scholarly journals Pharmacokinetics and Pharmacodynamics Models of Tumor Growth and Anticancer Effects in Discrete Time

2020 ◽  
Vol 8 (1) ◽  
pp. 114-125
Author(s):  
Ferhan M. Atıcı ◽  
Ngoc Nguyen ◽  
Kamala Dadashova ◽  
Sarah E. Pedersen ◽  
Gilbert Koch
Keyword(s):  
Tumor Growth ◽  
Discrete Time ◽  
Continuous Time ◽  
Discrete System ◽  
Model Parameters ◽  
Discrete Fractional Calculus ◽  
Pharmacokinetics And Pharmacodynamics ◽  
Fractional Difference ◽  
Nabla Operator ◽  
Anticancer Effects

AbstractWe study the h-discrete and h-discrete fractional representation of a pharmacokinetics-pharmacodynamics (PK-PD) model describing tumor growth and anticancer effects in continuous time considering a time scale h𝕅0, where h > 0. Since the measurements of the drug concentration in plasma were taken hourly, we consider h = 1/24 and obtain the model in discrete time (i.e. hourly). We then continue with fractionalizing the h-discrete nabla operator in the h-discrete model to obtain the model as a system of nabla h-fractional difference equations. In order to solve the fractional h-discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. After estimating and getting confidence intervals of the model parameters, we compare residual squared sum values of the models in one table. Our study shows that the new introduced models provide fitting as good as the existing models in continuous time.

scholarly journals Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Deccy Y. Trejos ◽  
Jose C. Valverde ◽  
Ezio Venturino
Keyword(s):  
Mathematical Model ◽  
Infectious Diseases ◽  
Discrete Time ◽  
Continuous Time ◽  
Control Strategies ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
Simulation Techniques ◽  
Biological Aspects ◽  
Tools And Methods

Abstract In this paper, the main biological aspects of infectious diseases and their mathematical translation for modeling their transmission dynamics are revised. In particular, some heterogeneity factors which could influence the fitting of the model to reality are pointed out. Mathematical tools and methods needed to qualitatively analyze deterministic continuous-time models, formulated by ordinary differential equations, are also introduced, while its discrete-time counterparts are properly referenced. In addition, some simulation techniques to validate a mathematical model and to estimate the model parameters are shown. Finally, we present some control strategies usually considered to prevent epidemic outbreaks and their implementation in the model.

Modeling the combined efficacy of rilotumumab (R; AMG 102) plus epirubicin/cisplatin/capecitabine (ECX) for the treatment of locally advanced or metastatic gastric or esophagogastric junction (G/EGJ) cancer.

2012 ◽  
Vol 30 (15_suppl) ◽  
pp. 2594-2594 ◽  
Author(s):  
Sameer Doshi ◽  
Steven Kathman ◽  
Rui Tang ◽  
Per Olsson Gisleskog ◽  
Elwyn Loh ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Dynamic Model ◽  
Discrete Time ◽  
Tumor Size ◽  
Survival Model ◽  
Population Pharmacokinetic ◽  
Model Parameters ◽  
Combined Effects ◽  
Phase 2 ◽  
Tumor Reduction

2594 Background: R is an investigational, fully human monoclonal antibody to hepatocyte growth factor/scatter factor (HGF/SF) that inhibits signaling though the MET receptor. In a double-blind, placebo-controlled, phase 2 trial of 121 patients with G/EGJ cancer, R (7.5 or 15 mg/kg) + ECX showed trends for improved progression-free survival (PFS) and overall survival compared to ECX alone. The combined effects of R and ECX on tumor reduction and PFS were modeled using the phase 2 data. Methods: A population pharmacokinetic (PK) model was used to estimate R PK parameters and individual R concentrations (C) over time. A tumor dynamic model was developed to characterize the combined effects of R with ECX on tumor growth and cell death and to evaluate the impact of baseline patient characteristics and lab values on model parameters. A discrete time-survival model was developed with PFS and C data to evaluate the effect of R, ECX, and the interaction between R and ECX on PFS within a given time interval. Results: R exhibited linear PKs with an estimated mean clearance of 0.216 L/d/70 kg. The tumor dynamic model suggested that R and ECX worked jointly to reduce tumor size from baseline via inhibition of the tumor growth rate constant (Kgrowth) and stimulation of the death rate of tumor cells (Kdeath). Assuming the maximal inhibition of Kgrowth is 100%, the estimated mean C that provided 50% maximal Kgrowth inhibition (EC50) was 6.71 µg/mL. The mean (SD) estimated effect of 7.5 and 15 mg/kg R on Kgrowth was 90.1% (3.8%) and 95.5% (1.9%) inhibition, respectively. None of the tested baseline factors appeared to significantly affect tumor reduction by R + ECX. In the discrete time-survival model, the R and ECX combination significantly improved PFS, and the model suggests that the magnitude of the effect of one treatment was dependent on the other. Conclusions: R and ECX appeared to work in combination to decrease tumor size and to improve PFS.

