scholarly journals In Silico Assessment of 5-FU Therapy via A Mathematical Model with Fuzzy Uncertain Parameters

2020 ◽  
Author(s):  
Sajad Shafiekhani ◽  
Amir. H. Jafari ◽  
L. Jafarzadeh ◽  
N. Gheibi
Keyword(s):  
Differential Equation ◽  
Immune Cells ◽  
In Silico ◽  
Parametric Uncertainty ◽  
Testable Hypothesis ◽  
Model Parameters ◽  
Ode Model ◽  
Ode Models ◽  
Mathematical Oncology ◽  
Uncertainty Band

Abstract Background: Ordinary differential equation (ODE) models widely have been used in mathematical oncology to capture dynamics of tumor and immune cells and evaluate the efficacy of treatments. However, for dynamic models of tumor-immune system (TIS), some parameters are uncertain due to inaccurate, missing or incomplete data, which has hindered the application of ODEs that require accurate parameters. Methods: We extended an available ODE model of TIS interactions via fuzzy logic to illustrate the fuzzification procedure of an ODE model. Fuzzy ODE (FODE) models, in comparison with the stochastic differential equation (SDE) models, assigns a fuzzy number instead of a random number (from a specific probability density function) to the parameters, to capture parametric uncertainty. We used FODE model to predict tumor and immune cells dynamics and assess the efficacy of 5-FU. The present model is configurable for 5-FU chemotherapy injection timing and propose testable hypothesis in vitro/ in vivo experiments. Result: FODE model was used to explore the uncertainty of cells dynamics resulting from parametric uncertainty in presence and absence of 5-FU therapy. In silico experiments revealed that the frequent 5-FU injection created a beneficial tumor microenvironment that exerted detrimental effects on tumor cells by enhancing the infiltration of CD8+ T cells, and NK cells, and decreasing that of myeloid-derived suppressor (MDSC) cells. We investigate the effect of perturbation on model parameters on dynamics of cells through global sensitivity analysis (GSA) and compute correlation between model parameters and cell dynamics. Conclusion: ODE models with fuzzy uncertain kinetic parameters cope with insufficient experimental data in the field of mathematical oncology and can predict cells dynamics uncertainty band. In silico assessment of treatments considering parameter uncertainty and investigating the effect of the drugs on movement of cells dynamics uncertainty band may be more appropriate than in crisp setting.

scholarly journals Generating Agent-Based Multiscale Multicellular Spatiotemporal Models from Ordinary Differential Equations of Biological Systems, with Applications in Viral Infection

2021 ◽  
Author(s):  
T.J. Sego ◽  
Josua O. Aponte-Serrano ◽  
Juliano F. Gianlupi ◽  
James A. Glazier
Keyword(s):  
Differential Equations ◽  
Viral Infection ◽  
Spatial Information ◽  
Biological Systems ◽  
Spatial Models ◽  
Model Parameters ◽  
Ode Model ◽  
Agent Based ◽  
Ode Models ◽  
Computationally Expensive

AbstractThe biophysics of an organism span scales from subcellular to organismal and include spatial processes like diffusion of molecules, cell migration, and flow of intravenous fluids. Mathematical biology seeks to explain biophysical processes in mathematical terms at, and across, all relevant spatial and temporal scales. While non-spatial, ordinary differential equation (ODE) models are often used and readily calibrated to experimental data, they do not explicitly represent spatial and stochastic features of a biological system, limiting their insights and applications. Spatial models describe biological systems with spatial information but are mathematically complex and computationally expensive, which limits the ability to calibrate and deploy them. In this work we develop a formal method for deriving cell-based, spatial, multicellular models from ODE models of population dynamics in biological systems, and vice-versa. We provide examples of generating spatiotemporal, multicellular models from ODE models of viral infection and immune response. In these models the determinants of agreement of spatial and non-spatial models are the degree of spatial heterogeneity in viral production and rates of extracellular viral diffusion and decay. We show how ODE model parameters can implicitly represent spatial parameters, and cell-based spatial models can generate uncertain predictions through sensitivity to stochastic cellular events, which is not a feature of ODE models. Using our method, we can test ODE models in a multicellular, spatial context and translate information to and from non-spatial and spatial models, which help to employ spatiotemporal multicellular models using calibrated ODE model parameters, investigate objects and processes implicitly represented by ODE model terms and parameters, and improve the reproducibility of spatial, stochastic models. We hope to employ our method to generate new ODE model terms from spatiotemporal, multicellular models, recast popular ODE models on a cellular basis, and generate better models for critical applications where spatial and stochastic features affect outcomes.Statement of SignificanceOrdinary differential equations (ODEs) are widely used to model and efficiently simulate multicellular systems without explicit spatial information, while spatial models permit explicit spatiotemporal modeling but are mathematically complicated and computationally expensive. In this work we develop a method to generate stochastic, agent-based, multiscale models of multicellular systems with spatial resolution at the cellular level according to non-spatial ODE models. We demonstrate how to directly translate model terms and parameters between ODE and spatial models and apply non-spatial model terms to boundary conditions using examples of viral infection modeling, and show how spatial models can interrogate implicitly represented biophysical mechanisms in non-spatial models. We discuss strategies for co-developing spatial and non-spatial models and reconciling disagreements between them.

