Nonlinear Elimination of Drugs in One-Compartment Pharmacokinetic Models: Nonstandard Finite Difference Approach for Various Routes of Administration

Egbelowo, Oluwaseun Francis

doi:10.3390/mca23020027

Cited by 10 publications

(9 citation statements)

References 20 publications

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“…where 𝐶: Concentration of drug in central compartment, 𝑉 𝑚𝑎𝑥 : Maximal velocity of the metabolism, 𝐾 𝑚 : Michaelis constant, 𝑅 1 : Infusion rate per unit time and 𝑉 1 : Apparent volume of distribution [8].…”

Section: One Compartment IV Bolus Infusion Model Nonlinear Pharmacoki...mentioning

confidence: 99%

“…One of these fields of study is the numerical solutions of distributed order differential equations, which will be mentioned in this article. For further detailed information about numerical solutions, source numbers [5][6][7][8][9] can be examined.…”

Section: Introductionmentioning

confidence: 99%

“…If there are two citations, use comma to separate [2,3]. If citations are more than two and in consecutive order, give the starting number and the last number [4][5][6][7][8]. For multiple citations with/without consequence, use the combination of the rules above [9,15,[17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Discretization and Stability Analysis for a Generalized Type Nonlinear Pharmacokinetic Models

Kocabiyik

Ongun

2023

Gazi University Journal of Science

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Estimating effects of drugs at different stages is directly proportional to the duration of recovery and duration of pulling through with the disease. For this reason, solving Pharmacokinetic models that investigate these effects is very important. In this study, numerical solutions of this type of one, two and three compartment nonlinear Pharmacokinetic models have been studied. Distributed order differential equations are used for the solution of the model. Numerical solutions have been found with the density function contained in distributed order differential equations and different values of this function. A Nonstandard finite difference scheme has been used for numerical solutions. Finally, stability analysis of equilibrium points of obtained discretized system has also been expressed with the help of the Schur-Cohn criteria.

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Section: One Compartment IV Bolus Infusion Model Nonlinear Pharmacoki...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Discretization and Stability Analysis for a Generalized Type Nonlinear Pharmacokinetic Models

Kocabiyik

Ongun

2023

Gazi University Journal of Science

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“…The effect of chemotherapy is modeled according to the Norton-Simon hypothesis (N-S), which states that solid tumor cells are killed proportionally to the growth rate of the unperturbed tumor [33,34]. We incorporate pharmacokinetics of cisplatin into the model, with cisplatin assumed to be administered via intravenous bolus injection [35]. For simplicity, we assume no delay between cisplatin injection and the time cisplatin concentration reaches a maximum in cancer cells.…”

Section: Plos Computational Biologymentioning

confidence: 99%

Mathematical model predicts response to chemotherapy in advanced non-resectable non-small cell lung cancer patients treated with platinum-based doublet

et al. 2020

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We developed a computational platform including machine learning and a mechanistic mathematical model to find the optimal protocol for administration of platinum-doublet chemotherapy in a palliative setting. The platform has been applied to advanced metastatic non-small cell lung cancer (NSCLC). The 42 NSCLC patients treated with palliative intent at Maria Sklodowska-Curie National Research Institute of Oncology, Gliwice Branch, were collected from a retrospective cohort of patients diagnosed in 2004-2014. Patients were followed-up, for three years. Clinical data collected include complete information about the clinical course of the patients including treatment schedule, response according to RECIST classification, and survival. The core of the platform is the mathematical model, in the form of a system of ordinary differential equations, describing dynamics of platinum-sensitive and platinum-resistant cancer cells and interactions reflecting competition for space and resources. The model is simulated stochastically by sampling the parameter values from a joint probability distribution function. The machine learning model is applied to calibrate the mathematical model and to fit it to the overall survival curve. The model simulations faithfully reproduce the clinical cohort at three levels long-term response (OS), the initial response (according to RECIST criteria), and the relationship between the number of chemotherapy cycles and time between two consecutive chemotherapy cycles. In addition, we investigated the relationship between initial and long-term response. We showed that those two variables do not correlate which means that we cannot predict patient survival solely based on the initial response. We also tested several chemotherapy schedules to find the best one for patients treated with palliative intent. We found that the optimal treatment schedule depends, among others, on the strength of competition among various subclones in a tumor. The computational platform developed allows optimizing chemotherapy protocols, within admissible limits of toxicity, for palliative treatment of metastatic NSCLC. The simplicity of the method allows its application to chemotherapy optimization in different cancers.

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“…One such numerical method used to solve the system of ordinary differential equations (ODEs) in compartment pharmacokinetic models is the nonstandard finite difference (NSFD) method for constructing numerical solution schemes. Originating from the standard finite difference (SFD) method developed by Mickens [11,12], the NSFD method has been shown in several previous studies to yield more stable numerical results and better consistency with differential equations compared with the original SFD method, irrespective of the chosen step size [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Development of a Compartment Model to Study the Pharmacokinetics of Medical THC after Oral Administration

Mahahong,

Saleewong

2024

Computation

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The therapeutic potential of delta9-tetrahydrocannabinol (THC), a primary cannabinoid in the cannabis plant, has led to its development into oral medical products for treating various conditions. However, THC, being a psychoactive substance, can lead to addiction if taken in inappropriate amounts. Thus, studying the pharmacokinetics of THC is crucial for understanding how the drug behaves in the body after administration. This study aims to develop a multi-compartmental model to investigate the pharmacokinetics of medical THC and its metabolites after oral administration. Using the law of mass action, the model was converted into ordinary differential equations (ODEs) to describe the rate of concentration changes of THC and its metabolites in each compartment. The nonstandard finite difference (NSFD) method was then applied to construct numerical solution schemes, which were implemented in MATLAB along with estimated pharmacokinetic rate constants. The results demonstrate that the simulation curves depicting the plasma concentration–time profiles of THC and 11-hydroxy-THC (THC-OH) closely resemble actual data samples, indicating the model’s accuracy. Moreover, the model predicts the pharmacokinetics of THC and its metabolites in various tissues. Consequently, this model serves as a valuable tool for enhancing our understanding of the pharmacokinetics of THC and its metabolites, guiding dosage adjustments, and determining administration durations for oral medical THC.

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Nonlinear Elimination of Drugs in One-Compartment Pharmacokinetic Models: Nonstandard Finite Difference Approach for Various Routes of Administration

Cited by 10 publications

References 20 publications

Discretization and Stability Analysis for a Generalized Type Nonlinear Pharmacokinetic Models

Discretization and Stability Analysis for a Generalized Type Nonlinear Pharmacokinetic Models

Mathematical model predicts response to chemotherapy in advanced non-resectable non-small cell lung cancer patients treated with platinum-based doublet

Development of a Compartment Model to Study the Pharmacokinetics of Medical THC after Oral Administration

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