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Fundamental Hypothesis
- Predictable relationship between
plasma drug concentration
and
effect 
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Therapeutic Window
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Major Pharmacokinetic Compartments
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Use TDM for What Kinds of Drugs?
- Drugs with
- Narrow safety margins
- Effects not immediately obvious
- Large inter-individual differences in pharmacokinetics
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Inter-individual Variation
- Differences among individuals are
greater for--
- Dose --> Plasma drug concentration
- Than for --
- Plasma drug concentration --> Effect
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Important Pharmacokinetic Variables
- First and Zero-order Kinetics (Michaelis-Menton plots)
- Half-life and Ke
- Clearance (CL)
- Volume of Distribution (Vd)
- Bioavailability (F)
- AUC (Area Under the Curve)
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Michaelis-Menton Plot
First Order Kinetics- Rate of process IS DEPENDENT on drug concentration. The absolute amount of drug, e.g., mg/h, increases as drug concentration increases and vice versa.
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Michaelis-Menton Plot
Zero Order Kinetics- Rate of process IS NOT DEPENDENT on drug concentration. The same absolute amount, e.g, mg/h, is eliminated / transformed regardless of drug concentration. The enzyme or transport system is "saturated".
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Half-life -- Defined on Plot
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Determining Vd(extrap)
- Fluid measure usually plasma
- Usually measure TOTAL DRUG
- Measuring FREE DRUG better, but not perfect indicator of drug at site of action
- May exceed Total Body Water!
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Volume of Distribution (Vd) Definition
- Definition
Virtual volume, of fluid in which concentration is measured (PLASMA?), required to explain the dilution of drug injected into the body
- Formula
- Vd = A / C
- Expressed in L or L/Kg
- A = Amount of drug in body ~= dose
- C = Concentration easily accessible fluid, e.g., plasma
- Vd = A / C
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Volume of Distribution (Vd) Usefulness
- The major usefulness of Vd is as a variable in pharmacokinetic computations
- Vd has no anatomic correlate
- Vd assumes drug is uniformly distributed throughout the volume indicated. This assumption is seldom warranted
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Vd -- Tidbits
- Virtual space
- not specifically identifiable as an anatomic space
- Does not imply equal drug concentration throughout the body
- Changes with --
- physiologic status, e.g., pregnancy
- disease and disease state, e.g., changes in protein binding
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Vd -- Types
- Vd(extrap)
- extrapolated from plot of Cp vs time
- Vd(ss)
- more complicated!
- Others
- Don't all give the same answer. Tendency today is to use Vd(ss) where possible
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Clearance (CL) Usefulness
- CL is a measure of the rate at which drug is eliminated from the body
- It reflects function of organ(s) of elimination
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Clearance Defined
- Definition
- Virtual volume of measured body fluid (usually plasma) completely freed of drug per unit of time
- CLB = Sum of all
clearances
- CL(body) = CL(renal) + CL(liver) + ...
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Extraction Ratio
- Extraction ratio is the fraction of drug removed by an organ of elimination per unit time
 & C(out) change. Initially,C(in) = initial C, thereafter, it = Ct (The C at specified time afterstart). In the following )
First minute
amount eliminated: 50
mcg/mL * 50 mL * 0.5 =
1,250 mcg
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Relating ER, CL, & Ke
- ER = constant if Flow, Vd, and renal function are constant.
- CL = Volume cleansed/min
= 25 ml/min
- If 0.5 of drug is removed and flow is 50 ml/min, then is equivalent to removing 100% of drug from 25 ml/min
- Ke = CL / Vd
- i.e., Fraction of Vd cleansed/min
- Note that this corresponds to fraction of drug removed/min!!!
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Extraction Rate Limited vs.
