A review on isoprene in human breath

We summarize the history and review the literature on isoprene in exhaled breath and discuss the current evidence and models that describe its endogenous origin and consequence for understanding isoprene levels and their variations in exhaled breath.


Introduction
Ideally, when end-tidal breath is collected or sampled, the subjects should be seated, have been at rest for several minutes before sampling commences, remain at rest during breath collection and be breathing normally. Under those circumstances, steady state conditions should be achieved in the lungs, with the pulmonary blood flow and ventilation being constant. Then it is generally safe to assume that the trace concentrations of the volatile organic compounds (VOCs) contained in exhaled breath have also achieved steady state conditions. Of the many VOCs found in exhaled breath, only for those with low blood:air partition coefficients (λ b:air < 10) do the end-tidal measurements provide accurate values of their alveolar concentrations [1]. Of the breath VOCs with low blood:air partition coefficients, isoprene (C 5 H 8 , λ b:air ∼ 0.95 [2]) is the volatile with the highest concentration in exhaled breath (∼100 ppbv at rest) after methane, accounting for up to about 70% of the total hydrocarbon removal via exhalation [3][4][5][6]. Isoprene is also a particularly abundant VOC in the human organism. In addition to end-tidal breath [6], isoprene has been detected in blood [7,8], urine [9], and skin emanation [10]. The physicochemical properties of isoprene relevant to its detection and quantification in human samples are listed in table 1. Isoprene is also arguably the most studied volatile in breath research, not only because it is the main endogenous hydrocarbon found in exhaled human breath but also because of its potential use as a non-invasive probe for assaying various metabolic processes occurring in the body, although as we will explain below it is not a useful biomarker probe.
In 2010, King et al presented a detailed model dealing with the end-tidal breath concentration dynamics of isoprene [12]. This model is the only one to date capable of describing quantitatively real-time end-tidal (alveolar) isoprene breath concentrations under non-steady state conditions, e.g. experiments involving exercise, various breathing maneuvers, and position changes. Importantly, the model predicts that isoprene blood concentrations are different in different body regions, and being highest in the blood contained in muscle tissue, where the major production of isoprene is considered to occur [12]. This work by King et al also predicts that it takes much longer for steady state conditions to be reached in different regions of the body, so that the assumption that isoprene concentration has also reached a steady state after a short resting period is not always correct.
There is a significant amount of misconception on how the levels of isoprene in breath can be correctly interpreted owing to the variations that can occur from changes in breathing patterns, movement, exercise, ventilation and perfusion. There is also much debate in the literature on where and how isoprene is produced in the body, and whether it serves any physiological function, as it has been suggested for plants [13]. Perhaps, it is simply a waste product. The major aim of this review is to address these issues by covering our current understanding of the origins and physiological behavior of isoprene in the body.  [11] Independent of how or where the isoprene is produced in the body, once it gets into the systemic circulation it can enter the lungs through an exchange between the blood capillaries and alveoli. From there isoprene is carried out in exhaled breath (in addition to other exchanged gases, including many VOCs [14,15]). Numerous analytical techniques have been employed to measure and monitor isoprene in exhaled breath, and therefore we start the next section with a brief review of the associated analytical studies.

A potted history of breath research and isoprene
To illustrate the extent to which isoprene in exhaled breath has been the focus of intense research, we provide in this section a very short review of the associated scientific progress over the last sixty years. Owing to the extensive research that has been undertaken over six decades, it is beyond the scope of this review to provide a full historical overview that covers all breath isoprene studies to be found in the literature. For the interested reader a more complete timeline dealing with published scientific research on isoprene in the human body and in exhaled breath is provided in appendix A.

Analytical Studies
Isoprene was first detected in breath in 1960 by gas chromatography (GC) equipped with an ionization detector [16]. In that pioneering study, ten other volatiles were identified but not quantified, including acetone and ethanol. In 1969, Jansson and Larsson [17] reported the first GC/mass spectrometry (GC/MS) identification of isoprene, in addition to methane, acetone, methanol and ethanol, in breath. However, they used GC with a flame ionization detector (FID) to quantify the isoprene concentrations, giving a range of 0.09-0.45 ppm. Further GC and GC/MS measurements of isoprene in exhaled breath are reported in the literature (see e.g. Conkle et al [18], Krotoszynski et al [19], DeMaster and Nagasawa [20], Gelmont et al [3]).
Although GC/MS measurements provide unambiguous assignments to identify breath volatiles, the real-time detection and monitoring (rapid temporal profiling) of exhaled breath and individual breath profiling are not possible. In the 1990s, two novel analytical techniques were developed that are capable of such measurements: selected-ion flow tube-mass spectrometer (SIFT-MS) [21], which simply applied the well-known SIFT apparatus developed by Adams and Smith in the late 70s [22], and a completely new analytical device called the proton-transfer-reaction mass spectrometer (PTR-MS) [23].
In 1996, SIFT-MS was used to record the breath profiles of acetone and isoprene of a volunteer who merely blew into the inlet of the instrument [24]. This real-time analysis of exhaled breath was followed in 1997 by a little known PTR-MS study by Jordan et al reporting-for the first time-a sharp rise in isoprene breath concentrations at the start of exercise [23]. This interesting observation was followed-up in 2001 in a PTR-MS study by Karl et al [25], confirming the rapid rise in isoprene concentrations within seconds after the start of exercise. In 2006, Turner et al [5] presented the results of a six-months SIFT-MS study of breath isoprene concentrations of 30 volunteers. In an extension to that work, in an off-line 2008 PTR-MS study involving 205 volunteers, using Tedlar bags to sample mixed expiratory exhaled breath, aspects of changes in isoprene concentrations in breath as a result of normal physiology relating to age, gender and cholesterol profiles were reported by Kushch et al [6]. In both the SIFT-MS and PTR-MS studies no correlation was found between breath isoprene concentrations and cholesterol levels. It has been known for years that in very rare occasions (perhaps less than one in a thousand random volunteers) the exhaled breath of a human contains no detectable isoprene [3,5,6,26]. For example, in an important PTR-MS study by Sukul et al [27], involving 1026 subjects, a young healthy female volunteer was found to have no traceable isoprene in here exhaled breath, a result that is crucial for elucidating the origins of isoprene in the body, as discussed further in section 2.3.
Although GC/MS, SIFT-MS, and PTR-MS analytical methods have dominated the detection and quantification of breath isoprene, alternative techniques have also been applied for this purpose, such as cavity ringdown spectroscopy [28], or sensor devices [29,30].

Modeling isoprene in breath
The modeling aspects of isoprene in breath started in 1996 by Filser et al [11]. They presented a five-compartment model to ascertain the pharmacokinetics of isoprene. Using a closed chamber system, they determined the concentration of isoprene when the inhaled concentration equals the exhaled concentration, which is reached at about 600 ppbv after approximately 2 h of rest. Based on their model they determined partition coefficients, metabolic rates and production rates for isoprene.
In 2001, Karl et al developed a physiological twocompartment model similar to the one of Filser et al [11], but with some modification to describe breath isoprene concentrations.
In 2009, King et al [31] developed for the first time a real-time experimental setup combining exhaled breath VOC measurements by PTR-MS with hemodynamic and respiratory data. The models of both Filser et al and Karl et al fail when applied to this full real-time dataset of hemodynamic, respiratory, and end-tidal isoprene concentration.
King et al followed this up in 2010 by modeling the end-tidal breath concentration dynamics of isoprene with a physiological three-compartment model [12]. This is currently the only mechanistic model capable of describing quantitatively end-tidal breath isoprene concentrations in real time under non-stationary conditions, e.g. exercise experiments, various breathing maneuvers, and position changes. Importantly, it predicts that isoprene blood concentrations are different in different body regions, being highest in the blood flowing through muscles, and predicts that the major production of isoprene occurs in muscle tissue.

