1 Introduction

When treating critically ill patients, it is important that the efficacy of administered drugs is obtained as rapidly as possible. Notably, approximately 50 % of intensive care unit (ICU) patients have been shown to be affected by catheter-associated bloodstream, ventilator-associated pneumonia, and surgical site infections as well as others, with subsequent increased mortality (Vincent et al. 2009). Therefore, it is essential for antimicrobials given at the initial phase of therapy to be efficacious. However, pathophysiologic changes such as capillary leakage, hypoalbuminemia, and pleural effusion, as well as other factors can occur in critically ill patients, leading to changes in the pharmacokinetics of administered antimicrobials. Previous reports have shown that the volume of distribution (Vd) of hydrophilic antimicrobials tended to increase (Roberts and Lipman 2006; Petrosillo et al. 2010; Varghese et al. 2011), while antimicrobial concentrations in plasma and tissue did not reach an effective level in critically ill patients with an infection (Joukhadar et al. 2001; Taccone et al. 2010a, b). Moreover, the starting doses for water-soluble antimicrobials have been found to be insufficient, which adversely affects the prognosis of these patients (Kollef et al. 1999; Ibrahim et al. 2000; Kumar et al. 2006). Therefore, it is important that an appropriate initial dose for antimicrobial therapy be set for critically ill patients suffering from infection.

Vancomycin hydrochloride, classified as a glycopeptide and water-soluble antibiotic, is recommended as first-line therapy for a methicillin-resistant Staphylococcus aureus (MRSA) infection. The only established criterion for setting the initial dose in critically ill patients is based on actual body weight (ABW) (Liu et al. 2011). However, it is thought that the Vd of vancomycin varies among individuals because of body fluid retention and other conditions. We considered that a more appropriate initial dose could be established by estimating the Vd of vancomycin for individual patients.

In the present study, we utilized the Acute Physiology and Chronic Health Evaluation (APACHE) II scoring system (Knaus et al. 1985), a classification method used to determine disease severity in the ICU for prediction of Vd. APACHE II scores are determined from physiological variables including body temperature, blood pressure, heart rate, respiratory rate, and white blood cell count, as well as information about previous health status and other data obtained at admission such as age, organ dysfunction, and immunodeficiency. We speculated that the obtained score reflects body fluid retention induced by systemic inflammatory response syndrome (SIRS) and organ dysfunction, and attempted to predict Vd and the elimination half-life (t 1/2) of vancomycin using APACHE II scores.

In this study, we attempted to establish a theoretical methodology by which the initial dose and administration interval of vancomycin could be established based on APACHE II score for providing an adequate antimicrobial effect from the first administration.

2 Materials and methods

2.1 Patient data

This study was conducted in a retrospective manner. We obtained data from patients admitted to the ICU of Saiseikai Yokohamashi Tobu Hospital from April 2010 to September 2012. All received vancomycin hydrochloride intravenously for 1–2 h, within 72 h after admission to the ICU. The blood sampling for measuring plasma concentration was performed at least once within 1–2 h after the end of the first intravenous infusion. Moreover, the blood samples were taken more than twice between the first and second administration of the drug (Rodvold et al. 1988; Patel et al. 2011; Matsumoto et al. 2013). Exclusion criteria were under the age of 20 years, severe renal impairment with an estimated glomerular filtration rate (eGFR) less than 30 mL/min/1.73 m2, and receiving hemodialysis.

2.2 Calculation of APACHE II score

The APACHE II severity of disease classification system is shown in Table 1 in detail. The APACHE II score was consisted of three domains (the Acute Physiology Score, the Age Score and the Chronic Health Score) (Knaus et al. 1985). The score ranged from 0 to 71 and high score was considered to indicate higher risk of death. The Acute Physiology Score point was calculated from 12 routine physiological measurements within the first 24 h after admission to the ICU. The Age Score point was determined by age. The Chronic Health Score point was determined by the previous health status such as a history of severe organ system insufficiency. In the present study, all scores were calculated retrospectively based on data in the patient records.

Table 1 The APACHE II severity of disease classification system (Knaus et al. 1985)
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2.3 Calculation of Vd and t 1/2 of vancomycin

The pharmacokinetic parameters Vd and t 1/2 for vancomycin were calculated using the Bayesian method with the VCM-TDM E_edition Ver. 3.00 software package (Shionogi & Co., Ltd. Japan). Patient data (age, gender, ABW, and Scr or creatinine clearance), vancomycin dosing history (administration time and date, dosage, and drip time), and vancomycin concentration history (sampling time and date, and plasma concentration of vancomycin) were extracted from medical records for this calculation. Then, the vancomycin dosing history, and concentration history between the first and second administration were acquired to establish a methodology for setting the initial dosage of vancomycin hydrochloride. Furthermore, the ratio between Vd and ABW was represented as Vd/ABW. The plasma concentration of vancomycin was measured using a particle-enhanced turbidimetric inhibition immunoassay (Dimension Xpand-Plus HM, Siemens Healthcare Diagnostics, Inc., Tokyo, Japan) in the hospital laboratory. Then, the pharmacists provided an optimal individual vancomycin dosage regimen based on the data of each patient to the physicians.

