# First order, 0 order, and Non-linear Kinetics

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What is CL (clearance) proportional to in first order kinetics?
CL = kel * Vd
Proportional to: elimination rate constant and the volume of distribution
Meaning: as the rate of elimination goes up, the amount of clearance goes up
as the volume of drug increases, the more clearance a drug has

What is the rate of elimination proportional to in first order kinetics?
Rate of elimination = CL*Cp
Rate of elimination = kel*Vd*Cp

Proportional to: clearance, concentration of drug in the plasma, volume of distribution, and the elimination rate constant

As rate of elimination goes up, more drug is cleared

What is the rate constant for elimination dependent on for first order kinetics?
(.7)/t1/2 = CL/Vd
Dependent on t 1/2, CL, and Vd
Proportional to: CL
Inversely proportional to: t1/2 and Vd

A higher rate constant for elimination gives more clearance. The longer it takes a drug to reach it’s half life (bigger half life), the smaller the rate constant for elimination.
The larger the Vd, the smaller the rate constant for elimination

What does the curve look like for first order elimination kinetics when plotted with Cp (concentration) vs. time?
exponential decay

What provides a straight (linear) downward slope for first order elimination kinetics?
A semi-log plot
Whne log(Cp) is plotted vs. time

What is slope equal to in the first order elimination kinetics semi-log plot?
-kelimination ~ semi-log plot can determine kelimination

What is the -kel (slope) proportional to/inversely proportional to?
-kel = -CL/Vd
Proportional to: Clearance
Inversely proportional to: volume of distribution

The larger rate constant for elimination, the faster the clearance (more steep the slope)
The larger the volume of drug, the smaller the rate constant for elimination (less steep slope)

What is t1/2 for 1st order kinetics?
t1/2 = initial concentration/kel

**Remember, kel = Vd/CL
The larger the rate constant for elimination, shorter the half-life
The larger the clearance value, the shorter the half life
The larger the volume of drug the longer the half-life

What is Vd dependent on?
Vd = D*F/Cp0
Dependent on drug, bioavailability, and the initial concentration in the plasma
Proportional to: dose and bioavailability
Inverse proportional to: initial concentration of drug in the plasma

As the bioavailability increases, the volume of drug increases
As the dose increases, the volume of drug increases
As the initial concentration of drug in the plasma increases, the volume of drug decreases

What is the t1/2 for first order kinetics proportional to and inversely proportional to?
Proportional to: Vd
Inversely proportional to: CL

How do you determine the % of drug remaining?
% remaining = 2^-t/t1/2
realize: % = 2^-t
if t = 2t1/2, 25% of the drug is remaining
if t = 4t1/2,

What does the rate of elimination depend on for renal excretion ONLY?
rate of elimination = UF*Cu
Proportional to: urinary flow and Concentration in the urine
As urinary flow and the concentration of drug in the urine increase, the rate of renal excretion/elimination go up

What happens if Cu = Cp (cocentration in the urine = the concentration in the plasma)?
CLren = UF
The renal clearance = urinary flow

What is renal clearance generally dependent on?
CLren = (Cu/Cp) * UF
Generally, the higher the concentration in the urine and the lower the concentration in the plasma, the higher the clearance
As urinary flow increases the clearance rate increases

When Cu+Cp, the renal clearance is only dependent/=to urinary flow

What are CLren, CLmetabolism, and CLother?
CLtotal = CLren +CLmet + CLother

What is total clearance dependent on?
Includes renal clearance, metabolism clearance, and other clearnance

What does the graph look like for zero order elimination kinetics when plotted in Cp vs. time?
Straight, linear downward slope

How can you determine a reaction is using zero order elimination kinetics?
There is a linear slope when plotted concentration vs. time
There is no t1/2
The rate of elimination is not dependent on concentration; it is CONSTANT
CL is not a defined constant
CL is dependent on concentration and dose

What is CL dependent on in zero order elimination kinetics?
concentration and dose

When is zero order kinetics seen?
Metabolic elimination
When an enzyme is at maximal capacity
When drugs are in very high concentration

What is nonlinear elimination kinetics also known as?
saturable
dose dependent
capacity-limited

What is different about the rate of elimination in nonlinear elimination kinetics?
Rate of elimination is dependent on the substrate concentration;
At higher substrate concentrations, the enzyme becomes saturated and cannot be act as fast

When can the rate of elimination constant (Vmax) be determined with nonlinear elimination kinetics?
When Cp >>> Km