Origin and fate of isoprene in the human body
Numerous publications have discussed the potential production mechanisms for isoprene in the human body. It is possible that a fraction of isoprene in the body derives from bacteria [32,33], but that is not considered to be a major production route.
Early discussions on isoprene production suggested that it derives from cholesterol biosynthesis via a mevalonate pathway (MVA), mainly by the liver. Certainly, it is evident from the studies of Deneris et al [34] that isoprene is produced nonenzymatically by acid-catalyzed formation from dimethylallyl pyrophosphate [35]. This led to suggestions that the exhaled breath concentrations of isoprene could be indirectly used to provide a measure of body cholesterol. If this was true, there should be a correlation between blood cholesterol levels and mean breath isoprene concentrations. However, none has been found [5,6,36]. Furthermore, this reaction route is too slow to explain the high levels of isoprene found in the human body [37,38]. In 1993, Stone et al [39] showed that lovastatin, a competitive inhibitor of the rate-limiting step of cholesterol biosynthesis, significantly reduced breath isoprene levels. However, statins are known to have muscular side effects, the mechanism of which is unclear [40]. In addition, it is now so well-proven that there is no correlation between breath isoprene concentrations levels and blood cholesterol levels [5,6,27,36]. Thus, the major production of isoprene in the body must be from a difference source.
By modeling exhaled breath isoprene levels, King et al have provided convincing evidence that muscle tissue acts as an extrahepatic production site of substantial amounts of isoprene in the body. In support of this, and by using a solid-phase microextraction GC/MS, Miekisch et al [41] analyzed arterial and venous blood samples taken from mechanically ventilated patients. Additional blood samples were taken from selected vascular compartments of 19 mechanically ventilated pigs. They discovered that isoprene was not equally distributed among the vascular compartments. Isoprene tended to be higher in portal and mixed venous blood and lower in hepatic venous and in arterial blood. Miekisch et al concluded that the decreasing isoprene concentrations in the hepatic venous blood resulted from isoprene being metabolized in the liver and that the high mixed venous concentrations suggested that there is a peripheral origin of isoprene, e.g. muscle cells.
The 2021 Sukul et al [27] study, mentioned above, as well as that by King et al [36] provided further evidence that breath isoprene is not correlated with cholesterol levels. Sukul et al demonstrated that endogenous isoprene does not originate from cholesterol synthesis by quantitative gene expression analysis of the MVA pathway enzymes of the female volunteer without isoprene in breath.

Steady state isoprene concentrations in exhaled breath
Owing to its low solubility, isoprene is not absorbed to the water-like mucus layer as it passes through the upper airways and out of the mouth or nose. This means that the end-tidal phase measurements provide a reasonably accurate value of the alveolar concentrations of isoprene, which in turn can be directly related to the blood concentrations [1]. For adults at rest, various end-tidal measurements show that the majority of people have steady state isoprene concentrations within a limited range, with the lower values starting at about 70 ppbv and the higher values being at about 133 ppbv (25%-75% quantile) [5,6]. For neonates, undetectable or very low levels are observed in breath [43]. In children and adolescents, isoprene levels in breath are generally found to be lower than found in adults, and tend to increase with age [26,[44][45][46], until reaching an age-invariant end-tidal value of about 100 ppbv (approx. 4 nmol l −1 at standard ambient pressure and temperature). The parallel increase of breath isoprene with increasing muscle mass with age provides additional support for the hypothesis that isoprene production is related to muscle tissue. Although isoprene is a commonly found endogenous volatile in exhaled breath in high levels, as mentioned previously a few studies have found subjects (approximately 1 in a 1000) whose isoprene levels are deficient or completely absent (below the detection limit) [3,5,6,26,27,34,47,48]. The cause of this lack of production is uncertain. Investigations involving people who have no measurable isoprene in their exhaled breath can be expected to provide an interesting insight into the possible production pathways of isoprene.
During sleep, exhaled breath isoprene concentrations tend to increase by a factor of two overnight [49,50]. Recent unpublished real-time measurements by us with volunteers who had been resting and avoiding any movements over a period of several hours demonstrate that this increase also happens without sleeping.

Isoprene is not a useful biomarker for diagnosing or monitoring disease
As mentioned in the introduction, isoprene in exhaled breath has been extensively researched owing to its potential to serve as a sensitive biomarker for the detection and/or monitoring of various metabolic effects, as shown in table 2. However, the use of isoprene as a potential disease marker is useless owing to its (i) breath levels being very sensitive to breathing patterns, movement and exercise and (ii) lack of specificity to a disease. To illustrate this for both (i) and (ii), we turn to lung cancer. Although lower levels of isoprene have been found in the exhaled breath of patients suffering from lung cancer compared to healthy controls, lower levels have also been associated with chronic heart failure, cystic fibrosis, and muscle dystrophy [36,51,52]. In addition, we can expect people suffering from lung disease to have impaired breathing compared to healthy individuals and the steady-state breath isoprene levels, following the simple Farhi equation, will therefore likely differ between these two groups even if the underlying systemic isoprene concentrations are similar. Apart from the factors indicated above, a number of additional clinical conditions and external influences have been reported to affect isoprene output, including renal dialysis [53][54][55][56], heart failure [57], sleep/sedation [49,50,58] and, as suggested above, exercise [47,51].
The physiological meaning of these changes has not been established in sufficient depth. At the onset of exercise, it has been discovered that isoprene concentration levels in breath increase within about 1 min, typically by approximately by a factor of three to five. Once the exercise is stopped and then resumed, the isoprene levels again show a sharp rise in concentration but reach a lower peak value than that measured in the first exercise session [23,25,31]. To provide an understanding of this, King et al applied a three-compartment model that successfully replicated the transition from a steady state at rest (constant exhaled isoprene concentration, constant cardiac output, and constant breath flow) to a new steady state at moderate constant exercise work load. The use of moderate exercise translates into a blood flow that approximately doubles and a breath flow that increases by about a factor of four [12]. While blood flow and breath rates reach a new equilibrium within about a minute, the isoprene breath concentrations only reach a new equilibrium after about 15 min. The relevance of the model by King et al associated with exercise is that it provides further evidence for the hypothesis that the main production of isoprene is in the muscle tissue. At the start of exercise, the blood flowing through the working muscle significantly increases resulting in higher quantities of isoprene entering the mixed venous blood. If we assume that the production of isoprene in muscle tissue is constant, then the level of isoprene in the blood coming from the muscle decreases until it reaches a new steady state during exercise. This explains the isoprene peak in the exhaled breath observed at the onset of exercise, which is then followed by the observed washout of isoprene until a new constant value is reached. This behavior is described in more detail in the next section.

