In the context of drug discovery and pharmacokinetics, exponential accumulation and decay curve fitting is used to model how drug concentrations change over time within a biological system. This approach is essential for understanding drug absorption, distribution, metabolism, and elimination (ADME).
This particular curve fit aims to model both the accumulation (absorption) and decay (elimination) phases of an oral drug dose in a biological system. If you are interested in modeling exponential accumulation and decay data sets in a context other than pharmacokinetics, please see this article.
To implement the PK Oral Dosing: Exponential accumulation and decay curve fit, users can follow these steps:
- Creating readouts for input data such as timepoint and plasma concentration
- Creating a plot type readout to generate the curve fit
- Data calculations for different intercepts (optional)
- Editing and saving the curve
Let’s work through an example where we will implement this curve fit within our “Pharmacokinetics PO Dosing” protocol.
Create a numerical readout for the X-axis values:
Create a numerical readout for the Y-axis values:
Create a readout to plot the curve and calculate any optional intercept values:
Pro tip: Consider adding readout definitions marked as protocol conditions for parameters such as species and dose. This will allow users to automatically calculate outputs such as the AUC for each dose in each species as shown below. Additionally, consider implementing different tissue concentration readouts, such as plasma and brain, to automate calculations like brain to plasma ratio (AUCBrain/ AUCPlasma). In order to ensure data integrity, CDD recommends implementing species as a pick list data type and dose as a pick list if users commonly use the same doses or as a number if the dose will be highly variable across different runs.
Fit Parameters:
The PO Dosing: Exponential Accumulation and Decay curve fit is performed using the following equation.
Derived from the Bateman function, this model quantifies the time course of a first-order accumulation (rate constant K1 or Ka) to, and a first-order elimination (rate constant K2 or Ke) from, a one-compartment body model.
Where
Y= The drug concentration at time, t
C= The scaling constant related to the maximum amplitude of the process
Ka= The accumulation rate constant.
t= Time after administration
Ke= The elimination rate constant.
The accumulation (Ka) rate constant is the rate at which the plasma concentration of a drug increases during the absorption phase before reaching steady state expressed with units of time^-1 (hour^-1). The elimination rate constant, Ke, is the fraction of drug eliminated per unit time expressed with units of time^-1 (hour^-1).
The following parameters will automatically be calculated by CDD Vault for this plot type:
- C - amplitude
- Cmax - highest measured concentration after the absorption phase
- Cmin - lowest measured concentration after the elimination phase
- Ka - absorption phase rate constant
- Ke - elimination phase rate constant
- T½ - half-life (ln(2)/Ke)
- Tmax - time where Cmax is reached
- AUC - area under curve in observed interval (0, t)
- AUCt-inf - extrapolated AUC after last measurement (Cmin (1/Ke - 1/Ka))
- AUC0-inf - extrapolated total area under the curve (AUC + AUCt-inf)
- N - total number of data points used to perform the curve fit
- Maximum measured - Maximum extremal value of all measured responses
- Minimum measured - Minimum extremal value of all measured responses
- R-squared - quality of fit
Given the biphasic nature of this curve type (accumulation and decay phases) it is important to note that two half lives can be calculated, one for each phase.
Half life is calculated by T ½ = ln(2)/k where k is either the accumulation rate constant or the elimination rate constant. In this case, our calculated output uses Ke to calculate the half life.
T ½ = ln(2)/ Ke
This is a commonly employed method as the accumulation phase is typically quite rapid (e.g., absorption through the gastrointestinal tract) while the elimination phase is comparatively quite long meaning the concentration-time course of the drug is dominated by the elimination phase.
If users have a data set where the accumulation phase is significantly longer than the decay phase (i.e., slow absorption and rapid elimination), this is known as flip flop kinetics. It will be important to define a custom half life calculation using Ka instead of Ke:
T/12 flip flop= ln(2)/ Ka
Area under the curve
- The CDD Vault AUC is calculated as the (positive area - negative area) under the dose response curve where:
- The curve is defined as straight line connections between responses, not the fitted curve (Linear Trapezoidal Non-uniform grid method)
- Units are (response units * dose units)
- The baseline is set at the negative control mean or 0 if control data is not available
Suggested additional calculations:
Please note that all auto-calculated parameters listed above can be used in custom calculations as separate readouts. These parameters can be accessed within our robust formula editor.
- Different tissues: i.e., brain to plasma ratio: AUC brain/ AUC plasma
- Clearance= Ke * Volume of distribution
- Volume of distribution = Dose/ C0
- Absolute bioavailability= 100*((AUCPO*DoseIV)/(AUCIV*DosePO))