Annals of Biomedical Engineering, Vol. 25, pp. 985-999, 1997 Printed in the USA. All rights reserved. 0090-6964/97 $10.50 + .09 Copyright 9 1997 Biomedical Engineering Society A Comprehensive Simulator of the Human Respiratory System: Validation with Experimental and Simulated Data LORENZO CHIARI, GUIDO AVANZOLINI, and MAURO URSINO Department of Electronics, Computer Science, and Systems, University of Bologna, Bologna, Italy Abstract--A comprehensive model of oxygen (O2) and carbon dioxide (CO2) exchange, transport, and storage in the adult hu- man is presented, and its ability to provide realistic responses under different physiological conditions is evaluated. The model comprises three compartments (i.e., lung, body tissue, and brain tissue) and incorporates a controller that adjusts alveolar venti- lation and cardiac output dynamically integrating stimuli coming from peripheral and central chemoreceptors. A new realistic CO z dissociation curve based on a two-buffer model of acid-base chemical regulation is included. In addition, the model explicitly considers relevant physiological factors such as buffer base, the nonlinear interaction between the 02 and CO2 chemoreceptor responses, pulmonary shunt, dead space, variable time delays, and Bohr and Haldane effects. Model simulations provide results consistent with both dynamic and steady-state responses mea- sured in subjects undergoing inhalation of high CO2 (hypercap- nia) or low O2 (hypoxia) and subsequent recovery. An analysis of the results indicates that the proposed model fits the experimental data of ventilation and gas partial pressures as some meaningful simulators now available and in a very large range of gas intake fractions. Moreover, it also provides values of blood concentra- tions of CO 2, HCO~, and hydrogen ions in good agreement with more complex simulators characterized by an implicit formula- tion of the CO 2 dissociation curve. In the experimental condi- tions analyzed, the model seems to represent a single theoretical framework able to appropriately describe the different phenom- ena involved in the control of respiration. Keywords--Respiratory system, Nonlinear modeling, Cardiore- spiratory control, Acid-base regulation, Carbon dioxide dissocia- tion curve, Hypercapnia, Hypoxia. INTRODUCTION Mathematical modeling of the respiratory system can be dated back to the mid-1950s with the pioneering works by Grodins et al. (14,15). The structure of these models was quite general, including a formulation of the control system, gas transport, and chemical buffering. Most of the models appeared recently; however, focus was on particu- lar aspects of the respiratory control system rather than on a synthesis of the overall system behaviour. For instance, Address correspondence to Guido Avanzolini, Department of Elec- tronics, Computer Science~ and Systems, University of B~logna, Viale Risorgimento, 2, 1-40136, Bologna, Italy. (Received 8Jut96, Revised 11Dec96, Revised 27Mar97, Accepted 18Apr97) some studies (18,32) provide a thorough description of the controller dynamics, with the aim of analyzing transition to instability, but do not incorporate chemical variables. Others (20) report on sophisticated descriptions of acid- base equilibrium and blood dissociation curves, but do not deal with the control of respiration. The aim of this study is to present and validate a com- prehensive model of the human respiratory system, which embraces both ventilatory and circulatory, as well as chemical, aspects. In this regard, it moves on the same line as the model by Grodins et aL (15). With respect to such a model, the proposed one includes a detailed description of the dynamics of the ventilation controller, a nonlinear interaction between the oxygen (02) and carbon dioxide (CO2) response in the peripheral chemoreceptors, and a CO 2 dissociation curve in closed form. The model does not aspire to extend the physiological knowledge on single aspects of the respiratory system, but rather aims at sum- marizing different aspects, considered separately in the recent literature, into a single theoretical framework. Fur- thermore, the model is orientated toward the analysis of clinical problems, with the focus on pathologies associated with acid-based equilibrium disorders. Hence, appropriate emphasis is given to the chemical regulation of the acid- base balance, incorporating reasonable details on chemical variables (e.g., bicarbonate and hydrogen ion concentra- tions). The presence of these quantities makes the model suitable for the study of clinical conditions in which the respiratory and/or renal control systems fail to ensure an adequate metabolic homeostasis. This work starts with the description of three- compartment plant dynamics, characterized by an innova- tive COz dissociation curve, followed by the definition of a dynamic cardiorespiratory controller. Then, to validate the model, hypercapnia and hypoxia conditions are simu- lated, and results refeffing to steady-state and transient conditions are presented, compared with experimental and simulated data, and discussed, MODEL FORMULATION Figure 1 shows a schematic diagram of the controlled system incorporating three compartments involved in gas 985