kinetics - drugs/medicines stability

• rate laws - zero order reaction

  • m=0 - zero order reaction → rate = k
  • if [A] doubles, the rate stays the same

  
• rate laws - first-order reaction


  • m=1 - first order reaction → rate = k[A]
  • if [A] doubles, the rate doubles

  
• the rate constant (k) unit CHANGES with the order
• most important reaction orders:

  zero + first most important, second not very common
• Zero-order reactions:

  A reaction that proceeds at a constant rate and is independent of the concentration of the reactant, A (if [A] doubles, the rate is the same)
• examples of zero-order reactions:

  • elimination of alcohol
  • suspensions off poorly soluble drugs e.g. Calpol
• the mathematical expression for zero-order:

  
• integrated zero-order law: the rate of reaction is proportional to the concentration of the reactants


  ...

  gradient = -(rate constant for zero-order reaction)

  
• first-order reactions:

  • The reaction proceeds at a rate that is dependent on the concentration of one component (reactant) e.g. A. If [A] doubles, the rate doubles.
  • Most drugs are eliminated following this mechanism
• mathematical expression for first-order reactions:

  k1 (rate constant of first order reactions) is in s-1 or time-1

  
• integrated first-order law:

  • remaining drug = [A]t
  • gradient = -k1/2.303

  
• second-order reactions:

  Two cases either one of the reactants is raised to the second power or two reactants each raised to the first power.

  A) 2

  
• integrated second-order law:

  • used log - to avoid appreciation/estimation error
  • gradient = k or k([A]0 - [B]0)

  
• Pseudo-first-order reactions:

  • Some reactions involve MORE THAN ONE reacting species and still follow FIRST order kinetics.
  • The most common example is when one of the reactants is in such LARGE EXCESS that its change in concentration during the reaction is negligible
  • Ester hydrolysis: the water is in large excess (and so can be ignored) compared with the drug
• define the half-life of reactions:

  The half-life of a reaction is defined as the time it takes for the concentration of the reactant to decrease by half of its original value
• half-life expression for zero order:

  A) 1/2

  
• half-life expression for first order reactions

  A) 0.693

  
• half-life expression for second order reactions (1 component):

  
• experimentation determination of the order of reaction sequence:

  A) integrated

  B) zero

  
• the stability of pharmaceutical products is:

  is the capability of a formulation in a specific container closure system to remain within its physical, chemical, microbiological, therapeutical and toxicological specification throughout its shelf life.
• define shelf life

  The shelf life is the time during which the product retains the same properties and characteristics it possessed when manufactured.
• what needs to be determined when testing a drug product's stability?

  Provide evidence as to how the quality of the drug product varies with time,

  • Establish shelf life for the drug product.
  • Determine recommended storage conditions
  • Determine container closure system suitability
• routes of chemical deviation of medicines:

  • Hydrolysis (most common one)
  • Oxidation
  • Photolysis: influence of light causing decomposition, heat, emission of light.
  • Chelating agents may form unwanted complexes
• conditions that can allow hydrolysis to occur:

  • pH (decomposition catalysed by H30+, OH-)
  • Buffer (decomposition catalysed by ions of the buffer chemical components)
  • Solvent (decomposition catalysed water, co-solvent or organic solvent: catalysis)
  • Heat
  • Drug’s concentration
• why is stability testing necessary?

  • chemical degradation leads to degradation of drug concentration in the dosage form
  • toxic product may be formed

  why testing?

  • assurance to the patient
  • economic considerations
  • legal requirement (FDA, EMA…)
• list of the tests each medicine is submitted to:

  (apart from toxicological/microbiological tests)

  A) heat

  B) moisture

  C) stress

  D) pH

  E) light

  F) oxidation

  
• influence of pH (and buffer) on stability:

  • Decomposition can be catalysed by H+, OH-, water or buffer components
  • In the absence of buffer components influence, this is called specific acid-base catalysis.
  • In the presence of buffer components influence, this is called general acid-base catalysis.
• the general equation for specific acid-base catalysis

  (absence of buffer components)\

  
• the general equation for general acid-base catalysis based on the decomposition of glucose in water in the presence of acetic acid and its conjugate form):

  (in the presence of buffer components)

  
• Buffer needs to be carefully selected to avoid drug decomposition.
• pH may affect the oxidation of drugs
• Accelerated stability testing (effect of temperature):

  • “Accelerated” reflects the need for a rapid evaluation of the kinetics of decomposition (especially rate constants, and shelf life).
  • Temperature is the most common test
  • Related to the Maxwell-Boltzmann distribution of particles: an increase in temperature results in an increase in the probability of collision between molecules i.e. here the decomposition.
• Decomposition is increased between 2 and 5 fold for each 10°C increase in temperature.
• what is the equation used to predict the shelf-life of a drug?

  Arrhenius equation.

  Assume that the mechanism of decomposition does not change with temperature and thus can extrapolate information.

  A) Ea

  B) T

  
• how do you work out the shelf life from accelerated stability testing?

  • Determine the rate constants of the decomposition reaction at temperatures between 30 °C and 60 °C.
  • Extrapolate the activation energy, Ea, of the system and the rate constant, k, of the decomposition reaction at room temperature
  • Work out the value of 1/T (for the temperature of the shelf-life you're trying to figure out) and read of the log k for that value of the graph.

  
• determination of the shelf-life, t90 (accelerated stability testing:

  If the drug follows a first-order kinetic mechanism, we have:

  (when T = 20ºC)

  A) 0.105

  
• what does t90 mean?

  The shelf life (t90) is the time it takes for 90% of the initial amount of drug to remain.
• The half-life of a drug is important to determine the shelf life of a drug.
• Drugs stability is assessed by accelerated stability testing which uses the Arrhenius equation.
• Most of drugs follow a first order decomposition kinetics