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Unless a drug is actively transported into cells, it is generally assumed that only free drug can distribute to tissues.

Unless a drug is actively transported into cells, it is generally assumed that only free drug can distribute to tissues.

Unless a drug is actively transported into cells, it is generally assumed that only free drug can distribute to tissues.

Unless a drug is actively transported into cells, it is generally assumed that only free drug can distribute to tissues.

Unless a drug is actively transported into cells, it is generally assumed that only free drug can distribute to tissues.

Unless a drug is actively transported into cells, it is generally assumed that only free drug can distribute to tissues.

From A Physiologic Perspective

Objectives

- Problems / Questions Related to Introduction
- Distribution From A Physiologic Perspective]
- Five “Distribution Problems” are provided starting
- at slide 21. Not all of these problems will be completed in class …
- but you are expected to work through them on your own.

Mr. JR receives 500 mg of Levofloxacin by intravenous bolus

(over 1 minute) and the serum concentration is measured

immediately and found to be 5.0 mg/L.

What is the apparent volume of distribution?

What percent of drug is located in serum?

Where does drug go?

Objective

Review Basic Principles related to

drug & chemical / metabolite

distribution in the body

Develop a definition for

Volume of Distribution

Is it confined to blood

or

is it mostly in the blood

or

is it largely confined to tissues?

Body Weights

Actual vs Ideal (IBW)

Male: 50 kg + (2.5 kg/inch over 5 ft)

Female: 45.5 kg + (2.3 kg / inch over 5 ft)

Blood Volume (L) ~ 8% of IBW

Body water (L)

~60% of IBW

- 1. GI Tract
- Intestinal wall prevents absorption
- … not all drugs are absorbed
- Vascular walls
- limits “escape” from serum / blood
- Cellular walls
- limits “free” movement within the body

Plasma or Serum ~ 55%

RBC’s, ~ 45% of whole blood

Extra-cellular

Water

~ 15 L

Intra-cellular Water

~ 25 L

Whole Blood ~ 5 L

Tissue % Water %Weight Water

per 70 kg

( L )

Skin 72 18 9.1

Muscle 75 42 22.1

Brain 75 2 1.1

Skelton 22 16 2.5

Adipose 10 ~10 0.7

Other 12 6.5

Total 100 42

1. Skelton, H. Arch Int. Med 1927; 40: 140.

General Principles of Distribution

If you add 1000 mg of a drug

to 10 L of water,

what is the final concentration?

1000 mg

Following complete mixing

Concentration (C) = 1000 mg/ 10L

= 100 mg/L

10 L

C = Amount / volume

Volume = Amount / C

General Principles of Distribution

1000 mg

If you add 1000 mg of a drug

to 10 L of water,

what is the final concentration?

C = Amount / volume

Volume = Amount / C

10 L

Could the concentration change

as a function of time after addition?

If you knew that you had added

1000 mg of drug and then drew a sample

from a corner of the vessel before

complete mixing occurred,

what would you conclude?

General Principles of Distribution

Again you add 1000 mg of a drug

to 10 L of water, but now

there is some charcoal in the water

that may bind the drug.

The observed concentration

after complete mixing is 50 mg/L

1000 mg

10 L

Since

Volume = Amount / C

then the

apparent volume of distribution is:

= 1000 mg/50 mg/L

= 20L …???

BUT The real volume is 10L

Charcoal

General Principles of Distribution

Again you add 1000 mg of a drug

but this time in addition to the charcoal

and 10L of water there is 1 L of oil.

You measure the concentration

in the oil (150 mg/L)

and in the water (25 mg/L).

1000 mg

1L

10 L

Now calculate the volume:

Based on the concentration in the water

Volume = Amount / C

then the

apparent volume of distribution is:

= 1000 mg/25 mg/L

= 40L

Charcoal

General Principles of Distribution

Again you add 1000 mg of a drug

but this time in addition to the charcoal

and 10L of water there is 1 L of oil.

You measure the concentration

in the oil (150 mg/L)

and in the water (25 mg/L).

1000 mg

1L

10 L

Now calculate the volume:

Based on the concentration in the oil

Volume = Amount / C

then the

apparent volume of distribution is:

= 1000 mg/150 mg/L

= 6.66 L

Charcoal

General Principles of Distribution

Mass Balance

Water:

Concentration 25 mg/L

True Volume: 10L

Amount of Drug = 250 mg

Apparent Volume = 40L

Oil:

Concentration 150 mg/L

True Volume: 1L

Amount of Drug = 150 mg

Apparent Volume = 6.66 L

Charcoal: (therefore)

Amount = 600 mg

1000 mg

1L

10 L

Charcoal

General Principles of Distribution

1000 mg

- Conclusions
- The calculated Apparent Volume
- depends on the fluid being
- sampled.
- 2. The volume depends on the host, and the physical/chemical properties of the drug or metabolite
- 3. The calculated Apparent Volume
- rarely reflects a real physiologic
- volume.

1L

10 L

Charcoal

General Principles of Distribution

…so what is the Apparent Volume of Distribution?

… it is the volume of sampled fluid need to account for the total amount of drug in the body … at distribution equilibrium … (following complete mixing).

