David W Kaczka

Intraoperative respiratory monitoring is a fundamental component of the standards for basic anesthetic monitoring. Monitoring of oxygenation and ventilation is essential for the safe conduct of an anesthetic. Current approaches to respiratory monitoring primarily assess pulmonary mechanical and global gas exchange processes. The majority of respiratory monitors in clinical use provide information at the systemic and whole-lung level, from which inferences are made regarding the regional lung and tissue-level conditions. Monitoring of gas exchange, and its response to various interventions, may differentiate etiologies for hypoxemia. Pulse oximetry is a simple and noninvasive method for continuous monitoring of arterial oxygen saturation. Systems utilizing near-infrared spectroscopy are used clinically to monitor regional tissue oxygenation, particularly in the brain. Capnography is the primary quantitative method to assess ventilation during surgery and in the perioperative period. Besides providing physiologic information on ventilation, pulmonary blood flow, and aerobic metabolism, capnography is important for verifying endotracheal tube placement, and determining the integrity of the breathing circuit. End-tidal carbon dioxide (CO2) is not always a reliable approximation of arterial CO2 tension, especially in the presence of significant heterogeneity in the distribution of ventilation and perfusion. Measurement of the pressures, flows, and volumes associated with ventilation is necessary to optimize mechanical ventilation, as well as to detect mechanical derangements of the respiratory system. Imaging techniques such as ultrasonography and electrical impedance tomography have also emerged as important tools for respiratory monitoring. The monitoring of tissue and subcellular respiration remains a desirable goal for future innovation.

This chapter reviews the methodologies of inverse and forward modeling for describing various structural and functional relationships of the mammalian respiratory system. As an organ of gas transport and exchange, the lung relies on mechanical processes to maintain normal function. A large portion of its mechanical behavior can be reduced to relatively simple mathematical descriptions.
Inverse modeling of respiratory mechanics: Inverse modeling relies on physiologic data to infer respiratory structure based on function, using parameters that encapsulate certain physical properties of the system. The arrangement of such parameters defines the topology of the inverse model. A simple single compartment model of the respiratory system can be constructed asP(t)=EV(t)+RV˙(t)+Powhere the time-varying distending pressure (P) is expressed as a function of gas volume (V) and flow (V˙), the coefficients E and R and denote the elastance and resistance of the system, respectively, and Po denotes the distending pressure at end-expiration. By monitoring volume and pressure at different time points and fitting this equation to the data by regression analysis, we may determine the values of the parameters of E and R. These parameters can be affected by different lung diseases, such as asthma, emphysema, or fibrosis. By determining the ranges of values for normal and diseased lungs, such a model may facilitate disease diagnosis.
Forward modeling of respiratory mechanics: In contrast to inverse modeling, forward modeling may utilize physiologic and anatomic data to predict respiratory function, by explicitly defining mechanical properties and topological arrangement of many different physical elements. Forward modeling is thus useful for testing mechanistic explanations of experimental observations, investigating complicated interactions among elements of complex systems, or generating new hypotheses that can be later tested experimentally. The behaviors predicted by forward models can be compared against observations of the system under similar conditions. By way of example, a simple forward model of pulmonary gas exchange can be constructed by defining the relative amounts of alveolar ventilation (V˙A) and perfusion (Q˙) of involves partitioning the lung distinct compartments, each with different gas exchange capacities: [V˙A/Q˙]1=1 for the compartment with matched ventilation and perfusion; [V˙A/Q˙]2=0 for the nonventilated but perfused compartment; and [V˙A/Q˙]3→∞ for the ventilated but nonperfused compartment;. Note that V˙A and Q˙ may be different in each compartment. By definition Q˙ is zero in the nonperfused compartment, while V˙A is zero in the nonventilated compartment. The net influx of O2 (V˙O2) may be expressed as the product of the alveolar fresh gas ventilation rate (V˙A) and the difference between inspired oxygen fraction (FiO2) and alveolar oxygen fraction (FAO2):V˙O2=V˙A(FiO2−FAO2)
This V˙O2 can also be expressed as the product of the perfusion rate (Q˙) and the difference between mixed venous oxygen content (Cv¯O2) and end-capillary oxygen content (CcO2):V˙O2=Q˙(CcO2−Cv¯O2)
The ventilation-to-perfusion ratio (V˙A/Q˙) can be expressed as by combining both expressions for V˙O2:V˙AQ˙=CcO2−Cv¯O2FiO2−FAO2
Similarly for the rate of CO2 removal, we can obtain:V˙AQ˙=Cv¯CO2−CcCO2FACO2−FiCO2where the values of mixed venous blood gas partial pressures are known quantities. Practically, the partial pressures of O2 and CO2 are easier to measure than their total contents in the blood. In this regard, we can express the alveolar gas fractions in terms of gas partial pressures:FAO2=PAO2Patm−PH2O,andFACO2=PACO2Patm−PH2Owhere PAO2 denotes the partial pressure of alveolar oxygen, PACO2 the partial pressure of alveolar carbon dioxide, Patm is atmospheric pressure, and PH2O is the water vapor pressure. The partial pressures of alveolar gases and end-capillary blood gases are assumed to be equilibrated (i.e., PcO2 = PAO2 and PcCO2 = PACO2). The partial pressures of mixed venous blood may be obtained by sampling the blood in the main pulmonary artery using a Swan-Ganz catheter. The relationship between O2 and CO2 partial pressures and their corresponding contents in the blood may then be obtained as:CxO2=1.34·[Hb]·SxO2+0.0031·PxO2CxCO2=46.2e+0.00415·PxCO2−34.0e−0.0445·PxCO2+6.2·(0.975−SxO2)where the subscript x represents the particular blood compartment (e.g., venous, arterial, end-capillary), [Hb] is the concentration of hemoglobin in g dL−1 blood, and SxO2 is the corresponding fractional saturation of hemoglobin with O2. The system of equations relating alveolar gas exchange to perfusion may be solved to obtain the end-capillary blood gas contents. The gas contents of mixed arterial blood may then be determined by a perfusion-weighted average of compartmental blood gas contents:Ca¯O2=∑l=13(CcO2)l·Q˙lQ˙TCa¯CO2=∑l=13(CcCO2)l·Q˙lQ˙Twhere l indexes the three compartments of the model, Q˙l denotes the perfusion to each compartment, and Q˙T denotes the total cardiac output. In this way, the forward model can be employed to predict oxygen and carbon dioxide contents of the arterial blood at the entrance to the pulmonary capillary and of the end-capillary oxygenated blood.
Conclusion: In this chapter, we have shown how to employ inverse modeling and forward modeling to characterize respiratory function for assessments of airway and tissue properties in lung disease.

