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\begin{document}

\title{Two-point limited sampling strategy is necessary to estimate the area
under the concentration-time curve for intravenous busulfan in infants
and young children}



\author[1]{Tomoyuki Utano}%
\author[1]{Motohiro Kato}%
\author[1]{Kenichi Sakamoto}%
\author[1]{Tomoo Osumi}%
\author[2]{Kana Matsumoto}%
\author[1]{Kimikazu Matsumoto}%
\author[1]{Akimasa Yamatani}%
\affil[1]{National Center for Child Health and Development}%
\affil[2]{Doshisha Women's College of Liberal Arts}%


\vspace{-1em}



  
  \date{May 18, 2024}


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\selectlanguage{english}
\begin{abstract}
Background: Therapeutic drug monitoring for busulfan is important to
prevent adverse events and improve outcomes in stem cell
transplantation. We investigated intravenous busulfan pharmacokinetics
and evaluated the utility of limited sampling strategy (LSS) as a simple
method to estimate the area under the concentration-time curve (AUC).
Procedure: The study comprised 87 busulfan measurements in 54 children
who received intravenous busulfan between August 2015 and May 2020. AUCs
were calculated from 3--5 blood sampling points in each patient, and the
correlation between AUC and plasma concentrations (ng/mL) at 1, 2, 3, 4,
and 6 h after initiating busulfan infusion (C\textsubscript{1},
C\textsubscript{2}, C\textsubscript{3}, C\textsubscript{4}, and
C\textsubscript{6}, respectively). Results: By one-point sampling
strategy, the most accurate predicted AUC was based on
C\textsubscript{6} (\emph{r\textsuperscript{2}} = 0.789; precision,
11.0\%) in all patients. The predicted AUC based on C\textsubscript{6}
was highly precise (\emph{r\textsuperscript{2}} = 0.937; precision,
5.9\%) in adolescent patients weighing \textgreater{} 23 kg, but the
correlation was poor in infants and young children weighing [?]23 kg
(\emph{r\textsuperscript{2}} = 0.782; precision, 11.4\%). By two-point
sampling strategy, the predicted AUC based on C\textsubscript{3} and
C\textsubscript{6} showed the most favorable performance
(\emph{r\textsuperscript{2}} = 0.943; precision, 6.4\%), even in infants
and young children, whereas the predicted AUC based on
C\textsubscript{3} and C\textsubscript{6} was acceptable
(\emph{r\textsuperscript{2}} = 0.963; precision, 5.7\%). Conclusions:
The AUC of busulfan can be predicted based on C\textsubscript{6} in
adolescent patients. However, there was substantial inter-individual
variation in busulfan pharmacokinetics in infants and young children, in
whom two-point LSS was necessary for accurate AUC prediction.%
\end{abstract}%



\sloppy


\textbf{Introduction}

Therapeutic drug monitoring for busulfan is important for improving
clinical outcomes in hematopoietic stem cell
transplantation.\textsuperscript{1} Busulfan exposure, expressed as the
area under the concentration-time curve (AUC), is an important parameter
for monitoring therapeutic efficacy and adverse events. A high busulfan
AUC increases the risk of adverse events such as sinusoidal obstruction
syndrome/hepatic veno-occlusive disease,\textsuperscript{2} while a low
busulfan AUC is associated with higher probability of graft failure or
disease relapse.\textsuperscript{1} Therefore, busulfan dosage is
adjusted to a target AUC of 75--100 mg/L \selectlanguage{ngerman}× h in myeloablative
conditioning regimens.\textsuperscript{3} Recent studies have
demonstrated that reduced-intensity conditioning regimens with busulfan
doses adjusted according to a target AUC of 45--65 mg/L × h are
effective in chronic granulomatous disease and Wiskott-Aldrich
syndrome.\textsuperscript{4,5} Busulfan pharmacokinetics varies greatly
among individuals,\textsuperscript{6} and target AUC depends on the
conditioning regimen and underlying disease; thus, it is clinically
essential to calculate the busulfan AUC.

AUC is determined using the pharmacokinetic modeling software or the
linear trapezoidal method; however, pharmacokinetic analyses require
frequent blood sampling. Limited sampling strategies (LSSs) are used to
estimate the AUC from a limited number of blood samples. Furthermore,
LSSs permit the easy estimation of AUC without using the pharmacokinetic
modeling software, and the drug dosage can be immediately adjusted
according to the blood concentrations, such as the trough value, which
is of great importance in clinical practice. In the present study, we
investigated the pharmacokinetics of intravenous busulfan and evaluated
the utility of LSS as an accurate and simple method to estimate AUC in
pediatric patients undergoing hematopoietic transplantation.

