All practice questions

A 55-year-old female patient is hospitalized for the management of severe pneumonia complicated by sepsis. Her current body weight is $80 \text{ kg}$. The medical team decides to initiate therapy with an intravenous antimicrobial agent. This medication has a volume of distribution ($V_d$) of $0.5 \text{ L/kg}$ and follows first-order elimination kinetics with a half-life ($t_{1/2}$) of $6.93 \text{ hours}$. The drug is prescribed to be administered intermittently as an intravenous infusion every $12 \text{ hours}$. To achieve optimal bactericidal activity, the target average steady-state plasma concentration ($C_{ss,avg}$) is $10 \text{ mg/L}$. Assuming $100\%$ bioavailability for the intravenous route, what maintenance dose should be administered every $12 \text{ hours}$?

A 75-year-old woman is evaluated in the hospital for acute kidney injury. She was admitted $5$ days ago for community-acquired pneumonia and has been treated with intravenous vancomycin and piperacillin-tazobactam. Her blood pressure is $122/76$ mm Hg, and heart rate is $82$/min. She appears euvolemic on physical examination. Today, her serum creatinine is noted to be significantly elevated compared to her baseline of $0.9$ mg/dL.

Laboratory studies today show:
Serum sodium: $140$ mEq/L
Blood urea nitrogen: $56$ mg/dL
Serum creatinine: $4.0$ mg/dL
Urine sodium: $63$ mEq/L
Urine creatinine: $60$ mg/dL

Urinalysis reveals muddy brown granular casts.

Based on the provided laboratory data, what is the patient's fractional excretion of sodium (FENa) as a percentage?

A $68$-year-old man presents to the clinic with progressive fatigue, lightheadedness, and reduced urine output over the past three days. His medical history is significant for ischemic cardiomyopathy and type 2 diabetes mellitus. His daily medications include aspirin, lisinopril, empagliflozin, and furosemide $40$ mg twice daily.

Vital signs:
Blood pressure: $92/60$ mmHg
Heart rate: $105$/min
Respiratory rate: $16$/min
Temperature: $36.8^{\circ}$ C ($98.2^{\circ}$ F)

Physical examination reveals dry mucous membranes, decreased skin turgor, and flat neck veins.

Laboratory results:

Because the patient is receiving active diuretic therapy, the fractional excretion of sodium (FENa) is considered unreliable for determining the etiology of his acute kidney injury.

What is this patient's fractional excretion of urea (expressed as a percentage)?

A $55$-year-old woman with a history of severe persistent asthma presents to the emergency department with progressively worsening shortness of breath and wheezing over the past $2$ days. She reports taking her prescribed oral theophylline inconsistently over the last week. On examination, she is in mild respiratory distress with diffuse bilateral expiratory wheezes. Her current serum theophylline concentration is measured at $4.0 \text{ mg/L}$. The physician orders an intravenous loading dose of aminophylline to rapidly achieve a target therapeutic theophylline concentration of $12.0 \text{ mg/L}$. The patient weighs $70 \text{ kg}$. The population volume of distribution for theophylline is $0.5 \text{ L/kg}$. Aminophylline is a water-soluble salt complex that contains $80\%$ theophylline by weight (salt factor $S = 0.8$). Assuming complete bioavailability for the intravenous route, what is the appropriate loading dose of intravenous aminophylline required to reach the target concentration?

A $45$-year-old man with a history of generalized tonic-clonic seizures is being managed in the neurology clinic with oral phenytoin. His seizure diary indicates incomplete control. His medication history and laboratory results show the following steady-state serum phenytoin concentrations based on his daily maintenance dose:

- At a dose of $300 \text{ mg/day}$, his steady-state concentration was $5 \text{ mg/L}$.
- His dose was then increased to $400 \text{ mg/day}$. After $4$ weeks of adherence, his steady-state concentration was $10 \text{ mg/L}$.

His seizures are less frequent but still occasionally occur, and he reports no symptoms of toxicity. The neurologist decides to target a steady-state serum concentration of $15 \text{ mg/L}$ to optimize efficacy. Phenytoin exhibits capacity-limited (Michaelis-Menten) elimination kinetics.

Assuming $100\%$ bioavailability and that no salt factor adjustments are needed ($S = 1.0$), what is the required new daily maintenance dose in $\text{mg/day}$ to achieve this exact target steady-state concentration?