scholarly journals Identifiability analysis for models of the translation kinetics after mRNA transfection

2021 ◽  
Author(s):  
Susanne Pieschner ◽  
Jan Hasenauer ◽  
Christiane Fuchs
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Ode Model ◽  
Kinetic Rate ◽  
Identifiability Analysis ◽  
Parameter Identifiability ◽  
Ode Models ◽  
Kinetic Rate Constants ◽  
Mrna Transfection ◽  
Model Equations

Mechanistic models are a powerful tool to gain insights into biological processes. The parameters of such models, e.g. kinetic rate constants, usually cannot be measured directly but need to be inferred from experimental data. In this article, we study dynamical models of the translation kinetics after mRNA transfection and analyze their parameter identifiability. Previous studies have considered ordinary differential equation (ODE) models of the process, and here we formulate a stochastic differential equation (SDE) model. For both model types, we consider structural identifiability based on the model equations and practical identifiability based on simulated as well as experimental data and find that the SDE model provides better parameter identifiability than the ODE model. Moreover, our analysis shows that even for those parameters of the ODE model that are considered to be identifiable, the obtained estimates are sometimes unreliable. Overall, our study clearly demonstrates the relevance of considering different modeling approaches and that stochastic models can provide more reliable and informative results.

scholarly journals Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 243
Author(s):  
Gabriella Bretti ◽  
Adele De De Ninno ◽  
Roberto Natalini ◽  
Daniele Peri ◽  
Nicole Roselli
Keyword(s):  
Immune Cells ◽  
Immune Cell ◽  
Spline Interpolation ◽  
Estimation Algorithm ◽  
Model Parameters ◽  
Ode Model ◽  
Lab On Chip ◽  
Chip Experiment ◽  
On Chip

The present work is motivated by the development of a mathematical model mimicking the mechanisms observed in lab-on-chip experiments, made to reproduce on microfluidic chips the in vivo reality. Here we consider the Cancer-on-Chip experiment where tumor cells are treated with chemotherapy drug and secrete chemical signals in the environment attracting multiple immune cell species. The in silico model here proposed goes towards the construction of a “digital twin” of the experimental immune cells in the chip environment to better understand the complex mechanisms of immunosurveillance. To this aim, we develop a tumor-immune microfluidic hybrid PDE–ODE model to describe the concentration of chemicals in the Cancer-on-Chip environment and immune cells migration. The development of a trustable simulation algorithm, able to reproduce the immunocompetent dynamics observed in the chip, requires an efficient tool for the calibration of the model parameters. In this respect, the present paper represents a first methodological work to test the feasibility and the soundness of the calibration technique here proposed, based on a multidimensional spline interpolation technique for the time-varying velocity field surfaces obtained from cell trajectories.

scholarly journals Prediction of anti-CD25 and 5-FU treatments efficacy for pancreatic cancer using a mathematical model

BMC Cancer ◽  
2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Sajad Shafiekhani ◽  
Hojat Dehghanbanadaki ◽  
Azam Sadat Fatemi ◽  
Sara Rahbar ◽  
Jamshid Hadjati ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Tumor Microenvironment ◽  
Kinetic Parameters ◽  
In Silico ◽  
Treatment Modalities ◽  
Ductal Adenocarcinoma ◽  
Rational Approach ◽  
Model Parameters ◽  
Tumor Escape ◽  
Uncertainty Band