Isoprene and Farhi's equation, physio-metabolic effects
When breath is sampled (ideally in a CO 2 -controlled end-tidal manner), subjects need to be seated and breathing normally, i.e. they are at rest. Under these circumstances, steady state conditions are achieved in the lung and pulmonary blood flow and alveolar ventilation are constant. According to Henry's law, the alveolar concentration C A is in equilibrium with the arterial concentration C a , i.e. C a = λ b:air C A , where λ b:air denotes the blood:air partition coefficient, which is approximately 1 for isoprene [2]. In addition, Farhi's equation [67] (for more details see appendix B.1) can be applied, which connects the end-tidal isoprene breath concentrations C end−tidal , with the mixed venous concentration Cv by the equation (1) Breath isoprene production in subjects with CHF was found to be significantly reduced compared to controls McGrath et al [57] Lung cancer Breath isoprene concentration is significantly higher in healthy individuals than in patients with lung cancer Wei et al [28], Poli et al [61], Bajtarevic et al [62] Hypoglycemia (Type 1 diabetes) Exhaled breath isoprene levels rise during hypoglycemia Neupane et al [63] Cystic fibrosis Breath isoprene production rate was observed to be significantly lower in patients during exacerbation than in controls McGrath et al [51], Alkhouri et al [52] Acute myocardial infarction Breath isoprene concentration was higher in the acute myocardial infarction group compared to the control group Mendis et al [64] Chronic liver disease Subjects with chronic liver diseases had significantly higher mean levels of isoprene Sehnert et al [65] Gastric cancer Isoprene was found to be significantly elevated in patients with gastric cancer and/or peptic ulcer compared to less severe gastric conditions Xu et al [66] Muscle dystrophy Muscle dystrophy patients have decreased breath isoprene concentrations compared to healthy controls King et al [36] HereV/Q is the ventilation-perfusion ratio, which is approximately 1 at rest. Analyzing equation (1) reveals immediately that the alveolar concentration C A is very sensitive to changes in the alveolar vent-ilationV (e.g. hyperventilation; an increase ofV will lower C A ) and to changes in cardiac outputQ. Changes of position alter alveolar ventilation and cardiac output and hence the Farhi equation predicts a corresponding change of the end-tidal isoprene breath concentration. This change was first demonstrated by real-time PTR-MS measurements for isoprene by King et al [31] (see protocol 3 in figure 5) and then for isoprene and butane by King et al [68] by a coupled PTR-MS/GC-MS study (see figure 4) and then later further confirmed by Sukul et al [69]. Another illustration of this point, is given by figure 1 (from Koc et al [70]) which shows two different data sets for the concentration of end-tidal isoprene in human breath. The box plots provide a summary of the population data collected from a large clinical study investigating lung cancer with volunteers at rest (Bajtarevic et al [62]). The results depicted by the box plots in figure 1 could be taken to imply that lung cancer can be detected based on decreased isoprene levels, with a tentative threshold isoprene concentration of about 70 ppbv being able to differentiate between people with and without lung cancer. However, the continuous real-time data set shows that the end-tidal concentrations of one individual (in red) can be changed within a few seconds by simply altering the breathing pattern from normal to a more rapid breathing (hyperventilation, see also Sukul et al [71]), which leads to an instantaneous drop in isoprene concentration, in agreement to what is expected from Farhi's equation. As a consequence, Koc et al proposed that a sensible interpretation of any breath VOC emission is only possible if information on its variability with changes of ventilation and blood flow is provided. Unfortunately, owing to difficulties in obtaining such information, this proposal is often ignored (and not only on isoprene). Unlike isoprene where the Farhi equation predicts a decrease in breath concentration when hyperventilating, for VOCs with large blood-air partition coefficients the end-tidal breath concentration increases as shown in figure 6 in King et al [72] for acetone for two different hyperventilation protocols.

Karl's model
In 2001 Karl et al [25] measured breath isoprene concentrations for volunteers on an exercise bike. The heartbeat frequency was continuously measured together with the PTR-MS data. The breath rate was not measured continuously but a relative breathing rate was determined several times during the exercise. They showed that breath isoprene concentration increases within a few seconds after exercise is started. They also developed a physiological twocompartment model similar to the five-compartment model by Filser et al [11], but with some modification. The model of Karl et al is based on the assumption that the increase in respiratory rate is delayed with respect to the increase in heart rate to describe this increase of breath isoprene concentration. In 2009 King et al [31] developed a set-up that allowed the simultaneous real-time measurements of cardiac output, alveolar ventilation, and end-tidal breath isoprene concentrations. They confirmed that breath isoprene concentration increases 3 -4 fold within a few seconds after exercise is started. However, when the model of Karl et al [25] was applied to the set of all measured data it failed (see figure 2) to reproduce the observed increase at the start of exercise and hence the model is not correct. The major shortcoming of Karl's model is that it assumes a significant time delay between the increase in respiratory rate and the increase in heart rate, an assumption that is inconsistent with experimental evidence.

King's model
To describe breath isoprene concentration profiles under non-steady state conditions King et al [12] introduced a three-compartment model. It consists of one lung (an alveolar compartment with gas exchange), and two body compartments (a peripheral tissue group containing the working muscles with metabolism and production, and richly perfused tissue containing the liver with metabolism and production). For more details, see appendix 5.1.2.
The essential difference between the model by King et al and the model by Filser et al is the introduction of an explicit isoprene production in the compartment containing the muscles. To illustrate the implications of this production term, in the following we provide some rough quantitative considerations. Due to isoprene production, venous blood from the peripheral muscle compartment, when in a resting steady state, has a very high isoprene concentration of approximately 75 nmol l −1 (see peripheral blood concentration shown in figure 2). In a steady state the production in the muscle tissue and the clearance by the blood flow through the muscle tissue are equal in this model. At rest, the blood flow through muscle tissue is roughly about 10% of the total cardiac output of about 6 l min −1 , and hence blood leaving the muscles only contributes about 0.6 l min −1 to mixed venous blood, amounting to a molar flow of isoprene of approximately 45 nmol min −1 (0.6 l min −1 × 75 nmol l −1 ) from muscle tissue. Conversely, the molar flow of isoprene from the richly perfused tissue group is about 27 nmol min −1 (5.4 l min −1 × 5 nmol l −1 ). With these two values, we get a combined molar flow of isoprene of approximately 72 nmol min −1 from both compartments, resulting in a mixed venous isoprene concentration of 12 nmol l −1 (72 nmol min −1 /6 l min −1 ) during rest. According to Farhi's equation (1), this corresponds to an alveolar concentration of roughly 6 nmol l −1 or 150 ppb at rest, in agreement with section 3. At the onset of moderate exercise with a constant workload of 75 Watts, alveolar ventilation increases fourfold and cardiac output doubles, reaching a new steady state within one minute. Simultaneously, the fractional blood flow through the working muscles increases from 10% to about 60 % of the total cardiac output of now about 12 l min −1 . Consequently, blood returning from the muscles now contributes 7.2 l min −1 or, equivalently, a molar flow of isoprene of about 540 nmol min −1 (7.2 l min −1 × 75 nmol l −1 ) to mixed venous blood. The molar flow of isoprene from the richly perfused tissue group is still comparable to its value during rest, about 24 nmol min −1 (4.8 l min −1 × 5 nmol l −1 ). This yields a mixed venous isoprene concentration of 47 nmol l −1 (564 nmol min −1 /12 l min −1 ). Again taking into account Farhi's equation (1) and a ventilation-perfusion ratio of about 2 at the start of exercise, we arrive at an alveolar isoprene concentration of approximately 16 nmol l −1 compared to 6 nmol l −1 at rest. This quantitatively explains the marked rise of breath isoprene concentration by a factor of roughly 3 in response to exercise. Furthermore, through the increased blood flow through the muscles, the isoprene concentration within the muscles decreases until it reaches a new steady state of about 20 nmol l −1 after about 15 min. This is called the washout of the muscle compartment. When the exercise is stopped, owing to the isoprene production term, the isoprene concentration in the muscles starts to increase again, but to reach the original steady state at resting conditions it takes at least 2 h. Therefore, when exercising commences after a short break of 12 min the isoprene concentration in muscle blood is still lower compared to the initial level at resting conditions. Hence, the second isoprene peak is lower than the first peak at the start of the second exercise period, and then following this argument through the third peak is even smaller after a break of only 5 min.
Summarizing, the logic underlying King's model is that high isoprene concentrations in the peripheral muscle compartment are masked by the small fractional blood flow through this compartment during rest, and unmasked as soon as blood flow in the muscle increases, e.g. by exercise. In this sense, isoprene concentrations in mixed venous blood and breath might also serve as an interesting novel indicator for muscular blood flow.

