Kinetics Exam 3

7/28/2019 Kinetics Exam 3

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Pharmacokinetics Lecture One

August 24, 2009

Pharmacokinetics is the study of drug Absorption, Distribution, and Elimination or how the

drug moves through the system; Elimination can be broken down into Metabolism and

Excretion; some drugs may go through either metabolism or excretion, and some drugs maygo through both

Clinical pharmacokinetics deals with how these concepts apply to individual drugs

Pharmacokinetics is employed in every aspect of pharmacy

Drug Interactions

Drug-drug, drug-food, and drug-disease interactions can either increase or decrease theeffect of a particular drug

Drug-food interaction: for example, if bisphosphonates are given with foodabsorption decreases causing a decreased drug response; if iron is given with

orange juice absorption increases causing an increased drug response

Drug interactions can either be kinetic or dynamic:

1. Kinetic interactions- 80% or more of drug interactions are kinetic in nature; anyalteration in kinetics will change the dynamics (or response), but alterations in

dynamics do not alter the kinetics; the more drug that gets to the receptor site,

the more intense the response [D -> DR -> Intensity]; the kinetics can alter theamount of drug that gets to the receptor site; the interaction of Probenacid and

Penicillin is kinetic because Probenacid decreases the renal excretion of Penicillin;

Zyvox can cause the levels of Demerol to increase; this interaction would only be a

problem if the patient continues to take the Demerol; if the patient takes their last

dose of Demerol and then takes Zyvox it would not be a problem because if the

patient is not still taking the Demerol it cannot accumulate in the body; Demerol

concentrations may increase in the body, but they will not be able to reach a toxic

level because there is not any accumulation; kinetic interactions involving absorption

can be overcome by spacing the drugs out, but kinetic interactions involving

distribution and elimination cannot because the drug is already in the system2. Dynamic interactions- i.e. Vancomycin and AminoglycosidesSome drugs work synergistically to cause a greater response:

- Aminoglycosides and Vancomycin used to treat MRSA; Aminoglycosides do not treatMRSA because they are strictly Gram - and Staph is Gram +, but for some reason

when Aminoglycosides are used with Vancomycin the killing activity increases;


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Aminoglycosides do not affect any kinetic parameters (absorption, distribution,

elimination) of Vancomycin so this is a pharmacodynamic interaction

- Probenacid decreases the renal excretion of Penicillin, because it blocks the renaltubular secretion of Penicillin; this causes the Penicillin response to increase

because less Penicillin is being excreted; this is a kinetic interaction

Drugs can either be bound or unbound to plasma protein:

1. Bound: highly protein bound drugs are inactive because they cannot crossmembranes to get to the site of action

2. Unbound: the unbound form of the drug is the active form because it can crossmembranes to get to the site of action

When we take a blood level it contains a combination of bound and unbound drug; ifprotein binding is affected, then distribution is affected; if something displaces a

drug from its protein binding site there is more unbound drug to interact with the

receptor site (increased distribution); when distribution increases, blood

concentration decreases

Volume of Distribution

- When the volume of distribution increases, the blood concentrations decreasebecause the drug has moved out of the blood and into the tissue

- A blood sample will contain bound and unbound drug, but most of it will be boundbecause the unbound drug has the potential to leave the bloodstream and diffuse

into the tissue

- If you give something that causes protein displacement the concentration of drug inthe blood will decrease because the unbound drug now has the potential to leave the

bloodstream and go into the tissue; this will cause an increased drug responsebecause more drug is able to get to the site of action; thus there can be situations

where the blood concentration is low, but the response is greater

- Example: it doesnt matter if you give Coumadin at 8 am and Aspirin at 8 pm, theAspirin will still displace whatever Coumadin is left on the protein binding sites

causing an increased Coumadin effect

The terms blood concentration, serum blood concentration, and plasma concentration do

not mean the same thing, but in practice they are often used interchangeably

Blood concentration- in practice we usually obtain a blood concentration, not aplasma concentration; the blood concentration measures the total amount of drug in

the plasma, as well as the blood elements

Plasma concentration- the blood is centrifuged and the RBCs, WBCs, and plateletsare removed (the clotting factors are still present); a plasma concentration only

measures the amount of drug present in the plasma, but some of the drug will be in

the blood elements that are removed


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Serum blood concentration- the blood is centrifuged again until just the wasteproducts are present (electrolytes, water, albumin); all blood elements and clotting

factors are removed so this concentration does not represent the amount of drug

present in those tissues

Things that can alter the pharmacokinetics of a drug include:- Diet: diet usually affects absorption, but not in every situation; an exception to this

would be foods high in Vitamin K and Coumadin; if someone is on Coumadin and they

are eating a lot of collard greens their Coumadin response will go down because

Coumadin works on Vitamin K dependent clotting factors (the more Vitamin K given,

the more clotting factors are produced)

- Disease: disease states can affect any aspect of kinetics (i.e. liver cirrhosis andelimination, Chrons Disease and absorption)

- Other drugs: other drugs can affect any aspect of kinetics (i.e. Questran preventsthe absorption of Digoxin in the GI tract, Aspirin increases the distribution of

Coumadin by displacing it from protein binding sites, Probenacid prevents theelimination of Penicillin by blocking renal tubular secretion)


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Pharmacokinetics Lecture Two

August 26, 2009

Factors that can alter pharmacokinetics:

- Food- Disease- Other drugs

If all you see is a change in response (synergism, antagonism), it is a pharmacodynamic

interaction; if there is an alteration in ADME then it is pharmacokinetic

Absorption Every route of administration has to be absorbed except for IV; intrathecal

injections have to be absorbed into systemic circulation as well in order to be

excreted; some drugs are broken down before they are absorbed by stomach acid,

bacteria, etc; some drugs are excreted through the feces unchanged (it got

absorbed, went through the enterohepatic circulation without being metabolized,

and went back into the intestines or it was never absorbed to begin with)

There are 3 basic rate limiting steps for oral absorption:1. Disintegration- this is the first thing that has to happen; the faster the

drug breaks down, the faster it is absorbed; this is where brand and generic

(or two different generics) products might differ; if one drug is bound

tighter than the other it will take longer to disintegrate; powders absorb

faster because they are already disintegrated (i.e. BC powder)

2. Dissolution- the faster it goes into solution, the faster it is absorbed(gelcaps vs. tablets); gelcaps will work faster because they disintegrate

faster and are already in solution

3. Absorption across the cell membrane Water crosses the cell membrane (which is lipid) freely; water moves

from a higher concentration to a lower concentration across a

concentration gradient (osmosis)

Things that cross the membrane freely: unionized particles that arenot too big; select small molecules; lipid soluble substances (lipid

soluble vitamins A, D, E, & K); Vitamin E is an antioxidant that is able

to cross into the CNS; if you eat a meal high in fat not all of the fat

will be absorbed, and Vitamin E absorption will decrease because the

Vitamin E will get trapped in the fat; this is a kinetic interaction

Things that do not cross the membrane freely: highly chargedparticles (just because a substance is highly charged it doesnt mean

that it wont cross, it just wont cross freely; it needs a carrier; if

something is said to be 100% ionized there is still a small portion that

is unionized; this small percentage of unionized particle will be able to


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cross the membrane; thus highly charged substances might absorb

slower, but they still absorb; if GI motility increases the drug will be

pushed through the GI tract and not have the opportunity to be

absorbed); large molecules, such as proteins, cannot cross the

membrane freely; these molecules can cross but they need energy or

a carrier The rate and extent of absorption depends on the solubility and

formulation (liquid, elixir, tablet, ER tablet) of the drug; the rate and

extent of absorption also depends on the pka and whether the drug is

acidic or basic, and the individuals physiological environment

(vascularity, GI motility, stomach pH, fat content, amount of lean

muscle mass with IM injections); warm drinks increase absorption and

cold drinks decrease absorption, but water is best absorbed when it

is cold

Bioavailability Absorption is a subcategory to bioavailability; anything that affects absorption will

affect the bioavailability, but everything that affects bioavailability does not

affect the absorption

Bioavailability describes how much drug is available in systemic circulation;absorption tells how much drug is absorbed; a drug has to be absorbed in order to

go through first pass metabolism; if the drug goes through first pass metabolism

there is less available in systemic circulation, thus absorption is not affected but

the bioavailability is

F tells us the amount of drug that is absorbed (the amount of drug that enterssystemic circulation); F does not represent the absolute bioavailability

F = (the amount of drug that reaches systemic circulation)/(the amount of druggiven)

Absolute bioavailability = 1 ER nonhepatic loss Dose x S x F = what is available to work S (the chemical form) does not affect absorption, but it does affect bioavailability

because it changes the amount that is available in systemic circulation; for

example, lets take Dilantin (Phenytoin sodium); Dilantin is 92% acid and 8% salt so

the S factor for Dilantin would be 0.92; if 100 mg of Dilantin were given by mouth

and all of it was absorbed the F would be 1.0 because all of the drug is absorbed

but only 92% is available to work so the absolute bioavailability would be different


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Pharmacokinetics Lecture Three

August 31, 2009

F represents bioavailability

F = how much drug that reaches systemic circulation/ the total amount of drug given

S is the chemical formDose x S x F = the amount of drug that reaches systemic circulation

Things that affect absorption/bioavailability:

1. Solubility2. Chemical form3. Physiologic environment of the individual4. First pass affect: does not affect absorption (because the drug has already been

absorbed), but does affect bioavailability; some drugs undergo first pass affect,

but it doesnt make that much of a difference (i.e. only 1% of the drug is lost); some

drugs do not undergo first pass at all; about 1,500 mLs of blood comes through theliver per minute; some of it comes from the hepatic artery and some comes from

the portal vein; about 75-80% of the 1,500 mLs comes from the portal vein whichgets its blood from the stomach and small intestines; thus 900-1000 mls of blood

comes from the stomach and small intestines into the portal vein; the first stop the

portal vein makes is the liver; this is why some drugs go through first pass affect;

when the drug goes to the liver some of the drug is extracted out and what is left

is the amount that is able to work in systemic circulation; thus, the amount that is

given by mouth is not the amount that is available to work; if the drug is given IV it

bypasses first pass; Morphine is an example of a drug that undergoes first pass

affect

Extraction ratio: ER = (Ca (amount that went in) Cv (amount that cameout))/Ca

ER = (10-2)/10 = 0.8; the ER = 0.85. GI motility: fast GI motility causes decreased absorption; slow GI motility causes

increased absorption

Gastric emptying: the first place the drug goes when it is taken orally is thestomach; the pH of the stomach is about 2 (it can be as low as 1 or as high

as 3); when a basic drug is taken it will increase the pH of the stomach;

when food comes into the stomach, acid is secreted to maintain a low pH;

anytime something causes the pH to drop, gastric emptying is triggered;

gastric emptying can take anywhere from 1-3 hours; the duodenum is small

part of the small intestine, but it is where most absorption takes place

(things can be absorbed anywhere in the intestine, but not as much as they

are in the duodenum); the average pH of the duodenum is 6; the pancreas

secretes pancreatic juices including bicarbonate directly into the duodenum

causing the pH to rise; the pancreas also secretes lipases that help to


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emulsify fats; if you want to avoid decreasing absorption of drugs when

taking antacids you should take the drug 1 hour before or 2-3 hours after

the antacid; it is easier to take the offended drug before the offending

drug (i.e. take Digoxin 1 hour before Questran rather than taking it 3-4

hours after Questran)

Small intestine transit time: SITT is the time it takes for food to beemptied into the duodenum and expelled through the anus; if something

causes gastric emptying to proceed faster it can cause GI motility to

increase; just because gastric emptying is increased (emptied faster) it

does not mean that SITT has to change (but it can change); SITT is roughly

3-4 hours; average GI motility is 4-8 hours; if SITT proceeds faster or GI

motility increases, absorption decreases because there is less time for the

drug to be absorbed

6. Vascularity: blood vessels under the tongue absorb drugs rapidly; we used to tellpeople with hypertensive urgency to chew up a Nifedipine and hold it between their

gums; this can lower the BP too fast7. Ionization state8. pH: enteric coated ASA will stay intact in the acidic environment of the stomach

and will dissolve in the basic environment of the duodenum; pH affects absorption

because of the ionization state but also because like dissolves like

AUC = concentration/time

True bioavailability takes AUC into account; F only deals with the extent of absorption;

true bioavailability not only takes into account how much gets there, but also how long ittakes to get there; true bioavailability deals with the concentration and the time (AUC)

Bioequivalent: same AUC, same Cmax, and same Tmax; this is usually the case for brand

and generics, but not all brand and generics are bioequivalent because they may have the

same AUC, but a different Cmax and Tmax; this difference has to do with the amount of

pressure used to bind the drug; if a drug is bound tighter it will release disintegrate more

slowly; brand vs. generic and generic vs. generic should be bioequivalent; if there is greater

than a 5% error in the Cmax and Tmax, the drug is considered to not be bioequivalent

Therapeutically equivalent: therapeutically equivalent drugs treat the same thing (Toradol

and Vicodin are considered to be therapeutically equivalent); not only does the drug have

to treat the same thing, but the dose has to match to get the equivalent therapeutic

effect (Zocor 20 mg = Lipitor 10 mg, Zocor 40 mg = Lipitor 20 mg, Zocor 80 mg = Lipitor

40 mg)


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Pharmacokinetics Lecture Four

September 2, 2009

We have a patient that normally takes Captopril first thing in the morning, before

breakfast; they called in their Rx the night before and forgot to pick it up; on this day

they do not take it first thing in the morning because they have to pick it up at thepharmacy; on the way to the pharmacy they eat some oatmeal; the pharmacy dispenses a

different generic than what the patient usually gets; now the patients blood pressure is

not being controlled as it normally is:

- This could be due to differences in the two generic medications (differentbioavailabilities)

- This could be due to eating before taking the medication; the absorption of thedrug was decreased due to food

- The blood pressure was checked at a different time than it usually is- The patient might have been under more stress than usual

When something is absorbed, the first place it goes is the liver; 75% of the blood that

goes to the liver comes from the portal vein; not every drug is affected by first pass

effect

Things that affect GI motility:

1. Cold drinks can slow GI motility because they cause blood vessels to constrict; thisdecreases blood flow to the stomach and intestines

2. High fat meals slow GI motility3. Anticholinergic drugs slow GI motility; Cholinergic drugs increase GI motility4. Prolonged affects of diabetes can slow GI motility (Diabetic Gastroparesis); we can

treat this by giving drugs that increase GI motility, such as Cholinergic Drugs,

Metoclopramide (Reglan), and Erythromycin

5. Severe diarrhea increases GI motilityDistribution

- Anytime a drug is absorbed into the body, it circulates the system and isdistributed throughout the entire body

- We have to use enough drug so that it reaches the site of action (if you have a bigtoe infection, all of the medication does not go to the big toe, but we have enough

drug in the system to treat the problem)

- If we know how the drug is distributed to different areas we can have an idea ofhow much drug will reach the site of action

- The amount of drug in the blood is proportional to the amount of drug at thereceptor site; as the amount of drug in the blood increases, the amount of drug at

the receptor site should increase (there are certain things that can cause this rule

to falter)


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- We need to dose the drug so that the concentration in the blood remains at a levelto where there is enough drug to reach the receptor site

- When a drug transfers from the GI tract to the bloodstream it is absorbed; when adrug transfers from the blood to a tissue it is distributed; if the drug then leaves

the tissue and goes back into the bloodstream it is reabsorbed

- Volume of distribution: a concept that helps us to understand the volume that thedrug is contained in; this is not an accurate number, it is an estimate; you only use

Vd to calculate the loading dose

- The loading dose allows us to achieve a certain concentration, provided we know thevolume we are putting it in

- If S and F are not given, use 1- If you put 100 mg in and the concentration came out to be 1 mg/L, then the volume

would be 100 L; use Vd = Dose/C (100 mg)/(1 mg/L) = 100 L

- If the volume is 10 L and we have a concentration of 10 mg/L we would need to give100 mg; use LD = Vd x C/(S x F) (10 L x 10 mg/L)/(1 x 1) = 100 mg

- Use the clearance to find the maintenance dose; use the Vd to find the loading dose- Loading dose is the same thing as a bolus dose; these give the concentration that

we need immediately

Equations:

D = S x F D = dose, F=bioavailability, S=chemical form

D = Vd x C Vd=volume of distribution, C=concentration

LD = (Vd x C)/(S x F) LD=loading dose

Cl = Vd x k Cl=clearance, k=rate constant

C = (D x S x F)/(Vd x k) or C = (D x S x F)/Cl


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Pharmacokinetics Lecture

September 4, 2009

Volume of distribution is used to determine the loading dose:

LD = (Vd x C)/(S x F) Vd = (LD x S x F)/C

Example:

A 22 year old female needs to receive Tobramycin at a concentration of 10 mg/L; calculate

the loading dose if she weighs 110 lbs and the volume of distribution is referenced as 0.25

L/kg (if S and F are not given, assume them to be 1)

1. (110 lbs)/(2.2) = 50 kg2. Vd = 0.25 L/kg (0.25 L/kg) x 50 kg = 12. 5 L3. LD = (Vd x (Cdesired - Cactual

))/(S x F) (12.5 L x (10 mg/L 0))/(1 x 1) = 125 mg

Answer: LD = 125 mg

Example:

Now assume a maintenance dose (MD) was not given; the concentration is later measured

to be 4 mg/ml; figure out the LD to get the patient back up to the desired concentration

of 10 mg/ml

1. LD2 = (Vd x (Cdesired Cactual

))/(S x F) (12.5 L x (10 mg/L 4 mg/L)/(1 x 1) = 75

mg

Answer: LD2

= 75 mg


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Example:

The patient receives the loading dose of 125 mg, but the concentration in the blood is

measured to be 6 mg/L (which is not the desired 10 mg/L); calculate the loading dose that

would be required to bring the patient to 10 mg/L; take into account the Vd for this

patient obviously came out different than the population average of 12.5 L

1. We need to find the patients VdLD = (Vd x C)/(S x F) Vd = (LD x S x F)/C (125 mg x 1 x 1)/6 mg/L = 20.8333 L

2. Using the correct Vd, recalculate the next LD to bring the patient up to thedesired concentration of 10 mg/L

LD2 = (Vd x (Cdesired Cactual

))/(S x F) (20.8333 L x (10 mg/L -6 mg/L))/(1 x 1) =

83.3332 mg

Answer: 83.3332 mg

The LD2

will add 4 mg/L of Tobramycin to bring the patient up to 10 mg/L

Dosing is usually based on ideal body weight (IBW); IBW only takes into account those who

are 5 feet tall and taller; this can be problematic for children and adults under 5 feet tall

since dosages are generally based on weight; people that do not fit into the normal

parameters for IBW dosing are dosed upon actual weight; depending upon the drug, this

patient is at risk for drug toxicity because the dose may be too high (this is a problem for

obese children)

IBW for men: 50 kg + (2.3 x every inch over 60 inches)

IBW for women: 45.5 kg + (2.3 x every inch over 60 inches)

Each inch greater than 60 inches is approximately 5 pounds; if someone is under 60 inches

tall, we can adjust the dosage based on this weight conversion

For example, if a person is 49 they are 3 inches under 60 inches; if they weigh 160

pounds we might subtract 5 pounds per inch under 60 inches (it is better to under dose

than overdose

Ex: (5 lbs x 3) = 15 lbs 160 lbs 15 lbs = 145 lbs


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We would dose the patient as if they were 145 lbs instead of 160 lbs

Round to four decimal places at the very end when working problems!

