Phenytoin Bayesian Dosing Calculator, Using the Lambert W Function to Explicitly Solve the Michaelis-Menten Equation, Downloadable Excel File. The spreadsheet contains a VB macro and requires the solver add-in to be available for the file to run. To install Solver in Excel do the following: Click File, Click Options, Click Add-ins, Manage Excel Add-in Click Go, Check Solver Add-in, and select OK. Then save the file.

Phenytoin Dosing Calculator, The spreadsheet contains several tabs which are used for specific dosing scenarios described on each tab using the methods discussed in Winter's Basic Clinical Pharmacokinetic, Downloadable Excel File

Phenytoin pharmacokinetics are non-linear, hard to conceptualize, and calculate due to capacity-limited metabolism. The following spreadsheets were developed to help simplify calculations. The first downloaded Excel spreadsheet is more flexible; and is easier to use and understand. It uses equations that explicitly solve bolus dosing elimination for Michaelis-Menten pharmacokinetics for a one-compartment open model. It allows for population and Bayesian dosing with data fitting of peak and trough levels using Excel's solver. The first tab is for a set dose and interval and troughs only. The second tab is for any type of dosing history and levels. The second downloadable Excel spreadsheet contains several tabs for population-based dosing, dosing after one steady state serum level, dosing after two steady state serum levels, dosing after two non-steady state serum levels for a consistent regiment, and dosing with two post-dose levels once absorption is complete. The spreadsheets incorporate adjustments for protein binding changes due to low albumin, hemodialysis and measured free levels. Please review the information below before using the spreadsheets. Hopefully your understanding of phenytoin pharmacokinetics will improve.

The most recent spreadsheet (8/2023) contains a VB macro and requires the solver add-in to be available for the file to run. To install Solver in Excel do the following: Click File, Click Options, Click Add-ins, Manage Excel Add-in Click Go, Check Solver Add-in, and select OK. Then save the file. The first tab on the spreadsheet is for a fixed dose and frequency with data fitting of troughs only. The second tab on the spreadsheet is more flexible allowing for varying doses and dosing intervals and fitting of peaks and troughs. Phenytoin Population and Bayesian Dosing Calculator With Peak and Trough Data Fitting

The second spreadsheet contains several tabs that are used for specific dosing scenarios described on each tab using the methods discussed in Winter's Basic Clinical Pharmacokinetics Phenytoin Dosing Calculator (File updated 2/15/2023). If you have questions or suggestions concerning the dosing tools please contact Marshall Pierce PharmD.

**Usage:** Tonic-clonic and complex partial seizures, seizure
prophylaxis after neurosurgery. Brain and CSF levels are similar to unbound
plasma levels.

**Oral Bioavailability (F):**
100% (F=1), slow-release formulations 100% (F=1).

**IV fraction (F):**
1

**Salt:** phenytoin sodium/fosphenytoin 92% (S=0.92),
Phenytoin acid as suspension and
chewable tablet (S=1)**Route of Administration:** Phenytoin
IV/Oral, Fosphenytoin IV/IM **Rate of Administration: ** Phenytoin IV maximum 50
mg/min in adults, 0.5 mg/kg/min neonates, 1 mg/kg/min for pediatric and
adolescents and adults; Fosphenytoin IV 150 mg PE/min
in adults, 3 mg PE/kg/min children and adolescents

**Peak concentrations:
2 hours after **IV at end of infusion, 4 hours after Fosphenytoin IM injection, oral non-extended release several
hours after dose, phenytoin extended-release time to peak is dose-dependent, 400
mg 8.4 hours, 800 mg 13.2 hours, 1600 mg 31.5 hours, oral loading
doses of extended-release 24-30 hours post-dose.**Protein binding: **90%
bound to albumin, fraction unbound 0.1, alterations in in plasma binding require an
adjustment of plasma concentrations for the change in bound concentration as assays measure total
concentrations (bound + unbound). Hypoalbuminemia and end-stage renal failure
affect plasma protein binding. **Metabolism:**
Capacity-limited hepatic metabolism, 90% CYP2C9, 10% CYP2C19, less than 5% is excreted renally.
90% of people are genetically classified as normal/extensive metabolizers of
phenytoin, 10% of people are CYP2C9 heterozygous or intermediate metabolizers,
and 1% are homozygous CYP2C9 or poor metabolizers.**Genetics:
**HLA-B15:02 gene carries has a higher risk of toxic epidermal necrolysis
and Stevens-Johnson syndrome

**Vd (L/kg): **

Neonates and infants (< 1year):
1 L/kg

Children and adults:

Normal 0.65
L/kg of ideal body weight (kg)

Obese
0.65 * (Ideal body weight + 1.33*(Total body weight - Ideal body weight))

**Vmax (mg/hour):** Maximum rate of metabolism, should be based on
ideal weight if total weight is greater. If the rate of intake is greater than Vm levels continually increase. Vmax will increase with enzyme inducers (carbamazepine,
phenobarbital) and levels will
decrease. Vmax will decrease in liver disease (cirrhosis) and levels will increase.
Typical values are for normal/extensive metabolizers. **Km (mg/L):**
Km is a dissociation constant and its reciprocal is the expression of binding
affinity. Km increases as affinity decreases. Km is the plasma concentration at which metabolism is half the maximum rate.
Km is increased by competitive inhibitors (e.g. cimetidine, valproic acid,
fluoxetine) and phenytoin levels will increase. Km is decreased by decreased
protein binding (lower serum albumin) and displacement from
plasma proteins (valproic acid, salicylate, sulfisoxazole) and total phenytoin serum levels will decrease.
Km is calculated based on total plasma phenytoin concentrations

