*Assessment of the effective sample size is important for some applications (e.g., blend uniformity analysis). The effective sample size during NIR measurements can be evaluated from the diameter of the NIR beam, its depth of penetration, and the density of material. The effective sample size is generally small because the NIR beam illuminates a small sample volume illuminated by the NIR beam. For blend uniformity analysis, the effective sample size should be comparable to a unit dose.*

The question now remains, how do I calculate the effective sample size given the above information?

This requires some background work on behalf of the company implementing the NIR system before method development is considered. In particular, to establish the instantaneous sampling size, this requires the following information to be taken into account,

- Blending/mixing,

a.The rotation speed of the blending equipment (for tumble blenders utilizing anymixing vessel configuration).

b.The speed of the powder flow across the sampling window for applications such ascontinuous blending. - The nature of powder flow of the product being monitored, i.e. cascade, rolling, cataracting,etc.
- The bulk density of the final blend composition when uniformity is deemed to be reached.

From this information, the effective scanning time can be calculated to achieve a unit (or near unit) dose measurement.

The information in this document is specific to the MicroNIR^{TM} range of sensors and is applicable to both moving powder streams (as found in continuous manufacturing operations) or for measuring samples from rotating blending equipment.

**Rotating Blending Equipment**

By far, the most common application of NIR for blending is its use in tumble blenders, particularly with the development of WIFI enabled instruments such as MicroNIR^{TM} PAT-W, which allows an easy, non-contact situation for sample measurement.

**Note:** The effective use of NIR for blend monitoring requires that the process meets the essential requirement that there are no dead spots produced in the process, otherwise, there is no point in measuring blend uniformity.

The blending equipment is usually optimized to a set rotation speed based on the flow characteristics of the powder blend, established during product and process development (see next section for details). At this speed, the effective sampling zone can then be established as follows.

*Blender Rotation Speed*

Typical blender rotation speeds are in the range of 10-20 rpm. This means that the blenders will make one rotation every 3-6 seconds depending of the speed chosen. Taking 15 rpm as an example, one rotation will occur 4 seconds. Breaking the rotations down into 4 quadrants, a quarter rotation will take 1 second.

The MicroNIR^{TM} PAT-W activates via an accelerometer at the 3 o’clock position (assuming clockwise rotation) and becomes inactive at the 9 o’clock position. This is shown diagrammatically in figure 1.

**Figure 1: Switching modes and scanning positions of the MicroNIR ^{TM} PAT-W spectrometer when used on a tumble blender.**

The delay time is a user set parameter which is dependent on,

- The flow and density characteristics of the powder blend.
- The rotation speed of the blender.

The setting of the delay time will be addressed after a discussion of the flow properties of the blend has been provided.

*Powder Flow Characteristics*

Unmixed and blended powders have different flow characteristics. In a rotating blender, techniques such as avalanche flow testers can be used to assess the angle of repose (a measure of the maximum angle to the horizontal before the powder starts to slump). In practice, this relates to the angle that the blender makes with the horizontal (3 o’clock position) and starts to flow over sampling window where the MicroNIR^{TM} PAT-W is located.

Figure 2 shows the two main angles that have to be calculated in order to set the point where to start scanning and when to stop scanning for a unit dose.

**Figure 2: Zones of measurement in a rotating blender configuration.**

The angle of repose is a measure of the powder blends flowability. It must be remembered that is in a dynamically changing property as the blend becomes less heterogeneous. The angle of repose can be determined using various systems utilized by the pharmaceutical industry, however a versatile instrument is an avalanche flow system. Not only can the angle of repose be determined from this system, but also the mode of powder flow can be determined. Figure 3 shows some diagrams of powder flow characteristics as determined by an avalanche system.

**Figure 3: Some typical powder flow characteristics as determined by an avalanche flow system.**

Out of the three mechanisms above, cascading flow is the most desirable as it results in the top of the powder peak folding over itself where most of the mixing is performed. Rolling flow may not be effective and cataracting may be too harsh on the blend.

In all cases, the nature of the flow and its angle are important for determining the angle (α in figure 2 as this determines the point where the sampling window of the MicroNIR^{TM} PAT-W is first covered. Referring back to the US FDA NIR guidance document, the following point is made.

*For on-line blending or mixing, a description of the system used to trigger spectral acquisition that ensures the interface window remains covered by the blend throughout the acquisition.*

To further ensure that the right angle (α is chosen, in a small pilot scale blender, or a clear (see through container), rotate the powder blend slowly to view the point at which the blend will cover the sampling window. If there is enough rotational control in the blend equipment, this can be viewed through the sampling port with the PAT-W sensor removed from the interface.

