Mathematical model for evaluating bicarbonate and lactate kinetics in metformin-associated lactic acidosis

The Michaelis–Menten equation is a fundamental model for describing capacity-limited kinetics in drug metabolism. It offers insights into the rate of decline of plasma drug concentration Cp over time, with Vmax and KM as pivotal parameters.
Vmax represents the maximum achievable process rate, while KM, known as the Michaelis constant, signifies the drug concentration at which the process rate reaches half its maximum. This relationship between Vmax, KM, and Cp gives rise to three distinct...

The one-compartment open model is a simplified approach used in pharmacokinetics to understand the distribution and elimination of a drug administered through an intravenous bolus. This model assumes rapid drug dispersal throughout the body and elimination using a first-order process. Key pharmacokinetic parameters, such as the elimination rate constant (k), half-life (t1/2), and the apparent volume of distribution (Vd), can be estimated from this model. The elimination rate is calculated...

Physiological and compartmental models are valuable tools used in studying biological systems. These models rely on differential equations to maintain mass balance within the system, ensuring an accurate representation of the dynamic processes at play.
Physiological models take a detailed approach by considering specific molecular processes. They can predict drug distribution, metabolism, and elimination changes, providing a comprehensive understanding of how drugs interact with the body.

The Michaelis constant (KM) and the theoretical maximum process rate (Vmax) are vital parameters in the Michaelis-Menten equation, central to many biochemical reactions. They provide essential insights into enzyme kinetics and drug metabolism.
These parameters can be estimated by analyzing plasma concentration data post-drug administration. A notable example of this application is phenytoin, a drug with capacity-limited kinetics. It's recommended that phenytoin should be administered at two...

The fundamental mathematical principles, such as calculus and graphs, play crucial roles in analyzing drug movement and determining pharmacokinetic parameters. Differential calculus examines rates of change and helps to determine the dissolution rate of drugs in biofluids, as well as how drug concentrations change over time. For instance, it can help calculate the rate of elimination of a drug from the body based on its concentration-time profile.
On the other hand, integral calculus focuses on...

The two-compartment model for intravenous (IV) bolus administration illustrates drug distribution in the body, subdividing it into central and peripheral compartments. This model operates on the concept of two-compartment kinetics. The drug's plasma concentration shows a bi-exponential decline following IV bolus administration, signaling the presence of two disposition processes: distribution and elimination.
The disparity between drug input and the sum of drug transfer rates between...