\textbf{Methods}

\emph{Patient selection}

This retrospective study included 87 busulfan measurements in 54
consecutive children (age, 0.2--19.2 years) who received intravenous
busulfan at the National Center for Child Health and Development from
August 2015 to May 2020. The study was approved by the ethics committee
of the National Center for Child Health and Development (approval
number: 1964), and written informed consent was obtained from the
guardian of each patient.

\emph{Busulfan} \emph{dosing and pharmacokinetic analysis}

Thirteen patients received body weight-based busulfan dosing (0.8--1.2
mg/kg)\textsuperscript{7} without test dose. Forty-one patients received
a test dose lower than the body weight-based busulfan dose, and the
first dose was determined based on target AUC determined by the
pharmacokinetics parameters obtained with the test dose. All patients
were administered intravenous busulfan as a 2-h infusion every 6 h for
four days, and pharmacokinetic analysis was performed based on the first
dose. Blood samples at 3--5 time points per patient were collected at 1,
2, 3, 4, and 6 h from the start of busulfan infusion and processed using
the dried blood spot method. Plasma busulfan concentrations were
measured by liquid chromatography with tandem mass
spectrometry.\textsuperscript{8} Actual AUC\selectlanguage{english}\textsubscript{0--[?]} values
were calculated from the data on plasma concentrations at all time
points by applying the one-compartment model using the Phoenix(r)
WinNonlin 7.0 pharmacokinetic analysis software (Certara LP, Princeton,
NJ, USA).

\emph{Evaluation of LSSs}

First, the regression equation was calculated from individual busulfan
concentrations at each sampling point and the actual
AUC\selectlanguage{english}\textsubscript{0--[?]} obtained from the pharmacokinetic modeling
software. Second, the predicted AUC\selectlanguage{english}\textsubscript{0--[?]} was calculated
from the regression equation and individual busulfan concentrations.
Finally, the relationship between the predicted
AUC\selectlanguage{english}\textsubscript{0--[?]}and actual AUC\selectlanguage{english}\textsubscript{0--[?]} was evaluated
using Pearson's correlation coefficient (\emph{r\textsuperscript{2}} ).
LSSs using two or three busulfan sampling points were developed by
multiple regression analysis. The precision of the predictive
performance of busulfan AUCs was assessed by calculating the mean
absolute percentage error (MAPE). Additionally, subgroup analysis was
conducted based on body weight (\textless{}9, 9--16, 16--23, 23--34, and
\textgreater{}34 kg). To verify the utility of LSSs in the present
study, the predicted AUC\selectlanguage{english}\textsubscript{0--[?]} was calculated using the
developed LSS and its predictive performance was evaluated in seven
patients in a cohort separate from the first cohort that was used to
develop the LSS. All statistical analyses were performed using SPSS
Statistics ver.23 (SPSS IBM Japan, Tokyo, Japan).

\textbf{Results}

\emph{Patient characteristics}

A total of 87 busulfan measurements in 54 patients were included. The
patient characteristics are shown in Table 1. There were 45, 87, 75, 84,
and 82 blood samples at 1, 2, 3, 4, and 6 h from the start of busulfan
infusion, respectively. The median actual AUC\selectlanguage{english}\textsubscript{0--[?]} was
773 (range, 331--1631) \selectlanguage{greek}μ\selectlanguage{english}mol*min/L.

