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2. In one compartment model with bolus dose in PK model, derive equation for concentration (C),...

2. In one compartment model with bolus dose in PK model, derive equation for concentration (C), half-life (t1/2), and clearance (ke) from mass-balance equation.

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Answer #1

one compartment model with bolus dose in PK model is first order reaction

ke = elimination rate constant

Mass balance equation

Initial rate of dose available in body - rate of dose out = rate of change of dose with time

0 - ke*X = dX/dt

dX/dt = - ke*X

Relation between dose amount (X) and concentration of plasma (C)

X = C*V

V = Apparent volume of distribution

dX/dt = - ke*X

d(C*V) /dt = - ke*(C*V)

dC/dt = - ke*C

dC/C = - ke*dt

Integrate the equation

Initial concentration (at time t = 0) = Co

Final concentration (at time t = t) = C

ln (C/Co) = - ke*t

Half life (t1/2) is when the final concentration C = Co/2

ln [C/(C/2)] = - ke*t1/2

ln 2 = - ke*t1/2

t1/2 = - 0.6932 / ke

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