Further evidence for the model
To confirm the prediction of the model that the high concentration in the muscle blood is the source of the peak at the start of the exercise, the following experiment was designed. Start an exercise with just one leg and then change the leg doing the exercise (see figure 3). In the model, the peripheral compartment is split into two equal compartments, one containing the left leg and the other containing the right leg. When the exercise starts with the left leg we see the typical peak in breath isoprene and when after a short brake one continues to exercise with the same leg this peak is much smaller since the original steady state concentration is not reached again in that leg within the short break. However, when one now starts to exercise with the right leg, which still has the steady state concentration according to resting conditions at the beginning, the full peak height is recovered.
Another experiment that confirmed the prediction of the model was one undertaken on an exercise bicycle for which a low concentration of d5-isoprene was introduced into the laboratory air. As one can deduce from figure 4, deuterated d5-isoprene, which has a blood:air partition coefficient of about 1, enters  the arterial blood stream quickly and it takes only about one minute until it reappears in breath. Thus, an equilibrium is rapidly established between the d5isoprene room air concentrations and the volunteer's blood concentrations. To ensure that the equilibrium was achieved, the volunteer was resting another ten minutes before starting the exercise regime. At the onset of exercise, unlabeled endogenous isoprene (blue line) shows a peak as it is well known. Given that d5-isoprene is not produced in the body, its concentration in breath is zero at the beginning of the experiment. However, after inhalation and equilibration, in every compartment of the body, the venous d5-isoprene concentration is uniformly distributed and hence any change of the fractional blood flows cannot change the mixed venous concentration. At the onset of exercise, the ventilation-perfusion ratio goes up and the d5-isoprene in exhaled breath declines in accordance with the Farhi equation, because the venous blood still has an unaltered isoprene level for about two minutes (see minute 22-24 in figure 4). However, due to the increased inhalation of d5-isoprene from the room air, the mixed venous blood gains a higher concentration level too, and the exhaled concentration of d5-isoprene reaches its former level (see minute [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. This decline of d5isoprene also excludes that the peak of endogenous breath isoprene at the start of exercise is due to a storage effect or due to a delayed rise of cardiac output compared to alveolar ventilation, as assumed by Karl's model. Thus, d5-isoprene does not exhibit a peak at start of exercise but behaves according to the Farhi equation and this is exactly what one would expect from the model.
The fact that production occurs in the muscle tissue was further confirmed in the study of King et al [36], which showed that individuals with nearly no muscle mass have very low isoprene concentration in breath but normal cholesterol levels. As mentioned earlier, by quantitative gene expression analysis of the MVA pathway enzymes, Sukul et al [27] provided convincing evidence that endogenous isoprene is not mainly originated from cholesterol synthesis. In an investigation using ventilated pigs, Miekisch et al have earlier already concluded that high mixed venous concentrations suggest that there is a peripheral origin of isoprene, e.g. from muscle cells [41].
The theory that the main production of isoprene occurs in muscle tissue also fits very well with the Figure 6. Cardiac output in red during a sleep session from [50]. The spikes indicate movements during sleep. Reproduced from [50]. © IOP Publishing Ltd. All rights reserved.
observation that isoprene concentrations in breath show the same age dependence as muscle mass [6,43,46,74].
In her thesis, Koc [75] extended the threecompartment model of King into a five-compartment model (lung, liver, fat, working muscle, and richly perfused tissue).
Since isoprene is produced in muscle tissue, the breath isoprene concentration reacts sensitively to every single movement, which yields a higher isoprene concentration contribution to the mixed venous blood. Even when blocking the blood flow through the quadriceps femoris muscle with a surgical tourniquet the release produces a breath isoprene spike (see figure 5) due to reactive hyperaemia of the muscle after occlusion (see, e.g. figure 2 in [76]). Usually at rest, the normal breath isoprene concentration is about 100 ppbv but after resting for an extended period, e.g. when sleeping, the cardiac output decreases after about three more hours. This leads to a new steady state in the muscle tissue with an even higher isoprene concentration in the muscle blood, leading to a further increase in the mixed venous blood concentration. Thus, breath isoprene concentration rises up to about 200 ppbv during extended resting periods. Figure 6, taken from [50], shows that the cardiac output decreases slowly in the first 3 h of sleep. This is the reason why breath isoprene increases during sleep [49,50]. It also explains the observed increase of breath isoprene concentrations during hemodialysis [53,54,56] and the results when performing sham dialysis [55]. The important take-home message from this, is that it is extremely important to know a volunteer's activity prior to measuring breath isoprene concentrations, e.g. if the patient was sleeping, resting, walking, cycling, driving etc prior to the sampling.

Discussion
According to our current state of knowledge, most of the isoprene in exhaled air comes from production in muscle tissue. Since the blood-air partition coefficient of isoprene is close to unity, breath concentrations at rest obey the Farhi equation and react sensitively to breathing maneuvers. Therefore, we propose to use C A (λ b:air +V/Q) (see equation (B.3) given in the appendix) to normalize isoprene concentrations in the breath. Although machine learning algorithms are a useful tool for building a clinical prediction model, they will only be successful with reliable data, which for VOCs with low blood-air partition coefficients must include alveolar ventilation and cardiac output to ensure that the laws of physics represented by the Farhi equation are obeyed. Otherwise, such algorithms will fail and lead to incorrect conclusions, as described in the article by Patnaik et al [77].
The isoprene concentration in the breath very much depends on the subject's history of activity, given that the isoprene concentration in muscle tissue is depleted by activity within 15 min, with the rate of depletion depending on the workload. To regain a normal resting level of about 100 ppbv, at least two hours are required at low activity (e.g. office work). After complete rest (e.g. sleep, haemodialysis, sitting still) for two to three hours the steady-state concentration will be about twice as high. Finally, we comment that the utilization of breath isoprene concentrations as a biomarker for disease must wait until its biochemical origin and role is fully elucidated.

Data availability statement
This is a review article. The data that support the findings of this study are available upon reasonable request from the authors. Appendix A. Timeline of selected articles of relevance to isoprene in exhaled breath 1960: Using improved GC, the first discovery of isoprene, together with eleven other VOCs, in exhaled breath was made at Southwest Research Institute [16].

1967:
Krishnaiah et al investigated the effect of dietary cholesterol and ubiquinone on isoprene synthesis in rat liver [78]. In addition, Farhi published his fundamental modeling paper, which describes the relation between the alveolar concentration C A and the mixed venous concentration Cv [67], which has considerable significance to isoprene levels in exhaled breath.

1969:
Jansson and Larsson made the first quantitative measurement of isoprene (0.09-0.45 ppm), among five other VOCs, in exhaled breath by direct injection of the breath samples into gas chromatographs with flame ionization detectors [17].

1971:
Pauling used a method of temperatureprogrammed gas-liquid partition chromatography to determine qualitatively the presence of about 250 volatile substances in a sample of breath. However, isoprene was not explicitly listed [79].

1975:
Conkle et al analyzed the breaths of eight male volunteer subjects to determine trace organic compounds in respired air. The human production rate was calculated by difference between the total production and the inspired amount of each compound. The range for isoprene was determined to be 15-390 µg h −1 ) [18].

1977:
Krotoszynski et al obtained expired air samples from subjects representing an urban population of 28 carefully selected normal healthy volunteers, categorized according to race, sex, and age. They detected 102 VOCs of which three major constituents account for 51% of the mean organic contents, namely acetone (120 ng l −1 ), isoprene (33 ng l −1 ), and acetonitrile (24 ng l −1 ) [19].

