PK all 2011

8/6/2019 PK all 2011

http://slidepdf.com/reader/full/pk-all-2011 1/83

PHARMACOKINETICSPHARMACOKINETICS

John Orton

Royal Oldham Hospital

8/6/2019 PK all 2011

What have the following got incommon?

8/6/2019 PK all 2011

What have the following got incommon?

kel’

re allmo

8/6/2019 PK all 2011

Models

Created to predict from limitedinformation what will happen in the realworld

Dependant of data Complexity can be at the cost of

accuracy

Often aims to predict in individualcircumstances from data obtained froma population

8/6/2019 PK all 2011

Why bother?

To adjust the dose of drug so that theresponse of the body is as much andfor as long as required

But...Problems measuring drug at biophaseDrug concentration may not correlate with

response

May not be possible to measure responseaccurately

8/6/2019 PK all 2011

Qualitative ApproachQualitative ApproachYou can get quite far without much maths

8/6/2019 PK all 2011

In (or uptake)

Intravenous Inhalational

main routes for anaesthesia

Intramuscular Oral

Bioavailability

○ Effective dose / Administered dose Transdermal

8/6/2019 PK all 2011

Around (or distribution)(Drug factors)

Lipid solubility Water solubility Molecular size pKa

8/6/2019 PK all 2011

Around (or distribution)(Tissue factors)

Lipid content○ Brain, CSF

Blood vessel content Highly perfused

○ Lung, kidney, spleen, thyroid, adrenal,brain

Poorly perfused○ Bone, fat

Variable○ Muscle, skin, gut

Tissue binding Tissue barriers

Blood brain barrier Placenta Glomerulus “Leaky Capillaries”

8/6/2019 PK all 2011

Around (or distribution)(Blood factors)

Plasma proteins Variable: depends on drug Effect is to slow down rate of diffusion Types

Albumin Acidic drugs Lipo- and GlycoproteinsBasic Drugs α 1 acid glycoprotein

Red blood cells Cardiac output Sequestration

Lungs and fentanyl StomachpH trap Muscle

8/6/2019 PK all 2011

Distribution: summary

Depends on: Molecular size

Ionisation Protein binding Tissue perfusion

eg Relaxants Low Protein binding

(<60%) so perfusion

affects distribution alot.

Highly ionised so tendto stay in ECF

BUT dTc undergoestissue binding, soVd is unexpectedlyhigher than ECF

8/6/2019 PK all 2011

“Diffusible Fraction”

Consists of: Drug unbound to plasma protein

which is also

Unionised

The more protein bound and ionised adrug is, the more it tends to stay in the

plasma.

8/6/2019 PK all 2011

Out (Metabolism, excretion andelimination) Liver

Lipid soluble drugs Kidney

Polar drugs Lung

Vapours and gases

Metabolism

8/6/2019 PK all 2011

Out (Liver)

First pass effectLipid soluble drugsOrally administered

HER = (Ca - Cv)/CaHER = 1

○ clearance is flow dependant○ liver has spare capacity

HER approx 0.3○ clearance is flow independant○ liver is working at maximum rate

8/6/2019 PK all 2011

A brief diversionA brief diversionNow for some maths

8/6/2019 PK all 2011

BASIC MATHS FORBASIC MATHS FOR

PHARMACOKINETIPHARMACOKINETI

Its easy – honest!

8/6/2019 PK all 2011

10 + 10

8/6/2019 PK all 2011

+1 0 1 0

is 1 0 x 2

8/6/2019 PK all 2011

1 0 x 1 0

8/6/2019 PK all 2011

10 x 10

8/6/2019 PK all 2011

10x10 x 10x10 is

102 x 102 is 104 10(2+2)

8/6/2019 PK all 2011

103 x 106

is 10 +3 6

8/6/2019 PK all 2011

t3 x t6

is t +3 6

8/6/2019 PK all 2011

tn x tm

t +n m

8/6/2019 PK all 2011

/10000 100

8/6/2019 PK all 2011

104 / 10 2

10000 / 100

8/6/2019 PK all 2011

10 -42

10000 / 100

104 / 102

8/6/2019 PK all 2011

t4 / t2

8/6/2019 PK all 2011

Logarithms

Multiply by adding the powers Divide by subtracting the powers

8/6/2019 PK all 2011

Logarithms

Any positive number can be expressed( )as a number usually 10 raised to

a power Eg

100 is 102

64 is 10 .1806

2 is 10 .0301

So how do you calculate 2 x 64 using

logarithms?

