kinetics exam 3 Flashcards
During a multiple-dose schedule the more recent a missed dose is, the less the effect the omission has on the current plasma drug concentration.
A
True
B
False
false! according to slide 24, it will have a greater effect!
PLASMA CONCENTRATION-TIME COURSE
AFTER ONE ORAL DRUG ADMINISTRATION
onset of action = when the drug reaches the minimum effective concentration
peak time = the time it takes to reach the peak concentration
duration = the time in which the drug is above the minimum effective concentration
intensity = the window between the peak concentration and the minimum effective concentration
therapeutic window = the window between the minimum toxic concentration and the minimum effective concentration
predicted plasma drug con concentrations for multiple-dose regimen using the superposition principle
taking/giving the patient the same dose at certain time intervals and as a result will result in a total dose after adding the doses taken previous to the one given
towards a steady state
taking a dose at different time intervals will increase the concentration in the body and keep it at a steady state
tou symbol:
At a steady state, concentrations will rise and fall according to a repeating pattern as long as we continue to administer the drug at the same dose level and with the same time period between doses.
This repeated dosing period is often called the dosing interval and is abbreviated using the Greek letter tau (τ).
Predicting Plasma Drug Accumulation
It is assumed:
– that a first-order process eliminates the drug
– that early doses do not affect the pharmacokinetics of later doses
i.e. the pharmacokinetics of later doses are only superimposed (stacked on top of) on those of earlier ones (the principle of superposition)
- Also, the entire 0 Cpdt for a single dose administration is equal to nn+1Cpdt for any dosing interval at a steady state in a multiple-dosing case - so
- the area under the curve of the first dose is equal to the area under the curve of any dose interval at steady state
Predicting Plasma Drug
Accumulation II
Based on the principle of superposition, the concentration-time curve in a multiple-dosing case can be predicted from the concentration-time data of a single-dose administration
- *Ref Table 8.1; if a constant dose is given at constant periods, the plasma concentrations after each dose consist of the same data obtained after the single dose. For each time point, then, the predicted plasma concentration is the sum of the residual concentration resulting from each previous dose
- The prediction holds even if the dosing interval is not fixed
Situations In Which Superposition Would Not Be Valid
The drug does not follow linear kinetics see Table 9.1 for examples
- A Drug’s carrier system gets saturated (for instance, the drug is eliminated by a saturable enzymatic process and so follows Michaelis- Menten kinetics. Recall Vmax and KM)
- There is enzyme induction
- There is enzyme inhibition
- The patient’s disease condition changes significantly between doses
Drug Accumulation
Multiple dosing is intended to keep plasma drug levels within the therapeutic window - which is always the goal!
- The dose and the time between doses () may be adjusted to achieve this.
- Accumulation will not occur if a second dose is given at an interval longer than that required for the elimination of the previous dose
- A steady state should eventually be achieved during accumulation (Cmax and Cmin should remain the same from dose to dose)
- There is no accumulation if at steady state Cmax is the same as for (Cn=1)max for the first dose.
- For drug safety, Cmax should always be less than the minimum toxic dose
Drug Accumulation II
the drug accumulation index:
R = (Cinfinity)max/(Cn=1)max
R = D0/VD[1 - e^-ktou]/(D0/VD)
R = (1/1 - e ^-k(τ))
Thus, accumulation depends not on the dose, but on the dosing interval (which is tau) and the elimination rate constant which is k
- The time required to attain a steady state is dependent on the elimination half-life but is independent of dose or interval between doses
- Average steady-state Plasma Concentration =[AUC]t1^t2/ tau
Drug Accumulation III
The time required to attain one-half of the steady-state plasma levels (the accumulation t1/2):
t1/2acc = t1/2(1 + 3.3log (ka/ka-k))
- For IV infusion administration ka is rapid»_space;>k
t1/2acc = t1/2(1 + 3.3log(ka/ka))
i.e. for an IV-administered drug
t1/2acc = t1/2
Thus t1/2acc is dependent on the elimination t1/2 but not on dose or dose intervals
Drug Accumulation IV
The time needed to reach 90% and 99% steady-state concentrations is 3.3 t1/2 and 6.6 t1/2 respectively.
- The number of doses needed to reach steady-state is dependent on t1/2 and .
