The Most Equations use for Therapeutic Drugs Monitoring : - TDM of Aminoglycoside - TDM of Vancomycine - TDM of Valproic Acid - TDM of Carbamazepine - TDM of Digoxin

1. Equations of TDM
units converter
1 pound = 0.453 kg
1 inch = 2.54 centimeters
1 foot = 30.48 centimeters
Plasma concentration
Zero Order eq . Frist Order eq .
Log A =
-kt
+ log A
2.3
Half Life =
0.693
k
A = Ao - Ko t
Half life = 0.5 . Ao
Ko
Extraction
E= Cin-Cout
Cin
CrCl =
Ucr . Vcr
Scr
Cockeroft / Gulft eq .
CrCl (male)(ml/min)=
(140 - age ) (w)
(72)(Scr)
CrCl (famale)(ml/min)= CrCl × 0.85
MDRD :
GFR ( ml / min / 1.73
m2
) = 186 × (Scr)
-1.159
× age
-0.203
K =
clT
ClT = Vd . K
Vd
Cp = Cpoe-kt
Jallffe :
CrCl (male)
(ml/min/1.73
m2
BSA)=
98-[0.8(age-20)]
Scr
BSA =
√ht×wt
3600
Ideal Body Weight (male)(kg)=50+[0.9(H-152)]
Ideal Body Weight (famale)(kg)=45.5+[0.9(H-152)]
bwadj =IBW+0.4(ABW-IBW)
Unstable Renal Function :
CrCl(male) = [(293-2.03(age))]×[1.035-0.01685(Scr+Scr2)]+[49(Scr1-Scr2)]
Salazar Eq :
CrCl(male) (ml/dl) =
(137-age)×[(0.285×w)+(12.1×H
2
)]
51×Scr
Salazar Eq :
CrCl(fmale) (ml/dl) =
(146-age)×[(0.287×w)+(9.74×H
2
)]
60×Scr
CrCl(famale) = CrCl(male) × 0.86
CrCl (ml/min) = CrCl . BSA
1.73
Prepared by : Mohammad Matouq Alghamdi

2. TDM of Aminoglycoside
1. Estimate Creatinine Clearance :
CrClest(ml/min) = [(140 - age ) BW]*0.85 .... ml/min
72×Scr
CrClest(ml/min) = [(140 - age ) BW] .... ml/min
72×Scr
(famale)
(male)
2. Estimate elemination rate constant :
3. Estimate Volume of Distribution :
VD= 0.26 L/kg
VD=0.26[IBM+0.4(TBW-IBW) ..... L/kg in Obese
VD=0.35 ..... L/kg in cystic
VD=(0.26×DBW)+(TBW-DBW) in liver cirrhosis
4.Choose desired stedy state serum concentrations
Css max | Cssmin ug/ml
5. Dosing interval :
interval is rounded to :
6 , 8 , 12 , 18 , 24 , 36 , 48 , 72
mg
mg Computing loding dose if more than 10%
of maintenance dose :
MD
100
LD
T=
[(InCssmax-InCssmin)] + t’ ..... hr
ke
6. Computing maintenance dose :
LD = Ko / ( 1- e
-keT
)
Ko=Cssmax.ke.V[(1-e-kT’
)
]1-e-kt’
Ke = 0.00293(CrCl)+0.014 ..... h-1
t1/2 = 0.693 .... h
ke
In papulation
w
τ
τ
τ
Prepared by : Mohammad Matouq Alghamdi

3. TDM of Aminoglycoside
1. Estimate Creatinine Clearance :
CrClest(ml/min) = [(140 - age ) BW]*0.85 .... ml/min
72×Scr(famale)
(male)
CrClest(ml/min) = [(140 - age ) BW] ..... ml/min
72×Scr
2. Estimate elemination rate constant :
3. Estimate Volume of Distribution :
VD=
D
× 1-e
-kt’
t’ ke [ Cssmax ( Cssmin × e-ket’
)]
4.Choose desired stedy state serum concentrations
Css max | Cssmin ug/ml
5. Dosing interval :
T=
[(InCssmax-InCssmin)] + t’ ..... hr
ke
LD = Ko / ( 1- e
-keT
)
6. Computing loading dose (LD) :
Ko=Cssmax.ke.V[(1-e-kt
)
]1-e-kt
Ke =
(InCssmax-InCssmin)
..... h-1
T-t’
t1/2 = 0.693 .... h
Ke
In individual
τ
τ
τ
τ
Prepared by : Mohammad Matouq Alghamdi