**Note:** This angle must be verified at the beginning of the blend, when segregation is maximum and at the end, when the blend is least heterogeneous.

We can now return to how the delay time is calculated to match the point where the sampling window is covered.

*Delay Time*

With knowledge of the blender rotation speed and the angle (α) the delay time can be calculated. This will be done by example using the rotation speed of 15 rpm and an angle (α) of 30° to the 3 o’clock plan.

At 15 rpm, the blender will traverse from 3 o’clock to 6 o’clock (i.e. 90°) in 1 second.

The time it takes to traverse 30° is

Therefore, the delay time (??????) is 0.33 seconds or 333 ms.

This approach can be applied to any rotation speed and angle of repose situation. The next step is to define the effective scanning arc for spectral collection.

*Scanning Time*

It is safe to assume that the angle of repose for setting the delay time is also the angle where the powder will also start to move off the sampling window. From the arc between 3 o’clock to 9 o’clock, the blender will travel through 180°. Using the example of 15 rpm and 30° angle of repose, the effective scanning arc (ß) is 120°

From differences, if it takes 2 seconds to traverse 180° and it takes 0.33 seconds to traverse 30° then the effective scan time in the 120° arc is ?????=2−2×0.33=1.33 seconds or 1333 ms.

*Powder Bulk Density*

The final consideration to be made before the effective sample volume can be calculated is the bulk density of the blended material. Bulk and tapped density are typical parameters calculated during product development and can be found in the regulatory submission documentation for the product. The bulk density is related to the depth of penetration (??) of the material under investigation.

Taking a number of end of run blends by means of a representative sampling protocol (i.e. not by a sample thief), a range of bulk densities should be determined for the product being investigated. From there, the depth of penetration can be calculated using a number of methods, including the layering of powder blend at different thicknesses in a NIR transparent glass vial and placing a material of known absorbance characteristics on top of that powder. Using principal component analysis (PCA), the point at which the known material cannot be seen in the powder blend determines the depth of penetration.

From a practical standpoint

- ?? is defined as the depth where the light intensity decays to 1/e (37%) of its original value.
- ?? relies on material absorption, packing density, as defined above.

Figure 4 shows the measurement of absorption of a powder material (density = 0.6 g/mm3) as a function of sample depth. In this case, ?? is estimated ~ 0.2 mm

**Figure 4: Plot of relative light intensity vs. depth of penetration (??)**

**Calculation of Sample Volume Measured**

Now that all of the necessary parameters for reliable spectra have been established for a rotating blender, this section describes how the effective sample volume and corresponding mass is calculated for both rotating blenders and powders flowing through pipes.

*Rotating Blender Sample Mass*

This calculation assumes that in the effective sampling arc the powder sample is stationary. Using the 15 rpm example, the arc can be measured for 1.33 seconds. If the integration time (????) has been optimized at 10 ms, then the number of averaged scans can be set to 133 (this would typically be set to 100 for convenience).

The MicroNIR^{TM} PAT-W (or PAT-U) has an effective sampling area of 10 mm. From there, the effective sampling volume measured by the sensor is,

This is the volume of a cylinder where ? is the diameter of the MicroNIR^{TM} PAT-W spot size and ?? is the depth of penetration. The mass of the sample measured under the optimized scanning conditions is given by,

Where ? is the instantaneous mass measured given the bulk density of the powder (?). It is then up to the organization implementing the MicroNIR^{TM} PAT unit to determine if the unit dose calculation is based on volume or mass.

*Moving Powder Mass Calculation*

The principles of the volume/mass calculations for the rotating blender situation also hold for the powder flowing through a pipe situation, except that the sample is now dynamic and the scan time must be adjusted to meet the requirements of unit dose. This situation is shown in figure 5.

**Figure 5: Using MicroNIR ^{TM} PAT to measure spectra of powder moving through a pipe.**

The powder moves through the pipe at a velocity (?), therefore the amount of powder passing across the sampling window is given by,

Where ? is the length of material that has passed by the sampling window and ?? is the scanning speed of the PAT sensor at its optimized ????. During the scanning period, the area of sample scanned is calculated as,

This calculation takes into account the circular area of the beam spot and the rectangular area traversed by the powder during the scanning period. From there, the volume of powder measured can be calculated from,

Where ?? is the volume scanned from the moving powder bed. The mass of sample scanned in this volume is calculated from,