A 62-year-old man is admitted to the pulmonary care unit for management of a severe, refractory asthma exacerbation. The medical team initiates a continuous intravenous infusion of an adjunctive bronchodilator at a rate of $40 \text{ mg/hr}$. The medication exhibits first-order elimination kinetics. For this specific patient, the drug has a volume of distribution ($V_d$) of $40 \text{ L}$ and an elimination half-life ($t_{1/2}$) of $6.93 \text{ hours}$ (note: $\ln(2) \approx 0.693$). To rapidly achieve therapeutic levels, the physician orders an initial intravenous loading dose designed to immediately establish the exact steady-state plasma concentration that the continuous infusion will eventually maintain.

What is the required loading dose of the medication in milligrams?

A 54-year-old man is maintained on an oral lipophilic beta-blocker for heart failure. The drug is eliminated exclusively via hepatic metabolism. It is completely absorbed across the gastrointestinal epithelium ($f_a = 1.0$) with no intestinal wall metabolism. Pharmacokinetic profiling reveals the drug has a baseline hepatic extraction ratio ($E_H$) of $0.80$. The patient's hepatic blood flow ($Q$) is estimated at $1,500 \text{ mL/min}$.

The patient is subsequently diagnosed with latent tuberculosis and started on rifampin, a potent cytochrome P450 inducer. This induction increases the beta-blocker's hepatic intrinsic clearance ($CL_{int}$) by exactly $50\%$. Assuming the well-stirred model of hepatic clearance and that hepatic blood flow remains constant, what is the patient's new absolute oral bioavailability of the beta-blocker? Express your answer as a percentage rounded to one decimal place.

A 65-year-old male with a history of symptomatic atrial fibrillation presents to the cardiology clinic to optimize his medical regimen. The physician decides to start an oral antiarrhythmic agent to maintain normal sinus rhythm. The selected drug has the following known pharmacokinetic parameters in this patient demographic:

* Volume of distribution ($V_d$): $40$ L
* Systemic clearance ($CL$): $2.5$ L/hr
* Oral bioavailability ($F$): $0.80$ ($80\%$)
* Half-life ($t_{1/2}$): $11.1$ hours

The target average steady-state plasma concentration ($C_{ss}$) for optimal efficacy without toxicity is $4.0$ mg/L. The physician plans to prescribe the medication to be taken orally every $12$ hours.

Based on these pharmacokinetic parameters, what is the appropriate single oral maintenance dose that should be administered every $12$ hours?

A $54$-year-old man is admitted to the intensive care unit with a severe bloodstream infection caused by *Pseudomonas aeruginosa*. He is to be started on an intravenous aminoglycoside. The patient weighs $80$ kg. His estimated volume of distribution for the drug is $0.25$ L/kg.

To ensure optimal bactericidal activity and minimize the risk of acute tubular necrosis, the clinical pharmacist recommends targeting a steady-state peak serum concentration of $8.0$ mg/L and a steady-state trough serum concentration of $2.0$ mg/L. Based on the patient's current renal function, the elimination half-life of the drug is determined to be $8$ hours.

Assuming the drug follows a one-compartment pharmacokinetic model and distributes instantaneously, what maintenance dose (in mg) must be administered at each dosing interval to achieve these exact steady-state target concentrations?

A 47-year-old woman is evaluated in the infectious disease clinic for treatment of a refractory systemic fungal infection following a recent hematopoietic stem cell transplant. She is currently taking tacrolimus and prophylactic acyclovir. The physician plans to start an oral formulation of a novel triazole antifungal agent. The patient's current body weight is $75 \text{ kg}$. According to the pharmacokinetic profile of this new medication, it has an oral bioavailability ($F$) of $50\%$, a volume of distribution ($V_d$) of $2.0 \text{ L/kg}$, and a systemic clearance ($Cl$) of $0.04 \text{ L/hr/kg}$. The therapeutic goal is to maintain an average steady-state plasma concentration ($C_{ss,avg}$) of $15 \text{ mg/L}$. The dosing regimen will consist of administration every 8 hours.

What is the required oral dose in milligrams ($\text{mg}$) to be given every 8 hours to achieve the target steady-state concentration?

