Некомпартментный анализ: статистическая теория моментов

Mean residence time (MRT) describes the average time drug molecules stay in the body. It represents a pivotal parameter that considers the individual movement of molecules within a system based on residence-time considerations. MRT is calculated using the moment curve obtained by integrating a probability density function of the drug multiplied by time, providing insights into drug absorption, distribution, metabolism, and elimination.

Statistical moment theory is a mathematical approach that describes the time course of drug concentration without assuming a specific compartmental model. It treats drug concentration versus time data as a statistical distribution of molecules in time. This model-independent method reveals distribution characteristics by examining how drug molecules move in and out of the system over time.

The zero moment corresponds to the area under the curve (AUC), a fundamental parameter in pharmacokinetic analysis. When the mth moment is substituted into the moment curve equation with m equals zero, it yields the total area under the concentration-time curve, representing the total drug exposure in the body.

The first moment defines the mean of the distribution through the area under the first moment curve, indicating the central tendency of drug residence times. The second moment characterizes the variance of the distribution, measuring the spread or dispersion of drug molecules' residence times around the mean value.

Higher moments beyond the second moment represent skewness and kurtosis of the drug distribution. Skewness describes the asymmetry of the distribution, while kurtosis measures the tailedness or peakedness. These parameters provide deeper insights into the shape and characteristics of how drug molecules are distributed temporally within the biological system.

Noncompartmental analysis does not assume a specific compartmental model structure, making it model-independent. Instead, it leverages statistical moment theory to examine macroscopic events and time-related changes directly from concentration-time data. This approach encapsulates collective outcomes from constituent elements without requiring predefined assumptions about how the body is divided into compartments.

The moment curve is obtained by integrating a probability density function of the drug multiplied by time. This mathematical integration yields the mth moment, which can be substituted with different values to generate various moment curves. Each resulting curve reveals specific distribution characteristics, facilitating a deeper understanding of the drug's temporal dynamics and behavior within the biological system.