Week 4 - Pharmacokinetics Continued Flashcards
How do drugs induce metabolism?
The drug will interact with another receptor (usually in nucleus) and then thee receptor tranduces a signal to upregulate transcription of certain metabolitic enzymes
Upregulation of metabolism actually will increase the metabolism of the drug!
What is the free plasma drug concentration determined by?
- Rate of absorption
- Volume of Distribution
- Rate of Elimination
Concentration vs Time Plot
Zero Order Kinetics
and
First order kinetics
Zero order kinetics
- Rate is constant (e.g., 10 µg/hr)
First order kinetics
- Rate changes with and is proportional to drug concentration
Zero Order Elimination
- A common cause: saturation of a rate-limiting enzyme pathway at high substrate concentrations
Alcohol in blood is a good example of this… Linear decline**
First Order Kinetics*
This is most common***
- The rate is proportional to concentration
- Constant fraction of drug absorbed or eliminated per unit time
Passive diffusion is first order - and also the primary way drugs get into body
Distribution (chemical distribution in blood) is first order, concentration of drug in blood, it it is high it will deliver more drug, if concentration is low hyou will deliver less drug.
First Order Elimination Plot
GIve pt bolus of a drug, what does drug conc. X time look like?
First order elimination plot - log transformed
Alpha phase - distributional phase, out of plasma into tissues
In a realitively short amount of time a equilibrium is reached, this transitions into elimination phase.
Beta phase - elimination phase - rate is now determined by metabolism of drug (secretion)
The alpha phase (it is quick) can be ignored (for many drugs) and get a nice slope from elimination phase.
Co is theoretical concentration at time = 0
X is concentration
so Vd = X / Co
This is a great way to model drugs!
Half Life, t1/2
Time it takes for half of the drug to be eliminated from system.
Can be extrapolated from the log tranformed drug concentration vs time
First Order Elimination Mathematics
Rate is propotional to the negative of KeCt
Ke is 1/time - elimination rate constant
Slope = -(Ke/2.3)**
Know above.
This allows us to deterimine what the elimination rate constant is if we KNOW THE SLOPE.
Questions on this most likely.
Look at graph, calc slope, and find elimination rate constant**
Deriving the half life…
So half life is
t1/2 = 0,693/Ke
This is an inverse relationship
If elimination rate goes up, half life decreases*
If elimination rate goes down (slower to get out of body), half life goes up*
Derivation of Whole Body Clearance (Cl)
So elimination rate constant Ke
Ke = Cl / Vd **
Remember:
Vd = Total drug Conc / Plasma conc of drug
Vd = Ct / Cp
Ke = Cl (Cp) / Ct
This is how we think about kinetics, how to calculate dosing, how to figure out what problems are…
What is Clearance? (Cl)
assume that Cl adn Vd are defined with respect to Cp
How is it related to half life?
It is the volume of plasma that you would have to clear of drug in a unit of time (e.g., L/h) to account for observed elimination from the body
As with VD you can normalize to body wt. (e.g., L/h/kg)
t 1/2 = 0.693 (Vd / Cl) **
Cl and VD, why bother?
- ●Basis for rational design of drug dosing
protocols - Allows for physiological interpretation of
“solved” values- e.g., Cl close to GFR or VD close to the extracellular fluid volume
- Allows for mechanistic interpretation of observed kinetics in clinical practice
- e.g., if t1/2 is >> than expected you can look to Cl and VD for an explanation
Consider pt given bolus of IV dose of a drug, 1st order elimination kinetics. Lineaar extrapolation of log transofmred concentration vs time. Can calculate what?
apparent volume of distribution (Vd)
elimination rate constant (Ke)
Plama half life
Steaty state concntration
duration of distribution alpha phase
A - apparent volume of distribution (Vd)
Vc is 50 L
the elimination rate constant is 0.1/hr what is the whole body clearance?
D - 5.0 L/hr
Patient Dosing
Continuous Infusion
Periodic administration of a fixed dose (oral)
Plateau Principal (steady state)
Drug Input = Drug Ouput
At first the concentration would go up quickley but then the rate of infusion would match the rate of elimination - steady state.