Factors that affect distribution:

- Differing characteristics of body tissue The higher the Vd the lower the blood concentration A very lipophilic drug in an obese person will have a larger Vd because it

distributes well to the adipose tissue thus they will have a greater affect; a

hydrophilic drug will not distribute very well in an obese person, thus they

might have a decreased affect

A very hydrophilic drug in a patient with fluid accumulation will have a higherblood concentration

- Disease states that alter physiology CHF causes edema which alters drug distribution Liver failure decreases albumin production leading to ascites; ascites is

accumulation of fluid in the peritoneal cavity; if a drug is hydrophilic, it willdistribute to this area, thus increasing Vd

- Protein binding Increased protein binding will decrease the Vd causing a decreased effect

(protein bound drug does not cross the membrane; as protein binding decreases,

more drug stays in the blood stream; this makes the concentration look high,

but the effect is decreased)

Decreased protein binding will increase the Vd causing an increased effect(more drug crosses the membrane to get to the site of action; the blood

concentration is lower, but the effect is increased)

We need to know if a drug is significantly protein bound to discern whether thiswill be an issue


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Pharmacokinetics Lecture SixSeptember 9, 2009

Volume of distribution (Vd) Concept that tells us how much volume the drug is contained in; it can appear

to be very high or very low; it is not accurate, it is just a concept Concentration and Vd are inversely proportional; if Vd increases, blood

concentration of the drug should decrease Concentration and therapeutic response are proportional; a higher drug

concentration in the blood should give a higher amount at the receptor siteand therefore produce a higher therapeutic response; this relationship canbe altered by protein binding

Protein Binding Protein binding can alter volume of distribution If we have a drug that is highly protein bound and we cause binding to

decrease, then the amount of drug in the blood will decrease; the volume ofdistribution increases because decreased protein binding allows more freedrug to get to the site of action which will lead to an increased response;when the blood concentration decreases, the response is supposed todecrease, however, decreased protein binding can lead to an increase inresponse because more drug is free to cross the membrane and get to thesite of action

A measured drug blood level contains the concentration of bound andunbound drug in the body; the unbound drug is the free drug/active form; it

has the ability to cross the membrane and work; if it is bound, 9 times out of10, it will not cross the membrane and work because it has to be free inorder to distribute across the membrane and reach the site of action; wetechnically only need a small amount of free drug to gain a therapeuticresponse; if 99% of a drug is protein bound, and 100 molecules are put in, allwe really need is 1 free molecule to produce the desired response

In theory, if protein binding increases, the Vd should decrease and so shouldthe response; if protein binding decreases, then volume of distributionincreases

Just because protein binding decreases, it doesnt mean there will be toxiceffects (it is just that the potential for toxic effects is there); theresponse should increase but sometimes it will and sometimes it wont

Example:o Phenytoin (Dilantin) is a highly protein bound drug; it is 80-90%

bound; if protein binding with this drug decreases, the bloodconcentration will decrease due to an increase in Vd; the therapeutic


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range for Dilantin is 10-20; if the patient has a concentration of 8, dowe adjust the dose?

In practice, if the concentration was 8 and the patient wasnthaving signs/symptoms of seizures and was doing fine, thenleave it as it is; if we adjust him to 15 and his therapeutic

range reaches 20 then he will start to experience toxicities;we should monitor the patient until an adverse event occursand then re-evaluate the patient

Example:o Scenario 1: a patient who is not on ASA comes in and is started on a

LD and MD of Phenytoin for his seizures; a blood level is taken and itreads 8; we can then adjust the level to 15 because we would wanthim to be in therapeutic range since hes just starting treatment

o Scenario 2: a patient has been on Phenytoin for a while and histherapeutic range is usually at 15; another physician prescribed him

Ibuprofen 600 mg TID everyday; now, all of the sudden he isexperiencing toxicities; his blood level is taken and it reads 12; eventhough it is still within normal range, the problem is a decrease inprotein binding because the Ibuprofen has caused the Phenytoin tobe displaced and more free drug is available to reach the receptorsites; we could stop the Ibuprofen but the physician wants it to becontinued, therefore, we need to decrease the dose of Phenytoin;doing this might cause the concentration to drop to a lower thannormal range but even though blood concentration is lower, theamount at the receptor site will be at normal range; we can assume

that at 8, this patient will be fineo A decrease in protein binding should mean more drug at the receptor

site, but if something also stimulates hepatic microsomal enzymes,then there will be increased excretion/metabolism; would we see anincrease in response? probably not; we would most likely need toincrease the dose of the drug


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Multiple compartments can exist depending on the drug and bodycomposition; generally, we deal with 1 and 2 compartment model

Compartment Models

Most of the drugs we talk about will follow a one-compartment model One-Compartment Model

o A one-compartment model says that the body is considered to be onecompartment and that when a drug is added to the system, itdistributes throughout the entire body instantaneously

o C = Coe-Kto After a drug is placed into the system, it distributes instantaneously

and the body will then try to eliminate it via metabolism or excretion

is the one compartment model equation

o The equation A=Aoe-Kt is essentially equal to the C= Coe-Kt

Co = A

equation; Cis equal to concentration, and A is equal to amount, thus A and Crepresent the same thing depending on what we are talking about

o = C1 = Cmax C = Cp = C

= Peak

2 = Cmino k, k = Troughel, ko t represents time

all represent the elimination rate constant

o k = slope of the conc vs time lineo t = Ln (C2/C1o K = Ln (C

)/k

2/C1o e

)/t-kt

A drug is placed into the system:

= factor of decline or % remaining; if this is 100 and thisanswer comes out to be 0.2, how much did we lose? 80% is lost and20% is remaining

At t=0, no drug is lost, therefore 100% is stillremaining and e-kt

If we allow time to pass, e= 1

-kt

It takes 5-7 half lives before C becomes 0; at 5 halflives, about 90% of drug will have been lost; at 7 halflives, about 97-99% of drug is lost and C is close to 0because the drug is almost completely eliminated fromthe system

will change


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Example:Given: t1/2

= 8 hours; 70 kg male; Vd = 0.5 L/kg; Cd = 15 mg/L; calculate aloading dose

1. LD = (Vd x C)/(S x F) [(0.5 L/kg x 70 kg) x 15 mg/L]/(1 x 1) =525 mg

Answer: LD = 525 mg

Example:The physician decides to give another bolus dose 24 hours later; what is theconcentration 24 hours later?

1. k = (0.693)/(t) 0.693/8 hrs = 0.0866 hr-1

2. C = Coe-kt C = 15 mg/L x e-(0.0866hr-1*24hrs)

= 1.8770 mg/L

Answer: C = 1.8770 mg/L


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Pharmacokinetics Lecture Seven

September 11, 2009

Example from Wednesday:

Given: 70 kg male; t1/2

= 8 hours; Vd = 0.5 L/kg; Cd = 15 mg/L

1. LD= (Vd x Cd)/(S x F) (35L x 15 mg/L)/ (1 x 1) = 525mg

2. Calculate A after 24 hours:k = ln2/t1/2 0.693/8 hours 0.0866 hr

-1

A= Aoe-kt

525mg x e-(0.0866hr-1 * 24hrs)

= 65.6934 mg after 24 hours

3. Calculate Concentration after 24 hours:C=Coe-

kt C= 15 mg/L x e-(0.0866hr-1*24hrs)

= 1.8770 mg/L

Example:

Using the concentration from the previous example (Wednesday), figure outthe loading dose (LD) required to bring the concentration up to 15 mg/L

1. LD = [Vd x (Cd-Ca)]/(S x F) [35 L x (15 mg/L 1.8758 mg/L)]/(1 x 1) =459.3470 mg

Answer: LD = 459.3470 mg


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Example:

If we gave 525 mg of drug as the LD, but the concentration measured in the

blood turned out to be 10 mg/L, calculate the necessary LD to get the

concentration up to the desired level

1. Calculate the patients actual volume of distribution; the Vd used inthe problem above was based off of population averages, but the

patients distribution was greater given that the concentration was

lower than what it should have been:

Vd = (LD x S x F)/C (525 mg x 1 x 1)/10 mg/L = 52.5 L

2. Now calculate the second loading dose given the patients specificvolume of distribution:

LD2 = [Vd x (Cd-Ca)]/(S x F) [52.5 L x (15 mg/L 10 mg/L)]/(1 x 1) =

262.5 mg



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Example:

After 36 hours, the physician returned and wanted to give another loading

dose to restore the concentration back to 15 mg/L (our desired level);

calculate the LD, not taking LD2

into account:

1. First we need to know the current blood concentration since it hasbeen 36 hours:

Co = 10 mg/L (because we gave 525 mg only)

t1/2 = 8 hours

Kel = 0.0866hr

-1

C = Co x e-kt 10 mg/Lx e-(0.0866hr-1*36hrs)

