Series Of Ordinary Differential Equations Research Articles

A numerical simulation of the unsteady MHD nanofluid flow over a rotating disk in a porous medium with uniform suction and convective effects

The current article focuses on permeability, uniform suction, and Joules heating as key convective effects influencing heat transmission characteristics in nanofluid magnetohydrodynamics flow on a rotating disk. In contrast to a standard Newtonian fluid, Al 2 O 3 nanoparticle water-based nanofluids are employed. The surface of the disk is also taken as convective. Following the implementation of similarity transformations, the leading equations are converted into a series of ordinary differential equations, which are subsequently solved numerically through the utilisation of the bvp4c MATLAB solver. The behavioural research on heat transmission for different parameter dominance is assessed using graphs. As the permeability parameter increases, the dominance of convective effects leads to increased fluid flow away from the disk, which reduces the radial velocity. Also, on the disk surface, the rate of heat transfer shows a direct relation with the permeability of the disk.

Nonlinear transient response of rotating graphene platelets reinforced metal foams blades with initial geometric imperfection

In this paper, a new mechanical model including initial geometric imperfection is developed to investigate the nonlinear transient response of graphene platelets reinforced metal foams (GPLRMF) blades subjected to blast load. Combined with higher-order shear deformation plate theory (HSDT) and von-Karman geometric nonlinearity, the nonlinear motion equations are established, in which the Coriolis force, centrifugal force as well as initial geometric imperfection are simulated. Considering cantilever boundary condition, the partial differential equations are transformed into a series of ordinary differential equations by Galerkin discretization. Using the four order Runge-Kutta algorithm, the nonlinear transient response is numerically researched, and the time histories and phase trajectories are obtained. In addition, the effectiveness of the current research is validated by comparing the results with the existing valuable literatures. The influences of rotating speed, presetting angle, initial geometric imperfection, material property, damping coefficient, and blast load parameter on the dynamic deflection and instantaneous speed are presented. Numerical results reveal that the nonlinear transient dynamics of the composite blades under blast load are significantly influenced by initial geometric imperfection.

Analyzing fuzzy fractional Degasperis–Procesi and Camassa–Holm equations with the Atangana–Baleanu operator

Abstract This article presents a new approach for solving the fuzzy fractional Degasperis–Procesi (FFDP) and Camassa–Holm equations using the iterative transform method (ITM). The fractional Degasperis–Procesi (DP) and Camassa–Holm equations are extended from the classical DP and Camassa–Holm equations by incorporating fuzzy sets and fractional derivatives. The ITM is a powerful technique widely used for solving nonlinear differential equations. This approach transforms the fuzzy fractional differential equations into a series of ordinary differential equations, which are then solved iteratively using a recursive algorithm. Numerical simulations demonstrate the proposed approach’s accuracy and effectiveness. The results show that the ITM provides an efficient and accurate method for solving the FFDP and Camassa–Holm equations. The proposed method can be extended to solve other fuzzy fractional differential equations.

Entropy optimization of non-Newtonian hybrid nanofluid EMHD flow by numerical and Levenberg–Marquardt backpropagation approach over a rotating disk

The goal of this study is to analyze the heat transfer characteristics of a Casson hybrid nanofluid flow system by incorporating EMHD (electromagnetohydrodynamic) and entropy production using the stochastic solver and Levenberg-Marquardt backpropagation neural networks. Self-similarity transformations are used to turn the mathematical model of a system of partial into a series of ordinary differential equations. The datasets are built through Runge–Kutta fourth order with a shooting approach, which aids in the generation of a continuous neural network mapping. To grasp the neural network mapping, the validation, training and testing processes are used to estimate the solutions of various physical constraints. For this hybrid model, the determination, convergence, verification and stability of Levenberg-Marquardt backpropagation neural network mappings are evaluated using regression-based statistical analysis, mean squared error and error histograms. To acquire high possibilities in drug delivery systems, hybrid nanofluids are regarded as blood-based nanofluids with dispersion of hybrid ( and ) nanoparticles. Due to this reason, this model might be beneficial for medication delivery systems, particularly if pharmaceuticals are injected into the bloodstream.

