---start pharm lec 1.9.98---- pharmacology 1/9/98 robinson pharmacokinetics Reinforcing stuff from yesterday. the handout is more comprehensive than the instructor's expectations as far as the exam. Realize the thought process is important and testable! Remember - we're going to hear about pharmacodynamics in which dose response relationships are used to define therapeutic and toxic concentrations of the drug - remember all drugs have therapeutic and toxic concentrations. We used a logarithmic scale to plot this before, and we called it pharmacodynamics. Now, since we treat more than just one species, pharmacokinetic variations in different species cats aspirin and similar drugs inactivated by glucoronide synthesis, are metabolized slowly. goal is to acheive therapeutic effects and avoid toxic effects. he's really just going over stuff from yesterday so far. nothing new yet. remember that in general weak acids will be absorbed in the stomach, because of the acid pH in the stomach which contributes protons to the weak acid, making COO- into an uncharged COOH. a weak acid in an acidic environment will get protonated, uncharged spp will predominate, will be absorbable. These tend to have pKa about 3 - 5. weak bases tend to have pKa about 7-10. In a relatively alkaline compartment, in which the pH approaches 7 or 8, the proton will be removed, uncharged spp will predominate, and the drug will be absorbed. HOWEVER - pills do not dissolve well in the stomach - they tend to dissolve in the small intestine and get absorbed there. so. acid base equilibrium also affects drug distribution. you should understand this: weak bases tend to be concentrated in an acidic compartment. This is the whole rumen trapping thing. We'll get back to this. The opposite is also true, with weak acids - they tend to be trapped or accumulated in basic compartments. All this means is that it is acidic or basic relative to what is on the other side of the membrane. consider this: weak acid with pKa 4.4 pH on one side of the membrane is 7.4 (plasma), and on the other side of the membrane is 1.4 (stomach) what we know is that the concentration of drug should be equal on opposite sides of the membrane, because transport is passive, not involving energy. So we can arbitrarily set it at one. Then, on both sides of the membrane is an equilibrium that exists, in which the charged spp and uncharged spp is going back and forth rapidly. Then, remember yesterday he said not to know henderson-hasselbach equation - just know how to think about it. remember that at pKa = pH, the concentrations of spp are equal. So, if the pH is one log unit away from pKa, ratio of the spp is 10:1 so remember if pH = pKa spp are equiv, 1 log unit away is 10:1, and figure out if protonated or unprotonated spp will predominate. So, if pH = 1.4, for a weak acid with pKa 4.4, the uncharged spp will predominate. it will predominate by 1000 fold, so ratio of HA:A- is 1:0.001 at pH 7.4, the charged spp will predominate at a ratio of 1000:1. so because of the pH gradient there is also a gradient such that the total amount of drug on the alkaline side is 1001 and on the acid side is 1.001 - what does this mean? at this steady state situation, the spp in the plasma, the concentration of total drug in the plasma, is greater than that in the stomach. now consider a base. we're talking about a weak base. plasma pH is 7.4, rumen pH is 6.4, and pKa of drug is 7.4 (weak base). which molecule is equal on each side of the membrane, charged or uncharged? uncharged - B. The unprotonated spp. B is in equilibrium with the charged spp BH+ which doesn't cross the membrane. Let concentration of B = 1 on each side of the membrane. so what is the ratio of B:BH+ in the rumen? well, environment is acidic relative to pKa, so will donate protons, so BH+ will predominate at 10:1 (because pH is 1 log unit from pKa). so, the amount of drug in the rumen is greater than that in the plasma. remember, the rumen can slow absorption or trap weak bases in ruminants - ivomec bolus, paratect bolus. this is an example of pharmacokinetic variation, just like the thing with aspirin in cats being metabolized slowly. he also said this principle governs not just absorption but also distribution. there are other acidic or basic compartments in which this might be relevant, too - milk is acidic relative to plasma (slightly), so when you consider drugs for use in lactating cows, they don't want to concentrate the drug in the milk, so they consider these things. urine can be acidic or alkaline relative to plasma, and this is another example of species variation in pharmacokinetics, also, because carnivores tend to have an acidic pH of their urine, whereas herbivores tend to have an alkaline pH of their urine. (pH 7-8 for herbivore, 5.5-7 for carnivore). This difference can affect drug clearance. remember there is a pH gradient as you travel down the intestine - does vary with species, but in general stomach pH 1-3, duodenum/jejunum sl acid, beyond that alkaline. please see table 2 p 6 for a nice chart of drugs and their absorption vs pH of intestinal solution. terms math units word definition bioavailability none none or mg fraction/amt/% of drug that makes it into circulation after the first pass effect if you give a 10 mg dose of a drug to a 2 kg dog, and 40% of the drug is absorbed (4 mg), and 75% is metabolized