Abstract Background Pancreatic ductal adenocarcinoma (PDAC) is a highly lethal disease with rising incidence and with 5-years overall survival of less than 8%. PDAC creates an immune-suppressive tumor microenvironment to escape immune-mediated eradication. Regulatory T (Treg) cells and myeloid-derived suppressor cells (MDSC) are critical components of the immune-suppressive tumor microenvironment. Shifting from tumor escape or tolerance to elimination is the major challenge in the treatment of PDAC. Results In a mathematical model, we combine distinct treatment modalities for PDAC, including 5-FU chemotherapy and anti- CD25 immunotherapy to improve clinical outcome and therapeutic efficacy. To address and optimize 5-FU and anti- CD25 treatment (to suppress MDSCs and Tregs, respectively) schedule in-silico and simultaneously unravel the processes driving therapeutic responses, we designed an in vivo calibrated mathematical model of tumor-immune system (TIS) interactions. We designed a user-friendly graphical user interface (GUI) unit which is configurable for treatment timings to implement an in-silico clinical trial to test different timings of both 5-FU and anti- CD25 therapies. By optimizing combination regimens, we improved treatment efficacy. In-silico assessment of 5-FU and anti- CD25 combination therapy for PDAC significantly showed better treatment outcomes when compared to 5-FU and anti- CD25 therapies separately. Due to imprecise, missing, or incomplete experimental data, the kinetic parameters of the TIS model are uncertain that this can be captured by the fuzzy theorem. We have predicted the uncertainty band of cell/cytokines dynamics based on the parametric uncertainty, and we have shown the effect of the treatments on the displacement of the uncertainty band of the cells/cytokines. We performed global sensitivity analysis methods to identify the most influential kinetic parameters and simulate the effect of the perturbation on kinetic parameters on the dynamics of cells/cytokines. Conclusion Our findings outline a rational approach to therapy optimization with meaningful consequences for how we effectively design treatment schedules (timing) to maximize their success, and how we treat PDAC with combined 5-FU and anti- CD25 therapies. Our data revealed that a synergistic combinatorial regimen targeting the Tregs and MDSCs in both crisp and fuzzy settings of model parameters can lead to tumor eradication.

scholarly journals Generation of multicellular spatiotemporal models of population dynamics from ordinary differential equations, with applications in viral infection

BMC Biology ◽  
2021 ◽  
Vol 19 (1) ◽  
Author(s):  
T. J. Sego ◽  
Josua O. Aponte-Serrano ◽  
Juliano F. Gianlupi ◽  
James A. Glazier
Keyword(s):  
Population Dynamics ◽  
Viral Infection ◽  
Spatial Information ◽  
Formal Method ◽  
Multiple Scales ◽  
Biological Systems ◽  
Spatial Models ◽  
Model Parameters ◽  
Ode Model ◽  
Ode Models

Abstract Background The biophysics of an organism span multiple scales from subcellular to organismal and include processes characterized by spatial properties, such as the diffusion of molecules, cell migration, and flow of intravenous fluids. Mathematical biology seeks to explain biophysical processes in mathematical terms at, and across, all relevant spatial and temporal scales, through the generation of representative models. While non-spatial, ordinary differential equation (ODE) models are often used and readily calibrated to experimental data, they do not explicitly represent the spatial and stochastic features of a biological system, limiting their insights and applications. However, spatial models describing biological systems with spatial information are mathematically complex and computationally expensive, which limits the ability to calibrate and deploy them and highlights the need for simpler methods able to model the spatial features of biological systems. Results In this work, we develop a formal method for deriving cell-based, spatial, multicellular models from ODE models of population dynamics in biological systems, and vice versa. We provide examples of generating spatiotemporal, multicellular models from ODE models of viral infection and immune response. In these models, the determinants of agreement of spatial and non-spatial models are the degree of spatial heterogeneity in viral production and rates of extracellular viral diffusion and decay. We show how ODE model parameters can implicitly represent spatial parameters, and cell-based spatial models can generate uncertain predictions through sensitivity to stochastic cellular events, which is not a feature of ODE models. Using our method, we can test ODE models in a multicellular, spatial context and translate information to and from non-spatial and spatial models, which help to employ spatiotemporal multicellular models using calibrated ODE model parameters. We additionally investigate objects and processes implicitly represented by ODE model terms and parameters and improve the reproducibility of spatial, stochastic models. Conclusion We developed and demonstrate a method for generating spatiotemporal, multicellular models from non-spatial population dynamics models of multicellular systems. We envision employing our method to generate new ODE model terms from spatiotemporal and multicellular models, recast popular ODE models on a cellular basis, and generate better models for critical applications where spatial and stochastic features affect outcomes.