1978:
DeMaster and Nagasawa identified isoprene in the breath of 25 subjects and observed a diurnal rhythm with the isoprene levels peaking at 6 h followed by a trough at 18 h [20].

1981:
Scheid et al published the first model consisting of two lung compartments to describe the endtidal breath concentration for VOCs with a blood:air partition coefficient λ b:air > 10 [80]. Also in this year, using 30 volunteers, with the exception of one individual, Gelmont et al identified isoprene as the main endogenous hydrocarbon of human breath, the amount ranging from 30% to 70% of the total hydrocarbons exhaled. An estimate of the quantity exhaled per day per individual was 2-4 mg/24 h. They speculated that isoprene is produced either as a by-product of isoprenoid biosynthesis or as an end product of isoprenoid degradation [3]. Isoprene was also identified in nursing rats, as well as for a short-time post weaning, but not in several other animals.

1983:
Manolis wrote one of the first reviews on breath analysis emphasizing that a 'standardized, reproducible breath sample is critically important for quantitative breath analysis' . He also mentions that values of the blood:breath ratio are available for only a few compounds [81].

1984:
Deneris et al reported, for the first time, the in vitro biosynthesis of isoprene from DL-MVA, utilizing the cytosolic fraction of rat liver. In addition, ATP exclusion from the complete system resulted in a 75% reduction of isoprene synthesis. The results provided evidence for an alternate fate of the MVA carbon skeleton, substantiating the hypothesis that breath isoprene is the product of MVA metabolism [34]. One individual measured in this laboratory repeatedly failed to produce detectable levels of isoprene in contrast to his family members who produced average amounts (same individual as in [3]).

1986:
In his 1986, review Wilson examines the physiological basis and sampling techniques for breath analysis and draws attention to the factors that may affect the blood:breath ratio. He stresses the importance of mathematical models and recalls the Farhi equation [82].

1987:
Peter et al studied the pharmacokinetic analysis of isoprene inhaled by male Wistar rats and male B6C3Fl mice and showed saturation kinetics in both species. Below atmospheric concentrations of 300 ppm in rats and in mice, the rate of metabolism was found to be directly proportional to the concentration [83].

1988: Stein and
Mead undertook experiments to determine whether peroxidized squalene forms isoprene in a manner such that peroxidation could be considered as a possible route for the formation of in vivo human breath isoprene. Their experiments indicate that adventitious peroxidation or peroxidase-derived 5-hydroperoxide on a polyisoprene side chain could also be a potential source of in vivo isoprene. They also showed that sonication of squalene in water produced isoprene as the major volatile hydrocarbon within 5 min [84].

1989:
Gargas et al measured partition coefficients of low-molecular-weight volatile chemicals in various liquids and tissues [85]. Cailleux et al measured isoprene during sleep. The concentration of isoprene seemed to vary with states of sleep and wakefulness, increasing during sleep and decreasing sharply just after awakening. For the measurements during sleep, the subjects were woken up! Therefore, they falsely assumed that samples obtained immediately after spontaneous or induced awakening were considered to be identical to those that might have been collected during sleep, not being aware of Farhi's equation [49].

1990:
Andersen published an article on physiological modeling of organic compounds in the body [86].

1992:
Cailleux et al determined blood isoprene concentrations in humans and in some animal species. In human blood, the concentrations of isoprene were found to range between 15 and 70 nmol l −1 (mean value of 37 ± 25 (SD) nmol l −1 ) [87].

1993:
Stone et al investigated the effect of regulating cholesterol biosynthesis on breath isoprene excretion in men. The acute effects of lovastatin, a competitive inhibitor of the rate limiting step of cholesterol biosynthesis, on breath isoprene excretion was determined by administering a single 20, 40 or 80 mg dose of this drug to five healthy male subjects at 8 p.m. and measuring their breath isoprene levels every 4 h for one 24 h cycle before and after treatment. When compared to the baseline cycle, all three doses of lovastatin significantly reduced breath isoprene levels at 6 and 10 h post-drug treatment [39]. Kohn and Melnik investigated the species differences in the production and clearance of 1,3-butadiene metabolites using a mechanistic model. The model included compartments for lung, blood, fat, liver, other rapidly perfused tissues (viscera) and slowly perfused tissues. Metabolism of butadiene was assumed to occur in viscera in addition to lung and liver. Physiological and biochemical parameters for the mouse, rat and human were obtained from the literature; they were not adjusted to produce a fit to experimental data [88].

1994:
Mendis et al performed gas chromatographic analysis of pentane and isoprene in a single breath of expired air from humans. In a group of 43 healthy volunteers, the mean concentration of end-expiratory isoprene was measured to be 7.05 ± 3.53 nmol l −1 . Isoprene concentrations showed no correlation with age or pentane concentrations [89].

1995:
Jones et al determined isoprene in human breath by thermal desorption GC with ultraviolet detection. In sixteen healthy subjects (six men and ten women), all of whom were non-smokers, the mean, median and spread of breath isoprene concentrations were found to be 3.73, 3.36 and 1.60-10.33 nmol l −1 , respectively. No statistically significant differences in the concentrations of breath isoprene were observed between the sexes [90]. Jones criticizes Phillips and suggests that the extreme negative alveolar gradient attributed to isoprene as reported by Phillips et al was caused by some closely related VOC, presumably an atmospheric pollutant in the room where the experiments were performed [91].

1996:
Foster et al evaluated whether respiratory isoprene output could serve as a monitor for ozone exposure [92]. Taalman investigated the toxicological properties of isoprene [93]. Filser et al presented a five-compartment model for the toxicokinetics of isoprene. They measured partition coefficients, metabolic rates and production rates. Using a closed chamber system, they also determined when the inhaled concentration equals the exhaled concentration, which reaches a steady state of about 600 ppbv after 2 h of rest. However, this model fails when it is applied to real time non steady state measurements using an exercise bicycle [11]. The

year 1996 also marks the beginning of a new era in breath gas analysis with the introduction of new instruments that allow real-time breath concentration measurements, namely proton transfer reaction mass spectrometry (PTR-MS) selected ion flow tube MS (SIFT-MS).
Smith and Spanel present SIFT technique as a sensitive, quantitative method for the rapid, real-time analysis of the trace gas content of atmospheric air and human breath and show that they can measure isoprene from a single exhalation [24].

1997:
Taucher et al report the detection of isoprene in expired air from human subjects using PTR-MS [26]. Jordan et al measure for the first time the peak of the breath isoprene concentration at the start of exercise [23].

1998:
Lindinger et al reported a PTR-MS system that allowed for on-line measurements of trace components with concentrations as low as a few pptv. They found no evidence for age dependence for the concentrations of isoprene within the group of adult test persons. However, the concentration of isoprene in young children was found to be demonstrably lower than in adults. In agreement with previous results, they found an increase by a factor of 2-4 in isoprene during the night for the adult participants in their study [44]. Nelson et al used a new analytical method GC combined with UV spectrophotometry to measure isoprene and acetone in expired breath collected from four different groups of children: 1) healthy newborn babies, 2) healthy preschool children, 3) healthy school children, and 4) diabetic children in different metabolic states. Both isoprene and acetone could readily be determined in one single analysis of a 250 ml air sample. Newborn babies during the first postnatal week had undetectable or very low levels of isoprene in their expired air, irrespective of their catabolic or anabolic state. Breath isoprene was found to increase with age, and healthy school children had higher levels than did healthy preschool children. No significant differences in breath isoprene were found between healthy and diabetic children [43].