2.4 Relationship between initial dose and peak plasma concentration (C peak) of vancomycin

Presently, the initial dose of vancomycin for critically ill patients with an MRSA infection is calculated based only on ABW (Liu et al. 2011). To examine the adequacy of that method, we investigated the relationship between the initial dose and C peak value of vancomycin at 2 h after the end of the first intravenous infusion in patients in whom C peak value was measured.

2.5 Relationship of APACHE II score with Vd and t 1/2 of vancomycin

We calculated the relationship of APACHE II score with Vd and t 1/2 of vancomycin for each patient. Based on those results, we examined the best prediction method for estimating the Vd and t 1/2 of vancomycin based on APACHE II score.

2.6 Relationship between predicted and observed plasma concentration of vancomycin

The prediction method used for estimating the Vd and t1/2 of vancomycin based on APACHE II score as noted above was validated. Those values were calculated using a regression equation for data from each patient, and then the plasma concentration of vancomycin at t hours after the end of intravenous infusion of vancomycin hydrochloride was predicted using the values. The predicted value (C t), plasma concentration at 0 h after the end of the infusion (C 0), and elimination rate constant (k e) were obtained using the following formulas.

$$C_{\text{t}} = C_{0} \times e^{{\text{ - }k_{e} \times t}} ,\;C_{0} = {\text{Dose/Vd}}$$
$$k_{\text{e}} = 0.693/t_{1/2}$$

Finally, we investigated the relationship between predicted and observed plasma concentration.

2.7 Ethical approval

The present study protocol was approved by the institutional review board of Saiseikai Yokohamashi Tobu Hospital. Patients were notified of this retrospective study with posters displayed in the hospital.

3 Results

3.1 Patients

Twenty-eight patients received intravenous vancomycin within 72 h of admittance to the ICU, of whom 13 were excluded based on the exclusion criteria. Consequently, 15 patients were enrolled (12 males, 3 females; 71 ± 8 years old; ABW 64 ± 12 kg) and their data are shown in Table 2. For all patients, Scr was 1.1 ± 0.4 mg/dL and eGFR was 53.0 ± 22.3 mL/min/1.73 m2, while the timing of the first administration of vancomycin after admission to the ICU was 29.3 ± 19.0 h.

Table 2 Patient characteristics
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3.2 Relationship between initial dose and C peak of vancomycin

The relationship between the initial dose of vancomycin based on ABW and C peak value is shown in Fig. 1. C peak was measured in 14 of the 15 patients. The initial doses and values for C peak were 26.1 ± 1.8 mg/kg (range 23.1–29.2 mg/kg) and 24.4 ± 3.7 mg/L (range 17.1–29.9 mg/L), respectively. There was no correlation between initial vancomycin dose based on ABW and C peak value.

Fig. 1
figure 1

Relationship between initial dose and peak plasma concentration of vancomycin

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3.3 Relationship of APACHE II score with Vd and t 1/2 of vancomycin

The APACHE II scores, and values for Vd/ABW and t 1/2 were 22 ± 6 pts, 1.03 ± 0.20 L/kg, and 20.1 ± 6.1 h, respectively (Table 3). The relationship between APACHE II score and Vd/ABW is shown in Fig. 2, while that between APACHE II score and t 1/2 is shown in Fig. 3. There was a significant correlation between APACHE II score and Vd/ABW (r = 0.58, p < 0.05), and between APACHE II score and t 1/2 (r = 0.74, p < 0.01). Furthermore, the Vd and t 1/2 of vancomycin could be estimated using the regression Eqs. (1) and (2), respectively.

$${\text{Vd/ABW}}\; = \;0.018\; \times \;{\text{APACHE II score}}\; + \;0.63$$
(1)
$$t_{1/2} = \, 0.70 \, \times {\text{ APACHE II score }} + \, 4.58$$
(2)
Table 3 APACHE II scores, volume of distribution, and elimination half-life of vancomycin in the present patients
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Fig. 2
figure 2

Relationship between APACHE II score and Vd/ABW. APACHE II Acute Physiology and Chronic Health Evaluation II, Vd volume of distribution, ABW actual body weight

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Fig. 3
figure 3

Relationship between APACHE II score and t 1/2. APACHE II Acute Physiology and Chronic Health Evaluation II, t 1/2 elimination half-life

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3.4 Relationship between predicted and observed plasma concentration of vancomycin

The relationship between predicted and observed plasma concentration of vancomycin at t hours after the end of infusion is shown in Fig. 4, with a significant correlation found (r = 0.71, p < 0.01). Consequently, we concluded that our results established a theoretical methodology for setting both appropriate initial dosage and dosage interval for vancomycin therapy based on APACHE II score (Fig. 5).