(specifically, it is for 99% steady state)
(6.6 x t1/2)/tau
interrelation of elimination half life, dosage interval, maximum plasma concentration, and the time to reach steady-state plasma concentration
table 8.3
Relation Between Loading Dose
and Accumulation Index
Maintenance Dose (DM ) = Loading Dose (DL) – Amount of Drug
Remaining at end of Dosing interval
DL = DM x (1/1-e^ktau)
You would recall the accumulation index
R = 1/(1 - e^ktau)
So the loading dose is the product of the maintenance dose and the accumulation index.
the dose of sulfisoxazole (Gantrisin, Roche) recommended for an adult female patient (age 26 years, 63 kg) with a urinary tract infection was 1.5 g every 4 hours. The drug is 85% bound to serum proteins. The elimination half-life of this drug is 6 hours and the apparent volume of distribution is 1.3 L/kg. Sulfisoxazole is 100% bioavailable.
a.Calculate the steady-state plasma concentration of sulfisoxazole in this patient.
b.Calculate an appropriate loading dose of sulfisoxazole for this patient.
c.Gantrisin (sulfisoxazole) is supplied in tablets containing 0.5 g of the drug. How many tablets would you recommend for the loading dose?
d.If no loading dose was given, how long would it take to achieve 95%–99% of steady state?
Drug Accumulation:
Repeated IV Injections
For a one-compartment open model following first-order
kinetics, after a single dose:
DB = D0e^-ktau
- So given that the interval between a first and second dose is
tau: DB = D0e^-ktau - The fraction of the dose remaining in the body:
f = DB/D0 = e^-ktau
Thus f depends on k and tau e.g. f is large if tau is small.
Drug Accumulation:
Amount of Drug in the Body
- The maximum amount of drug in the body:
Dmax = D0/(1-f)
Since the difference between the maximum and minimum amounts of drug in the body is equal to the administered dose (D0):
Dmin = Dmax - D0
Where F= fraction of dose absorbed (NB: for an IV dose F=1), the average amount of drug in the body at steady-state:
Dav = FD0/ktau
The respective concentrations can be determined by dividing the amounts by the apparent volume of distribution
A new drug is to be given by multiple IV bolus injections to a patient such that drug steady-state concentrations should be maintained between a maximum of 20 and a minimum of 1 mg/L.
Assume a one-compartment linear
the model applies to this drug in this concentration range. The elimination rate constant and apparent volume of distribution for this drug in this patient are 0.223 hr-1 and
40.6 L, respectively.
Calculate the dosing interval that will exactly achieve this concentration requirement.
Also, calculate the maintenance dose.
problem to solve! slide 22 of multiple dosages
table
table
Drug Accumulation: Plasma Level Equations
Cmax = C^0p/(1 - e^-ktau)
Cmin = (C^0pe^-ktau)/(1-e^-ktau)
Cav = (FD0/VDktau)
….
Drug Accumulation: Plasma Level Equations II
After administering n i.v.doses (time between doses), the plasma concentration at time t after the nth dose is given by:
CP = (D0/VD)(1-e^-nktau)
- At steady-state, e-nk approaches zero:
CP^infinity = D0/VD(1/1-e^ktau)e^-ktau
problem to solve
Non-Compliance:
Dose Skipped?
When a dose is missed, the concentration that should have been contributed by the missing dose ((D0/VD)e-ktmiss) is subtracted from the concentration at time t after the nth dose (given that time is time tmiss since that scheduled
dose). For i.v.:
CP = D0/VD[(1 - e^nktau/1 - e^ktau)e^-kt - e^-ktmiss]
Or at steady-state (where n is very large):
CP^infinity = D0/VD(e^-kt/ 1- e^-ktau) - D0/VD e^-ktmiss
NB: The more recent a missed dose is, the greater the effect it will have on the current plasma concentration.
- Missed doses greater than 5 half-lives later should be omitted because of their minimal impact
problem to solve
Non-Compliance: Wrong Time or Wrong Dose?
When a dose is late, the dose not taken on schedule should be regarded as a missed dose and subtracted as before. However, when the dose in question is actually taken (early or late) it is taken into account as follows for
i.v.:
CP = D0/VD(1 - e^-nktau/1 - e^-ktau) -e -ktmiss + e-tactual)
where tactual is the time since the dose is question was actually taken
* If a wrong dose (hopefully non-lethal) is given, Cp may be determined with the right dose and the correction made by subtracting the contribution due to the wrong dose
problem to solve
Repeat IV Infusions
Intermittent short IV infusions prevent transient extreme high plasma levels of a drug and so are better tolerated even though steady-state may not be attained.
where R is the infusion rate. Since R = D/tinf
(D is size of infusion; tinf is the duration of infusion) After any specified time t of IV infusion,
The concentration at any specified time t after IV infusion given Cstop is the concentration when infusion stops
problem to solve
table
table
Repeat Oral (Or Extravascular)
Administrations
- Recall, for a single dose, the plasma concentration at the time
where F is the fraction of drug absorbed and ka is the first-order rate constant for absorption.
