Towards therapeutic drug monitoring of antibiotic levels – analyzing the pharmacokinetics of levo ﬂ oxacin using DUV-resonance Raman spectroscopy †

Therapeutic drug monitoring (TDM) plays an important role in clinical practice. Here, pharmacokinetics has a decisive in ﬂ uence on the e ﬀ ective antibiotic concentration during treatment. Moreover, di ﬀ erent kinetics exist for di ﬀ erent administration forms. Accordingly, adjusting the correct concentration depends, in addition to gender, age, weight, clinical picture, etc ., on the dosage form of the antibiotic. This study investigates the capability of deep UV resonance Raman spectroscopy (DUV-RRS) to simulate the pharmacokinetics of ﬂ uoroquinolone levo ﬂ oxacin after two di ﬀ erent administration forms (intravenous and oral). Three di ﬀ erent pre-processing methods were applied, and the best agreement with the simulation was achieved using the extended multiplicative scatter correction. The resulting spectra were used for partial least squares (PLS) regression and ordinary least squares (OLS) regression. The kinetic parameters were compared with the simulated data, with PLS showing the best performance for intravenous administration and a comparable result to OLS for oral administration, while the errors are smaller. The acquired results show the potential of DUV-RRS in combination with PLS regression as a promising supportive method for TDM.


Introduction
Studies suggest that up to 50% of critically ill patients are underdosed with fixed-dose antibiotic regimens due to grossly altered pharmacokinetics in critical illness and failure of target attainment is associated with worse clinical outcomes. 1 Therapeutic drug monitoring (TDM) guided antibiotic therapy may be an appropriate strategy to overcome this pharmacokinetic variability and the problem of underdosing. In this process, serum antibiotic exposure is measured and dosing can be adapted during therapy to ensure optimal exposure. 2 In this context, today's well-established robust methods are mainly chromatography-based [3][4][5][6][7] and ensure sensitive detection of a specific group of drugs or a single antibiotic. [8][9][10][11][12] However, these techniques are time-consuming and laborintensive, require large volumes for sample preparation and processing and consume high amounts of organic solvents. 13,14 In addition, in some cases, samples must be forwarded to a central laboratory for analysis, which may delay the required results. 15,16 An all-encompassing application requires a rapid method with low sample demand and the ability for multicomponent detection.
In this respect, Raman spectroscopy 17,18 is a very promising technique, [19][20][21][22][23][24][25] as it is label-free and non-invasive, [26][27][28] fast and sensitive, [29][30][31][32] and provides an extremely high chemical selectivity [33][34][35][36][37][38][39][40][41] and potential as a point-of-care technique. For the evaluation of complex samples, e.g., human body fluids, a simple ordinary least squares (OLS) analysis may lead to insufficient results, and therefore multivariate data analysis may be helpful. The most widely used techniques in chemometrics for this task are principal component regression (PCR) and partial least squares (PLS) regression. 21,25,[42][43][44] Another important piece of information resulting from TDM is the time-dependent aspect of drug interaction in the host body, known as pharmacokinetics. 45 Depending on drug administration, specific kinetic models can be assumed, which, in addition to kinetic time constants, provide deeper insight into important parameters such as the bioavailability, dose, and volume of distribution of antibiotics. 46,47 These variables can be used to model the time-dependent interaction of drugs, which in turn can be used to adjust and improve antibiotic therapy. However, the pathology of critically ill patients may cause physiological changes that alter their pharmacokinetics 48,49 and complicate the prediction of drug exposure. 50,51 These physiological changes may lead to underor overdosage, which carries the risk of treatment failure in the case of underdosage and the risk of drug accumulation and toxic side effects in the case of overdosage. Above all, in vitro data show that sub-inhibitory antibiotic concentrations can foster multidrug resistance. [52][53][54] This necessitates robust, rapid, and sensitive spectroscopic and analytical methods.
This work therefore aims to demonstrate the potential of deep UV resonance Raman spectroscopy (DUV-RRS) in combination with PLS regression for monitoring of antibiotic pharmacokinetics.

Sample preparation
The fluoroquinolone levofloxacin (levofloxacin hydrochloride, Santa Cruz Biotechnology Inc., Dallas, Texas USA, see Fig. 1) was used without further purification. Starting from a 1 mM stock solution, a dilution series of 0 µM-50 µM (hereafter referred to as c cal ) was prepared using ultra-clear water from a feed system [SG Water GmbH, (Siemens, Barsbüttel, Germany) with κ > 0.06 µS cm −1 ], followed by several concentrations from 0 µM to 26.37 µM (c sim,int ) and 21.97 µM (c sim,o ). These samples were used for the calibration (c cal ) and simulation of two different kinetics (c sim,int and c sim,o ), respectively. Here, 15 and twelve different concentration values representing specific time points were taken from pharmacokinetic studies of 750 mg levofloxacin after intravenous 55 and oral administration, 56 respectively. All standard compounds are >95% pure as determined by HPLC analysis.

