the set of nonlinear ordinary differential equations (ODEs). The bvp4c technique with MATLAB software is utilized to obtain the solutions for the set of ODEs. The deviations in several physical quantities on the flow variables are deployed via graphs. An increment in Eckert number and radiation parameter accelerates the temperature. Entropy generation rate and Bejan number are accelerated for greater values of radiation parameter. The values of the skin friction and Nusselt number against various physical parameters are presented in tables.

Analytical analysis of spherical cavity expansion considering particle breakage effect of sand and its application for CPT tests

Particle breakage in sand significantly influences the stress and deformation predictions of the spherical cavity expansion theories. However, existing theories often overlook or lack a quantitative description of particle breakage, leading to significant errors in the actual results. Based on the Simple Critical State Sand (SIMSAND) model, considering the particle breakage effect, the traditional Euler’s problem of the drainage spherical cavity expansion is converted into a set of first-order ordinary differential equations described by Lagrangian. Fontainebleau sand is taken as an example, and the influence of the initial stress of the sand on the stress state and void ratio is studied. An analysis of the relative breakage surrounding the cavity reveals that the primary impact zone extends to a distance thrice the expansion radius. An axisymmetric model of the cone penetration test is established, the analytical and numerical solutions of expansion stress and cone tip resistance are analysed and the correctness of the spherical cavity expansion theory is verified. Furthermore, the cone tip resistance results, derived from the theory of spherical cavity expansion, are consistent with the results of numerical calculations. Notably, when the particle breakage effect is not considered, the calculated results of cone tip resistance significantly increase.

Series Solutions of Three-Dimensional Magnetohydrodynamic Hybrid Nanofluid Flow and Heat Transfer

Hybrid nanofluids have many real-world applications. Research has shown that mixed nanofluids facilitate heat transfer better than nanofluids with one type of nanoparticle. New applications for this type of material include microfluidics, dynamic sealing, and heat dissipation. In this study, we began by placing copper into H2O to prepare a Cu-H2O nanofluid. Next, Cu-H2O was combined with Al2O3 to create a Cu-Al2O3-H2O hybrid nanofluid. In this article, we present an analytical study of the estimated flows and heat transfer of incompressible three-dimensional magnetohydrodynamic hybrid nanofluids in the boundary layer. The application of similarity transformations converts the interconnected governing partial differential equations of the problem into a set of ordinary differential equations. Utilizing the homotopy analysis method (HAM), a uniformly effective series solution was obtained for the entire spatial region of 0 < η < ∞. The errors in the HAM calculation are smaller than 1 × 10−9 when compared to the results from the references. The volume fractions of the hybrid nanofluid and magnetic fields have significant impacts on the velocity and temperature profiles. The appearance of magnetic fields can alter the properties of hybrid nanofluids, thereby altering the local reduced friction coefficient and Nusselt numbers. As the volume fractions of nanoparticles increase, the effective viscosity of the hybrid nanofluid typically increases, resulting in an increase in the local skin friction coefficient. The increased interaction between the nanoparticles in the hybrid nanofluid leads to a decrease in the Nusselt number distribution.

How Plant Toxins Cause Early Larval Mortality in Herbivorous Insects: An Explanation by Modeling the Net Energy Curve.

Plants store chemical defenses that act as toxins against herbivores, such as toxic isothiocyanates (ITCs) in Brassica plants, hydrolyzed from glucosinolate (GLS) precursors. The fitness of herbivorous larvae can be strongly affected by these toxins, causing immature death. We modeled this phenomenon using a set of ordinary differential equations and established a direct relationship between feeding, toxin exposure, and the net energy of a larva, where the fitness of an organism is proportional to its net energy according to optimal foraging theory. Optimal foraging theory is widely used in ecology to model the feeding and searching behavior of organisms. Although feeding provides energy gain, plant toxins and foraging cause energy loss for the larvae. Our equations explain that toxin exposure and foraging can sharply reduce larval net energy to zero at an instar. Since herbivory needs energy, the only choice left for a larva is to stop feeding at that time point. If that is significantly earlier than the end of the last instar stage, the larva dies without food. Thus, we show that plant toxins can cause immature death in larvae from the perspective of optimal foraging theory.

Abstract A024: Ploidy as a predictive biomarker for gemcitabine sensitivity in triple-negative breast cancers

Abstract The polyploid giant cancer cell (PGCC) state is a common response of cancer cells to various stressors including chemotherapy, irradiation, hypoxia and viral infection. Upon stress, PGCCs adopt an endoreplication in which the genome replicates, mitosis is omitted, and cells grow in size, causing drug resistance. How accessible endoreplication is to a cell, therefore, directly translates to its resistance to therapy. In this study, we hypothesized that endoreplication and PGCC state are more accessible to cancer cells that already have a higher ploidy content prior to therapy. To test this hypothesis, we developed a comprehensive three-tier framework consisting of i) computational, ii) in-vitro and iii) in silico components. First, we designed a set of ordinary differential equations (ODEs) to mathematically model how cells enter and exit the PGCC state in response to a given stressor. We engineered how this in silico approach interacts with in vitro experiments into a broadly applicable software solution called CLONEID. The software uses computer vision to monitor phenotypic changes in cell and nuclear size from standard bright-field microscopy and classify cells into PGCC and non-PGCC states. We used CLONEID to test various therapeutic agents for their ability to select for a stable near-tetraploid (4N) population in a set of near-diploid (2N) cell lines. Through spontaneous cell fusions, we also obtained tetraploid breast cancer cells matched with their parental lines. Altogether, this framework enabled us to i) monitor the PGCC state experimentally in ii) two sets of matched isogenic cell lines with 2N and 4N DNA content to iii) model the successful entry and exit rates to and from the endoreplication state, respectively. As the first application of this framework, we tested the ability of our 2N and 4N TNBC lines (SUM159 and MDA-MB-231) to access the PGCC state upon treatment with 18 chemotherapy agents. Among those drugs, we observed that only gemcitabine caused continued cell growth without cell division in both tetraploid SUM159 and MDA-MB-231 cells whereas near-diploid parental lines were hypersensitive to the treatment. Consequently, tetraploid cancer cells continued to safely grow in the presence of gemcitabine. Furthermore, these PGCCs re-entered the proliferative cell cycle and grew in cell number when treatment is terminated. Gemcitabine-based chemotherapy is a standard treatment for patients with TNBC although its efficacy is limited mainly due to drug resistance. We expect our findings and three-component framework strategy to help stratify the TNBC patient population by their response to gemcitabine. In addition, our mathematical modelling approach has the promising potential to inform personalized dose optimization and to effectively decrease administered gemcitabine dose for a subset of patients, which would alleviate severe therapy-associated side effects and co-morbidities. Citation Format: Vural Tagal, Jackson Cole, Daria Miroshnychenko, Andriy Marusyk, Noemi Andor. Ploidy as a predictive biomarker for gemcitabine sensitivity in triple-negative breast cancers [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Translating Cancer Evolution and Data Science: The Next Frontier; 2023 Dec 3-6; Boston, Massachusetts. Philadelphia (PA): AACR; Cancer Res 2024;84(3 Suppl_2):Abstract nr A024.