累积：含义和计算方法

Drug accumulation occurs when a drug is administered repeatedly before the body has fully eliminated the previous dose. Over time, this leads to higher drug levels in the body until a steady-state is reached.

Drug accumulation refers to the relationship between the dosing interval and the drug’s rate of elimination. If the drug is given at longer intervals, little to no accumulation occurs. Conversely, if the drug is given at intervals shorter than its elimination time, it builds up in the body. In other words, adjusting the dosing interval directly impacts the degree of accumulation.

It’s important to note that accumulation itself is neither inherently “good” nor “bad”—it is a natural consequence of repeated dosing and the pharmacokinetics of the drug. The key concern is whether the accumulated drug levels lead to therapeutic benefits or unwanted toxicity. If excessive accumulation leads to toxicity, extending the dosing interval can help reduce drug levels and mitigate adverse effects.

Picture of a bathtub with a partially open drain. If you pour water into the tub slowly, the drain can keep up, and the water level remains low. However, if you pour water in faster than the drain can remove it, the water level will start to rise—this represents accumulation.

Over time, if you keep pouring water at a constant rate, the water level will stabilize at a point where the amount going in matches the amount draining out—this is the steady-state. But if you increase the rate of water input beyond what the drain can handle, the tub will eventually overflow, similar to how excessive drug accumulation can lead to toxicity.

The accumulation ratio (AR) quantifies how much higher drug concentrations are at steady-state compared to after a single dose. It reflects the balance between drug dosing frequency and rate of elimination for the drug.

In practical terms, AR helps predict drug levels at steady-state and assess whether adjustments to the dosing regimen are needed to optimize efficacy while minimizing toxicity.

The accumulation ratio can be calculated from observed data. All of these methods give reasonable estimates but have slightly different drawbacks. The first method is to use the dosing interval and elimination rate constant and the following equation to calculate the accumulation ratio (AR):

This method requires the terminal elimination rate constant (k), which can be derived from clearance and volume, terminal half-life, or the terminal slope of the concentration-time profile. The dosing interval (τ) is the time between doses (e.g., 24 hours for once-daily dosing). Ensure k and τ have the same units before calculation.

This equation assumes first-order elimination and estimates the proportion of drug eliminated per dosing interval. Its key advantage is flexibility—you can quickly predict accumulation ratios for various dosing regimens by adjusting τ (e.g., once-, twice-, or thrice-daily dosing). However, its accuracy depends on the reliability of k; poor estimates lead to biased accumulation predictions.

The second method is to use observed data from a study where you have measurements after a single dose and at steady-state, using one of the following equations:

All of these equations share a common approach: they calculate the ratio of an exposure parameter at steady-state to the same parameter after a single dose. The underlying assumption is that once steady-state is reached, no further accumulation occurs. At that point, the ratio of any exposure measure at steady-state will be proportional to its corresponding single-dose value, reflecting the accumulation ratio.

One advantage of this method is its simplicity—it can be directly calculated from observed data. For example, by measuring a partial AUC over the dosing interval on Day 1 and comparing it to AUCτ on Day 28 in a toxicokinetic study, the accumulation ratio can be determined. Additionally, multiple exposure metrics can be used to validate the calculations.

However, there are some limitations. If pharmacokinetic (PK) parameters vary significantly, different measures of accumulation may yield inconsistent results. For instance, Cmax at steady-state might be poorly estimated if tmax is delayed and the sampling schedule does not adequately capture the new peak concentration.

Another challenge is the assumption that steady-state has been achieved, often without independent confirmation from multiple steady-state measurements. Despite these drawbacks, this method remains a practical and efficient way to estimate accumulation ratio using observed data.

Combining these two approaches to calculating accumulation ratio allows pharmacokineticists to use observational data for prediction. The accuracy of the elimination rate constant (k) can be assessed by comparing AR values from both methods—if they align, k is likely accurate.

When k cannot be directly calculated (e.g., t1/2 >6 hours, τ=24 hours), method 2 (AUC or Cmax) can estimate AR, which can then be used in method 1’s equation to solve for k. Method 1 also enables AR calculations for different dosing intervals, which can then predict steady-state exposure parameters (AUC, Cmax, Ctrough) using method 2.

In summary, the accumulation ratio provides a simple but valuable link between dosing interval and elimination rate. While often associated with toxicity, accumulation simply reflects the balance between drug input and elimination over time—a relationship that can be controlled by adjusting dosing frequency.

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