Then if infusion is stopped.. Concentration will decrase quiclly
Rule of Thumb - during distribution and elimination phase, you will reach 93% of the steaty state (or elimination) in about 4 half lives*****
True for periodic oral dosing as well
What is a rule of thumb in drug dosing?***
Rule of Thumb - during distribution and elimination phase, you will reach 93% of the steaty state (or elimination) in about 4 half lives*****
Total drug vs Time plots
Ki - infusion rate
Ke - elimination rate
Xmax - Maximum plasma concentration of drug
Xmax = 1.44 Ki (t1/2) ***
Max conentration is directly proportional to Infusion rate and half life
If double infusion rate, the max conc will also double
The bar on the plot is the 4 half life rule (93% or max conc)
How does the elimination constant effect drug concnetration vs time and max concentration
By changing elimination constant, will get 93% of xmax in different ammounts of time
Max concentration is proportional to how fast the drug is eliminated…
Defining Steady State concentration
Css = Ki / Cl********
Most important equaiont
Concentration at steady state is proportional to the infusiton rate and inversly proportional to the clearance
So, if know clearance in an individual, and want to have a certain concentration in body can CALCULATE the infusion rate for the IV pump!
Now for periodic oral dosing…
Red line is constant infusion
Periodic oral dose is the blue line
Recognize that it is the same dosing rate*
If dosing interval is substantially larger than half life, the drug concentration fluctuates a lot but average concentration is the same (80 u/hr)
So pt may not be getting an effective dose periodically OR they may be getting a toxic dose of the drug periodically..
4 half life rule still applies***
What is the maintenance dose?
Maintenance dose = oral dose that will produce
the desired therapeutic level at steady state
= the amount that must be administered at plateau to replace drug that has been lost during the previous dosing interval
= the dosing rate (e.g., U/hr) that achieves the desired level of effect x the dosing interval (hr)/f**
where f is the fractional bioavailability - must account for fact that less than 100% of oral drug is getting into the system (some is extreted by gut) - so might have to double the dosage of an IV where you dont have to worry about losing part of the chemical in the GI tract…
Question:
Assume an infusion of 80 units/hr achieves the
desired average steady-state concentration for a
drug. Now assume that you’d like to achieve the same average concentration using an oral formulation, given once every 6 hours. Finally, assume that the oral drug has a fractional biovailability of 0.5 (50%). What would you prescribe as a maintenance dose?
Answer:
Maint. Dose = dosing rate x interval/f
= 80 units/h x 6 h/0.5
= 960 units, once every 6 h
So bascally with a bioavailability of .5 the drug must be doubled and be accounted for time
What is a loading dose?
If a drug takes a long time to get to steady state, can give a loading dose to incerease quicken this process…
It is the concentration we want to achieve multiplied by the volume of distribution devided by the bioavailability factor…
Loading dose = Css Vd / f ***
Question:
For a drug in question the steady-state plasma concentration that achieves the desired therapeutic effect is 5 mg/L. The published volume of distribution for this drug (based on average values for the population) is 2 L/kg and the expected oral bioavailability is 0.5 Your patient weighs 100 kg. What would you prescribe for this patient as a loading dose?
Answer:
First you need to know what the VD is for your particular patient, expressed in liters. Multiplying 2 L/kg times 100 kg gives a VD of 200 L.
Next, recall our relationship: Loading Dose (LD) = CSS VD/f
Doing the math, the LD = (5 mg/L)(200 L)/0.5 = 2000 mg
How does this actually happen in clinical practice?
- For most drugs (esp. those with a large TI), recommended dosing regimens based on “population” kinetic parameters (taking into account things like age, gender, etc.) can be used as a first step in patient care with relatively little concern for toxicity. These compounds have a LARGE TI (therapudic index)
- Under these circumstances optimization of drug dosage may be achieved by measurement of a clinically defined endpoint* that is responsive to the drug (e.g., blood pressure - can change drug based on results, clotting time, serum cholesterol).