When does a reaction go back to first order after being nonlinear elimination kinetics?
When Cp <<< Km ** remember that at low concentrations all drugs show first order kinetics** CL = Vmax/Km Smaller Km = faster clearance Bigger Vmax = faster clearance

What are common examples of nonlinear elimination kinetics?
Phenytoin and aspirin

What is a common example of zero order elimination kinetic?
Ethanol

What is shown in a nonlinear elimination kinetics graph?
There are 2 points:
At the top is 0 order with no 1/2 life and as reaction proceeds it shows first order kinetics, where a half life is shown
The 2 graphs are broken at the point of Km

How is Cp>>Km shown on a graph?
As 0 order kinetics
Looks like a linear direct plot with slope = Vmax

How is Cp<
As 1st order kinetics
Looks like an exponential decay

What does a semi-log plot look like for nonlinear elimination kinetics?
0 order at the top and 1st order as the time continues
At 0 order (top) there is an exponential decay (Cp>Km)
At 1st order (bottom) there is a linear slope; slope = -kel (Cp

How is Cp>>Km shown on a semi-log graph?
Zero order – nonlinear/exponential line

How is Cp<
1st order – linear semi-log plot
slope = -kel = -CL/Vd = (-Vmax/KmVd)

What is another name for nonlinear kinetics?
Dose-dependent

Which order is a drug at a high dose?
zero order

Which order is a drug at a low dose?
first order

What does a single compartment graph look like when graphed in Cp vs. time
initial spike and then steady state for the rest of time (drug is not eliminated)

What does a single compartment graph look like for first order elimination when graphed Cp vs. time
nonlinear/exponential decay

What does a two compartment graph look like when graphed Cp vs. time?
Initial spike, then decrease to steady state (drug is not eliminated)

What does a two compartment graph look like with elimination when graphed Cp vs. time?
Nonlinear elimination kinetics
2 exponential decays, first representing 0 order is not often important when determining the pharmacokinetics
Elimination phase determined by looking at the bottom half of the graph (the first order kinetics)

The dependence of Cp (concentration of drug in the plasma) on the dosing rate (dose/change in time) with continuous administration

Rate of administration = rate of elimination

What can steady-state pharmacokinetics tell us?
Also the fluctuations of Cp in dosing interval

What is a maintenance dose (Dm)
Periodic dose needed to maintain target drug concentration

What is rate of administration dependent on?
Rate of administration = Dm*F/delta t

Dependent on: maintenance does (Dm), bioavailability (f), and the amount of time (delta t)

Proportional to: Dm and F
Inversely proportional to: amount of time
**??

What is maintenance dose inversely proportional to?
bioavailability

For first order kinetics, rate of elimination = CL * Ctarget
If this is true what is the equation for steady state?
rate of administration = rate of elimination
Dm*F/delta t = CL*Ctarget

ULTIMATELY::
Dm=CL*Ctarget*delta t/F

What is Dm proportional to?
Ctarget
CL
Rate of elimination
delta t = dosing interval

What is Dm inversely proportional to?
F = bioavailability

When is Dm enhanced?
When F < 1

What does a graph look like at steady state for first order elimination kinetics when plotted in Cp vs. Dm/delta t?
Straight, linear positive slope

What is Cp proportional to when at steady state for first order elimination kinetics?
Cp = DmF/delta t/CL
Proportional to: Dm and bioavailability

Inversely proportional to: Clearance

What does a graph look like at steady state for first nonlinear elimination kinetics when plotted in Cp vs. Dm/delta t?
nonlinear, exponential increasing line

Seen with drugs that have a narrow therapeutic window and become toxic

Makes it hard to determine maintenance dose

What does a graph look like when your dosing interval < t1/2 when varying dosing intervals?
exponential increase
takes a lot of doses to get to steady state (Ctarget)
shows smaller difference between Cmax and Cmin

What does a graph look like when your dosing interval > t1/2 when varying dosing intervals?
exponential increase
takes much less dosings to get to steady state (C target)
shows much bigger difference between Cmax and Cmin

Dose required to IMMEDIATELY achieve target drug concentration

Dl = Ctarget *Vd/F
Proportional to: target concentration and volume of drug

Inversely proportional to: bioavailability

The higher the bioavailability, the lower the loading dose **because you don’t need as much drug to give you a good effect

ONLY on the target drug concentration (Ctarget), the drug’s bioavailability (F) and the drug’s volume of distribution (Vd)

Which order of kinetics cannot be steady state?
0 order

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