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doi: 10.1007/s11538-018-00556-ypmid: 30693431
The goals of this article and special issue are to highlight the value of mathematical biology approaches in industry, help foster future interactions, and suggest ways for mathematics Ph.D. students and postdocs to move into industry careers. We include a candid examination of the advantages and challenges of doing mathematics in the biopharma industry, a broad overview of the types of mathematics being applied, information about academic collaborations, and career advice for those looking to move from academia to industry (including graduating Ph.D. students).
Wu, Xiaotian; Nekka, Fahima; Li, Jun
doi: 10.1007/s11538-019-00651-8pmid: 31420841
In this paper, a typical pharmacokinetic (PK) model is studied for the case of multiple intravenous bolus-dose administration. This model, of one-compartment structure, not only exhibits simultaneous first-order and Michaelis–Menten elimination, but also involves a constant endogenous production. For the PK characterization of the model, we have established the closed-form solution of concentrations over time, the existence and local stability of the steady state. Using analytical approaches and the concept of corrected concentration, we have shown that the area under the curve ( $$\hbox {AUC}^{corr}_{ss,\tau }$$ AUC s s , τ corr ) at steady state is higher compared to that at the single dose ( $$\hbox {AUC}^{corr}_{0-\infty }$$ AUC 0 - ∞ corr ). Moreover, by splitting the dose and dosing interval into halves, we have revealed that it can result in a significant decrease in the steady-state average concentration. These model-based findings, which contrast with the current knowledge for linear PK, confirm the necessity to revisit drugs exhibiting nonlinear PK and to suggest a rational way of using mathematical analysis for the dosing regimen design.
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