Compartmental modeling for the volatile organic compound isoprene in human breath

Der menschliche Atemluft enthält hunderte von flüchtigen Spurenelementen, die entweder im Organismus als Folge von biochemischen und metabolischen Prozessen entstehen, oder von der Umwelt absorbiert werden. Der Quantifizierung von flüchtigen organischen Spurenelementen (VOCs) im menschlichen Atem wird ein diagnostisches Potential zugeschrieben. Atemgasanalyse ist die wissenschaftliche Untersuchung der Atemluft und ihre Hauptmotivation ist die Suche nach Marker-Substanzen, die als Indikatoren von pathophysiologischen Erkrankungen dienen können. Aufgrund ihrer nicht-invasiven Natur haben atemgasanalytische Untersuchungen in den letzten Jahren enorm an Interesse gewonnen. Allerdings ist der nicht-invasive Test noch in Entwicklung und hat in der klinischen Routine noch nicht Eingang gefunden. Neben Problemen bezüglich der Standardisierung der Atemluftabnahme und der Analysemethoden, verhindert das unzureichende Wissen über die Herkunft und die biochemischen Prozesse dieser Substanzen die Anwendung der Atemtests. Die physiologisch basierte mathematische Modellierung spielt bei der quantitativen Analyse der experimentellen Daten eine entscheidende Rolle. Ihre Aufgabe ist es, eine mechanische Beschreibung der zugrundeliegenden physiologischen Phänomene unter Berücksichtigung aller relevanten experimentellen Daten zu liefern. Somit ermöglicht die mathematische Modellierung einerseits ein detailliertes Verständnis der physiologischen Vorgänge und kann andererseits aufgrund dessen bei der Standardisierung und Entwicklung der Atemluftentnahmemethoden eine wichtige Rolle spielen. Die Arbeit konzentriert sich auf Isopren, welches eine der wichtigsten organischen Substanzen in der menschlichen Atemluft ist. Das Ziel der vorliegenden Arbeit war, den quantitativen Zusammenhang zwischen den Atemluftkonzentration und der zugrundeliegenden endogenen Blut/und Gewebekonzentrationen von Isopren zu beschreiben. Um die Kurzzeiteffekte der relevanten physiologischen Faktoren (sowie Blutfluss und Atemfluss) zu bestimmen, wurden Echtzeitmessungen unter Ergometerbelastung durchgeführt. Die herkömmlichen Modelle, die sich hauptsächlich auf die funktionellen Änderungen der Lunge konzentrieren, sind nicht in der Lage, eine physiologisch relevante Beschreibung der experimentellen Daten zu liefern. Im Gegensatz dazu wurde ein neues Modell auf Basis einer peripheren Herkunft von Isopren von unserer Arbeitsgruppe entwickelt. Die neue Hypothese wurde in der vorliegenden Arbeit durch weitere Experimente bekräftigt und das zugrundeliegende Modell verfeinert, was uns zu der Schlussfolgerung führte, dass die Skelettmuskeln eine wichtige Rolle bei der Isoprenformation spielen. Diese Hypothese wirft ein neues Licht auf die bisherigen Untersuchungen und eröffnet neue Diskussions- und Interpretationsmöglichkeiten über die Herkunft von Isopren.The interest in the diagnostic potential of volatile organic compounds (VOCs) in breath increases as a result of constantly improving modern analyzing techniques. Unfortunately, physicians have paid little attention to a causal mathematical description of the underlying physiological processes yet. Even if mathematical models are idealized representations of the reality, their impact on combining all the information and in prediction is undisputable. The emphasis of this work was to derive a mechanical description of the physiological processes governing the gas exchange dynamics of isoprene under physical exercise. Isoprene has been classified in the group of biomarkers and can be seen as a prototypic example of low-soluble substances concerning its gas exchange mechanisms. Modern mass spectrometric techniques allow its online quantification in exhaled breath in real time. Describing short-term effects is crucial to get a deeper understanding of the determining factors of the underlying mechanisms. Changes in physiology occurring during physical exercise, such as increased ventilation and increased cardiac output, offer an opportunity to examine and understand the exchange processes that determine absorption, desorption, and distribution of this important volatile organic compound. Thus, for the present work cycling exercises on a medical ergometer were carried out and an experimental setup allowing parallel and real-time measurements of exhaled isoprene time-courses in conjunction with physiological parameters was used to collect relevant information for modeling purposes. Isoprene concentrations show a distinct peak shaped response to exercise, which has been recognized before by several investigators. The existing model describing exhaled dynamics of isoprene in response to exercise is able to explain its dynamics only on the basis of physiological assumptions, which contradict physiological facts and real-time measurements. As conventional knowledge suggests isoprene is expected to be sensitive to the regional inhomogeneities in the lung due to its low solubility in blood. For this reason, we focused our attention onto various existing lung models first, which take into account regional inhomogeneities of the lung. However, such representations also fail to describe the observed data. On the contrary, experimental evidence suggests a relationship between muscle compartment activity and isoprene excretion. The first known physio\-logical model developed for isoprene exposure studies assumes a production of isoprene in the liver as the solely source of isoprene in the human body and fails to describe its exchange dynamics under physical exercise. Based on this model, we derived a compartment model, which suggests a metabolic activity of the skeletal muscles. The new model is capable to explain the observed isoprene profiles within a range of acceptable parameter sets. Even if further investigations are necessary to consolidate this hypothesis, several findings about isoprene, such as the linkage of its output to age and statin therapy, and the effect of bilateral deficit when switching from two-legged to one-legged exercise appear to fit into this hypothesis

