# Monitoring Theophylline Concentrations in Saline Using Terahertz ATR Spectroscopy
## 1 Introduction  
To assist in the appropriate usage of pharmaceutical agents, therapeutic drug monitoring (TDM) plays a fundamental role in clinical practice. TDM has been used for the determination of blood concentrations of drugs with narrow therapeutic ranges, drugs with marked pharmacokinetic variability, medications for which target concentrations are difficult to monitor, and drugs known to cause therapeutic and adverse effects. In this regard, TDM can allow for the optimization of individual dosage regimens [1]. However, because TDM is generally performed with immunoassays based on antigen-antibody reactions using serum, plasma, or whole blood, repeated blood collection can be stressful for patients. Additionally, it takes tens of minutes to determine the blood concentrations of agents, even though the measurement process is totally automated. Thus, the development of novel TDM methods for non-invasively and rapidly evaluating drug levels in blood is required. Terahertz (THz) waves lie between the optical region and microwave region. The energy of a THz wave corresponds to the motion of a relatively large molecule; thus, THz waves offer the ability to observe absorption of a highly polymerized compound [2]. The energy is also related to the rotation of a hydrogen bond of water molecules and the rotation of free water molecules [3], so THz waves have the potential to observe water dynamics in a solution. Features of THz waves include transmission performance for an object, like microwaves, and spectral performance, like visible light. Although it has been difficult to use THz waves due to the lack of a good emitter to date, recent developments in the technology of THz emitters and detectors have allowed many applications of THz technology, such as non-destructive inspection, security checks, and communications [4; 5]. Further, they also have potential for novel medical tools, because the photon energies of THz waves are relatively low and safe for the human body. One feature of THz waves is that they are strongly absorbed by liquid water. This is mainly based on the modes of interaction with water mentioned above. This absorption becomes both anadvantage and a disadvantage in some cases using THz waves to observe liquid materials. It is difficult to observe water or some solutions using THz transmission measurements, so the THz attenuated total reflection (ATR) method is used for measurements with water-related materials [3; 6; 7; 8]. When light is reflected at an interface between a material of refractive index \(n_{1}\) and one of \(n_{2}\) (Figure 1), if the incident angle \(\theta_{\rm c}\) is greater than \(\theta=\sin^{-1}(n_{2}/n_{1})\), total light reflects at the interface. At this time, the light enters and propagates through a slight distance inside the second material. This is an evanescent wave. If the material is transparent for THz waves, then all evanescent waves pass through the second material with no absorption. However, if the second material, like water, has large absorption, the evanescent wave is absorbed and a decrease of light amplitude is observed even with a short passing distance of the light. Using the decrease, we can estimate some information. This is the THz ATR measurement, by which it is possible to measure a sample that has strong absorption in THz frequencies. Furthermore, because non-invasive characterization is possible with evanescent waves, they can be used for medical applications. In the THz region, some studies for solutions have been reported using ATR methods [3; 6; 7; 8]. For example, there are determinations of hydration numbers in solution and observations on the relaxation mode of water molecules [8]. These studies were primarily fundamental studies. In contrast, reports based on medical applications are rare. Moreover, there are very few THz studies on blood [9; 10]. Because the energy level of THz waves corresponds to the dynamics of hydrogen bonds, they have the potential to observe the state of water molecules in a solute.