= 0.4426 mg/L

2. Now calculate a LDthat would increase the blood concentration from0.4426 mg/L (what it is after 36 hours/currently) to the desired

level of 15 mg/L

LD = [Vd x (Cd-Ca)]/(1 x 1)

[52.5 L x (15 mg/ml 0.4426 mg/L)/(1 x 1) = 764.2635 mg


C0 = (LD x S x F)/Vd C = C0 x e-kt C = [(LD x S x F)/Vd] x e

-kt


20/79

- When a drug is given and does not distribute instantaneously to all tissues, itcannot be considered a one-compartment model; instead, the drug rapidly

distributes to the central compartment and then slowly distributes to the

peripheral compartments

Two Compartment Models

- The drug moves slowly from the central compartment to the peripheralcompartments until equilibrium between the 2 compartments is reached

- The central compartment consists of highly perfused areas including the: Lungs Kidneys Liver Blood Heart

- The peripheral compartments consist of tissues whereby distribution occursat a slower rate; these include:

Adipose tissue Skeletal muscle Cerebrospinal Fluid (CSF)

- The two compartment model consists of 4 stages:I. Initial injection- everything distributes quickly to the central

compartment

II.Distribution- small amounts of drug are transferred from thecentral compartment to the peripheral compartment until

equilibrium is reached between the two

III. Equilibrium- reached between the central and peripheralcompartments

IV.Elimination- elimination ONLY occurs from the centralcompartment; as drug is eliminated from the central

compartment, drug will transfer from the peripheral compartment

back to the central compartment to re-establish equilibrium; as

more drug continues to be eliminated from the central

k 12

k 21

Central

Compartment

Peripheral

Compartment


21/79

compartment, more drug will shift from the peripheral

compartment until the drug is completely eliminated; the central

compartment is considered the eliminating compartment because

it contains the kidneys and the liver

Two Compartment Model Equation- C = A x e-kt + B x e-kt

T = time; it is the same for both k

o (K= distribution rate constant

1-2 + K2-1 = K A is a concentration obtained by residual method

)

K B is a concentration obtained by extrapolation

= elimination rate constant

- A will ALWAYS be larger than B; if upon calculation, A doesnt turn outto be larger than B, then something in the calculation is WRONG

- Therefore, distribution (represented by A x e-kt) is ALWAYS faster thanelimination (represented by B x e-kt

- Also, k)

(Distribution rate constant) will ALWAYS be higher than K

- Because k

(Elimination rate constant)

> K

- Once equilibrium occurs, the system will eliminate exactly like a onecompartment model; clinically, we can wait until we know equilibrium has

occurred before we take blood concentration levels; therefore, we can

calculate blood levels using the one-compartment model equation; this is

accomplished by knowing the distribution half-life; after 5-7 half lives,

distribution can be considered complete and therefore, equilibrium has

occurred and only elimination is going on

, the distribution half-life will be SMALLER than the

elimination half-life; this means it will take less time for distribution to

occur than it does elimination

Proof: Consider the distribution half-life is 2 hours:o 5 half-lives x (2 hours/1 half life) = 10 hourso A x e-kt = A x e-k(10 hours)

= A * 0 = 0


22/79

Pharmacokinetics Lecture Eight

September 14, 2009

Be able to distinguish:

- One compartment models from two compartment models just by looking at a graph- First order kinetics from zero order kinetics by knowing the drug

Methods of residual can be used to find A.

ka should always be greater than k

B

I

II

III

IV

I: Initial injection

II: Distribution

III: Equilibrium

IV: Elimination

Semi-log

Paper

Concentration

A

B

Time


23/79

If we are given one concentration (C) and t 1/2a (or ka

) we can calculate A.

A = C/(e-kat

)

Vancomycin is an example of a drug that undergoes a two compartment model. After

infusing it, it takes approximately 2 hours to reach equilibrium, at which point it follows aone compartment model. We infuse Vancomycin over at least one hour. For class purposes,

we measure Cb (for the peak) one hour after the start of the infusion.

Example:

t1/2a = 0.5 hours A = 30 mg/L

t1/2B

= 24 hours B = 20 mg/L

A) Find the concentration after 1 hour has passed1. Calculate ka and kB

given their respective half-lives

ka = 0.693/0.5 hr = 1.386 hr

-1

kB = 0.693/24 hr = 0.0289 hr

-1

2. Calculate CC = A x e-kat + B x e-kBt

[(30 mg/L x e-(1.386 hr-1 x 1 hr)) + (20 mg/L x e-(0.0289 hr-1 x 1 hr)

)

7.5022 mg/L + 19. 4303 mg/L = 26.9325 mg/L



24/79

B) If the drug reaches equilibrium at 5-7 half-lives, calculate C after 7 hoursC = A x e-kat + B x e-kBt

[(30 mg/L x e-(1.386 hr-1 x 7 hr)) + (20 mg/L x e-(0.0289 hr-1 x 7 hr)

)

0.0018 mg/L + 16.3370 mg/L = 16.3388 mg/L


Digoxin also undergoes two-compartment model kinetics. It is recommended that theloading dose be split into 3 doses, but some practitioners split it in half. If given all at

once, too much Digoxin will distribute rapidly to the central compartment leading to

toxicity. It will take about 4 hours for Digoxin to reach equilibrium because the t1/2a for

Digoxin is 35 minutes (35 minutes x 7 half-lives = 245 minutes or 4.0833 hours). We then

wait 12-24 hours after the loading dose to get the blood concentration (Cb). The t1/2B for

Digoxin is 36-48 hours.


25/79

Pharmacokinetics Lecture Nine

September 16, 2009

In two compartment models there are four stages:

- Stage I: this is time zero (but it really isnt at zero time); we are looking at thesystem as if we got all of the drug in

- Stage II: this is the distribution stage (elimination is also occurring); if distribution(or elimination) is altered the entire process is affected

- Stage III: in stage III, equilibrium is reached; distribution has taken its courseand we are at steady state (if you wait until distribution has occurred, you can

treat it as if it were a one compartment model)

- Stage IV: this stage represents elimination

*** There are 3 types of people that will remember change down to the penny

(because pennies make dollars):

Broke people Stingy people Drug dealers/pimps

I

II

III

IV

I: Initial injectionII: Distribution

III: Equilibrium

IV: Elimination

Semi-log

Paper

Concentration

A

B

Time


26/79

How to Calculate the Concentration at Normal Protein Binding

The following equation will correct concentration measurements based on fluctuations in a

patients normal albumin levels

Equation: Cb = Cbactual/[((1 ) x (Pactual/Pnormal

)) + a]

** The albumin levels need to be altered

in order to use this equation; if albumin levels are

not altered, we do not use this equation**

Cb = concentration

Pactual = actual protein (patients actual albumin level)

Pnormal = normal protein (normal albumin levels range from 3.5-5.5 g/dL; in this class we will

use 4.5 g/dL)

a = amount or % unbound (if there is a range, apply the amount or % that makes it more

significant)

Example:

A patient had an actual measured plasma concentration of 8 mg/L of Phenytoin and an

albumin level of 2.5 g/dL. Find the actual concentration of Phenytoin if it is 90% bound.

Cb = Cbactual/[((1 a) x (Pactual/Pnormal

)) + a]

Cb = (8 mg/L)/[((1 0.1) x (2.5 gdL-1/4.5 gdL-1

)) + 0.1] = 13.3333 mg/L

Answer: Cb = 13.3333 mg/L


27/79

In patients that are less than 5 feet, BSA is the most accurate parameter to use; this is

especially true for pediatric patients

BSA = kg0.425x cm0.725

x 71.84

Normal BSA = 1.73 m

2

If BSA dosage is less than the IBW dosage, we use the lower dose; we always want to air

on the side of caution and therefore underestimate rather than take the chance of

overmedicating

Osmosis vs. Diffusion

Osmosis deals with the transfer of water from one area to another; it does not deal with

concentration because water does not have a concentration

Diffusion deals with concentration; it is the transfer of a molecules from an area of higher

concentration to an area of lower concentration; diffusion can further be broken down into

active diffusion and passive diffusion; anytime a drug is in a system and can cross the

membrane, it will constantly move back and forth


28/79

Kinetics

Dr. Scott

11/13/09

SCENARIO

Pt has been taking an over the counter bronchial dilator Primatene tab or mist. Which would be a bigger

problem when looking at systemic effects?

- The tablet because the it has a greater systemic absorption & thus more adverse effects takingthis po formulation versus mist

- we prefer someone to use the mist, it is formulated to work more topically in the lungs, therewill be some systemic absorption but the person will feel better faster

- albuterol also has systemic effectsTA 30 yo female 142lbs comes in, & has been taking primatene mist w/ no relief, has had wheezing &

SOB for the past 3 hours, she has never been to the doctor for asthma, theyve just been taking otc

products. Labs: SCr 1.1., BUN 19, Na 138 K 4.2

Problem #1

The physician wants to give a LD of theophylline (aminophylline) 650 mg to maintain conc 15mg/L. Do

you agree or disagree with this dose?

Solution:

Theophylline LD 650mg, S= 0.8, F = 1, Conc 10-20mg/L, t1/2 = 8hr, Vd = 0.5L/kg,

1) find wt, 142lbs/2.2. = 64.5452) find Vd, Vd = 0.5kg/L*64.545kg = 32.273L3) LD = (Vd*Conc)/(S*F); Conc = (LD*S*F)/Vd = (650mg*0.8*1)/(32.273L) = 16.113mg/L, yes we

agree with that dose; it is in btwn the range of 10-20mg/L

Problem #2

The physician comes back and says, after the LD start a continuous infusion dose that will maintain a

conc of 15mg/L?