Mathematical models of lung function

This thesis is concerned with an approach to the assessment of respiratory gas transport in individual subjects, which is based on the techniques of mathematical modelling. The general mathematical modelling approach to a physiological system while similar to that for a physical system is sufficiently different to warrant discussion (Chapter 1). Models have been frequently employed in the study of respiratory gas transport and the different models are reviewed in Chapter 2. A method of characterising these models is suggested. Many of the models consist of simple algebraic equations which describe steady-state conditions. An extension to these models to quantify ventilation-perfusion distribution is presented (Chapter 2 and Appendix 10). The main deficiencies of steady-state models are the restrictions which they impose on experimental conditions both limiting the information content of the experiment and making it difficult to perform tests on certain subjects. A new approach to the measurement of respiratory gas exchange is suggested based on dynamic as opposed to steady-state models and using the techniques of parameter estimation. The necessary experimental and computing techniques have been developed and details are presented in Chapter 3. The feasibility of this approach is proved by application to the study of inert gas wash-out experiments (Chapter 4). While this method of analysis can utilise the within-breath detail of the expired concentration measurements, the physiological mechanisms underlying this aspect of function are not fully clarified. An investigation of one of the relevant mechanism (Taylor diffusion) using a distributed model is also presented in Chapter 4. The techniques of dynamic modelling are applied to the development of a new non-invasive method for the measurement of cardiac output and CO2 lung volume. (Chapter 5). Models can also be of value for educational purposes and a special simulator of gas transport is presented in Appendix 4

Noninvasive Stroke Volume Monitoring by Electrical Impedance Tomography

In clinical practice it is of vital importance to track the health of a patient's cardiovascular system via the continuous measurement of hemodynamic parameters. Cardiac output (CO) and the related stroke volume (SV) are two such parameters of central interest as they are closely linked with oxygen delivery and the health of the heart. Many techniques exist to measure CO and SV, ranging from highly invasive to noninvasive ones. However, none of the noninvasive approaches are reliable enough in clinical settings. To overcome this limitation, we investigated the feasibility and practical applicability of noninvasively measuring SV via electrical impedance tomography (EIT), a safe and low-cost medical imaging modality. In a first step, the unclear origins of cardiosynchronous EIT signals were investigated in silico on a 4D bioimpedance model of the human thorax. Our simulations revealed that the EIT heart signal is dominated by ventricular activity, giving hope for a heart amplitude-based SV estimation. We further showed via simulations that this approach seems feasible in controlled scenarios but also suffers from some limitations. That is, EIT-based SV estimation is impaired by electrode belt displacements and by changes in lung conductivity (e.g. by respiration or liquid redistribution). We concluded that the absolute measurement of SV by EIT is challenging, but trending - that is following relative changes - of SV is more promising. In a second step, we investigated the practical applicability of this approach in three experimental studies. First, EIT was applied on 16 mechanically ventilated patients in the intensive care unit (ICU) receiving a fluid challenge to improve their hemodynamic situation. We showed that the resulting relative changes in SV could be tracked using the EIT lung amplitude, while this was not possible via the heart amplitude. The second study, performed on patients in the operating room (OR), had to be prematurely terminated due to too low variations in SV and technical challenges of EIT in the OR. Finally, the third experimental study aimed at testing an improved measurement setup that we designed after having identified potential limitations of available clinical EIT systems. This setup was tested in an experimental protocol on 10 healthy volunteers undergoing bicycle exercises. Despite the use of subject-specific 3D EIT, neither the heart nor the lung amplitudes could be used to assess SV via EIT. Changes in electrode contact and posture seem to be the main factors impairing the assessment of SV. In summary, based on in silico and in vivo investigations, we revealed various challenges related to EIT-based SV estimation. While our simulations showed that trending of SV via the EIT heart amplitude should be possible, this could not be confirmed in any of the experimental studies. However, in the ICU, where sufficiently controlled EIT measurements were possible, the EIT lung amplitude showed potential to trend changes in SV. We concluded that EIT amplitude-based SV estimation can easily be impaired by various factors such as electrode contact or small changes in posture. Therefore, this approach might be limited to controlled environments with the least possible changes in ventilation and posture. Future research should scrutinize the lung amplitude-based approach in dedicated simulations and clinical trials

