Rachel Martin Displacement and Density

Introduction Animals are dosed by being given a specific volume of a test item (or control) formulation. Therefore, to ensure accurate dosing, formulations with a known w/v test item concentration (i.e. mg of test item per mL of formulation) need to be provided to the animal units. Two factors that can effect the accuracy of these formulations and that need to be considered when preparing them are: -Displacement -Density

Displacement Displacement occurs due to the amount of space or volume taken up by the solid test item and increases with concentration. At low concentrations, displacement will be minimal so it may not be necessary to take it into account when formulating. More of a problem at high concentrations due to large amount of solid test item and should be taken into account: -e.g. if you add 1 litre of a vehicle to 200 g of test item the final volume will be greater than 1 litre and thus the final test item concentration < 200 mg/mL.

Density Density is mass per unit volume. If solid does not cause displacement then there must be an increase in density. Increases with concentration. Where possible, Formulation Sciences prefer to utilise density to enable formulation by weight, rather than volume, as we consider this to be more : -accurate. -practical. Likewise, it is often preferable to add specific volumes of vehicles by weight too.

Accuracy Error on a balance likely to be less than that on a measuring cylinder (limited by the precision). Warping of measuring cylinder over time can effect accuracy. Human error! Foam/froth formation at the surface can make it difficult to see the meniscus when making up to the final volume. Introduction of air into the preparation can lead to expansion of the volume and therefore errors when making up to volume (resulting in a more concentrated formulation). Formulating by weight, removes the additional transfer step of having to go into a measuring cylinder and potential loss of test item.

Practicality Quicker – less steps. Uses less equipment (less washing-up!). Can be difficult to handle large measuring cylinders when formulating by volume. Can use less test item… -Loss of formulation on measuring cylinders. -Restricted by increments on measuring cylinders- may need to make more than required or use a syringe to add volumes that can’t be measured in the cylinder (adding another source of inaccuracy).

Formulating by Weight Need to know the density of the final preparations at the concentrations to be formulated. Or use an assumed density. -Can’t assume that it is 1 g/mL. Will often be >1g/mL but some vehicles <1 g/mL (e.g. oils). If density information is not available then we can formulate by volume on first occasion and measure density.

Measuring density We use a portable density meter from Anton Paar. Mainly utilised in this part of the world in the cider industry! Also measures temperature. Calibrate with distilled water at known temperature. Uses oscillating U-tube technique. Sample taken up allowing exact volume to enter the glass U-tube. Electronically excited to make it oscillate. Natural frequency of oscillation allows calculation of mass and thus, density.

Formulating by Weight Once have density, can use this information to prepare formulations for the rest of the study by weight. Will only apply the density factor if measured density is >1.01 g/mL (or <0.99 g/mL). If measured density is within that range then any error from not applying the factor will be ≤1 % which is deemed to be acceptable.

Some resistance from Study Directors They prefer to see x mg of test item made up to y ml with vehicle. Uncertainty about how and when to apply the correction for density. Don’t like the perceived inconsistency. -If you get good results from first prep formulating by volume why change? More complicated paper work. Unsure about using graphs of existing data for a compound to extrapolate or read density for concentrations not previously formulated.

QA comments: Have got comments from auditors who don’t under stand that ‘v/v’ is there to clarify the % concentration – not to give an indication of how something was prepared. For example: “Study plan states that vehicle is 20 % v/v propylene glycol in water. Vehicle preparation records show that g of propylene glycol was made up to 1 litre. Vehicle was prepared w/v. This is a deviation from the Study Plan”. The density of propylene glycol (1.036 g/mL) means that weighing 207.2g gives a volume of 200 mL. The final concentration is therefore 20 % v/v despite the fact that a balance was used to dispense the correct volume rather than a measuring cylinder.

Standardised approach agreed: Will formulate by weight if: -Have density data at all of the specific concentrations being formulated. OR -Have density data at a higher concentration than that being formulated that shows that application of a density factor is not required ( g/mL). HOWEVER, with some formulations in the past it has not been possible to accurately formulate by volume especially at high concentrations. If don’t have density data at that specific concentration then we would need to use an assumed density or displacement factor.

Aim: To assess at what concentration we should start to take displacement into consideration. NaCl Sucrose HPβCD DISPLACEMENT STUDIES

A range of nominal concentrations for each solid, between 2.5 and 50 mg/mL were prepared. For each concentration the required amount of solid was dissolved in 100 g purified water. Weight (g) Nominal Concentration (mg/mL) Solid UHP WaterTotal weight Table 1: A table to show the weight of solid (NaCl, sucrose and HPβCD), water and total weight of the components used to obtain the ten different solution concentrations. Procedure

Mean density (g/ mL) Concentration (mg/mL)NaClSucroseHPβCD Density results The density of each solution was measured and the mean density calculated (table 2). The results show that density increases with concentration. The mean density results were used to calculate the volume prepared and the displacement. Table 2: A table to show the mean density for NaCl, sucrose and HPβCD at each concentration.

Graph 1: Percentage Displacement For each chemical as the concentration increases the percentage displacement increases. HPbetaCD shows the greatest percentage displacement, followed by Sucrose and NaCl. At concentrations ≤ 15 mg/mL, 1 % or less displacement is seen and can be considered negligible.

Graph 2: Displacement Graph 2 shows the displacement for the three compounds; NaCl, Sucrose and HPβCD, with increasing concentrations. The mean displacement was calculated and is presented below for each solid (graph 3). Graph 3:

Density data review Graph 4: Density with increasing concentration of NaCl, Sucrose and HPβCD Wanted to assess if we could read or extrapolate density for concentrations not previously prepared by plotting density against test item concentration for existing data. Plotted data from 36 compounds with a suitable concentration range. Majority of the graphs showed linear trends. Graph 5: Example of a compound showing the linear trend.

Graph 6: Compound B showing aerated reading at 100 mg/mL.

Graph 7: Compound C - formulations showing aeration. Improvement was seen after the 200 mg/mL formulation was allowed to de-gas overnight.

Graph 8: Density against test item concentration for 21 compounds.

Graph 9: Density against solid concentration for 21 compounds.

Graph 10: graph to show the intercept point of the compound showing the smallest increase in density and HPβCD.

Conclusion At concentrations of ≤10 mg/mL displacement was found to be 1 % or less so may be considered negligible. At higher concentrations (>10 mg/mL) need to make up to the final required volume rather than just adding the final volume of vehicle. This can be done by formulating in approximately 80-90% of the final volume and then transferring to a measuring cylinder to make up to the final volume – or alternatively use a beaker pre-calibrated to the final volume. -Calibrate by weighing in 1 g of water per mL of required volume and marking the meniscus. Can problematic for solution as reduces the volume available to dissolve the test item.

Conclusion Can read or extrapolate density for new concentrations to be prepared from graphs of existing density data in the main -Some historical exceptions (mainly due to aerated samples). If difficulty preparing by volume, can use assumed density or assumed displacement factor (average 0.74 mL/g) based on data. Potential inaccuracy increases as the concentration increases.

Thanks Pavandip Lallie