The volume is not associated with a particular space or anatomical area or tissue.

It is a proportionality constant relating concentration and amount in the body.

1000 mg

1L

10 L

Charcoal

General Principles of Distribution

- …so, if it is not real, how useful is it?
- Uses:
- It tells us how much drug must be added to the body so as to achieve a specified concentration in the sampled fluid.
- In a general way it tells us where the drug is stored in the body or where it might be found.

1000 mg

1L

10 L

Charcoal

General Principles of Distribution

L/70 kg

50,000

20,000

10,000

5,000

1,000

500

100

50

10

5

Quinacrine

Chloroquine

Nortriptyline

Digoxin

Propranolol

Quinidine

Quinolones (1- 2 L/kg), Tetracycline

Phenobarbital

Phenytoin

Theophylline (0.45 L/kg)

Aminoglycodises (0.25 L/kg)

ASA

Warfarin

General Principles of Distribution

Question:

If the drug is distributing to total body water, why are there large differences in the volume for different drugs?

Physical Chemical properties of the drug

High molecular weight (mabs) and even ICG (MW = 775)

are confined to plasma volume.

Ions (Cl-, Br-) rapidly distribute throughout extra-cellular

fluid but do not easily cross cell membranes.

Other Ions (K+, Ca2+) are actively transported across

membranes. Potassium is predominately intra-cellular.

Protein Binding

General Principles of Distribution

Protein Binding:

Unless a drug is actively transported into cells, it is generally assumed that only free drug can distribute to tissues.

In blood, drugs often

bind to albumin.

The unbound (free) drug

can diffuse out of the

blood, into the

extra-cellular water

and often into cells

(intra-cellular water).

Equilibrium is established

General Principles of Distribution

Protein Binding:

Unless a drug is actively transported into cells, it is generally assumed that only free drug can distribute to tissues.

The equilibrium

between

Bound & Free

remains in place.

It is also assumed

that at equilibrium

the free concentration

is equal in all tissues

General Principles of Distribution

Protein Binding:

Unless a drug is actively transported into cells, it is generally assumed that only free drug can distribute to tissues.

If a drug

is highly bound

within tissues,

the equilibrium

established between

bound and free

will find the majority

of the drug in tissues,

(based on binding

and mass).

General Principles of Distribution

Protein Binding:

Protein binding in

blood will <effectively>

keep drug in blood.

However, since

tissue mass

exceeds blood volume,

any binding in tissues

will shift the equilibrium

toward drug in tissues.

General Principles of Distribution

Protein Binding:

The volume of distribution

of a drug can be viewed as

a relationship between

tissue binding and

binding to protein

within the blood.

If a drug is

highly protein bound

within blood but has

little tissue binding,

the volume of distribution

will be small

(~10L – e.g. warfarin).

General Principles of Distribution

Protein Binding:

Even if a drug is

highly protein bound

within blood but also has

high tissue binding,

the volume of distribution

will be large.

General Principles of Distribution

Protein Binding:

The volume of distribution

of a drug can be viewed as

a relationship between

tissue binding and

binding to protein

within the blood.

VdTOTAL = VB + VT (fB/fT)

Where VB is blood volume ~ 5L

and VT is body water

(between 30-50 L).

fB and fT is the fraction unbound

in tissue and in blood

General Principles of Distribution

Protein Binding:

VdTOTAL = VB + VT (fB/fT)

Where VB is blood volume ~ 5L

and VT is body water

(between 30-50 L).

If fB is 5% (free in blood or plasma)

and fT is 100%

(free in issues – no binding)

The final volume

is 5L of blood volume

plus ~2.5L of tissue volume.

7.5L total.

The volume of distribution

of a drug can be viewed as

a relationship between

tissue binding and

binding to protein

within the blood.

General Principles of Distribution

Protein Binding:

VdTOTAL = VB + VT (fB/fT)

Where VB is blood volume ~ 5L

and VT is body water

(between 30-50 L).

If fB is 5% (free in blood or plasma)

But fT is 1%

(free in issues – 99% binding)

The final volume

is 5L of blood volume

plus ~250 L of tissue volume.

255L total.

The volume of distribution

of a drug can be viewed as

a relationship between

tissue binding and

binding to protein

within the blood.

General Principles of Distribution

Effect of Protein Binding on Volume of Distribution

VdTOTAL = VB + VT (fB/fT)

This makes the

assumption that

the drug may

distribute to all

places in the body

where water exists

and this may not

be true if there is

active transport

in or out

of a particular

tissue.

eg. BBB etc.

General Principles of Distribution

Observe the Effect of Protein Binding

on Volume of Distribution of Propranolol

For propranolol

as the free fraction

increases from

~5% to ~30%

Volume (Vd)

increases from

~125 L to ~800 L.

6-fold increases in

both FF and Vd.