Novel strategies and multiscale modeling in respiratory mechanics

Despite tremendous technological and scientific advancements in the 20th century, clinically feasible assessment of detailed macroscopic respiratory mechanics is still limited. Additionally, a comprehensive understanding of macroscopic behavior in terms of microscopic description of alveolar mechanics and extracellular matrix properties is also absent. Combined together, these two limitations may explain why there has been a slow progress in optimizing mechanical ventilation for patients with lung disease. Addressing these two limitations, and, more importantly, linking macroscopic emergent phenomena to microscopic behavior could provide improved understanding and better health care. To this end, (1) a 3-D printed flow sensor was designed and evaluated to continuously measure airway opening flow and pressure in mice. (2) Using this sensor, we introduced a novel technique (ZVV) which provides continuous monitoring of the respiratory system’s physiological condition through evaluating cycle-by-cycle respiratory impedance (ZRS) during variable ventilation (VV). The feasibility and accuracy of ZVV was demonstrated by applying it in mice before and after inducing lung injury mimicking acute respiratory distress syndrome (ARDS), as well as in a computational study. Furthermore, when ZVV was applied to previously collected data, the analysis demonstrated for the first time that VV improved lung mechanics in human patients with ARDS. Additionally, two analytical models were developed to relate macroscopic to microscopic mechanical behavior of the lung parenchyma. (3) The first alveolar-unit model related alveolar septal wall properties (i.e., thickness) and constituents (i.e., fibers) to alveolar pressure-volume relationship providing insight into the importance of calculating true stress, the role of the collagen waviness and elastic modulus in alveolar stability and protection from over distension, as well as the multiscale relation between fiber stresses and macroscopic pressures. (4) The second intermediate tissue-level model described the mechanics of alveolar wall alignment under uniaxial stretching and estimated alveolar wall stiffness and stress demonstrating its ability to extract fiber-level properties from tissue strip stress-strain relations. When applied to pressure-volume and stress-strain data from lungs of old subjects, both models predicted alveolar wall and collagen fiber stiffening in aging. In summary, this study, presented a novel technique which can assess respiratory mechanics in clinical settings and multiscale models to enhance our understanding of how macroscopic behavior is related to alveolar constituent properties.2020-06-04T00:00:00

Fractional order models of the human respiratory system

The fractional calculus is a generalization of classical integer-order integration and derivation to fractional (non-integer) order operators. Fractional order (FO) models are those models which contain such fractional order operators. A common representation of these models is in frequency domain, due to its simplicity. The dynamical systems whose model can be approximated in a natural way using FO terms, exhibit specific features, such as viscoelasticity, diffusion and a fractal structure; hence the respiratory system is an ideal application for FO models. Although viscoelastic and diffusive properties were intensively investigated in the respiratory system, the fractal structure was ignored. Probably one of the reasons is that the respiratory system does not pose a perfect symmetry, hence failing to satisfy one of the conditions for being a typical fractal structure. In the 70s, the respiratory impedance determined by the ratio of air-pressure and air-flow, has been introduced in a model structure containing a FO term. It has also been shown that the fractional order models outperform integer-order models on input impedance measurements. However, there was a lack of underpinning theory to clarify the appearance of the fractional order in the FO model structure. The thesis describes a physiologically consistent approach to reach twofold objectives: 1. to provide a physiologically-based mathematical explanation for the necessity of fractional order models for the input impedance, and 2. to determine the capability of the best fractional order model to classify between healthy and pathological cases. Rather than dealing with a specific case study, the modelling approach presents a general method which can be used not only in the respiratory system application, but also in other similar systems (e.g. leaves, circulatory system, liver, intestines). Furthermore, we consider also the case when symmetry is not present (e.g. deformations in the thorax - kyphoscoliose) as well as various pathologies. We provide a proof-of-concept for the appearance of the FO model from the intrinsic structure of the respiratory tree. Several clinical studies are then conducted to validate the sensitivity and specificity of the FO model in healthy groups and in various pathological groups