- *As opposed to measurement of the drug itself which requires periodic blood sampling and is generally expensive
What is therapudic drug monitoring? (TDM)
Refers to patient-specific monitoring of serum drug levels and optimization of the dosing regimen as a means of tailoring treatment to the individual
When required (one or more of the following):
- Drugs with a narrow TI
- Poor correlation between administered dose and observed effects
- Large individual differences in CL
- A toxicity profile that is difficult to recognize clinically before serious damage occurs
Drugs that are commonly monitored include:
Aminoglycoside antibiotics (e.g., gentamicin)
Antiepileptics (e.g., phenytoin)
Cardioactive agents (e.g., digoxin, lidocaine)
Theophylline, lithium, methotrexate, cyclosporine
Involves a close relationship between the attending physician, a clinical pharmacy department, and (as needed) other specialists (e.g., for neonates, the elderly, dialysis patients)
How does TDM work?
Therapudic Drug Monitoring
Population kinetic parameters appropriate to a patient’s age, gender, weight, etc., are used in along with knowledge of a compound’s kinetic behavior (e.g., principle route of elimination) and routine measures of organ function (e.g., creatinine clearance) to design a dosing protocol (i.e., the same approach used for other drugs).
**Measured drug concentrations **are then used to monitor the patient and, if necessary, develop patient-specific kinetic parameters for use in adjusting the dosing regimen.
Adverse Drug Reactions
Others occur only in susceptible patients and may be difficult to predict prior to a drug’s approval for use. These are likely to have, at least in part, a genetic basis and include:
Intolerance; a lower dose threshold for the drug’s normal action. May have CL or VD basis.
Allergic reactions; effect unrelated to normal pharmacological action. Typically requires prior exposure which elicits an immune response.
Idiosyncratic reactions; effect unrelated to normal pharmacological action. Mechanism often unclear although some are probably immune responses
Adverse Drug Reactions
Some can be expected to occur in anyone (no special susceptibility is required). These include:
- *Overdose**
- Generally (but not always*) results in extreme manifestation of a drug’s usual pharmacological action
- *Drug-drug interactions;** recall various mechanisms
- One drug impacts the CL or VD of a second
- Two drugs operate on the same or opposing signaling pathways
- Physiological antagonism
*Recall: a higher dose may “unmask” a different effect
Non-Compartmental Analysis (for completeness)
Dont worry about this.
- Makes no assumptions about the “compartmental” nature of a system
- Based on statistical approaches
- Increasingly popular for drug development because it facilitates simple comparisons among drugs
- Gives Cl, VD, and Mean Residence Time (MRT): average time that a drug resides within the body following i.v. dosing
- MRT is conceptually similar to the elimination t ½
What is the concentration in the box (plasma)?
Know it.
First order elimination
Clearance and volume of distribution are now very important relationships we derived.
Problem solving guide
Key Relationships
Maintenance and Loading Dose
A single dose of 2 mg/kg is administered to a 75 kg patient. From a plot of the log drug concentration vs. time relationship you estimate the concentration of the drug at t0 to be 300 μg/dl. What is the VD of this drug in the patient?
Using the same plot that we generated in Question 1 we find that the slope of the elimination curve is -0.0434/h. What is the half-life for drug elimination (t ½)?
Numbers here are too complicated for exam so numbrers would be much simpler
Based on your responses to Questions 1 and 2, what would you calculate as the drug clearance this patient?
For the same patient in Questions 1-3 you may assume an average glomerular filtration rate (GFR) of 125 ml/min, or 7.5 L/h. You may also assume that the drug in question is 100% free in plasma and has a relatively low molecular weight.
What might your answer to Question 3 suggest to you with respect to the renal handling of this compound?
The compound is likely to be filtered by the kidney and the plasma Cl of 5.0 L/h estimated from your elimination experiment is somewhat smaller than the GFR. We might speculate, therefore, that this compound is partially reabsorbed in the kidney tubule, decreasing its renal clearance
Instructors note: In this absence of other information, however,
this type of speculation must be regarded with extreme caution)
Now let’s suppose that this drug is a weak acid and is
known to be partially ionized at the normal pH of urine
(typically around 6.0). Suppose further that when we
treat this patient with sodium bicarbonate the Cl increases to 7.5 L/h. Would this provide support for your response to Question 4, and if so why?
Yes. When you increase urine pH by adding base you tend to trap weak acids by shifting the equilibrium between the neutral and ionized forms toward the ionized form (which cannot be reabsorbed). This finding suggests that by adding base you have trapped all of the drug that is being filtered at the glomerulus (accounting for the fact that Cl now equals the GFR) and is consistent with the suggestion that this drug is eliminated primarily in urine
A single dose of 1 mg/Kg is administered to a 50 Kg patient. From a plot of the log drug concentration vs time, you estimate the concentration of the drug at t0 to be 1 mg/dl. What is the VD of this drug in this patient?