Flow Rate Limited CL- For Some Drugs
changes in --
- Organ function change CL very little
- blood flow rates change CL much
- For Other Drugs
changes in --
- Organ function change CL much
- Blood flow change CL very little
- For Still Others,
changes in --
- Both change CL significantly
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Clearance and Ke
- CL= virtual volume
of plasma completely
freed of drug per unit
time, (e.g., L/hr)
- CL = Ke * Vd
Ke = Fraction of Vd cleansed of drug per unit time and Fraction of drug removed per unit time (not shown here!) (e.g., frcn/hr )
- Ke = CL/Vd
- Note: Same terms are in both equations
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Clearance -- Tidbits
- CL = constant when plasma drug concentration ([drug]p) is less than that which "saturates" the elimination system(s)
- CL = variable when [drug]p is at or near the Vmax of elimination process(es)
- CL often changes with disease and stage of disease
Bioavailability (F) -- Definition
- Definition
- Fraction of administered drug that reaches the systemic circulation
- Dose calculation
example
- Recommended dose = 20 mg/Kg
- F = 0.5
- True dose = Recommended dose / F
- True dose = (20 mg/Kg) / 0.5 = 40 mg/Kg
- Note: "true dose" = dose actually reaching systemic circulation
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Bioavailability (F) -- Usefulness
- Bioavailability (F) is multiplied by the dose given to determine the TRUE DOSE
- It accounts for loss prior to drug reaching the central circulation
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Bioavailability (F) -- Tidbits
- Use systemic circulation
because --
- it is EASY to sample
- it is in contact with all body tissues
- Not 100% because of
drug loss through --
- elimination prior to reaching central systemic plasma
- Binding of drug to tissue components thus preventing absorption
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Bioavailability (F) -- Sites of Loss
- Example -- PO Adm.
- Penicillin G, 1000 IU
- 90% destroyed in stomach so only 10% reaches systemic circulation
- Other drugs
- propranolol -- extensive inactivation in liver
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Bioavailability (F) -- Determination
- Look-up in reference
- Measure: Compare exposure by desired route to IV, which is defined as 1.0.
- Exposure i.e., integral of drug concentration and time plot (AUC)
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Constant IV Infusion
- Steady state (accumulation)
- Time to reach steady state
- Cp rise and fall
- Initial dose rate
- Dosage adjustment
- Estimate patient's CL?
- Real life more complex
- Loading dose
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IV Infusion to Steady State
"Accumulation"- IV infusion at constant rate causes drug concentration to rise until it plateaus at the steady state
- Css = Concentration of drug at steady state plateau
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IV Infusion
Time To Steady State- Time to reach steady state concentration during constant IV infusion is determined by elimination rate!
- Examples
- 50% Css = 1 half-life
- 75% Css = 2 half-lives
- 87.5% Css = 3 half-lives
- 93.75% Css = 4 half-lives
- 96.87% Css = 5 half-lives
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Infusion -- Cp Rise and Fall
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IV Infusion -- Initial Dose Rate
- Look up values in literature
- Population (desired /
predicted) values
- Css = 30 mg/L
- CL = 0.33 L/hr
- Predicted DR = Css x
CL
- 30 mg/L x 0.33 L/hr = 10 mg/hr
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IV Infusion -- Adjust Dose
- Initial Dose Rate
- 10 mg/hr
- Css
- Measured = 20 mg/L
- Desired = 30 mg/L
- Use simple proportion
- New Dose Rate = Initial Rate * (Desired Css / Measured Css)
- New Infusion Rate = 15 mg/hr
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IV Infusion -- Adjust Dose
Estimate Patient's CL from data?- Infused 10 mg/hr and produced 20 mg/L concentration in plasma
- CL = DR / Css
- (10 mg/hr) / (20 mg/L) = 0.5 L/hr
Note: CL predicted by population (literature) was 0.33 L/hr, slower than found in this patient, therefore, had to adjust dose to higher amount
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IV Infusion -- Dose Adjustment Complications
- Real life slightly more complicated than the example
- Must account for
- Formula weight of drug as supplied vs the Molecular weight of drug as measured
- May need to give "loading dose" to produce concentration equivalent to Css faster
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Load Dose -- Simple Approach
- Need
population/literature
estimates
- Css(desired)
- Vd (note if is for "std 70 kg person" or "per kg"
- Loading dose =
Css(desired) *
Vd(predicted)
- In earlier example --
- Css(desired) = 30 mg/L & Vd(predicted) = 21L:
- Dose(loading) (mg) = Css (mg/L) * Vd (L)
- Dose(loading) = 630 mg
- In earlier example --
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Bolus
&
Multi-Dose Regimens- Multi-dose regimens -- definitions
- Two major approaches to pharmacokinetics
- One compartment model
- Two compartment model
- Multi-dose -- adjust
- Sample calculation
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Multi-Dose Regimens --
Additional Concentration Definitions- Css(max) = peak concentration at steady state
- Css(min) = trough concentration at steady state
- Css(ave) = average concentration at steady state
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Two Major Approaches To Pharmacokinetics
- Model Dependent
- One compartment model
- Two compartment model
- Three compartment model
- etc.
