Phenytoin & Fosphenytoin Pharmacokinetic Dosing

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Phenytoin Dosing Calculators
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 Pharmacokinetic Dosing Information
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.

Phenytoin Dosing and Data Analysis Programs:
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): 4-8 mg/kg/day
     Children (1 to less than 12 years): 4-10 mg/kg/day
     Adolescents(12 - <18 years): 4-8 mg/kg/day
     Adults: 4-7 mg/kg/day
Loading Dose: Do not adjust the initial loading dose for protein binding when no drug is on board as the desired concentrations decrease proportionally to protein binding. BP and heart rate should be monitored during the loading dose. If drug is on board the current total level and desired level must be adjusted to equivalent levels for normal protein binding, see equation below).
     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_l/kg*Loading Dose Weight_kg* (Cp_mg/L desired Equivalent Normal Binding - Cp_mg/Lobserved Equivalent Normal Binding).
Therapeutic Levels: 10-20 mg/L (total free and bound phenytoin), 1-2 mg/L free
Serum Sampling Times and Recommended Monitoring: Peak: 2 hours after IV injection to allow for distribution of phenytoin and 4 hours after fosphenytoin to allow for distribution and hydrolysis of fosphenytoin. Four (4) hours after intramuscular administration of fosphenytoin. Twenty four hours after oral loading dose. Troughs are suggested for routine monitoring. Trough every 2-3 days during initiation of therapy, then weekly until stable levels are achieved, then monthly, then every 3-12 months. 
Empirical Dose Adjustments: assumes the patient is currently receiving at least 300 mg/day
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)
Hemodialysis: removes little phenytoin as the unbound volume of distribution is extremely large 6.5 L/kg.
Continuous Renal Replacement Therapy Removal_(mg) = (Effluent Flow_L/hr)* Hours of CRRT * Unbound Concentration_(mg/L)
Plasmapheresis or plasma exchange: 5-10% loss during plasmapheresis as most phenytoin (95%) is in the tissue compartment
Pharmacokinetic Model: one-compartment non-linear with capacity-limited metabolism (non-dose proportionality) 
Side effects: high infusion rate can cause bradycardia, hypotension, widened PR, QRS, or QT intervals. Nystagmus, ataxia, slurred speech, confusion, and coma may occur as levels increase.
Toxicity:
Common Drug interactions:
     Decreased absorption: antacids, cisplatin, tube feedings
     Decrease clearance:  enzyme inhibitors, amiodarone, chloramphenicol, cimetidine, disulfiram, fluconazole, fluoxetine, isoniazid,  phenylbutazone, sertraline, sulfonamides, ticlopidine, trimethoprim, voriconazole
     Increased clearance:  enzyme inducers, carbamazepine, ciprofloxacin, folic acid (reduced Km), rifampin
Protein binding displacement interactions: salicylates (>50mg/L), sulfonamides, valproic acid
Disease state or physiologic condition interactions:
     Decrease clearance:  cirrhosis
     Increase clearance: pregnancy

Dosage Calculations

Ideal Body Weight
IBW_(kg)  (Devine Formula) Adult Males (18 years and older) in kg: 50 kg + 2.3*(Height in inches greater than 60 inches)
IBW_(kg) (Devine Formula) Adult Female (18 years and older): 45.5 + 2.3*(Height in inches greater than 60 inches)

Adjusted Body Weight (kg) Used for Vd Calculation = IBW + 1.33* (Total Body Weight - 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_mg/L*(S*F*Dose_mg/Tau) / (Vmax_mg/hr - (S*F*Dose_mg/Tau))

Concentration Adjustment for Protein Binding:
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 (non-dialysis patient) = Cp measured / ([(0.9*(albumin patient/4.4)] +0.1)
     Concentration equivalent to normal protein binding (hemodialysis patient) = Cp measured / ([(0.9*0.48*(albumin patient/4.4)] +0.1)
     Concentration equivalent to normal protein binding with know total and free level pair = measured level*(free level/total level)/0.1
     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.

Time to Change In Serum Level During Consistent Dosing
Time to steady states is dependent on the rate of administration, Km and Vmax.
Time = (Vd/(Vmax-Rin))*(Km*Vmax/(Vmax-Rin)) *Ln[(Rin*Km - (Vmax-Rin)*Cp1) / (Rin*Km - (Vmax-Rin)* Cp2)]
Time to 90% of Steady State (hours) = (Km_mg/L*Vd_L/ [Vmax_mg/hr - S*F*(Dose_mg/Tau)]² ) * (2.3*Vmax_mg/hr - 0.9*S*F(dose_mg/Tau))

Time for level to decline (hours) = [(Km_mg/L*(Ln(C_1mg/L/C_2mg/L)) + (C_1mg/L-C_2mg/L)] / (Vmax_mg/hr/Vd_L), assumes drug has been stopped and not further absorption during the time interval. This equation is best used with IV dosing due to the prolonged time of oral absorption.

Determination of Pharmacokinetic Parameters
Mass Balance Calculation Can Be Use To Determine Vmax with Two Non-Steady State Levels With a Consistent Dosage Rate
     Amount of drug change in body/Time = Rate of administration - Rate of Metabolism    
    Amount of elimination_mg/hour =(S*F*Dose/Tau) - (((C_p2-C_p1)*Vd_L)/(Hours between C_p2 and C_p1))
    Vmax_mg/hr = [Amount eliminated_mg/hour from above *(Km + ((C_p1+C_p2) / 2 ))] / ((C_p1+C_p2) / 2), Km must be assumed
    Vmax_mg/hr = [ (S*F*Dose/Tau) - (((C_p2-C_p1)*Vd_L) / (Hours between C_p2 and C_p1)) * (Km + ((C_p1+C_p2) / 2 ))] / ((C_p1+C_p2) / 2), Km must be assumed
     Caveats for using the mass balance equation: The time between levels should be greater than or equal to 3 days. If levels are increasing C₂ should be < 2 x C₁. If levels are decreasing C₂ should be > 1/2* C₁.
Determining Vmax Using One Known Steady State Level
Vm_mg/hr = S*F*Dose_mg/Tau_hours * (Km_mg/L +Cpssavg_mg/L)/Cpssavg_mg/L , Km must be assumed
Km and Vmax determination Using Two Known Steady State Levels from Two Different Dosage Rates
     Km_mg/L= - (SFDose₁/Tau₁ - SFDose₂/Tau₂) / [(SFD₁/(Tau₁*Cpss₁)) - (SFD₂/(Tau₂*Cpss₂))]
     Vm_mg/hr = S*F*Dose_mg/Tau_hours * (Km_mg/L +Cpssavg_mg/L)/Cpssavg_mg/L, Dose can be either dose one or dose two with the corresponding Cpssavg


Explicit Solution to One-Compartment Pharmacokinetic Bolus Model with Michaelis-Menten Elimination using Lambert W-Omega Function

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