Strandquist's graphs and the new mathematical formula for cumulative biological effect

Constrained by limited energy and resources, organisms must compromise between offspring quantity and parental investment. This trade-off is represented by two primary reproductive strategies; K-strategists produce few offspring but provide substantial parental support, whereas r-strategists produce much progeny that receives little care. These strategies are related to an organism’s survival likelihood across its lifespan, which is represented by a survivorship curve. Three general types of...

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...

Biopharmaceutical studies constitute a vital field aiming to enhance drug delivery methods and refine therapeutic approaches, drawing upon diverse interdisciplinary knowledge. In research methodologies, the choice between controlled and non-controlled studies significantly influences the study's reliability and accuracy.
Non-controlled studies, commonly employed for initial exploration, lack a control group, rendering them susceptible to biases and external influences. In contrast, controlled...

The linear concentration–effect model, underpinned by the principle that pharmacological effect (E) is directly proportional to plasma drug concentration (C), emerges as a pivotal simplification of the Emax model for conditions where C is significantly less than EC50. This model portrays a linear trajectory of the concentration–effect relationship when drug levels are markedly below the EC50 threshold.Despite its inherent assumption of continuous effect augmentation with increasing drug...

The correlation between a drug's dosage and its impact on a biological system is a cornerstone of pharmacology and toxicology. Conventional dose–response curves, which include graded and quantal relationships, are key to this understanding. Graded dose–response curves depict the spectrum of a biological reaction to different doses within an individual, indicating that as the drug dosage increases, so does the intensity of the response. On the other hand, quantal dose–response relationships...

Survival curves are graphical representations that depict the survival experience of a population over time, offering an intuitive way to track the proportion of individuals who remain event-free at each time point. These curves are widely used in fields such as medicine, public health, and reliability engineering to visualize and compare survival probabilities across different groups or conditions.
The Kaplan-Meier estimator is the most common method for constructing survival curves. This...