- Model Independent
- Dosing rate = Clearance * Css
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One Compartment Model -- Diagram
pk02_03.gif Return to -- (Syllabi) (Overview) (Constant Infusion Start) (Bolus / Multidose Start)
One Compartment Model -- Assumptions
- Instant mixing in body (relative to other process rates and time of first measurement of drug concentration)
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One Compartment Model -- Plot Cp(t) = A * e-(Ke * t)
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One Compartment Model -- Formula Cp(t) = A * e-(Ke * t)
- A = 0-time intercept of line drawn through data points
- Ke = negative slope of line
- t = time elapsed
- e = base of natural logs
- Cp(t) = Plasma drug concentration at time = "t"
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Two Compartment Model -- Diagram
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Two-Compartment Model Assumptions
- Instant mixing in each compartment (relative to other process rates and frequency of measurement)
- Input and output from central compartment
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Two Compartment Model -- Plot
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Two Compartment Model -- Formula Cp(t) = A * e-(a * t) + B * e-(b * t)
- A = Cp(0) intercept for faster rate
- a = (alpha) = -slope of faster rate
- B = Cp(0) intercept for slower rate
- b = beta = -slope of slower rate
- e = base of natural logarithms
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Multi-Dose
- Css(min), Css(ave), Css(max)
- Similarities to constant infusion
- Css(ave) calculation
- Dosage adjustment - Which Css?
- Dosage adjustment -- What about peak?
- Effect of regimen on oscillation
- Prediction of Css(max) -- Peak
- Prediction of Css(min) -- Trough
- Optimizing dose interval
- Determining dose rate for oral dose forms
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Multi-Dose -- Similarities to Constant Infusion
- Time to 97% of SS is 5 elimination half-lives
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Multi-Dose Adjust -- Css(ave)
- Formula for Css(ave)
Css(ave)=(FD/T) * [1 / (Ke * Vd)]
- Note similarity of the formulae for infusion and mulitple doses Css = DR * [1 / CL ]
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Multi-Dose -- Use Which Css??
Css(min)!
pk02_11.gif Return to -- (Syllabi) (Overview) (Constant Infusion Start) (Bolus / Multidose Start) (multi-dose)
Multi-Dose Adjust -- What about the Peak?
- If peak concentration is too high, could produce toxicity
- Must be concerned about degree of oscillation in dose schedule
- If route is other than IV, the degree of oscillation will always be less than predicted by calculation of Css(max) and (min)
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Effect of Ka on Oscillation [Need illustration]
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Effect of Ka/Ke Ratio on Oscillation [Need illustration]
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Effect of Regimen on Oscillation
- If dose interval (T) = elimination half-life, then Peak is 2x Trough!
- Increased T, increases oscillation
- Decreased T, decreases oscillation toward that of IV infusion.
- Calculation of oscillation requires ability to estimate peak and trough at SS.
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Effect of Regimen on Oscillation [Need illustration]
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Sample Problem -- Need Regimen for PO Administration
- Respiratory crisis is controlled. No need to patient on a maintenance PO regimen
- Need best dose (DM) and dose interval (T).
Know CL, but not half-life. Measure conc. after stopping infusion that produced 15 mg/L. Conc = 12 mg/L 4 hr after stop.
Half-life = _______ hr; Ke = _______/hrReturn to -- (Syllabi) (Overview) (Constant Infusion Start) (Bolus / Multidose Start) (multi-dose) (Sample calculation start)
Sample Problem -- Test Regimens Pharmacokinetically
- Use: Enteric Coated aminophylline tablets (0.79 mg theophylline / mg aminophylline)
- Tablets available include 100 mg & 200 mg
- Recommended PO aminophylline dose = ___________ given q_____h to produce Css (ave) of 15 mg/L of theophylline
- Need ______ tablets of ________ mg each Predicted Css(max)? ________ mg/L
- Predicted Css(min)? _________ mg/L
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Practice Questions --#1
- Elimination half-life of 5 hr corresponds to Ke = _______ /h
- What assumptions are made in 1-COM?
- How can we use 1-COM when we know assumptions are strictly false?
- What are relationships among: extraction ratio, CL, Vd, and Ke?
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Practice Questions -- #2
- What is meant by the idea that an elimination process is extraction limited and/or flow limited?
- What is the major usefulness of the term Vd? Simplest way to measure it?
- How does one determine F?
- How do we find values of A and "alpha" and B and "beta" when we analyze 2-COM plot?
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Last modified: 8/18/96 glc
- Penicillin G, 1000 IU
- CL= virtual volume
of plasma completely
freed of drug per unit
time, (e.g., L/hr)
- For Some Drugs
changes in --
- Drugs with
- Predictable relationship between
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First minute
amount eliminated: 50
mcg/mL * 50 mL * 0.5 =
1,250 mcg 
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