1999:
Capodicasa et al examined breath volatile hydrocarbon concentrations in exhaled air of hemodialysis patients. They assessed both C2-C5 alkanesamong them ethane and pentane-the production of which in humans is essentially due to the action free radicals exert on polyunsaturated fatty acidsand isoprene. Dialysis did not modify the levels of the C2-C5 saturated hydrocarbons ethane, propane, butane and pentane, but there was a marked increase in isoprene in all patients (basal values rose by 270% on average) [53]. Unfortunately, they did not use a control group of volunteers resting for the same period of time. Spanel et al used SIFT mass spectrometric method (SIFT-MS) to study isoprene levels in the alveolar breath of 29 healthy volunteers during normal working hours at the varying states of nutrition occurring during this period. The data indicate that the spread of the alveolar isoprene levels in this sample of healthy individuals is 22 to 234 ppbv and that the mean value is 83 ppbv with a standard deviation of 45 ppbv [94]. Fenske and Paulson measured human breath concentrations of isoprene and pentane using both direct sampling into a GC/Flame Ionization Detector and sampling with Teflon bags. The major VOCs in the breath of healthy individuals were recorded to be isoprene (12-580 ppbv), acetone (1.2-1880 ppbv), ethanol (13-1000 ppbv), methanol (160-2000 ppbv) and other alcohols [95]. Risby and Sehnert present the clinical application of breath biomarkers of oxidative stress status [96].

2000:
Mitsui et al suggest that great care is required in the measurement of breath pentane so that endogenous isoprene and ambient isopentane are not coeluted [97]. Hyspler et al determined isoprene in human expired breath using solid phase microextraction and GC-MS. However, they were not aware of Farhi's equation and its consequences [98]. Senthilmohan et al measured how the concentration of the breath gases ammonia, acetone, and isoprene vary with time during exercise using the SIFT-MS technique. Preexercise expired isoprene concentration was observed to be between 55-185 ppbv for the eight subjects. The isoprene concentration decreased during the time of exercise. However, they missed the peak at the start of exercise [99]. McGrath et al investigated breath isoprene during acute respiratory exacerbation in cystic fibrosis and concluded that breath isoprene cannot be considered a reliable marker of oxidative stress. However, they were not aware of Farhi's equation [51].

2001:
Csanády and Filser discusses the relevance of physical activity for the kinetics of inhaled gaseous substances using a five-compartment model. They assumed that metabolism takes place only in the liver [100]. Watson et al discusses the metabolism and molecular toxicology of isoprene [42]. Davies et al present a new online method to measure increased exhaled isoprene in end-stage renal failure. The previously reported increase in breath isoprene following dialysis treatment was further confirmed [60].
McGrath et al investigated breath isoprene in patients with chronic heart failure. However, they are not aware of Farhi's equation. Breath isoprene production in subjects with chronic heart failure was significantly reduced compared to controls 83 (23) vs. 168 (20) pmol min −1 kg −1 . They concluded that breath isoprene does not directly reflect oxidative stress in chronic heart failure [57]. Miekisch et al analyzed volatile disease markers in blood. Arterial and venous blood samples were taken from mechanically ventilated patients. Additional blood samples were taken from selected vascular compartments of 19 mechanically ventilated pigs. In pigs, substances were found to be not equally distributed among vascular compartments. In humans, median arteriovenous concentration differences were 3.58 nmol l −1 for isoprene and 1.56 nmol l −1 for pentane. The median isoprene concentration was 9.08 nmol l −1 in venous and 5.73 nmol l −1 in arterial blood (range, 0.52-24.4 nmol l −1 in venous blood and 0-18.0 nmol l −1 in arterial blood). In pigs, isoprene concentrations tended to be higher in portal and mixed venous blood and lower in hepatic venous and in arterial blood. Decreasing substance concentrations in the hepatic venous blood suggest that isoprene is metabolized in the liver. High mixed venous concentrations suggest that there is a peripheral origin of isoprene, e.g. from muscle cells [41]. Karl et al further investigated breath isoprene concentration under non-stationary conditions by performing an increasing five-steps exercise (each for 5 min) on an exercise bicycle. They showed that breath isoprene concentration increases within a few seconds after exercise is started. Unfortunately, they did not measure alveolar ventilation and cardiac output directly, and their model does not work when applied to a complete real-time data set 'including cardiac output, alveolar ventilation, and isoprene breath concentration' [25]. Anderson studied the genetic and reproductive toxicity of butadiene and isoprene. Butadiene did not induce somatic cell mutation and recombination or sex-linked recessive lethal mutation in Drosophila melanogaster and isoprene produced no increase in chromosomal aberrations in CHO cells in vitro [101].

2002:
Risby reviews in his book chapter 'VOCs as Markers in Normal and Diseased States' the current knowledge on isoprene. He stresses the fact that breath should be collected or sampled when subjects are seated and are breathing normally at rest. Under these circumstances steady state conditions are achieved and pulmonary blood flow and minute ventilation are constant [102]. Lärstad et al determined ethane, pentane, and isoprene in exhaled air using a multi-bed adsorbent and end-cut gas-solid chromatography. The levels of exhaled ethane, pentane, and isoprene in healthy subjects (n = 4) are reported to be 8.1 ± 5.8 pmol l −1 , 11 ± 5.8 pmol l −1 , and 2.4 ± 0.90 nmol l −1 , respectively. The endogenous concentrations of ethane, pentane and isoprene were calculated by subtracting the mean concentrations of the analytes in room air from the mean concentrations in exhaled air [103]. Capodicasa et al noticed the lack of isoprene overproduction during peritoneal dialysis [104]. Sehnert et al investigated breath biomarkers for detection of human liver diseases. When the various molecules detected in exhaled breath were examined, the mean concentrations of carbonyl sulphide, carbon disulphide and isoprene in the breath of subjects with liver diseases were found to be significantly different from the corresponding means in the breath of normal subjects. The study subjects with liver disease were stratified into two populations: study subjects with hepatocellular injury and study subjects with diseases of the bile duct. The difference between the mean levels of isoprene in these two study groups was also found to be significant [65].

2003:
Lirk et al investigated breath isoprene during haemodialysis. Significant changes in breath isoprene concentration were observed when comparing patients before (39.14 ± 14.96 ppbv) and after (63.54 ± 27.59 ppbv) dialysis (p < 0.001). The quotient of values before and after dialysis was 1.84 (SD 1.41) [54]. Unfortunately, they did not include a control group of volunteers resting for the same period of time. Diskin et al investigated quantitatively the time variation of ammonia, acetone, isoprene and ethanol in breath over 30 days by a quantitative SIFT-MS study. The mean concentrations of isoprene is reported to be 55-121 ppbv with no obvious patterns in the distributions between the five individuals [105]. Anderson et al presented a model for soluble gas exchange in the airways and alveoli. The model simulated the excretion of ten soluble gases whose blood:air partition coefficient λ b:air , a measure of blood solubility, ranged over 5 orders of magnitude. They found that gases with λ b:air < 10 exchange almost solely in the alveoli and gases with λ b:air > 100 exchange almost exclusively in the airways. Gases with λ b:air between 10 and 100 have significant interaction with the airways and alveoli [106].

2004:
Doyle et al studied the effects of 1,3-butadiene, isoprene, and their photochemical degradation products on human lung cells [107]. Cope et al studied the effects of ventilation on the collection of exhaled breath in humans [108].

2005:
Salerno-Kennedy and Cashman review potential applications of breath isoprene as a biomarker in modern medicine [109].