Open circles – Liver disease patients

General Principles of Distribution

L/70 kg

50,000

20,000

10,000

5,000

1,000

500

100

50

10

5

Quinacrine

Chloroquine

Nortriptyline

Digoxin

Propranolol

Quinidine

Quinolones (1- 2 L/kg), Tetracycline

Phenobarbital

Phenytoin

Theophylline (0.45 L/kg)

Aminoglycodises (0.25 L/kg)

ASA

Warfarin

Five Examples:

Example 5: Cyclosporin … 3000L

Example 2: Ciprofloxacin … 120L

Example 1: Levofloxacin … 100L

Example 4: Levofloxacin … 83.3L

Example 3: Theophylline … 36L

Notice that the

Volume of distribution

is different

for all drugs and

will also be different

for each patient (levo).

Male Acute Community Acquired Pneumonia

Distribution Problems

Five Examples:

Example 1: Levofloxacin

Calculate Volume

Example 2: Ciprofloxacin

Given Volume,

Calculate Concentration

Example 3: Theophylline

Calculate Volume

…then predict new dose

Example 4: Levofloxacin

Example 5: Cyclosporin

General Principles of Distribution

- Summary
- The calculated apparent Volume depends on the fluid being sampled.
- Drugs can go anywhere (phys.-chem. prop.) leaving extra-cellular water to distribute into bone, fat or … anywhere, any tissue.
- 3. The apparent Volume depends on the host, and the physical/chemical properties of the drug or metabolite.
- 4. The calculated apparent Volume rarely reflects a real physiologic volume.
- The minimum volume* of distribution is vascular volume (8% IBW: 6’ ♂ = 6.4L).
- 6. There is no maximum volume*.

Male Acute Community Acquired Pneumonia

Distribution Problem 1

Calculate Volume

Male with Pneumonia

Age: 45 yr

Weight: 80 kg

Drug: Levofloxacin

Observe: Serum levofloxacin

concentration following

i.v. bolus of 500 mg

5 g/mL (mg/L)

Additional Information:

Blood Volume: 8% of body weight

Hematocrit: 0.45

Male Acute Community Acquired Pneumonia

Distribution Problem 1

- Questions
- What is the Volume of distribution of levo?
- 2. Where in the body does levo appear
- to be located? What percent is located
- in the Serum?
- 3. If the serum levo concentration
- is at the mid-point of target…3 g/mL
- how much drug is in the serum?
- what is the total amount of drug in
- your patient (MAC)?

Male Acute Community Acquired Pneumonia

Distribution Problem 1

Equations

Conc = Dose / V

V = Dose/Conc

Answers.

1. What is the Volume of distribution of levo?

Dose =

Initial [ ] =

Levo Volume: =

2. Proportion in Serum: =

Male Acute Community Acquired Pneumonia

Distribution Problem 1

Equations

Conc = Dose / V

V = Dose/Conc

Answers.

1. What is the Volume of distribution of levo?

Dose = 500 mg

Initial [ ] = 5 g/mL (mg/L)

Levo Volume: = Dose / Conc

= 500 / 5

= 100 L

2. Proportion in Serum: =

Male Acute Community Acquired Pneumonia

Distribution Problem 1

Equations

Conc = Dose / V

V = Dose/Conc

Answers.

2. Proportion in Serum:

Weight : 80 kg

Levo Volume: 500 mg/ 5 mg/L

Blood Volume: 8% of body weight

Hematocrit: 0.45

Blood volume: =

Serum (55%): =

Levo Volume: =

Proportion in Serum: =

Male Acute Community Acquired Pneumonia

Distribution Problem 1

Equations

Conc = Dose / V

V = Dose/Conc

Answers.

2. Proportion in Serum:

Weight : 80 kg

Levo Volume: 500 mg/ 5 mg/L

Blood Volume: 8% of body weight

Hematocrit: 0.45

Blood volume: = 0.08 x 80 kg = 6.4 L

Serum (55%): =6.4 x 0.55 = 3.5 L

Levo Volume: = 500 mg/ 5 mg/L = 100 L

Proportion in Serum: =

Male Acute Community Acquired Pneumonia

Distribution Problem 1

Equations

Conc = Dose / V

V = Dose/Conc

Answers.

2. Proportion in Serum:

Weight : 80 kg

Levo Volume: 500 mg/ 5 mg/L

Blood Volume: 8% of body weight

Hematocrit: 0.45

Blood volume: = 0.8 x 80 kg = 6.4 L

Serum (55%): =6.4 x 0.55 = 3.5 L

Levo Volume: = 500 mg/ 5 mg/L = 100 L

Proportion in Serum: = 3.5 L/100.0 L

= 3.5%

Male Acute Community Acquired Pneumonia

Distribution Problem 1

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- 3. If the serum levofloxacin concentration
- is at the mid-point of target … ~ 3mg/L …
- how much drug is in the serum?
- what is the total amount of drug in MAC?
- Therapeutic Range: 5 - 1 g/mL = mg/L
- mid point: 3 mg/L
- Amount in body at equilibrium:
- =
- Amount in serum:
- =

Male Acute Community Acquired Pneumonia

Distribution Problem 1

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- 3. If the serum levofloxacin concentration
- is at the mid-point of target … ~ 3mg/L …
- how much drug is in the serum?
- what is the total amount of drug in MAC?
- Therapeutic Range: 5 - 1 g/mL = mg/L
- mid point: 3 mg/L
- Amount in body at equilibrium:
- = 3 mg/L x 100.0 L = 300 mg
- Amount in serum:
- = 3 mg/L x 3.5 L = 10.5 mg
- Percent in serum: = 10.5 mg/ 300 mg
- = 3.5%

Levofloxacin Distribution Problem 1 Review

Answers.

