ToxicokineticsToxicokinetics is not rocket science is not rocket science

Kent R. Olson, MDKent R. Olson, MDMedical Director, SF DivisionMedical Director, SF Division

California Poison Control SystemCalifornia Poison Control System

. . . a. . . astepwise stepwise

approach approach to to

complicatecomplicatesimple simple

kineticskineticsconcepts concepts

andandfreak out freak out fellowsfellows

Dr. Bart’s blackboard fun™ presents ...

Kinetics for DUMMIES Kinetics for DUMMIES !!

1. Absorption1. Absorption

2. Distribution2. Distribution

3. Elimination3. Elimination

Case 1Case 1

Biff says he drank “2 beers”Biff says he drank “2 beers” His serum ethanol = 0.28 gm/dLHis serum ethanol = 0.28 gm/dL

Possible Questions:Possible Questions: How big is Biff?How big is Biff? How big are his beers?How big are his beers? How honest is Biff about his beers?How honest is Biff about his beers?

““2 beers” = ? EtOH2 beers” = ? EtOH

Assume:Assume: Pint-sized: 500 mL eachPint-sized: 500 mL each 6.8% EtOH v/v6.8% EtOH v/v EtOH ~ 0.7 g/mLEtOH ~ 0.7 g/mL

Calculation:Calculation: 1000mL x 6.8mL EtOH/100mL beer x 0.7 1000mL x 6.8mL EtOH/100mL beer x 0.7

g/mLg/mL

= 47.6 g EtOH= 47.6 g EtOH

AbsorptionAbsorption

““First-pass effect”First-pass effect”

Removal of drug after ingestion, by:Removal of drug after ingestion, by: Enzymes in the gut wallEnzymes in the gut wall Uptake by the liverUptake by the liver Vomiting, AC, WBI, etcVomiting, AC, WBI, etc

Ethanol: first-pass removal ~ 6-7%Ethanol: first-pass removal ~ 6-7%

Biff’s absorbed dose: down to Biff’s absorbed dose: down to 44.5 g44.5 g(47.6 x 93.5% = 44.5)(47.6 x 93.5% = 44.5)

EtOH FP effect modified by:EtOH FP effect modified by:

Gastric emptying timeGastric emptying time FoodFood Medications (eg, Reglan, ranitidine)Medications (eg, Reglan, ranitidine)

GenderGender AgeAge Most rapid and complete

EtOH absorption:• older• female• empty stomach• on metoclopramide

Most rapid and complete EtOH absorption:• older• female• empty stomach• on metoclopramide

Some drugs w/ high FP effectSome drugs w/ high FP effect a.k.a. “low bioavailability”a.k.a. “low bioavailability” PropranololPropranolol CyclosporineCyclosporine MorphineMorphine Desipramine & other TCAsDesipramine & other TCAs

ImplicationsImplications:: FP removal can be saturated in an ODFP removal can be saturated in an OD Greater proportion of drug will reach the Greater proportion of drug will reach the

systemic circulationsystemic circulation

Other absorption issues:Other absorption issues:

Delayed or altered absorptionDelayed or altered absorption Massive ODMassive OD GI motility altered by drug effectGI motility altered by drug effect

AnticholinergicsAnticholinergics OpioidsOpioids

Solubility Solubility Modified-release preparationsModified-release preparations

Modified-releasepreparation

1

10

100

1000

0 5 10 15 20 25

APAP(mg/L)

Poss. Toxic

Prob. Toxic

hrs

Serum APAP level

Note: co-ingestion of Nyquil plus up to 44 g Tylenol ERRef: Bizovi K et al: J Toxicol Clin Toxicol 1995; 33:510

Tylenol “Extended Relief” ingestionTylenol “Extended Relief” ingestionTylenol “Extended Relief” ingestionTylenol “Extended Relief” ingestion

Volume of Distribution (Vd)Volume of Distribution (Vd)

Where the drug goesWhere the drug goes

VdVd ==

= mg/kg / mg/L = L/kg= mg/kg / mg/L = L/kg

Total body waterTotal body water = 0.7 L/kg or ~ = 0.7 L/kg or ~ 50 L50 L ECFECF = 0.25 L/kg or about = 0.25 L/kg or about 15 L15 L in adult in adult PlasmaPlasma = 0.07 L/kg or ~ = 0.07 L/kg or ~ 5 L5 L

For EtOH: Vd ~ 0.7 L/kgFor EtOH: Vd ~ 0.7 L/kg

amount in body

Cp

Vd for some common drugsVd for some common drugs

Large Vd:Large Vd:

camphorcamphor antidepressantsantidepressants digoxindigoxin opioidsopioids phencyclidinephencyclidine phenothiazinesphenothiazines

Small Vd:Small Vd:

alcoholsalcohols lithiumlithium phenobarbitalphenobarbital phenytoinphenytoin salicylatesalicylate valproic acidvalproic acid

Back to Biff’s beers . . .Back to Biff’s beers . . .