8/6/2019 PK all 2011

Logarithms

Any positive number can be expressed( )as a number usually 10 raised to

a power Eg

100 is 102

64 is 10 .1806

2 is 10 .0301

( )+ ( ) = .log 64 log 2 1 806+0.301 = 2.107 Antilog(2.107)=128 (ie 128 = 102.107 )

8/6/2019 PK all 2011

Wierdness

What is 10-1? 103/104 (103-4 ) [10 x 10 x 10] / [10 x 10 x 10 x 10] [10 x 10 x 10] / [10 x 10 x 10 x 10] 1/10 t-1 = 1/t

If t-n = y, 0<y<1 (y is between 0 and 1)

8/6/2019 PK all 2011

Wierdness

What is 100.5 ? =√10 t0.5 = √t

8/6/2019 PK all 2011

Wierdness

What is 100? =1 t0 = 1

10 x 10 / 10 x 10 = 1 = 102/102=10(2-2)

8/6/2019 PK all 2011

Wierdness

What is 100? =1 t0 = 1

10 x 10 / 10 x 10 = 1 = 102/102=10(2-2)

8/6/2019 PK all 2011

Summary

100 is 102

64 is 101.806

1 is 100

0.1 is 10-1

0.001 is 10-2

Notice you cannot express a negative as

a logarithm 100.5 is √10

8/6/2019 PK all 2011

eeWhat is it and where does it come from?

8/6/2019 PK all 2011

=2.718

8/6/2019 PK all 2011

As frequencyapproaches infinity thisbecomes e!(2.718)

8/6/2019 PK all 2011

y = 10t

Simplify y = 10t

Use a logarithmic transform log y = t

Strictly speaking log10y = t

8/6/2019 PK all 2011

y = et

Simplify using logs to base e instead of base 10, ie loge instead of log10

y = et becomes loge(y) = t

Also written as ln instead of loge ie ln(y)=t

Natural logarithms

8/6/2019 PK all 2011

y = ek.t

Logarithmic transform: y = ek.t becomes Ln(y) = k.t

Logarithmic transform:

Ct = C0.e-k.t becomes Ln(Ct) = (Ln C0) - k.t

Ct = C0.e-k.t

8/6/2019 PK all 2011

y = mx + c

General eqation for a straight line graph m = slope of line c = intercept of y axis

8/6/2019 PK all 2011

Logarithmic transform

Lets you convert a complicated equation: Ct = C0e-tk

8/6/2019 PK all 2011

Lets you convert a complicated equation: Ct = C0e-tk

Into a linear equation Ln(Ct) = Ln(C0)-t.k

8/6/2019 PK all 2011

Into a linear equation Ln(Ct) = Ln(C0) - t . k

= – .y c x m

=y – . +m x c

8/6/2019 PK all 2011

Ka = [H+].[Drug-][H.Drug]

log 1/[H+] = -log[H+] = pHandlog 1/Ka = -logKa = pKa

1 1 [Drug-][H+] Ka [H.Drug].=i.e

8/6/2019 PK all 2011

pH = pKa+log [Drug- / H.Drug] or

pH = pKa+log [Ionised / Unionised]

or pH = pKa+log [Proton acceptor / Proton Donor ]

If Ionised = Unionised

pH = pKa (since log(1)=0)

8/6/2019 PK all 2011

So what? If pKa is near

physiological pHthen patients

condition willinfluence degreeof ionisation andtherefore clinical

effect cf local anaesthetics

% unionised at differentpH

Lignocaine pKa 7.9pH 7.0 11.2pH 7.4 24pH 7.8 44

Bupivacaine pKa 8.1pH 7.0 7pH 7.4 16pH 7.8 33

k h l l l l

8/6/2019 PK all 2011

Pk at the molecular levelDiffusion

Law of mass actionFlow along concentration

gradients

Major assumption in Pk models○ no active processes influencing

distribution

8/6/2019 PK all 2011

Rt α Ct

Rt α Ct1

That is, elimination is proportional toconcentration raised to the first

power, hence ‘first order kinetics’

8/6/2019 PK all 2011

But if….

Rt α Ct0 and Rt = k.Ct

Anything raised to the power of zero is 1

So Ct0

=1, therefore Rt α 1 Rt = k.1

So, Rt = k

In other words elimination is constant. Hence ‘zero order kinetics’.