MD = (Cl*Conc*)/(S*F)

1) Cl = 0.04L/kg/hr *wt = 0.04L/kg/hr*64.545kg = 2.582L/hro we dont calculate CrCl for this drug b/c it is not significantly cleared renally, only 10-15%;

using CrCl in this pt wont help

o if a drug is metabolized and it has an active metabolic most times the metabolite will beexcreted really unchanged, in this situation renal clearance is important; e.g. Prozac has an

active metabolite which is probably excreted renal and if it has a longer half life than a

primary drug then this is a problem; most drugs once broken down are more hydrophilic

and thus renally excreted

o there are exceptions to the rule, a drug could be broken down to an active metabolite andmay be conjugated


29/79

o if a drug active and is broken down to an active metabolite and the person is experiencinghepatic cirrhosis; the drug effect will stay the same but stay longer b/c the liver has not

completely broken down and active metabolite conc will increase

o if parent drug was inactive then there may be a decreased in effect b/c there is a slowerturn over from inactive drug to active drug [slower metabolism] but excretion is still at the

same rate; in this situation we need to change the drug e.g. enalapril has to be converted to

enalaprat, if pt has hepatic failure and liver func is declined the conversion of the drug is less

but renal Cl is the same so any drug changed is still excreted at the same rate

2) MD = (Cl*Conc*)/(S*F) = (2.582L/hr*15mg/L*1hr)/(0.8*1) = 48.413mg; 48mg/hr will be givencontinuous infusion

Problem #3

Physician wants the drug conc 10 hr after start of infusion; LD was given at 7 am and continuous infusion

at 8am.

The eq we need to use is C = [(LD*S*F)/(Vd)*(e-kt) ]+ [((MD*S*F)/(Cl*)) * (1-e-kt

the value of k first:

) but we have to find

1) Cl = Vd*k, k = Cl/Vd = 2.582L/hr 32.273L = 0.08hr2) C = [16.113mg/L* (e

-1-0.08*10hr

)] + [14.872 * (1-e-0.08 *10hr

o (Refers to drawing) if conc was taken 1 hr after infusion our peak conc was 16.113 at 8 am; ifcontinuous infusion is started immediately at the end of LD we can say the t (time values) for

both parts of the equation is the same b/c after 1 hr the LD peak conc begins to decline we use

the end of the LD to start the time b/c thus is the time before that was continuous infusion

)] = [16.113mg/L * .499] + [14.872 * (1-

.499)] = 7.240 + 8.190 = 15.43 = class said 15.49

Factor of decline (e-kt

o at t = 0, conc = 1)

o at ss it = 0Factor of incline (1-e

-kt

o at t = 0, conc = 0 b/c no drug has accumulated),

o at ss it = 1o C= [(LD*S*F)/(Vd)*(e-kt)]+ [((MD*S*F)/(Cl*)) * (1-e-kt

), the bolded part of the equation was

found in problem #1.


30/79

DYNISHA M. IVY

Pharmacokinetics

Dr. Scott

9.21.2009

Exam is Friday at 9 am

ELIMINATION

- deals w/ is drug leaving the body

- looks at 2 basic things in elimination:

1) Metabolism

2) Excretion

Metabolism

- the major site for metabolism is the liver it can also occur in other places; the hepatocyte are designed to

metabolism drugs

- transforms one substance into another sub, a drug goes to liver biotransformed to another drug

- another name for metabolism is biotransformation (when a drug goes in the sys it is transformed inside the

body to something else); biotransformation is a form of metabolism b/c there is still something in the syst but it

is not the same substance we started w/, the new substance can still be active or inactive, an active metabolite

or inactive metabolite, e.g:

1) Active metabolites - Fluoxetine (Prozac) when metabolized it is broken done into a metabolite and it has an

active metabolite (active metabolites have a half-life just as long as the parent cmpd) but when looking at

the sys if we look for flouxetine it has been transformed to another drug so we take into account the active

metabolite

2) Prodrugs - some drugs are prodrugs which are in an inactive form, then metabolized to its active form and

then it begins to work e.g. enalipril is metabolized to enalaprat, the active form and the drug begins to work;

as time goes on if we looked for enalapril in the sys it wont be there

- most times we metabolize a drug so that it will be:

1) inactive

2) more water soluble to be renally excreted

- it is important to know

1) if a drug has an active metabolite AND

2) if so how long is the half-life of the active metabolite b/c most times the metabolite is more water soluble

and it wont be metabolized but excreted; this means a drug can have good liver function and has poor

renal function; if a drug is primarily broken down in the liver but the kidneys are not working well this is ok

unless the metabolites are active b/c most metabolites are renally excreted- a drug can be metabolized to an active metabolite and that metabolite can be biotransformed to something else

but most times it becomes water soluble for renal excretion

- looking at metabolism there are

1) phase 1 rxns

2) phase 2 rxns

Phase 1

o primary phase 1 type rxn include: cyp 3A4, 2D9, oxidation, hydrolysis ,reduction ect


31/79

DYNISHA M. IVY

1) require P450 enzymes

2) requires liver func to be at its best

Phase 2

o are conjugative processes that include: glucoronidation, methylation

o doesnt require liver function to be at its best

o as we get older drugs that undergo phase 2 rxn are handled better by the elderly

- in Pediatric cases < 5 yo, these pt dont conjugate well so drugs that have to go thru conjugation we want to

avoid especially in new born pt e.g. bilirubin has to be conjugated & in some pt when they are young, some pt

have a problem conjugating bilirubin and their bilirubin levels become high so they are given some time under a

light to get their bilirubin levels to come down and the pt will be fine

- but we have to avoid drugs like rocephin b/c it can interfere w/ the conjugation process in pediatric pt, newborn

pt and pt less than 1 yr old, this is seen more often in these situations but after they get older it can still happen

but not as much

- in pediatric cases pt have 80% of P450 enyzmes running at a high level, remember the heart rate is faster in

these pt so distribution is higher, drugs go to the liver faster and the metabolism of these drugs are a lot higher

than w/ phase 2 type rxn but phase 1 rxn work well; in phase 2 rxn the conjugative process is not the same in

pediatric pt; when child is 2-3 yr old things start normalizing almost to levels we see in adults, b/c kids are bigger

a child may have the same Vd as an adult depending on the drug.

- so at the start of life give drugs that undergoes phase 1 type rxn and at end of life use drugs that undergoes

phase 2 type rxn, normally phase 2 drugs will have a shorter half-life e.g.:

o an alcoholic is in the hospital & cant drink (some hospitals keep alcohol on stock) after 24-48h they can

go thru withdrawal or delirium tremors (DTs), DOC in this situation is (valium) diazepam, or (Librium)

chlordiazepoxide can be used; both these drugs have a very long half- life, in a pt drinking alcohol for a

long period of time can decreased liver function, so if this person has this or liver cirrhosis we dont want

to give valium but in some situations we will give it 1 time only dose of valium just to have some control

o a benzodiazepine we would use under previous circumstances would undergo conjugation & include:

DOC is (Ativan) lorazepem, (Restoril) temazepam or (Serax) Oxazapem; so even though liver func is

declining our focus is on phase 2 rxn b/c liver funt is not required to be at its highest and these tend to

have a lower half-life

Elimination

- we start talking about order of kinetics 0, order 1st, 2nd

- most of the drugs in practice go thru 1

ect.st

- 1

order (from a metabolism pov, point-of-view) there are few drugs that

we deal in practice that deals w/ 0 order kineticsst

1) another name is linear b/c when plotted on graph paper it gives a straight line

order kinetics:

2)

as the amt of drug in the body decrease the amt eliminated decreases3) the fraction or percent eliminated is constant, k is the fraction or percent eliminated (in 1 st

4) while the percent is constant/the same the amt varies e.g. 1000 mg of Drug A w/ half-life of 5 h

order k is

constant) over a given period of time

DRUG TIME (h) Percent lost

1000 mg 0

500 mg 5 50%

250 mg 10 50%


32/79

DYNISHA M. IVY

- but the amt varies in 2nd

- In zero order kinetics:

order and there is no k really

1) is nonlinear when graph on semi log paper it gives a curve

2) the drug amt eliminate over a period of time is constant fraction or percent will vary; this is why there is

not a k and therefore no true half-life

3) depending on the drug at low doses it will go thru 1st order kinetics but the higher the dose given it can gothru zero order kinetics

4) is concentration dependent b/c we can saturate its metabolism cycle, we can be at one level and be in a

normal range but if we saturate it, drug level will be toxic; in other words in zero order kinetics, the > conc,

the longer the drug will be in the sys e.g. giving a drug that under goes zero order kinetics losing 100 mg/hr

(constant drug amt)

Concentration dependant zero order kinetics e.g.