by the first pass effect (3 mg), what is the bioavailability? I think it is 1 mg. that is in fact the case. you could also say 10%, 0.1, or 0.5 mg/kg what's the bioavailability of a drug given IV? 100%. volume of distr. bioavailable drug a hypothetical volume of plasma ----------------- L/kg that a drug would distribute in conc of drug in plasma if it only distributed in plasma note: distribution is determined by solubility factors - if drug isn't lipid soluble, probably won't get distributed into the CNS. also by blood flow and binding to plasma proteins. look at the handout drug table for digoxin (end of handout) - Vd is 440 L in a 70 kg person. Now, the most body fluid in a 70 kg person would be 70 L under the most extreme circumstances - normally about 42 L. So Vd is NOT a real volume. So, Vd tends to tell you something about how a drug distributes, if it is trapped somewhere, etc. You use Vd to figure out how much drug to give. If you have a 10 kg patient, and Vd = 10 L/kg, and therapeutic concentration is 2 mg/L, how much drug do you give? Hmm. Ok, total Vd is 100 L, so you give 200 mg? Is that right? I think Vd 10 L/kg x 10 kg = 100 L, and 100 L x 2 mg/L = 200 mg. Yay. I am right. now. how does binding of drugs to plasma protein affect volume of distribution? well, if it's heavily bound to plasma proteins, does Vd increase or decrease? I think it decreases. why? because it will just stay in the plasma. so you tend to analyze the total amount in the plasma, and for analytical reasons you can't tell b/w free and bound drug all the time. Some drugs w/low Vd have that due to binding to plasma proteins. sometimes you can quantitate free vs bound drugs. realize that distribution reflects a lot of different parameters, not just absorption terms math units word definition t1/2 0.693/Ke hours time needed to clear/metab. 50% of drug ke 0.693/t1/2 1/hrs rate constant for elimination clearance CL=Ke*Vd mL/kg/hr the vol of plasma cleared of drug per unit of time by all routes models of drug distribution and elimination - all we've discussed so far is drug being distributed in one compartment, so that the concentration rises and remains steady. see handout p 11. top right of diagram shows first order elimination - drug enters blood and then is eliminated. drugs tend to be metabolized in liver and excreted in urine. you make drugs more polar to make them excreted in urine. biliary excretion is less common. what's the math governing the metabolism/excretion of a drug? generally drugs are cleared by first order elimination. You can consider what is called a "half-life" or t1/2. First order elimination means, in simple terms, that the fraction of drug metabolized in any given time will always be the same. So consider the half-life - the time required to metabolize or clear one half of the drug that was administered. Rate of elimination is related to a rate constant Ke. There's a relationship b/w t1/2 and Ke of 0.693 (ln 0.5) if a half life is 6 hrs, how much of the drug is cleared in 24 hrs? at 6 hrs, 1/2 remains, 1/2 cleared or metabolized (50% remains) at 12 hrs, 1/4 remains, 3/4 cleared or metabolized (25% remains) at 18 hrs, 1/8 remains, 7/8 cleared or metabolized (12.5% remains) at 24 hrs, 1/16 remains, 15/16 cleared or metabolized (6.2% remains) go back to considering species variation. Remember the cats, that metabolize aspirin and other drugs via glucuronide synthesis very slowly. In humans, t1/2 of aspirin is 10-15 hrs; in dogs, it's about 4.5 hrs, and in cats, it is about 35 hrs. This is huge variation. so *again* remember there are huge difference in pharmacokinetics between species! when we discussed horses the other day he said the nutritive status of a horse depends on microbial digestion of polysaccharides - so some abx will threaten the life of a horse, and others must be given at certain times relative to food - either before or after feeding - rifamycin bioavailability is 26% if given 1 hr after feeding or 68% if given 1 hr before feeding! and for drugs excreted in the urine, pH of urine is another factor to consider. Now, if you have a patient with weak base poisoning with a drug that is excreted in the urine, would you acidify the urine, or make it alkaline? You'd want to acidify the urine to trap the weak base in that compartment. clearance: can be useful for you because as you see, there is going to be disease that affects clearance, and you have ways of assessing how well a drug will be cleared in a patient based on how well the kidneys are functioning. You can measure creatinine clearance, for example. You use this information to adjust dosing regimen. now - we're not getting more equations here, but things are not really so simple. how does varying these parameters affect the peak/trough concentrations of a drug? see your handout on p 10. we want to minimize the peaks and troughs and maintain a flat line, steady state concentration, right? ha. remember you might want a slow rate of absorption to avoid toxicity and acheive a steady concentration. if rate of absorption equals the rate of elimination, you can get a nice constant concentration. IV infusion, transdermal patches, etc help you do this. One reason for using time release formulations is to blunt these peaks and troughs. now. most drugs do not get into just one compartment - most drugs distribute into multiple compartments. look