ArticleJournal of pharmacokinetics and pharmacodynamics2010
Fractional kinetics in multi-compartmental systems.
Article in Journal of pharmacokinetics and pharmacodynamics, 2010. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 24 papers, 1 of them a synthesis that pooled it.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
24 citing papers in PubMed, 1 synthesis or guideline pooled it.
- Comparison of the gamma-Pareto convolution with conventional methods of characterising metformin pharmacokinetics in dogs.Journal of pharmacokinetics and pharmacodynamics · 2020Pooled it
- Article
- Modeling drug retention as memory effects in obese patients using fractional and augmented models.Scientific reports · 2025Article
- Bridging the gap between models based on ordinary, delayed, and fractional differentials equations through integral kernels.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- A Generalized Kinetic Model of Fractional Order Transport Dynamics with Transit Time Heterogeneity in Microvascular Space.Bulletin of mathematical biology · 2024Article
- Implementation of non-linear mixed effects models defined by fractional differential equations.Journal of pharmacokinetics and pharmacodynamics · 2023Article
- Fractal Kinetic Implementation in Population Pharmacokinetic Modeling.Pharmaceutics · 2023Article
- The impact of a power law-induced memory effect on the SARS-CoV-2 transmission.Chaos, solitons, and fractals · 2022Article
- A series acceleration algorithm for the gamma-Pareto (type I) convolution and related functions of interest for pharmacokinetics.Journal of pharmacokinetics and pharmacodynamics · 2022Article
- Plasma Distribution of Methotrexate and Its Polyglutamates in Pediatric Acute Lymphoblastic Leukemia: Preliminary Insights.European journal of drug metabolism and pharmacokinetics · 2022Article
- Article
- Tailored Pharmacokinetic model to predict drug trapping in long-term anesthesia.Journal of advanced research · 2021Article
- Fractional model for the spread of COVID-19 subject to government intervention and public perception.Applied mathematical modelling · 2021Article
- Diffusion through skin in the light of a fractional derivative approach: progress and challenges.Journal of pharmacokinetics and pharmacodynamics · 2021Review
- Mathematical Models as Tools to Predict the Release Kinetic of Fluorescein from Lyotropic Colloidal Liquid Crystals.Materials (Basel, Switzerland) · 2019Article
- Fractional calculus in pharmacokinetics.Journal of pharmacokinetics and pharmacodynamics · 2018Article
- Membrane capacitive memory alters spiking in neurons described by the fractional-order Hodgkin-Huxley model.PloS one · 2015Article
- Cloxacillin concentrations in serum, subcutaneous fat, and muscle in patients with chronic critical limb ischemia.European journal of clinical pharmacology · 2014Article
- Exponential tails of drug disposition curves: reality or appearance?Journal of pharmacokinetics and pharmacodynamics · 2014Article
- How to avoid unbounded drug accumulation with fractional pharmacokinetics.Journal of pharmacokinetics and pharmacodynamics · 2013Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
3 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we extend that theory to multi-compartmental models. Unlike systems defined by a single ordinary differential equation (ODE), considering fractional multi-compartmental models is not as simple as changing the order of the ordinary derivatives of the left-hand side of the ODEs to fractional orders. The latter may produce inconsistent systems which violate mass balance. We present a rationale for fractionalization of ODEs, which produces consistent systems and allows processes of different fractional orders in the same system. We also apply a method of solving such systems based on a numerical inverse Laplace transform algorithm, which we demonstrate that is consistent with analytical solutions when these are available. As examples of our approach, we consider two cases of a basic two-compartment PK model with a single IV dose and multiple oral dosing, where the transfer from the peripheral to the central compartment is of fractional order α < 1, accounting for anomalous kinetics and deep tissue trapping, while all other processes are of the usual order 1. Simulations with the studied systems are performed using the numerical inverse Laplace transform method. It is shown that the presence of a transfer rate of fractional order produces a non-exponential terminal phase, while multiple dose and constant infusion systems never reach steady state and drug accumulation carries on indefinitely. The IV fractional system is also fitted to PK data and parameter values are estimated. In conclusion, our approach allows the formulation of systems of FDEs, mixing different fractional orders, in a consistent manner and also provides a method for the numerical solution of these systems.
Indexed as
Identifiers
20886267What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.