VIBRATION: What Is It and How Might It Affect Dissolution Testing?

Charles C. Collins, Ph.D., Duquesne University, Pittsburgh, PA

INTRODUCTION

There is no mention in the USP of vibration requirements, except for the statement "No part of the assembly, including the environment in which the assembly is placed, contributes significant motion, agitation, or vibration beyond that due to the smoothly rotating stirring element." (1) Vibration is a complicated concept that can result in the addition of energy to a system. The addition of energy from an external source can alter the results of a dissolution evaluation. Such an alteration is an unacceptable source of error that must be minimized. It can be minimized by eliminating all external sources so that only the tester machinery is left as a potential vibration source that is external to the drug delivery system under evaluation.

WHAT IS VIBRATION?

According to Webster's New Collegiate Dic-tionary (2), vibration is defined as "a periodic motion of the particles of an elastic body or medium in alternately opposite directions from the position of equilibrium when that equilibrium has been disturbed". Concerning dissolution, the body is the components of the dissolution tester. The energy (vibration) causing this movement is an interrelated function involving acceleration, velocity, displacement, and frequency (which can occur in three dimensions and can be designated z, x, and y). For the purpose of this discussion, a frame of reference must be established. Using the vessel plate as a starting point, the x axis will begin at the front left edge and go toward the back of the plate. This leaves the left to right vector as the y axis and the up and down vector as the z axis. (See Figure 1.) From the available research, the more important of these vectors has been the z axis [i.e. up and down]. Most current research has concentrated on the up and down (z axis) plane, and the value most reported is displacement. The units used for displacement are mil, which is an English unit that corresponds to 0.001 inch.

Figure 1.

Figure 1. Illustration of the frame of reference for the x, y, and z axis relative to a dissolution vessel plate.

However, as stated above, vibration consists of four interrelated measurements. These are mathematically described based upon sinusoidal vibrations and using the equations for uniform circular motion. Equation 1 relates velocity {V}, the radius of the circle {r} (which corresponds to the amplitude {A}of a sinusoidal wave), and the inverse of the period of the sine wave {T} (which corresponds to the frequency {f}). Making these substitutions yields equation 2.

V/r = (2) / T ( E q . 1 )

V = 2 A f ( E q . 2 )

The displacment {D} is defined as the total distance moved relative to a reference point, which in this case would be for a sine wave from the positive peak above the eqilibrium plane to the negative peak below the equilibrium plane. Each of these distances was previously defined as the radius of the circle, or the amplitude {A}. Thus the displacement is equal to the sum of these amplitudes, or in this instance double the amplitude since each value is the same, as given in equation 3.

D = 2 A (Eq. 3)

Combining Eq. 2 and Eq. 3 yields Eq. 4.

V = f D (Eq .4)

Acceleration {a} is also a measured factor. In fact most meters that measure vibration contain an accelerometer, which generates an electrical signal proportional to acceleration. (4-6) This measured value is used to determine the other parameters. According to the physics of a sine wave (3), acceleration is defined by Eq.5.

a = 4 2 A f2 (Eq.5 )

Rearrangement yields equation 6. Combining this with Eq.2 results in equation 7.

a = (2 A f ) (2 f ) (Eq .6)

a = ( V ) (2 f ) (Eq. 7)

To solve Eq. 7 for V yields equation 8.

V = 1/( 2 ) (a/f) (Eq. 8)

To simplify Eq. 8, all constants have been gathered, including a conversion of the acceleration units. Common vibration meters display acceleration in units of gravities (g), which allows easier conversion between metric and common (English unit) values of velocity and displacement. If the displacement is measured in inches and the velocity in inches per second, acceleration needs to be converted to gravity units, which requires multiplication by 386.0886 inch/sec2/g. The collection of constant values now include this conversion value, and result in equation 9.