How big is Biff?How big is Biff?

If Vd = amount in body, thenIf Vd = amount in body, then Cp Cp

0.7 L/kg x Biff (kg) = 44.5 g0.7 L/kg x Biff (kg) = 44.5 g 0.28 g/dL 0.28 g/dL

and Biff = 22.7 kg (and Biff = 22.7 kg (50 lb50 lb) ??) ??

Practice Question:Practice Question:

Boff ingested the contents of his Boff ingested the contents of his mother’s old Rx of theophyllinemother’s old Rx of theophylline

What is the highest possible serum What is the highest possible serum concentration he could achieve?concentration he could achieve?

Boff weighs 80 kgBoff weighs 80 kg Vd theophylline 0.5 L/kgVd theophylline 0.5 L/kg Bottle had # 20 pills 300 mg Theo-DurBottle had # 20 pills 300 mg Theo-Dur

Cp = dose / VdCp = dose / Vd

Max dose = 20 x 300 = 6000 mgMax dose = 20 x 300 = 6000 mg

Vd = 0.5 L/kg x 80 kgVd = 0.5 L/kg x 80 kg = 40 L= 40 L

Max Cp = 6000 mg = 150 mg/LMax Cp = 6000 mg = 150 mg/L

40 L40 L

Try this on your own:Try this on your own:

How many vials of Digoxin-Fab How many vials of Digoxin-Fab would be needed to neutralize would be needed to neutralize a digoxin serum concentration a digoxin serum concentration of 4 ng/mL? (assuming of 4 ng/mL? (assuming equilibrium)equilibrium)

Vd = 6 L/kgVd = 6 L/kg 50 kg elderly woman50 kg elderly woman Each vial binds ~ 0.5 mg digoxinEach vial binds ~ 0.5 mg digoxin

Question:Question:

Joe has a serum phenytoin level of Joe has a serum phenytoin level of 10 mg/L10 mg/L w/ serum albumin w/ serum albumin 4.4 gm/dL4.4 gm/dL

Josette has a serum phenytoin level Josette has a serum phenytoin level of of 5 mg/L5 mg/L w/ albumin w/ albumin 2.2 gm/dL2.2 gm/dL

What do they have in common?What do they have in common?

Protein bindingProtein binding

Cnormal binding = C’

(1 – fu) + fu P’

Pnormal

fu = fraction unbound

Cnormal binding = 5 mg/L

(1 – 0.1) + 0.1 2.2

4.4

Cnormal binding = = 9.09 mg/L 5 mg/L0.55

Some drugs w/ high Pr bindingSome drugs w/ high Pr binding

CarbamazepineCarbamazepine fu = fu = 0.20.2 PhenytoinPhenytoin 0.10.1 Salicylic acidSalicylic acid 0.160.16 Valproic acidValproic acid 0.150.15 WarfarinWarfarin 0.030.03

Note: Pr binding can be saturated in Note: Pr binding can be saturated in OD, resulting in greater free fractionOD, resulting in greater free fraction

Effect of saturated Pr bindingEffect of saturated Pr binding

Plasma protein

bound drugFree drug

Drug in

tissues

Plasma proteins

SATURATEDFree drug

Drug in

tissues

Salicylate: increasing Salicylate: increasing Vd with incr. doseVd with incr. dose

Salicylate: increasing Salicylate: increasing Vd with incr. doseVd with incr. dose

pHpH and and

VdVd

Salicylate is a Weak Acid (Salicylate is a Weak Acid (pKpKaa 3.5 3.5))Salicylate is a Weak Acid (Salicylate is a Weak Acid (pKpKaa 3.5 3.5))

TISSUESTISSUES(pH 6.8)(pH 6.8)

BLOODBLOOD(pH 7.4)(pH 7.4)

URINEURINE(pH variable)(pH variable)

SHSH

HH++ + S + S--

SHSH

HH++ ++ SS--

SHSH

HH+ + ++ SS--

Acidosis Alkalosis

Log = pKa – pHLog = pKa – pH

OR . . .OR . . .