An $80 \text{-kg}$, $60 \text{-year-old}$ male patient is undergoing treatment in the intensive care unit for severe hospital-acquired pneumonia. The clinical team initiates continuous intravenous therapy with a novel narrow-therapeutic-index antimicrobial agent. The pharmacokinetic profile of this drug in the patient indicates a volume of distribution of $0.5 \text{ L/kg}$ and a systemic clearance of $0.04 \text{ L/hr/kg}$. The desired steady-state plasma concentration of the medication is $20 \text{ mg/L}$.

To maintain this target steady-state concentration, what should be the continuous intravenous infusion rate in mg/hr?

A 62-year-old man with a history of alcohol use disorder and severe cirrhosis is admitted to the hospital with generalized weakness. His vital signs are within normal limits. Physical examination reveals temporal wasting, scleral icterus, and a distended abdomen with shifting dullness.

Laboratory studies show:

Based on these laboratory results, what is this patient's corrected serum calcium concentration in mg/dL?

A 19-year-old woman with a history of type 1 diabetes mellitus is brought to the emergency department by her roommate due to severe nausea, vomiting, and confusion for the past 24 hours. She has recently been suffering from a gastrointestinal viral illness and has not been taking her insulin because she was not eating. On physical examination, her mucous membranes are dry, and she is breathing rapidly and deeply.

Laboratory testing shows the following:

Based on these laboratory results, what is the patient's serum anion gap?

A $65$-year-old man is hospitalized for treatment of methicillin-resistant *Staphylococcus aureus* (MRSA) osteomyelitis. For the past week, he has been receiving a continuous intravenous infusion of a novel antimicrobial agent at a rate of $40$ mg/hr. His renal and hepatic functions have remained stable. Routine therapeutic drug monitoring reveals a steady-state plasma concentration of $8$ mg/L.

The patient is now clinically stable and is being prepared for discharge to complete a prolonged course of therapy. The infectious disease specialist recommends transitioning the patient to an oral formulation of the same medication. To ensure adequate bone penetration for the remainder of the therapy, the specialist also recommends targeting a higher average steady-state plasma concentration of $12$ mg/L.

The oral formulation of this medication has a known bioavailability of $60\%$ ($F = 0.60$). The planned dosing interval for the oral regimen is every $8$ hours.

Assuming the patient's pharmacokinetic parameters remain constant, what oral dose (in mg) should be administered every $8$ hours to achieve the new target concentration?

A healthcare system is evaluating a novel pharmacist-led medication reconciliation intervention to reduce 30-day hospital readmissions for patients with congestive heart failure. In a randomized controlled trial, the standard of care group had a 30-day readmission rate of 20%. The intervention group, which received the new pharmacist-led program, had a 30-day readmission rate of 15%.

Based on these trial results, what is the number needed to treat (NNT) to prevent exactly one additional hospital readmission?

An epidemiologist is reviewing surveillance data for tuberculosis in a specific municipality. On January 1, the municipality has a total population of $50,500$. At that time, $500$ individuals are already living with active tuberculosis. Over the next year, $100$ new cases of active tuberculosis are reported. Assuming a stable population with no migration or deaths, what is the incidence of active tuberculosis per $1,000$ at-risk individuals over this $1$-year period?

A regional health system enters into a Medicare Shared Savings Program (MSSP) Accountable Care Organization (ACO) agreement involving two-sided risk. The ACO has 20,000 attributed Medicare beneficiaries. The Centers for Medicare & Medicaid Services (CMS) establishes the ACO's annual benchmark expenditure at $12,000 per beneficiary.

To improve quality metrics and reduce unnecessary healthcare utilization, the health system implements a high-risk care coordination program led by specialized pharmacists and nurse practitioners. The total annual operational cost to run this new program is $2,500,000, which is funded directly by the health system out of its operating budget.

At the end of the performance year, the ACO's actual annual expenditure is calculated to be $11,700 per beneficiary.

The MSSP contract includes the following terms:
- Minimum Savings Rate (MSR): The ACO must generate savings of at least 1.5% of the total benchmark to be eligible for any shared savings. If the MSR is not met, the ACO receives no shared savings.
- Shared Savings Rate: If the MSR is met, the ACO retains 60% of the total savings generated below the benchmark.
- Quality Performance: The ACO achieved a quality score of 96%, fully qualifying them for the maximum 60% shared savings rate without any deductions.

Based on these results, what is the health system's net financial gain in dollars from this population health initiative for the performance year?