scholarly journals A study on discrete and discrete fractional pharmacokinetics-pharmacodynamics models for tumor growth and anti-cancer effects

2019 ◽  
Vol 7 (1) ◽  
pp. 10-24 ◽  
Author(s):  
Ferhan M. Atıcı ◽  
Mustafa Atıcı ◽  
Ngoc Nguyen ◽  
Tilekbek Zhoroev ◽  
Gilbert Koch
Keyword(s):  
Tumor Growth ◽  
Bayesian Method ◽  
Tumor Volume ◽  
Difference Operator ◽  
Discrete Models ◽  
Fractional Difference ◽  
Nabla Operator ◽  
Anti Cancer ◽  
Fractional Models ◽  
Definition Of

AbstractWe study the discrete and discrete fractional representation of a pharmacokinetics - pharmacodynamics (PK-PD) model describing tumor growth and anti-cancer effects in continuous time considering a time scale $h\mathbb{N}_0^h$, where h > 0. Since the measurements of the tumor volume in mice were taken daily, we consider h = 1 and obtain the model in discrete time (i.e. daily). We then continue with fractionalizing the discrete nabla operator to obtain the model as a system of nabla fractional difference equations. The nabla fractional difference operator is considered in the sense of Riemann-Liouville definition of the fractional derivative. In order to solve the fractional discrete system analytically we state and prove some theorems in the theory of discrete fractional calculus. For the data fitting purpose, we use a new developed method which is known as an improved version of the partial sum method to estimate the parameters for discrete and discrete fractional models. Sensitivity analysis is conducted to incorporate uncertainty/noise into the model. We employ both frequentist approach and Bayesian method to construct 90 percent confidence intervals for the parameters. Lastly, for the purpose of practicality, we test the discrete models for their efficiency and illustrate their current limitations for application.

Design of Programmable Wideband Low Pass Filter with Continuous-Time/Discrete-Time Hybrid Architecture

2017 ◽  
Vol E100.C (10) ◽  
pp. 858-865 ◽  
Author(s):  
Yohei MORISHITA ◽  
Koichi MIZUNO ◽  
Junji SATO ◽  
Koji TAKINAMI ◽  
Kazuaki TAKAHASHI
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Architecture ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass

scholarly journals Time to Intervene: A Continuous-Time Approach to Network Analysis and Centrality

Psychometrika ◽  
2021 ◽  
Author(s):  
Oisín Ryan ◽  
Ellen L. Hamaker
Keyword(s):  
Network Analysis ◽  
Discrete Time ◽  
Continuous Time ◽  
Centrality Measures ◽  
Time Interval ◽  
Direct Effects ◽  
Network Approach ◽  
Var Models ◽  
Auto Regressive ◽  
Conceptual Shift

AbstractNetwork analysis of ESM data has become popular in clinical psychology. In this approach, discrete-time (DT) vector auto-regressive (VAR) models define the network structure with centrality measures used to identify intervention targets. However, VAR models suffer from time-interval dependency. Continuous-time (CT) models have been suggested as an alternative but require a conceptual shift, implying that DT-VAR parameters reflect total rather than direct effects. In this paper, we propose and illustrate a CT network approach using CT-VAR models. We define a new network representation and develop centrality measures which inform intervention targeting. This methodology is illustrated with an ESM dataset.

On quasi-stationary distributions in absorbing continuous-time finite Markov chains

1967 ◽  
Vol 4 (1) ◽  
pp. 192-196 ◽  
Author(s):  
J. N. Darroch ◽  
E. Seneta
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Present Note ◽  
Time Parameter ◽  
Stationary Distributions ◽  
Finite State ◽  
Absorbing Markov Chains ◽  
Finite Markov Chains ◽  
Finite State Space

In a recent paper, the authors have discussed the concept of quasi-stationary distributions for absorbing Markov chains having a finite state space, with the further restriction of discrete time. The purpose of the present note is to summarize the analogous results when the time parameter is continuous.

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