1. Part 3: Metrology & Pharmaceutical Calculations
References:
1- Remington 2006, Chapter 11, Meterology & Pharmaceutical Calculations.
2- Ansel H.C., Mitchell J.S., 11th Edt., Pharmaceutical Calculations, 2001

2. Roman numbers ss = 1/2 I or i = 1 II or ii = 2 V or v = 5 X or x = 10
L or l = C or c = 100
D or d = M or m = 1000
LX = XL = 40

3. 2- Avoirdupois system
The basic unit of weight in the avoirdupois system is the grain (gr). The larger units are the ounce (oz) and the pound (lb).

4. WEIGHT: AVOIRDUPOIS SYSTEM
a. You must know the following relationships between the avoirdupois units:
1 lb = 16 oz =7000 gr
b. To convert from the avoirdupois system to the metric system, you must know these conversion factors:
1 kg = 2.2 lb
1 lb = 454 g

5. 3- Apothecary system Apothecary weight units 1 pound (lb) = 12 oz
1 pound (lb) = 5760 grain = 373 g
1 oz Apot = 31.1 g
The units of volume in the apothecary system are Minim, fluid dram (fζ), fluid ounce (fξ), pint (pt), quart (qt), and gallon (gal).

6. VOLUME: APOTHECARY SYSTEM
Know the following relationships between apothecary units:
1 gal = 4 qt
1 qt = 2 pt
1 pt = 128 fζ (fl dram)
1 fl dram = 60 minim
To convert from the apothecary system to the metric system, you must know the following factors:
1 gal = 3785 ml

7. Length Uinits Inch Foot 1ft = 12 inch =30 cm 1ft = 0.30480m

8. Length units
1 meter
39.37 inch
1 inch
2.54 cm
1 foot
0.305 m

9. Different Kinds of Balances
Single-beam equal arm balance
Unequal arm balances
Preferred in laboratory works when large amounts are to be weighed
Electronic Balances
Single pan balances, much more sensitive than the traditional ones, easier & quicker to use, but usually more expensive.

10. Single-beam equal arm balance

11. Different Kinds of Balances
Single-beam equal arm balance
Unequal arm balances
Preferred in laboratory works when large amounts are to be weighed
Electronic Balances
Single pan balances, much more sensitive than the traditional ones, easier & quicker to use, but usually more expensive.

12. Unequal arm balances

13. Prescription Balance

14. Electronic Balances

15. NIST (National Institute of Standards and Technology)
Weight & Measure Division:
Discuss about the specifications and standards used primarily in weights and measures and commercial applications.

16. Sensitivity (readability) of a balance:
Minimum weight that causes the indicator of balance change one unit.
If addition of 6mg weight to balance causes one unit movement of indicator , sensitivity of balance is 6mg.
Class 3 balances:
Minimum sensitivity 6mg up to 60g.
Electronic divices have usually a sensitivity less than 10mg.

17. Accuracy of a balance
if a known calibration standard weight of grams was placed on a balance and the display shows grams we could say the accuracy of the balance is grams or 2 milligrams. 
Accuracy tells how close a balance gets to the real value. 

18. Different terms related to balances
Capacity (maximum weight can be weight by balance)
Readability minimum weight can be weight by the balance
Repeatability ( variation in different measurements of one object)
Are usually mentioned by the manufacturer for electronic devices.
E.g. Capacity 60g, readability 6mg, repeatability ±1mg

19. Protection & Maintenance of a Balance
Position chosen for balance should be flat.
Should be far from dampness, dust & corrosive vapor
Analytical balances are kept in glass cases.
Some balances can be locked & protect from vibration when they are not in use.
Should be cleaned just by a clean clothe.
Should be checked & calibrated periodically.

20. Protection & Maintenance of a Balance
For compounding, accurate sets of weights from 10mg to 10g should be kept precisely in a closed box.
For analytical purposes, weights from 1mg to 100g should be available.
The weight should not be handled by finger.

21. Torsion Prescription Balance

23. Checking a balance periodically
Calibration:
Weighing a standard mass on balance to see how much it is different from the real weight.
It tells us accuracy (how much the balance work accurate).

24. Periodically checking of a prescription balance
Sensitivity requirement
Arm Ratio test
Shift test

25. Minimum Weighable Quantity (MWQ)
The USP allows a maximum error of 5% in a single weighing operation
The percent of the error depend on the amount of drug weighed & sensitivity of balance according to the formula below:
The percent of error will increase as the amount of drug decreases

26. Examples

27. Percent of Error

28. Aliquot Method for weighing & measuring
A torsion prescription method has a sensitivity requirement of 6 milligram. Explain how you would weight 4 milligrams of atropine sulfate with an accuracy of ± 5%, using lactose as the diluent?

29. Measuring (for liquids)
In pharmacy, measuring usually refers to the exact determination of a definite volume of liquid.
Reading should be made at the bottom of this meniscus.

30. Measuring (for liquids)
Glassware are preferred.
Metal devices some times are used but should be preferably stainless steel or copper not iron.
If there are materials susceptible to oxidation in the formulation. Copper should not be used.
There are two types of Graduated glassware for measuring:
Conical (less accurate)
Cylindrical (more accurate)
For volumes less than 1.5 mL, a graduated pipette, burette or
dropper should be used.

34. Volume of drop can be differ by many factors, density,
temperature, viscosity, surface tension, size & shape of orifice.
When drugs are potent, a calibrated dropper should be used.

35. Unmarked portion of graduated glassware
To improve accuracy, the lower portion of graduates should not be used.

36. Alligation Alternate Method

44. Potency of a Drug
The Potency of some antibiotics, hormones, vitamins & Biologics (Vaccines) is based on their activity & expressed in terms of Units or Micrograms per milliliters (µg/mL).
Insulin & Penicillin antibiotics
These preparation should obey USP standard reference,
Penicillin G 1590 Units/mg are USP reference standard
1500 U/mg < Penicillin G <1750 U/mg is acceptable

45. محاسبه دوز دارو در کودکان:
روش مساحت سطح بدن (Normogram method)
روش یانگ
روش کلارک
روش فراید

46. روش مساحت سطح بدن (Normogram method)

48. روش مساحت سطح بدن (Normogram method)
The nomogram method is the best method:
because it is formulated on the patient's size.
It takes into consideration the person's body
surface area in meters square.
1.73 M2 is the surface area of the
average adult ( lbs.).

49. روش مساحت سطح بدن (Normogram method)
Child's surface area in m2
× Adult dose = Child's dose
1.73 m2

50. فرمول محاسبه مساحت سطح بدن BSA
BSA= W0.425 x H0.725 x 71.84
W; kg
H; cm
BSA; Square Centimeter

51. Fried's Rule Child's age in months × Adult dose
Child's dose =
150

52. c. Young's Rule:
Child's age in years × Adult dose
Child's dose = (Child's age in years + 12)
d. Clark's Rule:
Child's weight in lbs × Adult dose
Child's dose =
150

53. Examples

54. Answers

55. Aliquot Method for weighing & measuring
A torsion prescription method has a sensitivity requirement of 6 milligram. Explain how you would weight 4 milligrams of atropine sulfate with an accuracy of ± 5%, using lactose as the diluent?

56. Aliquot Method for weighing & measuring
A prescription calls for 0.2 mL of olive oil, using a 5 mL graduate calibrated in units of 0.5 mL, how would you obtain the required amount of olive oil using the aliquot method & alcohol, as the diluent?