## IVIVC – Convolution/Deconvolution Techniques

A plasma drug concentration-time profile is usually the net effect of two simultaneous processes: (1) absorption of the drug from the GI tract. As absorption is proportional to drug dissolution thus absorption and dissolution are used interchangeably; (2) elimination of the drug from the blood. These two actions, and their net effect, are represented by three profiles and are shown in the figure. In mathematical terminology, these three curves (profiles) are known as functions, dissolution or absorption as input, blood concentrations as output and the elimination as the weighting factor or function. To further simplify, in the analogy of linear regression used for calibration curves, output function may be considered as “Y or dependent variable”, “X or input function” and “M or slope/proportionality constant”. In case of linear regression analysis X, Y and M parameters have values (numbers), however, in the case of drug concentration profiles, these are functions. So solving these function based equations is a bit more complicated.

The procedure is similar to that of linear regression which is commonly used in establishing calibration curves and then using the calibration curve to determine the unknown concentrations or response (e.g. absorption or peak height/area values). So, if “Y” is known then “X” may be determined and vice versa. Similarly, if input function is known, one can determine output function and vice versa. Determining output function (plasma blood concentrations), if input function (dissolution results) is available, the procedure will be called **convolution **technique and inverse of it, that is obtaining input function (absorption/dissolution results) if output function is provided, the procedure will be called **deconvolution**.

There are computer software available which provide the capability of solving for a function when the others are available. However, the convolution approach could be simpler where use of commonly available spreadsheet software may also be used. For further detail see, Qureshi, SA. In Vitro-In Vivo Correlation (IVIVC) and Determining Drug Concentrations in Blood from Dissolution Testing – A Simple and Practical Approach. The Open Drug Delivery Journal, 2010, 4, 38-47. (Link)