After dosing n times ( intervals), the plasma concentration at time t:
At steady-state, n approaches infinity and e-nka approaches zero.
Repeat Oral (Or Extravascular) Administrations II
Repeat Oral (Or Extravascular) Administrations III
tp corresponds to a time after many doses (i.e. n approaches infinity); also tp corresponds to a peak concentration
- tp is the repeat-dosing equivalent of a tmax for a single dose at a steady state.
Example
A drug is given by multiple oral dose of 30 mg every 6 hours. Assume a one compartment linear model applies to this drug in this concentration range. The Clearance and VD for this drug in this patient are 10.7 L/hr and 52.3 L, respectively. For this dosage form and patient
-1
the bioavailability is 0.63 and ka is 1 hr
Assume that e-ka * approaches 0 and ka»_space; k. Calculate the expected Cpaverage, Cpmin value and a ‘very’ approximate Cpmax value at steady state.
Example
A drug is to be given by multiple oral doses every 24 hr. After consideration of the patient’s clinical condition it is decided that the average drug concentrations should be maintained at 9 mg/L. Assume a one compartment linear model applies to this drug in this concentration range. For this dosage form and patient, the bioavailability is 0.65 and the absorption rate constant is 1 hr-1. The half- life and VD for this drug in this patient are 4.3 hr and 35.7 L, respectively. Calculate the dose that will achieve this average concentration of 9 mg/L.
Example
A drug was given by multiple oral doses of 200 mg every 6 hr. Assume a one compartment linear model applies to this drug in this concentration range. For this dosage form and patient the bioavailability is 0.67 and the
-1
absorption rate constant is 3.21 hr
VD for this drug in this patient (63.1 kg) are 0.155 hr-1 and 0.53 L/kg, respectively. Calculate the average drug concentration.
* Solution:………….
Loading Dose Determination
Used to achieve the desired plasma concentration (C ) av
promptly, circumventing the delay that the processes of absorption and elimination introduce.
- Dose Ratio = DL/D0
When the dosage interval is equal to the half-life, the dose ratio has value 2.
Bioavailability
Estimation of ka (in multi-dose regimens ) is difficult because of superposition of doses
- Determination of bioavailability is possible at steady-
state (Cav , AUC0 , tmax and Cmax ). - First sample should be taken just before the administration of the second dose, thereafter, samples should be taken regularly after the administration of each dose
- Multi-dose regimen bioavailability studies can reveal changes that would not be obvious in a single-dose study e.g. the existence of non-linear pharmacokinetics, drug-induced malabsorption syndrome etc…
Bioequivalence
A multiple dose study can be designed to ascertain bioequivalence. Equal doses of a test and reference product may each be administered repeatedly in turn (two-way cross- over) to steady state, separated by a time period required to completely eliminate the drug from the body.
- The AUC and Cmax of the test product should be within 80 -125% of the corresponding values for the reference product using a 90% confidence interval.
relation Between Loading Dose
and Accumulation Index
Maintenance Dose (DM ) = Loading Dose (DL) – Amount of Drug Remaining at end of Dosing interval
So the loading dose is the product of the maintenance dose and the accumulation index.
