A Stochastic Analysis of the One Compartment Pharmacokinetic Model Considering Optimal Controls

Liu, Qianning; Shan, Qingsong

doi:10.1109/access.2020.3028741

Cited by 4 publications

(3 citation statements)

References 21 publications

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“…Drug concentration levels in the body vary among different patients according to their weight, age, stress, or genetic factors [1]. In addition, it has also been observed that the food intake, special excercises and some vitamin can affect the drug absorption [2]. Due to the variability and uncertainty of such factors, several researches have introduced stochastic corrections on the well known compartmental pharmacokinetics deterministic models [3].…”

Section: Introductionmentioning

confidence: 99%

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One-compartment stochastic pharmacokinetic model

Macias

Moscoso

Vera

2023

Universitas Scientiarum

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In this work, we consider a pharmacokinetic (PK) model with first-order drug absorption and first-order elimination that represent the concentration of drugs in the body, including both the absorption and elimination parts, and we also add a random factor to describe the variability between patients and the environment. Using Itô’s lemma and the Laplace transform, we obtain the solutions in integral form for a single and constant dosage regimen in time. Moreover, formulas for the expected value and the variance for each case of study are presented, which allows the statistical assessment of the proposed models, as well as predicting the ideal path of drug concentration and its uncertainty. These results are important in the long-term analysis of drug concentration and the persistence of therapeutic level. Further, a numerical method for the solution of the stochastic differential equation (SDE) is introducedand developed.

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Section: Introductionmentioning

confidence: 99%

“…In addition, the problem to determine an optimal dosing timing schedule to control the blood drug concentration is studied in [2]. The authors combine optimal control theory and stochastic methods, prove existence, uniqueness of the solution and present the corresponding stability analisys.…”

Section: Introductionmentioning

confidence: 99%

One-compartment stochastic pharmacokinetic model

Macias

Moscoso

Vera

2023

Universitas Scientiarum

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“…We augmented the ODE PK one‐compartment model as an SDE PK model in Liu and Shan 23 . In this paper, we build a new two‐compartment PK model for IV administration by integrating optimal control theory and stochastic analysis.…”

Section: Introductionmentioning

confidence: 99%

An optimization‐based stochastic model of the two‐compartment pharmacokinetics

Liu

Shan

2022

Math Methods in App Sciences

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The original pharmacokinetics (PK) two-compartment model illustrates the change law of the drug in the central and peripheral chambers after administration, respectively. Although this deterministic model has derived many practical conclusions, it is based on simplifications and neglects noise, which is inherent to pharmacological processes. The actual pharmacological processes are always influenced by factors that cannot be entirely understood or modeled explicitly.Modeling without considering these phenomena may impact the accuracy and the related conclusions. A stochastic type of model can capture such noise. We proposed a novel two-compartment PK model concerning drug administration through intravenous route by combining optimal control theory and stochastic analysis. The selection of the objective function was based on the goal of obtaining the best possible therapeutic effect with the least possible drug dosage.Firstly, we extended the original PK two-compartment model based on optimal control and proved the existence and uniqueness of the switch in the control.Moreover, considering the possible uncertain factors, we added disturbances to the distance between the drug concentration and equilibrium point of the dynamic system and extended the model to a stochastic differential equation model. Qualitative and quantitative analyses showed that optimal controls were bang-bang, that is, alternating the drug dosages at a full dose with rest-periods in-between. Our analysis provided a schedule for optimal dosage and timing.The solutions of the model provided estimates of the drug concentration at any given time. Finally, we simulated the model using R and showed that the numerical method is stable.

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On Asymptotic Behavior of Solutions of Linear Inhomogeneous Stochastic Differential Equations with Correlated Inputs

Palamarchuk

2022

Diff Equat

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A Stochastic Analysis of the One Compartment Pharmacokinetic Model Considering Optimal Controls

Cited by 4 publications

References 21 publications

One-compartment stochastic pharmacokinetic model

One-compartment stochastic pharmacokinetic model

An optimization‐based stochastic model of the two‐compartment pharmacokinetics

On Asymptotic Behavior of Solutions of Linear Inhomogeneous Stochastic Differential Equations with Correlated Inputs

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