Remember Henderson-Hasselbalch?Remember Henderson-Hasselbalch?

protonated/unprotonated = 10pKa-pH protonated/unprotonated = 10pKa-pH

protonated species

unprotonated species

Question:Question:

What is the proportion of salicylate in What is the proportion of salicylate in the the non-ionized (protonated)non-ionized (protonated) state state compared with the compared with the ionized (non-ionized (non-protonated)protonated) state in urine with: state in urine with:

pH = 3.5 ?pH = 3.5 ?

pH = 7.5 ?pH = 7.5 ?

Answer:Answer:

pH 3.5pH 3.5Protonated / nonprotonated = 10Protonated / nonprotonated = 103.5-3.53.5-3.5

Salicylic acid / salicylate = 10Salicylic acid / salicylate = 1000 = 1 = 1

Ratio = 1:1Ratio = 1:1

pH 7.5pH 7.5Protonated / nonprotonated = 10Protonated / nonprotonated = 103.5-7.53.5-7.5

Salicylic acid / salicylate = 10Salicylic acid / salicylate = 10-4-4

Ratio = 1:10,000Ratio = 1:10,000

Dose was 150 mg IV . . . Dose was 150 mg IV . . . Vd = ?Vd = ?

Dose was 150 mg IV . . . Vd = ?Dose was 150 mg IV . . . Vd = ?

Cp at t = 0

~ 7.5 mg/L Vd = dose / Cp= 150 / 7.5

= 20 L

Digoxin OD in a childDigoxin OD in a child

LithiumLithium

Elimination:Elimination:

Can you say “haff-life”?Can you say “haff-life”?

2 half-lives

1 half-life

Half-lifeHalf-life = the = the time it takes time it takes for the Cp to for the Cp to drop in halfdrop in half

Half-lifeHalf-life = the = the time it takes time it takes for the Cp to for the Cp to drop in halfdrop in half

No. of half-livesNo. of half-lives IncrementIncrement Percent of maximumPercent of maximum11 50%50% 50%50%22 25%25% 75%75%33 12.5%12.5% 87.5%87.5%44 6.25%6.25% 93.75%93.75%55 3.125%3.125% 96.875%96.875%66 1.5625%1.5625% 98.4375%98.4375%

No. of half-livesNo. of half-lives IncrementIncrement Percent of maximumPercent of maximum11 50%50% 50%50%22 25%25% 75%75%33 12.5%12.5% 87.5%87.5%44 6.25%6.25% 93.75%93.75%55 3.125%3.125% 96.875%96.875%66 1.5625%1.5625% 98.4375%98.4375%

K = slope of Slope =

the proportion ofdrug elimination

per unit time(natural log graph)

Slope =the proportion ofdrug elimination

per unit time(natural log graph)

What is Clearance? (Cl)What is Clearance? (Cl)

VOLUMEVOLUME per unit per unit

TIMETIME cleared cleared

of the drugof the drug

VOLUMEVOLUME per unit per unit

TIMETIME cleared cleared

of the drugof the drug

units =units = mL/minmL/min oror L/hrL/hrunits =units = mL/minmL/min oror L/hrL/hr

Clearance calculation:Clearance calculation:

If the reported Cl is 200 mL/min,If the reported Cl is 200 mL/min,

What is the Half-life?What is the Half-life?

How much drug is gone after 2 How much drug is gone after 2 hours?hours?

““They reported the CLEARANCE was They reported the CLEARANCE was really good - - - 200 mL/min . . .”really good - - - 200 mL/min . . .”

But, Cl is expressed in But, Cl is expressed in mL/minmL/min . . . . . .

(NOT mg/min or gm/hr or tons/day)(NOT mg/min or gm/hr or tons/day)

Total drug elimination depends on Total drug elimination depends on drug concentration:drug concentration:

mcg/mL x mL/min = mg/minmcg/mL x mL/min = mg/min

Now try again:Now try again:

Cl is 200 mL/minCl is 200 mL/min

Drug concentration is 1000 ng/mLDrug concentration is 1000 ng/mL

Cl x Cp = 200 mL/min x 1000 ng/mL

= 200,000 ng/min

= 200 mcg/min

= 0.2 milligrams/minute !

What is the relationship What is the relationship between between ClCl and and VdVd??

Slope = ClSlope = Cl VdVdSlope = ClSlope = Cl VdVd

ClClt t 1/21/2 = =

0.693 Vd.693 Vd

First-order kineticsFirst-order kinetics

Elimination is LINEARwhen plotted on semi-log graph

Elimination is LINEARwhen plotted on semi-log graph

a.k.a.“concentration-

dependent”kinetics

What happens in OD?What happens in OD?