2006:
Lechner et al investigated gender and age specific differences in exhaled isoprene levels. A total of 126 test persons were enrolled in the study: 66 females and 60 males. Moreover, the participants were classified into six groups with regard to their age. Isoprene was found to be highly significantly elevated (p < 0.001) in the exhaled air of male subjects. Furthermore, it was shown that 19-29 years old subjects exhaled significantly lower levels of isoprene than did older adults (p = 0.002) [74]. Turner et al presented a longitudinal study of breath isoprene in healthy volunteers using SIFT-MS with thirty volunteers (19 males, 11 females). The mean isoprene level was found to be 118 ppbv with a standard deviation of 68 ppbv and the range of values for breath samples given is 0-474 ppbv. Cholesterol levels analyzed for only three of the subjects were not obviously correlated with isoprene concentration in breath. One male volunteer had no isoprene in breath [5].
2007: Capodicasa et al shows that breath isoprene concentrations increased when performing sham dialysis [55]. Lärstad et al investigated the effects of breath-holding, flow rate and purified air on ethane, pentane and isoprene in exhaled air, but did not consider Farhi's equation [110].

2008:
Kushch et al investigated breath isoprene in terms of aspects of normal physiology related to age, gender and cholesterol profile as determined in a PTR-MS study. The cohort consisted of 205 adult volunteers of different smoking background without health complaints. Total cholesterol in blood serum was measured in 79 of these volunteers. Isoprene concentrations ranged from 5.8 to 274.9 ppbv, with an overall geometric mean (GM) of 99.3 ppbv. There was no statistically significant difference in mean isoprene in breath between males and females (GM 105.4 and 95.5 ppbv, respectively). Ageing led to a decrease in concentration in men, but did not influence isoprene levels in women. They did not observe any significant correlation between isoprene breath content and cholesterol level in blood, even after adjusting for the possible influence of age. Similarly, no correlation was found between isoprene levels and BMI [6]. Kushch et al carried out a pilot study to define typical characteristics of the trace gas compounds in exhaled breath of non-smokers and smokers to assist interpretation of breath analysis data from patients who smoke with respiratory diseases and lung cancer. Interestingly, isoprene was evaluated in smokers (median 137.2 ppbv) compared to non-smokers (median 100.9 ppbv) [111].

2009:
King et al presented for the first time a realtime recording setup combining exhaled breath VOC measurements by PTR-MS with hemodynamic and respiratory parameters [31]. Exhaled breath concentration profiles of two prototypic compounds, isoprene and acetone, during several exercise regimes and position changes were acquired, reaffirming and complementing earlier experimental findings regarding the dynamic response of these compounds reported by Senthilmohan et al [99] and Karl et al [25]. O'Hara et al used PTR-MS and solid phase micro-extraction GC/MS to obtain the first direct comparisons of endogenous breath and blood VOC concentrations in healthy volunteers. Mean (range) breath concentrations in parts per billion by volume are reported to be 1090 (515-2335) for acetone and 465 (308-702) for isoprene. The mean (range) blood concentrations are reported to be for acetone in radial arterial blood 26 (10-73) µmol l −1 and in peripheral venous blood 18 (9-39) µmol l −1 and for isoprene in radial arterial blood 6.8 (3.7-11) µmol l −1 and in peripheral venous blood 14 (5.5-30) µmol l −1 . Arterial blood/breath ratios mean (range) are reported to be 580 (320-860) for acetone and 0.38 (0.19-0.58) for isoprene [112]. Hryniuk and Ross presented the detection of acetone and isoprene in human breath using a combination of thermal desorption and SIFT-MS [113]. Enderby et al used SIFT-MS for measurements of the levels of several metabolites in the exhaled breath of 200 healthy school children. The median values (in parentheses) of the concentrations in ppbv are reported to be ammonia (628), acetone (297), methanol (193), ethanol (187), isoprene (37), propanol (16), acetaldehyde (23) and pentanol (15) [45].

2010:
Smith et al reviewed published results of breath isoprene studies and constructed a concentration distribution from the data obtained and compared it to that for healthy adults obtained from SIFT-MS data. The results reveal mean breath isoprene levels (±SD) for pupils within the given age ranges: 7-10 years (28 ± 24 ppbv), 10-13 years (40 ± 21 ppbv), 13-16 years (60 ± 41 ppbv) and 16-19 years (54 ± 31 ppbv). The more rapid increase that occurs between the second and third age ranges is statistically highly significant (p = 0.001). In this study, isoprene was not detected in the breath of two young children [46]. King et al presented a thorough modeling study of end-tidal breath concentration dynamics of isoprene. The model is the only model capable of describing real-time end-tidal isoprene breath concentrations under non-steady state conditions. It also predicts that isoprene blood concentrations are different in different body regions and are highest in muscle blood where the major production of isoprene occurs in muscle tissue [12].

2011:
Mochalski et al measured the isoprene solubility in water, human blood and plasma by multiple headspace extraction GC coupled with solid phase microextraction. The blood:air partition coefficients at 37 • C determined for ten normal healthy volunteers spread around a median value of 0.95 ± 0.09 (g ml −1 l ) /(g ml −1 a ) and were approximately 16% lower than the plasma:air partition coefficients (1.11 ± 0.2) [2]. Koc et al discussed the role of mathematical modeling in VOC analysis using isoprene as a prototypic example [70].

2012:
To support their new hypothesis [36] that muscle tissue acts as an extrahepatic production site of substantial amounts of isoprene King et al measured isoprene breath concentrations of muscle dystrophy patients. The cohort consisted of late stage Duchenne muscle dystrophy patients (median age 21, 4 male, 1 female). For these test subjects isoprene concentrations in end-tidal breath and peripheral venous blood range between 0.09-0.47 and 0.1-0.72 nmol l −1 , respectively, amounting to a reduction by a factor of about 8 or more as compared to established nominal levels in normal healthy adults. Moreover, where obtainable, the serum cholesterol levels of the patients investigated fall within normal ranges, so that a general distortion of cholesterol biosynthesis with potential effects on systemic isoprene production can largely be excluded [36]. King et al measured real-time endogenous acetone and isoprene in exhaled breath during sleep. For this purpose, six normal healthy volunteers (two females, four males, age 20-29 years) were monitored over two consecutive nights (the first one being an adaption night) by combining realtime proton-transfer-reaction mass spectrometry measurements from end-tidal exhalation segments with laboratory-based polysomnographic data. For breath isoprene, a nocturnal increase in baseline concentrations of about 74% was observed, with individual changes ranging from 36%-110%. Isoprene profiles exhibited pronounced concentration peaks, which were highly specific for leg movements as scored by tibial electromyography. Furthermore, relative to a linear trend, baseline isoprene concentrations decreased during the transition from the NREM to the REM phase of a complete sleep cycle [50]. Schubert et al confirmed the well known behavior of the end-tidal isoprene breath concentration when exercising [114].

2013:
Spanel et al studied quantitatively the influence of inhaled compounds on their concentrations in exhaled breath. They showed that exhaled breath concentration depends linearly on the inhaled concentration. For isoprene they showed that 66% of the inhaled concentration is exhaled again [115]. Khan et al studied the relations between isoprene and nitric oxide in exhaled breath and the potential influence of outdoor ozone [116].

2014:
Lourenco et al wrote in their review: 'King and co-workers joined efforts in investigating the potential stores of isoprene in peripheral tissue groups. Their findings suggested that breath isoprene variability during exercise is linked to local variations of gas exchange in peripheral tissues. The observable wash-out behavior of isoprene was attributed to an increased fractional perfusion of potential storage and production sites' [117]. Mochalski et al investigated blood and breath profiles of VOCs in patients with end-stage renal disease. Both blood and breath levels of isoprene increased significantly after hemodialysis, confirming earlier results [56]. Mochalski et al measured isoprene and other VOCs released and consumed by rat L6 skeletal muscle cells in vitro [118].