Overview of Gene Regulatory Network Inference Based on Differential Equation Models

2020 ◽  
Vol 21 (11) ◽  
pp. 1054-1059
Author(s):  
Bin Yang ◽  
Yuehui Chen
Keyword(s):  
Differential Equation ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Network Inference ◽  
New Drugs ◽  
Gene Regulatory Network Inference ◽  
Ode Models ◽  
Differential Equation Models ◽  
Linear Ode ◽  
Gene Regulatory

: Reconstruction of gene regulatory networks (GRN) plays an important role in understanding the complexity, functionality and pathways of biological systems, which could support the design of new drugs for diseases. Because differential equation models are flexible androbust, these models have been utilized to identify biochemical reactions and gene regulatory networks. This paper investigates the differential equation models for reverse engineering gene regulatory networks. We introduce three kinds of differential equation models, including ordinary differential equation (ODE), time-delayed differential equation (TDDE) and stochastic differential equation (SDE). ODE models include linear ODE, nonlinear ODE and S-system model. We also discuss the evolutionary algorithms, which are utilized to search the optimal structures and parameters of differential equation models. This investigation could provide a comprehensive understanding of differential equation models, and lead to the discovery of novel differential equation models.

A stochastic differential equation model of diurnal cortisol patterns

2001 ◽  
Vol 280 (3) ◽  
pp. E450-E461 ◽  
Author(s):  
Emery N. Brown ◽  
Patricia M. Meehan ◽  
Arthur P. Dempster
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Plasma Cortisol ◽  
Equation Model ◽  
Plasma Cortisol Level ◽  
Model Parameters ◽  
Kinetic Properties ◽  
Simulation Studies ◽  
Physiological Factors ◽  
Diurnal Patterns

Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.

scholarly journals An OGI model for personalized estimation of glucose and insulin concentration in plasma

2021 ◽  
Vol 18 (6) ◽  
pp. 8499-8523
Author(s):  
Weijie Wang ◽  
◽  
Shaoping Wang ◽  
Yixuan Geng ◽  
Yajing Qiao ◽  
...  
Keyword(s):  
Kalman Filtering ◽  
Gaussian Noise ◽  
Particle Filtering ◽  
In Silico ◽  
Insulin Concentration ◽  
Model Parameters ◽  
Bayesian Filtering ◽  
Extended Kalman Filtering ◽  
External Disturbances ◽  
Non Gaussian

<abstract><p>Plasma glucose concentration (PGC) and plasma insulin concentration (PIC) are two essential metrics for diabetic regulation, but difficult to be measured directly. Often, PGC and PIC are estimated from continuous glucose monitoring and insulin delivery data. Nevertheless, the inter-individual variability and external disturbance (e.g. carbohydrate intake) bring challenges for accurate estimations. This study is to estimate PGC and PIC adaptively by identifying personalized parameters and external disturbances. An observable glucose-insulin (OGI) dynamic model is established to describe insulin absorption, glucose regulation, and glucose transport. The model parameters and disturbances can be extended to observable state variables and be identified dynamically by Bayesian filtering estimators. Two basic Gaussian noise based Bayesian filtering estimators, extended Kalman filtering (EKF) and unscented Kalman filtering (UKF), are implemented. Recognizing the prevalence of non-Gaussian noise, in this study, two new filtering estimators: particle filtering with Gaussian noise (PFG), and particle filtering with mixed non-Gaussian noise (PFM) are designed and implemented. The proposed OGI model in conjunction with the estimators is evaluated using the data from 30 in-silico subjects and 10 human participants. For in-silico subjects, the OGI with PFM estimator has the ability to estimate PIC and PGC adaptively, achieving RMSE of PIC $ 9.49\pm3.81 $ mU/L, and PGC $ 0.89\pm0.19 $ mmol/L. For human, the OGI with PFM has the promise to identify disturbances ($ 95.46\%\pm0.65\% $ accurate rate of meal identification). OGI model provides a way to fully personalize the parameters and external disturbances in real time, and has potential clinical utility for artificial pancreas.</p></abstract>

Sign in / Sign up

Export Citation Format

Share Document