Body Weight: 80 kg

Blood Volume: 8% of body weight

Serum is 55% of Blood

Serum = (0.08) x (0.55) x (80) = 3.52 L

Serum conc. = 3 g/mL

= 3 mg/L

Amount in Serum:

= (3.5 L) x 3 mg/L)

= 10.5 mg

Amount in Body, based on volume of 100 L

= (3) x (100) = 300 mg

Percent in Serum: 10.5 mg / 300 mg = 3.5%

Volume

100 L

100 L/80kg

= 1.2 L/kg

Recall Levo

monograph

indicated

volume was

between

74 & 112 L.

Male Acute Community Acquired Pneumonia

Distribution Problem 2

This time … given Volume

Male with Pneumonia

Age: 45 yr

Weight: 80 kg

Drug: Ciprofloxacin

Goal: Serum ciprofloxacin

concentrations ranging

3 - 4 g/mL (target)

Additional Information:

Cipro Volume: 1.5 L/kg

Blood Volume: 8% of body weight

Hematocrit: 0.45

Male Acute Community Acquired Pneumonia

Distribution Problem 2

- Questions
- What dose should be given to MAC to
- achieve a peak concentration of between
- 3 and 4 g/mL?
- What percent is located in the Serum?
- If the serum cipro concentration
- is at the mid-point of target…3.5 g/mL
- how much drug is in the serum?
- what is the total amount of drug in MAC?

Male Acute Community Acquired Pneumonia

Distribution Problem 2

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- What dose should be given to MAC to
- achieve a peak concentration of between
- 3 and 4 g/mL?
- Cipro Volume: 1.5 L/kg
- Pt weight: 80 kg
- 6.4 x 0.55 = 3.5 L
- Cipro Volume (L): =

Male Acute Community Acquired Pneumonia

Distribution Problem 2

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- What dose should be given to MAC to
- achieve a peak concentration of between
- 3 and 4 g/mL?
- Cipro Volume: 1.5 L/kg
- Pt weight: 80 kg
- 6.4 x 0.55 = 3.5 L
- Cipro Volume (L): = 1.5 L/kg x 80 kg
- = 120.0 L
- Peak target [ ] mg/L = 3 g/mL
- Req. Cipro Dose =

Male Acute Community Acquired Pneumonia

Distribution Problem 2

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- What dose should be given to MAC to
- achieve a peak concentration of between
- 3 and 4 g/mL?
- Cipro Volume: 1.5 L/kg
- Pt weight: 80 kg
- 6.4 x 0.55 = 3.5 L
- Cipro Volume (L): = 1.5 L/kg x 80 kg
- = 120.0 L
- Peak target [ ] mg/L = 3 g/mL (mg/L)
- Req. Cipro Dose = 3 mg/L x 120 L
- = 360 mg

Male Acute Community Acquired Pneumonia

Distribution Problem 2

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- What dose should be given to MAC to
- achieve a peak concentration of between
- 3 and 4 g/mL?
- Cipro Volume: 1.5 L/kg
- Pt weight: 80 kg
- 6.4 x 0.55 = 3.5 L
- Cipro Volume (L): = 1.5 L/kg x 80 kg
- = 120.0 L
- Peak target [ ] mg/L = 4 g/mL (mg/L)
- Req. Cipro Dose = 4 mg/L x 120 L
- = 480 mg

Male Acute Community Acquired Pneumonia

Distribution Problem 2

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- What dose should be given to MAC to
- achieve a peak concentration of between
- 3 and 4 g/mL?
- Peak target 3 mg/L = Dose = 360mg
- Peak target 4 mg/L = Dose = 480mg
- Common dose of Cipro IV?

Male Acute Community Acquired Pneumonia

Distribution Problem 2

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- What dose should be given to MAC to
- achieve a peak concentration of between
- 3 and 4 g/mL?
- Peak target 3 mg/L = Dose = 360mg
- Peak target 4 mg/L = Dose = 480mg
- Common dose of Cipro IV?
- 400 mg

Male Acute Community Acquired Pneumonia

Distribution Problem 2

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- What percent is located in the Serum?
- Weight : 80 kg
- Cipro Volume: 1.5 L/kg
- Blood Volume: 8% of body weight
- Hematocrit: 0.45
- Blood volume: 0.8 x 80 kg = 6.4 L
- Serum vol. (55%): 6.4 x 0.55 = 3.5 L
- Cipro Volume: 1.75 L/kg x 80 kg
- 140.0 L
- Proportion in Serum: 3.5 L/140.0 L = 2.5%

Male Acute Community Acquired Pneumonia

Distribution Problem 2

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- What percent is located in the Serum?
- Weight : 80 kg
- Cipro Volume: 1.5 L/kg
- Blood Volume: 8% of body weight
- Hematocrit: 0.45
- Blood volume: 0.08 x 80 kg = 6.4 L
- Serum vol. (55%): 6.4 x 0.55 = 3.5 L
- Cipro Volume: 1.5 L/kg x 80 kg
- 120.0 L
- Proportion in Serum: 3.5 L/120.0 L = 2.9%

Ciprofloxacin Distribution Problem 2 Review

Answers.

