PK/PD associates, experts in pharmacokinetic and pharmacodynamic training for students, industry professionals and other interested individuals. Hello, my name is. Nathan – sure from PK/PD associates and this is a practical guide to calculating a UC or area under the curve. The outline for this lecture will include a definition of a UC, the different flavors or forms of a UC and methods for calculating area Under the curve. A UC is the area under the concentration time curve and is a measure of the total systemic exposure of a drug over time it can be calculated from the concentration time data, however, it is not a primary PK parameter it is derived from clearance and dose, making it a secondary parameter. The AUC can be visualized as the area between the concentration time curve shown in red and the x-axi’s because AUC is a secondary peak, A parameter it can be calculated exactly from the primary PK parameters or it can be estimated using concentration time data, some common. AUC estimates include the exact day. You see, a UC 0 2 T or a UC 0 2 last AUC all and a UC 0 to infinity. Each of these estimates, described in part the total exposure of the drug. Let’s start with the exact calculation. We start with a relationship that AUC is equal to the integral of the concentration time curve from time 0 to infinity. Assuming IV administration, we can represent the concentration time curve with the equation dose over volume times, the exponential – clearance over volume times, the time, substituting this equation into the integral and pulling out the constants we arrive at dose over volume times, the integral of the exponential, This is a solvable integral and can be represented by 1 over the quantity clearance over volume. This then simplifies to dose over clearance as the area under the curve. This equation is very simple and very useful to know, but what do we do? If we don’t have an exact solution for the concentration time curve in this case, we use numerical estimation methods. The area under the curve can be estimated by a discrete set of blocks that we set up under the curve as you can see. Each rectangle represents an approximation of the area for that interval. Some approximations are better than others. These rectangles are equivalent to trapezoids, which extend linearly between concentration observations to then estimate the area under the curve. We follow a two-step process. We calculate the area of each trapezoid, and then we sum all trapezoids together to get the AUC to calculate the area of each trapezoid. We can use these equations. The area is equal to the average of the two concentrations times. The time interval this is called the linear trapezoidal method as you can see. The linear trapezoidal method does not always accurately capture the AUC. Thus, the logarithmic trapezoidal method was developed using a log linear average of the two concentrations times the time interval to estimate the area. Let’s look at a simple example of how to calculate AUC as you can see here in this. Excel spreadsheet. I have a column of data, which includes the time and then includes the concentration. I then take the sum of the two concentrations and then the time interval and then we can calculate the fractional area under the curve by summing by taking the sum dividing by two and then multiplying by the Delta T that gives us the linear AUC estimate for that interval from 0 to 1 hours. We can do that for each discrete interval. Then we can sum the intervals together to get a total area under the curve of 1257 point, seven, nine, three, three five that would represent the area under the curve, using the linear trapezoidal method of this peak. A concentration curve. We can also use a logarithmic method as Ill. Explain a little bit later. The logarithmic method is only effective when concentrations are decreasing so from the peak down to the end, we can use a logarithmic method from the zero point to the peak. We can only use the linear method in this one. We have the same. AUC the linear rate you see for the first four data points and then we use the logarithmic method for the remainder in that we subtract c2 from c1 And then we have the log of c1 minus the log of T c2 We divide the first number by the second number. Multiply it by the time interval to get the area of there. AUC for that interval again. Summing those together, we can get a total area under the curve of one thousand two hundred twenty-five point zero six, one five. If you’ll remember with the linear method, we got 1258 the logarithmic method. We have 1225 The linear method slightly overestimates the area under the curve, that’s why the logarithmic method is sometime used sometimes used for decreasing concentrations since there are two estimation and methods. It is often asked when to use each method. There are many complicated algorithms that have been developed to help. Answer this question! However, in my mind, it probably doesn’t make too much difference. These are estimates only so as long as you are consistent, The interpretation will not change very much The Office of Generic Drugs that the FDA prefers the linear method. So you should use it on all generic drug studies, the linear method should be used when concentrations are increasing over time or when they are decreasing in poly exponential fashion. Overall, the linear method is the most commonly used method. The logarithmic method is slightly more accurate when concentrations are declining in mono exponential fashion. This is because this method uses log-linear instead of linear interpolation in the calculation. This method is particularly accurate at the end of a curve when the time difference between data points is very large. Now that you know how to calculate. AUC, let’s review the definitions. AUC zero to T or AUC zero to last is the AUC calculated from time zero to the time of the last observed concentration measurement. All samples below the limit of quantitation at the end of the curve are ignored. A you see All is similar, but extends to the last sampling point, not just the last observed concentration. This means that terminal time points with measurements below the limit of quantitation must be replaced with another value. Common replacements are 0 and 1/2 the limit of quantitation finally. AUC zero to infinity is the sum of AUC 0 to T and AUC T to infinity, assuming constant clearance and low drug levels at the end of the concentration time curve, The AUC T to infinity is calculated as see last divided by the terminal elimination rate constant also, AUC 0 to infinity is also known as the exact AUC when the concentration time equation is known and solvable. In summary, AUC is a measure of total drug exposure and can be calculated exactly if we have the equation or it can be estimated from the concentration time data. We reviewed how to calculate AUC areas and then describe the different AUC values that are commonly requested in pharmaceutical development for more training videos. Please visit us at wwlpcom you.