Fig. 4
figure 4

Relationship between predicted and observed plasma concentrations of vancomycin

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Fig. 5
figure 5

Predicted method for initial vancomycin dosing regimen. APACHE II Acute Physiology and Chronic Health Evaluation II, Vd volume of distribution, ABW actual body weight, t 1/2 elimination half-life, C peak peak plasma concentration of vancomycin

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4 Discussion

It is essential to establish the effects of antimicrobial drugs from the time of initial therapy in critically ill patients with an infection. However, since the degree of body fluid retention such as edema, pleural effusion, and peritoneal effusion vary greatly in those patients, the Vd of hydrophilic antimicrobials also varies, making it difficult to set an appropriate initial dose. In the present study, we attempted to establish a theoretical methodology to establish an initial dosage and dosage interval to provide an adequate antimicrobial effect with the initial administration of vancomycin hydrochloride, a water-soluble antibiotic.

There was no correlation between initial dose based on ABW and the C peak value of vancomycin, indicating that it is difficult to set the initial dosage in individual patients based on ABW, because the Vd of vancomycin varies greatly. Therefore, we considered that it is necessary to predict Vd and t 1/2 prior to administration for establishing an appropriate therapeutic strategy.

In the present study, we focused on the APACHE II scoring system (Knaus et al. 1985), a system for disease severity classification of patients in the ICU, and investigated the relationships of APACHE II score with Vd/ABW and t 1/2 of vancomycin, which showed significant correlations (r = 0.58, p < 0.05 and r = 0.74, p < 0.01, respectively). Furthermore, our results showed that the Vd and t 1/2 of vancomycin can be predicted prior to administration using the following regression Eqs. (1) and (2). However, there were few adult patients (<65 years) in the present study. When the APACHE II score is 0 in a patient at the age of 44 or younger with low severity, the estimated values of Vd/ABW and t 1/2 using those equations indicate 0.63 L/kg and 4.58 h, respectively. These values were within 0.39–0.92 L/kg and 2.9–9.1 h which were reported in healthy subjects, respectively (Matzke et al. 1986). Consequently, we concluded that this methodology was effective and suitable for all ages except children.

In critically ill patients with an infection, the variable factors related to the Vd of hydrophilic antimicrobials are capillary leakage due to SIRS caused by inflammatory cytokines and body fluid retention due to organ dysfunction such as heart, hepatic, or renal failure (Roberts and Lipman 2006; Petrosillo et al. 2010; Varghese et al. 2011). APACHE II scores are calculated from the Acute Physiology Score including values for body temperature, heart rate, respiratory rate, and white blood cell count, which are required for diagnosis of SIRS (Bone et al. 1992), as well as the Age Score and the Chronic Health Score including information about organ dysfunction. Therefore, APACHE II score may reflect the degree of capillary leakage, body fluid retention, and total body clearance of drugs due to various clinical conditions. We found significant correlations between APACHE II score and the Vd and t 1/2 of vancomycin. As for related factors, patients with higher APACHE II scores had higher blood levels of inflammatory cytokines such as tumor necrosis factor and interleukin-6 (Damas et al. 1997), which cause an increase in capillary permeability and fluid shift from the intravascular compartment to interstitial space (Lee and Slutsky 2010), resulting in leakage of vancomycin. Moreover, patients with higher APACHE II scores have a potential for decreased glomerular filtration rate due to renal impairment, thus increasing body fluid retention from edema and vascular permeability. Therefore, we concluded that an increase in Vd and prolongation of t 1/2 easily occur following vancomycin administration.

Pathophysiologic changes due to various clinical conditions lead to alterations in the Vd of hydrophilic antimicrobials in critically ill patients, making it difficult to set an appropriate initial dose. In the present study, we found that the Vd and t 1/2 of vancomycin could be estimated based on APACHE II score, and established a theoretical methodology for vancomycin therapy regarding initial dose and administration interval in individual patients (Fig. 5). In the future, to confirm whether this methodology is suitable, the study should be performed at all ages.