This page compares a continuous IV infusion of theophylline with both intermittent IV and PO dosing.

A patient requires a continuous IV infusion of theophylline to prevent bronchoconstriction. The desired plasma concentration is 15 mg/L. Theophylline has an average half-life of 4.3 hours (in a pediatric population) and volume of distribution of 25 liters. Calculate the appropriate maintenance dose to maintain a steady-state level of 15 mg/L.

First, you need to estimate clearance using Cl = 0.693 * Vd / t1/2 = 0.693 * 25 L / 4 hours = 4.3 L/hr. Now, it is easy to calculate the desired infusion rate: rate_in = [drug]ss * Cl = 15 mg/L * 4.3 L/hr = 64.5 mg/hr.

Below, we simulate the patient's plasma drug concentration over time. You should see that the limiting [drug] ~ 15 mg/L.

You probably can't wait the ~ 12 hours for the drug to accumulate in the patient's body and start to approach the steady state value; therefore, the patient will be given a single loading dose. Normally these are given over some short duration of time (e.g. 30 minutes). However, here, we are going to assume the loading dose is given instantaneously. Calculate the necessary loading dose to immediately reach a [drug] ~ 15 mg/L.

This is simple. Use "loading dose" = [drug] * Vd = 15 mg/L * 25 L = 375 mg. Change load to 375 in the below example. Note that this example uses all three of the fundamental equations we recommend you memorize.

Although you probably wouldn't really do this in reality, let us try and devise an intermittent dosing schedule where the patient is given IV bolus injections of the drug every few hours (we imagine that the infusion pump is broken and we must resort to intermittent IV injections). The therapeutic range for theophylline is 10 - 20 mg/L. We would like an average steady state value of 15 mg/L with peaks below 20 mg/L and troughs above 10 mg/L. We know that 64.5 mg/hr infusion provides a steady state of 15 mg/L. So, what if we just did injections of that amount every hour? This is simulated below.

You should have observed that after steady state is achieved, which takes almost a day, the patient starts to oscillate between ~ 13.7 and 16.2 mg/L, keeping them well within the therapeutic range. But, this is a demanding schedule for the staff, as they have a lot of patients, so we now want to see how much we can reduce the frequency of injections. Try simulating injection of 2*64.5 mg every 2 hours, or 3*64.5 mg every 3 hours, 4*64.5 mg every 4 hours, etc. - up to a dosing interval of 6 hours.

You should have observed that the largest dosing interval that can be tolerated without the patient "peaking" over 20 mg/L or dropping below 10 mg/L is about 4 hours (with doses of 258 mg). This becomes very important when we consider prescribing theophylline pills to be taken by mouth (PO) in an outpatient setting. If you ask an asthmatic child to take 3 x 500 mg pills per day (each every 8 hours), what will happen? Note that the oral bioavailability of theophylline pills is 100% (or 1.0). I also recommend changing the number of doses to eight to make things easier to visualize.

Ouch. Peaks are over 25 mg/L and troughs are close to 5 mg/L. This will not work. However, we aren't properly considering the effect of absorption. For that let's go to the next pharmacokinetic model: intermittent dosing with delayed absorption (Model 4).

Okay, still on the same patient, all the inputs to the model should be the same except now we can select an absorption half-life. An uncoated theophylline tablet is absorbed quickly with a half-life no longer than 15 minutes. This is simulated below with t12a = 0.25 hours. Although peaks are still over 20 mg/L and troughs are below 10 mg/L, they are blunted relative to the previous model that did not consider absorption kinetics.

Taking the pills with food slows down absorption even more, with half-lives between 0.5 and 1 hour, depending on fat content of the meal. Increase t12a and see the effect.

Lastly, extended/sustained release tablets are absorbed even slower, with effective half-lives of 2 - 4 hours. These are typically administered every 12 hours (twice per day). Shown below is 750 mg dosing twice per day with a four hour absorption half-life. Note that sustained-release and extended-release formulations are not always absorbed with linear/first-order kinetics (i.e. an exponential increase). Ideally, they would release a fixed amount per hour thereby approximating a continuous infusion. In reality, their absorption kinetics are probably more complex and show properties of both first-order and zero-order kinetics.