Body Weight: 80 kg

Blood Volume: 8% of body weight

Serum is 55% of Blood

Serum = (0.08) x (0.55) x (80) = 3.52 L

Serum conc. = 3 g/mL

= 3 mg/L

Amount in Serum:

= (3.5 L) x 3 mg/L)

= 10.5 mg

Amount in Body, based on volume of 120 L

= (3) x (120) = 360 mg

(Dose = 400 mg)

Percent in Serum: 10.5 mg / 360 mg = 2.9%

Volume

1.5 L/kg

120.0 L

Severe Asthmatic Male

Male Asthmatic

Age: 45 yr

Weight: 80 kg

Drug: Theophylline

Goal: Serum theophylline

in the therapeutic range

10 – 20 g/mL

Additional Information:

Initial Theophylline Dose of 300 mg

produces a peak following a bolus

iv dose of 8.33 mg/L.

Severe Asthmatic Male

- Questions
- What is the volume of distribution
- of theophylline?
- What percent is located in the Serum?
- If we need to produce a peak serum
- theophylline concentration near the
- mid-point of target… (~15 mg/L),
- what should the dose be?

Severe Asthmatic Male

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- What is the volume of distribution
- of theophylline?
- Theophylline Dose = 300 mg
- Peak [ ] mg/L = 8.33 mg/L.
- 0.55 = 3.5 L
- Theophylline Volume: =
- Vol. Expressed as L/kg: =

Severe Asthmatic Male

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- What is the volume of distribution
- of theophylline?
- Theophylline Dose = 300 mg
- Peak [ ] mg/L = 8.33 mg/L.
- 0.55 = 3.5 L
- Theophylline Volume: = 300 mg / 8.33 mg/L
- = 36 L
- Expressed as L/kg: = 36 L / 80 kg
- = 0.45 L/kg

Severe Asthmatic Male

Equations

Conc = Dose / V

V = Dose/Conc

Answers.

2. Proportion in Serum?

Weight : 80 kg

Theophylline Volume: 0.45 L/kg

Blood Volume: 8% of body weight

Hematocrit: 0.45

Blood volume: 0.8 x 80 kg = 6.4 L

Serum (55%): 6.4 x 0.55 = 3.5 L

Theophylline Volume: 0.45 L/kg x 80 kg

36.0 L

Proportion in Serum: 3.5 L / 36.0 L = 9.8%

Severe Asthmatic Male

Equations

Conc = Dose / V

V = Dose/Conc

Answers.

2. Proportion in Serum?

Weight : 80 kg

Theophylline Volume: 0.45 L/kg

Blood Volume: 8% of body weight

Hematocrit: 0.45

Blood volume: 0.08 x 80 kg = 6.4 L

Serum (55%): 6.4 x 0.55 = 3.5 L

Theophylline Volume: = 0.45 L/kg x 80 kg

= 36.0 L

Proportion in Serum: = 3.5 L / 36.0 L

= 9.8%

Severe Asthmatic Male

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- If we need to produce a peak serum
- theophylline concentration near the
- mid-point of target… (~15 mg/L),
- what should the dose be?
- Therapeutic Range: 10 – 20 g/mL = mg/L
- mid point: 15 mg/L
- Amount in body at 15 mg/L:
- 15 mg/L x 36.0 L = 540 mg
- Dose:
- 15 mg/L x 3.5 L = 52.5 mg

Severe Asthmatic Male

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- If we need to produce a peak serum
- theophylline concentration near the
- mid-point of target… (~15 mg/L),
- what should the dose be?
- Therapeutic Range: 10 – 20 g/mL = mg/L
- mid point: 15 mg/L
- Amount in body at 15 mg/L:
- 15 mg/L x 36.0 L = 540 mg
- Dose: actual dose???
- 540 mg peak of 15 mg/L

Severe Asthmatic Male

Equations

Conc = Dose / V

V = Dose/Conc

- Answers.
- If we need to produce a peak serum
- theophylline concentration near the
- mid-point of target… (~15 mg/L),
- what should the dose be?
- Dose: actual dose???
- 540 mg = peak of 15 mg/L
- 600 mg = peak conc?
- = 600 mg / 36 L
- = 16.6 mg/L
- 500 mg = peak conc?
- = 500 mg / 36 L
- = 13.9 mg/L

Answers.

Body Weight: 80 kg

Blood Volume: 8% of body weight

Serum is 55% of Blood

Serum = (0.08) x (0.55) x (80) = 3.52 L

Serum conc. = 15 g/mL

= 15 mg/L

Amount in Serum:

= (3.5 L) x 15 mg/L)

= 52.5 mg

Amount in Body, based on volume of 36 L

= (15) x (36) = 540 mg

Percent in Serum: 52.5 mg / 540 mg = 9.8%

Volume

0.45 L/kg

36.0 L

Fourth Example: Levofloxacin in a different patient

Volume of

Distribution

IV

Dose

Blood

Kidney

Liver

Oral

Dose

GI Tract

Example 4

- Mr. JR, as 45 yr old male
- weighing 80 kg and
- appears to have Community
- Acquired Pneumonia. He is
- prescribed 500 mg of levofloxacin,
- once per day for 7 days.
- Immediately following the first
- dose, given by I.V. bolus, a plasma
- concentration is measured as 6.0 mg/L.
- Calculate the apparent volume of distribution.
- What percent of the drug is in plasma?
- 3. Other Questions about “Distribution”?