back at p 11. drugs will equilibrate immediately with some organs, then slowly with other organs. look at the two compartment first order elimination diagram. we knwo a drug will distribute first in the central compartment - without having said enough about it, know that the central compartment isn't always the same - it depends on the properties of the drug. Sometimes it will include the brain, sometimes not. plasma is always included. but spleen, heart, liver, brain - highly perfused tissues - are sometimes included, sometimes not. how does this affect pharmacokinetics of a drug? we had on the board an example of a graph in which we had first order elimination - log of concentration vs time. this isn't going to be on the test! it was a flat line with downward slope. in a situation where drug was distributed b/w multiple compartments, it would be a biphasic curve because of redistribution and elimination. a short acting general anesthetic follows this biphasic redistribution - it doesn't stop acting because it is being metabolized - it stops acting because it is being redistributed. you give an IV drip of it, patient falls asleep right away. drug equilibrates with central compartment right away, then redistribution starts occuring - so if you want a therapeutic concentration, elimination won't have much of a role in limiting the duration of the drug, but redistribution will, as drug moves into fat and other compartments, and person will wake up. again - drug is given to central compartment (say into blood/plasma via IV drip), rapidly distributes into brain, then more slowly redistributes into fat and other tissues, and then more slowly than that gets metabolized and excreted. in the handout are equations for the two compartment model - you don't have to memorize them but need to use them to answer question 12 for the review session. see the diagram on p 12 for more info on redistribution followed by elimination - the key factor is redistribution in getting below the therapeutic dose. p 13 of handout - repeated dosages. concentration vs time (multiples of half life). based on what we've already seen, can we rationalize some of the things going on? your client isn't sick enough to be on an IV so you're giving oral meds at a halflife interval. The first thing we see is that the plateau state is obtained after about 4 half-lives. what's that about? you give a drug q 6 hrs. t1/2 = 6 hrs. what is the concentration going to be at various times? you're giving enough to achieve 1 mg/L. So, after dose 1, you have 1 mg/L at time 0. doses repeated q 6 hrs: time conc 0 1 mg/L 6 hr 0.5 mg/L + 1 mg/L = 1.5 mg/L 12 hr 0.75 mg/L + 1 mg/L = 1.75 mg/L 18 hrs 0.87 mg/L + 1 mg/L = 1.87 24 0.935 + 1 = 1.93 now it will just yoyo b/w 1.87 and 1.93 so that's basically your steady state. so we obtain a plateau after 4 half-lives. Also, the total body store is about 1.5 the amount you give. But, hey - we're giving 1 mg and getting about twice that, right? No...the trough is about the same as the dose, and the peak is about twice the dose, so average total body store is about 1.5 the dose. Time to plateau is independent of dosage -take his word for it. The fluctuations are proportional to dosage interval/half life and are blunted by slow absorption. plateau concentratoins are proportional to dose/dosage interval, and are proportional to half-life. if you prolong the dosage interval, the amount of drug left after a certain time will be reduced, that makes sense. one of the themes of this lecture has been that pharmacokinetics vary among species. also can vary for other reasons - you can saturate the system for metabolism. first order elimination occurs when you do not saturate the system. but, for example, you can saturate alcohol dehydrogenase - a case against binge drinking -this is why people die. it is hard to get that much alcohol in your system, but some people do it and die. dilantin can saturate its elimination system also. when you do this you prolong the apparent half-life, so the concentration does not fall as quickly as you would expect it to. Also, disease and age can affect pharmacokinetics, as can the presence of multiple drugs in one patient. what might happen if you give your patient multiple drugs? the rate of elimination may be affected. it may be speeded up or it may be slowed. apparent half life may be prolonged by saturation of elimination systems or may be decreased. many aged patients have multiple drugs on board and compliance is often a problem. how does age affect pharmacokinetic principles? both neonatal and geriatric populations may have altered pharmacokinetics. neonatal calves don't have fully developed rumens. Most neonates have altered liver enzyme activity. In aged populations there is often slowed metabolism/excretion of drugs due to decreased liver and kidney function. if half life is prolonged, you might think you should reduce the dosing interval. However, this reduced compliance. it is harder to give a drug every other day than to give every day - so you probably would alter the dose, and give half as much every day. renal and hepatic disease can also have large effects on half-lifes and dosing intervals. goal of pharmacokinetics: achieve therapeutic concentration, avoid toxic concentrations. review questions are VERY SIMILAR to exam questions. email robinson@pharm.med.upenn.edu --end----