Spectroscopy
The deep UV resonance Raman spectra were acquired with a Raman spectrometer (IsoPlane, Teledyne Princeton Instrument, Trenton, USA) equipped with a UV laser. An excitation wavelength of λ exc. = 232 nm was applied (laser power: 42 mW at the sample). A 2400 g mm −1 grating and an exposure time of 7.5 s (four accumulations) were used to measure five replicate repetitions of each sample. To avoid any photo-degradation during the measurements, the samples were constantly stirred in a rotational cuvette.
The absorption spectrum was recorded from a 0.1 mM aqueous solution of the antibiotic using a Cary 5000 system (Varian, Darmstadt, Germany) with a step size of 1 nm and the Fourier transform (FT) Raman spectrum of the solid was recorded with a resolution of 4 cm −1 using a Nd:YAG laser with an excitation wavelength of λ exc. = 1064 nm, a laser power of 500 mW, and 256 scan exposures, in combination with a Ram II spectrometer (Bruker, Bremen, Germany).

Data preprocessing
All preprocessing and analysis of the raw Raman data were performed with statistical programming GnuR 3.6.1. 57 The packages 'signal', 58 'EMSC', 59 'Peaks', 60 'minpack.lm', 61 and 'pls' 62 were utilized and their functions were complemented by an in-house written procedure. First, the Raman data were truncated to the wavenumber region of interest (2000 cm −1 -1000 cm −1 ), and a median filter (window = 3) was applied for spike removal. Then, different algorithms were tested for their results in predicting the sample concentration. The treated Raman spectra were either baseline corrected using the SNIP algorithm 63 (iterations = 18, order = 2) and normalized to the water band or scatter corrected using extended multiplicative scatter correction (EMSC) 64,65 (degree = 1) with the median spectra of water as a reference or processed using a combination of both methods.
For quantification, the difference spectra were calculated using the median water spectra as a reference and a Gaussian peak profile was fitted to the marker band at about 1400 cm −1 . The resulting peak intensities of the calibration samples were correlated with the corresponding concentration (c cal ), showing a linear relationship (see Fig. 2A) that was used to predict the simulated concentration (c sim,int and c sim,o ). A representation of the preprocessing workflow can be found in the ESI (see Fig. S1 †). Furthermore, the preprocessed data were vector normalized and partial least squares (PLS) regression 66 was applied. The optimal number of five components was calculated minimizing the root-mean-square error of prediction (RMSEP) via 100-fold cross-validation using the concentrations of the calibration (c cal , see Fig. 2B). Here, the data were divided into train (c cal,train , 80%) and test (c cal,test , 20%) data sets, showing a good correlation (see Fig. 2C). This regression model was then used for the prediction of the concentrations of the pharmacokinetic simulations c sim,int and c sim,o , referred to as c pred,int and c pred,o in the following.

Density functional theory calculation for vibrational assignment of Raman marker bands
For a better understanding of the assignment and an interpretation of the Raman marker bands used for the quantification, the molecular structures were optimized and the vibrational modes and Raman activities were calculated with density functional theory (DFT) using Gaussian 09. 67 The hybrid exchangecorrelation functional with Becke's three-parameter exchange functional (B3) 68 slightly modified by Stephens et al. 69 coupled with the correlation part of the functional from Lee, Yang, and Parr (B3LYP) 70 and Dunning's triple correlation consistent basis sets of contracted Gaussian functions with polarized and diffuse functions (cc-pVTZ) 71 were applied. For alignment, the wavenumber positions of the FT-Raman peaks (threshold: 20% of the maximum intensity) were scaled to the vibrational frequencies of the calculation. The frequency scaling factor was calculated by minimizing the mean average error (MAE), and an intensity correction was applied to the scattering activities. 72 Finally, the scaled scattering activities were fitted with a Gaussian peak profile with the median value of the full width at half maximum (FWHM) of all experimental peaks investigated to simulate Raman bands with finite resolution (see Fig. S2 †).

