Two Compartment Models II

Two Compartment Models II - Compartmental Models OneTwo...

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Unformatted text preview: Compartmental Models OneTwo Compartments 1 Practice Problems • Equation List • Which equations do we use? 2 • After termination of an intravenous constant rate infusion the plasma concentration of a drug declines monoexponentially (C=C*e-kt). Concentrations measured 2 and 12 hours after the end of the infusion are 12.9 mcg/L and 6.0 mcg/L, respectively. Calculate the initial concentration at the end of the infusion, and predict the concentration 24 hours after termination of the infusion. If the infusion was of 1 hr duration what was the infusion rate (assume VD=4L). 3 • Edgar W (20 yo 58 kg) is receiving 80 mg of gentamicin as an iv infusion over a 30 min period q8hr. Two plasma samples are obtained to monitor serum concentrations as follows: 30 min after the end of the infusion and 30 min before the next dose. The plasma concentrations at these times are 4.9 and 1.7 mg/L. Assume a steady state. Develop a reasonable dosing regimen that will produce peak and trough concentrations of approx. 8 and 1 mg/L respectively. 4 Two Compartments Vi Vt ke Drug given into “initial” volume (Vi, central compartment) and it slowly distributes into larger “tissue” volume (Vt, peripheral compartment) Drug Eliminated from the central compartment 5 (Pages 23-26 in you text) When do we see this? Vi ke Vt Partitions slowly into a “large” compartment lots of tissue binding (fu,p and fu,t) What if these occur and drug “slowly” permeable binding in tissue and low lipid solubility/charged Very lipid soluble – partitions into fat low blood flow into fat tissues so this process is 6 Plasma Time Course 100 α β AMOUNT 10 1 0 2 4 6 8 10 12 14 Time Log Plot – Not a straight line! Looks like there is a fast phase (α)and a slow phase (β ) 7 Conceptual Approximation • Fast phase – α – Distribution into peripheral compartment – t ½ for distribution • Slow phase = β – Elimination from the peripheral compart. – t ½ for elimination • Not precisely correct mathematically • (What if distribution is slower than elimination?) 8 It’s the sum of two lines (exponentials) 100 α AMOUNT 10 β 1 0 5 10 15 20 25 30 Time Long times – it’s just the slower phase (elimination), fast phase has petered out Early times – plasma curve is balance of slow and fast phase (both occuring) can strip out the slow phase to reveal the fast phase 9 100 α β ke Vt AMOUNT Vi 10 1 0 2 4 6 8 10 12 14 Initially drug “only” distribution through small Vi (e.g. plasma) slowly drug distributes into the tissues (peripheral comp.) What is VD??? Apparent Volume of Distribution changes with time! Initially it’s small, then it gets bigger and bigger At long times distributes through initial and tissue apparent VD = Vi + Vt Clearance calculation – need to be careful Time 10 100 AMOUNT Vi ke Vt 10 1 0 2 4 6 8 10 12 14 Time Volumes of Distribution For example – give a 2000 mg dose Back-extrapolate for long compartment Get at long times Apparent VD of 2000 mg/(10 mg/L) = 200L If Measured blood conc at 1 min and it was 100 mg/L would calculate a apparent VD ~ 20L Apparent Volume of Distribution changes with time! 11 100 Vi ke Vt AMOUNT 10 1 0 2 4 6 8 10 12 14 Where’s the receptor In initial (central) compartment Time In peripheral (tissue) compartment It makes a difference 12 Scenarios-Where is the Drug? Vi AMOUNT 100 α β ke Vt 10 1 0 2 4 6 8 10 12 14 Time Closed circles –plasma concentration Cp Now open circles are the amount in the peripheral compartment In initially there is none, and then it builds up Time course of drug action 13 Scenarios – Clearance Issues Vi AMOUNT 100 α β ke Vt 10 1 0 2 4 6 8 10 12 14 Time RED shading – How we would calculate Clearance i.e. – we ignore the initial (distrubution phase) and assume 1 compartment Early on Plasma concs higher than we would predict amt eliminated is higher than we predict Does it matter? 14 Does it matter? 100 α β AMOUNT 25 30 100 AMOUNT 10 10 1 0 5 10 15 20 1 0 5 10 15 20 25 30 Time Time Black – amount of drug excreted in early (distribution) phase that is NOT predicted by the long term phase On LEFT – excess amount excreted early on is large fraction of total – this is problematic On RIGHT – excess amount excreted early on is small fraction (e.g. 20% or less) MOST drugs are like this Can ignore these early events and still get reasonable approximation 15 “Non-significant” vs “Significant” • Non-significant – Very little drug eliminated during distribution phase – AND – initially high blood levels aren’t harmful – (would you do plasma drug monitoring here?) • Significant – Early elimination during distribution and/or harm 16 Practically• Two Compartment and receptor is central – Calculate loading dose on Vi – and ignore peripheral compartment – drug can accumulate in peripherally • antibiotics • Two compartment and receptor is peripheral – if “non-significant” ignore central compartment – But need to be sure that drug monitoring for clearance determination etc. is at approp. 17 Practicality AMOUNT 100 α β 10 • Receptor is peripheral – iv – can be problematic – Oral – usually absorption slow enough that it rate limits and don’t see the “early” phase 0 5 10 15 20 25 30 1 Time • There are exceptions, like digoxin • Receptor is peripheral (tissue) and need to worry about toxicity in distribution phase – Don’t give large bolus (loading dose) – Give it slowly so equilibrates with peripheral • (e.g. iv drip versus iv bolus) 18 AMOUNT A typical Antibiotic 100 α β 10 • 98% elim. during distribution! • Pharmacol effect is central, toxicity peripheral • JUST APPROXIMATION for 100 mg doses • Dose 1 2 3 4 …..8…..16 1 0 5 10 15 20 25 30 Time • “Central” • “Peripheral” 98 2 98 98 98 98 98 4 6 8 16 32 19 Digoxin • • • • 100 (Drug monograph 4) Vi (plasma) ~ 10% of Vt Vt 7.3 L/kg Distrib. (α) t ½ is ~ 35 min AMOUNT α AMOUNT 10 β 1 0 5 10 15 20 25 30 Time – Will plasma go down this fast? 100 α β • What’s the relationship between plasma and heart 10 1 0 2 4 6 8 10 12 14 Time 20 Plasma vs Heart • α = 35 min • ClT ~ 0.1 L/min/kg AMOUNT 100 α β 10 1 0 2 4 6 8 10 12 14 Time • Time in t ½ 0 1 2 3 10 • Plasma 10 5.5 3.25 2.125 … 1 µ g/L • Heart 0 0.5 0.75 0.875 1 µ g/L • 1 t ½ – heart 50% to SS, is Cp predictive? 21 ...
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Two Compartment Models II - Compartmental Models OneTwo...

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