Saturation of normal routes of Saturation of normal routes of elimination elimination “zero-order kinetics” “zero-order kinetics”

First-order Half-life = 1 hourHours Level00:00 6001:00 3002:00 1503:00 7.5

First-order Half-life = 1 hourHours Level00:00 6001:00 3002:00 1503:00 7.5

Zero-order Elim. = 30 mg/L/hrHours Level00:00 21001:00 18002:00 15003:00 120

Zero-order Elim. = 30 mg/L/hrHours Level00:00 21001:00 18002:00 15003:00 120

Nonlinear kineticsNonlinear kinetics

Css =Km x dose rateVm – dose rate

Vm = maximum rate of metabolism Km = Cp at which the rate of metabolism is ½ of maximum

Vm = maximum rate of metabolism Km = Cp at which the rate of metabolism is ½ of maximum

What happens when

the dose = Vm?

Other factors affecting Other factors affecting elimination rate in OD elimination rate in OD

Continued absorption from the GUTContinued absorption from the GUT Combined effect on Cp vs time plot Combined effect on Cp vs time plot

makes it makes it appearappear that half-life prolonged that half-life prolonged Hepatic Hepatic

Decreased hepatic blood flowDecreased hepatic blood flow Liver damageLiver damage

RenalRenal Oliguria due to hypotensionOliguria due to hypotension Acute renal failureAcute renal failure

Clearance can be:Clearance can be:

Metabolic (ClMetabolic (ClMM)) Renal (ClRenal (ClRR)) Lungs (ClLungs (ClLL)) etc (Cletc (Cletcetc))

and even hemodialysisand even hemodialysis (Cl (ClHDHD) ) and and other extracorporeal methodsother extracorporeal methods

Total Cl = ClTotal Cl = ClM M + Cl+ ClRR + Cl + ClLL + Cl + Cletc etc + Cl+ ClHDHD

““Intrinsic clearance”Intrinsic clearance”(by the body)(by the body)

Extracorporeal removalExtracorporeal removal

Blood from

patient

ARTERYor

VEINVEIN

Return to

patient

HemodialysisHemodialysis

Question:Question:

What is the hemodialysis What is the hemodialysis clearance of clearance of EnditalEndital™™, a new , a new (but not very effective) (but not very effective) antidepressant?antidepressant?

Vd = 40 L/kgVd = 40 L/kg Cp = 1000 ng/mLCp = 1000 ng/mL CCoutout = 340 ng/mL = 340 ng/mL Dialysis flow rate = 300 mL/minDialysis flow rate = 300 mL/min

Hemodialysis ClHemodialysis Cl

Flow rates = 250-350 mL/min (w/catheter)

Extraction ratio =

Clearance = Flow rate x Extraction ratioClearance = Flow rate x Extraction ratio

Cin

Cout

Cin – Cout

Cin

Extraction ratio

1000 - 340

1000= = 2/3

ClHD = flow rate x ER

= 300 x 2/3= 200 mL/min

What’s the “half-life” on HD?What’s the “half-life” on HD?

Clt 1/2 =

0.693 Vd

= 0.693 x 40 L/kg x 100 kg / 12 L/hr

= 231 hours !

OK, what’s really the half-life?OK, what’s really the half-life?

Clt 1/2 =

0.693 Vd

Clintrinsic = 1500 mL/min (90 L/hr)

Ctotal = 90 L/hr + 12 L/hr (HD) = 102

t1/2 = 0.693 x 4000 L / 102 L/hr

= 27.2 hours

Need to useCltotal not ClHD

Need to useCltotal not ClHD

Continuous Renal Replacement TherapyContinuous Renal Replacement Therapy

(or vein)

(CVVH)

(CVVHD)

(or vein)

Rate of ultrafiltrate production = up to 3 L/hr

Clearance = xClearance = x

Cp Cu

CCultrafiltrateultrafiltrate

CCplasmaplasma

Volume/timeVolume/timeof ultrafiltrateof ultrafiltrate

Beckmann U et al: JTCT 2001; 39:393-7

Estimate for LithiumEstimate for Lithium

Usual renal Cl 25-35 mL/minUsual renal Cl 25-35 mL/min Hemodialysis adds 100-150 mL/minHemodialysis adds 100-150 mL/min

But only for 3-4 hours at a timeBut only for 3-4 hours at a time Rebound between dialysis sessionsRebound between dialysis sessions

CVVH adds 20-35 mL/minCVVH adds 20-35 mL/min But can be provided continuouslyBut can be provided continuously Volume cleared ~ 50L/dayVolume cleared ~ 50L/day

vs 36 L/day w/ 4 hours of HDvs 36 L/day w/ 4 hours of HD No rebound No rebound