Less DRUG TIME (h) More DRUG Variable percent

1000 0 2000 100%

500 5 1500 75% = (15002000*100)

0 10 1000 66.7% =(10001500*100)

15 500 50% = (5001000*100)

20 0

o in 1st order, no matter how much drug is given if the half-life is 5 hours then half of the drug

will be gone and in 7 half-lives most of that drug will be gone

- enzymes can also be saturated c/ing a persons levels to go even higher and have drug stay in the system even

longer e.g. phenytoin

- there is not a true half-life w/ zero order kinetics but we can look at a drug and get an average e.g. phenytoin

and dilantin half-life is 24 hours however they are nonlinear so we can c/ sites to be saturated and have drug

stay in the sys much longer- there are some drugs that will have 0 order kinetics when it comes to absorption but once it gets into the system

it undergoes 1st

1) Ca++ - after giving so much Ca++ it wont be absorbed

order kinetics e.g:

2) Rafampin no matter how much is given after a while it wont be absorbed anymore and this means

absorption sites can be saturated and only a certain amt is absorbed over a certain period of time; this may

vary from person to person but we have a set standard for the population then see how each individual

person deals with it

- zero order can also be in distribution, saturation, absorption, elimination

- there can be zero order kinetics in excretion e.g PNC goes thru active tubular secretion (ATS) which can be

saturate but this is not significant, sometimes we use drugs to try to keep PNC from excreted too rapidly

Excretion

- main site is the kidney, the renal system

- if drug A is put in the system Drug AB should be excreted, AB is a metabolite, something has changed

- if a drug undergoes excretion only then what we started w/ should be what we finish w/, if we see anything

differ then it was metabolized first, so then the question becomes: for the sub being excreted, was it

metabolized before excretion, was it an active metabolite or an inactive metabolite?


33/79

DYNISHA M. IVY

- most drugs excreted by the kidneys should be unchanged if they are changed than they have been metabolized

eg Drug A is in the system and is 100% excreted as drug AB, this is 100% metabolized

- drug excreted renally is excreted unchanged

- in the kidney we look at a drug to undergo:

1) glomerular filtration OR

2) tubular secretion (active) and be excreted in the urine or be

3) reabsorption

- (Refers to drawing) all this takes place at the nephrons the active part of the kidneys, where things are forced in

or filtered thru glomerular filtration e.g. some drugs, Na+, waste products; larger substances go thru ATS

(actively transported thru the nephron) and once something goes out of the blood, goes in the nephron,

circulates and goes back into the blood this is reabsorbed

- if a drug undergoes 100% of glomerula filtration (GF) then its rate of Clearance is = GF rate, since GF rate is = to

CrCl, whatever the CrCl is, then that is the drugs Clearance, e.g.

1) gentamicin gets into the sys and is cleared 100% of the kidneys by glomerular filtration, drug Cl of

aminoglycoside is = to CrCl

2) a drug is cleared 100% by the kidney but it is cleared 65% by GF and 35% ATS, then drug Cl is = 0 .65 * CrCl

b/c only 65% went thru GF

- CrCl formulas:

1) Male CrCl = ((140-pt Age)*pt wt in kg)(72*SCr)2) Female CrCl = [((140-pt Age)* pt wt in kg)(72*SCr)]*0.85

- for class purposes calculate pt actual and IBW, use the lower of the 2 when doing any calculations

Key points:

- finding Clearance

1) Cl = Vd *K- finding K:

1) Prefer method , K = (ln (C2C1)* -1) t OR K = (ln (C2C1)* -1) (t1-t2)2) 2

)nd

3) least preferred method, K = 0.693t1/2preferred method, K = ClVd

- Maintenance Dose eq, MD = (Cl*Conc* )(S*F), , is the dosing interval how often we give the drug

- when looking at the CrCl for a drug excreted 100% by the kidney by GF and using this MD equation make sure

that if dosing interval () is hours then convert CL units from minutes to hour Remember units of Cl mL/min

- MD replaces what is lost; as successive amt of a drug is given the drug begins to accumulate

- steady state (ss) is the point where the amt of drug given over a specified time = the amt of drug that is lost or

eliminated over that same period of time OR ss is when the first dose no longer affects successive doses e.g. it

takes 5-7 half-lives to reach steady state but if 1 dose of drug A is given it takes 5-7 half-lives for the drug to be

eliminated from the body- to reach ss we have to have more than one dose; one dose is automatically eliminated but giving more than one

dose causes a drug to accumulate

- every drug has the potential to reach ss, even intermittent infusion can reach ss

- (Refers to drawing) Intermittent infusion e.g if Dr Scott gives you ten dollars, the half-life of that money is 5 hr at

which half the money will be taken away but ten dollars will be given; so 5 hours later Dr. Scotts takes half the

money 10 dollars and gives you ten more dollars, the max amt of money you can have at that point is 15 dollars;

we continue this and the graph up to 20:


34/79

DYNISHA M. IVY

Time (hr) Result of half of max money being

taken away @ half life (5hr)

Money given (dollars) Max money

at that time

0 10 10

5 5 10 15

10 7.5 10 17.5

15 8.75 10 18.75

20 9.375 10 19.375

25 (5th 9.6875half-life) 10 19.6875

30 9.84375 10 19.84375

35 (7th 9.921875half-life) 10 19.921875

9.9609375 10 19.9609375

9.98046875 10 19.98046875

- it keeps going up and down until we reach $20 and Dr. Scott takes half of $20, leaving us $10 (the original amt he

gave) but gives us 10 more dollars making the max amt we can reach is $20; then half of $20 is taken away again

(which is $10) leaving us w/ $10 again, we are now at ss where the amt of drug (or money in this case, $10)given over a specified time = the amt of drug (or money in this case, $10) lost or eliminated over that same

period of time OR we lost 10 dollars over 5 hours and we get 10 dollars back so the most money we can have at

one point is ~20 dollars in 5-7 half- lives or close enough

- the MD only replaces what is lost over a given period of time

- intermittent infusion eq is a type of MD but it is not the same eq; in intermittent infusion a certain amt is given

after so many hours and after a while the drug begins to accumulate so that now what is given over a certain

amt of time begins to = what is eliminated over that same period of time


35/79

DYNISHA M. IVY

Pharmacokinetics

9.23.09

Dr. Scott

STEADY STATE

- everything (drug )can reach ss- ss occurs when the amt given over a period of time = amt lost over the same period of time e.g. if Dr. Scott

gives 100 mg every 8hr then when it gets to the point over 8hr where we lose 100mg then this is ss

- (Refers to Drawing) so looking at elimination t1/2 it says we need 5-7 half-lives to reach steady state; it alsotakes 5-7 half-lives to be eliminated from the body, so another way to look at steady is that it will be reached

when the 1st

Loading Dose

dose is at zero or eliminated out of the body b/c nothing can accumulate or build off of that

dose

- ss can never be reached in one dose; LD conc is not ss, it doesnt achieve ss, it achieves the conc that wewant when we reach steady state; the LD will not achieve ss unless the LD is the same as the MD and if they

are the same then the LD still didnt get us to steady state

- LD doesnt accumulate but to reach ss the LD would have to be the same as the MD, meaning the LD had toaccumulate to get to steady state (but REMEMBER: LD does not accumulate)

- the LD is always larger than MD- to calculate a LD all we need is a Vd and the desired Conc to know exactly how much drug to give to get to X

conc; the LD gets you to the conc but cant maintain the conc

- giving a LD more than once will c/ the conc to accumulate beyond ssMaintenance Dose

- MD doesnt achieve the desired conc we want at first, it must accumulate until we get to ss; once we reachss the conc will stay the same; MD is designed to keep accumulating until ss is reached and once we reach ss

it stays there where the amt given = the amt lost over the same period of time

- the eq, MD = (Cl*Conc* ) (S*F) , assumes ss (that Conc represents the conc at ss)has been reached forexample if Dr Scott ask us to calculate a MD that will maintain a conc of 15mg/L, he wouldnt ask for a MD

before reaching ss

- w/o a LD wed have to wait for accumulationAccumulation

- Accumulation eq Acc = D*(1/(1-e-kProblem #1

)), is a dosing interval, a type of time that specifies what type of time

we are looking at e.g. if = 8h then it means the time btwn doses is 8 hours

- Given D = 10 mg, = 5 hr, t1/2 = 5h then how much drug will accumulate?1)

k = 0.6935h = 0.1386h-1

2) Acc = D*(1/(1-e-k)) = 10mg*(1/(1-e-0.1386h1-*5h- (1-e

)) = 10mg *2.0003 = 20.003mg; so 20mg is the most that will

accumulate, after dosing every 5h with 10 mg-kt

) is the accumulation factor or the percent of steady state e.g. if (1-e-kt

) = .8 this means we are 80% at

steady state


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DYNISHA M. IVY

Continuous Infusion

- to solve for conc change MD eq: C = MD*S*F/Cl*, this eq also assumes ss has been reached- is used when we want a particular time before ss,Continuousinfusion eq: C = ((MD*S*F)(Cl*))*(1-e-kt);

we use this b/c (1-e-kt

) is the accumulation factor & it tells the percent of ss, therefore when (1-e-kt

- if given a continuous infusion and asked the conc after X hours of starting the dose and it hasnt reached ssyet then we use this eq

) = 1 then

ss has been achieved

- it assumes we havent reached ss yet- b/c (1-e-kt

- e

) = 1 once it reaches ss, and 1 times any number is that number (e.g. 1*3=3), then at ss all we have

left of the Continuous Infusion eq is C = ((MD*S*F)(Cl*)) *1 which is the same as MD =( Cl*Conc* ) (S*F)

and this is why we say this eq assumes ss-kt

at time 0 is = 1, so 1-1 = 0, and 0 times any number is 0, so at time = 0 the conc is also zero, when we

start accumulating e-kt

Problem #2 Continuous infusion, for purpose of this class = 1h for a continuous infusion

= 0 at ss, so 1-0 = 1 which says we are 100%???