Circulatory System and Distribution
Drug is borne by blood (via blood vessels) to the site of action
- Volume of blood pumped by the heart per minute (cardiac output) is important
- Cardiac output = stroke volume X heart rate
- At rest, average cardiac output (due to 69 left ventricle contractions per minute) is 5.5 L per minute
- Blood pressure = cardiac output X peripheral resistance
- Left ventricle contraction produces a systolic blood pressure of 120 mmHg, and moves blood at 300 mm/sec through the aorta
Water Volumes in 70 kg Adult
intracellular water volume: 27
interstitial water volume: 12
plasma water volume: 3
blood cell water volume: 2
total blood volume 5L
Factors Affecting Drug Entry Into
Tissues
Physicochemical nature of cell membranes:
Protein + bi-layer of phospholipid
Under certain pathophysiological conditions (e.g. burns and meningitis) permeability could change
Unique features of tissue such as blood-brain barrier
- The physicochemical properties of the drug:
Lipophilic drugs traverse cell membranes more easily than polar ones
Small molecules traverse membranes more easily than larger ones or those forming drug-protein complexes
Diffusion
Most drugs enter cells by way of spontaneous passive diffusion
- Passive diffusion is temperature-dependent and governed by Fick’s Law of Diffusion. The rate of
drug diffusion
Where h=thickness of membrane; A=surface area of membrane; D=diffusion constant; K=lipid-water partition coefficient;Cp=drug concentration in plasma; Ct=drug concentration in tissue
*negative sign because there is a net transfer of drug from the capillary lumen to the extracellular fluid and tissue
Hydrostatic Pressure
The pressure difference between capillaries entering and those leaving tissue
- Hydrostatic (filtration) pressure is caused by capillary blood pressure being higher than that of tissue at the arterial end
- This is responsible for the transfer of water-soluble drugs penetrating spaces between endothelial cells
- Blood pressure of tissues higher than venous capillaries (creating ‘absorptive’ pressure), so filtrate gets transferred to venous capillary
Distribution
Distribution may be flow limited (such as in congestive heart failure) or diffusion limited (such as during inflammation when there is increased capillary permeability)
* The first-order distribution constant for a drug into an organ:
kd = Q/VR
concentration in the organ to that in the venous blood
* R may be estimated from the oil/water partition coefficient (Po/w). A drug with high Po/w will have a high R
* Thus large blood flow (Q) decreases distribution time; a large volume
Q VR
kd
Where Q=blood flow to the organ; V= volume of the organ; R=ratio of drug
(V) increases distribution time.
* The first-order distribution half-life:
td1/2 = 0.693/kd
Accumulation
R indicates the extent to which an organ accumulates a drug. A high R (due to either protein binding or high solubility of the drug in the tissue) means it takes longer
for distribution to be complete
*e.g. flutamide, digoxin
- A high level of accumulation in tissues results in: a long elimination half-life (e.g. etretinate, DDT); plasma levels may not correlate well with pharmacodynamic action if tissue is target tissue*
- Mechanisms of accumulation: dissolution in lipids, reversible binding to biomolecules (e.g. proteins, melanin, calcium), irreversible binding to biomolecules (e.g. in cancer chemotherapy purine/pyrimidine drugs that bind to nucleic acids), enzymatic or active transport systems
image
Drug Protein Binding
Irreversible binding to protein sometimes occurs when an activated form of a drug attaches to a protein via a covalent bond (e.g. acetaminophen hepatotoxicity, chemical carcinogenesis)
- Reversible binding (typical) is usually due to weak bonds such as hydrogen bonds and van der Waals forces
- Protein-bound drugs are usually not active pharmacologically
- Protein-bound drugs are usually not able to cross cells or cell membranes
Drug Protein Binding II
Drug-protein binding may be allosteric: There can be cooperativity in protein binding i.e. binding of first drug molecule can affect the binding of successive molecules to the same protein molecule (e.g. O2 binding to Hb)
- Drug protein binding can result in non-linear pharmacokinetics
- Drug protein binding can result in a “depot” effect (longer duration of action).
Factors Affecting Protein Binding
Drug properties: physicochemical properties and quantity of drug in body
- Protein properties: physicochemical properties and the quantity of protein available for binding
- Drug-protein affinity: Ka.
- Drug-drug interactions: competition for binding site; the binding of one drug alters affinity of protein for another drug e.g. after ASA acetylates lysine in albumin, albumin’s capacity to bind other anti-inflammatory drugs changes
- Disease condition of patient: may reduce blood-protein binding (e.g. in hepatic disease)
Drug Protein Binding:
Blood Proteins- Albumin
albumin: MW 65kDa.
* Largely responsible for maintaining the osmotic pressure of blood.
* Weak acidic drugs (e.g. salicylates, penicillin), free fatty acids, bilirubin, and some hormones (e.g. cortisone, thyroxine) bind to albumin.
* Albumin has several binding sites for which different drugs compete. For instance, sulfonamides, phenytoin, valproic acid and phenylbutazone compete for Binding Site I; medium chain fatty acids, probenecid , benzodiazepines and some penicillins compete for Binding site II
Drug Protein Binding: Blood Proteins- Globulins
1-acid glycoprotein (AAP or orosomucoid): A globulin, 44kDa.
* Many basic drugs (e.g. propranolol, lidocaine) bind to AAP.
* Globulins (, , and ) have low capacity and high affinity for endogenous substances such as corticosteroids.
* Also Immunoglobulins (IgG)