V = 61.45 (a/f) (Eq. 9)

Acceleration can be described in terms of displacement and frequency. Starting with equation 5, and gathering the constants and conversion factor (inch/sec2 to g) yields equation 10.

a = 0.0511 D f 2 (Eq. 10)

Acceleration can also be described in terms of velocity and frequency. Starting again with equation 5, including equation 4, and gathering the constants and conversion factor (inch/sec2 to g) yields equation 11.

a = 0.01627 V f (Eq. 11)

Frequency can be estimated based upon a rearrangement of equation 1.

f = V/(D ) ( Eq . 12)

As a measure of vibration, displacement is often reported, since it is this relative motion that can be sensed by placing a hand on the tester. This is a measure of the up and down (in the z axis) motion of the item of interest, in this instance a dissolution tester. How often this up and down motion occurs is of equal importance, and this is the frequency. To measure one without the other does not provide sufficient information concerning the overall vibration. Vibrations of the same displacement but with differing frequency would not input the same amount of energy into a system over a given period of time.

DISCUSSION

Reports of the adverse effects of vibration have appeared in the literature as early as 1971, when Beyer and Smith (7) reported a sixfold increase in the dissolution rate of tolbutamide tablets using a basket method. This increase was observed when the measured displacement was increased from 0.05 mil to 0.8 mil. However, the frequency of this displacement was not reported. Hanson (8) reported a similar effect for salicylic acid calibrators in apparatus 1, and recommended that the horizontal displacement should be kept below 0.1 mil when the frequency is in the range of 50 to 60 Hz.

Utilizing two meters (Columbia Research Labs, Inc., Vibration meter model VM-103 and a VanKel Technology Group QA II), the readings found in table 1 were recorded for the vessel plate of a VK 7010 dissolution tester under normal operation. Normal operation consists of paddles (at either 50 or 100 rpm as listed in table 1) with six vessels each containing 900 mL water, with the heater circulator operating at a set water bath temperature of 37.3°C. The heater/circulator was positioned behind the tester and partially under the back of the vessel plate, but not touching the water bath or the frame of the tester. It can be noted that these meters are in general agreement. Differences occur for the lower values, since the Columbia meter has an analog dial with an accuracy of ± 5% (4) for frequencies between 15 and 1000 Hz. The lowest setting is for 1 mil, full scale, divided into tenths, and each of these subdivided into 0.02 units. The QA II unit has a reported accuracy of ± 1% (5) for displacement readings between 0 and 20 mil for frequencies between 0.5 and 120 Hz. The accuracy changes to ± 5% for the same displacement range if the frequency is between 120 and 200 Hz.

Table 1.

Table 1. Vibration measurements for dissolution vessel plate. (#) Columbia meter does not measure frequency-manual suggests calculation using equation 12 (*) best estimate, no divisions below 0.02 on meter dial.

CONCLUSION

In this limited study, each of the displacement readings is below 0.05 mil in a frequency range of 50 to 100 Hz. This is well below the guidelines suggested by Hanson (8). Further studies need to be conducted, including dissolution tests during which an external vibration of specific magnitude is applied. If you are interested in participating in such a study, please contact the author for further information. It is hoped that such a collaborative study can positively contribute to the establishment of more definitive vibration requirements.

Note: A PhRMA Dissolution subcommittee on Mechanical Calibration is currently conducting studies that includes measuring the effects of vibrations. This subcommittee is evaluating the proposed displacement limit of less than or equal to 0.2 mil.

REFERENCES

1. USP 23/NF 18, United States Pharmacopeial Convention, Rockville, MD, Eighth Supplement, page 4323.

2. Woolf, H. B., Editor in Chief, Websterís New Collegiate Dictionary, G. & C. Merriam Co., page 1294, 1981

3. Weast, R. C. and Lide, D. R., CRC handbook of Chemistry and Physics, pages F-129, F-130, 1989

4. Instruction Manual for VM-103 Vibration Meter, Columbia Research Laboratories, Inc., Woodlyn, PA, page ii, 1 , 5, current edition.

5. Dissolution QA II Testing Station Operator's Manual & Reference (Revision 3), VanKel Technology Group, Cary, NC, pages 18,19, July 1998.

6. Practical Solutions Volume Three (1), VanKel Technology Group, Cary, NC, pages 2 and 5, 1997.

7. Beyer, W. and D. Smith, "Unexpected Variable in the USP/NF Rotating Basket Dissolution Rate Test", J. Pharm. Sci., 60, 496-497, 1971.

8. Hanson, W. A., handbook of Dissolution Testing, (Second Edition, Revised), Aster Publishing Corporation, Eugene, Oregon, pages 74-76, 1991.