¨DataKinetics Equations
MDK, Inc.

NOTE:  These equations are not to be used in children, infants, or
       neonates.

General:

IBW = 50 Kg + (2.3 Kg x Inches over 5 ft) [Males]
IBW = 45.5 Kg + (2.3 Kg x Inches over 5 ft) [Females]

       (140 - Age) x IBW
CrCl = ------------------ [x 0.85 for females]
          72 x SCr



AMINOGLYCOSIDES (First order/one compartment equations):
VANCOMYCIN
LITHIUM

Assumptions:
  The equations assume that steady state has been achieved.
  If steady state has not been achieved, then a pre-dose
  C(min) should be used in place of the C(min-actual)
  in the Vd equation.

Definitions:
  Kel = elimination rate constant
  CrCl = creatinine clearance
  IBW = ideal body weight
  C1 = first concentration
  C2 = second concentration
  T1 = time of C1
  T2 = time of C2
  LD = loading dose
  C(desired) = desired level
  T(inf) = time of infusion or time to peak level
  Tau = dosing interval
  C(max) = maximum serum concentration
  C(min) = minimum serum concentration
  Cx = any given concentration
  Tx = time of Cx
  Vd = volume of distribution in liters
  MD = maintenance dose


Kel = 0.015 + (0.00285 x CrCl) [Gentamicin/Netilmicin]

Kel = 0.01 + (0.0031 x CrCl) [Tobramycin]

Kel = 0.01 + (0.0024 x CrCl) [Amikacin]

Kel = (0.65 x CrCl) x 0.06 / Vd [Vancomycin]


      ln C1 - ln C2
Kel = ---------------
         t2 - t1

     Vd x T(inf) x Kel x C(desired)
LD = ------------------------------
            -Kel x T(inf)
       1 - e

       1       C(max)
Tau = --- x ln ------ + T(inf)
      Kel      C(min)


                -Kel x Tau
MD = LD x (1 - e          )


                 [ln Cx + (Kel x Tx)]
C(max-actual) = e


                 [ln C(max-actual) - (Kel x (Tau - T(inf)))]
C(min-actual) = e


                 -Kel x T(inf)
      MD x (1 - e             )
Vd(l)=-----------------------------------------------------------------
                                                        -Kel x T(inf)
      Kel x T(inf) x [C(max-actual) - (C(min-actual) x e             )]


                                        -Kel x Tau
     C(max) x Kel x T(inf) x Vd x (1 - e          )
MD = ----------------------------------------------
                    -Kel x T(inf)
               1 - e



                    -Kel x T(inf)
         MD x (1 - e             )
C(max) = -------------------------
                                   -Kel x Tau
         Kel x T(inf) x Vd x (1 - e          )


          -Kel x (Tau - T(inf))
C(min) = e                      x C(max)



DIGOXIN:


Definitions:
  Cl = clearance
  CrCl = creatinine clearance
  MD = maintenance dose mg/day
  C(ss) = steady state level ng/ml
  TBS = total body stores in mcg/kg
  ABW = actual body weight
  F = adjustment for concurrent drugs


If no level is available:

Cl = [(1.104 x CrCl) + 28.9] x F


If level if available:

     MD x P                              Dosage Form            P Value
Cl = ------                              -----------            -------
     C(ss)                               Tablet (68% absorbed)   472
                                         Elixir (77% absorbed)   535
                                         Capsule (90% absorbed)  625
                                         IV (100% absorbed)      694

     C(ss) x Cl
MD = ----------
         P


        MD x P
C(ss) = ------
          Cl


LD = TBS x ABW


PHENYTOIN:

R = dose in mg/day
Css = steady state concentration

1 level -

Km = 4 mcg/ml

                   R
Vmax = R + Km * --------
                  Css

2 levels -

        R1 - R2
Km = -------------
      R2       R1
     ----  -  ----
     Css2     Css1


        Km * R2
Vmax = --------- + R2
         Css2


              Vmax * Css(desired)
(new dose)R = -------------------
              Km + Css(desired)


THEOPHYLLINE:

F = adjustment for concurrent drugs/conditions
B = percent theophylline in product

            (10 - C(current))
LD(mg/kg) = ---------------
                 1.6

Infusion rate (mg/kg/hr) = 0.5 * F


           Current Dose
New Dose = ------------- * C(desired)
           Current Level


Cl = BaseCl(adjusted to L/hr) * F

Dose = (Css * Cl * Tau * weight) / B

      Dose * B
Css = -----------------
      Cl * Tau * Weight


Adjust Therapy -

1 level -

                 Current Daily Dose * Css(desired)
New Daily Dose = ---------------------------------
                 Css(current)

2 levels - refer to first order/ one compartment equations.