Example 4

Equations

Conc = Dose / V

V = Dose/Conc

- Mr. JR, receives 500 mg
- and the initial plasma
- concentration is measured as 6.0 mg/L.
- Calculate the apparent
- volume of distribution.
- Conc = Dose / Volume
- Volume = Dose / Conc
- = 500 mg / 6.0 mg/L
- =

Example 4

Equations

Conc = Dose / V

V = Dose/Conc

- Mr. JR, receives 500 mg
- and the initial plasma
- concentration is measured as 6.0 mg/L.
- Calculate the apparent
- volume of distribution.
- Conc = Dose / Volume
- Volume = Dose / Conc
- = 500 mg / 6.0 mg/L
- = 83.33 liters
- Expressed per kg of body weight
- =

Notice that this volume is slightly different

than the 100 L calculated for a different patient

Example 4

Equations

Conc = Dose / V

V = Dose/Conc

- Mr. JR, receives 500 mg
- and the initial plasma
- concentration is measured as 6.0 mg/L.
- Calculate the apparent
- volume of distribution.
- Conc = Dose / Volume
- Volume = Dose / Conc
- = 500 mg / 6.0 mg/L
- = 83.33 liters
- Expressed per kg of body weight
- = 83.33 liters / 80 kg
- =1.04 L/kg

Example 4

Equations

Conc = Dose / V

V = Dose/Conc

- Mr. JR, receives 500 mg
- and the initial plasma
- concentration is measured as 6.0 mg/L.
- Calculate the apparent volume of distribution.
- Volume = 83.33 liters
- Vol per kg of body weight = 1.04 L/kg
- What percent of the drug is in plasma?
- Blood is ~8% of body weight
- Mr. JR weighs 80 kg.
- Blood Volume is ~ 6.4 L
- Plasma volume is ~55% of blood volume.
- Plasma volume = 6.4 L x 0.55 = 3.52 L.

Example 4

Equations

Conc = Dose / V

V = Dose/Conc

- Mr. JR, receives 500 mg
- and the initial plasma
- concentration is measured as 6.0 mg/L.
- What percent of the drug is in plasma?
- Plasma volume = 6.4 L x 0.55 = 3.52 L.
- Conc in plasma = 6.0 mg/L
- Amount in plasma =

Example 4

Equations

Conc = Dose / V

V = Dose/Conc

- Mr. JR, receives 500 mg
- and the initial plasma
- concentration is measured as 6.0 mg/L.
- What percent of the drug is in plasma?
- Plasma volume = 6.4 L x 0.55 = 3.52 L.
- Conc in plasma = 6.0 mg/L
- Amount in plasma = 3.52 L x 6.0 mg/L
- = 21.12 mg.
- How much is in the body?
- volume distrib. = 83.33 L
- Conc in plasma = 6.0 mg/L
- Amount in body =

Example 4

Equations

Conc = Dose / V

V = Dose/Conc

- Mr. JR, receives 500 mg
- and the initial plasma
- concentration is measured as 6.0 mg/L.
- What percent of the drug is in plasma?
- Plasma volume = 6.4 L x 0.55 = 3.52 L.
- Conc in plasma = 6.0 mg/L
- Amount in plasma = 3.52 L x 6.0 mg/L
- = 21.12 mg.
- How much is in the body?
- volume distrib. = 83.33 L
- Conc in plasma = 6.0 mg/L
- Amount in body = 6.0 mg/L x 83.33L
- = 500 mg (dose)

Example 4

Equations

Conc = Dose / V

V = Dose/Conc

- Mr. JR, receives 500 mg
- and the initial plasma
- concentration is measured as 6.0 mg/L.
- What percent of the drug is in plasma?
- Amount in plasma = 3.52 L x 6.0 mg/L
- = 21.12 mg.
- Amount in body = 6.0 mg/L x 83.33L
- = 500 mg (dose)
- Proportion in plasma ?
- =

Example 4

Equations

Conc = Dose / V

V = Dose/Conc

- Mr. JR, receives 500 mg
- and the initial plasma
- concentration is measured as 6.0 mg/L.
- What percent of the drug is in plasma?
- Amount in plasma = 3.52 L x 6.0 mg/L
- = 21.12 mg.
- Amount in body = 6.0 mg/L x 83.33L
- = 500 mg (dose)
- Proportion in plasma
- = 21.12 mg / 500 mg
- = 0.042
- = 4.2%

- Cyclosporin (CsA),600 mg is
- administered to a female transplant
- patient – MJ, who weighs 55 kg, by IV
- bolus. Cyclosporin is “highly bound to
- RBC” and the “Blood : Plasma ratio is 2”.
- Immediately after the dose a blood
- sample is taken and the blood concentration
- is measured as 200 ng/mL.
- What is the apparent volume of distrib?
- What percent of CsA in the body is
- located in blood / plasma in this patient?