A semi-analytical solution for the transient response of one-dimensional saturated single-layer porous media with general boundary conditions

Based on the basic equations for saturated porous media wave equations proposed by Biot, a mathematical model for one-dimensional transient response of single-layer saturated porous media were established with general boundary condition, arbitrary initial conditions and arbitrary vertical load. Firstly, the independent parameters total stress σ, fluid pressure p, soil absolute displacement u and fluid relative displacement w were advised to describe the boundary conditions by linear combination in pairs. Through adjusting the parameters, the linear combination boundary conditions could represent various boundary conditions. The eigenvalues and the eigenfunctions of the undamped governing equations were obtained by means of the variable separation method. With the help of undetermined coefficients and orthogonality of eigenfunctions methods, the solution to the problem could be converted to solve the initial value problem of a series of ordinary differential equations. The semi-analytical solutions were approached by the precise time-integration method. Compared with previous research, the semi-analytical solutions of this research were more general and could be degenerated into various conditions exactly. Several numerical simulations were carried out to validate this method. Finally, the one-dimensional transient responses of single-layer saturated soil with general boundary conditions under step load were analyzed. The results demonstrate that the responses of semi-permeable condition are between permeable condition and impermeable condition and the solid and fluid displacement increase first and then decrease with time.

Modeling Neurons in 3D at the Nanoscale.

For decades, neurons have been modeled by methods developed by early pioneers in the field such as Rall, Hodgkin and Huxley, as cable-like morphological structures with voltage changes that are governed by a series of ordinary differential equations describing the conductances of ion channels embedded in the membrane. In recent years, advances in experimental techniques have improved our knowledge of the morphological and molecular makeup of neurons, and this has come alongside ever-increasing computational power and the wider availability of computer hardware to researchers. This has opened up the possibility of more detailed 3D modeling of neuronal morphologies and their molecular makeup, a new, emerging component of the field of computational neuroscience that is expected to play an important role in building our understanding of neurons and their behavior into the future.Many readers may be familiar with 1D models yet unfamiliar with the more detailed 3D description of neurons. As such, this chapter introduces some of the techniques used in detailed 3D, molecular modeling, and shows the steps required for building such models from a foundation of the more familiar 1D description. This broadly falls into two categories; morphology and how to build a 3D computational mesh based on a cable-like description of the neuronal geometry or directly from imaging studies, and biochemically how to define a discrete, stochastic description of the molecular neuronal makeup. We demonstrate this with a full Purkinje cell model, implemented in 3D simulation in software STEPS.

A mass-temperature decoupled discretization strategy for large-scale molecular-level kinetic model

The molecular conversion of complex mixture involves a large number of species and reactions. The corresponding kinetic model consists of a series of ordinary differential equations with severe stiffness, leading to an exponentially growing computational time. To reduce the computational time, we proposed a mass-temperature decoupled discretization strategy for a large-scale molecular-level kinetic model. The method separates the mass balance and heat balance calculations in the rigorous adiabatic reactor model and divided the reactor into several isothermal segments. After discretization, the differential equations for heat balance can be replaced by algebraic equations between nodes. We used a molecular-level diesel hydrotreating kinetic model as the case to validate the proposed method. A good agreement between the discretization model and rigorous model was observed while the computational time was significantly shortened. Moreover, the method was also extended to heavy oil fluid catalytic cracking and accurately calculated the product composition and temperature distribution.

