Chapter 7: Mutiple Dose Regiment

Ex 4

Mr. J.M., a nonsmoking 60 kg patient with chronic obstructive pulmonary disease, is to be started on an oral regmen of aminophylline (85%of which is theophylline). The pharmacokinetics parameter values for a typical patient population with this discasc are:
* F = 1.0 (for theophylline)
* V = 0.5 L/kg
* CL = 40 Ml/hr/kg
Design an oral dosage regimen of arninophylline (100 and 200-mg tablets are marketed) for this patient to attain and maintain a plasma concentration within the therapeutic window, 10 to 20 mg/L. The absorption of theopllylline is complete and rapid.

Summary

options(digits = 0)
weight <- 60 # kg
F <- 1.0 # for theophelline
V <- 0.5 # L/kg
CL <- 40/1000 # L/hr/kg
Cmax <- 20 # mg/L
Cmin <- 10 # mg/L

Answer

Estimating t_1/2 using the equation, \[ t_{1/2} = \frac{ln2 * V}{CL}\]

ex4_t_hf <- (log(2) * V)/CL
ex4_t_hf

## [1] 9

ex4_k <- log(2)/ex4_t_hf

Calculate T_max using t_1/2 base on equation \[ T_{max} = \frac{ln(\frac{C_{max}}{C_{min}})}{k}\]

ex4_Tmax <- log(Cmax/Cmin)/ex4_k
ex4_Tmax

## [1] 9

Maximum of matainance dose was calculate using the equation \[D_{M, max} = \frac{V}{F}(C_{max} - C_{min})\]

ex4_Dm <- V/F * (Cmax - Cmin) * weight
ex4_Dm

## [1] 300

With weight of patient is 60 kg, so D_{M, max} is 300 mg of theopllylline

and dosing rate is \[DosingRate = \frac{D_{M,max}}{T_{max}}\]

ex4_dosing_rate <- ex4_Dm / ex4_Tmax
ex4_dosing_rate

## [1] 35

Then, calculating the C_ss,Max, C_ss,Min using these equations \[C_{max,ss} = \frac{F * D}{V*(1 - e^{-kt})}\] \[C_{min, ss} = C_{max,ss} * e^{-kt}\]

Here is the data frame demonstrate the resutls.

# Create data frame with interval time from 4 hr to 24hr
interval <- seq(4, 24, 1)

# number of tablets from 1 to 5 tablets each time
number_tablets <- rep(c(1:5), each = length(interval)*2)

# aminophylline marketed 100 and 200 mg
aminophylline_tablets <- rep(c(100, 200), length(interval) * 5)

# create data frame interval time and estimated doses
interval_time <- rep(interval, 5, each = 2)
ex4_dat <- data.frame(tablets = aminophylline_tablets, interval = interval_time, number = number_tablets)

# actual dose of theopllylline_dose = 85% of aminophylline
# Css_max, and Css_min were calcualted using 85% of estimated_aminophylline_doses

ex4_dat <- ex4_dat %>% mutate(theopllylline_dose = tablets * number * 85/100,
    Css_max = theopllylline_dose / (V * weight * (1 - exp(-ex4_k*interval))),
                   Css_min = Css_max * exp(-ex4_k*interval))

# add stastus of each dose and interval time

ex4_dat <- ex4_dat %>% mutate(status = ifelse(Css_max <= 20 & Css_min >= 9, "consider", "not ok"),
                              loading_dose = V * weight * Css_max / F)

# plot the results
ex4_dat %>% ggplot(aes(x = Css_min, y = Css_max, color = status)) +
    geom_hline(yintercept = 20, lty = 2, color = "darkgrey") +
    geom_vline(xintercept = 10, lty = 2, color = "darkgrey") +
    geom_point()

# chose interval == 8
ex4_dat %>% filter(status == "consider" & interval == 8)

Chapter 7: Mutiple Dose Regiment

Nguyen Van Lam