Intraoperative respiratory monitoring is a fundamental component of the standards for basic anesthetic monitoring. Monitoring of oxygenation and ventilation is essential for the safe conduct of an anesthetic. Current approaches to respiratory monitoring primarily assess pulmonary mechanical and global gas exchange processes. The majority of respiratory monitors in clinical use provide information at the systemic and whole-lung level, from which inferences are made regarding the regional lung and tissue-level conditions. Monitoring of gas exchange, and its response to various interventions, may differentiate etiologies for hypoxemia. Pulse oximetry is a simple and noninvasive method for continuous monitoring of arterial oxygen saturation. Systems utilizing near infrared spectroscopy are used clinically to monitor regional tissue oxygenation, particularly in the brain. Capnography is the primary quantitative method to assess ventilation during surgery and in the perioperative period. Besides providing physiologic information on ventilation, pulmonary blood flow, and aerobic metabolism, capnography is important for the verifying endotracheal tube placement, and determining the integrity of the breathing circuit. End-tidal carbon dioxide (CO2) is not always a reliable approximation of arterial CO2 tension, especially in the presence ofsignificant heterogeneity in the distribution of ventilation and perfusion. Measurement of the pressures, flows, and volumes associated with ventilation is necessary to optimize mechanical ventilation, as well as to detect mechanical derangements of the respiratory system. Imaging techniques, such as ultrasonography and electrical impedance tomography, have also emerged as important tools for respiratory monitoring. The monitoring of tissue and subcellular respiration remains a desirable goal for future innovation.

In its broadest sense, monitoring in pulmonology refers to the assessment of gas exchange between the environment and the blood. ere are two key events that take place in this sequence: (1) transport of gas between the environment and the alveoli, via the branching airway tree, and (2) diusion of gases across the physical barrier separating the alveoli from the pulmonary capillaries. ere are a variety of methods for assessing the eciency and eectiveness of each of these two events, all of which involve specialized equipment to measure the relevant physical variables, as well as specialized procedures to ensure that the measured variables accurately reect the underlying physiological phenomena of interest.

The function of the mammalian respiratory system is the facilitation the transfer of gas exchange between the organism’s environment and its internal transport medium, the blood. Evolutionary processes have optimized the anatomic structure of the lung as a tree-like branching network of airways terminating in thin-walled elastic ducts and alveoli, where this gas exchange occurs. Both dissipative and elastic properties of the respiratory system contribute to its unique static and dynamic mechanical behavior. In this chapter, we will explore the various structural and functional relationships of the respiratory system, and review several computational and modeling analyses that provide insight into the pathophysiology of common respiratory diseases. Particular emphasis is placed on studies that utilize imaging to help understand and/or validate the distributed regional nature of lung function.