DRUG STABILITY

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• DRUG STABILITY KINETICS
• General Outline
• Definition of drug stability and drug kinetics
• Importance of studying kinetics
• Basic math principles
• Drug kinetics reaction orders
• Determination of reaction orders
• Shelf life and half life
• Overage
• Degradation pathways
• Influence of packaging on drug stability
• Influence of temperature on drug stability
• Influence of catalysts on drug stability

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• Definition of drug stability and drug kinetics
• Stability
• It is defined as the study of the extent
  to which the properties
• of a drug substance or drug product remain within
  specified limits at
• certain temperature. Properties may be physical,
  chemical,
• microbiological, toxicological or performance
  properties such as
• disintegration and dissolution.
• Drug Kinetics
• It is defined as how drug changes with time
  i.e., study of rate
• of change. Many drugs are not chemically stable
  and the
• principles of chemical kinetics are used to
  predict the time span for
• which a drug (pure or formulation) will maintain
  its therapeutic
• effectiveness or efficacy at a specified
  temperature.

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• Importance of studying kinetics
• It determines
• Stability of drugs (t1/2)
• Shelf life ((t0.9)
• Expiration date
• Stability of drugs (t1/2)
• The half life (t1/2) is defined as the time
  necessary for a
• drug to decay by 50 (e.g., From 100 to 50, 50
  to 25, 20 to
• 10)
• Shelf life (t0.9)
• It is defined as the time necessary for the
  drug to decay to
• 90 of its original concentration.

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• Basic Math principles
• i) The straight Line
• General equation Y mx b
• Y dependent variable
• m slope
• X independent variable
• b intercept
• also
• Ordinate dependent variable axis
• abscissa independent variable axis

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m slope ?Y / ?X
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• Advantages of use of straight line
• Easier to determine parameters (slope and
  intercept)
• Simultaneous determination of two parameters (m
  b)
• Logarithms
• (a) Common log (base10)
• log 100 log 102 2
• log 1000 log 103 3
• (a) Natural log (base e 2.72)
• In 100 In ex
• In 100 In 2.72x 4.61

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• Relation between Log and Ln
• Ln X 2.303 Log X
• Rules for calculating with Log
• log (a . b) log a log b
• log (a / b) log a - log b
• log an n log a
• log ex X
• (iii) Differentiation
• Determination of the rate of change ( slope
  in graph)

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Straight Line
Slope m ?Y / ?X constant
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Curve
Slope is not constant but function of X Slope
1st derivative of y with respect to X
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Rules of differentiation y axn
dy/dx anxn-1 e.g., y x2
dy/dx 2x y n eax dy/dx an
eax e.g., y 3e-2x dy/dx
-6e-2x y ln x dy/dx
1/x y 1/x dy/dx -
1/x2 y ex dy/dx ex
Example y 10 x3 2 x2 5x 5
dy/dx 30 x2 4 x 5
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(iv) Integration Determination of area under
the curve i.e., sum or amount.
a
b
AUC
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Where Y is the function of the graph b
upper limit a Lower limit Rules of
Integration
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• Example
• Determine the area under the curve for the
  relationship
• y mx b, upper limit a and Lower limit 0

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• If you do not know the equation of the line you
  can use the trapezoidal
• rule to calculate the area under curve (AUC)
• 4) Order of Reactions
• Law of mass action
• The rate of a reaction is proportional to the
  molar concentrations of the reactants each raised
  to power equal to the number of molecules
  undergoing reaction.
• a A b B
  Product
• Rate a Aa .Bb
• Rate K Aa .Bb
• Order of reaction sum of exponents
• Order of A a and B b
• Then Overall order a b

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• Example
• The reaction of acetic anhydride with ethyl
  alcohol to form ethyl acetate and water
• (CH3 CO)2 2 C2H5OH 2 CH3
  CO2 C2H5 H2O
• Rate K (CH3 CO)2 O . C2H5OH2
• Order for (CH3 CO)2 O is 1st order
• Order for C2H5OH2 is 2nd order
• Overall order of reaction is 3rd Order

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• Types of reaction orders
• Zero order reaction
• It is a reaction where reaction rate is not
  dependent on the concentration of material i.e
  concentration is not changing (i.e. negligible
  amount of change).
• Example Fading of dyes

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Equation for zero order a A k
Product (P) Rate - dc/dt K c0 - dc/dt
k dc - k dt co Initial
concentration ct Concentration at time
t
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C
T
Units of the rate constant K c co
Kt K co c /t K Concentration / time
mole / liter . second M. sec-1
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• Determination of t1/2
• Let c co /2 and t1/2 t
• substitute in equation
• c co k t
• t1/2 co / 2K
• Note Rate constant (k) and t1/2 depend on co
• Determination of t0.9
• Let c 0.9 co and t t0.9
• substitute in equation
• c co k t
• t90 t0.9 0.1 co / k

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• (b) First order reaction
• The most common pharmaceutical reactions e.g
  drug absorption
• 
  drug degradation
• The reaction rate of change is proportional to
  drug concentration i.e.
• drug conc. is not constant.
• a A
  k Product (P)
• Rate - dc/dt K c1
• Equation

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C co e ktDifficult to determine slope
lnco
lnc lnco kt Slope c1 c2 / t1 t2 Slope
-k
C
Lnc
Log co
Log c log co kt / 2.303 Slope c1 c2 / t1
t2 Slope -k / 2.303
Logc
Or use semi log paper
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Semi log paper Slope -K / 2.303
Slope log c1 log c2 / t1 t2 NOT c1 c2 /
t1 t2 Units of K lnc lnco Kt K ( lnco
lnc ) / t Unit time-1
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• Determination of t1/2
• Let t t1/2 and c co /2
• substitute in ln c ln co Kt
• t1/2 ln 2/ K 0.693 / K
• K units 0.693 / t1/2 time-1
• Determination of t0.9
• Let t t0.9 c 0.9 co
• substitute in ln c ln co Kt
• t0.9 0.105 / K and K 0.105/ t0.9

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• Example A drug degrades according to the
  following
• Time (min.) Conc. ()
• 0 100
• 1 65.6
• 2 43.0
• 3 28.19
• 4 18.49
• 10 1.50
• Plot c against t on semi log paper and determine
  slope, K and t1/2

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Solution log 28.195 1.45 and log 1.5
0.176 slope 1.45 0.176 / 3 10 1.27 /
-7 - 0.181 Equation log c log co Kt /
2.303 slope -K/ 2.303 - 0.181 - K /
2.303 K 0.417 min-1 t1/2 0.693 / K t1/2
0.693 / 0.417 1.66 minute
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• Special Case
• Apparent zero order of reaction
• In aqueous suspensions of drugs, as the dissolved
• drug decomposes more drug dissolve to maintain
  drugconcentration
• i.e. drug concentration kept constant, once all
  undissolved drug is
• dissolved, rate becomes first order.
• Another special case Pseudo 1st order
• When we have two components, one of which is
  changing appreciably from its initial
  concentration and the other is present in excess
  that it is considered constant or nearly
  constant.
• Note In first order reactions, neither K or nor
  t1/2 is dependent on
• concentration

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• (c) 2nd Order reaction
• When you have two components reacting with
  each
• other or one component reacting with itself.

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• 2nd order graph

Units of K 1/C 1/Co Kt K (1/C - 1/Co)
/ t K M-1. sec -1
i.e, K is dependent on initial drug
concentration. Half life t1/2 1 /
KCo Shelf life t0.9 0.11 / KCo