4. TDM of Vancomycine
1. Estimate Creatinine Clearance :
CrClest(ml/min) = [(140 - age ) BW]*0.85 .... ml/min
72×Scr(famale)
(male)
CrClest(ml/min) = [(140 - age ) BW] ..... ml/min
72×Scr
4. Estimate elemination rate constant :
3. Estimate Volume of Distribution :
VD= 0.7 .... L/kg
4.Choose desired stedy state serum concentrations
Css max | Cssmin ug/ml
5. Dosing interval :
interval is rounded to :
6 , 8 , 12 , 18 , 24 , 36 , 48 , 72
if CrCl < 60
T=
[(InCssmax-InCssmin)]
..... hr
ke
7. Computing loading dose (LD) :
6. Required dose (D) :
D=Cssmax*V(1-e-keT) .... mg
Ko=Cssmax.V
Ke = Cl / V ( Result*0.06) .... hr
-1
t1/2 = 0.693/ke ... h
2. Estimate clearance of Vancomycine :
Cl = 0.695 ( CrCl / TBW ) + 0.05 ..... ml/min/kg
In papulation
τ
τ
Prepared by : Mohammad Matouq Alghamdi

5. TDM of Vancomycine
1. Estimate Creatinine Clearance :
CrClest(ml/min) = [(140 - age ) BW]*0.85 .... ml/min
72×Scr(famale)
(male)
CrClest(ml/min) = [(140 - age ) BW] ..... ml/min
72×Scr
2. Estimate elemination rate constant :
3. Estimate Volume of Distribution :
VD= D
Cssmax - Cssmin
4.Choose desired stedy state serum concentrations
Css max | Cssmin ug/ml
5. Dosing interval :
T=
[(InCssmax-InCssmin)]
..... hr
ke
7. Computing loading dose (LD) :
6. Required dose (D) :
D=Cssmax*V(1-e-keT
) .... mg
Ko=Cssmax.V
Ke =
(InCssmax-InCssmin)
..... h-1
T-t’
t1/2 = 0.693 .... h
Ke
In indevidual
mg
L
τ
τ
Prepared by : Mohammad Matouq Alghamdi

6. Valproic Acid
Age Condition Rang
Adult 7-12 ml/h/kg
Chlidren without drugs induce enzym 10 - 20 ml/h/kg
Chlidren with drugs induce enzym 20-30 ml/h/kg
Liver Cirrosis & Acute hepatits 3 - 4 ml/h/kg
in adult in children ( under 12 y )
Vd = Weight × 0.15 .... L Vd=Weight × 0.2 ...L
1. Estimate Clerance - Rate of Clearce ......... ml / h
2. Volume of Distrbution
3. t2
/1
& Ke
t2
/1
= ..... H
4. Compute dose regmint :
D= Css × Cl × τ
F
5. Loading dose in I.V :
LD = Css × V ... mg
• Literature - Based recomended dose :
D= Wight × Rang of dose according to age .... mg
• Seudoliner PK method :
Dnew=
Css new
× D old ... mg
Css old
• PK parametar :
Cl=
F( D )
.... L/hr
τ
Css old
0.693×V
Cl
0.693
t2
/1
Ke= .... hr-1
In oral Dose F = 1
In Oral sustaind relase F=0.9
if Dose increase Css change %10 - 20 :
(Css = Css new × 0.9) ( Css=Cssnew×0.8)
if Dose Decrease Css change %10 - 20 :
(Css = Css new × 1.1) ( Css=Cssnew×1.2)
For pediatric 10 mg/kg/day
For pediatric ( Take enzyme inducer ) 20 mg/kg/day
For adult 7.5mg/kg/day
For adult ( Take enzyme inducer ) 15mg/kg/day
Prepared by : Mohammad Matouq Alghamdi

7. Carbamazepine
1. Estimate Carbamazepine dose according to disease state and condotion in patient :
• to compute Css new
Css new=
D new
× Css old ... mg
D old
Conditions Dose
Children under 6 years old 10 - 20 mg/kg/dose
Children 6 - 12 years old 200 mg /day
Adult 400 mg /day
Prepared by : Mohammad Matouq Alghamdi

8. Digoxin
1. Estimate creatinine clearance :
• If not obese  use Cockcroft - Gault equation
• If obese  use Salazar & Corcoran
2. Estimate clearance
Cl = 1.303 ( CrCl ) ClNR
• ClNR = 40 mL/min since the patient has to mild heart failure
• ClNR = 20 mL/min since the patient has to sever heart failure
3. Use average Css equation to compute digoxin (MD) :
D/τ =
Css × Cl .... ug/d
F
•Note: the result must × by factor 1.44
4. Compute ( LD ) if needed :
• Compute V :
(in patient with renal dysfunction (Cl =< 30 mL/min ) :
V= [ 226 + ( )×( )] ... L
(in patient ( Cl > 30 mL/min ) :
V = 7 × kg .. L
•LD =
( Css × V )
... ug
F
298×CrCl wt
29.1 +CrCl 70
Prepared by : Mohammad Matouq Alghamdi
mmoa92@gmail.com