8/6/2019 PK all 2011

Clearance, Vd, k, T1/2 and

8/6/2019 PK all 2011

Clearance

Rate of elimination (R) (mg.sec-1) Concentration (C) (mg.ml-1)

Law of mass action dictates:Rt α Ct

Rate of elimination at time t is proportional to concentration at time t

(assuming system isn’t saturated)

8/6/2019 PK all 2011

Clearance

Rt α Ct

Rt = Ct.k, k=Rt/Ct

k is a constant – what sort of constant? Rt/Ct units are [mg].[sec]-1/ [mg].[ml] -1

Rearranging: [mg].[sec]-1.[mg]-1.[ml]

8/6/2019 PK all 2011

Rt α Ct

Rt = Ct.k

k is a constant – what sort of constant? Rt/Ct units are [mg].[sec]-1/ [mg].[ml] -1

Rearranging: [mg].[sec]-1.[mg]-1.[ml]

Cancelling out: ml.sec-1

It’s Clearance!

Clearance

8/6/2019 PK all 2011

Volume of Distribution (Vd)

Theoretical; rarely relates to aphysiological volume

After an IV bolus:

Dose (D)Concentration at time zero (C0)VVdd==

8/6/2019 PK all 2011

How to find C0CC00

n t r a t i o

C o n c

t ra t i o

TimeTime

8/6/2019 PK all 2011

e n t r

a t i o

n t r a t

TimeTime

8/6/2019 PK all 2011

Vd and Cl

Rate of drug elimination is constantlychanging

But…

Percentage (or fraction) eliminated in unittime is constant (k)actually it’s

the natural log (ln) of the fraction ln{ C 0 / C t }

where t=1 Units are min-1

8/6/2019 PK all 2011

k = Cl / Vd

Another way of looking at k The fraction of Vd cleared of drug in unit

i.e. Cl / Vd

k = Clearance expressed as a fraction of Volume of Distribution

k is the Rate Elimination Constant

8/6/2019 PK all 2011

k, T1/2 and With k, the denominator is unit time

(minute, second, hour, whatever), thevariable is the fraction

With T1/2 , the denominator is a fraction(which in this case is 1/2), the variableis time

But T1/2 is not 1/k (or not exactly)

8/6/2019 PK all 2011

k, T1/2 and

Ct =C0e-k.t (basic decay function)

Ct/C0 =e-k.t

8/6/2019 PK all 2011

k, T1/2 and

Ct/C0 =e-k.t

When Ct/C0 =0.5(C has dropped to half original conc)

e-k.t =0.5

Ln{e-k.t } = Ln{0.5} = -k.t

Ln{0.5 } = -0.693 k.t = 0.693, k=0.693 / t Since t=T1/2 , k = 0.693 / T1/2

8/6/2019 PK all 2011

k, T1/2 and

τ is the time constant

It is the time taken for to reach zero if rate of fall were constant or the time taken for Ct to fall to 1/e

(instead to 1/2)

8/6/2019 PK all 2011

k, T1/2 and

Ct/C0 =e-k.t

When t=τ , Ct/C0 =1/e e-k.t

Ln{e-k.t } = -k.t

Ln{1/e } = -1 k.t = 1 or k=1 / t

Since t=τ , k = 1/τ

8/6/2019 PK all 2011

k, T1/2 and

Since k = 1/τ And since k = 0.693 / T1/2

0.693 / T1/2 = 1/τ

T1/2 = τ x 0.693

= τ x ln(2)

V k Cl T

8/6/2019 PK all 2011

Vd k elCl T1/2

Vd volume of distribution

○ If <5L corresponds to vascular space○ If >15L corresponds more to ECF (or an organ is

concentrating the drug)

kel proportion of drug eliminated in unit time (or more

precisely the logarithm: ln(Ct / Co)

Cl Clearance, ml/second

T1/2 Time taken for drug concentration to change by 1/2 T1/2 = 0.693 / kel

Cl = Vd.ke = Total Dose / AUC

8/6/2019 PK all 2011

Different Vd

VdssSteady state

elimination phase

Infusion Kinetics

8/6/2019 PK all 2011

Infusion KineticsHow to calculate rate of infusion to achieve a given blood

concentration

Assume that at steady statein = outi.e. rate of infusion = rate of elimination

Rate of elimination = Clearance x Concentration Concentration you know Clearance you either look up or calculate from

Cl = Vd.k For an infusion you will require Vdss (not ordinary Vd from a

bolus) Calculate this by doing an actual study, infusing at a constant

rate to steady state and measuring blood levels (see nextslide)

8/6/2019 PK all 2011

Exponential Change(decay in this example)