EMPIRICAL MODELING OF KINETICS OF TRANSESTERIFICATION AND COLD FLOW PROPERTIES OF USED SOYA OIL BIODIESEL

This research work focused on empirical modeling of kinetics of transesterification and cold flow properties of homogeneous catalyzed used soya oil fatty acid methyl ester (USOFAME]. Used soya oil (USO) was prepared by frying food (yam, potato plantain etc) with virgin soya oil for a total of 72 hours [1]. The oil was characterized based on American Society for Testing and Materials (ASTM) method. The fatty acid profile of used soya oil was analyzed using gas chromatography mass spectroscopy (GC MS) while the functional groups of the triglyceride were determined using Fourier transform infrared spectroscopy (FTIR). The oil was pretreated to reduce the free fatty acid level below 1% and then transesterified using methanol in the presence of sodium hydroxide catalyst. The fuel properties of the USOFAME produced were determined based on ASTM standards. Kinetic experiments were conducted in batches at different temperatures of 450C, 550C and 650C. Application of rate laws to the three-step reversible reaction scheme of transesterification yielded a series of ordinary differential equations (ODEs) solved with polymath 5.1 software to give the forward and reverse rate constants k1,k2, k3, k4, k5 and k6 from which the rate limiting step (RLS) and activation energy (∆E) were derived. The cold flow properties, cloud point (CP), cold filter plugging point (CFPP) and pour point (PP) were determined experimentally for different blends of biodiesel with #2 diesel, at a percentage volume ratio of biodiesel to diesel 0, 20, 40, 60, 80, and 100. The values obtained for CP, CFPP, and PP were plotted against the biodiesel fraction in the blends. Least square regression of the data of the plots were tested on linear, quadratic and polynomial models using Microsoft excel. The fuel properties of the USOFAME which is within the ASTM standards were determined as acid value 0.4mgKOH/g, density 863mm2/s, kinematic viscosity 4.60mm2/s, flash point 1620C, cetane number 61.00, calorific value 40.06MJ/Kg, pour point -40C, cold filter plugging point -2.80C, cloud point 00C, iodine value 30.60gI2/100g. Kinetic modeling of transesterification of USOFAME shows that the forward rate constants K1, K2, and K3 are greater than those of the reverse reaction k2, k4, k6, imply that the forward reaction dominates while the reverse reaction could be neglected. The rate constant k1 for triglyceride conversion to diglyceride is the least among the forward rate constants at 450C, 550C and650C imply that this step is the rate limiting step (RLS). Application of least square regression analysis of Microsoft excel on the data of variation of cold flow properties with biodiesel fraction, revealed polynomial model to be the best fitting equation.

Dynamics of aluminum oxide and copper hybrid nanofluid in nonlinear mixed Marangoni convective flow with entropy generation: Applications to renewable energy

One of the hottest topics in industrial and engineering applications of applied mathematics is the advances in nanotechnology particularly in nanofluids, hybrid nanofluids which consist of a typical base fluid saturated with nano-size metallic particles with enhanced thermophysical properties. In this regard, current study reports an entropy nature of steady, laminar, relative contributions of thermal and solutal Marangoni convections on passage in Casson Al2O3−Cu−H2Ohybrid nanofluid stream past over a disk under the impact of nonlinear heat source/sink, viscous dissipation, radiation, and nonlinear convection. Suitable similarity transformation is apt to reduce the governing partial differential equations to a series of ordinary differential equations. The obtained nonlinear ODE set is then solved numerically by using bvp4c method. The impact of various pertinent flow parameters on the velocity, thermal, concentration, entropy production, rate of heat and mass transfer fields are discussed in detail through graphs. The results reveal that, boost up values of Marangoni number and radiation parameter inclines the heat transfer of the fluid flow system. The upsurge in Exponential heat source/ sink parameter and thermal source/sink parameter inclines the thermal profile. Further, increase in value of volume fraction inclines the rate of mass transfer.

Stagnation-point flow and heat transfer of power-law MHD fluid over a stretching surface with convective heat transferboundary condition

PurposeThis paper aims to discuss the stagnation-point flow and heat transfer for power-law fluid pass through a stretching surface with heat generation effect. Unlike the previous considerations about the research on stagnation-point flow, the process of heat transfer and the convective heat transfer boundary condition use the modified Fourier’s law in which the heat flux is power-law-dependent on velocity gradient.Design/methodology/approachThe similarly transformation is used to convert the governing partial differential equations into a series of ordinary differential equations which are solved analytically by using the differential transform method and the base function method.FindingsThe variations of the velocity and temperature fields for different specific related parameters are graphically discussed and analyzed. There is a special phenomenon that all the velocity profiles converge from the initial value of velocity to stagnation parameter values. And the larger power-law index enhancesthe momentum diffusion. A significant phenomenon can be observed that the larger power-law index causes a decline in the heat flux. This influence indicates that the higher viscosity restricts the heat transfer. Furthermore, both velocity gradient and temperature gradient play an indispensable role in the processes of heat transfer.Originality/valueThis paper researches the process of heat transfer of stagnation-point flow ofpower-law magneto-hydro-dynamical fluid over a stretching surface with modified convective heat transfer boundary condition.