Imagine that the VD calculated in Question 6 is smaller than you expected to see, based on average PK parameters. Based on other information you know that this drug usually exhibits a moderate degree of plasma protein binding. Could plasma binding explain this unusual result?
Possibly. If the patient had unusually high levels of plasma binding protein (esp. the protein responsible for binding this particular drug) this would tend to decrease the VD. For drugs that are very highly bound to plasma proteins the theoretical minimum VD is approximately equal to the plasma volume. The plasma volume is about 4% of total body volume. In this particular case the solved-for VD is about 10% of total body volume, which is still quite small. This would suggest a high level of plasma binding.
What is the half-life (t1/2) of a drug assuming the following average (for a 75 kg patient) kinetic parameters: VD = 55 L; total body clearance (Cl) = 7 L/hr?
What does the VD from Question 8 (i.e., 55 L) suggest to you in terms of the distributional behavior of this drug?
If you express this VD in weight-normalized terms you get a value of 55 L/75 kg, or about 0.73 L/kg. This is approximately equal to a person’s whole-body water content. Based on this finding one might speculate that the drug distributes evenly into whole-body water.
A drug is known to be eliminated primarily by CYP enzyme activity. Your patient, who is taking this drug, is thinking seriously about quitting smoking. Is this fact relevant? If so, why, and what if any steps might you take as the individual’s doctor?
Yes, potentially. Smoking tends to induce CYP activity. If the patient quits smoking CYP activity could decline over time which could cause the Cl to decrease. It might be necessary, therefore, to reduce the drug dosing rate. Factors such as the drug’s therapeutic index and potential for toxicity would factor into the decision.
While in the hospital, a patient is infused with a drug at a rate of 10 mg/hr (as recommended for their age, wt., etc.), providing the desired therapeutic benefit. The patient is going to be discharged soon and you’d like to transition them to an oral dose once every 8 hr. Also, the oral bioavailability (f) of this drug is 80%. What would you prescribe for a maintenance dose?
Now suppose that the patient in Question 11, once discharged, exhibits a response which suggests that the drug is no longer working very well. Can you speculate on why this might be?
The most likely reason is that the drug’s oral bioavailability in this patient is lower than expected resulting in a reduced average concentration in plasma
Based on your response to Question 12, what questions would you ask the patient and what additional information would you like to know about this particular drug?
Reduced bioavailability may be due to higher-than-expected metabolism in the liver and/or GIT as well as dietary habits that promote retention of the drug in the gut contents (e.g., eating fatty foods, assuming that the drug is lipophilic). So, you might want to know how this drug is metabolized and whether there is any reason to think that metabolism would be induced in this patient (occupational exposures, other drugs they may be taking, etc.). You also might inquire about their dietary habits.
Now let’s suppose that by some means you determine that oral bioavailability in this patient is 80% (as originally expected). What else could explain the patient’s poor response to this drug? Hint: while doing your research you find that the elimination t1/2 is 2 hr. Recall that you have prescribed a pill that is to be taken once every 8 hr.
Now let’s suppose that by some means you determine that oral bioavailability in this patient is 80% (as originally expected). What else could explain the patient’s poor response to this drug? Hint: while doing your research you find that the elimination t1/2 is 2 hr. Recall that you have prescribed a pill that is to be taken once every 8 hr.
Your patient is male, middle-aged, and weighs 100 kg. You’d like to start them on an oral drug, beginning with a loading dose. Standard tables suggest that they be given a loading dose of 500 mg. You question this, however, given patient’s height (5’ 7”), physical conditioning (poor), and the lipophilic character of this drug. What is your reasoning and, if you need to adjust the loading dose, will you have to increase it or decrease it?
Given the drug’s lipophilic character and the fact that this patient is obese we might expect the VD for this drug in this patient is greater than the average value. Recalling that the L.D. is impacted by VD we question the table value. Finally, noting that L.D. = CSS (VD)/f we can speculate that the required L.D. (to achieved the desired CSS) will have to be increased
