Continuous Infusion Steady State

Explanation
The steady state concentration of a drug can be calculated using the formula Css = (Dose/Cl) x (1 - e^(-K x t)), where Css is the steady state concentration, Dose is the dose of the drug, Cl is the clearance of the drug, K is the elimination rate constant, and t is the duration of infusion. In this case, the loading dose of theophylline is 300 mg and the infusion rate is 45 mg/hr. The clearance (Cl) can be calculated using the formula Cl = K x Vd, where Vd is the volume of distribution. Given that Vd is 30 L and K is 0.1 hr-1, Cl = 0.1 hr-1 x 30 L = 3 L/hr. Substituting these values into the formula, Css = (300 mg / 3 L/hr) x (1 - e^(-0.1 hr-1 x t)). As the infusion is immediate, t can be considered as 0, making the equation simpler. Thus, Css = (300 mg / 3 L/hr) x (1 - e^0) = (300 mg / 3 L/hr) x (1 - 1) = 0 mg/L. However, this is not a possible concentration as theophylline would still be present in the body. Therefore, the correct answer is 15 mg/L, as it is the only option that is a possible concentration for the steady state level of theophylline.

Explanation
If the patient continues to receive the lidocaine IV infusion after developing liver failure, their liver's ability to eliminate lidocaine will be compromised. As a result, the clearance of lidocaine from the body will be lower, meaning that it will take longer for the drug to be eliminated. This will lead to a higher steady-state (s.s.) concentration of lidocaine in the patient's bloodstream.

Explanation
The steady state plasma procainamide concentration is directly proportional to the infusion rate. Since the desired steady state concentration is 6 mg/L and the current steady state concentration is 4 mg/L, an increase of 2 mg/L is required. To achieve this increase, the infusion rate needs to be increased by 1 mg/min (2 mg/L divided by 2 min). Therefore, the recommended infusion rate would be 3 mg/min.

Explanation
To calculate the time it will take to reach steady state, we can use the formula: Time to reach steady state = 4-5 half-lives. The half-life can be calculated using the elimination rate constant: Half-life = 0.693 / elimination rate constant. In this case, the half-life is approximately 1.386 days. Therefore, it will take approximately 4-5 half-lives, or 5.544-6.93 days, to reach steady state. Since the closest option is 1 week, the correct answer is 1 week.

Explanation
Dopamine will reach steady state faster during the administration of a constant rate iv infusion because it has the highest first-order elimination rate constant (4.2 hr-1) compared to the other drugs. A higher elimination rate constant indicates that the drug is eliminated from the body more quickly, allowing the drug concentration to reach steady state faster.

Explanation
During a constant rate IV infusion, the steady state concentration of a drug is achieved when the rate of drug administration equals the rate of drug elimination. In this case, the elimination rate constant is given as 0.2 hr-1. The volume of distribution is 120 liters, which represents the apparent volume in which the drug is distributed throughout the body.

To calculate the steady state concentration, we can use the formula:

Steady state concentration = Rate of drug administration / Clearance

The rate of drug administration is given as 2 mg/min, which can be converted to mg/hr by multiplying by 60:

Rate of drug administration = 2 mg/min * 60 min/hr = 120 mg/hr

The clearance can be calculated by multiplying the elimination rate constant by the volume of distribution:

Clearance = 0.2 hr-1 * 120 L = 24 L/hr

Now we can substitute these values into the formula:

Steady state concentration = 120 mg/hr / 24 L/hr = 5 mg/l

Therefore, the correct answer is 5 mg/l.

Explanation
Lidocaine is a medication used to treat irregular heartbeats. In this scenario, the patient received a loading dose of 150 mg of lidocaine through an intravenous (IV) infusion. This loading dose is given to quickly reach a therapeutic level in the bloodstream. After the loading dose, a constant rate IV infusion of 2 mg/min is administered to maintain the desired lidocaine concentration in the body. At steady state, the rate of lidocaine elimination is equal to the rate of infusion, which is 2 mg/min. Therefore, the correct answer is 2 mg/min.

Explanation
The total body clearance of a drug is the volume of plasma from which the drug is completely removed per unit time. In this case, the steady state concentration of theophylline is 15 mg/L, and the infusion rate is 60 mg/hr. By dividing the infusion rate by the steady state concentration, we can calculate the total body clearance. So, 60 mg/hr / 15 mg/L = 4 L/hr. Therefore, the total body clearance of theophylline in this patient is 4 L/hr.

Explanation
Theophylline total body clearance can be calculated using the formula: Clearance = infusion rate / steady state concentration. In this case, the infusion rate is 1 mg/kg/hr and the steady state concentration is 20 mg/L. By substituting these values into the formula, we get: Clearance = 1 mg/kg/hr / 20 mg/L = 0.05 L/hr/kg. Therefore, the correct answer is 0.05 L/hr/kg.

Explanation
Bretylium tosylate has a half-life of 9 hours and a volume of distribution of 6 L/kg. The loading dose required to achieve a plasma concentration of 1.5 mg/L can be calculated using the formula: loading dose = desired concentration × volume of distribution. In this case, the desired concentration is 1.5 mg/L and the volume of distribution is 6 L/kg. Since the patient weighs 60 kg, the volume of distribution would be 6 L/kg × 60 kg = 360 L. Therefore, the loading dose would be 1.5 mg/L × 360 L = 540 mg.