Ct=C0e-kt

Universal process

Where something changes according to its own magnitude

8/6/2019 PK all 2011

Compartmental Modelsand some basic Pk terms

One compartmentRapid bolusRapid mixingOpen (ie drug leaves as 1st order process)

Central CompartmentVd

k elCl

Estimation of Pk parameters

8/6/2019 PK all 2011

Estimation of Pk parameters

in a one compartment model

0 1 2 3 4 5 6 7 8 9 1 0

Drug Concentration

(Log plot)

Gradient = k el

Ct = Coe-k el

Drug Concentration Ct Drug concentration (Log Axis)

8/6/2019 PK all 2011

Two Compartment Model

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Co = Ae-α t

+ Be-β t

Drug Concentration (Log plot:: looks flattish because of log transform)t

8/6/2019 PK all 2011

TwoCompartment

ModelLogarithmic Plot

• NB α and β (calledhybrid rate

constants) are notk 12 , k 21 , k 10 in the

•They are hybrids of k 12 , k 21 and k 10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

g ( g p g )

A (Distribution)

B (Elimination)

C- t -β

o = Aeα

Gradient = βBe-

β t Gradient = α

PK all 2011

Documents

i heart cvs: 01/09-01/15 adimages.iheartcvs.com/ad_scans/2011/0109/010911.pdf · 2011. 1. 6. · 8 Pk. 9.volt 4 Pk. bat Household Cleaners or Ziploc Scrubbing Bubbles 16 oz. Shout

Circa Survivor - Sports · 2020. 9. 13. · Circa Survivor Week 1 Selections ENTRY NAME SELECTION ALL BALD DOME-2 17. COLTS PK All Day-1 17. COLTS PK ALMOST PERFECT-1 8. BILLS PK

PK 11001-12001 EH e Layout 1 - cranenetwork.com€¦ · All-rounders in municipal use ) ) *) PK 11001 / PK 12001 .EH High Performance. Reliable and versatile The PK 11001 displays

PK-Glossary PK Working Group 2004

Analysis of pk data- Pop PK analysis

PK 250A PK 320A

PK 36502 / 41002 EH - Gruas Eugeniogruaseugenio.com/wp-content/uploads/2016/02/PLUMA-PK-36.pdf · ALL INFORMATION AT A GLANCE All important information about the crane can be seen

PK 250A PK 320A - delmac

Provincial Constituency Reference Map - District Peshawar · T uc l fa j n between ALHASAN [] ... PK - 9 PK - 5 PK - 11 PK - 4 PK - 3 PK - 2 PK - 1 Legend Districts Boundary Provincial

CCG 2011 Final Latest Eg Pk 033647

ENRICH PK-8 COMPUTING EDUCATION AND PREPARE ALL … · ENRICH PK-8 COMPUTING EDUCATION AND PREPARE ALL STUDENTS FOR THE FUTURE WHY IS COMPUTING IMPORTANT? Computing and computational

Installation Instructions Boiler Burner Unitcdn.efmheating.com/PK-Series-Manual.pdfInstallation Instructions Boiler Burner Unit Models PK 400, PK 440, PK 450 SPK 600, PK 750, K950,

Pk nair icraf may 2011

CCG 2011 Final Latest Eg Pk 033647 (1)

1 CHRISTIAN VALLEY GEOLOGY MAP - Geoscience BC · 2019-04-22 · 2016, Report 2017-1, ... Epk Epm1 Epm1 Epm1 Epm1 Pw Pw Pk Pk Pk Pk Pk Pk Pk Pk Pk Pk Pk Pk CPa Pk Pk Pk Pk1 Pk Ec

PK RANGE - Palfinger5 stAbiLizER systEm fOr OPTiMuM STabiLiTy The PK 3400 and PK 4200 are available with two stabilizer widths to ensure optimum stability at all times. all models

Reorder Number BE1023 Figuras de Deportes (Pk/45) 1€¦ · Figuras de Deportes (Pk/45) Beaded Sports Figures (Pk/45) Figuras de Deportes (Pk/45) PLEASE READ ALL INSTRUCTIONS BEFORE

2011 Model Curriculum: PK-12 Social Studies American History Curriculum/Social... · 2011 Model Curriculum: PK-12 Social Studies ... The OSS RC reviewed this website, ... PK-12 Social

PK ˝.ˆˆˇ SLD ˇ | PK ˝.ˆˆˇ SLD | PK ˝. ˆˇ SLD HIGHER

PK 11.001 SLD 1 | PK 12.001 SLD 3 PK 11.001 SLD 3 | PK 12