## 1 Introduction  
Kidney failure is a major global health concern and is recognized as an extensive public health problem. In most cases, a kidney transplant represents the only strategy to improve the quality of life and life expectancy of CKD-affected patients [1]. In clinical practices, blood and urine tests, glomerular filtration rates, imaging, and kidney biopsies [2] are used to detect chronic kidney failure [3] and to diagnose transplanted kidney rejections. Some of these methods are complex, expensive, invasive, time-consuming, require skilled technicians, and may cause pain in some individuals. In the last few years, exhaled breath analysis has captured the interest of scientists and clinicians, providing important information regarding crucial biochemical changes linked to certain pathologies [4; 5; 6; 7; 8; 9; 10]. Exhaled breath comprises condensates (EBCs; cytokines, H\({}_{2}\)O\({}_{2}\), isoprostanes, and leukotriene), volatile inorganic compounds (e.g., O\({}_{2}\), NO, CO\({}_{2}\)), and, notably, organic compounds [11; 12; 13], which are produced by cellular metabolism. These enter the blood, travel to the lungs, and are finally exhaled through the respiratory tract. When a person suffers from a certain disease, the components in the exhaled air change and can provide useful clues for clinical diagnoses and/or monitoring of a patient's condition. Breath analysis involves collecting breath samples from patients, and their subsequent analysis, and data processing. The advantages of breath analysis are that it is safe, non-invasive, reproducible, acceptable for patients, easy to operate, and fast. Another benefit is that samples are readily obtained, and compared to blood and urine collection, breath analysis is less time-consuming and requires a smaller sample [10]. Therefore, breath analysis is unique compared to traditional technologies, making it a research hotspot in the field of disease diagnosis, even though it is an old technique for diagnosing physical conditions. [PERSON] (460-370 BCE) first described it in his \"_treastie on respiratory aromas and diseases_\". Over the past thirty years, scientists have identified thousands of different breath organic compounds, employing emerging analytical techniques, including proton-transfer-reaction-mass spectrometry (PTR-MS) [14; 15; 16; 17], proton-transfer-reaction time-of-flight-mass spectrometry [18; 19; 20; 21], selected ion stream tube-mass spectrometry (SIFT-MS) [22; 23; 24; 25; 26], laser spectroscopy [27; 28], ion mobility spectrometry [29; 30; 31] sensor array [32], and electronic nose technology [33; 34; 35; 36], even if the gold standard for detecting respiratory biomarkers is a combination of gas chromatography and mass spectrometry [37; 38; 39]. However, independently of the diagnostic technique employed, several studies have demonstrated that breath analysis may be a promising strategy for the detection and follow-up of kidney disease. Nitrogen-containing VOCs, such as ammonia and amines, have been shown to be elevated in the breath of subjects with renal failure [40; 41; 42]. From ancient times, in fact, a \"fishy-like\" smell of exhaled breath was attributed to renal disorders [43], and ammonia and trimethyl amine (TMA) were used as useful biomarkers for real-time monitoring of hemodialysis efficacy [41; 42]. Other than for the nitrogen-containing compounds, little is known about other classes of VOCs, including, sulfur compounds, ketones, alkenes, and aliphatic hydrocarbons, with short and long chains (e.g., propane, butane, pentane, hexane, decane, etc. ), organic acids (e.g., acetic acid, butanoic acid, etc. ), benzene derivates (e.g., toluene, xylenes, etc. ), halogen-containing, and alcohols, whose concentrations in human breath change in response to the onset of specific pathologies [44; 45; 46], and have been shown to be essential in the fingerprint breath profile of healthy subjects [47; 48; 49; 50; 51].