\emph{Development of the LSS}

The relationship between the predicted and actual
AUC\textsubscript{0--[?]} values using the one-point sampling strategy
with plasma busulfan concentrations (ng/mL) measured at 1, 2, 3, 4, and
6 h after the initiation of busulfan infusion (C1, C2, C3, C4, and C6,
respectively) is shown (Figure 1). The most accurate predicted
AUC\textsubscript{0--[?]} in all patients using the one-point sampling
strategy was based on C\textsubscript{6} (\emph{r\textsuperscript{2}} =
0.789; MAPE, 11.0\%). The multiple regression analysis of the predicted
AUC\textsubscript{0--[?]} values based on C\textsubscript{3},
C\textsubscript{4}, and C\textsubscript{6} using the two-point and
three-point sampling strategies revealed that the one-point sampling
strategy was highly precise. By the two-point sampling strategy, the
AUC\textsubscript{0--[?]} predicted based on C\textsubscript{3} and
C\textsubscript{6} exhibited the most favorable performance
(\emph{r\textsuperscript{2}} = 0.943; MAPE, 6.4\%). The
AUC\textsubscript{0--[?]} predicted based on the three-point sampling
strategy using C\textsubscript{3}, C\textsubscript{4}, and
C\textsubscript{6} showed excellent predictive performance when compared
with the actual AUC\textsubscript{0--[?]} (\emph{r\textsuperscript{2}} =
0.955; MAPE, 5.9\%) (Table 2).

The predictive performance of busulfan AUC based on body weight are
shown in Table 3. In adolescent patients (body weight \textgreater{} 23
kg), the AUC\textsubscript{0--[?]} predicted based on
C\textsubscript{6}was highly precise (\emph{r\textsuperscript{2}} =
0.937; MAPE, 5.9\%); however, this correlation was poor in infants and
young children weighing [?]23 kg (\emph{r\textsuperscript{2}} = 0.782;
MAPE, 11.4\%). By the two-point sampling strategy using
C\textsubscript{3} and C\textsubscript{6}, the predicted
AUC\textsubscript{0--[?]} was acceptable even for infants and young
children (\emph{r\textsuperscript{2}} = 0.963; MAPE, 5.7\%) and was as
accurate as the AUC\textsubscript{0--[?]}based on C\textsubscript{6} in
adolescent patients (\emph{r\textsuperscript{2}} = 0.937; MAPE, 5.9\%).

\emph{Validation of the LSS}

The accuracy of the predicted AUC\textsubscript{0--[?]} by one-point and
two-point sampling strategies was determined in a cohort of seven
patients who were not included in the development of the LSS (Table 4).
All seven patients weighed [?]23 kg. By the one-point sampling strategy,
the predicted AUC\textsubscript{0--[?]} had more than 15\% errors compared
to the actual AUC\textsubscript{0--[?]} in four patients. In contrast,
none of the patients had more than 15\% error by the two-point sampling
strategy.

\textbf{Discussion}

In the present study, AUC prediction based on C\textsubscript{6} was the
most accurate one-point blood sampling strategy. Watanabe \emph{et al}
.\textsuperscript{9} reported that the AUC of busulfan was best
predicted by C\textsubscript{6} in pediatric hematopoietic stem cell
transplant recipients, supporting the results of the present study. The
reason for the poor predictive performance of AUC based on
C\textsubscript{1} could be because the individual differences in the
absorption phase were smaller than in the elimination phase due to the
intravenous administration of busulfan. C\textsubscript{2} represents
the blood sampling immediately after the end of busulfan infusion and
may reflect the sampling of the distribution phase. Therefore, the blood
concentrations may significantly change within a few minutes, which
might explain the weaker relationship between the predicted AUC based on
C\textsubscript{2} and the actual AUC.

In the present study, the predictive performance of AUC based on
C\textsubscript{6} was lower (\emph{r\textsuperscript{2}} = 0.789) than
that reported by Watanabe \emph{et al.}
\textsuperscript{9}(\emph{r\textsuperscript{2}} = 0.929). More than 60\%
of all patients weighed [?]23 kg in that study, whereas in our study, 24\%
of the patients weighed [?]23 kg, which might have reduced the accuracy of
predicted AUC based on C\textsubscript{6}. In fact, from the predictive
performance of AUC performance by body weight, the predicted AUC based
on C\textsubscript{6} was highly precise in adolescents.

In infants and young children, the accuracy of AUC predicted by
one-point sampling with C\textsubscript{6} was poor. Kishimoto \emph{et
al} .\textsuperscript{10} reported that errors in AUC prediction based
on C\textsubscript{6} were higher in young children and infants using
the Monte Carlo simulation in the population pharmacokinetic model.
Furthermore, McCune \emph{et al} .\textsuperscript{6} reported that the
accuracy of prediction for busulfan to reach the therapeutic range was
lower in patients younger than five years than in adolescent patients
using the population pharmacokinetic model. Therefore, in early
childhood, the busulfan pharmacokinetics significantly varies among
individuals, and predicting AUC by the one-point sampling strategy may
not be sufficient. In the present study, the AUC prediction based on
C\textsubscript{3} and C\textsubscript{6} using the two-point sampling
strategy was acceptable even for infants and young children. In the
validation cohort, more than half of the patients had more than 15\%
errors with the one-point sampling strategy compared to the actual AUC.
Errors \textgreater{}15\% are a deviation from the guidelines on
bioanalytical method validation in pharmaceutical
development,\textsuperscript{11} which states that the accuracy and
precision should be within \selectlanguage{ngerman}±15\% deviation of the theoretical
concentration. Thus, in infants and young children, the AUC should be
predicted using the two-point sampling strategy.