The effects of radiation on heat and mass transfer of magnetohydrodynamic Marangoni flow in the boundary layer over a disk

This study investigated the problem of radiation effects on the flow heat and mass transfer of magnetohydrodynamic steady laminar Marangoni convection in the boundary layer over a disk in the presence of a linear heat source and first-order chemical reactions. The governing partial differential equations of the disk model were established and transformed to a series of ordinary differential equations via suitable self-similar transformations, which were solved numerically by the shooting technique coupled with Runge-Kutta scheme and Newton’s method. The Marangoni number related to temperature and concentration was derived, the effects of the magnetic Hartmann number, Marangoni number, radiation number, heat source number and chemical reaction number related to velocity, temperature, and concentration profiles were analyzed. The results demonstrate that the Hartmann number and Marangoni number have significant impacts on the heat and mass transfer of the Marangoni boundary layer flow. The temperature tends to increase with heat generation and decrease with heat absorption, and it exhibits a delay phenomenon for significant heat generation cases. Negative/positive chemical reactions tended to increase/decrease the concentration, similar to the effect of heat generation/absorption on the temperature.

Power-law fluids over a viscous sheet with mass suction/blowing: Multiple solutions

Multiple states emerge in the fluid flow with certain or sudden external interference. In this paper, multiple solutions of the velocity and temperature distributions of power-law fluids are found when the fluid is flowing through a viscous sheet with suction or blowing. By coupling the sheet dynamics with the surrounding fluid equations by the stress balance, the investigation results shed some light on many engineering applications of flow on various soft surfaces, for example, the synthetic plastics. The present research considers the nonuniformity of the mass suction or blowing effects, which is connected with both the stretching velocity and the thickness of the sheet. A similar transformation is adopted to transform the boundary layer equations into a series of ordinary differential equations, and multiple solutions are obtained. The existence of similar solutions has some limitations. The multiple solutions of the friction coefficient and the generalized Nusselt number affected by the power-law index n and the suction/blowing rate fw are shown, and we also discuss the influence of the generalized Prandtl number Npr and the Eckert number Ec on the velocity and temperature distributions.

Experimental and analytical study on the superharmonic resonance of size-dependent cantilever microbeams

The superharmonic resonance (SR) of size-dependent cantilever microbeams is investigated experimentally and analytically. Nickel cantilever microbeams are employed with concentrated harmonic force on the tip. The SR of order two, three, four, five, and six are observed. The frequency–response curves (FRCs) near the SR frequencies as well as the time histories are obtained. The FRCs indicate that the superharmonic resonant frequencies are different from the classical situation. Furthermore, a nonlinear model within the framework of modified couple stress theory is derived to interpret the observations by aid of Hamilton's variation principle. The resulting partial differential equation of motion is discretized into a series of ordinary differential equations (ODEs) by a two-mode Galerkin scheme. The ODEs are then solved analytically with the multi-dimensional Lindstedt–Poincaré method. Analytical results are in good agreement with experimental results in SR of order three. The effects of different nonlinear terms, length scale parameter, and damping coefficients on the nonlinear system are then discussed.

Abstract 686: Quantitative analysis of the role of homologous recombination in response to radiotherapy for prostate cancer