- Given D = 60mg, = 1 hr, t1/2 = 8h VD = 05.L/kg, pt wt = 70 kg, what would the Conc be at 10h?1) Vd = (0.5L/kg)*70kg = 35kg2) k = 0.693t1/2 = 0.693 8 hr = 0.08662 h-13) Cl = Vd*k = 35kg*0.8662h-1 = 3.0317L/h4) Continuous infusion eq, C = ((MD*S*F)(Cl*))*(1-e-kt) = ((60mg*1*1)(3.0317L/h*1h))*(1-e-0.08662h-1*10h

Solving the eq in sections, C = (19.7909 mg )* (0.5794) = 11.4668 mg/L at 10h, this is not ss so the drug is

still accumulating and will do so until we reach ss

) =

- (0.5794) tells us that it is 57.94% ssProblem #3

- Given same inform from Problem #2 , what would be the Conc be at 48h?1) C = ((MD*S*F)(Cl*))*(1-e-kt) = ((60mg*1*1)(3.0317L/h*1h))*(1-e-0.8662h-1*48h- LD declines and continuous infusion increases and the 2 balance out to maintain the desired conc

) = 19.4809mg/L

CLEARANCE

- Clearance is a form of elimination, clearance (that we plugged into the eq above) doesnt tell if it is renal ornonrenal , it tells clearance total (ClT

- Digoxin is a drug that is metabolized and renal cleared

); Cl total = renal + nonrenal , this says a drug can be put in the body and

be eliminated thru metabolism or excretion; just understand that the clearance we use doesnt distinguish

btwn the renal or nonrenal

- e.g. a drug is 75% excreted renally and 25%hepatic metabolism . if there is s problem w/ the kidneys thehepatic metabolism will increase but not increase enough to make up for the 75% then well start to see

alterations; but if the elimination is 50: 50 or 60: 40 and there is a slight decrease in the renal function thenhepatic func can increase to make up for the extra 5-10% but now the problem is that it is not supposed to

do that which means the liver is working harder so over time we see problems w/ the liver b/c it is working

hard to do something it doesnt normally

END EXAM # 1 MATERIAL


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Pharmacokinetics Lecture Twelve

September 28, 2009

Intermittent Infusions

Example of an intermittent infusion:Say we put 120 mg of Gentamicin in 100 ml of NSS and we infuse the medication over an

hour every 8 hours (120 mg infused over an hour every 8 hours); after the end of the

infusion we wait 8 hours and then start the process again; intermittent infusions do reach

steady state; once the drug reaches steady state, the Cmax and Cmin will not change

unless the dose, dosing interval, or pharmacokinetics (elimination, distribution) are

affected

Intermittent infusions are a type of maintenance dose because it is replacing what is

eliminated

Equations:

Cmax: Cmax = (DSF x 1 e-ktinf)/(Cl x tinf x 1 e-kT

)

Dose: D = (Cmax x Cl x tinf x 1 e-kT)/(S x F x 1 e-ktinf

)

Cmin: Cmin = Cmax x e-k(t2-t1) t1 = conc. at Cmax, t2 = conc. at Cmin

C (same as Cmin) = Co (same as Cmax) x e

-kt

8 am 4 m


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- The three main aminoglycosides that we will look at are Gentamicin, Tobramycin,and Amikacin; the volume of distribution and clearance for these drugs are pretty

much the same

Aminoglycosides

- These drugs are used for Gram infections; are not used for anaerobicmicroorganisms; they are not used for Gram + infections

- These drugs affect protein synthesis at the 30s ribosome; aminoglycosides areactively transported into the bacteria; they need oxygen in order to function (this

is why they will not work against anaerobic microorganisms)

- A lot of toxicity with aminoglycosides is seen with a high trough, not necessarily ahigh peak

- Aminoglycosides are not absorbed orally; the only aminoglycoside that we give bymouth is Neomycin (used for hepatic encephalopathy; Lactulose is also used to

decrease ammonia levels in hepatic encephalopathy); if given this way, Neomycin will

work locally; if something is not absorbed, it will not work systemically; Neomycincan be given IM, but absorption is sporadic and consistent peak and trough levels

cannot be obtained; IM absorption is affected by muscle mass, adipose tissue,

blood supply, muscle movement (because muscle movement affects blood supply); if

the vein is lost and the therapy is almost complete we can just give the dose IM

- We do not give aminoglycosides as a continuous infusion; they are given asintermittent infusions; Aminoglycosides are infused over 30 minutes to 1 hour; for

class purposes use 1 hour (i.e. t inf- We take the peak 1 hour after the start of the infusion, even if it was infused over

30 minutes (i.e. if the infusion starts at 8 am, take the peak at 9 am); if we infuse

the drug over an hour just take the peak right after the end of the infusion

= 1 hour)

- We take the trough 30 minutes to right before the next dose; say the dose is givenat 4 pm, the earliest we could take it is 3:30 and the latest we could take it is 3:59

- Gentamicin Gentamicin does not work well against Haemophilus or Mycobacteria You wont really see Gentamicin used in Pseudomonas infections because

some strains of Pseudomonas are resistant to Gentamicin

Peak = 5-10 mg/L Trough < 2 mg/L (for the trough, the closer to 0, the better; if it is 2, it is a

no go; if it is 1.99, it is ok)

-

Tobramycin Does not work well against Mycobacteria Peak = 5-10 mg/L Trough < 2 mg/L

- Amikacin Peak = 20-30 mg/L Trough < 10 mg/L


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Pharmacokinetics Lecture Thirteen

September 30, 2009

Aminoglycosides are hydrophilic, thus they do not distribute to adipose tissue;

aminoglycosides are distributed to pericardial fluid, synovial fluid, pleural fluid, ascites

fluid (fluid in the abdomen that is caused by decreased albumin levels in people with liverfailure; albumin is responsible for protein binding and oncotic pressure (pressure that

stops water from spilling over))

Distribution vs. Volume of Distribution

- Vd is a component of distribution; Vd just tells the volume that the drug iscontained in; this gives an idea of how well the drug is distributed, but does not tell

exactly how a drug distributes from one tissue to another

- If you put 1 gram of a drug in certain volume, and the concentration comes out tobe 1 mg/L, the volume would be 1,000 L; this does not take into account how the

drug distributes from one tissue to the next (tissue A, B, C, etc)

- Distribution tells us how well the drug penetrates the tissue; volume of distributiondoes not

- Protein binding affects distribution and volume of distribution; protein binding canalter how much drug stays in the blood to make the Vd look like it goes up or down;

protein binding can also affect how much drug can cross the membrane to get to

the site of action; when protein binding decreases, more drug is able to cross the

membrane causing the Vd to increase; decreased protein binding will cause more

drug to reach the receptor site to cause a response, thus it also affects

distribution; ascites increases the volume, but it does not increase the therapeutic

affect; for people with ascites, more drug will have to be given because they have

more volume

A

10%

C

30%

E

20%

B

10%

D

15%

F

15%


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- Aminoglycosides are not highly protein bound, but they are hydrophilic;aminoglycosides distribute well to areas of volume (ascites, edema); if the Vd

increases we might have to increase the dose to make sure that we are getting a

therapeutic concentration; when the volume of distribution increases, the

concentration decreases and the net effect decreases; highly protein bound drugs

are an exception to this rule; when protein binding decreases the volume ofdistribution increases and the net effect can increase because more drug is

available to reach the receptor; this is not an issue if the drug is not highly protein

bound

- Aminoglycosides are not metabolized- Aminoglycosides do not distribute well to adipose tissue; if we give a dose of an

aminoglycoside, say 5 mg/kg to every patient based on weight this can be

problematic for obese patients because they are at risk for toxicity; the dose of

aminoglycosides should be lowered for obese patients because the dose is being

based on a weight that the drug will not distribute to (aminoglycosides do not

distribute to adipose tissue); if the dose is not lowered, obese patients mayexperience symptoms of toxicity

- Small amounts of every dose of an aminoglycoside have the ability to distribute andbind tightly to parts of the kidney and inner ear; aminoglycosides cause

nephrotoxicity and ototoxicity; the higher the dose, the more can accumulate in the

kidney and ear causing toxicity

- The Vd we use for aminoglycosides (which is the population parameter) is 0.25 L/kg;in infants the volume of distribution is higher and as the person gets older the

volume of distribution declines; when the patient reaches about 2-5 years of age

the Vd is about the same as an adult

- Because aminoglycosides are hydrophilic and do not distribute to adipose tissue, weare definitely going to use lean body mass to calculate the dose; in calculating the

dose for an aminoglycoside, we use the lower of the actual or IBW (it does not

make sense to use the IBW if the actual body weight is lower); we stick with this

weight when calculating other parameters (CrCl) to keep consistency

- We usually determine someone to be obese if their BMI is > 30 or if the person is20-30% above their IBW

- To calculate the Vd for an obese person: Vd = 0.25 L/kg x IBW + CF(ABW IBW) The CF, correction factor, tells us what percentage of the extra weight is

volume; the normal CF factor is from 10-40% (0.1-0.4); for class purposes

use 10% (0.1)

Elimination

- Aminoglycosides are cleared 100% by the kidneys through glomerular filtration- Aminoglycoside clearance is equal to CrCl (which is in milliliters per minute); we

convert this to L/h; to do this, multiply the ml/min by 0.06


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- Creatinine clearance: CrCl = (((140 age) x kg)/(72 x SCr)) x 0.85 (if female) Multiply this answer by 0.06 and you will have the CrCl in L/h

- The elimination half-life for aminoglycosides is 2-4 hours (average of 3 hours); ittakes 5-7 half lives to reach steady state; in about 15 hours, aminoglycoside

concentration will be close to steady state; this is not a large amount of time so wedo not need to give a loading dose; within 15 hours the first dose is pretty much

gone; to reach steady state, more than one dose has to be given; if only dose is

given, the drug will not accumulate; by the 3rd dose (if it is given every 8 hours) we

are at steady state


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Pharmacokinetics Lecture Fourteen