- Cyclosporin (CsA),600 mg is
- administered to a female transplant
- patient – MJ, who weighs 55 kg, by IV
- bolus. Cyclosporin is “highly bound to
- RBC” and the “Blood : Plasma ratio is 2”.
- Immediately after the dose a blood
- sample is taken and the blood concentration
- is measured as 200 ng/mL. (200 ug/L)
- What is the apparent volume of distrib?
- Conc = Dose / Volume
- Volume = Dose / Conc
- =

Equations

Conc = Dose / V

V = Dose/Conc

- Cyclosporin (CsA),600 mg is
- administered to a female transplant
- patient – MJ, who weighs 55 kg, by IV
- bolus. Cyclosporin is “highly bound to
- RBC” and the “Blood : Plasma ratio is 2”.
- Immediately after the dose a blood
- sample is taken and the blood concentration
- is measured as 200 ng/mL. (200 ug/L)
- What is the apparent volume of distrib?
- Conc = Dose / Volume
- Volume = Dose / Conc
- = 600 mg / 200.0 ug/L
- = 600 mg / 0.2 mg/L
- = 3,000 liters

Equations

Conc = Dose / V

V = Dose/Conc

- Cyclosporin (CsA),600 mg is
- administered to a female transplant
- patient – MJ, who weighs 55 kg, by IV
- bolus. Cyclosporin is “highly bound to
- RBC” and the “Blood : Plasma ratio is 2”.
- If, immediately after the dose a blood
- sample is taken and the plasma concentration
- is measured as 100 ng/mL. (100 ug/L)
- What is the apparent volume of distrib?
- Conc = Dose / Volume
- Volume = Dose / Conc
- =

Equations

Conc = Dose / V

V = Dose/Conc

- Cyclosporin (CsA),600 mg is
- administered to a female transplant
- patient – MJ, who weighs 55 kg, by IV
- bolus. Cyclosporin is “highly bound to
- RBC” and the “Blood : Plasma ratio is 2”.
- If, immediately after the dose a blood
- sample is taken and the plasma concentration
- is measured as 100 ng/mL. (100 ug/L)
- What is the apparent volume of distrib?
- Conc = Dose / Volume
- Volume = Dose / Conc
- = 600 mg / 100.0 ug/L
- = 600 mg / 0.1 mg/L
- = 6,000 liters

Equations

Conc = Dose / V

V = Dose/Conc

- Cyclosporin (CsA),600 mg is
- administered to a female transplant
- patient – MJ, who weighs 55 kg, by IV
- bolus. Cyclosporin is “highly bound to
- RBC” and the “Blood : Plasma ratio is 2”.
- Immediately after the dose a blood
- sample is taken and the blood concentration
- Is measured as 200 ng/mL.
- What is the apparent volume of distrib?
- What percent of CsA in the body is
- located in whole blood in this patient?
- Blood is ~8% of body weight
- Ms. MJ weighs 55 kg.
- MJ’s hematocrit is 0.45 (45% cells)
- Blood Volume =

Equations

Conc = Dose / V

V = Dose/Conc

- Cyclosporin (CsA),600 mg is
- administered to a female transplant
- patient – MJ, who weighs 55 kg, by IV
- bolus. Cyclosporin is “highly bound to
- RBC” and the “Blood : Plasma ratio is 2”.
- Immediately after the dose a blood
- sample is taken and the blood concentration
- Is measured as 200 ng/mL.
- What is the apparent volume of distrib?
- What percent of CsA in the body is
- located in whole blood in this patient?
- Blood is ~8% of body weight
- Ms. MJ weighs 55 kg.
- MJ’s hematocrit is 0.45 (45% cells)
- Blood Volume = 55 kg x 0.08
- = 4.4 L

Equations

Conc = Dose / V

V = Dose/Conc

Cyclosporin (CsA),600 mg is

administered to a female transplant

patient – MJ, who weighs 55 kg, by IV

bolus. Cyclosporin is “highly bound to

RBC” and the “Blood : Plasma ratio is 2”.

Immediately after the dose a blood

sample is taken and the blood concentration

Is measured as 200 ng/mL.

(b) What percent of CsA in the body is

located in whole blood in this patient?

Blood Volume = 4.4 L

How much is in Blood?

=

Equations

Conc = Dose / V

V = Dose/Conc

- Cyclosporin (CsA),600 mg is
- administered to a female transplant
- patient – MJ, who weighs 55 kg, by IV
- bolus. Cyclosporin is “highly bound to
- RBC” and the “Blood : Plasma ratio is 2”.
- Immediately after the dose a blood
- sample is taken and the blood concentration
- Is measured as 200 ng/mL.
- What percent of CsA in the body is
- located in whole blood in this patient?
- Blood Volume = 4.4 L
- How much is in Blood?
- = 4.4 L x 0.2 mg/L
- = 0.88 mg
- How much is in the body?
- Amount in body =

Equations

Conc = Dose / V

V = Dose/Conc

Cyclosporin (CsA),600 mg is

administered to a female transplant

patient – MJ, who weighs 55 kg, by IV

bolus. Blood sample measures 200 ng/mL.