2015:
Unterkofler et al developed a simple twocompartment model to explain Spanel's findings [115] for VOCs with low blood:air partition coefficients. The model connects the exhaled breath concentration of systemic VOCs with physiological parameters such as endogenous production rates and metabolic rates. In addition, its validity was tested with data obtained for isoprene and inhaled d5-isoprene. In this article they also showed that d5-isoprene does not exhibit a peak at the start of exercise, which excludes that this peak is due to a storage effect [73]. Sukul et al confirmed qualitatively Farhi's equation for isoprene by measuring the breath isoprene concentration with parallel monitoring of hemodynamics and capnometry. However, they did not attempt to make a quantitative simulation with their data [69]. Alkhouri et al investigated isoprene in the exhaled breath as a novel biomarker for advanced fibrosis in patients with chronic liver disease. Unfortunately, they did not include a healthy control group and show no awareness of Farhi's equation [52].

2018:
Ager et al extended the investigation concerning the influence of inhaled concentrations on exhaled breath concentrations to VOCs with higher Henry constants [119]. Sukul et al investigated the effects of the natural menstrual cycle and oral contraception on VOCs, but did not use the Farhi equation to normalize the data [120].

2019:
Using PTR-MS, Mochalski et al studied the reactions of H 3 O + with a number of several deuterated VOCs and the subsequent sequential reactions of the primary product ions with water under normal and humid drift tube conditions. They discuss the implications of their findings for the use of deuterated compounds for breath analysis. The effect of D/H exchange considerably varies between the compounds under study. The product ion distributions of the H 3 O + d5-isoprene reaction is more complicated owing to some fragmentation following proton transfer. However, the data show that isotope exchange is not significant for d5-isoprene [121].

2020:
Sukul et al used curve fitting to relate isoprene breath concentrations to the end-tidal partial pressure of exhaled carbon dioxide (pET-CO 2 ) and the minute volume ventilation (VE). However, no attempt was made to verify the prediction of the Farhi equation in their study [71]. In their review, Das et al claim that there is no definable anatomic dead space for highly water-soluble respiratory biomarkers, namely acetone and isoprene, and further claim that they can be used as biomarkers for diabetes. The statement that isoprene is highly water-soluble and a biomarker for diabetes is wrong [122].

2021:
Sukul et al provided further evidence that breath isoprene is not correlated with cholesterol levels. They demonstrated that endogenous isoprene does not originate from cholesterol synthesis by quantitative gene expression analysis of the MVA pathway enzymes of a female volunteer without isoprene in breath [27]. Hori et al confirmed the results of King et al [36] by providing further evidence that breath isoprene concentrations correlate with muscle mass [123]. Sukul et al studied the effects of COVID-19 protective face masks and wearing durations on respiratory haemodynamic physiology and exhaled breath constituents, but did not use the Farhi equation to normalize the data [124].

2022:
Patnaik et al identified isoprene as a marker of liver function by machine learning, not being aware of Farhi's equation [77]. Wang et al present data showing that isoprene levels in breath decrease during sexual arousal [125].

B.1. Farhi's model
In 1967, Farhi [67] published his fundamental modeling paper that describes the relation between the alveolar concentration C A and the mixed venous concentration Cv. The Farhi equation is valid for all VOCs but only for VOCs with a low blood:air partition coefficient, that is λ b:air < 10, the end-tidal concentration C end−tidal is equal to the alveolar concentration.
The Farhi equation is derived from a single mass balance differential equation for the lung assuming a concentration equilibrium in the alveoli, i.e. Henry's law is fulfilled, which states that the arterial concentration C a = λ b:air C A V A dC A dt concentration change in lung HereV is the alveolar ventilation,Q the cardiac output, and V A the volume of the lung. When in a steady state, i.e. the concentration does not change in time and with a negligible inhaled concentration C I = 0, we get Farhi's equation The ventilation-perfusion ratioV/Q is approximately 1 at rest. Note that our experience is that under a moderate constant workload of 75 Watts on an exercise bicycle the blood flow approximately doubles and the breath flow increases by about fourfold. The new steady state of these two quantities is reached within about one minute after the start of exercise. The blood:air partition coefficient for isoprene is λ b:air ≈ 1 [2]. We also want to point out that Farhi's equation is valid for all VOCS, but only for small blood:air partition coefficients we have C A = C end−tidal .
Analyzing equation (B.2) reveals immediately that the alveolar concentration C A is very sensitive to changes of the alveolar ventilationV (e.g. hyperventilation: an increase ofV will lower C A ) and to changes in cardiac outputQ.
Unfortunately, many investigations on breath isoprene have ignored and are still ignoring this simple fact.
We suggest to use for VOCs with λ b:air < 5 instead of C A the value for normalization.

B.2. Extension of Farhi's model
Spanel et al [115] investigated the short-term effect of inhaled VOCs on their exhaled breath concentrations. They showed for seven different VOCs, including isoprene, that the exhaled breath concentration closely resembles an affine function of the inhaled concentration. Unterkofler et al [73] extended Farhi's model by a body compartment and showed that indeed the exhaled concentration as a function of the inhaled concentration has the form where C A (0) is the concentration, when the inhaled concentration C I = 0. C A (0) depends on the production rate and the slope a depends on the metabolic rate (see formulae in [73]). However, it is easier to determine a directly by experiments. For isoprene a ≈ 2/3 [73,115] and hence 2/3 C I must be subtracted from the measured concentration C A (C I ) to get C A (0). One third of the inhaled isoprene concentration is metabolized. Figure B1. Sketch of the model structure. The body is divided into three distinct functional units: alveolar compartment (gas exchange), richly perfused tissue (containing the liver with metabolism and production) and peripheral tissue (containing muscles with metabolism and production). Dashed boundaries indicate a diffusion equilibrium. Abbreviations connote as in table B1.
When we assume that we reach an equilibrium when rebreathing, that means C A (C I ) = C I , we get therefore C A (C I ) = 3 C A (0).
That means that someone who exhales 200 ppbv after resting 2 h (our experiments show that after complete rest the normal values of 100 ppbv of isoprene approximately double to 200 ppb) should reach 600 ppbv when rebreathing in a closed system. It is interesting to compare this estimate with the results from a chamber experiment in figure 2 in Filser et al [11], which shows a good agreement.
In a further article by Ager et al the validity of equation (B.4) was also shown for VOCs with blood:air partition coefficient λ b:air > 10 [119].

B.3. The three-compartment model for isoprene
To describe real-time end-tidal isoprene breath concentration profiles under non-stationary-state condition King et al [12] used a three-compartment model (similar to the five-compartment model by Filser et al [11]) consisting of one lung (an alveolar compartment with gas exchange), and two body compartments (a peripheral tissue containing the working muscles with metabolism and production, and richly perfused tissue containing the liver with metabolism and production), see figure B1. However, the  [6]. b Mechanically ventilated patients in [41]. c Mörk and Johanson [126]. d Hughes and Morell [127]. e Comprising viscera, brain and connective muscles according to table 8.2 in [128]. f Corresponding to 20% of maximum exercise intensity in [129]. g Johnson [130]. h Obtained by q rest per = 2 (single leg blood flow/cardiac output) according to table 1 in [131]. i Mochalski et al [2]. j Filser et al [11]. essential difference to the model by Filser et al is the introduction of a production in the compartment containing the muscles. Using the notation from table B1 the mass balance equations for King's model according to figure B1 are as follows.
The mass balance equation for the alveolar compartment is while for the richly perfused and peripheral tissue compartment we find that respectively. This model describes correctly realtime end-tidal isoprene breath concentration profiles under non-stationary-state condition, e.g. various breathing maneuvers, position changes, and exercise challenges and by splitting the peripheral compartment in two parts, one containing the left and one containing the right leg it is also able to describe the profiles of figure 3.
The three-compartment model of King et al was extended by Koc [75] by adding a liver compartment and a separate working muscle compartment into a five-compartment model (lung, liver, fat, working muscle, and richly perfused tissue).