October 2, 2009

Aminoglycosides are cleared 100% by the kidney via glomerular filtration; renal function is

critical when aminoglycosides are used; if renal function is decreased, Houston We Have a

Problem; liver function does not affect the excretion of aminoglycosides

Drugs can be excreted from the kidneys in two ways:

1. Glomerular filtration- When the kidneys fail, glomerular filtration is the first thing to go;

decreased kidney function will affect glomerular filtration before it will

affect tubular secretion; glomerular filtration relies heavily on the ability of

the kidneys to work properly; because aminoglycosides are excreted 100%

through glomerular filtration, they are very dependent on the kidneys

functioning properly

2. Active tubular secretion- Active tubular secretion puts the drug into the urine- Tubular reabsorption puts the drug back into the blood

Types of Pneumonia

- Klebsiella: seen in alcoholism, diabetes, chronic debilitating diseases, andsickle cell anemia (Pseudomonas can also occur in people with sickle cell)

- Haemophilus: seen in smokers, COPD, and asthma; the person probably has aproblem with the lungs

Alcoholism: causes ascites and liver failure; ascites affects the distribution ofaminoglycosides; liver failure will not affect aminoglycoside therapy because

aminoglycosides are not eliminated by the liver; **liver function does not affect the

clearance of aminoglycosides; it is only when you see complications of liver failure, such as

ascites and edema, that aminoglycoside clearance is affected

Factors that Affect Pharmacokinetics/Disposition of Aminoglycosides:

a. Renal function:- If renal function decreases, clearance of the drug decreases- If the clearance of the drug decreases, the concentration will increase- The half life of the drug will increase if the clearance decreases

b. Age:- Pediatric patients have a larger volume of distribution; renal clearance

increases in pediatric patients; pediatric patients have a faster heart rate

and a lower blood pressure; for these reasons, pediatric patients usually

clear drugs faster; when the child reaches about 5 years of age these

parameters mimic that of an adult


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- The renal clearance decreases in the elderly; when someone reaches the ageof 65 there is a good chance that renal function will decrease by 40%;

cardiac output decreases in the elderly; if the cardiac output decreases,

renal blood flow decreases; if renal blood flow decreases, glomerular

filtration decreases causing decreased clearance of the aminoglycoside;

clearance can decrease in the elderly, but this does not mean that it will- We do not want to base our decisions on age; we should base our decisions on

how the patient is doing

c. Hypermetabolic states:- Fever: if a person has a fever, their heart rate increases; this will cause

renal blood flow to increase; people that have a fever usually go to the

bathroom a lot; patients with a fever should drink a lot of fluid because they

can become dehydrated if they do not; when a patient is on an antibiotic,

within a day or two, the fever will go away thus fever is a transient factor

- Burns: patients with severe burns will have increased cardiac output; renalblood flow will increase, and drugs will be cleared faster; burns might

increase volume of distribution due to blistering; aminoglycosides can

accumulate in the fluid of the blisters; because blisters ooze, some people

look at this as clearance; either way the concentration goes down

; if

we use a higher dose in a patient with fever we have to be careful because

the fever can go away and the dose may be too high

- Cystic fibrosis: usually affects Caucasians, but not always; if a person withcystic fibrosis develops pneumonia, Pseudomonas is the usually the causative

organism; cystic fibrosis is a hypermetabolic state and physicians will usually

put patients with cystic fibrosis on a higher dose of medication

d. Factors that alter the volume of distribution:- Dehydration: if a person of dehydrated, the volume decreases and the

concentration increases; if a person is dehydrated due to a fever, the

dehydration is the more important factor to look at in terms of the

aminoglycoside dose

- Edema- Ascites- CHF: in severe CHF, there is a two-fold problem: edema and decreased renal

blood flow; edema will cause fluid build-up which will increase the volume and

decrease the concentration; decreased renal blood flow will decrease the

clearance; distribution is altered because the heart is not pumping strong

enough to distribute the drug throughout the body; thus edema can increase

volume and heart failure can decrease volume; to determine whether the

volume has increased or decreased we look at a blood level

- Obesity: in obesity, volume of distribution goes down becauseaminoglycosides do not distribute to adipose tissue


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- Dialysis: dialysis removes the drug from the system causing theconcentration to drop; we can still put patients receiving dialysis on an

aminoglycoside depending on the patient and situation; the drug should be

given after dialysis so it does not get removed in the dialysis process; we do

not start dialysis until the patient is in end-stage renal failure (CrCl < 10-15

ml/min); renal failure (some sources call this renal insufficiency) is when theCrCl < 30 ml/min

- Inappropriate sample time: if the trough is taken too early the trough willlook high (if the trough is high we would adjust the dose or the dosing

interval; if we adjust the dosing interval we usually have to adjust the dose,

but if we adjust the dose it does not mean that we have to change the

dosing interval); if the peak is taken too late the peak will look low (or if the

peak looks like it is in normal range it could actually be in the toxic range);

the peak should be taken an hour after the start of the infusion; the trough

should be taken 30 minutes to just before the next dose


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Pharmacokinetics Lecture FifteenOctober 5, 2009

The aminoglycoside peak should be taken 1 hour after the start of the infusion; becauseaminoglycosides have a short half life, steady state is reached quickly; steady state

concentrations can be taken around the 3rd

dose

K = [(ln(C2/C1) x -1)/t] (this tells us that we must know 2 points on the line)

Toxic/adverse effects of aminoglycosides:- Ototoxicity: the concentration does not have to be high for this to happen because

the drug accumulates over time; we need to monitor for signs and symptoms ofototoxicity; we look for 4 main things: tinnitus (ringing in the ears; tinnitus can also

occur due to long term NSAID use), sensation of fullness in the ears, vertigo (the8th cranial nerve is being affected; in vertigo there is something going on with thenervous system; vertigo and dizziness are different; in dizziness, it feels like theroom is spinning; in vertigo, it feels like you are spinning), and nausea/vomiting

- Nephrotoxicity: the concentration does not have to be high for this to happenbecause the drug accumulates over time; nephrotoxicity can begin within 5 days oftherapy; we want to get a baseline CrCl, BUN, and SCr prior to initiation oftreatment; the patient probably will not complain of any symptoms of

nephrotoxicity thus labs are very important; an

; inthe early stages, ototoxicity is reversible; if the damage continues to progress,ototoxicity (hearing loss) will become permanent

increase in SCr greater than 0.5 isconsidered to be significant; normal SCr is 0.6-1.2; SCr levels can fluctuate dailybecause it is a waste product from the breakdown of muscle; we also want to lookfor an increase in BUN and urinary casts

- Aminoglycosides interact with muscle relaxants; urinary casts are dead cells found in the

urine

Peak and trough levels can cost anywhere from $70-$80 per level

Chemo patients can be on long-term aminoglycoside therapy


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Factors that will increase aminoglycoside toxicity:1. Peak and trough concentrations: toxicity is more so associated with high trough

levels, but it can also occur with high peak levels2. Duration of therapy: when the therapy exceeds 10 days there is an increased risk

of toxicity (it is not uncommon for therapy to exceed 10 days)

3. Dose: the higher the dose the greater the risk because a small amount of each dosecan accumulate in the inner ear and kidney

4. Decreased renal function: aminoglycosides are cleared 100% by glomerularfiltration so if renal function is impaired the aminoglycoside will not be eliminatedfrom the body leading to increased toxicity

5. Other drugs: Vancomycin: Vancomycin can also cause ototoxicity and nephrotoxicity; we

can still use Vancomycin with an aminoglycoside, we just have to monitor thepatient more closely

NSAIDs: NSAIDs can cause tinnitus and ototoxicity; we can still use anNSAID with an aminoglycoside, we just have to monitor the patient moreclosely; NSAIDs can cause renal failure (analgesic nephropathy) if used overa long period of time; we also need to monitor renal function more closelywhen an NSAID is used with an aminoglycoside

Aminoglycoside Dosing:- In practice, many clinicians dose by weight instead of CrCl; a normal adult would be

dosed at 3-5 mg/kg/day with the dose divided into three doses- But as pharmacists we use pharmacokinetic principles to calculate the dose- Since aminoglycosides are given by intermittent infusion, we are going to use the

Cmax and Cmin equations to determine the dose- Once-a-day dosing: in practice, aminoglycosides can be dosed q 8, 12, 18, 24, 36, 48

hours; for class purposes we will use q 8, 12, 24, 36, 48 hours (DO NOT USE 18HOURS); if we are doing once-a-day dosing we want the peak to be 15-24; somepeople do not take a peak and trough for once-a-day dosing, they just take arandom level; the trough needs to be less than 2 mg/L within 24 hours

- For Tobramycin and Gentamicin, peak should be > 10 mg/L; we prefer the peak to bebetween 15-24 mg/L; some sources say 15 mg/L is too low; > 24 mg/L does notproduce a greater effect, it just causes more side effects

A drug could be concentration dependent or time dependent:- Concentration dependent: the higher the dose the more killing effect; examples

include aminoglycosides and quinolones; the higher the dose the better they kill;the closer the trough is to zero, the better; if it is below 2 mg/L we are ok

- Time dependent: the longer the drug is given the more killing effect; an example isVancomycin; the trough of Vancomycin is 5-10 mg/L; if the concentration drops less


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Kinetics Exam 3