(b) What percent of CsA in the body is

located in whole blood in this patient?

Blood Volume = 4.4 L

How much is in Blood?

= 4.4 L x 0.2 mg/L

= 0.88 mg

How much is in the body?

Amount in body = 0.2 mg/L x 3000L

= 600 mg (dose)

Proportion in whole blood ?

Equations

Conc = Dose / V

V = Dose/Conc

- Cyclosporin (CsA),600 mg is
- administered to a female transplant
- patient – MJ, who weighs 55 kg, by IV
- bolus. Blood sample measures 200 ng/mL.
- What percent of CsA in the body is
- located in whole blood in this patient?
- How much is in Blood?
- = 0.88 mg
- How much is in the body?
- = 600 mg (dose)
- Proportion in whole blood ?
- = 0.88 mg / 600 mg
- = 0.0015
- = 0.15%

Equations

Conc = Dose / V

V = Dose/Conc

Cyclosporin (CsA),600 mg is

administered to a female transplant

patient – MJ, who weighs 55 kg, by IV

bolus. Cyclosporin is “highly bound to

RBC” and the “Blood : Plasma ratio is 2”.

Immediately after the dose a blood

sample is taken and the plasma concentration

is measured as 100 ng/mL.

(b) What percent of CsA in the body is

located in plasmain this patient?

Plasma Volume = 4.4 L x 0.55 = 2.42 L

How much is in plasma?

=

Equations

Conc = Dose / V

V = Dose/Conc

- Cyclosporin (CsA),600 mg is
- administered to a female transplant
- patient – MJ, who weighs 55 kg, by IV
- bolus. Cyclosporin is “highly bound to
- RBC” and the “Blood : Plasma ratio is 2”.
- Immediately after the dose a blood
- sample is taken and the plasma concentration
- is measured as 100 ng/mL.
- What percent of CsA in the body is
- located in plasma in this patient?
- Plasma Volume = 2.42 L
- How much is in Plasma?
- = 2.42 L x 0.1 mg/L
- = 0.242 mg
- How much is in the body?
- Amount in body =

Equations

Conc = Dose / V

V = Dose/Conc

Equations

Conc = Dose / V

V = Dose/Conc

Cyclosporin (CsA),600 mg is

administered to a female transplant

patient – MJ, who weighs 55 kg, by IV

bolus. Plasma sample measures 100 ng/mL.

(b) What percent of CsA in the body is

located in whole plasma in this patient?

Plasma Volume = 2.42 L

How much is in Plasma?

= 2.42 L x 0.1 mg/L

= 0.242 mg

How much is in the body?

Amount in body = 0.1 mg/L x 6000L

= 600 mg (dose)

Proportion in Plasma ?

Equations

Conc = Dose / V

V = Dose/Conc

- Cyclosporin (CsA),600 mg is
- administered to a female transplant
- patient – MJ, who weighs 55 kg, by IV
- bolus. Plasma sample measures 100 ng/mL.
- What percent of CsA in the body is
- located in plasma in this patient?
- How much is in Plasma?
- = 0.242 mg
- How much is in the body?
- = 600 mg (dose)
- Proportion in plasma ?
- = 0.242 mg / 600 mg
- = 0.000403
- = 0.0403%

~ 0.88 mg

Comparison Blood : Plasma

Concentration (ng/mL) 200 100

Tissue Volume (L) 4.4 2.42

Amount in Tissue (mg) 0.88 0.242

App Vol. Dist. (L) 3,000 6,000

Dose (mg) 600 600

Percent in blood/plasma (%) 0.15 0.04

Does the difference in apparent volumes imply

anything about where cyclosporin distributes to?

If you are told*(published knowledge) that a

particular concentration must be achieved

in this patient; e.g. 400 ng/mL in whole blood …

What volume of distribution would you use?

What is your recommended dose?

~ 0.88 mg

Comparison Blood : Plasma

Concentration (ng/mL) 200 100

Tissue Volume (L) 4.4 2.42

Amount in Tissue (mg) 0.88 0.242

App Vol. Dist. (L) 3,000 6,000

Dose (mg) 600 600

Percent in blood/plasma (%) 0.15 0.04

Does the difference in apparent volumes imply

anything about where cyclosporin distributes to?

If you are told*(published knowledge: ~ MIC, ED , therap range)

that a particular concentration must be achieved

in this patient; e.g. 400 ng/mL in whole blood …

What volume of distribution would you use? (VolBLOOD)

What is your recommended dose? (1.2 gm)

50

General Principles of Distribution

- Summary
- The calculated apparent Volume depends on the fluid being sampled.
- Drugs can go anywhere (phys.-chem. prop.) leaving extra-cellular water to distribute into bone, fat or … anywhere, any tissue.
- 3. The apparent Volume depends on the host, and the physical/chemical properties of the drug or metabolite.
- 4. The calculated apparent Volume rarely reflects a real physiologic volume.
- The minimum volume* of distribution is vascular volume (8% IBW: 6’ ♂ = 6.4L).
- 6. There is no maximum volume*.6

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