Results and discussion
Resonance Raman spectroscopy for simulation of pharmacokinetic models The excitation wavelength λ exc. = 232 nm enables strong resonance and sensitive detection of the fluoroquinolone levofloxacin (see Fig. 1). As a proof-of-principle measurement, the pharmacokinetics of an intravenous and an oral 750 mg dose of levofloxacin were simulated with aqueous solutions of various antibiotic concentrations c sim,int and c sim,o . First, the best preprocessing routine had to be selected, i.e., baseline correction, EMSC correction, or their combination, followed by two different quantification approaches: OLS and PLS regression.
For the first regression model, the marker band was examined with a Gaussian peak profile. For a better understanding of this Raman signal, DFT calculations were aligned with the experimental FT-Raman spectra and their vibrational modes were assigned. For levofloxacin, the vibration at about 1400 cm −1 can be construed as a combination of CH 2 -wagging of the piperazine system and CH-bending vibration of the quinolone ring (see Fig. 3). In this case, the fitted peak intensity of the marker band of the dilution series was correlated with their concentration, and the resulting linear regression model was used to quantify the concentration of the simulated samples (see Fig. 2A).
For the PLS regression model, the dimensions of the calibration data set were reduced via the minimization of the RMSEP. Then, the spectral data were divided into train (c cal,train ) and test (c cal,test ) data sets. The error between the predicted (from regression with the training data) and the test data set was calculated via 100-fold cross-validation, resulting in an optimal number of five components (see Fig. 2B). When correlating the predicted concentrations of the test set with the adjusted concentrations, a good linear relationship was obtained (see Fig. 2C). With this optimized model, the concentrations of the simulated samples could be predicted.
As a marker for the 'best' model of the selection presented, the RMSEP was calculated for the simulated sample concentrations c sim,int and c sim,o and their prediction resulting from the regression model (c pred,int and c pred,o , see Table 1). It is evident that the prediction of the intravenous model is superior to that of the oral model, regardless of the regression model and data treatment, and the OLS regression shows an overall worse performance than the PLS regression. In addition, the concentration of the EMSC data shows higher similarities to the adjusted data, but the baseline correction has a greater impact on the calibration and prediction result, as the combined data treatment differs only slightly from the baseline-corrected one. Therefore, in further evaluation, the focus is on the EMSC data.
The limit of detection (LoD) may provide a possible explanation for the differences in the performance of the models. According to the IUPAC definition, 73 the LoD is calculated from the mean (c bl ) and the standard deviation (σ bl ) of the blank sample concentration: The LoD of the blank values of the PLS model is significantly lower than that of the OLS model (see Table 1). Therefore, the lower sample concentrations could not be satisfactorily determined for the latter, resulting in poorer performance. Fig. 3 Assignment of the vibrational mode of the Raman marker band used for ordinary least squares analysis. The atomic displacement vectors of the Raman band of levofloxacin at 1400 cm −1 are shown and can be assigned to a combination of CH 2 -wagging of the piperazine system and CH-bending vibration of the quinolone ring. The color code for the individual atoms is: hydrogen, white; carbon, grey; oxygen, red; nitrogen, blue; and fluorine, cyan. Table 1 Evaluation of the different models for preprocessing and prediction. The RMSEP for the baseline and EMSC correction and their combination were calculated using the simulated (c sim,int and c sim,o ) and predicted (c pred,int and c pred,o ) sample concentrations for both pharmacokinetics. The OLS regression shows overall poorer performance than the PLS regression, and the concentrations of the intravenous model are better predicted than those of the oral ones. In addition, the concentrations of the EMSC-corrected data show higher similarities to the simulated ones, but the baseline correction has a greater impact on the calibration and prediction results since the combined data treatment differs only slightly from the baseline correction  Various kinetic parameters can be derived from the timedependent concentration profile resulting from a pharmacokinetic study. Two different kinetic models were simulated (vide supra). Intravenous treatment can be expressed as linear absorption and first-order elimination where [E] and [E] 0 are the concentrations of the educts at any time point t and at the starting point t 0 , respectively, and k e is the kinetic time constant of the elimination. Oral administration follows Bateman kinetics, 74 in which the absorption, resorption, and elimination of the antibiotics take place: ÞÀexp Àk a Á t ð Þ ½ : Here, [P] is the product concentration at any time point t, V is a factor representing the relationship between the bioavailability f, dose D, and volume of distribution V, and k a and k e are the kinetic time constants for absorption and elimination, respectively.
As an additional indicator of the quality of the algorithm used, these pharmacokinetic models were fitted to the predicted concentration profiles and their results were compared with the simulated values (see Fig. 4 and Table 2). Here, the PLS regression yields a near-perfect agreement for the intravenous model and provides values of the same order of magnitude for the oral administration model. For the latter, the OLS model is slightly better than the PLS model but has higher errors. Thus, the experiments performed demonstrate the potential of resonance Raman spectroscopy in combination with PLS regression as a promising method providing reliable results for TDM.

Conclusion
In this work, the potential of deep UV resonance Raman spectroscopy in combination with PLS regression could be shown for two different administration forms of the antibiotic levofloxacin. The stable regression model enables good agreement of important kinetic parameters with the simulated data. These additionally provide important information on pharmacokinetics, which can further be used for better antibiotic dose adjustment. For the antibiotic quantification with deep UV resonance Raman spectroscopy, only a small sample volume (200 µL) and a short integration time (7.5 s) were required for sufficient results.
The measurements carried out in this study can be applied to body fluids, such as blood plasma, without significant modifications. Using a precisely selected wavelength in the DUV range, no fluorescence appears in the Raman spectrum and the analyte signals are resonantly enhanced. The complex composition of body fluids will result in several signals in the Raman spectrum, which may cause poorer results with OLS regression since the antibiotic marker band could be overlaid by the signals of the body fluid. However, the PLS regression could be applied to quantify antibiotic levels in body fluids comparatively well, as a larger spectral range is utilized in comparison with the OLS regression.
In summary, the UV resonance Raman experiments performed show high potential for the quantification of the levofloxacin pharmacokinetics and provide the foundation for future TDM studies.

Conflicts of interest
There are no conflicts to declare.