Abstract The purpose of this study is to computationally analyze how the interaction between androgen receptor (AR) and homologous recombination (HR) affects the treatment outcome for ionizing radiation (IR) combined with androgen deprivation therapy (ADT) for prostate cancer (PCa). Combination treatment with radiation and ADT is currently a standard treatment for PCa. The effectiveness of radiation treatment alone depends on the cells’ capacity to repair the damage that is mostly in the form of double-strand breaks (DSBs). Two major pathways that repair DSBs are non-homologous end joining (NHEJ) and HR. The experimental data in the literature show that AR promotes both NHEJ and HR following IR, and inhibition of AR by ADT impairs both of these pathways in PCa cells leading to either increased radiosensitivity or sensitization to PARP inhibitors. In our previous work, we developed mathematical models of the NHEJ pathway and in this current work we have developed such models for HR to comprehensively analyze the response of PCa cells to IR combined with ADT. We have modeled HR using a series of ordinary differential equations. The parameters that needed to be estimated are the kinetic rate constants, and we have used least square estimation to obtain these model parameters. The data sets used in the parameter estimation were obtained from the literature and they were from both in vitro experiments as well as clinical data from PCa patients. The experimental data show that AR influences the DNA end resection that is required for proficient HR and we have computationally included this effect in the kinetics of the models. We have developed models for IR treatment alone or in combination with ADT. We have carried out sensitivity analysis and identifiability tests on all the parameters from both models in order to determine the parameters that are reliably estimated. The outputs from both NHEJ and HR models show that the suppression of AR activity through ADT has the potential to enhance the IR treatment outcomes for PCa patients. The impairment of HR by ADT also opens up an avenue for achieving synthetic lethality using PARP inhibitors as shown in the literature; in the future we are planning to extend our modeling efforts to include the effect of PARP inhibitors on the treatment outcome. Citation Format: Mengdi Qian, Alexandru Almasan, Evren Gürkan-Çavusoglu. Quantitative analysis of the role of homologous recombination in response to radiotherapy for prostate cancer [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 686.

Transition-event duration in one-dimensional systems under correlated noise

Transition-event duration (TED) is the spent time of a particle which enters a neighborhood of one state to reach another one without ever returning back to the state where it starts. In this paper, an approximate theoretical method is proposed to obtain the transition-event duration distribution (TEDD) of one-dimensional bi-stable strongly nonlinear systems under correlated noises. It strongly extends the existing theoretical methods for obtaining the TEDD. Actually, an approximate theoretical solution of the TEDD is determined by the Fokker–Planck equation (FPE) with two absorbing boundary conditions. Here, we set each absorbing boundary condition at stable and unstable points of a bi-stable potential function. Firstly, a solution to the FPE is presented by the C-type Gram–Charlier expansion. Subsequently, based on the weighted residual scheme, the FPE is reduced to a series of ordinary differential equations (ODEs) with unknown coefficient. Then, an analytical solution to TEDD is derived by solving this series of ODEs. Especially, the concerning stochastic excitations of the system can be divided into five kinds of situations: Gaussian white noise, colored Gaussian noise, two Gaussian white noises with white cross-correlation, two Gaussian white noises with exponential correlation and two colored Gaussian noises with exponential correlation. We mainly discuss the influences of correlation and the parameters of noise on the TEDD. Our corresponding analytic results are compared with Monte Carlo simulations, and good agreements are found.

Flow and heat transfer of non-Newtonian power-law fluids over a stretching surface with variable thermal conductivity

PurposeThe purpose of this paper is to investigate the flow and heat transfer of power-law fluids over a non-linearly stretching sheet with non-Newtonian power-law stretching features.Design/methodology/approachThe governing non-linear partial differential equations are reduced to a series of ordinary differential equations by suitable similarity transformations and the numerical solutions are obtained by the shooting method.FindingsAs the temperature power-law index or the power-law number of the fluids increases, the dimensionless stream function, dimensionless velocity and dimensionless temperature decrease, while the velocity boundary layer and temperature boundary layer become thinner for other fixed physical parameters. The thermal diffusivity varying as a function of the temperature gradient can be used to present the characteristics of flow and heat transfer of non-Newtonian power-law fluids.Originality/valueUnlike classical works, the effect of power-law viscosity on the temperature field is considered by assuming that the temperature field is similar to the velocity field with modified Fourier’s law heat conduction for power-law fluid media.

Mathematical analysis of gefitinib resistance of lung adenocarcinoma caused by MET amplification

Gefitinib, one of the tyrosine kinase inhibitors of epidermal growth factor receptor (EGFR), is effective for treating lung adenocarcinoma harboring EGFR mutation; but later, most cases acquire a resistance to gefitinib. One of the mechanisms conferring gefitinib resistance to lung adenocarcinoma is the amplification of the MET gene, which is observed in 5–22% of gefitinib-resistant tumors. A previous study suggested that MET amplification could cause gefitinib resistance by driving ErbB3-dependent activation of the PI3K pathway. In this study, we built a mathematical model of gefitinib resistance caused by MET amplification using lung adenocarcinoma HCC827-GR (gefitinib resistant) cells. The molecular reactions involved in gefitinib resistance consisted of dimerization and phosphorylation of three molecules, EGFR, ErbB3, and MET were described by a series of ordinary differential equations. To perform a computer simulation, we quantified each molecule on the cell surface using flow cytometry and estimated unknown parameters by dimensional analysis. Our simulation showed that the number of active ErbB3 molecules is around a hundred-fold smaller than that of active MET molecules. Limited contribution of ErbB3 in gefitinib resistance by MET amplification is also demonstrated using HCC827-GR cells in culture experiments. Our mathematical model provides a quantitative understanding of the molecular reactions underlying drug resistance.

