Week 2 Flashcards
rate
equation
the rate of a chemical reaction is the velocity at which it occurs drug A --> drug B rate = - dXa/dt rate= dXb/dt X = amount units: amount per time (ex: mg/hr)
order of a reaction
concentration, C, or the amount, X, of drug or reactants influences the rate – zero order – first order – second order – Michaelis-Menten
zero order equation
constant
changes in the drug concentration (mg/L) doesn’t affect the rate (mg/hr)
doesnt depend on amount (or conc) of drug
first order equation
changes in the drug concentration do affect the rate
similar to radiologic decay
k is 1/time (ex: min-1). whatever the x axis is, if its hours, then hours^-1
– Michaelis-Menten equation
for saturable enzyme kinetics required to remove the drug from the body
rate constant (k)
rate of the process
• independent variable is usually time, t
• dependent variable is usually amount, X,
or concentration, C
• the units for k depends on the order of the
reaction –> look at the equation
order of a pk process
is the way the amount/concentration of the drug influences the rate of the process.
linear processes
- zero-order
- first-order
- can be algebraically solved by Laplace Transformation
non linear
- Michaelis-Menten
the amount (X) can be converted to
concentration (C) by dividing both sides of
an equation by a ‘volume of distribution’ V
dX/dt = - k x X becomes dC/dt = -k x C
• most (but not all) rate processes are
first or zero order
- numerical methods - Euler’s method
- analytical method - Laplace transform
(k0) —> 1 (k1)—>2 (k2) –> 3
what do these mean?
k0- zero order k1, k2 - first order rate constants 1, 2, and 3 are compartments. you can assign diff meanings to these. example: 1 can be gi tract, 2 can be plasma, 3 can be urine. write the mass balance equations around each compartment
direction of arrow
- Accumulation = IN – OUT
* Rate (dX/dt) = Rate IN – Rate OUT
Rules for Writing Mass Balances
• the type of rate process
first order
zero order
- if first order: multiply first order rate constant by the amount/conc of drug in the component at the tail of the arrow
– if zero order: just enter the rate constant
(k0) —> 1 (k1)—>2 (k2) –> 3
example for compartment 1
dX1/dt = material in compartment 1 dX1/dt = +k0 - k1 x X1
(k0) —> 1 (k1)—>2 (k2) –> 3
example for compartment 2
dX2/dt = +k1 x X1 - k2 x X2
(k0) —> 1 (k1)—>2 (k2) –> 3
example for compartment 3
dX3/dt = +k2 x X2
laplace equation
• Laplace transform converts differential
equation f(t) into the Laplace f(s) domain
• Laplace equations can be rearranged
algebraically
• inverse transform to provide the solution
transform of variable such as drug amount X
L bar (X) = X bar
if a constant A is multiplied with X
L bar (A x X) = A x X bar
• transform of a differential equation
L bar (dX/dt) = s × X bar - Xo s = independent variable that replaces t in the laplace space X bar = X as a function of s Xo = initial amount of material in that compartment at time zero
general steps of laplace equation
1. for each compartment, write the differential equation(s) in time, t, domain 2. transform to the Laplace, s, domain 3. rearrange to solve algebraically 4. using a chart, reverse transform to t domain to obtain the integrated equation
zero order kinetics
linear graph paper
semi log paper
straight line
gives a curve
the value of ko may be taken from the slope of the line using
two points taken from the best fit line (not raw data points)