In the one-point sampling strategy, the LSS equation for AUC was 2.866
C\textsubscript{6} + 108.9 in adolescent patients. Consequently, the
target C\textsubscript{6} was 360--500 ng/mL for myeloablative
conditioning (target AUC, 75--100 mg/L × h) and 200--300 ng/mL for
reduced-intensity conditioning (target AUC, 45--65 mg/L × h). In
contrast, in the two-point sampling strategy, the target
C\textsubscript{3} depended on C\textsubscript{6} and target AUC. It
should be noted that the accuracy of the predicted AUC by LSS will
decrease if the blood sampling time is significantly different from the
correct sampling time. Thus, it is important to pay close attention to
blood sampling times.

Concomitant medications that may affect the busulfan pharmacokinetics
should be considered in the interpretation of our findings.
Kangarloo\emph{et al} .\textsuperscript{12} reported that phenytoin, an
anticonvulsant agent, increased the busulfan clearance. In the present
study, levetiracetam or clonazepam were used as anticonvulsants, which
do not affect the busulfan
pharmacokinetics.\textsuperscript{13,14}Therefore, the anticonvulsant
agent did not have a significant effect on the busulfan pharmacokinetics
in the present study.

The present study also has certain limitations. It remains unclear why
busulfan pharmacokinetics varies significantly in infants and young
children. Polymorphisms in glutathione \emph{S} -transferase (\emph{GST}
)\textsuperscript{15} affect busulfan pharmacokinetics. Additionally,
age-dependent variations in intrinsic busulfan clearance were reported
to be associated with higher GST activity\textsuperscript{16}; thus,
differences in the GST expression might explain individual differences
in busulfan pharmacokinetics. Further investigation is warranted to
establish the parameters for personalized administration of busulfan.

In conclusion, the AUC of busulfan could be predicted based on
C\textsubscript{6} in adolescent patients. However, for infants and
young children, there was substantial inter-individual variation in
busulfan pharmacokinetics and the two-point sampling strategy was
necessary for accurate AUC prediction.

\textbf{Conflicts of interest}

The authors have no conflicts of interest.

\textbf{Acknowledgments}

We would like to thank the staff at the National Center for Child Health
and Development. The authors also thank the medical editors from the
Division of Education for Clinical Research at the National Center for
Child Health and Development for professionally editing this manuscript.

This study was supported in part by a grant from the National Center for
Child Health and Development (grant no, 2020A-1) and by the Japan
Society for the Promotion of Science through Grants-in-Aid for
Scientific Research (KAKENHI) (grant no, 19K17316).

\textbf{References}

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2. Dix SP, Wingard JR, Mullins RE, et al. Association of busulfan area
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10. Kishimoto K, Hasegawa D, Irie K, et al. Pharmacokinetic analysis for
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14. Carreras E, Cahn JY, Puozzo C, Kroger N, Sanz G, Buzyn A. Influence
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15. Nishikawa T, Yamaguchi H, Ikawa K, et al. Influence of
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\textbf{Legends}

\textbf{Figure 1. Predictive performance of busulfan AUC using the
one-point sampling strategy.} Relationship between actual
AUC\selectlanguage{english}\textsubscript{0--[?]} calculated by the pharmacokinetic modeling
software and predicted AUC\selectlanguage{english}\textsubscript{0--[?]} calculated by the limited
sampling strategy based on plasma busulfan concentrations at 1
(C\textsubscript{1}), 2 (C\textsubscript{2}), 3 (C\textsubscript{3}), 4
(C\textsubscript{4}), and 6 (C\textsubscript{6}) h after initiating
busulfan infusion is shown.

AUC, area under the concentration-time curve\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Fig/Fig}

\end{center}
\end{figure}

\selectlanguage{english}
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