Symplectic Analysis of Wrinkles in Elastic Layers With Graded Stiffnesses

Wrinkles in layered neo-Hookean structures were recently formulated as a Hamiltonian system by taking the thickness direction as a pseudo-time variable. This enabled an efficient and accurate numerical method to solve the eigenvalue problem for onset wrinkles. Here, we show that wrinkles in graded elastic layers can also be described as a time-varying Hamiltonian system. The connection between wrinkles and the Hamiltonian system is established through an energy method. Within the Hamiltonian framework, the eigenvalue problem of predicting wrinkles is defined by a series of ordinary differential equations with varying coefficients. By modifying the boundary conditions at the top surface, the eigenvalue problem can be efficiently and accurately solved with numerical solvers of boundary value problems. We demonstrated the accuracy of the symplectic analysis by comparing the theoretically predicted displacement eigenfunctions, critical strains, and wavelengths of wrinkles in two typical graded structures with finite element simulations.

Abstract 4265: Computational models of the role of base excision repair in sensitization of cancer cells to 5-fluorodeoxyuridine

Abstract The purpose of this study is to computationally analyze the effect of inhibition of base excision repair (BER) in the response of cancer cells to treatment with 5-fluorodeoxyuridine. 5-fluorouracil (5-FU) and its metabolite 5-fluorodeoxyuridine (5-FdU) are standard treatments for different solid tumors and especially for colon cancer. In the literature, it is shown that the depletion of uracil DNA glycosylase (UDG), one of the enzymes that initiate the BER pathway, enhanced the cytotoxicity of 5-FdU, making UDG a potential target to enhance efficacy of chemotherapeutic agents. It is also shown that the activity of UDG is significantly higher in colon cancer cells compared to normal tissue. We have developed a computational model of the BER pathway to capture the BER dynamics in colon cancer cell lines after treatment with 5-FdU. Our model is composed of a series of ordinary differential equations where the parameters are the kinetic rate constants and the enzyme concentrations. We have used the data from the literature to initially parameterize our models. We have then used least square estimation to find the parameters that will capture the BER time course for colon cancer cells after 5-FU treatment using the experimental data from the literature. We have performed sensitivity and identifiability analyses to determine the parameters that are reliably estimated. The experimental data from the literature showed that the depletion of UDG resulted in incorporation of uracil and 5-FU in the DNA. We have computationally replicated this effect by decreasing the protein concentration of UDG in the models and simulating the amount of remaining 5-FU in the DNA after BER with reduced activity has taken place. We have studied the depletion effect for different protein concentrations of UDG and the results have shown that the accumulation of 5-FU in these colon cancer cells correlate with the level of UDG. The suppression of UDG activity has the potential to enhance the outcome of treatment with 5FdU, and we will use the developed computational models to quantitatively optimize these effects in our future work. Citation Format: Mengdi Qian, Alexandru Almasan, Evren Gürkan-Çavusoglu. Computational models of the role of base excision repair in sensitization of cancer cells to 5-fluorodeoxyuridine [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 4265.

Kinetics for De-Extracellular Matrix(ECM)

ABSTRACTA kinetic model for ECM decellularization with Trypsin and Deoxycholic Acid as reactants in a batch system has been developed. The decellularization mechanism has been analysed by solving a series of ordinary differential equations relating heterogeneous reaction kinetics at the solid/liquid interface to mass transfer of reactant and products. In order to remove the Deoxyribonucleic acid (DNA) of porcine, special emphasis has been given to the surface area for regulating the depth and amount of the penetration of the reagent, the numerical analysis thereof, and the corresponding experiment were carried out. The effect of chemical reaction order, rate constants and mass transfer coefficients on the overall decellularization rate has been analysed and discussed.