Newly Developed Methodologies Of PK/PD Modeling: Fractal Models, Fractional Models And Stochastic Models

Pharmacokinetics (PK) and pharmacodynamics (PD)， function as the twofundamental parts of modern pharmacology, are now gaining great importance invarious stages of the drug development and clinical application. Following them are largevarieties of PK/PD models, desires to form a more complete system of theorems andapplications. The ordinary differential equation (ODE) based traditional models, whichcan give a whole description of the dynamic systems under classical diffusion conditionsand deterministic situations, used to make a breakthrough in a way, for making apossibility of the transfer on PK/PD, from theoretical descriptions to mathematicalcalculation. And till today, it still serves as the main modeling methods.While as the research of biomedical, bioinformatics, modern biological informationmonitoring tools and computer technology become more and more intensive, we havefound that, the ordinary differential equation based traditional models can’t cover up theirdefects, such as the failure to describe the features of anomalous diffusion dynamics aswell as the uncertainty parts of random factors in a model. Though large quantities ofmodels which are newly developed can make up the disadvantage of the traditionalmodels in some way, they are still in the weak point, and receive rare attentions. So in thispaper, we are trying to introduce and analyze three kinds of newly developed PK/PDmodels, in order to make contrasts with traditional models. And make prediction of thetrends in PK/PD models, on the bases of a comprehensive comparison.Firstly, basic concepts of PK and PD are introduced, especially the ordinarydifferential equation based traditional models (in the forms of PK model, PD model andPK-PD combined models), which are also called classical models.Secondly, we have presented three kinds of newly developed PK/PD modeling arepresented, namely fractal model, fractional calculus model and stochastic model, whichare separately based on the theories of fractal dynamics, fractional order calculus andstochastic differential equations. In addition to a detailed introduction of their relevanttheories, models, characteristics and research status, a comparison and the following advantages of the classical models are also summarized. And make further summaries andevaluations of these models.Finally, a comparison between three kinds of modeling has been made, in order toforecast their tendency of development and application, desiring to provide credible andpower tools for the practical application of the fields in pharmacology.