Designing a 3D Representation of Drug Efficacy

The purpose behind this project was to potentially create a simple graph that could be used by both consumers and physicians and would inform the consumer or physician on the medication’s effectiveness depending on the dose and duration of time since the ingestion of the dose. Since there are multiple variables of the human body that could affect the effectiveness of the drug, the graphical representation must also contain multiple variables that represent conditions of the human body that can alter the effect of the medication. To simplify this system, we only used equations that calculate for plasma concentration, dose response, and dose toxicity. To combine these equations and find the effect of the prescribed drug dosage, we multiplied the plasma concentration equation and the dose toxicity equations.

This project also used 3D modeling in Mathematica and the subsequent contour graphs to represent the results of changing drug dosage. The x-axis represents time that has passed since the dosage and the y-axis represents the dosage of the drug given. The resulting z-value represents the quality of the drug’s impact on the patient based on plasma concentration and therapeutic or toxic effects. The final graph can be considered more conceptual and more qualitative in nature, rather than completely quantitative. This qualitative characteristic means that the resulting z-value in the 3D and contour graphs represents whether the drug dosage has a negative or positive effect on the patient’s condition over time.