**Cl (L/hour): ** Vmax / (Km + Cp), decreases with increasing
serum concentrations

**K (1/hours):** (Vmax/(Km + Cp))/Vd, decreases with increasing
concentrations

**Half-life (hours): ** 0.693/K, as concentration increases half-life
increases.

Dosage Forms:
injection, tablets, capsules, suspension**Usual Interval: ** every 6, 8,
12, 24 hours,

**Usual Oral Dose Maintenance Therapy:** use ideal body weight to calculate
the
dose in the obese, usually in divided doses
unless oral extended-release is administered. **Normal/extensive metabolizers
receive the full dose, intermediate metabolizers receive 75% and poor receive
50% of the normal dose.**

Neonates (< 4 weeks):**
** 3-5 mg/kg/day** **Infants(4 weeks -
<1year):

Neonates (< 1 year) IV 15-20 mg/kg in divided doses every 2 hours, oral give 5 mg/kg every 2 hours until total load administered

Children (1 - <12 years) IV 15-18 mg/kg in divided doses every 2 hours, oral give 5 mg/kg every 2 hours until total load administered

Adolescents and Adults IV 15-18 mg/kg IV given in divided doses every two hours, oral give 5 mg/kg every 2 hours until total load administered

Intravenous Supplement for suboptimal level (mg): 0.65

Serum Sampling Times and Recommended Monitoring:

Serum level < 7 mg/L increase by 100 mg/day (a more conservative approach is 50-75 mg/day)

Serum level 7-12 mg/L increase by 50 mg/day (a more conservative approach is 30-50 mg/day)

Serum level > 12 mg/L increase by 30 mg/day (30 mg/day)

**Dosage Calculations **

IBW

IBW

**Dosing Weight**_{(kg)}** =**

**Vd **- Use Adjusted Body Weight if total body weight is larger
than IBW

**Vmax** - Use IBW if total body weight is
larger than IBW

**Clearance(L/hr) = **Vmax_{mg/hr} / ( Km_{mg/L}+ Cssavg_{mg/L}), Clearance decreases
with increasing concentrations

**Volume of Distribution(L)**

Vd(liters) = 0.65 * Ideal Body Weight (kg)

Obese = 0.65*(Ideal Body Weight + 1.33 (Actual
Body Weight - Ideal Body Weight))**K(1/hours) = Clearance / Vd = (Vm/(Km
+ Cp))/Vd = Vm/((Km +Cp)*Vd)**

T1/2 = 0.693*Vd_{L}* (Km_{mg/L}+Cp_{mg/L})/Vm_{mg/hr} ,
increases with increasing levels

**Maintenance Dose**_{(mg) } =
(Vmax_{mg/hr}*Cssavg_{mg/L}*Tau) / (S*F* (Km_{mg/L}+Cpssavg_{mg/L}))

**Cpaverage _{(mg/L)}**
= Km

Protein binding is altered by hypoalbuminemia, renal failure and displacement by other medications.

Adjustments are required in conditions with decreased albumin: burns, hepatic cirrhosis, nephritic syndrome, pregnancy, cystic fibrosis, and in conditions with decreased affinity for albumin: renal failure, severe jaundice, and drug displacement interactions. When Creatinine clearance is above 25 ml/min no adjustments are required for renal dysfunction. Patients with creatinine clearance 10-25 ml/min have unpredicted binding and a free & total pair are recommended.

Concentration equivalent to normal protein binding (concurrent Valproic Acid Cp >20 mg/L) = (0.095 + 0.001*Valproic Acid Cp)*(phenytoin Cp)/0.1, drawn both levels at the same time.

T

Time to steady states is dependent on the rate of administration, Km and Vmax.

Amount of drug change in body/Time = Rate of administration - Rate of Metabolism

Amount of elimination

Vmax

Caveats for using the mass balance equation: The time between levels should be greater than or equal to 3 days. If levels are increasing C

Vm

Km

Vm

Lambert W-Omega Function

W(x) = 1.4586887 * ln ((1.2*x)/ln(2.4*x/ln(1+2.4*x)))
- 0.4586887 * ln (2*x/ln(1+2*x))

For a single bolus dose or declining levels future level
may be calculated using the following equations

C(t) = Km * W(x)

C(t) = Km * W[Co/Km *exp((Co-Vmax/Vd*t)/Km)] where Co in the starting concentration and t is the time of level post concentration. If a bolus is given at time zero Co =Dose/Vd, The value of the expression in the brackets,[ ], is x to be placed in the Lambert W-Omega Function or first equation. The result is W(x) which is replaced in the second equation. The third equation shows the complete expression. Simple but confusing.

**Steady State Levels for a period dose at a set
interval**

Z = Dose/(Vd*(1-exp((Dose-Vmax*Tau)/(Km*Vd))))

Cssmin = Km * W[Z/Km *exp ((Z-(Vmax/Vd)*Tau)/Km)]

Cssmax = Km*W[Z/Km*exp((Z-(Vmax/Vd)*Tau)/Km)] + Dose/Vd

The value of the expression in the brackets, [ ], is x to be placed in the lambert W-Omega function. The result of W(x) is placed in the Cssmin and Cssmax equations.

Suggested Readings for Lambert W-Omega Function

Golicnik M. Exact and Approximate Solutions for the decades old Michaelis-Menten Equation: Progress-curve Analysis Through Integrated Rate Equations. Biochemistry and Molecular Biology Education 2011; 39:117-125

Golicnik Marko Explicit reformulations of the Lambert W-Omega function for calculations of the solutions to one-compartment pharmacokineti model with Michaelis-Menten elimination kinetics. Eur J Drug Metab Pharmacokinet 2011;36:121-127

Tang S Xiao Y. One-compartment model with Michaelis-Menten elimination kinetics and therapeutic window: an analytical approach. J Pharmacokinet Pharmacodyn. 2007;34;807-827

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